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Effect of parabolization on viscous resistance of displacement vessels Klaptocz, Voytek R. 2006

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EFFECT OF PARABOLIZATION ON VISCOUS RESISTANCE OF DISPLACEMENT VESSELS by VOYTEK R. KLAPTOCZ B.A.Sc, University of Waterloo, 2002 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE STUDIES (Mechanical Engineering) THE UNIVERSITY OF BRITISH COLUMBIA March 2006 © Voytek R. Klaptocz, 2006 ABSTRACT The addition of parabolic side bulbs at the ship's mid body is aimed at reducing wave-making resistance. This concept was first successfully tested on a coaster tanker and then extended to the UBC Series Model 3, a typical Canadian West Coast fishing vessel. A series of systematic tow tank experiments revealed that while parabolization decreases the total resistance (due to a drop in wave-making resistance) the form factor suffers an increase. This thesis focuses on numerical predictions of the influence of side bulbs on the viscous resistance characteristics of a displacement vessel. An integral boundary method solver and a 2D RANS solver were chosen as tools to predict the effect of parabolization on viscous drag for the UBC Series Model 3 hulls and the UBC Series Model 4. The concept of parabolization was then extended to an NPL Trimaran hull. A 3D RANS code was used to compare the calculated values of skin friction and boundary layer thickness to those calculated by the integral boundary layer solver. The RANS code was also used to numerically predict the effect of parabolization on viscous pressure drag for the NPL hull. In total, three different bulbs were studied numerically in addition to the parent NPL hull. The numerical results were compared to experimental data obtained from calm water resistance predictions obtained from tow tank testing. Further effort to decrease the impact of parabolization on form factor was made by applying moving surface boundary layer control to the UBC Series Model 4. ii TABLE OF CONTENTS Abstract ii List of Tables vi List of Figures vii List of Symbols, Nomenclatures and Abbreviations ix Acknowledments x 1 Introduction 1 1.1 Previous Work/Motivation 2 1.2 Objectives and Scope of Work 3 1.3 Hull forms 5 2 Numerical methods 7 2.1 Introduction 7 2.2 Three Dimensional Boundary Layer 8 2.3 Integral Boundary Layer Method 11 2.3.1 Derivation of Integral Boundary Layer Equations 11 2.3.2 Integral Boundary Layer Solver 12 2.4 Navier Stokes Elliptic Solvers 14 2.5 Turbulence Modeling 15 2.6 Model to Full Ship Scaling 17 2.7 Numerical Prediction of Form Factor 19 2.8 Summary 19 3 Viscous Drag of Parabolized UBC Hull 21 3.1 Introduction 21 3.2 Viscous Drag Prediction using IBL Solver 22 3.2.1 Model Setup and Considered Ship Condition 22 3.2.2 Skin Friction prediction 23 3.2.3 Boundary Layer Parameters 27 3.3 2D RANS Model 30 3.3.1 Model Setup 31 3.3.2 Results 32 iii 3.3.2 Results 32 3.4 Discussion 37 4 Viscous Drag of Parabolized NPL Hull 39 4.1 Introduction 39 4.2 Experimental Work 40 4.2.1 Experimental Setup 40 4.2.2 Experimental Results 42 4.3 IBL Model 46 4.3.1 Model Setup and Considered Ship Condition 47 4.4 3D RANS Model 47 4.4.1 Model Geometry 47 4.4.2 Mesh Generation 48 4.4.3 Boundary Conditions 50 4.4.4 Turbulence Model/Dicretization 51 4.4.5 Full Scale Model Considerations 52 4.4.6 Mesh refinement 53 4.5 Numerical Results: Model Scale 53 4.5.1 Skin Friction 53 4.5.2 Boundary Layer Parameters 56 4.5.3 Form Drag 60 4.6 Numerical Results: Full Scale NPL 62 4.7 Discussion 62 5 Experimental work: MSBC 66 5.1 Introduction/Previous Work 66 5.2 Moving Surface Using Cylinders 67 5.2.1 Experimental Setup 67 5.2.2 Tow Tank Drag Data ....67 5.2.3 Wind Tunnel Visualization 69 5.3 Moving Surface using belt 71 5.3.1 Tow Tank Drag Data 72 5.4 Discussion 73 iv 6 Conclusions and Future work 75 6.1 Conclusions 75 6.2 Future Work 79 References 80 Appendix A: Boundary layer parameters 83 Appendix B: HLLFLO Calculation Process 85 Appendix C: NPL Form Factors 89 v LIST OF TABLES Table 1-1: Vessel Particulars 6 Table 2-1: Value of Shape Factor at Separation 10 Table 3-1: Comparison of Integral Quantities for UBC Hulls 35 Table 3-2: Comparison of C p along Hull 35 Table 4-1: Form Factor for NPL hulls 43 Table 4-2: Percent Difference in Cf compared to ITTC57 line 54 Table 4-3: Form Factor Comparison 61 Table 4-4: Skin Friction Coefficient for Full Scale NPL hull 62 vi LIST OF FIGURES Figure 1-1: Parametric study of UBC Series Model 3 [3] 3 Figure 2-1: Boundary Layer growth along hull [9] 8 Figure 2-2: 3D Boundary Layer Profile [10] 9 Figure 2-3: a) inviscid flow, b) viscous flow [11] 10 Figure 2-4: Turbulent Boundary Layer Profile [25] 17 Figure 3-1: Models of UBC hull used for numerical study 23 Figure 3-2: Comparison of IBL Solver Calculation of Cf to ITTC 24 Figure 3-3: Skin friction percentage comparison at model scale 25 Figure 3-4: Skin friction percentile comparison at full scale 25 Figure 3-5: Skin Friction Coefficient (Re=1.5 x 106) 26 Figure 3-6: Shape Factor for UBC hull (Re=1.5 x 106) 28 Figure 3-7: Displacement Thickness for UBC hulls (Re=1.5 x 106) 29 Figure 3-8: Tangent of Cross Flow (Re=l .5 x 106) 30 Figure 3-9: UBC 2D Mesh and Boundary Conditions 31 Figure 3-10: Boundary Layer Thickness along UBC hulls 33 Figure 3-11: Comparison of wake size (m) 34 Figure 3-12: Wall Shear Stress along hull 36 Figure 4-1: NPL Hulls 40 Figure 4-2: NPL6 bulbs (metre stick included for comparison) 41 Figure 4-3: NPL7 Bulbs (metre stick included for comparison) 41 Figure 4-4: NPL Parent Hull Testing 42 Figure 4-5: NPL 7 Testing 42 Figure 4-6: NPL Monohull EHP curves 45 Figure 4-7: a) NPL Trimaran EHP curves, b) NPL Trimaran % difference from NPL Parent 45 Figure 4-8: Comparison of NPL Parent and NPL 7 Trimaran at full scale 46 Figure 4-9: NPL Model mesh and near-wall resolution 48 Figure 4-10: Mesh adaptation based on y+ value 49 Figure 4-11: Model Domain and Boundary Conditions 50 Figure 4-12: Skin Friction for NPL hulls 54 Figure 4-13: Comparison of Cf for NPL Parent and NPL 6 55 Figure 4-14: Comparison of Cf between RANS and IBL solvers for NPL Parent (Re= 1.68 x 106) 56 Figure 4-15: NPL shape factor comparison (Re = 1.68 x 106) 57 Figure 4-16: NPL crossflow comparison at (Re = 1.68 x 106) 58 Figure 4-17: Comparison of BL thickness at four separate stations along hull (Re = 1.68 x 106) 59 Figure 4-18: NPL boundary layer thickness comparison (IBL solver) (Re = 1.68 x 106)60 Figure 5-1: General Cylinder Arrangement 67 Figure 5-2: C T VS . Fn for MSBC using cylinders 68 Figure 5-3: Tuft Visualization Model Setup 70 Figure 5-4: Bubble path visualization around cylinders 71 Figure 5-5: UBC Series Model 3 with moving belt 72 Figure 5-6: C T vs. Fn for MSBC using belts 73 Figure 6-1: Relationship between L/B ratio and Form Factor for a) NPL Hull, b) UBC Hull 78 viii A C K N O W L E D M E N T S First and foremost, I would like to thank Dr. Sander M. Calisal for taking me under his wing the past two years and sharing his breadth of knowledge in naval architecture and fluid dynamics. His dedication to challenging the status quo and enthusiasm to explore new ideas is a true inspiration. I would also like to thank Dr. David Hally from DRDC for his assistance in the setup and use of the IBL Solver and for generously sharing his knowledge of ship hydrodynamics. I am also thankful to Dr. Peter Ostafichuk for his help with the wind tunnel visualization experiments and to Gary Novlesky from Vizon Scitec for sacrificing his personal time to build and install the cylinders and the moving belt on the UBC hull to make sure I could achieve a deadline. Furthermore, I am grateful to my co-workers Dan Vyselaar and Kevin Gould as well as all the residents of the Naval Lab for their openness in sharing of ideas, help during the experimental testing and most importantly, for making the last two years a pleasant experience even during trying times. Timothy Wang also deserves special mention for his aid with creating the meshed models for the RANS simulations. I would also like to thank Aker Marine, Oceanic Corporation and NSERC for their financial support and their endorsement of the project, as well as Dr. Dunwoody for being the chair at my defense. Finally, a warm appreciation is deserved for my family and friends for their support, encouragement, ski trips and 175 sessions. I am most indebted to my sister Nika for taking on the mammoth task of editing this thesis having no previous background or particular interest in hull form parabolization. x CHAPTER 1 1 INTRODUCTION With every passing year, naval architects are shifting from empirical formulations and experimental testing to sophisticated numerical simulations capable of predicting ship performance to within a few percent of actual values. Numerical methods are providing naval architects with new insight into the complex physics of flows around marine vehicles which are leading to significant advancements in ship performance. Traditional hull designs are being replaced with more complex vessels tuned to minimize their resistance while traveling through the water. Bulbous bows, for example, have proved successful in reducing overall ship resistance at the design speed by taking advantage of wave cancellation effects. Trimaran vessels have also made use of wave cancellation effects through strategic positioning of their outriggers. In addition, the gain in stability resulting from the presence of the outriggers has allowed trimarans to be much smaller in beam than a similar monohull vessel, thus decreasing their viscous resistance. One of the design aspects of marine vessels that has received considerable interest at the University of British Columbia (UBC) is the shape of the hull. Traditionally, a significant portion of large marine vessels consists of a parallel mid-body. This design methodology dates back to studies done by Kent in 1919, who concluded that total resistance could be minimized by maintaining a long parallel middle-body in hand with a decrease in beam [1]. At UBC, the focus has been to replace this section of the hull with a more parabolic shape that, if strategically designed, can lead to a decrease in wave drag through wave interaction effects. Numerical methods play a key role in this strategic design. 1 1.1 Previous Work/Motivation The concept of parabolization of waterlines was first applied while modifying the hull of an oceanographic vessel to improve stability using sponsons. Calisal et al. found that the modifications to the hull showed improved ship resistance characteristics [2]. This unforeseen result launched an experimental and numerical investigation into applying the concept of parabolization to a coaster tanker. In 2002 Calisal et al. reported a 10% decrease in Effective Horsepower (EHP) at Fn = 0.275 for the coaster tanker, by parabolizing the tanker's parallel mid body at the waterlines, ensuing in a 20% beam increase and the elimination of shoulders [2]. The decrease in EHP was attributed to a significant drop in wave resistance through wave cancellation effects in certain speed ranges. The local beam increases were found to modify the pressure field in their vicinity and generate a stronger shoulder wave system to interact with bow and stern wave systems. [2] Further work was needed to understand the flow physics and the applicability of parabolization to other types of marine vessels. In 2003-2004, Tan and Sireli conducted a systematic parametric study on the effect of parabolization of waterlines on the UBC Series Model 3 west coast fishing vessel [3]. An experimental program examined the consequences of introducing incremental beam increase between 5% and 20% by applying add-on side bulbs to the parent model. The study also established the desired bulb placement location that yielded the most beneficial wave cancellation effects. In addition, the degree of bulb fairing towards the aft was examined as a method of decreasing form drag. A summary of the experimental work done by Tan and Sireli is shown graphically in Figure 1-1. Based on the findings of the study, a revised UBC Model 3 with 11% beam increase was built and tested. This new model, referred to as the UBC Series Model 4 for the purposes of this work, was built with a matching displacement to that of the Parent Hull. The greater beam of the new model allowed for a shift in volume away from the stern region resulting in a 5% decrease in width at the transom. A 15% decrease in EHP was achieved for the new model configuration. The study concluded that while a penalty exists due to a form drag increase for a parabolized hull, the benefits of wave cancellation can result in a significant decrease in total resistance in the targeted speed range. 2 baseline mid-beam increase l fore-bulb aft-bulb bulb-fairing »1" Figure 1 -1 : Parametric study of UBC Series Model 3 [3] 1.2 Objectives and Scope of Work To date, parabolization of waterlines relied heavily on experimental testing and inviscid codes to establish an ideal middle body shape. The observed form drag increase spawned an interest in numerically predicting the effect of parabolization on viscous resistance. Ultimately, the parabolic middle body will be designed to achieve the maximum reduction in total resistance by finding a balance between viscous penalties and wave interaction gains. The purpose of this thesis is to numerically predict the impact various parabolic bulb shapes have on the viscous resistance of displacement vessels. Two types of numerical solvers were available for calculating the viscous drag of the vessels: an Integral Boundary Layer solver (IBL) and an elliptic Navier-Stokes solver. Each solver type has advantages and drawbacks depending on the requirements of the user. A comprehensive discussion of the relevant parameters unique to each solver is presented in Chapter 2. In addition, Chapter 2 gives a general overview of three-dimensional boundary layer viscous flow and the equations governing the flow physics. The numerical study first focuses on the UBC Series fishing hulls since experimental results were easily accessible from previous towing tank experiments. In Chapter 3, the 3 calculated values of viscous drag were compared to empirical formulations as well as experimental test results from Tan and Sireli's parametric study. Conclusions drawn from the study of the UBC hulls are used to develop design parameters for the evaluation of the impact that various bulb configurations have on the viscous drag of other displacement type vessels. In Chapter 4, hull form parabolization is extended to a high speed trimaran. Parabolization of the trimaran was done in collaboration with Dan Vyselaar using an iterative design process. Vyselaar's work focused on the calculation of wave drag and prediction of the wave profile along the hull while this thesis concentrates on the viscous flow characteristics [4]. The initial phase of the design process was aimed at decreasing the wave drag of the NPL Trimaran by introducing wave cancellation effects along the main hull. The first iteration of the waterline shape was designed based on the premise that an increase in beam at locations where a wave trough existed in the wave profile of the Parent Hull would create a new wave that would interact beneficially with the existing wave system. A number of different waterline shapes were analyzed by Vyselaar. The most promising modified hull was analyzed for changes in viscous drag and subsequently experimentally tested in the tow tank. The second phase of the design process was aimed at creating a hull geometry that produced wave interaction effects not only along the main hull but also for the outriggers. A strategic placement of the bulbs on the main hull of the trimaran was found to interact favourably with the bow wave generated by the outriggers. Parabolization of the trimaran's main hull could therefore lead to considerable drag reduction, especially at the design speed where wave-making contributes significantly to the total drag of the vessel. The viscous drag was subsequently calculated for two variations of the main hull and the most promising hull geometry was tested experimentally in the towing tank. As well, experimental work was done on the UBC Series Model 4 to actively decrease the viscous resistance by applying a momentum injection technique. This technique has been demonstrated successfully in aerospace applications and to some degree on control 4 surfaces of marine vehicles. The experimental procedures and results are outlined in Chapter 5. 1.3 Hull forms Two distinct hull forms were chosen for this study: the UBC Series and the NPL Trimaran. The UBC Series hull was first designed in 1993 as part of a study into the resistance characteristics of typical fishing vessels used off the coast of British Columbia [5]. Over the years, it was the subject of a plethora of geometric studies ranging from bulbous bows to various chine and stern configurations. In 2003, the UBC Series Model 3 hull was identified as a suitable Parent Hull by Tan and Sireli to study the possibility of extending the concept of hull form parabolization to a vessel with a parallel mid-body and low length-to-beam ratio. The parametric study used various configurations of side bulbs shown in Figure 1-1, to determine a combination of beam increment, maximum beam location and parabolic shape that yielded the highest decrease in drag. A combination of 11% beam increment from the Parent Hull as well as a shift of the maximum beam location L/10 aft of mid-beam, and faring of the bulb towards the stern was identified as the most promising drag reduction configuration. The UBC Series Model 4 was built based on this configuration, with a displacement matching that of the UBC Series Model 3 Parent Hull. Not all bulb shapes used for the parametric study were selected for numerical analysis. Only the bulbs described in Chapter 3 were chosen. The aim of the numerical analysis was to identify which numerical methods were capable of predicting changes in viscous resistance and also which methods were practical to be used for extending parabolization to the NPL trimaran. Unlike the UBC fishing vessel, the NPL trimaran is a very slender ship designed for high speed ferry or military applications. The Parent Hull geometry is based on a design by the United Kingdom National Physical Laboratory (NPL). The outriggers, mainly serving as stabilizers, are essentially scaled down versions of the main hull except for a higher L/B ratio of 22.5. The outriggers are positioned in line with the stern of the main hull and 5 span 36% of the vessel length. The position of the outriggers was determined experimentally to produce maximum wave cancellation effects at the design speed. [6] A comparison of the vessel particulars for both hulls is given in Table 1-1. NPL Trimaran (Main hull) UBC Series Model 3 L W L 160 m 27.734 m B 11.884 m 6.968 m T 11.674 m 2.799 m L/B 13.46 3.98 Model Scale 1 : 53.33 1 : 13.75 Table 1-1: Vessel Particulars The NPL Trimaran was identified as a candidate hull because it was designed to operate in the speed range 0.35 < Fn < 0.5, which encompasses the range within which the UBC hull reported positive wave cancellation effects. Parabolization at the waterlines was solely applied to the main hull therefore the outriggers were not considered in the numerical investigation of viscous drag on the NPL Trimaran hull. In total, three candidate bulb shapes were analyzed in addition to the Parent Hull as described in Chapter 4. 