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Some measurements of heat transfer to air flowing parallel to a tube bundle in square array Chandrasekharan, Kuppanna 1958

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SOME MEASUREMENTS OF HEAT TRANSFER TO AIR FLOWING PARALLEL TO A TUBE BUNDLE IN SQUARE ARRAY by KUPPANNA CHANDRASEKHARAN A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in the Department of CHEMICAL ENGINEERING We accept this thesis as conforming to the standard required from candidates for the degree of MASTER OF APPLIED SCIENCE Members of the Department of CHEMICAL ENGINEERING THE UNIVERSITY OF BRITISH COLUMBIA November, 19!?8 ABSTRACT Heat transfer measurements were made i n a heat exchanger where a i r flows parallel to an unbaffled tube bundle and where steam i s condensing inside the tubes. The tubes were one-inch outside diameter and were arranged i n a square l a t t i c e with one-inch clearance between adjacent tubes. The Reynolds Number range covered i n this investigation was 630 - 8220. Pseudo-j^-factors have been calculated for the a i r film i n the central unit c e l l and are presented along with the results of Mi l l e r et a l and Inayatov and Mikeev, who worked with other la t t i c e arrangements. The present data are insufficiently numerous and too unreliable for empirical correlation, but they do show a trend which i s consistent with the work of the above investigators. The temperature measurements showed an apparent dissymmetry inside the shell of the heat exchanger, and suggestions are made for the improvement of these measurements for more dependable results. Further work that can be done, using the present set-up with slight modifications, i s also cited. 1 In presenting t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree that the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r reference and study. I f u r t h e r agree th a t permission f o r extensive copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted, by the Head of my Department or by h i s r e p r e s e n t a t i v e s . I t i s understood that copying or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be allowed without my w r i t t e n permission. Depa rtment The U n i v e r s i t y of B r i t i s h Columbia, Vancouver $, Canada. Date N*0«*~*>W. ACKNOWLEDGEMENTS I wish to express my sincere thanks to Dr.Norman Epstein, under whose guidance this investigation was made. I also wish to acknowledge the assistance and encouragement received from other faculty members of the Department of Chemical Engineering and. the helpful suggestions and assistance of Mr. Rolf Muelchen, Workshop Technician, i n the design and construction of the equipment. I am also indebted to the National Research Council for providing financial assistance. TABLE OF CONTENTS ACKNOWLEDGEMENTS ABSTRACT I INTRODUCTION 1 II DESCRIPTION OF EQUIPMENT 8 (a) The Heat Exchanger 8 (b) The Air System 11 (c) The Steam System 12 (d) The Auxiliary Equipment 13 II I ASSEMBLY OF EQUIPMENT AND EXPERIMENTAL PROCEDURE 1$ IV PROCESSING EVALUATION OF DATA 18 (a) Tube wall temperature 18 (b) Mass velocity 20 (c) Air inlet and outlet temperatures 20 •V DATA AND RESULTS 23 SUMMARY OF DATA AND RESULTS Tables XVI Viscous Region 23a Tables XVII Turbulent Region 23b VI DISCUSSION OF RESULTS 2k VII RECOMMENDATION FOR FUTURE WORK 28 NOMENCLATURE 30 REFERENCES 33 APPENDIX 3k TABLES I - XV 3$ LIST OF FIGURES FIGURE NO, 1 Schematic of Equipment 9a 2 Heat Exchanger 9b 3(a) Seating of O-rings 10a 3(b) Thermocouple Positions 10a k piot v x y v a v g 50 5 Correlation of Data of Inayatov & Mikeev 51 6 Temperature Profiles - Heat Exchanger 23c 7 Temperature Profiles - Central Unit Cell 23d 8 Summary of Results 23e 9 Calibration Graph of Thermocouple £2 1 I - INTRODUCTION The subject of the design of heat exchangers has been extensively studied and data and correlations are available for the various types of commercial exchangers that are i n use. The absence of industrial heat exchangers where a single-phase f l u i d flows outside banks of tubes and parallel to the tube axes may be the reason for the sparsity of data on such equipment. But the need for more data on such heat exchangers has arisen with the advent of nuclear reactors, where large amounts of heat must be removed from cylindrical reactor rods. This must be done at very high heat fluxes and the heat i s generally removed by water under high pressure or l i q u i d metals. The object of the present , work i s to study a system where a f l u i d , a i r i n this case, flows outside and parallel to tubes while steam condenses on the inside of the tubes. The results reported f a l l within both the viscous and turbulent flow ranges. Among the recent text books on heat transfer McAdams (11) and Jakob (9) do not discuss the case of parallel flow, although McAdams in his treatment of cross-baffled multitube heat exchangers suggests for the case of parallel flow the use of the same