"Applied Science, Faculty of"@en .
"Mechanical Engineering, Department of"@en .
"DSpace"@en .
"UBCV"@en .
"Klaptocz, Voytek R."@en .
"2010-01-07T00:30:00Z"@en .
"2006"@en .
"Master of Applied Science - MASc"@en .
"University of British Columbia"@en .
"The addition of parabolic side bulbs at the ship's mid body is aimed at reducing wavemaking\r\nresistance. This concept was first successfully tested on a coaster tanker and then\r\nextended to the UBC Series Model 3, a typical Canadian West Coast fishing vessel. A\r\nseries of systematic tow tank experiments revealed that while parabolization decreases\r\nthe total resistance (due to a drop in wave-making resistance) the form factor suffers an\r\nincrease. This thesis focuses on numerical predictions of the influence of side bulbs on\r\nthe viscous resistance characteristics of a displacement vessel.\r\nAn integral boundary method solver and a 2D RANS solver were chosen as tools to\r\npredict the effect of parabolization on viscous drag for the UBC Series Model 3 hulls and\r\nthe UBC Series Model 4. The concept of parabolization was then extended to an NPL\r\nTrimaran hull. A 3D RANS code was used to compare the calculated values of skin\r\nfriction and boundary layer thickness to those calculated by the integral boundary layer\r\nsolver. The RANS code was also used to numerically predict the effect of parabolization\r\non viscous pressure drag for the NPL hull. In total, three different bulbs were studied\r\nnumerically in addition to the parent NPL hull. The numerical results were compared to\r\nexperimental data obtained from calm water resistance predictions obtained from tow\r\ntank testing. Further effort to decrease the impact of parabolization on form factor was\r\nmade by applying moving surface boundary layer control to the UBC Series Model 4."@en .
"https://circle.library.ubc.ca/rest/handle/2429/17670?expand=metadata"@en .
"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 \u00C2\u00A9 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 \u00C2\u00BB1\" 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 \u00E2\u0080\u0094\u00E2\u0080\u00A2 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 \u00E2\u0080\u00A2 {A \u00E2\u0080\u00A2 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 \u00C2\u00A3 2.50% O \" 2.00% _c o o \u00C2\u00A7 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\u00C2\u00B0 o E 4.00% E o \u00C2\u00A3 & 3.50% a o c 3.00% i b 2.00% 3.00E+07 \u00E2\u0080\u0094 - ITTC 57 \u00E2\u0080\u0094Q\u00E2\u0080\u0094 UBC Parent - * - UBC 5% \u00E2\u0080\u0094 \" - U B C 10% \u00E2\u0080\u0094 \u00E2\u0080\u00A2 - U B C 15% \u00E2\u0080\u0094 U B C 2 0 % \u00E2\u0080\u0094 \u00E2\u0080\u00A2 - 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. \u00E2\u0080\u00A2 _ \u00E2\u0080\u0094 I S F C 00080 UBC Parent 0.0054 ^^mmm\ BP^v^-00041 \"\"^ 5^ | \u00E2\u0084\u00A2 ^ ^ i e o o \u00C2\u00B0\u00C2\u00B0C 2ioor .^\u00E2\u0080\u00A2B^P^^^'\"'\" 200 \\u00E2\u0080\u009E wSP^eoo * 1 0 0 0^*400 S F C \u00E2\u0080\u00A2 o.ooeo UBC 5% ~ 0.0074 ^ ^ B ^ S P 0.0067 t\u00E2\u0080\u0094 0.0061 _^\u00C2\u00ABBJ H> I \u00E2\u0080\u0094 0.0054 ^ ^ ^ B l B P ^ I 0.0048 ,^MmW B ^ \u00E2\u0080\u00A2 0 0 0 4 1 ^ f l J i B ^ V \u00C2\u00BB > ^ 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 _^^\u00C2\u00BB\u00C2\u00BBB v^-~ 0.0041 ^\"\"^l P^ \"^>>-*J'J' 2 0 0 t 00035 B P ^ ^ ^ 8 0 0 P^P^P^^^1600 \ 00 r |\"\u00E2\u0080\u00A2\" ^ ^ ^ r ^ ^ ^ i . 1 0 0 V ^ * ^ B u u S F C \u00E2\u0080\u00A2 i 00080 UBC 15% 0.0074 _.^r\u00C2\u00ABBBk ^ ^ a B V H B B V :\u00E2\u0080\u0094 0.0061 ^mmw r - o.oo54 ^mtmfm !