6 CHAPTER 2 2 N U M E R I C A L M E T H O D S 2.1 Introduction The decomposition of the total resistance into components is vital to the understanding of the fluid flow around a ship's hull. It allows the designer to focus on the influence specific changes in hull shape have on individual resistance components. The total resistance is typically broken down into residuary resistance and skin friction resistance. Residuary resistance takes into account the pressure resistance due to wave-making as well as the pressure resistance due to the viscosity that results from the presence of the boundary layer and eddies. While it is convenient to decompose resistance into individual components, there exists a degree of interaction between these components [7]. This interaction, however, is very difficult to quantify, especially without the use of numerical tools. Hull form parabolization hinges on the premise that the decrease in wave-making resistance will outweigh the potential increase in viscous resistance. To date, the wave-making resistance has been measured experimentally or by using inviscid solvers based on either Mitchell's integral or Dawson's method [3][4]. Prior to this work, no attempt was made to numerically predict the impact of localized increases in beam introduced by parabolization on viscous resistance. Work by Tan has focused on quantifying the change in viscous resistance from experimental results by determining a form factor using the Hughes-Prohaska method, where the skin friction was calculated using the ITTC 1957 formulation [3]. A more accurate calculation of the viscous resistance can be obtained with solvers based on the solution of the Navier-Stokes equations capable of predicting the 3D flow characteristics within the boundary layer. There exists a hierarchy of solvers based on the Navier-Stokes equations ranging in sophistication and computational requirements. State-of-the-art codes solve the complete 7 Navier-Stokes equations. More economical codes are either based on viscous-inviscid interactions using boundary-layer equations to solve the viscous flow physics or they simplify the Navier-Stokes equations by time averaging the turbulent flow properties in. 2.2 Three Dimensional Boundary Layer In high Reynolds number flows, the flow field can be divided into two regions: a viscous boundary layer region adjacent to the surface of the vessel and an inviscid region where viscous effects play a small role. The boundary layer is formed because particles directly on the hull surface are carried along with the hull. The presence of shear forces in viscous fluid results in subsequent particle layers to be slowed by the hull surface and entrained into the boundary layer region [8]. Thus, the boundary layer grows thicker from bow to stern. At a certain distance away from the hull, the particles are no longer affected by the presence of the hull and move with the free stream velocity. If the curvature of the hull becomes too abrupt, especially near the stern, the boundary layer separates from the hull surface resulting in a large increase in viscous pressure drag as shown in Figure 2-1. Avoiding or at least delaying this condition is crucial to minimizing viscous resistance. Not0: Boundary layr thickness mxaggmralud Smaller tddlms direction Figure 2-1: Boundary Layer growth along hull |9) A fundamental feature of the three-dimensional boundary layer is the existence of a cross-flow velocity component in the viscous region as shown in Figure 2-2. This velocity component is perpendicular to the external streamlines. The existence of the cross-flow velocity component is mostly due to a pressure gradient acting transversely on the hull [10]. The lower-momentum fluid near the hull surface responds more rapidly to 8 the pressure gradient than higher-momentum fluid near the edge of the boundary layer, thus skewing the velocity vector across the boundary layer [10]. Modeling the three-dimensional flow around the ship hull is not only important for drag prediction but also for appendage placement and propeller performance prediction. 1 edge —• streamline \ Figure 2-2: 3D Boundary Layer Profde [10] The flow characteristics in the boundary layer can be described using various parameters such as boundary layer thickness, momentum thickness and shape factor. All parameters are calculated from the solution of the momentum equations and continuity equation. An assessment of the boundary layer parameters along the hull gives important insight into the behavior and changes of near-field flow for different hull configurations. A brief definition of these parameters is given in Appendix A. Particular importance is paid to the prediction of the location of boundary layer separation and the wake because it will have a large effect on the overall form drag of the vessel. The form drag, also referred to as viscous pressure drag, results from the pressure imbalance between the bow and the stern of the vessel. In an inviscid flow without free surface effects, the opposing pressure at the bow is equal to the pressure at the stern aiding the motion. Without viscous effects there is no net resistance as shown in Figure 2-3a. When the viscosity of the fluid is considered, the existence of the boundary layer and flow separation in the wake reduces the magnitude of the pressure acting at the stern, 9 thus creating a pressure drag component as shown in Figure 2-3b. The magnitude of this pressure difference is directly related to the shape of the hull. Therefore, a change in beam introduced by parabolization, or a change in stern width will have a direct impact on the form drag. Figure 2-3: a) inviscid flow, b) viscous flow [11] The numerical prediction of the turbulent boundary layer separation location has been a topic of research for many years. Strictly speaking, the location of separation is defined as the location along the hull where the wall shear stress is equal to zero. It is not always possible, however, to predict this location, especially when using numerical solvers that are not capable of modeling flow in the vicinity of the separation point such as solvers based on the integral boundary layer equations. Another method of predicting the separation point is based on the magnitude of the shape factor. The magnitude of shape factor at separation as proposed by a number of researchers is summarized in Table 2-1. Experiment Shape Factor at Separation ( H s e D ) Aving & Fernholz [12] 2.78 Bertin& Smith [13] 1.8 to 2.8 Castillo, Wang & George [14] 2.76 +/- 0.23 Ludwieg & Tillmann [15] 2.04 Newman [16] 2.46 Schubauer & Klebanoff [17] 2.84 Simpson et al. [18] 2.62 Simpson et al. [19] 2.97 Table 2-1: Value of Shape Factor at Separation 10 2.3 Integral Boundary Layer Method One way of calculating the boundary layer parameters and gaining insight into the near hull flow is to use Integral Boundary Layer Methods. These methods employ a combination of a panel method solver for the incompressible inviscid external flow and an Integral Boundary Layer (IBL) solver for the three-dimensional viscous flow near the hull surface. 2.3.1 Derivation of Integral Boundary Layer Equations This section only gives an overview of the process of deriving the Integral Boundary Layer Equations. The aim is to point out the assumptions which were made during the derivation process and the resulting limitations of using a code based on the integral form of the boundary layer equations. For the interested reader, a complete derivation of the equations can be found in [10]. A more concise derivation and presentation of the integral equations as used in the integral boundary layer code BLAYER, can be found in the DRDC report 85/107 [20]. Boundary layer theory was first formulated by Ludwig Prandtl in 1904. Using an order of magnitude analysis of the momentum equations in Cartesian coordinates, Prandtl showed that for a flow aligned with the x-direction, the pressure gradient, dp/dy, can be assumed to be zero [10]. This assumption is true for all boundary layer flows but not for separated flows. Since the pressure is no longer a function of y, it can be determined from the inviscid portion of the flow field by solving the Euler equations [10]. The implementation of the order-of-magnitude assumptions to the momentum equations leads to the derivation of the Prandtl boundary layer equations for steady flow. For turbulent flow, the introduction of a fluctuating component into the boundary layer equations and time-averaging leads to the time-averaged boundary layer equations for turbulent flow [10]. In order to further simplify this set of equations, the 3D boundary layer equations in differential form are integrated with respect to the surface normal direction resulting in an integral form of the boundary layer equations in two-dimensional space [10]. 11 A third equation, called the entrainment equation, is derived to account for the net flux of mass through the boundary layer surface resulting from boundary layer growth [10]. A form of the entrainment equation can be obtained by integrating the continuity equation [10]. Another form, proposed by Head, aims to relate the three unknown parameters, theta, H and Cf for a given external velocity distribution [20]. In integral methods, the number of unknowns introduced by deriving the integral equations exceeds the number of equations, namely two momentum integral equations and one entrainment equation. Velocity profiles for calculating the two wall-parallel velocity components and density in the wall-normal direction are used to close the problem [10]. Boundary layer methods have shown to be very accurate and efficient and can be used for viscous flow over a large part of the hull, as long as the boundary layer assumptions are valid [21]. The formulation does, however, often break down near the stern, or for geometries which lead to boundary layer separation. This occurs, because near the stern, the assumption of a thin boundary layer that does not influence the potential flow solution is no longer valid. In the case of a transom stern, the breakdown of the integral equations due to inevitable separation will propagate upstream thus affecting the flow region near the stern [20]. 2.3.2 Integral Boundary Layer Solver An IBL solver, BLAYER, developed by DRDC Atlantic was used to calculate the flow within the ship hull turbulent boundary layer. The solver uses two momentum integral equations and a choice of three entrainment equations to determine three independent parameters, which are used to specify the boundary layer completely [20]. The three entrainment methods available to the user are Green's method, Head's method and Head's improved method. There are also two choices of velocity profiles given to the user: Mager's Power Law Profile and Coles' Profile [20]. The boundary layer 12 calculations are carried out for a given pressure distribution obtained from the potential flow solver HLLFLO. The velocity at the edge of the boundary layer is approximated by the potential flow solver, with the assumption that the presence of the boundary layer does not significantly alter the potential flow around the hull [20]. The laminar-turbulent transition location and the starting location for beginning the calculation of the boundary layer growth along the hull are specified by the user. To start the boundary layer calculation, BLAYER specifies the momentum thickness at the first station using flat plate boundary layer theory [20]. At the starting location, BLAYER assumes that the shape factor value is 1.3 and that there is no cross-flow. Corrections are then applied to the momentum thickness and the shape factor to account for the favorable pressure gradient that would make the boundary layer thinner [20]. The resistance of the hull is calculated using the program RESIST. The resistance is calculated by evaluating the pressure force obtained using the potential flow solver and the viscous forces calculated by BLAYER at the centroid of each panel, then multiplying by the area and summing. According to Dave Hally, the calculation is as follows: "Downstream of the BLAYER starting station, the BLAYER skin friction is used to calculate the viscous force. The resistance is calculated by evaluating the pressure and viscous forces at the centroid of each panel, multiplying by the area and summing. Downstream of the BLAYER starting station, the BLAYER skin friction is used to calculate the viscous force. Near the starting station it will depend on all the corrections mentioned above. Upstream of the starting station but downstream of the transition line (turbulent flow), the skin friction coefficient is calculated by 0.0576/Rx**0.2, where Rx is the Reynolds number based on the distance of the point from the forward perpendicular. Upstream of the transition line (laminar flow) the skin friction coefficient is given by 0.664/sqrt(Rx). On the forward most row of panels a special calculation is done which accounts for the fact that these two expressions vary rapidly as Rx goes to zero. Instead the integration is performed explicitly assuming that the velocity is constant." [22] 13 All calculations were based on a potential flow solution at Fn = 0, thus neglecting free surface effects. A complete derivation of the integral equations, velocity profiles and numerical iteration schemes for BLAYER is given in [20]. 2.4 Navier Stokes Elliptic Solvers Over the past decade, Computational Fluid Dynamics (CFD) methods concerned with solving the Navier-Stokes equations in elliptic form have evolved tremendously from highly specific codes developed at centres of research to commercial packages available for use by the industry for a wide variety of problems. To accommodate the application of CFD packages to problems ranging from automotive to aerospace and from HVAC to the research community, the available software comes with a wide range of numerical models and built-in options. In marine flows elliptic solvers are used where turbulence, boundary layers, wake and viscous resistance are important. These solvers are based on the solution of the Navier-Stokes and the continuity equations. The presence of a large turbulence spectrum in the flow, however, makes it possible to obtain a direct solution to the Navier-Stokes equations, termed DNS, only with the use of supercomputers and typically for simple flows at a low Reynolds number. With the ongoing increase in computational power, the use of DNS will become more widely used for problems where the resolution of turbulence on all scales is of importance. At this point, however, DNS is not economically justifiable to be adopted by industry. One method of decreasing the computational requirements is by filtering out the small scale turbulent eddies using a Large Eddy Simulation method (LES). In LES, the large-scale eddies are calculated directly and the small-scale (subgrid) eddies are modeled by means of wall functions or an eddy viscosity model [23]. The LES method is presently at the forefront of simulations of viscous flow around ship hulls with the inclusion of free surface effects. One of the main reasons for using LES is to study the turbulent wake behind navy ships where wave signature detection is of concern [24]. 14 The most widely used approach at present by industry (and the one chosen by the author) is termed the Reynolds-Averaged Navier-Stokes Equations (RANS). For a RANS solver, the mean properties of the flow are calculated by time-averaging the Navier-Stokes and continuity equations thus resulting in a new set of equations expressed in terms of both mean flow and fluctuation quantities [25]. The RANS solvers are less computationally expensive than DNS and LES but provide limited information about turbulence characteristics and almost no details on the large-scale unsteady structures of the flow field [24]. The reason for this is that in RANS simulations, the turbulence is modeled to be isotropic on all scales. In complex flows where large scale eddies are not stationary the isotropic turbulence model leads to an inaccurate solution [24]. In such a case LES is more suitable because only the small scale turbulent eddies are assumed to be isotropic, while the large scale eddies are directly modeled. Another option which has received some attention in recent years is the use of a hybrid LES/RANS model termed "detached eddy simulation" or DES. DES applies RANS close to the wall, where viscosity dominates, and LES in the region where large turbulence scales play an important role [25]. 