equation as for flow inside pipes. Eckert (5), Kern (10) and McAdams i n his contribution to the Chemical Engineers' Handbook (1) recommend for parallel flow outside tubes the use of an equivalent diameter instead of the diameter of tubes, in the equations that are applicable for heat transfer to or from f l u i d flowing inside a tube. The equivalent diameter that has been suggested i s the hydraulic diameter defined as k (flow area/wetted perimeter). Kern mentions that when a f l u i d flows along tubes i t i s analogous to the 2 flow i n the annulus of a double pipe heat exchanger and as such i t . can be treated i n a similar manner. I t i s to be noted, however, that a l l this treatment refers to turbulent flow. Experimental results on the shell-side heat transfer coefficients of unbaffled multitube heat exchangers have been published by Donohue (U). He finds that substituting the equivalent diameter for the diameter of tubes does not give correct results i f the Sieder and Tate equation^, for turbulent flow inside tubes i s used. Donohue uses the results reported by Short (13), Heinrich and Stuckle (7) and finds that i f I / f ° h 1^" 3 i s P l o t t e d against /DQG-\ V 7 J / Ktj 1 7 / a series of parallel lines, one for each unit taken for consideration, result. The data are correlated by the equation 0.6 /„ ^0.33 ( 1 ) ft •0 (F (?) In this equation one finds that the Reynolds Number i s raised to the power of 0.6 and not 0.8 as i n the Sieder and Tate equation, and also DQ refers to the' outside diameter of the tubes rather than to the hydraulic diameter. In addition, one has to bear i n mind that a l l the results reported are for cooling operations, C used i n equation (1) i s a constant for each unit, and i t i s found that the only correlating variable for the different units i s the arrangement of tubes i n the she l l , as manifested i n the equivalent diameter. By plotting C against the equivalent diameter DQ^ Donohue finds the relation C - 0.128 ( D ^ °*6 (2) where De i s i n feet, and by sustituting equation (2) i n equation (1) he derives his f i n a l dimensional equation 3 A l l the test points are correlated by this equation with an average deviation of only - 12%, However, the local velocity i n the tube bundles i s not known and an average velocity i s used i n the correlation. I f the space between the tube bundle and the shell i s considerable, there w i l l be a large leakage through this space and the local velocity i n the tube bundle w i l l be much less than the average velocity. I t i s not surprising, therefore, that the values predicted by this correlation are 1/2 to l / 3 those obtained by using equivalent diameter instead of tube diameter i n equations for flow inside tubes. The discrepancy between average and local tube bundle velocity makes i t unsafe to use Donohue's correlation i n cases other than the shell-and-tube heat exchangers of the type for which the original data were obtained. Results on heat transfer measurements for the turbulent flow of water parallel to rod bundles are reported by Mill e r et a l (12). They used a 6-I/I4." diameter shell which carried thirty-seven 5/8" diameter rods, and eighteen p a r t i a l rods of the same size were attached to the wall to minimise the wall effect. The rods were heated el e c t r i c a l l y and water up to a maximum velocity of 20 feet/second was circulated. Measurements were made at relatively high heat fluxes (50,000 to 20,000 B.t.u./(sq.ft.) (hr.) corresponding to a maximum power density as high as 0.8 KW per inch of heated length. The rods were arranged i n an equilateral triangular l a t t i c e with a pitch of 0.911t" from centre to centre. The maximum inle t water temperature used was 325°F,at an imposed pressure of 1U0 psig., and this.'.', reached a maximum outlet temperature of 360°F. Openings for the flow of water were provided i n the plates supporting the rods. These k openings were O.U8j>" i n diameter and were arranged i n a hexagonal pattern which resulted i n an average of two openings for each rod. The free flow area of thi s distributor plate i s hh»3% of the total flow area and the void fraction available for the flow of water i n the heat exchanger i s 0.5>U» The experimental results were plotted asWhoA //c against Re^. The correlation obtained from the data, covering a range of Reynolds number(based on hydraulic diameter)of 70,000 - 700,000, i s f c p N 1 / 3 = 0.032 /D G\ 0 , 8 (U) This correlation gives values hO% higher than would be predicted by the modified Dittus-Boelter equation (3) for heat transfer to fluids flowing inside tubes, where the viscosity i s evaluated at the "film" temperature, taken as ( t ^ + i ^ ) ^ as recommended by Colburn (2), rather than at the average bulk f l u i d temperature t ^ . The modified equation, using De for D±, i s 3P r f \ 1 / 3 * 0 , 0 2 3 / v \ 0 , 8 ( 5 ) It i s worth while to mention at this stage that from experiments done on f l u i d f r i c t i o n i n the same heat exchanger, the experimental values were found to be 6$% higher than i s given by the Fanning equation, using V Recently A. Ya. Inayatov and M.A. Mikeev (8) published their data, also on experiments where water flowed parallel to e l e c t r i -cally heated tube bundles. They used a shell of 2.87" (73 mm.) diameter i n which nineteen tubes of 0.U7" (12 mm.) diameter were arranged concentrically with a radial pitch of 0.58" (li+.6U mm.) between centres. Surrounding the tube at the centre of the shell were sixoand twelve tubes respectively i n two concentric circ l e s . This arrangement gave an equivalent diameter of 0.3U" (8 mm.). The water rates were varied from 6.