\u00E2\u0080\u0094 0.0048 ^ - \u00C2\u00AB B l \^^r mm 0.0041 I ^ ^ ^ V \" \" ^ 2 0 0 1 \u00E2\u0080\u00A2 0.0035 ^P^-'\"\"' 1 8 0 0 ,^ ^^ ^^ ^^ H^ P^ P^ P^ P^ 1^600 200 \ , \u00E2\u0080\u00A2\u00E2\u0080\u00A2 ..\u00E2\u0080\u00A2 ^ ^ ^ ^ ^ A i O o X ^ ^ 6 0 0 0*^400 \u00E2\u0080\u00A2 \u00E2\u0080\u00A2 1 SFC M M UBC 20% -* ^ ^ \u00E2\u0080\u00A2 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 ^ * ^ ^ \u00C2\u00B0 ^ 0^400 \u00E2\u0080\u00A2 S F C UBC Model 4 ^ 0.0080 w ^ w u c ^^fA i 0.0074 ^^mmW^ftm. \u00E2\u0080\u00941 0.0061 ^_B1 H P 0.0054 ^ ^ ^ B \W^^ j . \u00E2\u0080\u0094 0.0048 ^'-'^Bj B P ^ ^ ^ C , \u00E2\u0080\u00A21 0.0041 ^B] B^^>-^^ \u00E2\u0080\u00A2 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 \u00E2\u0080\u009E t \u00E2\u0080\u00A2 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 ^ ^ ^ ^ \u00E2\u0080\u00A2 M M *30^-mamwm9r ^L^T ys^\"^ 2 0 0 0 1.34545 ^ ^ ^ H >^*^ -< -^>\"''~\"^ 1600 200 e | ^ ^ 1 4 0 0 ,nnf- fl \u00E2\u0080\u00A2 K ^ m ^ ^ 1200 . N 1 0 \u00C2\u00B0 0 | \u00E2\u0080\u00A2 | 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\u00C2\u00B0 N \u00E2\u0080\u009E l \u00E2\u0080\u00A2 S^^^ IOOO^ l ^ \u00C2\u00B0 \ ^ \u00E2\u0080\u00A2 ^ ^ 800 * \ k , > 200 V > 1 0 0 6 0 0 I 2.50909 ^jg&B 2.36364 \u00E2\u0080\u00A2 ^^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 ^ ^ \u00E2\u0080\u0094 \u00E2\u0080\u0094 \ _>\"\"'^ A l 0 \u00C2\u00B0 f j i ^ ; 4 0 0 x SF 1.92727 ^ ^ t ^ . ^ j ^ ^ ^ ^ i ^ ^ r \u00C2\u00B1 ^ 1.78182 ^BEk 1.34545 ^ ^^^^^^^^^^jJJ^^^^^^^^^^^^ \u00E2\u0080\u00A2 MS F UBC Model 4 ^ * 2-05455 '^K^Ztm^K 2.5090!) / ^^\u00E2\u0080\u00A2\"^AWm-W^mW^ 2.38364 - ^ M P ^ j ^ 1 9 2 7 2 7 ^^mmmm ^ \u00E2\u0080\u00A2 \u00E2\u0080\u00A2 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 ^ ' \u00E2\u0084\u00A2 ; 2000 1200 \u00C2\u00BB ' 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 . . * , - \u00C2\u00A3 > - 5 _>S\u00C2\u00ABP^A \u00E2\u0080\u0094] 2.5 ^ * * \ > \u00E2\u0080\u0094 o \u00E2\u0080\u009E.*\"' -2 5 < 0 4 \u00C2\u00BB 0 tanCF(deg) \u00E2\u0080\u00A2 io UBC 5% . f l i ^ 7 5 mmmm ~\ 5 ^ -S/^>. 2 5 \u00E2\u0080\u0094 0 ^ \u00E2\u0080\u0094 j 25 >r \u00E2\u0080\u00941 -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 \u00E2\u0084\u00A2 U BC 2 0 % ^ ^ ^ ^ ^ ^ ^ ^ ^ / ^ ^ 1 6 0 0 20\u00C2\u00B0\- - ^ ^mT^^ ^* ^ (,^\"400 tanCF(deg) UBC Model 4 Fl 7.5 5 \u00E2\u0080\u0094 -2.5 \u00E2\u0080\u00A2 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 < \u00C2\u00A3 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 y////////////////7>, \u00E2\u0080\u0094 Ideal -+ fluid \u00E2\u0080\u0094 - \u00E2\u0080\u00A2 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 - _ \u00E2\u0080\u0094Linear (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 \u00E2\u0080\u0094Linear (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 \u00E2\u0080\u0094Linear (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 \u00E2\u0080\u0094Linear (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 -- - ^\u00E2\u0080\u0094Linear (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 -^\u00E2\u0080\u0094Linear (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 "@en .
"Thesis/Dissertation"@en .
"2006-05"@en .
"10.14288/1.0080736"@en .
"eng"@en .
"Mechanical Engineering"@en .
"Vancouver : University of British Columbia Library"@en .
"University of British Columbia"@en .
"For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use."@en .
"Graduate"@en .
"Effect of parabolization on viscous resistance of displacement vessels"@en .
"Text"@en .
"http://hdl.handle.net/2429/17670"@en .