2.5 Turbulence Modeling The time-averaged Navier Stokes equations, which form the basis of RANS solvers, contain a number of unknowns. Turbulence models are used to close the system of equations by solving for the unknown parameters. There exist a number of turbulence models, each catered to work best with specific types of physical flows. The turbulence models range in complexity from the one-equation Spalart-Allmaras model to the seven-equation Reynolds stress model (RSM). The choice of turbulence model often depends on the complexity of the fluid flow, the computational resources and the choice of mesh density. Mesh generation is highly coupled with the choice of turbulence model. For boundary layer flows, the required near wall grid resolution is dependent on the type of approach taken to resolve the buffer layer and the viscous sublayer within the turbulent boundary layer region. Because the normal gradients in the flow become very large close to the 15 wall it is necessary to generate a very large number of mesh points. In addition, as the flow nears the wal l , the turbulent fluctuations are suppressed and eventually viscous effects become dominant in the viscous sublayer region [26]. This means that certain turbulence models, such as the standard k-s model are no longer valid. A common approach is to use wall-functions based on semi-empirical formulations to bridge the gap between the wal l and the fully turbulent boundary layer region. Conversely, the f low in the buffer layer and viscous sublayer can be calculated directly with a val id turbulence model and adequate grid resolution. Experimental results have shown turbulent boundary layers to have a velocity profile as shown in Figure 2-4. The profile in the viscous sublayer is represented using Equation 2-1 while the profile in the fully turbulent region is represented using Equation 2-2 [27]. The near-wall grid resolution is typically computed using a non-dimensional wal l distance y+ as defined in Equation 2-3 [27]. SLsBiL Equation 2-1 u 1 , Jpury^ K M J Equation 2-2 Where u is the velocity parallel to the wal l , uT is the shear velocity, y is the distance from the wal l and K is the von Karman constant (0.4187) and E = 9.793 [25]. y* = EHiL Equation 2-3 M If a standard k-s turbulence model with wall functions is chosen, the cell adjacent to the wall should be located within the turbulent region of the flow, namely 30 < y + < 300. It is recommended for best results to have a y + value near the lower bound [25]. For a turbulence model capable of resolving the flow within the viscous sublayer, the cell adjacent to the wal l should have a y + value near unity. 16 Figure 2-4: Turbulent Boundary Layer Profile [25] It is important to note that the y value is calculated based on quantities which are not fixed based on geometry but are solution-dependent. Therefore, when creating a mesh, it is only possible to approximate the expected value of y+ based on results for known flows such as turbulent flows for a flat plate given by Equation 2-4. Once the solver reaches a semi-converged solution, it is necessary to check the computed values of y+ and other relevant turbulence quantities and make appropriate mesh refinements. y + = 0.172 • {A • R e 0 9 Equation 2-4 2.6 Model to Full Ship Scaling Predicting ship's resistance dates back to experiments conducted by William Froude in 1874. Froude hypothesized that ship resistance can be divided into frictional resistance and wave-making resistance. Through his development of a "law of comparison" for 17 wave making resistance, he was able to show that model scale ship resistance could be extrapolated to predict full scale ship performance [6]. However, true dynamic similarity between the model and full-scale ship is not satisfied by Froude scaling because of an increase in Reynolds number typically on the order of 103 [6]. Consequently there exists an increasing interest in using numerical methods to calculate the viscous drag at full scale. In model-scale tow tank testing of ships, slow speed tests are used to determine the added resistance the ship has due to viscous pressure drag and the change in the skin friction value from that predicted by empirical formulations. The classic approach is to use the Hughes-Prohaska method (with N=4) to break down the total resistance coefficient, CT, as shown in Equation 2-5 [6]. CT = Cw + (1 + k)C, Equation 2-5 The (1+k) term is termed the form factor, used to quantify the effect of the hull shape on boundary layer growth as well as the added resistance due to the viscous pressure drag component. Cf is the skin friction coefficient, typically calculated using the ITTC 1957 friction line represented by Equation 2-6. C w is the wave resistance coefficient. The form factor is assumed to be independent of both Re and Fn thus it does not change from model to full scale ship [6]. This important characteristic allows for performance prediction of full scale ships based on model scale experimental data. c 0.075 Equation 2-6 f ( l og l 0 Re -2 ) 2 The Hughes-Prohaska approach is widely used for slow speed vessels without immersed transoms [28]. However, its application to transom, stern vessels such as the U B C Model 3 and the N P L is disputed because of the different flow regime at the transom at slow speed and high speed [28]. Furthermore, for high speed slender vessels, such as the N P L hull, the total resistance is dominated by the viscous resistance component. Therefore, an 18 inaccurate calculation of the magnitude of this resistance component will lead to a lack of precision in resolving the impact of parabolization on wave drag. In addition, the small magnitude of the drag of slender hulls at slow speed makes it difficult to obtain accurate measurements for form factor calculations. 2.7 Numerical Prediction of Form Factor As the available computational power increase significantly every year, it is becoming more economically feasible to look to numerical approaches to calculating ship drag and abstain from using empirically based scaling methods. A RANS solver was used to calculate the skin friction and viscous pressure drag on the NPL monohull with and without the addition of a parabolized mid body. A breakdown of the pressure and skin friction components of viscous drag can only be calculated using Navier-Stokes elliptic solvers. In a numerical simulation without free surface, CT can be decomposed as shown in equation 2-6: CT=CP+ Cj Equation 2-7 where C P is the pressure coefficient. An expression for form factor can be obtained by comparing equations 2-5 and 2-6 with C W = 0 [23]. Equation 2-8 2.8 Summary This chapter gave an introduction to the flow physics associated with three-dimensional viscous flow around ship hulls. A condensed derivation of the governing equations specific to IBL solvers is given; however, the interested reader is urged to consult the cited references for a more detailed derivation. An overview of the existing state of the art codes for solving the complete flow around ship hulls is also presented, including a guideline for choosing the appropriate turbulence model. Based on the computational resources and requirements of the study, a RANS solver was selected over more 19 sophisticated solvers such as LES and DNS. Furthermore, a turbulence model capable of resolving the flow field down to the viscous sublayer was chosen to increase the accuracy of the results. The majority of ship resistance studies remain highly dependent on experimental data measured in the towing tank to evaluate the resistance of the bare hull. The experimental methods have been highly refined over the past century and serve as a good basis of comparison for resistance values obtained using numerical methods. For this reason, Sections 2.6 and 2.7 outlined he equations and methods used for the comparison of the numerical results to those obtained in the towing tank. 20 CHAPTER 3 3 VISCOUS DRAG OF PARABOLIZED UBC HULL 3.1 Introduction The experimental investigation by Tan and Sireli into the addition of parabolic side bulbs to the UBC Series Model 3 hull reported an increase in form resistance for all hull configurations. However, a substantial decrease in wave resistance showed to outweigh the detrimental viscous effects. The results from the parametric study were used to design UBC Series Model 4, a new hull form with an 11% beam increase placed L/10 aft of midship as well as considerable fairing of the bulbs towards the stern. The UBC Series Model 4 was built to have a displacement exactly equal to that of the Parent Hull. One consequence of parabolization is the shifting of hull volume towards the midbody of the vessel owing to an increase in beam. This allows for the design of a narrower stern section while preserving the same displacement. This approach proved successful in reducing the form factor to a value only slightly higher than that of the Parent Hull. The purpose of this chapter is to compare Tan and Sireli's experimental findings to numerical prediction of viscous drag using an IBL solver and a RANS solver. The numerical evaluation of the UBC Series hulls is meant to serve as a baseline for the understanding of the impact parabolization has on viscous drag of vessels. The knowledge of the strengths and limitations of the numerical tools used facilitates the extension of parabolization to the NPL trimaran and other candidate vessels. The skin friction drag of the UBC Series hulls was calculated using the IBL solver and compared to the ITTC 1957 correlation line. A two dimensional RANS simulation at the waterline was done for the UBC Series Model 3 Parent Hull; it was compared to a hull with 15% beam increase at midbody and to the UBC Model 4. These simulations were done to study the effects that beam increase, location of maximum beam and changes in hull slope have on boundary layer growth and wake regions. A three-dimensional 21 RANS simulation of the UBC hulls was not attempted because of the complicated hull shape, but instead reserved for the NPL hulls which have a less complex geometry. 3.2 Viscous Drag Prediction using IBL Solver 3.2.1 Model Setup and Considered Ship Condition Six different model geometries were evaluated using the IBL solver as shown in Figure 3-1. The bow of the ship is not shown because it is considered to be governed by laminar flow. Thus the IBL solver does not directly calculate the boundary layer parameters over this part of the hull but estimates them as described in Section 2.3.2. The goal of the study was to determine whether the IBL solver was a suitable tool for examining the differences in calculated skin friction values and boundary layer parameters. The process of creating input data representing the hull geometry, performing the calculation process and post processing the results is described in Appendix B. There are two features inherent to the UBC Series that complicate the hull representation: the upper and the lower chines as well as the keel. Through manipulation of the points at each station, and through indication of the hull discontinuity at the chines, it was possible to generate a B-spline representation of the hull using HLLSPL, a hull definition program built into HLLFLO. The keel, on the other hand, was excluded in all cases in order to avoid introducing further discontinuity in the B-splines. This assumption was warranted because the presence of the side bulbs did not extend significantly below the design waterline. The side bulbs would therefore not have a pronounced influence on the flow near the keel. The validity of this assumption was confirmed during the flow visualization study using yarn-tufts described in Chapter 5. The majority of calculations for the UBC hull were done at model scale in order to compare to experimental results without the inclusion of scaling factors. In addition, the skin friction was computed at full scale speed to compare the percent deviation from the ITTC'57 line. All models were tested for 0.9xl06 < Re < 2.1xl06 (O.K Fn < 0.22) which was the range of speeds used during experimental testing for calculating form factor. For 22 full scale, the skin friction was computed at Re = 4.16 x 107 and Re = 9.06 x 107 (Fn = 0.1, Fn = 0.22). L . UBC Parent ... i ... i 400 600 800 1OO0 1200 1400 1600 1800 2000| X (mm) UBC Series Model #3 Parent hull UBC 5% 400 600 800 1000 1200 1400 1600 1800 2000| X (mm) UBC Series Model #3 hull with 5% beam Increment at mid-beam UBC 10% L . UBC 15% 1 1---.- i i I- i... i 400 600 800 1000 1200 1400 1600 1800 2000| X (mm) U BC Series Model #3 hull with 10% beam increment at mid-beam '- I i i i i I 400 600 800 1000 1200 1400 1600 1800 2000| X (mm) UBC Series Model #3 hull with 15% beam increment at mid-beam UBC 20% UBC Model 4 i * . . . i . i i -i 400 600 800 1000 1200 1400 1600 1800 2000| X (mm) UBC Series Model #3 hull with 20% beam increment at mid-beam 400 600 800 1000 1200 1400 1600 1800 2000 X (mm) UBC Series Model #3 hull with 11% beam increment at L/10 aft of mid-beam and matching displacement to UBC Model 3 Parent Hull Figure 3-1: Models of UBC hull used for numerical study 3.2.2 Skin Friction prediction The skin friction was calculated by the program RESIST which is built into the IBL solver. A comparison between the calculated values of Cf using the IBL solver and the ITTC'57 correlation are shown in Figure 3-2. The values of Cf closely follow the trend of the ITTC'57 correlation line. However, the magnitude of the drag coefficient is between 0.5% and 1.5% higher at model scale. The UBC Parent Hull shows the highest values of Cf while the UBC Model 4 shows the lowest C f followed by UBC 5% through to UBC 20%. This is shown graphically in 23 Figure 3-3. At full scale, the difference between calculated values and empirically derived values increases to about 4% as shown in Figure 3-4. Furthermore, the Parent Hull no longer shows the highest skin friction coefficient. This result points to the fact that it is important to evaluate the performance of the hull both at model scale to help interpret towing tank results as well as at full scale, to quantify the actual operational performance. 4.90E-03 4.00E-03 J 1 9.00E+05 1.10E+06 1.30E+06 1.50E+06 1.70E+06 1.90E+06 2.10E+06 Re Figure 3-2: Comparison of IBL Solver Calculation of Cf to ITTC Because the UBC Series Model 3 vessel has an upper and lower chine, as well as a low L/B ratio, the inherent inability of the IBL solver to give accurate predictions near the stern could lead to a false interpretation of trends. A comparison of C f values excluding the aft 20% of the hull demonstrated the same trends. In addition, the hull representation and the calculation procedure for the UBC 5% was revisited due to the inconsistencies with the trends shown in Figure 3-3, namely the second highest C f in the low Re range and the lowest C f in the high Re range. The magnitudes of the skin friction were the 24 same for both the original calculations and the repeated calculations. The deviation from the trendline was therefore attributed to an unexpected flow phenomenon. 4.00% o t £ 2.50% O " 2.00% _c o o § 1.50% 1 Q 1.00% ITTC 57 - UBC Parent - UBC 5% - U B C 10% UBC 15% UBC 20% - U B C Model 4 9.00E+05 1.10E+06 1.30E+06 1.50E+06 1.70E+06 1.90E+06 2.10E+06 Re Figure 3-3: Skin friction percentage comparison at model scale 1° o E 4.00% E o £ & 3.50% a o c 3.00% i b 2.00% 3.00E+07 — - ITTC 57 —Q— UBC Parent - * - UBC 5% — " - U B C 10% — • - U B C 15% — U B C 2 0 % — • - U B C Model 4 5.00E+07 7.00E+07 Re Figure 3-4: Skin friction percentile comparison at full scale 25 The distribution of the skin friction coefficient along the hull, shown in Figure 3-5, revealed a larger region of high Cf (.0048-.0067) near the bow as the degree of parabolization increased. In the case of the UBC Model 4 this region was similar to that seen on the Parent Hull. One possible reason for a higher calculated Cf value for the Parent Hull is the extension of the .0041-.0048 region of Cf further aft than seen on the other hulls. There also exists an isolated location at the stern of the Parent Hull that has a highly elevated Cf value. As previously mentioned, however, the exclusion of this location by omitting the last 20% of the hull did not show this location to be the root cause of a consistently higher Cf value calculated for the Parent Hull. No other noteworthy difference are seen between the varying hull geometries beyond approximately x = 1200 mm which explains why globally, the skin friction does not vary significantly between the models. • _ — I S F C 00080 UBC Parent 0.0054 ^^mmm\ BP^v^-00041 ""^ 5^ | ™ ^ ^ i e o o °°C 2ioor .^•B^P^^^'"'" 200 \„ wSP^eoo * 1 0 0 0^*400 S F C • o.ooeo UBC 5% ~ 0.0074 ^ ^ B ^ S P 0.0067 t— 0.0061 _^«BJ H> I — 0.0054 ^ ^ ^ B l B P ^ I 0.0048 ,^MmW B ^ • 0 0 0 4 1 ^ f l J i B ^ V » > ^ 2 0 0 < B 0.0035 B P T ^ ' l S O O pjP^pP^^'h..f: *oor sB^^^^^^^**1^^"^ 200% ^ P ^ ^ M M > 1 0 0 \ _ > ^ ^ 6 0 0 0 400 B S F C 0.0080 UBC 10% 0.0054 ^^^Lm W^r _^^»»B v^-~ 0.0041 ^""^l P^ "^>>-*J'J' 2 0 0 t 00035 B P ^ ^ ^ 8 0 0 P^P^P^^^1600 \ 00 r |"•" ^ ^ ^ r ^ ^ ^ i . 1 0 0 V ^ * ^ B u u S F C • i 00080 UBC 15% 0.0074 _.^r«BBk ^ ^ a B V H B B V :— 0.0061 ^mmw r - o.oo54 ^mtmfm !— 0.0048 ^ - « B l \^^r mm 0.0041 I ^ ^ ^ V " " ^ 2 0 0 1 • 0.0035 ^P^-'""' 1 8 0 0 ,^ ^^ ^^ ^^ H^ P^ P^ P^ P^ 1^600 200 \ , •• ..• ^ ^ ^ ^ ^ A i O o X ^ ^ 6 0 0 0*^400 • • 1 SFC M M UBC 20% -* ^ ^ • H B k ^^mMm BV 0.0054 B P ^ 0.0048 ^--fB 0.0041 JJJ B ^ ^ - ^ " * 0 0 ' 0.0035 BP^>"">'1800 1 B ^ ' T B ^ ^ i s o o i. 1 0 0 X 0 ^ * ^ ^ ° ^ 0^400 • S F C UBC Model 4 ^ 0.0080 w ^ w u c ^^fA i 0.0074 ^^mmW^ftm. —1 0.0061 ^_B1 H P 0.0054 ^ ^ ^ B \W^^ j . — 0.0048 ^'-'^Bj B P ^ ^ ^ C , •1 0.0041 ^B] B^^>-^^ • 0.0035 H P ^ - ^ 1 8 0 0 ^ O o f M jmmmmmWf^^^^^KI!^ Figure 3-5: Skin Friction Coefficient (Re=1.5 x 106) 26 3.2.3 Boundary Layer Parameters The advantage of using an IBL solver or a RANS solver over empirical methods is the ability to study the flow characteristics at a particular location along the hull. Variations in hull geometry introduced through parabolization have local effects that are not necessarily reflected in the value of the skin friction coefficient but may have an impact on form drag. Since the integral boundary layer formulations generally give good results over the majority of the hull it is possible to evaluate the impact of the added side bulbs on boundary layer parameters. One of the greatest concerns is the increase in form drag associated with an increase in beam. While a direct calculation of form drag is not possible using an IBL solver, considering the magnitude of shape factor, and displacement thickness can aid with establishing preferred bulb shapes. S h a p e F a c t o r Figure 3-6 shows contour plots of the magnitude of shape factor for the six UBC Series hulls studied. The shape factor remains largely unchanged between all six hulls. At the aft end of the bulb, however, a small region with a shape factor of approximately 1.5 begins to appear for the UBC 5%. As the beam is augmented up to 20%, this region of increased shape factor grows. The magnitude of the shape factor also increases steadily up to a value of 1.6. According to Table 2-1, this is a region of concern but not necessarily a region of imminent separation. Fairing the bulb on the downstream side and possibly moving the location of maximum beam, as is the case with the UBC Model 4, appears to reduce the magnitude of the shape factor to that seen on the UBC 5%. 