^ 6 to 72.10 ft./sec. (2-22 meters/sec), the heat load of the heating surface from 3690 to 11,061* [te-3)10^cal~| B.t.u./(sq.ft.)(sec), and the temperature of the surface from 99.6°F. to lU3.6°F. (32 to 62°C). They covered a hydraulic Reynolds Number range of hSOO - 26,900. They have also used the data of Sinelnikova and Mikeev (Ik) who had worked with different radial pitches. They give an equation and the function of Reynolds Number i s given as (bo.) K = 0.021 Re 0 , y o The term € which occurs i n this equation i s not explained, but the authors of this work came to the conclusion that the heat transfer coefficient for water flowing along a tube bundle i s predicted by the same equation as for the case of a liquid flowing inside round pipes, with the modification of using D for D.. In the absence of any know-ledge of £ , their data were correlated by the present author (Appendix, Figure 5) in'.the form of the modified Dittus-Boelter equation, and the result obtained was Thus we find, that the data from this work d i f f e r from the values predicted by the modified Dittus-Boelter equation by less than 5%, In every one of these studies the data and correlations 6 are limited to the region of turbulent flow. Since a study of the viscous region i s of theoretical interest, one of the objects of the present work i s to obtain data for the viscous region as well. In the method adopted here for making heat transfer measurements, a knowledge of velocity profiles i n the heat exchanger i s of great use,. Unfortunately such knowledge i s available only for viscous flow, i n the nature of a theoretical solution of the Navier-Stokes basic hydrodynamical equations. Emersleben (6) has treated these equations for the case of a f l u i d flowing through a bed of periodically spaced circular cylinders of equal size i n square array with the axes parallel to the flow. Emersleben's solution of the Navier-Stokes equations applies to a case where the cylinders are not quite circular but are represented by contours of a constant value Zn (£) of the Epstein zeta function Z(x/a,y/a), where r i s the radius of the cylinders, a i s the pitch from centre to centre and x and. y are rectangular coordinates. By taking the contours which most nearly f i t the circular cylinders of given radius, the solution was then an approximate one for the case of circular cylinders. This approximation, while poor for large values of £, becomes successively better as — becomes smaller. For — = 0.25 (corresponding to a void a a fraction of 0.80U) i t i s impossible on an actual plot to distinguish between the contours represented by Z Q (£) and a ci r c l e of radius r. Emersleben's integral solution i s , then, c F ( Z ) V / ~ V l Z <£>- F (Z ) - / Z° (F)dF J (8) avg LJ* 12TTJ ^ o a o •'o o J In addition, the velocity at any point (x,y) i s given by 7 Substituting from equation (8) the value for , we get Xi v(x,y) «= V ( z Q ( g ) - Z(x/a,y/a))  a T g /" r F<Zh> \ Curves are given i n his ar t i c l e (6) which allow easy evaluation of Z(x/a, y/a) i n this equation for any given case. Tables i n Emersleben's ar t i c l e also give values of the functions Z (—) and F (Z ) for various values of o a o' r/a. Plots of 7 (x,y) based on equation (10) are given i n Figure k of the V avg Appendix. Using this plot and making sufficient local temperature measurements, one can give proper weight to each of the temperatures recorded and thereby get a bulk average temperature. Such a procedure i s explained i n the section t i t l e d "Processing and Evaluation of Data". 