27 2m. U B C P a r e n t 2.21818 ^^m\ ^mMW^ 2000 149091 ^ ^ ^ H MWWJ>>^ N „ t • B ^ ^ ^ I O O O ^ K ^ > IOOX^^ 6 0 0 -1 2.50909 <^ J^MM^Mm&P^^0^'X" 2.21818 / ^r^^mm s r ^ ^ i s ^ ^ ^ ^ • M M *30^-mamwm9r ^L^T ys^"^ 2 0 0 0 1.34545 ^ ^ ^ H >^*^  -< -^>"''~"^ 1600 200 e | ^ ^ 1 4 0 0 ,nnf- fl • K ^ m ^ ^ 1200 . N 1 0 ° 0 | • | P * ^ 0 0 ^ ^ 0 * ^ 4 0 0 - 2 f F UBC 10% 2.65453 . * 2.36364 ^^dSkw 2.21818 / ^rfr^L^I^^^HHP^V, >^ 2.07273 Ir^^^^BHHHP^^SiB^^ 1.92727 V -" -" 1.781B2 ^ ^ ^ B j 200C 200 r . t ^ f l W^^^ A0° N „ l • S^^^ IOOO^ l ^ ° \ ^ • ^ ^ 800 * \ k , > 200 V > 1 0 0 6 0 0 I 2.50909 ^jg&B 2.36364 • ^^JmmW 2.07273 ^r^\^^^m\\\mmm^^^mm\\\w^ 1.78182 ^ ^ ^ B j B ^ ' ^ V>*""^ 200C 1 63636 ^ ^ f l I S J B B B B P ^ > - > ' > ' 1 8 0 0 1.49091 ^ ^ — — \ _>""'^ A l 0 ° f j i ^ ; 4 0 0 x SF 1.92727 ^ ^ t ^ . ^ j ^ ^ ^ ^ i ^ ^ r ± ^ 1.78182 ^BEk 1.34545 ^ ^^^^^^^^^^jJJ^^^^^^^^^^^^ • MS F UBC Model 4 ^ * 2-05455 '^K^Ztm^K 2.5090!) / ^^•"^AWm-W^mW^ 2.38364 - ^ M P ^ j ^ 1 9 2 7 2 7 ^^mmmm ^ • • P ^ 1 70182 Wm^^\>*>>*~^ ^^^t SjjH^H^^ >1600 o -*oo Figure 3-6: Shape Factor for UBC hull (Re=1.5 x 106) Displacement Thickness, Boundary Layer Thickness, Momentum Thickness The local value of displacement thickness is another useful parameter for studying the impact of the addition of side bulbs. The displacement thickness is a measure of the influence the presence of the boundary layer has on the flow streamlines. A larger displacement thickness will have the effect of increasing viscous pressure drag. A plot of displacement thickness for the UBC models is shown in Figure 3-7. The displacement thickness is shown to increase at a higher rate at midship as the beam of the vessel increases from 5% to 20%. This increase is shown to be much more gradual for the UBC Model 4 hull. The length of the arrow in Figure 3-7 graphically demonstrates this phenomenon. The increases in boundary layer thickness and momentum thickness follow the same trend as shown in Figure 3-7. 28 1200 ,. l oo^ to"" 0 ^ 4 0 0 UBC 5% DT (mm) UBC 10% 2000 1200 v "1000 j ^ ' ™ ; 2000 1200 » ' 1000 v Vj*4*** 1200 . 000 . ^ ( J C * * 1 ' Figure 3-7: Displacement Thickness for UBC hulls (Re=1.5 x 10*) In Figure 3-7 it can also be seen that the increase in displacement thickness is delayed by the addition of the side bulbs. The UBC 5% through 20% hulls all demonstrate a delay of about L/10 for the first contour level. The UBC Model 4 shows a further delay of L/20. Thus, the boundary layer grows gradually up to the point of maximum beam. Past this point, the growth in the adverse pressure gradient region is governed by the curvature of the waterlines. In other words, fairing of the bulbs towards the aft has the effect of slowing boundary layer growth. Cross Flow As described in Section 2.2, the presence of the cross-flow velocity component is a fundamental feature of the three-dimensional boundary layer. High cross-flow increases boundary layer thickness and results in the generating of vortices, especially in the vicinity of the upper and lower chine. Both of these phenomena can lead to an increase 29 in viscous drag. As shown in Figure 3-8, the cross-flow angle increases in the vicinity of the bulb as the degree of parabolization increases. Furthermore, a region of high cross-flow (circa 8 degrees) begins to develop along the bottom of the hull for the UBC 10%, UBC 15% and UBC 20%. These regions of cross-flow are largely eliminated on the UBC Model 4, which shows similar flow direction characteristics to that of the UBC Parent Hull. anCF(deg) UBC Parent .. , " 7.5 . . * , - £ > - 5 _>S«P^A —] 2.5 ^ * * \ > — o „.*"' -2 5 < 0 4 » 0 tanCF(deg) • io UBC 5% . f l i ^ 7 5 mmmm ~\ 5 ^ -S/^>. 2 5 — 0 ^ — j 25 >r —1 -5 | l o BP^J ^ - ^ 2 0 0 ( P J P ^ > ^ 1 8 0 0 200 r ^ - ^ 1 4 0 0 v n B W ^ ^ s o o 2 0 0 V TpSP-finn 0^^400 t UBC 1 0 % ^ ^ ^ ^ ^ ta 1 t jnCf (deg) I ™ U BC 2 0 % ^ ^ ^ ^ ^ ^ ^ ^ ^ / ^ ^ 1 6 0 0 20°\- - ^ ^mT^^ ^* ^ (,^"400 tanCF(deg) UBC Model 4 Fl 7.5 5 — -2.5 • P T ^ - ^ 1 8 0 0 200 e ^rSl ^ ^ 4 0 0 100 f fR 2 0 0 V ^ " ^ 6 0 0 1 . 1 0 0 \ _ P - * ^ 0 0 0 Figure 3-8: Tangent of Cross Flow (Re=1.5 x 10*) 3.3 2D RANS Model The IBL analysis as well as tow tank testing showed that considerable attention needs to be given to the blending of the side bulbs to the hull, in order to gain the maximum wave drag reduction with a minimal tradeoff in viscous drag. The fairing of bulbs, especially in the pressure recovery region can have a significant effect on form drag. As mentioned 30 previously, only a RANS solver is capable of directly quantifying the form drag. A full three-dimensional simulation of the flow around the hull would be ideal for studying the effects of various degrees of bulb fairing. Nonetheless, such simulations are very computationally and labour intensive and are not practical at an early design stage. Instead a two-dimensional simulation of the flow around the parabolized waterline can be used to look at beam increment and fairing effects. The trends established by the two-dimensional simulation can then steer the designer towards more optimized bulb shapes which could subsequently be evaluated in the towing tank or with a full three-dimensional simulation. 3.3.1 Model Setup The models were created with identical domain size, boundary conditions and mesh configuration. The only variable was the waterline geometry. Out of the six models studied in the previous section, only the UBC Parent Hull, the UBC 15% and UBC Model 4 hull were selected to determine the effect that beam width, location of maximum beam and bulb fairing have on viscous drag. The domain size and mesh are shown in Figure 3-9. A structured mesh with 400 000 elements was used with near wall mesh density based on a y+ value of unity calculated using Equation 2.4. Care was also taken in creating a fine mesh at the stern of the vessel in order to resolve the turbulent wake region. 4 Symmetry 3 nlet i o >- 2 ssure < j ssure < £ 1 Symmetry i Wall Symmetry i u-4 -2 0 2 X 4 6 8 10 Figure 3-9: UBC 2D Mesh and Boundary Conditions 31 The imposed boundary conditions are also shown in Figure 3-9. In order to cut down on domain size and computational time, only half of the hull was modeled. A symmetry condition was therefore imposed at the centre-plane. A symmetry condition was also used for the far field flow where the disturbance of the hull will have a minimal impact on the free-stream flow. A more detailed explanation of the specifics of the boundary conditions is given in Section 4.4.3. A k-s turbulence model with enhanced wall functions for near wall resolution was selected to resolve the flow within the turbulent boundary layer. Guidelines on the selection of a suitable turbulence model were given in Section 2.5. All three models were calculated based on a model scale Re = 2.05 x 106 corresponding to Fn = .23. Mesh adaptation (described in Section 4.2.2) was used to maintain a y+ value near unity over the entire surface of the hull. All simulations were run until a convergence criterion of six orders of magnitude was met. 3.3.2 Results The performance of the three hulls was compared based on field quantities and integral quantities. The field quantities, specifically boundary layer growth and recirculation at the stern, were used to study the flow features. Integral quantities, namely the coefficient of pressure and coefficient of friction served to quantify the effect of the flow around each hull shape. F i e l d Q u a n t i t i e s The growth of the boundary layer for all three hulls is shown in Figure 3-10. Analogous to the results obtained by using the IBL solver, the location of maximum beam and bulb fairing in the aft region has a significant effect on the boundary layer thickness. The boundary layer growth shows a pronounced increase beyond the location of maximum beam. By eliminating the shoulders through parabolization, the boundary layer growth is delayed from .45L to .5L for the UBC 15% and to .6L for the UBC Model 4. However, the increase in beam and replacement of the parallel midbody has the effect of increasing 32 the boundary layer thickness near the stern. Moving the location of maximum beam IV10 aft of midship on the UBC Model 4 had the effect of increasing the thickness of the boundary layer by 28% at the stern compared to the Parent Hull and by 13% compared to the UBC 15%. This increase in boundary layer thickness would increase the viscous pressure drag for a vessel with the same transom width. 0.3 > 0.25 0.2 0.15 UBC Parent 0 8 1 l!i ' 14 ' 1.6 X(m) 1.8 J 03 ? >-0.25 0.2 0.15 UBC 15% 0 8 1 l!i l!4 i!6 X(m) i!e i 0.3 ? > 0.25 0.2 0.15 UBC Model 4 0 8 \ 1.2 1.4 1.6 X(m) I 8 i Figure 3-10: Boundary Layer Thickness along U B C hulls The size of the wake behind a ship is a good indication of the expected form drag. Figure 3-11 shows a comparison between recirculation regions for all three models. The UBC 15% and the Parent Hull have very similar recirculation lengths, mainly because both hulls have the same transom width. The UBC Model 4 was build with a transom narrower by approximately 5% thus resulting in a shorter recirculation region. A narrower stern is analogous with lower form drag thus resulting in a decrease in form factor. This result was confirmed by Tan and Sireli with a reported form factor of 1.303 for the UBC Model 4 (having 11% beam increment) compared to a form factor of 1.444 and 1.398 for the UBC 10% and UBC 15%, respectively [3]. 33 It is important to note that the predicted recirculation region is only used to serve as comparison between the three models. The actual length and flow physics within the recirculation region would be significantly different if the complete hull was modeled instead of using the symmetry condition at the centre-plane. In such a case, the recirculation region would have highly transient effects. In addition, the isotropic modeling of turbulence employed by the RANS model is not well suited for large scale eddy prediction. An LES model would therefore be more suitable for more accurate prediction of the length and behaviour of the turbulent wake region. UBC Parent i <r~o:2 0:4 0:6 '6:6' • v 1:2 1:4 YA YA 2' 2:2 2:4 '2:6' 2:8 • 3' • '3:2' 3:4 AA AA UBC 15% ! 6 6:2 0:4 o:e 6:e i 1:2 1:4 16 i:6' 2' 2:2 2:4 2:6 2:6 3 3:2 3I4 ie' 3:8' 4 UBC Model 4 6 0:2.0:4 file 0:8'1"i:2 f4 YA YA 2 2.2 2:4 2:6 2:8 3 3:2 3!4 3!6 3!8 Figure 3-11: Comparison of wake size (m) Integral Quantities The skin friction coefficient, Cf, and the coefficient of pressure drag, C P ) are given in Table 3-1. The integral quantities were calculated based on the length of the waterline for each hull, excluding the length of the transom. To ascertain that the choice of nondimensionalization did not lead to erroneous results, the hulls were also compared 34 based on actual forces calculated by the RANS solver. Both methods yielded very similar results. UBC Parent UBC 15% UBC Model 4 UBC Parent % difference UBC 15% UBC Model 4 cB 2.29E-02 2.24E-02 2.07E-02 0.00% -2.30% -9.90% c, 4.16E-03 4.15E-03 4.15E-03 0.00% -0.16% v • ' -0.13%" . . ; c, 2.71 E-02 2.66E-02 2.48E-02 0.00% . -1.98%. %;*t 78.40% Table 3-1: Comparison of Integral Quantities for UBC Hulls The skin friction for the three hulls remains largely unchanged. The minimal difference in Cf can be attributed to slight variations in the near wall mesh. Had there been boundary layer separation the values of Cf would have had a greater disparity. It is the changes in viscous pressure drag that have the greatest effect on total resistance in the case of the UBC hulls. The UBC Model 4 hull showed a decrease in viscous pressure of nearly 10% compared to the Parent Hull. Table 3-2 gives a decomposition of the viscous pressure drag into C p acting on the stern and the C p acting on the hull (excluding the stern). The negative sign indicates that pressure is acting in the direction of ship travel. The breakdown of C p reveals that the drop in form drag for the revised hull is not only owing to the decreased transom width. The waterline shape affecting the boundary layer growth accounts for approximately 15% of the decreased form drag. Even the UBC 15% shows a slight decrease in form drag compared to the Parent Hull. c P % difference UBC UBC UBC Parent 15% Model 4 UBC Parent UBC 15% UBC Model 4 stern 2.88E-02 2.77E-02 2.51 E-02 0.00% -3.78% -12.77% hull -5.87E-03 -5.31 E-03 -4.47E-03 0.00% -9.54% -23.97% total 2.29E-02 2.24E-02 2.07E-02 0.00% -2.30% -9.90% Table 3-2: Comparison of C p along Hull S h e a r Stress The magnitude of the shear stress on the hull surface is the most commonly considered parameter when evaluating the possibility of separation. A zero shear stress location is identified as the location of boundary layer separation. Figure 3-12 depicts the shear stress distribution along three unique waterline shapes on the UBC hull. Near the bow, where the hull shape remains unchanged, the magnitude of shear stress is nearly identical. 35 Beyond this location, the shear stress distribution is shown to vary significantly with peak in shear stress occurring in the vicinity of the maximum beam location. These differences in shear stress distribution along the hull waterline imply that changes in skin friction can be expected between the various UBC hulls which cannot be predicted by the ITTC-1957 line. A direct calculation of the shear stress distribution is therefore needed to predict the impact that bulb size, span and placement have on the frictional resistance of the vessel. In addition, neither one of the models showed a shear stress value below zero. This indicates that there is no expected separation aft of the stern. This result is supported by the experimental studies explained in Chapter 5 and partially by the fact that the IBL solver was able to calculate the boundary layer parameters up to the stern of the hull. 4 2 o L _, 1 1 _ _ _ _ _ , , 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 X(m) Figure 3-12: Wall Shear Stress along hull 36 3.4 Discussion The use of numerical methods to predict changes in viscous drag gave significant insight into the changes in flow physics associated with varying the shape of the UBC hull. The IBL solver and the RANS 2D simulations exhibited small differences in Cf between the hulls. The increase in form factor for the parabolized hulls was therefore largely attributed to an increase in viscous pressure drag. The magnitude of this component of drag could only be predicted using the RANS solver. However, studying the changes in boundary layer parameters calculated by the IBL solver provided important understanding on how the form drag could be affected by changes in hull geometry. One of the key contributors to increased form drag is boundary layer thickness. Pronounced increases in beam along the length of the vessel can result in high adverse pressure gradients creating a favorable environment for boundary layer growth and potential separation. Significant growth of the boundary layer along the UBC hulls was shown by both solvers to be delayed up to the point of maximum beam. Beyond this point, beam increase and degree of bulb fairing played a pivotal role in controlling boundary layer growth. As shown by the IBL solver, successive increases in beam from 5% through to 20% steadily increased the boundary layer thickness aft of the maximum beam location. This boundary layer growth resulted in an increased displacement thickness creating a larger wake region behind the ship. Fairing of the bulbs towards the aft succeeded in slowing the growth of the boundary. In the case of the UBC Model 4, decreasing the width of the stern by 4.5% compared to the other hulls by shifting the volume to mid-ship successfully reduced the wake of the vessel. Another contributor to an increased viscous drag is the occurrence of boundary layer separation. The exact location and even the occurrence of separation are difficult to predict. Neither the IBL solver nor the RANS 2D solver showed signs of separated flow. An inspection of the shape factor calculated by the IBL solver revealed that the area directly in the vicinity of maximum beam is a possible separation location. The probability of separation increased with an increase in beam. Therefore even if predicted benefits to wave drag reduction point in the direction of a sizeable beam 37 increase, the possibility of boundary layer separation beyond a certain beam width must be considered. A three dimensional elliptic solver is necessary to perform a complete evaluation of the performance of each ship model. With present computational limitations, however, it is not a practical tool, especially in the preliminary design stage. The use of less computationally expensive viscous codes such as the IBL solver and simplified models such as the 2D RANS, along with skilled interpretation of results could be used to narrow the design of the parabolized hull to only a small number of candidate hull geometries. Only then is it warranted to evaluate the selected candidate hulls with more complex numerical solvers or with experimental testing. Ultimately, the viscous solvers should be used to evaluate and fine tune promising hull geometries designed with inviscid free-surface solvers. 38 CHAPTER 4 4 V I S C O U S D R A G O F P A R A B O L I Z E D N P L H U L L 4.1 Introduction The knowledge gained from the investigation of the parabolized UBC Series Model 3 hulls and the UBC Model 4 hull was used as a stepping stone to extend parabolization to the NPL Trimaran. The addition of parabolic side bulbs to the NPL hull consisted of an iterative approach of using an inviscid solver to predict the wave profile along the hull. Once a prospective configuration was identified, the hull was evaluated using a viscous solver. Since parabolization was only applied to the main hull of the trimaran the outriggers were omitted in the viscous drag calculations. In addition to the Parent Hull, the viscous drag of three different parabolized hulls was studied in detail. Figure 4-1 gives a description and the naming convention for all four hulls. NPL 6 was created to provide wave cancellation along the main hull. NPL 4 was identified as a suitable candidate for cancellation of the bow wave created by the outriggers. NPL 7 is a modified version of NPL 4 with fairing for and aft of the bulb to reduce viscous drag. The Parent Hull, NPL 6 and NPL 7 were all tested in the towing tank to provide validation data for the numerical models. The generation of the NPL model geometry and the free surface calculations are described in detail by Vyselaar [4]. The viscous resistance of the NPL trimaran was computed with the IBL solver to determine the magnitude of skin friction drag and to compare it to the ITTC 1957 line. The IBL solver was then used to evaluate the changes in Cf and to study the changes in boundary layer parameters. A three-dimensional RANS model was then created to predict the form drag of the Parent Hull and the NPL 6 hull. The numerical simulations were done at Reynolds numbers corresponding to the low speed model tests used for calculating the form factor. The findings were compared to both experimental results obtained in the towing tank and to traditional empirical methods used by naval architects. In addition, a full scale RANS simulation of the Parent Hull was done to study the 39 possibility of replacing conventional model to full scale scaling techniques with numerical methods. NPL Parent HH 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 Max beam: 0 .111 m<§ Jx = • .97m X(m) NPL 4 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 Max beam: ( ).130m<j gx = 1.79m X(m) NPL 6 „ — —• -0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 Max beam: D.127m( g x = 1.76m X(m) NPL 7 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 Max beam: 0.127m g x = 1.79m X(m) Figure 4-1: N P L Hulls 4.2 Experimental Work All of the experimental work was conducted at the Vizon Scitec towing tank facility. In total, three different hulls were tested in both monohull and trimaran configuration: NPL Parent, NPL 6 and NPL 7. The tests were conducted to validate the numerical predictions of viscous resistance and wave resistance and to observe the changes in wave profiles and wave interactions between the Parent Hull and the parabolized hulls. 4.2.1 Experimental Setup The NPL parent model and the bulbs for NPL6 were built by a professional model maker out of foam and fiberglass. The main hull had an additionally reinforced core made of wood which served as a secure point of attachment and a location for ballast placement. The bulbs for NPL6, shown in Figure 4-2, were attached to the hull using double-sided 40 tape for ease of removal for future testing of other bulb configurations. On the other hand, the bulbs for NPL7 were built out of ABS plastic using rapid prototyping (RP) technology as shown in Figure 4-3. The RP machine "printed" each bulb in three sections due to the limitation of the working bed (406 x 355 x 406 mm). It was possible, however, to print up to three bulbs simultaneously by arranging them accordingly on the working bed. Each layer of ABS plastic was .01" thick, thus resulting in a ridged bulb surface due to the curved shape of the bulbs. It was also possible to set the RP machine to "print" at .005" thickness but the process would have taken approximately nine times longer. Since it took several hours to print a single bulb, using a higher tolerance setting was not feasible. To reduce construction cost, Waterworks™ support material was used where a solid ABS structure was not required. The support material was washed after printing in the wash station. The bulbs were connected at the ribs with ABS cement. The outer surface of the bulbs was initially sanded with sand paper mesh to eliminate the large ridges, and subsequently wet-sanded for a smooth finish. The final finishing coat was created by applying methylene chloride to the bulb surface with a foam paint brush. The methylene chloride also provided sealant to the bulbs against water impregnation. « — , i S Figure 4-2: NPL6 bulbs (metre stick included for comparison) Figure 4-3: NPL7 Bulbs (metre stick included for comparison) 41 The bulbs for NPL7 were attached to the hull using wood screws at four locations along the rib section. Hot glue was applied at the extremities and intermittently along to bulb edges to ensure a good seal and to minimize the amount of water entering the bulb cavities. Finally, plasticine was used to fair the bulb edges into the hull surface and avoid locations of large discontinuity. The NPL Parent and NPL7 as tested models are shown in Figure 4-4. Figure 4-4: N P L Parent Hul l Testing Figure 4-5: N P L 7 Testing Turbulence pins 3mm in diameter were placed at x = 0.1 L distance from the bow to stimulate a turbulent flow and to guarantee the presence of a turbulent boundary layer. The model was free to trim and squat. The Parent Hull was ballasted to the required design waterline. NPL 6 and NPL 7 were tested based on matching displacement in order to facilitate the comparison process. 4.2.2 Experimental Results All NPL models were tested in the slow speed range of 0.10 < Fn < 0.20 to determine hull form factors using Hughes-Prohaska method (with N=4) and in the high-speed range of 0.20 <Fn < 0.47 to measure the effect the bulbs have on wave resistance and to observe any incurring changes in wave profile. The experiments were conducted several months apart due to the time required to build the model and the two distinct bulbs, as 42 well as the availability of the testing facility and because of new developments from the numerical work. The Parent Hull was therefore tested in May 2005, the NPL6 hull was tested in August 2005 and the NPL7 hull was tested in January 2006. In addition, the Parent Hull was retested in January 2006 to provide a more recent baseline to the NPL7 and to test for repeatability of results. The form factor derivations for all tested hulls are shown in Appendix C. F o r m F a c t o r The form factors calculated using the Hughes-Prohaska method (with N = 4) are summarized in Table 4-1. N p £ p a r e n t Date of Test May-05 Jan-06 Aug-05 Jan-06 Monohull 1.159 1.153 1.214 1.234 Trimaran 1.22 1.212 1.236 1.237 Table 4-1: Form Factor for N P L hulls In the case of the NPL Monohull, the form factor increased by approximately 5% with the addition of the side bulbs. Moreover, the use of a shorter bulb on the NPL7 with a more pronounced deviation from the Parent Hull surface profile had the effect of further increasing the form factor. This result is supported by the previous work done on the UBC Model 3 hulls that showed that for a parabolized hull with the same beam width, fairing of the bulb (ie. increasing bulb length) had the effect of decreasing form factor. A less pronounced form factor variation was observed in the case of the NPL Trimaran hulls. This was primarily due to the added surface area from the outriggers that had the effect of decreasing the percentage of hull affected by the presence of the bulbs compared to the monohull configuration. The increase in form factor between the Monohull and the Trimaran may be the result of viscous interactions. Studies on high-speed NPL catamarans with the same L/B ratio have shown an increase in viscous resistance to be in the order of 10% [28]. These studies were performed in towing tanks as well as wind tunnels, and have consistently 43 shown viscous interaction effects. Since the outriggers of the NPL Trimaran only span 36% of the hull, the degree of interaction is significantly less than for a catamaran as supported by the experimental data summarized in table 4-1. The experimental results were scaled up to full ship scale to determine the impact each hull configuration would have on the Effective Horsepower (EHP) required as shown in Figure 4-6 and Figure 4-7. An EHP comparison gives the advantage of taking into account the lower viscous drag expected at a Reynolds number that is two orders of magnitude higher than at model scale and also allows for a direct comparison between the experimental results conducted several months apart in varying towing tank water temperatures. The trimaran results are also presented in Figure 4-7b in a percent difference from Parent Hull format to give a better indication of potential horsepower savings. A percent difference graph is not shown for the monohull because of the oscillations in Parent Hull resistance data at higher speeds. This phenomenon of oscillations in resistance was observed in both May and January tests. The repeatability of the towing tank is about 1.5% but the oscillations are outside of this range [29]. Therefore, the reason may either be an unexplored physical phenomenon or a small angular deformation of the heave post connecting the model to the carriage, thus allowing the model to travel at a slightly varying angle of attack. The Trimaran data was much more consistent, mostly due to the added directional stability provided by the outriggers. Figure 4-7b clearly shows a decrease up to 6% in total resistance in the 0.31-0.44 Fn at full ship scale. To better understand the source of the decrease in total resistance, a breakdown in terms of resistance coefficients is given in Figure 4-8. The 6% drop in total resistance is shown to be attributed to a decrease in wave-making resistance of up to 20% at Fn = 0.36. Since the viscous resistance constitutes almost 60% of the total resistance for the NPL Trimaran, the benefits resulting from a decrease in wave-making resistance are not as substantial compared to the UBC Series hulls where wave-making drag was almost 70% of total drag at the same speed. 44 40000 3500O 30000 25000 - N P L Parent Monohull (Jan) N P L 7 Monohull N P U 6 Monohull - N P L Parent Monohull (may) 20000 -15000 10000 5000 0.250 0.270 0.290 0.310 0.330 0.350 0.370 0.390 0.410 0.430 0.450 0.470 0.490 Fn Figure 4-6: NPL Monohull EHP curves 45000 40000 35000 30000 25000 20000 -15000 10000 5000 a) - NPL Parent Trimaran NPL6 Trimaran NPL7 Trimaran 0.25 0.27 0.29 0.31 0.33 0.35 0.37 0.39 0.41 0.43 0.45 0.47 0.' Fn b) NPL Parent Trimaran -*— NPL6 Trimaran NPL7 Trimaran 0.49 Figure 4-7: a) NPL Trimaran EHP curves, b) NPL Trimaran % difference from NPL Parent 45 —•— Parent Cv -m- Parent Cw Parent CT —•— NPL7 Cv —— NPL7Cw - » - N P L 7 C T 3.8E-03 -i ! . T i 1 T 1-3 2.6E-03 -§ 2.2E-03 -6.0E-04 -1 i 1 1— —I— i —I 1 0.25 0.27 0.29 0.31 0.33 0.35 0.37 0.39 0.41 0.43 0.45 0.47 0.49 Fn Figure 4-8: Comparison of NPL Parent and NPL 7 Trimaran at full scale 4.3 IBL Model Integral boundary layer methods have shown to give very accurate results for slender hulls without significant discontinuities in hull shape. The main hull of the NPL is extremely slender, having an L/B ratio of nearly 13.5. It is a very streamlined vessel without any complicating features such as chines, knuckles or bulbous bows. Therefore, the IBL solver was expected to give good results over the majority of the hull as long as the increase in beam applied through parabolization didn't cause boundary layer separation. 46 4.3.1 Model Setup and Considered Ship Condition The calculation process was carried out according the steps outlined in Appendix B. The model performance was studied over a range of speeds analogous to experimental conditions used for determining the form factor, namely at 1.68 x 106 < Re < 3.67 x 106. Additionally, the magnitude of Cf was calculated for a Re = 1.39 x 109 corresponding to the full scale speed at Fn = 0.22 used for comparison with the RANS simulation. 4.4 3D RANS Model A RANS solver was used to study the entire flow field around the Parent Hull and NPL 6. The NPL 4 and the NPL 7 hulls were not included in the RANS study because the hull shape was developed at a later stage based on improved inviscid solver predictions. Nonetheless, the primary objective of the simulations was to study the effect that parabolization has on the skin friction and viscous drag for a slender vessel. Only an elliptic solver is capable of separating the viscous drag into respective components. Further design optimization of the shape of the parabolic section can only be achieved if phenomena such as flow separation at the stern and boundary layer growth can be modeled and understood. 4.4.1 Model Geometry In total three different models were created: 1. A model scale Parent Hull model 2. A model scale parabolized hull model 3. A full scale Parent Hull model The first two models are identical in domain size and grid spacing except for the different hull geometry. A third model was created with a greater grid resolution near the hull surface because the computation was done at a Re ~ 109, three orders of magnitude higher than model scale due to Froude scaling. The computational domain was created spanning one ship length upstream of the model, two ship lengths downstream and one ship length deep. Furthermore, only half of the hull was modeled to conserve on the computational expense. This is a common practice used in the marine industry when modeling ships at zero angle of attack [26]. 47 4.4.2 Mesh Generation Generation of a mesh capable of capturing the complicated flow phenomenon near the hull surface and behind the transom stern of the NPL is key to achieving good predictions of skin friction and viscous pressure drag. Typically, the first choice to make is whether to use a structured or unstructured mesh, or a combination of the two types. While unstructured meshes are more suitable for complex model geometry, it is much more difficult to maintain high mesh quality, especially in near-wall regions. A structured mesh approach was therefore chosen for all the models. Since the NPL hull is a very slender and streamlined vessel, a large portion of the total drag will be dominated by the viscous effects. It was therefore important to correctly model the flow within the turbulent boundary layer. Preliminary studies using wall-functions did not show satisfactory results; therefore a mesh with near wall resolution around y+ equal to unity was created for the NPL hull. The near-wall cell distance was calculated using Equation 2-4 derived from flat-plate boundary layer theory by setting y+ equal to unity and solving for y. Figure 4-9: N P L Model mesh and near-wall resolution 48 Figure 4-9 shows the mesh generated on the surfaces of the entire domain as well as the boundary layer mesh at the bow of the NPL hull as calculated using Equation 2-4 for Re = 2.0 x 106. The mesh generated for the full scale NPL hull is finer in the boundary layer region to account for the higher Reynolds number namely Re ~ 2.0 x 109. It is also important to note that the same mesh was used for all model scale simulations even though the simulations were done for a range of speeds. The added time cost of generating a different boundary layer mesh was not warranted since further mesh coarsening/refinement techniques are available within the software. These techniques are referred to as mesh adaptation. Once a simulation begins to converge, it is possible to adapt the mesh spacing based on relevant parameters such as y+ value, velocity gradient, pressure gradient, and so on. A comparison of an original mesh at the hull surface and a mesh adapted based on y+ value is shown in Figure 4-10. original mesh size Figure 4-10: Mesh adaptation based on y+ value In addition to generating a fine near-wall mesh, it was important to have adequate mesh resolution around the stern of the hull to resolve the recirculation region behind the transom. Initial mesh generation attempts consisting of about 400 000 elements did not have adequate resolution near the stern resulting in inaccurate predictions of viscous pressure drag. The final meshes consisted of approximately 1.3 million elements to provide adequate mesh refinement near the hull and at the stern. 49 4.4.3 Boundary Conditions Physical conditions imposed on the boundaries of the domain are necessary to solve the governing equations. Figure 4-11 shows the solution domain with the imposed boundary conditions common to all three models. Because the simulations were done to obtain viscous drag values, the effects of the free surface were neglected and replaced with a symmetry boundary condition. The condition implies that there is no flow through the surface and that the gradients of u, v and p in the z-direction must be equal to zero [23]. Since only half of the hull is represented, a symmetry condition was also used on the vertical central plane. In addition symmetry conditions were used on the vertical plane opposite the central plane, as well as on the bottom plane. These boundary conditions are valid provided that the domain is large enough that the presence of the hull is not "felt" in the far-field, namely that the disturbance caused by the hull disappears and the velocity components are identical to the free stream value. Figure 4-11: Model Domain and Boundary Conditions 50 On the hull itself, a no-slip boundary condition which imposes that the velocity components of the fluid particles relative to the body must equal and that the pressure gradient normal to the surface must also equal to zero [23]. Upstream of the hull, a velocity inlet boundary condition is used to define the flow velocity as well as relevant scalar properties required by the chosen turbulence model. The velocity was specified based on magnitude and direction because the shape of the inlet was not normal to the flow field. For the k-e turbulence model, values for turbulence intensity and length scale were also specified. The turbulence intensity, defined as the root-mean-square of the velocity fluctuations, u', to the mean flow velocity, uaVg, was given the value of 0.1% [25]. While this is generally considered to be a low value, low-turbulence wind tunnels typically have a turbulence intensity value as low as 0.05% [25]. Furthermore, the data was compared to towing-tank results where the turbulence intensity in the free-stream region is theoretically zero because the fluid is at rest. Finally, a pressure-outlet boundary condition was specified on the vertical plane downstream of the hull. The far field static pressure was specified at the outlet. 4.4.4 Turbulence Model/Dicretization Two types of turbulence models were used: k-e solver with enhanced wall functions with pressure gradient effects for the model scale simulations, and an Shear Stress Transport (SST) model for the full scale simulations. For a description of the turbulence models please refer to Section 2.6.2. It was the author's original intent to use the same turbulence model for the full scale simulation as that for the model scale. The near-wall grid spacing required to resolve the flow in the viscous sublayer and buffer layer without using wall functions was too computationally expensive, resulting in well over a million elements. An SST model was therefore used based on the recommendations of the Fluent manuals [25]. 