8 I I - DESCRIPTION OF EQUIPMENT For descriptive purposes the equipment can be conven-iently dealt with as four sections: (a) the heat exchanger, (b) the air system, (c) the steam system and (d) the auxiliary equipment. The schematic diagram i n Figure 1 shows the f i r s t three sections i n assembly, (a) The Heat Exchanger The heat exchanger i s of the single pass shell-and-tube type and i s ill u s t r a t e d i n Figure 2. The s h e l l , made of l/kn 65 ST aluminum sheet, i s one foot square and i s i n five parts. The five parts, from the top down, are (1) the steam inl e t section, (2) the a i r outlet section, (3) the experimental test section, (U) the air inl e t section and (5) the steam condensate section, respectively. These sections are joined, by means of flanges three inches wide, sealed from the atmosphere by 1/8" Buna-N rubber gaskets. The flanges have twenty 7/16" diameter holes at a pitch of 3" from centre to centre, starting 1-1/2" from the edges, and are assembled with 3/8" bolts. The steam inl e t section and the experimental test section are insulated by 2" thick magnesia-asbestos blocks. A detailed description of the five parts mentioned above i s now given. (1) Steam in l e t section:- The inside dimensions of this section are 12" x 12" x U" and i t i s open at one end. Four one-inch standard nipples (6" long) are screwed at the centre of each side of the shell. Two of these nipples are connected to the steam line while the third carries a thermometer and the fourth i s connected to a pre-set safety r e l i e f valve and to a Bourdon pressure gage. 9 (2) Air outlet section:- The dimensions of this section are the same as for the previous one, but i t i s open at both ends. I t has four two-inch diameter holes bored centrally on each side to l e t the a i r out to atmosphere, A thermometer can be inserted to measure the temperature of the a i r i n t h i s section, through a 3/8" hole provided on one of the sides, (3) Experimental test section:- The inside dimensions of this section are 12" x 12" x 59". A l / l 6 " aluminum plate i s screwed on to each end. These aluminum plates have t h i r t y - s i x 1-1/32" diameter holes through which tubes carrying condensing steam are passed and held i n position. These plates have twenty-five one-inch diameter a i r distribution holes located at the intersections of the diagonals joining the tube centres. This section, which i s 59" high, has a 23" calming section at the a i r entrance side and a 6" calming section at the a i r exit side. These calming sections are provided on the basis that the 1/16" plates can be treated as orif i c e plates requiring calming lengths of eight and two hydraulic diameters at the downstream and the upstream sides, respectively, i n order to restore the undisturbed flow characteristics i n the test section. The hydraulic diameter of the test section based on the actual cross-section and "wetted-perimeter" of the air flow i s 2,87 i n . At the inside terminals of both calming sections provision i s made for the introduction of a thermocouple at l/kn$ 2", U", 5-2/3", 5-3/U" and 6" from a wall on one side, (Thermocouple position numbers 1, 2, 3, kt 5, 8, 9, 10, 11, 12, l i | and 15 as shown i n Figure 3(b).) The provision i s i n the form of 1/2" diameter holes i n an adjacent wall containing 1-3/U" long bakelite sleeves, which i n turn have 3/l6" diameter holes through which the thermocouple i s made to travel. These plastic sleeves minimise conduction of heat from the F I G U R E I. Schematic Of Equipment. KEY TO FIGURE 1. 1. Blower 2. Sliding disc to control air supply-3. Stove pipe connections h. U-tube manometers 5. Orifice meter and ori f i c e flanges 6. 6" i.d. common header 7. Heat exchanger 8. Steam line 9. Gate valve 10. Strainer 11. Pressure regulator 12. Sarco steam traps 13. Thermometers 1]+. Pressure r e l i e f valves 15. Pressure gage 9b F I G U R E 2 . H e a t E x c h a n g e r y2 <3> 7. draboll /|6 1  holes o o © O ( o o o o i 00 shell to the aluminum tube shielding the thermocouple. The experimental test zone i s 30" long and i s bracketed by the bottom and the top thermocouple positions. At distances of 10" and 20" up and 10" down from the bottom thermocouple positions and 6" from a wall, provision i s also made for the further introduction of the thermocouple (No. 6, 7 and 13 i n Figure 3). (k) Air i n l e t section:- The inside dimension of this section are 12" x 12" x U". Four two-inch long-sweep elbows are attached to each side of the shell with the help of floor flanges which are held i n position by floor screws. These elbows are connected to the a i r inl e t manifold. This arrangement ensures even distribution of a i r itito the heat exchanger. A 3/8" diameter hole through whcih a thermometer can be inserted i s also provided i n t h i s section, (5) Steam condensate section:- The inside dimensions of this section are 12" x 12" x 1". A 1/2" standard nipple i s attached at the centre of the bottom wall to drain out any condensate through a steam trap. The tubes used i n the heat exchanger are 1" o.d. (9,931" i.d,) Alcan 6£ ST aluminum tubes, and there are thirty-six of them arranged i n a square l a t t i c e with a two-inch pitch between adjacent centres. The outside rows of tubes have a clearance of 1/2" from the walls of the shell, to minimise wall effects. A l l the tubes are passed through two 1/2" thick aluminum plates (18" x 18" x 1/2") held i n position between sections 1 and 2, and k and J>, respectively. The holes i n the plates through which the tubes pass are constructed with specified standard grooves to take i n 1" o.d. 0-rings (S-19 of Anchor Packing Company). These 0-rings are slipped on to the tubes and are then firmly F I G U R E 3 -(a) Seatingof 0-rings and (b) Thermocouple Positions I. Plate 16 \_ -1.226 _^.0-Ring 12 13 2 3 45 » * * • II109 8 • • • 15 14 1,12 13 14,15 lodged i n the grooves made for them i n the 1/2" thick plate (Ref. Figure 3(a).) The pressure on the O-rings due to the construction and dimensions of the grooves not only keeps the tubes i n position but also prevents leakages between the steam and the air sections. Buna-N rubber gaskets 1/8" thick are provided between the 1/2" plates and the shell flanges to prevent leakage of ai r or steam to the outside. (b) The Air System The a i r i s fed by a centrifugal blower which can supply 100 CFM at a head of 10.55" of water. The blower has a k»5" i . d . outlet and the a i r rate i s controlled by adjusting the opening on the i n l e t side of the blower by a sliding disk. The a i r then passes through a 5*8" i . d . stove pipe to an orifice meter. From the ori f i c e meter which measures the a i r rate, the a i r flows into a 6" i . d . mild steel common line to which four 2" standard pipes are so welded as to give a gradual contraction and equal distribution of a i r into the four pipes (Ref. Figure 1). These pipes are i n turn connected via standard 2" unions to the four long-sweep elbows coming from the a i r i n l e t section of the heat exchanger. The temperature of the incoming a i r i s measured by a thermometer inserted into the a i r inl e t section. The a i r i s then evenly distributed into the test section by twenty-five 1" diameter holes i n the 1/16" aluminum plate screwed to the ends of the test section. At the start of the test zone, the temperature of the air can be measured right along the cross-section of the heat exchanger by using six thermocouple positions, Nos. 8-12 and lkt Ten inches below this section the temperature of the a i r can be measured along a line 6" away from the walls using thermocouple hole 12 number 13. At 10" and 20" above the start of the test zone, temperature measurements parallel to those taken i n position 13 can be made using the thermocouple holes 7 and 6 respectively. At the end of the test section temperature measurements corresponding to those of positions 12 to 8 and lit. can be made by 1 to 5 and 15 respectively. From here the air i s distributed again by twenty-five 1" diameter holes into the a i r outlet chamber and. thence to the atmosphere. In this manner i t was attempted to minimise cross-flow i n the heat exchanger. Two orifice meters (1" and 3" i n diameter) are used to measure the a i r flow rate. The orifice meters are made of brass, according to the ASME specifications (15) using flange taps. The orifice differential pressure and the static pressure on the upstream side of the orifice meter are measured by using U-tube manometers and a gage o i l of specific gravity 0.826. A draft gage was used to measure differential pressure for one low velocity run with the 3" diameter or i f i c e meter, (c) The Steam System Steam ifrom the 30 psig building supply i s controlled by a gate valve f i r s t . I t then passes through a strainer and Fisher pressure regulator. The entrained moisture i s removed from the line by gravity and by the strainer and drained out through a Sarco thermostatic steam trap. Steam pressure i s measured by a calibrated pressure gage and the temperature of the steam i s also measured with a thermometer. The pressure gage was calibrated with the help of a dead weight pressure tester. The steam then passes down through the tubes i n the heat exchanger where some of i t condenses by giving up heat to the cold a i r . The condensate i s collected i n the bottom section of the heat exchanger and i s drained out by another Sarco thermostatic steam trap. The two steam traps as well as a vent i n the steam line preceding the heat exchanger, serve to eliminate any accumulation of noncondensables i n the heat exchanger. (d) The Auxiliary Equipment The auxiliary equipment consists mainly of the temperature measuring device, which i n this case i s a 20-gage copper-constantan thermocouple. The thermocouple was calibrated i n an o i l bath against a standardised platinum resistance thermometer. The thermocouple wires are insulated with plastic material and the hot junction i s enclosed i n a 22" long 3/l6" o.d. aluminum tube. The inside diameter of this tube i s such that there i s very l i t t l e space between the plastic coated thermocouple wire and the walls of the tube, and by making the inside diameter of the tube larger at the point where the hot junction i s lodged, the chances of the hot junction touching the walls of the tubes are minimised. Also, before the thermocouple i s introduced into each position, i t i s checked to see that the hot junction i s not touching the walls of the tube. The use of this tube gives r i g i d i t y to the thermo-couple i n order to f a c i l i t a t e i t s introduction i n a straight horizontal