51 4.4.5 Full Scale Model Considerations The ability to predict the flow around naval vessels at full scale is the ultimate goal of numerical simulations. The flow field and the drag components contributing to the overall resistance of the vessel are routinely studied at model scale. An in-depth knowledge of the flow field in specific areas around the hull is very important for the design of appendages and for propulsion system performance. Empirical relations can be used for extrapolating total resistance; however, no reliable methods exist for extrapolating the measured model scale flow field to full scale flow [30]. The difference between the model scale flow field and the full scale lies in the discrepancy in Reynolds scaling. Extrapolating the model scale data using Froude scaling typically results in an increase of two to three orders of magnitude in Reynolds number. Consequently, a complete understanding of the flow field at full scale can be achieved by measuring the full scale flow field. Actual physical measurement of the flow field around a full size ship has only been done a select few times due to the limitations in the instrumentation techniques and the costs associated with installing the equipment and running the experiments in a sufficiently controlled manner [30]. With recent advances in numerical techniques and increased computation power, it is becoming possible to create numerical simulations of ship flows at full scale. A simulation of ship performance at full scale using RANS codes requires a much finer near-wall mesh resulting in a larger number of elements. The computational cost is therefore increased. The goal of the study was to determine how easily the RANS simulations done for the model scale NPL monohull could be extended to full scale. Since no full scale date was available, the skin friction coefficient was compared to the ITTC'57 correlation line as well as to the calculated value using the IBL solver. The full scale NPL monohull numerical model was almost identical to the model scale case except for the mesh density near the wall and the size of the domain. The larger domain was created to be able to include free surface calculations in future simulations. The dimensions of the computational domain are shown in Figure 4-11. 52 The near-wall mesh spacing was calculated using Equation 2-4. Ensuring a y+ spacing of approximately unity resulted in a number of elements in excess of 1 million, which proved to be beyond the available computational power. A structured mesh with a y+ of 50 was therefore created. A coarser near-wall mesh no longer permitted the use of a turbulence model with enhanced wall functions. 4.4.6 Mesh refinement The results obtained from CFD calculations are highly dependent on the mesh quality and the resolution. Typically, a mesh refinement study is done by starting with a relatively coarse mesh and proceeding to increase the number of elements up to the point where the mesh density no longer affects the final converged solution. In the case of the NPL models, mesh density refinements were done locally based on the y+ value by using mesh adaptation. The original model had circa 0.8 million cells. Multiple mesh adaptations increased the number of cells in proximity of the hull resulting in approximately 1.2 million cells. The near-wall mesh adaptation had a pronounced impact on the convergence as well as on the calculated frictional values. The limitations to mesh refinement came largely from the available computational power. However, in all the simulations at model scale, once the required near-wall resolution of y+ = unity was achieved, further mesh refinement did not have a pronounced impact on the frictional resistance values. 4.5 Numerical Results: Model Scale The numerical results obtained from both the IBL solver and the RANS solver are presented and compared in this section. The experimental results from tow tank testing are also compared to the RANS predictions. 4.5.1 Skin Friction IBL Solver The skin friction was calculated by the program RESIST which calculates the skin friction by integrating the skin friction coefficient over the wetted hull surface. A 53 comparison between the calculated values of Cf using the IBL solver and the ITTC'57 correlation are shown in Figure 4-12. The computed values of Cf follow the same trendline as the ITTC'57 correlation line but range in magnitude. The Parent Hull exhibited the lowest skin friction followed by NPL 6, NPL 7 and NPL 4. A percentile basis comparison of average Cf at model scale and Cf at full scale between the calculated results and the ITTC'57 line is given in Table 4-2. 4.3E-03 -3.5E-03 \— —,— , 1.6E+06 2.0E+06 2.4E+06 2.8E+06 3.2E+06 3.6E+06 Re Figure 4-12: Skin Friction for NPL hulls ITTC 1957 NPL Parent NPL 4 NPL 6 NPL 7 Average at Model Scale 0.00% -1.43% -0.11% -0.72% -0.59% Full Scale 0.00% -1.26% -0.61% -1.08% -0.83% Table 4-2: Percent Difference in Qcompared to ITTC'57 line 54 RANS Solver A comparison of C f for the Parent Hull and the parabolized hull are shown in Figure 4-13 for both the RANS and IBL calculations. In both cases, the numeric solvers predicted a lower C f than the ITTC correlation line. This was an expected result for such a streamlined slender vessel. More importantly, both solvers predicted approximately a 1% increase in C f for the parabolized hull. The lower magnitude of skin friction calculated by the RANS solver compared to the IBL solver is shown to be attributed to a lower C f prediction near the bow of the vessel. The IBL solver predicts a band of a much higher C f at the bow as shown in Figure 4-14. Beyond x = 0.8, the skin friction predicted by both solvers matches very well. A small region of low C f (< 2.26e-03) is predicted by the IBL solver near the stern of the vessel. Since this region occurs close to the stern it may be a result of the inability of the IBL solver to accurately resolve the flow near the stern. 4.4E-03 n ITTC '57 RANSE NPL Parent 4.2E-03 4.0E-03 3.8E-03 -o 3.6E-03 -3.4E-03 -3.2E-03 3.0E-03 1.6E+06 2.0E+06 2.4E+06 2.8E+06 3.2E+06 3.6E+06 Re Figure 4-13: Comparison of Cf for NPL Parent and NPL 6 55 SFC NPL Parent: IBL Solver SFC NPL Parent: RANS Solver Figure 4-14: Comparison of C f between RANS and IBL solvers for NPL Parent (Re = 1.68 x 10s) 4.5.2 Boundary Layer Parameters The calculated magnitude of Cf is useful for evaluating the impact that hull changes have on resistance, but it does not necessarily give direct feedback to the designer for future improvement. An evaluation of various boundary layer parameters is therefore very useful for identifying specific regions of interest which may need further refinement to arrive at a more optimum hull geometry. Shape Factor The shape factor along the surface of the NPL hulls is shown in Figure 4-15. The calculations for the NPL Parent Hull did not reveal any regions of concern, namely a shape factor in the range of 1.8 and 2.8 that are typically associated with possible flow separation. The addition of the side bulbs for the NPL 6, NPL 4 and NPL 7 crated a zone of increased shape factor near the location of maximum beam. NPL 7 had the highest 56 shape factor magnitude (about 1.6) of all the hulls, compared to a maximum value of 1.44 for the Parent Hull. NPL Parent S F .600E+00 .573E+00 .545E+00 .518E+O0 491E*00 .464E+00 .436E+00 4O9E+O0 382E+00 355E*00 .327E*00 300E+00 ).4 N P L 4 Figure 4-15: NPL shape factor comparison (Re = 1.68 x 106) Cross Flow The cross flow angle as calculated by the IBL solver is shown in Figure 4-16. All four NPL hulls show a similar cross-flow angle near the bottom of the vessel. The Parent Hull has almost no cross-flow along the majority of the hull, as to be expected of such an extremely streamlined vessel. The addition of the bulbs introduces localized changes in flow direction along the hull which can be expected to increase the viscous drag properties. In addition, as seen on the NPL4 hull, the bulb geometry at the stern of the 57 vessel changes the flow direction by about 2 deg thus modifying the flow entering the propeller plane. This effect is decreased significantly for NPL7 by fairing the bulbs at the aft end. Figure 4-16: NPL crossflow comparison at (Re = 1.68 x 106) Boundary Layer Growth As the speed increases, the IBL solver follows the ITTC'57 line, while the RANS solver predicts a larger decrease in Cf (Figure 4-13). Since it was not possible to compare the values of Cf to actual measured data, a boundary layer thickness comparison, shown in Figure 4-17, was done between the two solvers. Near the bow of the vessel, where the boundary layer remains thin, there is very close agreement between the two solvers. Near 58 the stern, however, the inability of the velocity profiles to predict reverse crossflow leads to a breakdown of the IBL code [20]. This unfortunate limitation to the IBL code means that it is not possible to accurately predict the existence or location of separation that may occur as a result of an increase in beam. Figure 4-17: Comparison of BL thickness at four separate stations along hull (Re = 1.68 x 1 ()'') Figure 4-17 also suggests that the boundary layer growth predicted by the IBL solver up to at least two thirds of ship length is sufficiently accurate to draw conclusions about the effect different bulb shapes have on boundary layer growth. Figure 4-18 shows a comparison between all four NPL hulls. Compared to the Parent Hull, NPL6 has the most similar boundary layer profile along the hull. The bulb on NPL6 spans the greatest extent on the hull therefore the slope changes introduced by the increase in beam are less than on the NPL4 and NPL7. The NPL4 on the other hand has a much shorter bulb span and greater entrance and exit angles since minimal fairing of the bulbs was done during the design process. As a result, the boundary layer is shown to grow much faster at the 59 aft end of the bulb. The boundary layer growth is shown to be less pronounced on the NPL7 which is a faired version of NPL4. BLT (m) 9.00E-02 8.29E-02 7.58E-02 6.87E-02 6.16E-02 5.45E-02 4.75E-02 4041-02 — 3 33IE-02 • - 2.62E-02 • 1.91E-02 1.20E-02 0-4 NPL Parent BLT (m) NPL 4 4-NPL 6 4_ Figure 4-18: NPL boundary layer thickness comparison (IBL solver) (Re = 1.68 x 10*) 4.5.3 Form Drag The form factor was calculated based on RANS results using Equation 2-7. A comparison between the RANS results and the experimental results for both NPL Parent and NPL 6 monohulls is given in Table 4-3. In general, the predicted form factor using the RANS solver was of comparable magnitude to the values obtained experimentally. As discussed in section 4.5.1, the C f value was shown to slightly increase for NPL6 60 compared to the Parent Hull. The same cannot be shown for the magnitude of C p . The pressure contribution of the viscous force showed some variance, ranging between a form factor of 0.166 and 0.188. This result suggests that the use of an absolute form factor value applicable throughout the entire working speed of a vessel may not be entirely adequate. Moreover, the RANS simulations reveal that the changes in hull geometry between NPL Parent and NPL 6 have an effect on both components of viscous drag. Therefore, the experimentally determined form factors presented in section 4.2.2 do not give an accurate breakdown of C f and C p because they are based on the ITTC'57 friction line. Studying the viscous drag numerically allows a more direct understanding of the strengths and weaknesses of the proposed bulb geometry. NPL Parent RANS Exp RANS RANS ITTC'57 RANS Exp* Fn C v | 8 C O U 8 C V | S C 0 U S C p C F C F Cp/Cp Cp/Cp formFactor formFactor 0.104 4.71E-03 4.84E-03 6.70E-04 4.04E-03 4.20E-03 0.166 1.156 0.145 4.35E-03 4.53E-03 6.47E-04 3.72E-03 3.93E-03 0.174 1.156 0.186 4.22E-03 4.31 E-03 6.89E-04 3.53E-03 3.74E-03 0.195 1.156 0.227 4.00E-03 4.15E-03 6.48E-04 3.36E-03 3.60E-03 0.193 1.156 * Average from May 2005 and Jan 2006 tests NPL 6 RANS Exp RANS RANS ITTC'57 RANS Exp C _ P P r r r C P /C F C P /C F Fn C n - o ^ C v l s c o u s c p c F Qp f o r m F a c t o r fo r m F actor 0.104 4.78E-03 5.10E-03 6.94E-04 4.09E-03 4.20E-03 0.170 1.214 0.145 4.42E-03 4.77E-03 6.64E-04 3.76E-03 3.93E-03 0.177 1.214 0.186 4.22E-03 4.54E-03 6.68E-04 3.55E-03 3.74E-03 0.188 1.214 0.227 4.02E-03 4.37E-03 6.37E-04 3.38E-03 3.60E-03 0.188 1.214 Table 4-3: Form Factor Comparison It is important to note that there is a degree of uncertainty in the values because a complete mesh refinement study was not done in the vicinity of the stern. Furthermore, as was the case with the 2D RANS simulation of the UBC Model, the choice of turbulence model, the imposed symmetry condition along the length of the hull and the exclusion of transient effects simplified the actual flow physics. 61 4.6 Numerical Results: Full Scale NPL Full scales numerical studies of the flow around vessels are seldom done because of the high mesh density requirement and the difficulty of turbulence models to accurately calculate the flow physics in the Re = 109 range. The choice of turbulence model was therefore very important in preventing the solver from diverging. The k-e model with wall-functions used for the model scale simulations showed a lot of instability and did not converge well. The use of the SST Model gave much more reasonable results. The SST model combines the k-e model used to calculate the far field flow with the k-w model in the near-wall region [25]. It is recommended for higher Reynolds number flows. A comparison of Cf calculated with the SST model vs. the ITTC'57 friction line and the IBL solver at Re=1.39 x 109 corresponding to a Fn=.22 is given in Table 4-4. The IBL solver gave a result very close to the ITTC'57 line while the RANS solver calculated a much lower value. The RANS solver only converged by 4 orders of magnitude and showed fluctuations in both Cf and C p. The mesh density near the hull also needed further refinement because the y + value exceeded 100 in certain locations. Additional mesh refinement, however, was impeded by the computational resources. Further work is needed using multiple processors to continue the study. 1 R A N S I B L n T C ' 5 7 I 1.13E-03 1.45E-03 1.47E-03 Table 4-4: Skin Friction Coefficient for Full Scale NPL hull 4.7 Discussion By decomposing the viscous resistance components into skin friction drag and pressure drag, it was possible to determine how the presence of the side bulbs influenced the performance of the hull. The skin friction values calculated by the IBL solver and the RANS solver were compared directly to the ITTC '57 line. Both solvers predicted a lower Cf value than predicted by the ITTC line as well as approximately a 1% increase in Cf for the NPL6 hull compared to the Parent Hull. The Cf value was computed over a 62 range of speeds in order to investigate if there is any deviation in slope from the ITTC '57 correlation line. The slope of the Cf curve calculated with the IBL solver was found to be identical to that of the ITTC '57 line for all four hulls studies. The RANS solver, however, predicted an increasing deviation from the ITTC'57 line with increase in Re (1.6E6 to 3.6E6). This behavior requires further investigation either through a more elaborate mesh refinement study and evaluation of the solver's sensitivity to the choice of turbulence model and turbulence parameters or through further experimental work in the wind tunnel where free surface effects are non-existent. Nonetheless, the primary objective of the study was to establish which bulb configuration would result in minimal viscous drag penalties, thus increasing the net impact of a projected decrease in wave drag. The computed values of Cf alone indicated that the Parent Hull had the lowest Cf and any change in hull geometry would result in higher skin friction. Out of the parabolized hulls, NPL 6 showed the smallest increase in Cf followed by NPL 7 and NPL 4. Upon closer examination of the Cf distribution along the hull, as well as the boundary layer growth, shape factor and the cross flow angle, it was apparent that the presence of the bulbs disrupted the flow in the vicinity of the hull. The smallest amount of disturbance was observed on NPL 6, supporting the belief that by minimizing the change in hull curvature by fairing the bulbs into the hull will minimize the increase in viscous drag. Experimental results revealed that NPL 6 did in fact have lower viscous drag compared to NPL 7, but did not achieve significant enough reductions in wave drag to overcome the penalty paid in an increased viscous drag compared to the Parent Hull. Conversely, the more pronounced wave interactions between centre hull and outriggers created by the NPL7 bulbs resulted in an overall reduction in EHP on the order of 5% in the targeted speed range. The experimental data was also used to evaluate the ability of the RANS simulation to predict the form factor, which is a necessary parameter for scaling of the model results to full ship scale. The magnitude of the form factor from the numerical and experimental studies was very similar. However, while the towing tank data predicted a 5% increase in form factor between the Parent Hull and NPL6, the RANS solver showed no definite 63 increase. The primary cause of this discrepancy is the inclusion of changes in Cf in the form factor term derived by traditional experimental methods. The RANS solver on the other hand, is capable of separating the viscous drag into well defined components. Thus, if both Cf and C p increase, as was the case with both hulls, the ratio of these components remains largely unchanged. At model scale, this discrepancy can be avoided by simply comparing the total viscous drag terms. But at full ship scale, it is necessary to recalculate the viscous drag by performing a RANS simulation at full scale since traditional laws based on form factor scaling no longer apply. As demonstrated in Section 4.6, full scale numerical simulations are much more computationally expensive and remain beyond the limits of most naval architecture firms. A survey was made of model tanks to assess the level of usage or RANS and it was found that there is currently no commercial usage of RANS methods for the model/ship extrapolation for powering predictions [31]. A final option which remains to be explored is the combination of form factor predictions at model scale with RANS codes and calculations of Cf at full scale using the IBL solver which gave results for the NPL Parent Hull and NPL6 comparable to the ITTC'57 correlation line. Hence, for the analysis of the NPL hull, the IBL code proved very useful in estimating the magnitude of Cf in the range of operating speeds. Although it is only possible to calculate the viscous pressure resistance and resolve the flow in the stern region of the vessel with Navier-Stokes elliptic solvers, the computational power and time requirements continue to favor the use of an IBL code for preliminary design use. The IBL code can be used as a powerful tool for determining the feasibility of applying parabolization to a chosen vessel, when used in combination with a Michell's integral based solver or a Rankine source panel method for calculating the wave resistance. Only when the design of the bulb is narrowed down to a few promising candidates, does the use of RANS codes for final optimization work become warranted. When a candidate bulb shape is identified for experimental testing, the use of the RP machine vs. conventional model making methods can be used to cut the cost of making the bulbs and help automate the design process. The use of the RP machine to make the 64 NPL7 cut the cost of building by half compared to NPL6 with had a bulb made of fiberglass and foam. The cost of using the RP machine, however excluded the cost of labour, therefore the true cost would be significantly higher. Nevertheless, having gone through the process, a number of improvements can be made to cut costs and minimize the necessary post-printing work. The primary method of cutting costs is by using less ABS material. The bulbs created for this study could have had their thickness reduced by half and needed only half the rib thickness to maintain structural integrity. The easy transition from CAD to the software used by the RP machine makes using the RP machine a very attractive choice for further parabolization studies. 65 CHAPTER 5 5 EXPERIMENTAL WORK: MSEC 5.1 Introduction/Previous Work The principle objective of Moving Surface Boundary Layer Control (MSBC) is to prevent or delay the separation of the boundary layer through momentum injection and to reduce the viscous pressure drag. MSBC has been successfully applied to numerous 2D aerodynamics cases including airfoils, bluff bodies, and flat plates [32]. Limited studies have also been done on 3D shapes such as a truck and a barge-like structure [33]. In the majority of experimental cases, MSBC has been implemented through motor driven cylinders. A moving surface has also been demonstrated using an airfoil with its top surface formed by moving belts [33]. The parametric experimental testing conducted by Tan and Sireli revealed the trend of an increasing form factor with an increase in beam. It was therefore hypothesized that an injection of momentum in the pressure recovery region could aid in slowing the growth of boundary layer and avoid possible separation near the stern. The experimental work was conducted prior to the numerical evaluation of the UBC hull discussed in Section 3. Therefore, a detailed understanding of the flow quantities was not yet known. The placement location and design of the moving surface devices was therefore based on a more general understanding of the flow characteristics of the vessel and naval architecture principles. The UBC Model 4 was chosen as a base hull for studying the effects of MSBC on near field flow effects and total vessel resistance. The first phase of testing was comprised of placing a rotating cylinder vertically at location x = 0.7 L, a distance of 0.1 L aft of the location of maximum beam, on each side of the hull. Since boundary layer separation was suspected aft of the bulbs, the cylinder placement just aft of maximum beam was intended to inject momentum in the pressure recovery region. To The second round of 66 testing saw the replacement of the cylinder with a moving belt. In both cases, the actively controlled portion of the surface extended from the upper chine to above the design waterline. It is important to note that while the implementation of a rotating cylinder or a moving belt to a full scale ship would not be feasible, other more cost effective forms of implementing MSBC could be engineered if the drag reduction benefits so warranted. 5.2 Moving Surface Using Cylinders 5.2.1 Experimental Setup The cylinders were designed to partially protrude beyond the hull into the boundary layer region. The cylinders were machined out of Delrin material to follow the section profile of the hull at the location of installation and were slightly faired at the bottom to decrease the flow disturbance at the upper chine. Two DC motors in conjunction with a power supply and optical diodes were used to control the speed of rotation. Figure 5-1 shows the general arrangement of the cylinders. Figure 5-1: General Cylinder Arrangement 5.2.2 Tow Tank Drag Data A testing procedure identical to Tan's was used to compare the acquired data to the baseline hull. The model was tested in the slow speed range of 0.10 < Fn < 0.20 to determine hull form factors using Hughes-Prohaska method (with N=4) and in the high-speed range of 0.20 <Fn < 0.45 to measure total resistance and assess the impact of MSBC on wave resistance. A preliminary run with stationary cylinders was conducted, 67 followed by runs with cylinders spinning at twice and three times the speed of the vessel. The additional thrust provided by the rotating cylinders was measured using the load cell on the heave post with the stationary model and added to the total resistance value obtained during each run. This method of isolating the thrust component was not ideal because the actual thrust at speed for the model would be lower then the thrust the cylinders produced in stationary conditions. Figure 5 -2 therefore shows a comparison of C T between the test cases and the base hull without removing the thrust component. O 0.030 0.025 0.020 0.015 + 0.010 0.005 0.05 0.15 0.25 Fn 0.35 0.45 Figure 5-2: C T vs. Fn for MSBC using cylinders In all instances, the use of M S B C resulted in an increase in total resistance compared to the base hull. At speeds above Fn = 0 . 2 5 , the rotation of the cylinders increased the total drag compared to stationary cylinders. Furthermore, the rotation speed did not have a noticeable impact on C T . The placement of the cylinder coincided with a wave trough. Therefore, as the speed increased, the exposed area of the cylinders diminished. 68 In the slow speed range, the effect of the cylinders showed no definite trend other than a higher C T compared to the base hull. On average the form factor was found to increase by 19% compared to the baseline hull. This affirmed that the penalty paid for disrupting the flow near the hull surface could not be overcome with momentum injection. 5.2.3 Wind Tunnel Visualization Wind tunnel visualizations were conducted to gain a better understanding of the flow around the cylinders and determine how a more successful MSBC device could be designed. The flow visualization study of the UBC Model 4 with cylinders was conducted in the Boundary Layer Wind Tunnel located in the Department of Mechanical Engineering at the University of British Columbia. The wind tunnel is capable of speeds of up to 20 m/s, equivalent to Re = 2.7 x 106 based on the length of the UBC Model 4. In order to account for the low Reynolds number of the model, boundary layer trips made of zigzag cut tape were installed at location x = 0.1 L. This location coincided with the placement of the turbulence pins during the towing tank testing. The model was mounted on a custom frame close to the entrance of the wind tunnel, where the boundary layer growth of the walls of the tunnel was negligible. Special care was taken to ensure the keel (i.e. the model) was aligned with the direction of flow and the design waterline was parallel to the floor of the wind tunnel. Tuft Visualization The first flow visualization technique constituted of yarn tufts (approximately 5 cm in length and 3 cm apart) attached to the model, with each row starting closely behind the last one. Figure 5-3 shows the model setup. The wind tunnel was run in a range of speeds between 5m/s and 15m/s. 69 Figure 5-3: Tuft Visualization Model Setup For the range of speeds, the case of the cylinder at rest showed appreciable tuft flutter in the region aft of the cylinder as well as a disturbance in the flow two rows ahead of the cylinder. The rotation of the cylinder greatly reduced this turbulent behavior of the tufts both for and aft of the cylinder and aligned the tufts with the free stream flow direction. While tuft visualization did not lead to an accurate study of the flow near the hull surface, it did outline the area of impact of the cylinders as well as the ability of momentum injection to decrease the turbulence in the flow. Bubble Path Visualization A Bubble Path technique was used in order to study the near hull flow field around the cylinders. The technique involved photographing helium-filled soap bubbles injected into the flow [35]. Although the bubbles are not perfectly neutrally buoyant, they have been found to track the flow quite well with generally small deviations from the actual fluid flow [36]. The hull surface and the cylinders were painted black, and a 5 mega pixel digital SLR camera was used to capture the images. Additional digital manipulation in PhotoShop was subsequently needed to improve the images as shown in Figure 5-4. The wind tunnel was run at approximately 7m/s corresponding to the slow speed tow tank tests (Fn = 0.11). Beyond this speed it became extremely difficult to photograph the flow of helium bubbles. 70 u Figure 5-4: Bubble path visualization around cylinders Top: Stationary case, Bottom: Rotating The top portion of Figure 5-4 reveals a significant separation region aft of the cylinder when the cylinder is stationary. The bottom portion of Figure 5-4 shows this region largely eliminated with the rotation of the cylinders. A disturbance closely aft of the cylinder is also observed in the case of the rotating cylinder, which may be attributed to the high velocity particles being directed at the hull. This phenomenon could be lessened with the addition of a fairing near the trailing edge of the cylinder. In general, wind tunnel flow visualizations revealed that the disturbance to the flow introduced by the spinning cylinders was not able to be overcome by MSBC. 5.3 Moving Surface using belt In order to minimize the disturbance to the flow caused by the protrusion of the spinning cylinders, a second attempt at decreasing viscous drag using MSBC made use of a moving surface in the form of a belt driven by two cylinders with the same sectional profile as the hull. The belt was made of neoprene in order to conform to the variable cylinder diameter. Grooves were machined into the cylinders at three locations and a non-elastic string was sown into the belt and secured to ride inside each groove. This prevented the belt from slipping and ensured it was driven at the same rpm as the motor output shaft. Figure 4-5 shows the model setup. 71 Figure 5-5: UBC Series Model 3 with moving belt 5.3.1 Tow Tank Drag Data The same test procedure was followed as outlined in section 5.1.1 for the tow tank testing. A comparison of C T at various belt speeds to the Parent Hull is given in Figure 5-6. The deviations in resistance values fell within the error band of the test equipment. While the introduction of a moving surface did not cause a flow disturbance as in the case of protruding cylinders, it concurrently did not yield any measured improvements. In the high speed range, a modification of the pressure field around the hull can result from a change in viscous phenomena thus having an effect on the wave generated [37]. The occurrence of this phenomenon, however, was not observed during the model testing, possibly due to the correspondence of the belt placement with a wave trough. A change in location of the belts may lead to a more pronounced effect. 72 0.005 o.ooo J . 1 1 1 1 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 Fn Figure 5-6: C T vs. Fn for MSBC using belts 5.4 Discussion The motivation for studying the effects of MSBC on the UBC Model 4 was fueled by the belief that increases in beam introduced through parabolization caused accelerated boundary layer growth and earlier boundary layer separation compared to the UBC Model 3 Parent Hull. Subsequent numerical work done on the UBC Models subsequently revealed that the boundary layer growth was delayed to the point of maximum beam and no conclusive evidence was found on premature boundary layer separation. Since the UBC Model 4 proved to be a well streamlined vessel, it was very difficult to show the applicability of MSBC as a method of drag reduction. A base model with a large discontinuity, causing strong adverse pressure gradients, should therefore be chosen for further studies of MSBC. Cylinders or moving belts mounted on a load cell independent of the model would also be beneficial for monitoring the true thrust force of MSBC system in "at speed" conditions. In addition, all of the tests were performed in straight ahead conditions without the existence of any cross-currents. Since MSBC on 73 airfoils and other control surfaces is shown to work best at angles of attack which typically exhibit large separation regions, perhaps the use of MSBC on vessels in cross-current conditions would show some measurable benefit. 74 CHAPTER 6 6 C O N C L U S I O N S A N D F U T U R E W O R K 6.1 Conclusions The principal objective of this thesis work was to use numerical methods to quantify the change in viscous resistance that will result from the addition of parabolic side bulbs to a displacement vessel. Previous hull form parabolization studies concluded that there is always a penalty to be paid due to an inherent increase in viscous drag [3]. As long as a substantial decrease in wave resistance can outweigh the detrimental viscous effects, substantial savings in powering requirements can be achieved. This scenario was demonstrated for both the UBC Series hull and the NPL Trimaran hull. Of course, the range of expected powering savings is highly dependent on the hull geometry and operating speed. Because the UBC Series hull has a low L/B ratio, the wave-making drag contribution to the total resistance is considerably higher than in the case of the extremely streamlined and slender NPL Trimaran hull. This is reflected in the anticipated 15% savings in EHP for the UBC Series hull compared to a 5% EHP savings for the NPL Trimaran hull. Therefore, when evaluating the suitability of extending parabolization to a specific class of vessels, it is important to consider the operating speed range and the contribution of the drag component to the total resistance of the vessel. As discussed in Chapter 2, a hierarchy of solvers ranging in sophistication and computational requirements is available to the designer. For a preliminary feasibility assessment, the use of a potential flow code such as a Mitchell's integral based solver or a Rankin source panel method solver for predicting the wave resistance curve, in conjunction with an IBL solver for predicting the skin friction drag, gives a good estimate of the contribution of the drag components. Conversely, at this early stage, available experimental data for the vessel, or a vessel of similar geometry, can also be used in conjunction with the ITTC '57 correlation line to predict the balance between viscous and wave drag. Once a candidate hull is identified, it becomes important to decompose the 75 total resistance into respective components in order to gain a complete understanding of the fluid flow around a ship's hull. The experimental investigation by Tan and Sireli into the addition of parabolic side bulbs to the UBC Series Model 3 hull reported an increase in form factor for all hull configurations. The increase in form factor for the parabolized hulls was therefore largely attributed to an increase in viscous pressure drag. Prior to the knowledge gained through this numerical study, it was believed that the increase in beam introduced by parabolizing the parallel midship section caused premature flow separation. Moving surface boundary layer control was identified as a possible method of preventing or delaying the flow separation. The first set of experiments using vertical spinning cylinders installed directly behind the location of maximum beam on the UBC Series Model 4 produced an increase in total resistance in all speed ranges. Tow tank and wind tunnel experiments showed that the disturbance in flow resulting from the protrusion of the cylinders could not be overcome by momentum injection. Replacement of the cylinders with a moving belt conforming to the shape of the hull did not show a measurable effect on the total drag of the revised UBC Series Model 3. Subsequent numerical studies using both the IBL solver and the 2D RANS solver revealed that there is no indication of premature boundary layer separation. The numerical study of the UBC Series fishing hull presented in Chapter 3 revealed that the increase in beam and the degree of bulb fairing played a pivotal role in controlling boundary layer growth. As was shown by the IBL solver, successive increases in beam from 5% through to 20% steadily augmented the boundary layer thickness aft of the maximum beam location. This boundary layer growth resulted in an increased displacement thickness, creating a larger wake region behind the ship. This result would have the effect of increasing the viscous pressure drag. Furthermore, the IBL solver only predicted minor changes in Cf between the different UBC hull configurations. A 2D RANS simulation of the flow around the hull design waterline also attributed most of the change in viscous drag to a changing pressure drag 76 component. In the case of the UBC Model 4, decreasing the width of the stern by shifting the volume to midship successfully reduced the separation zone behind the transom, resulting in a lower viscous pressure drag. Consequently, a vessel with a parabolic waterline strategically designed for minimum wave drag can benefit from a decreased stern width and a smaller wake region. The inclusion of a three-dimensional RANS simulation for analyzing the NPL Parent Hull and the NPL6 hulls allowed for a more direct study of the viscous pressure drag. It also provided