l i n e . The aluminum tube also acts as a radiation shield for the hot junction of the thermocouple from the hot walls of the heat exchanger tubes. This single calibrated thermocouple i s used i n a l l the fifteen positions. While the thermocouple i s introduced i n one position, the rest of the holes are plugged with an insulating material to prevent any leakage of a i r or heat through these holes, A low vacumm i s applied to the thermocouple tube when the readings are taken, so that a sample of air i s sucked continuously into the tube where the hot junction i s housed. The suction i s provided by a water aspirator. This arrangement for minimising radiation error by increasing convective heat transfer to the hot junction gives more accurate as well as faster and steadier readings than those obtained without suction. The cold junction of the thermo-couple i s kept at the ice point constantly. The e.m.f, generated by the thermocouple i s measured by a Rubicon high precision 'Type B' potentiometer and a Rubicon spot-light galvanometer, A Weston standard c e l l i s used with this potentio-meter. I l l - ASSEMBLY OF EQUIPMENT AND EXPERIMENTAL PROCEDURE While the assembly of the different sections of the heat exchanger shell was performed with relative ease, the assembly of the tubes inside the shell was done with great care to ensure good alignment of the tubes. The pitch between adjacent tube centres must be constant while the clearance between the tube bundle and the shell walls must be the same a l l around. This alignment was made easier by the accurate machining of the holes i n the distributor plates at the top and bottom of the experimental test section of the heat exchanger. The 1-1/32" diameter holes i n the distributor plates guided the assembly of each of the tubes and this prevented the tubes from going out of alignment by more than 1/6U". The ve r t i c a l i t y of the heat exchanger and the tubes was checked by a plumb bob before and after the assembly. As mentioned under the sub-heading "Heat Exchanger" i n section I I of this thesis, O-rings were used to hold the tubes i n position and also to prevent leaks between the steam and a i r chambers. Pressure tests were made to check for any leaks. The tests consisted of f i l l i n g the steam-side of the heat exchanger with cold water under a pressure of 15 p.s.i.g. and leaving i t thus for a couple of hours. No reduction i n the pressure was observed, thereby indicating no leakage either to the a i r chambers or to the atmosphere. Then hot water was introduced and a similar test was made. Finally steam under a pressure of 10 p.s.i.g. was introduced* After a l l these tests i t was found that there were no leaks. The connections which were made to join the stove pipe sections carrying a i r from the blower to the common header, were checked 16 for leaks with soap water. The few leaks that were found were stopped by the use of 3M rubber-base cement and adhesive tape. Two orifice meters, 3" and 1" i n diameter, were used i n the investigation, for runs 1-9 and 10-13 respectively. U-tube manometers were used to measure the orif i c e upstream static pressure and the o r i f i c e differential pressure for a l l but run No. 9, when a draft gage was used to measure the very low differential pressure. In making a run the a i r flow rate was adjusted to the desired value f i r s t and then the steam was turned on. In each run, the steam pressure was maintained at some constant value between k»0 and 5.0 ;>* p.Skiig, The system was allowed to run for over two hours to reach steady state before measurements were taken. The approach to and attainment of steady state was observed by reading the thermometers i n the a i r i n l e t and outlet sections of the heat exchanger. The aluminum tube shielding the thermocouple was marked on the outside so as to indicate the position of i t s other end i n the heat exchanger. After pushing the tube to the desired length, a slight vacuum was put on the tube to suck air past the hot junction of the thermocouple. The cold junction was kept i n an ice bath. Five minutes after the suction was applied the temperature measurements were made. The thermocouple was then pushed to different positions i n the heat exchanger and m i l l i v o l t readings were taken at intervals of about one minute. The experimental runs can be classified under two headings, (a) central unit c e l l temperature measurements and (b) runs to check symmetry of temperatures i n the heat exchanger. In the f i r s t case, measurements were made at distances of l / i t " between successive points using the thermocouple positions 1, 5, 15, 12, 8 and Ik, Also the centre-point temperatures of thermocouple positions 6, 7 and 13 were recorded from run k onwards. In the symmetry runs, measurements were made at distances of l/U", 1", 2", 3", U", 5", 6", 7", 8", 9", 10", 11" and 11-3/1+" from the wall through which the thermocouple was introduced. In these runs a l l the thermocouple positions 1 vr. 1$ were used. For every run, the room temperature, the barometric pressure, and the manometers for orifice differential and upstream static pressure were read, as assflethe steam temperature and pressure. The estimated precision of the measurements was i 0.2°F for thermocouple readings, + 0.5°F for thermometer readings, * 0.1 inch for U-tube manometers, ± 0.01 inch for the draft gage, and - 0.1 mm. of mercury for the barometer. The accuracy of the steam thermometer, of the travelling thermocouple, and of the orifice differential manometer was within the limit s of precision i n each case. 18 IV - PROCESSING AND EVALUATION OF DATA The basic equation that was used to calculate the heat transfer coefficients i s q «= h.A. A t l m -a'S.C .(tg-t^) (11) The data were correlated according to the form of the Colburn (2) equation St. P r f 2 / 3 = [3. Re f n (12) The dimensionless Stanton group ( /C G) can be obtained by rearranging P equation (11) (h/C a) - ( S/A).(!f^l) ( l l a ) P S i Q In a l l these calculations ( /A) i s fixed by the design and construction of the equipment and the remaining terms that one has to know are (a) the wall temperature t w , (b) the mass velocity G, and (c) the a i r i n l e t and outlet temperatures t ^ and t£ respectively. The evaluation of each of these terms w i l l now be discussed, (a) Tube wall temperature:- The present system has been chosen on the assumption that the only resistance to heat transfer between condensing steam and a i r i s on the a i r film side, with the steam condensate film and the metal walls of the tubes offering practically no resistance. That this i s a v a l i d assumption i s shown by the following calculations. The total resistance R can be written as 1 * fw V A s V Aw V A a R - - J ^ * - ^ * - ! - (13) V 19 From a heat balance between the a i r and steam sides of the exchanger, one finds q = ws.\s - w.C ..(t^-t^) (1U) Using the known experimental data from run 8 which gives the highest heat transfer coefficient for a i r , i t i s found that the pounds of steam condensing per hour per tube i s 0.5875* With a safety margin for additional heat losses, this amount can be taken as lO^/hr.) per tube and from the Nusselt equation,(11), one gets the steam film coefficient as 3 1 0 0( B , t* uyhr.sq.ft. oF). Taking B.t.u ^F the value for the thermal conductivity of aluminum as 118 * * */hr.sq.ft.(—) i t . and working out the individual resistances, i t i s found that the steam f i l m resistance per foot length i s R = 1 = 1 - 0.000212 , (13a) S h g.A s 3100 x 0.214; the metal wall resistance per foot length i s R w «= = 0.003 = 0.000016 , (13b) k ^ 118 x 0.253 and the a i r film resistance per foot length i s R = 1 = 1 = 0.236 . (13c) h a.A a 2.588 x 0.262 From these figues, i t i s found that 99.9$ of the total resistance i s i n the a i r film, and hence the outside wall temperature of the tubes can be taken as that of the condensing steam inside. 20 (b) Mass velocity:- The orif i c e plates that are used i n the experiments were not calibrated because of the practical d i f f i c u l t i e s involved due to their sizes. But they were made s t r i c t l y according to the ASME specifications (li?) and i t i s assumed that the general flow equations for ori f i c e meters, using the discharge coefficient for flange taps, are applicable. The equation that i s used i n these calculations i s v = 359.1.(D 2) 2. cc .K.Y r JT rh w m as recommended by Stearns et a l (15). This equation relates the weight rate of flow i n 1^/hr. to the orifice differential pressure 1^  i n inches of water. I t i s assumed that CC , the area multiplier for the thermal expansion of the metal i n which the orifice meter i s made, i s equal to unity since the temperature of the orifice meter i s essentially the same as the room temperature. Stearns et a l (15) have suggested procedures for obtaining the values of K and Y^ to be used i n equation (II4.) and charts are given for the same. Knowing the actual flow area S, which i s fixed by the design of the heat exchanger, one can get the value of G from w, since G - w (15) s (c) Air i n l e t and outlet temperatures:- In using equations (11) or (11a), the inlet and outlet temperatures to be used are the respective bulk temperatures. To calculate the bulk temperature from the temperature profile i n the viscous region, use i s made of Emersleben's solution (6) of the Navier-Stokes equations for the case of a f l u i d flowing parallel to rod or tube bundles. In the present work, only the central 21 unit c e l l of the square l a t t i c e i s taken for consideration, as this c e l l i s more free from wall effects than any of the others and can therefore be most likened to Emersleben's system of rod bundles with no f i n i t e boundaries. The ratio of the point velocities to the average velocity i n the unit c e l l i s given by equation (10). A chart of (v^ y/^ a Vg) for different