a comparison between RANS solver, the IBL solver and experimental towing tank data. Both numerical and experimental methods agreed that a penalty is paid when adding the parabolic bulbs near midship. The numeric solvers predicted an increase of approximately 1% in Cf at model scale between Parent Hull and NPL6. The IBL solver also predicted a further increase in Cf for NPL7 and NPL4. The IBL solver also showed significant flow disturbance near the hull surface resulting from the presence of the bulbs. Local increases in shape factor near the maximum beam location were observed but the values remained below those associated with boundary layer separation. Higher cross flow angles were also observed, especially in the case of NPL4 and NPL7. All of these factors pointed to an expected increase in viscous drag for the NPL6 hull and a further increase for the NPL7 and NPL4 hulls. Experimental data confirmed this anticipated trend through a form factor comparison. The experimentally determined form factors for both the NPL hull and the UBC hull showed a trend of increasing form factor for decreasing L/B ratio as shown in Figure 6-1. With the exception of the UBC Model 4 hull, all parabolized hulls had bow and stern geometries identical to that of the parent hull. Therefore, the increase in form factor due to the addition of the parabolic side bulbs was mainly due to an increase in shear stress along the hull. 77 a) 1.19 1.21 Form Factor (1+k) 00 4 3.9 3.8 3.7 3.6 3.5 X UBC Parent X UBC 5% X UBC Model 4 X UBC 10% X U B C 15% b) 1.3 1.35 1.4 Form Factor (1+k) 1.5 Figure 6 -1 : Relationship between L/B ratio and Form Factor for a) NPL Hull, b) UBC Hull The calculated values of Cf for the NPL hulls using the IBL solver and the RANS solver fell below the ITTC'57 correlation line. Although this may be expected of a very slender vessel, it brings awareness to the designer that the experimentally determined form factor also encompasses the change in Cf between the hulls. Unlike the UBC hull, where most of the change in viscous drag came from the pressure drag component, the NPL hull experiences both an increase in Cf and C p . Calculating the form factor numerically using the RANS solver emphasized this result. Since both viscous drag components increased, the numerically predicted form factor remained mostly unchanged between the Parent Hull and NPL6. For a more direct comparison of experimentally and numerically determined form factors, the RANS Cf could be adjusted to match the ITTC '57 correlation line. The form factor would then be recalculated by dividing the total viscous drag by the adjusted Cf value. Unfortunately, further complications arise because the slope of the Cf line predicted by the RANS solver differs from that of the ITTC '57 line. 78 This deviation requires further study into the accuracy of the RANS simulation before a definite conclusion can be drawn. In general, the knowledge gained by evaluating the UBC and NPL hulls numerically will allow for a more systematic approach of optimization when applying parabolization to the next candidate vessel. This study, in conjunction with Vyselaar's work, successfully extended parabolization to an extremely streamlined vessel that was already benefiting from wave cancellation effects through the outrigger placement. The 5% decrease in EHP for the 160m long full scale Trimaran could result in considerable savings in fuel costs over the operational life of the vessel. In addition, the advantage of designing a vessel with lower wave drag minimizes the disturbance created by the wash of the vessel. In areas where the speed of a ship is limited by the wake it creates, such as ferry routes near inhabited areas, a smaller wake will allow ship owners to provide faster and more cost-effective service. 6.2 Future Work The numeric work for evaluating the impact that hull parabolization has on viscous drag outlined in this thesis, in conjunction with the work done by Vyselaar for numerically predicting the wave drag, has laid the foundations for future studies of other candidate vessels. Up to this point, parabolizing a chosen vessel was based on a parametric approach. The integration of the IBL solver, the Rankin source panel method solver, and an optimization code is the next step to improving the parabolization process. With access to supercomputers, using a RANS solver with the inclusion of free surface effects for optimization studies is also worth exploring. There is a plethora of parameters such as the amount of beam increase, the location of maximum beam and the entrance and exit angles for the bulbs that need to be optimized. This is especially true for minimizing the detrimental increase in viscous resistance that, to this point, has shown to be unavoidable. 79 REFERENCES [I] Kent, J.L. "Model experiments on the effect of beam on the resistance of mercantile ship forms," Transactions, Institute of Naval Architects, LXI, 311-319, 1919 [2] Calisal, S.M., Goren, O. and Danisman, D.B., "Resistance Reduction by Increased Beam for Displacement-Type Ships," Journal of Ship Research, Vol. 46, No. 3, pp. 208-213, Sep. 2002 [3] Tan, B-Y.J. "An Experimental Investigation for Resistance Reduction on Displacement Type Ships by Parabolization of Hull Form at Waterline," Master's Thesis, University of British Columbia, 2004 [4] Vyselaar, Dan. "Using parabolic waterlines to reduce the resistance of a Trimaran," MASc Thesis, University of British Columbia, 2006 [5] Calisal, S.M., McGreer, D., "A Resistance Study on a Systematic Series of Low L/B Vessels", Marine Technology, Vol. 30, No.4, pp. 286-296, Oct. 1993 [6] Yang, C , Noblesse, F., Lohner, R., "Practical Hydrodynamic Optimization of a Trimaran", SNAME, Vol. 109, 2001 [7] Bertram, V. "Practical Ship Hydrodynamics", Butterworth-Heinemann, 2000 [8] Lewis, E.V. "Principles of Naval Architecture", The Society of Naval Architects and Marine Engineers, Vol. 2, 1988 [9] Larsson, L., Eliasson, R. "Principles of Yacht Design", The McGraw-Hill Companies, 2000 [10] Mughal, B., "Integral Methods for Three-Dimensional boundary-Layers", PhD Thesis, Massachusetts Institute of Technology, 1998 [II] "Resistance and Powering of Ships", United States Naval Academy, Online Course Notes, EN200, 2003 [12] Alving, A. E., and Ferholz, H. H., "Turbulence measurements around a mild separation bubble and down-stram of reattachment," J. Fluid Mech., 322, pp. 279-328, 1995 [13] Bertin, J. and Smith, M. "Aerodynamics for Engineers," Prentice-Hall, 1998 [14] Castillo, L., Wand, X., George, W., "Separation Criterion for Turbulent Boundary Layers Via Similarity Analysis", J. Fluid Mech., 126, pp. 297-303, 2004 80 [15] Ludweig, H., and Tillmann, W., "Investigations of the wall shearing stress in turbulent boundary layers", NACA TM 1285, 1950 [16] Newman, B.G., "Some Contributions to the Study of the Turbulent Boundary near Separation", Austr. Dept. Supply Rep. ACA-53, 1951 [17] Schubauer, G.B., and Kelebanoff, P.S., "Investigation of separation of the turbulent boundary layer," NACA Report 1030, NACA Technical note 2133, 1951 [18] Simpson, R.L., and Strickland, J.H., "Features of a separating turbulent boundary layer in the vicinity of separation", J. Fluid Mech., 79, pp. 553-594, 1977 [19] Simpson, R.L., and Chew, Y.T., "The structure of a separating turbulent boundary layer. Part 1 . Mean flow and Reynolds stresses", J. Fluid Mech., 113, pp. 23-51, 1981 [20] Hally, D., "An Integral Method for the Calculation of Boundary Layer Growth on a Ship Hull," DREA Report 85/107, 1985 [21] Janson, C , Larsson, L., "A method for the Optimization of Ship Hulls from a Resistance Point of View," Twenty-First Symposium on Naval Hydrodynamics, 1997 [22] Hally, D. Direct email correspondence, 2005 [23] Simonsen, CD. , "Rudder, Propeller and Hull Interaction by RANS," PhD Thesis, Technical University of Denmark, 2000 [24] Lillberg, E., Svennberg, U., "Large Eddy Simulation of the Viscous Flow aournd a ship hull including the free-surface," 25th Symposium on Naval Hydrodynamics, 2005 [25] Fluent Inc. "User's Manual," Fluent 6.2.2, Ch 11, 2005 [26] WS Atkins Consultants and members of the NSC, "Best practice guidelines for marine applications of computational fluid dynamics," Marnet-CFD, 2002 [27] Versteeg & Malalasekera, "An introduction to Computational Fluid Dynamics," Prentice Hall, 1995 [28] Couser, P.R., "Calm Water Powering Predictions for High-Speed Catamarans," Fast'97, Sydney, Australia, 1997 [29] Vyselaar, D. "Experimental Validation of Computational Models for the Platform Supply Vessel "El Pionero" Report submitted to the Department of Mechanical Engineering, 2005 81 [30] Bull, P et al., "Prediction of High Reynolds Number Flow Around Naval Vessels," 24th Symposium On Naval Hydrodynamics, 2003 [31] The Specialist Committee on Powering Performance Prediction, "Final Report and Recommendations to the 24th ITTC," ITTC 2005 [32] Modi, V.J., "Moving Surface Boundary-Layer Control: A Review," Journal of Fluids and Structures, Vol. 11, pp. 627-663, 1997 [33] Modi, V.J., Akinturk, A. "Effect of Momentum Injection on Drag Reduction of a Barge-like Structure," International Journal of Offshore and Polar Engineering. Vol. 13, no. 2, pp. 81-87, June 2003 [34] Favre, A."Contribution a l'Etude Experimentale des Mouvements Hydrodynamiques a Deux Dimensions," University of Paris, 1938 [35] Ostafichuk, P.M., "Low Speed Wind Tunnel Flow Visualization for the Study of Submarine Control Surface Effectiveness," CHMSC, 2002 [36] Merzkirch, W., "Flow Visualization," Academic Press Inc., New York, 1997 [37] Tzou, T. S., "Secondary Flow Near a Simulated Free Surface," M.SC Thesis, Department of Mechanical Engineering, The University of Iowa, Iowa City, la., 1966 [38] Sandborn, V.A., and Kline, S.J., "Flow models in boundary-layer stall inception," J. Basic Eng., 83, pp. 317-327, 1961 [39] Janson, C , Larsson, L., "A method for the Optimization of Ship Hulls from a Resistance Point of View," Twenty-First Symposium on Naval Hydrodynamics, 1997 [40] Apsley, D. "Integral Analysis of the Boundary Layer," Lecture Notes, 2005 [41] Banks, C. "Boundary Layers: An aerospace 508 midterm," www.aeroiockey.com/papers/bl/, 1999 [42] Hally, D. "User's guide for HLLFLO Version 2.0," DRDC Technical Communication 93/309, 1993 82 APPENDIX A: BOUNDARY L A Y E R P A R A M E T E R S The following is intended to give a general background to the boundary layer parameters which were used to study the effect hull form parabolization had on the flow dynamics in proximity to the surface of the vessel. The main parameters used to describe the size and shape of the boundary layer are: Boundary Layer Thickness (8) The thickness of the boundary layer region represents the near wall region where the particle velocity is slowed by viscous effects. The thickness is typically measured up to the point u(5) = 0.99 U [40] y u(y) • — r — u(S) = 0.99 U Displacement Thickness (5*) The distance a streamline just outside the boundary layer is displaced away from the wall compared to the inviscid solution [41]. y u(y) y a = 0.99 u Ideal fluid u(S) = 0.99 U Equal areas rrTTf 83 Momentum Thickness (9) 0 represents the total loss of momentum flux due to viscous near wall effect. In other words, it is equivalent to the removal of momentum through a distance 9. The momentum thickness can be visualized in a similar way as displacement thickness but the momentum flux distribution u(yf replaces the velocity distribution u(y) [40]. y ufyf y — Real -» fluid \ j 6 J 1 > y////////////////7>, — Ideal -+ fluid — - • Equal areas Shape Factor (H) H = ^ The shape factor is the ratio of displacement thickness to momentum thickness. As explained in Section 2.2, a large shape factor is an indication of possible boundary layer separation. The effect of shape factor on the boundary layer profile is given below [40]. small H large H 84 APPENDIX B: H L L F L O CALCULATION PROCESS The general process for calculating the flow around a hull using the IBL solver is shown in flow chart format in Figure A- l . Pre-processing CAD Model 1 ' XYZ to .off converter (matlab) Solver HLLSPL POTSET, POTINF, POTSLV, POTVEL, VELSPL BLAYER RESIST HLLPNL Hull Definition Potential Flow Solver Viscous Solver Post-processing TECPLOT Figure A - l : Flow chart for IBL solver The solver HLLFLO was written in FORTRAN programming language on a UNIX operating system. While it would be possible to run HLLFLO on a Windows operating system using a suitable compiler, it would take a significant effort to resolve the compatibility issues. HLLFLO was therefore installed on a UNIX operating system. The 85 pre-processing of the input data and the post-processing of results was done within Windows through the use of data conversion programs written in MatLab. Rhinoceros was selected as the CAD program for generating the 3D hull geometry because it is widely used in industry. Once the desired hull shape is created, the points are exported in Cartesian coordinates to a data file. It is important to have the hull oriented with increasing x-coordinate from bow to stern, y-coordinate increasing from the center plane of the ship and with the z-coordinate aligned with the location of maximum draft as shown in Figure A-2. The points should be distributed so that the x-coordinate represents stations along the hull. z Figure A -2 : Required Hul l Orientation A MATLAB script was written to convert the x,y,z points file into a ".off file as required for input by HLLFLO. A scaling function is already built into the script. Further customization can be done to increase the automation of the process. Once the ".off file is created, it can be read by HLLSPL which creates hull representation which is common to all HLLFLO programs. Figure A-3 shows a flow chart of the HLLFLO calculation process including a brief description of each program's function. As seen in Figure A-3, HLLFLO is comprised of multiple individual programs with specific functions. The programs highlighted with a thicker border are at the core of HLLFLO. The other programs are used for visualizations or additional inclusion of options such as a bilge keel. 86 INPUT FILE HLLOFF creates an offset table in O F F S R F format from H L L S R F hull representation H L L S P L used to generate HLLSRF hull representations M O D H L L used to generate HLLSRF hull representations X ^LEGEND) USER FILE GRAPHICS NO-GRAPHICS NO-GRAPHICS NO-INPUT POTSET defines the grid of panels into which the hull is broken J POTINF calculates the matrix of influence coefficients and Fn at each of the control points: it prepares the linear system to be solved for the unknown source strengths by POTSLV STMHLC displays the potential flow or boundary layer parameters in the hull coordinates (x,s) PRPPLT calculates the velocity due to the potential flow and boundary layer at a series of points in the propeller disk, then creates displays of the velocity field in the propeller disk. DSPHLL displays boundary layer velocity profiles at a given points on a ship hull BLDSPY displays boundary layer parameters along hull lines ISOVEL displays either the iso-velocity contours or the boundary layer, streamwise momentum, and streamwise displacement thickness at a given station on a ship hull DSPPFL displays boundary layer velocity profiles at given points on a shop hull POTSLV solves the linear system for the panel source strengths using the Gauss-Seidel iterative method 1 POT calculates the velocity pa VEL at each of the control nts CLCBKL adds bilge keels to an existing HLLSRF hull representation OFFSET draws an offset diagram and/or a display of the buttock lines and waterlines of the splined hull WVPRFL calculates the wave profile along a ship hull using thin ship theory O F F W V displays ship hull offset data obtained from an offset file in OFFSRF format VELSPL calculates a smooth parametric B-spines approximation to the contravariant components of the potential flow velocity at the surface of the hull by splining the velocities at the panel control points calculated by POTVEL DSPSRF creates a 3D display of various types of hull lines as viewed from a given line of sight BLAYER Uses the HLLSRF hull representation and the spline representation of the potential flow to calculate the development of a turbulent boundary layer on the hull. An integral method is used. POTRHS allows user to change the influence of the actuator disk or to include the effects of the transpiration velocity induced by the boundary RESIST Calculates ship resistance by pressure integration HLLPNL Converts all data calculated to Cartesian coordinates ] Figure A-3: HLLFLO Program Flowchart 87 The suite of programs comprising HLLFLO come with documentation manuals describing the function of each program in detail as well as example inputs for each program [42]. 88 APPENDIX C: NPL F O R M FACTORS NPL Parent Mainhull (may2005) yjntercept = (1+k) = hull form factor = 1.159 1.5 1.3 1.0 O & 0.8 0.0 y = 0.2845x+ 1.1594 O 0.5 - o overall X selected 0.3 - _ —Linear (selected) 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Fn4/CFOM 0.7 0.8 0.9 1.0 NPL Parent Mainhull (Jan 2006) yjntercept = (1 +k) = hull form factor = 1.153 1.8 -1.5 1.3 OM 1.0 -y = 0.3721x + 1.1531 o 0.8 o 0.0 o overall 0.5 -X selected 0.3 —Linear (selected) 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Fn4/CFOM 89 NPL Parent Trimaran 1.5 yjntercept = (1 +k) = hull form factor = 1 . 2 1 2 O fe 0.8-0.0 y = 0.2317x+ 1.2121 O 0.5 - o overall 0.3 -X selected Linear (selected) 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Fn4/CFOM 90 NPL6 MainHull yjntercept = (1+k) = hull form factor = 1.214 o overall X selected —Linear (selected) 1 ' 1 1 1 1 : ' 1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Fn4/CFOM O 1-0 H LL. O S 0.8 O 0.5 0.3 0.0 c NPL6 Trimaran 1.8 1.5 1.3 0 1.0 LL O 1 0.8 -o 0.5 4 0.3 0.0 ^ yjntercept = (1+k) = hull form factor = 1.236 y = 0.319x + 1.2359 o overall X selected —Linear (selected) 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Fn4/CFOM 91 NPL7 Mainhull yjntercept = (1+k) = hull form factor = 1 . 2 3 4 1.8 T -O 1.0 + 2 0.8 -h-o o overall 0.5 X selected 0.3 -- - ^—Linear (selected) 0.0 -I 1 1 1 1 1 : ' ' ' i 1 1 1 < 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Fn4/CFOM NPL7 Trimaran 1.5 0.0 yjntercept = (1+k) = hull form factor = 1 . 2 3 7 O 0.5 - o overall X selected 0.3 -^—Linear (selected) 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Fn4/CFOM 92 

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