distances from the centre of the tube was established by means of equation (10) and i s given i n the Appendix Figure U. The values of (v /v ) given are i n conformity with the known fact that the x,jr avg velocity at the tube wall i s zero and with the condition that s. V .s • J v .ds = 2.v\s. (16) avg "6 x,y i i The numerical values of the zeta functions were taken from Emersleben's ar t i c l e (6), Knowing the ratio of the point velocities to the average velocity, the unit c e l l was divided into smaller squares of area s^ and an enthalpy balance (reference temperature 0°F.) between the sum of the smaller squares and the overall unit c e l l affords a method of getting the bulk temperature i n the unit c e l l , as Vn™» s"P • c„ »K e v..s..^.C . t . , (17) avg avg p _ bulk x l i p. i avg * i where the subscript i refers to local values and s^ i s the small area i n which the averaged velocity i s taken as v^. Since the variation of temperature i n the unit c e l l i s relatively small, the density .P and heat capacity terms are taken as constant, giving a solution for the bulk temperature as *bulk- £ ( vi Aavg (> ( s i / s ) * i ( 1 7 a ) Equation (17a) i s based on the assumption that the velocity distribution for the isothermal gas flow as given by equations (8) and (9) i s unaffected by radial temperature gradients, especially when they are small as i n the present case* This procedure of getting a bulk temperature could not be applied to the turbulent flow runs since neither the point velocities nor their ratios with the average velocity are known. It was therefore decided to use the centre-point temperatures at the start and end of the test zone, as the air i n l e t and outlet temperatures, respectively. This would only give a pseudo-coefficient of heat transfer. For comparison, calculations were also made i n the viscous region using centre-point temperatures. In a l l the calculations, the values for the properties of a i r were taken from "Heat Transmission" by McAdams (11). V - DATA AND RESULTS As mentioned i n the previous section, the runs made are i n two categories, namely the central unit c e l l measurements and symmetry-check runs. Tables I - XII i n the Appendix give the data obtained from the measurements made i n the central unit c e l l , while Tables XIII - XV give the data on the symmetry check runs. Tables XVI and XVII summarise the data used for calculation purposes and the results obtained from them, i n the viscous and the turbulent regions, respectively. Figure U shows the values of (v /V ) i n the central unit c e l l for different values of x and y. The data from the work of Inayatov and Mikeev (8) are correlated i n the form of the modified Dittus-Boelter equation i n Figure 5, while Figure 8 gives the results obtained from the data of the present work as well as the lines obtained from the empirical equations of Miller et a l , Inayatov and Mikeev and Oolburn. Temperature profiles of the present work are presented i n Figures 6 and 7, Figure 9 i s the calibration curve of the thermocouple used i n these experiments. Table XVI Summary of Data and Results Viscous Region - (Reynolds Number ^ 2100) RUN NO. No. 13 Ho. 12 No. 11 No.10 No.9 1. Room temperature ° F 76 71+ 72 70 71+ 2. Barometric pressure mm.Hg 757.6 751+.6 751+.0 755.0 758.7 3. Orifice upstream pressure inches of water 3.1*69 5.865 8.095 10.903 0.1+96 h. Orifice differential pressure inches of water 3.1+69 6.112 8.1+25 11.320 0.32 5. Air i n l e t temperature t ^ ° F 176.9 157.7 15U.0 11+9.9 11+8.0 6. Air outlet temperature t^f 200.0 193.1+ 190.8 185.1 173.7 7. Weight rate of flow w lbs./hr. 111.1 11+7.1+ 173.0 201.1 321+.5 8. Mass velocity G lb./(hr.)(sq.ft.) 138.2 183.3 215.2 250.1 I+0U.0 9. Reynolds Number DQG/ jul^ 633.1 81+1.1 987.8 1152.1+ 1861.5 10. Stanton Number (h/C G) bulk 0.021+60 0.02669 0.02725 0.02203 0.011+56 (h/C G) centre-point 0.01985 0.021*20 0.021+1+0 0.020U5 0.01321 11. Heat transfer coefficient h ^ j j . B.t.u./(hr.)(sq.ft.)(°F) 0.830 1.181+ 1.1+19 1.333 1.1+21+ hcentre-point B.t.u./(hr.)(sq.ft.)(°F) 0.665 1.073 1.271 1.238 1.292 12. j h-factor ( j h ) bulk 0.01928 0.02092 0.02136 0.01727 0.0111+1 (jy.) centre-point 0.01556 0.01897 0.01913 0.01603 0.01036 Table XVII Summary of Data and Results Turbulent Region (Reynolds Number > 2100) RUN NO. No.l No.2 No.U No,5 No.7 N0.8 N0.6 1. Room temperature °F 79 80 82 80 80 76 81 2. Barometric pressure mm.Hg 757*5 755.0 75U.5 75U.5 75U,0 752.8 75U,0 3. Orifice upstream pressure inches of water I.I1.OI4. 2.602 5.1;52 6.608 7.930 9.10-6 10.077 U. Orifice differential pressure inches of water 0.867 1.652 3.387 U.130 U.956 5.865 6.360 5. Air i n l e t temperature t ^ °F 11*3.2 137.9 137.9 136.6 132.2 121.9 131.0 6. Air outlet temperature tg °F 168.5 162,3 155,6 151.2 1U7.U 138.9 Uiiu7 7. Weight rate of flow w lbs./hr. 516.8 722.6 1028.k 1136.U 121*5.3 1358.1 1U06.5 8, Mass velocity G lbs./(hr.)(sq.ft.) 61*2.8 898.8 1279.1 llil3.U 15U8.9 1689.2 nk9.k 9. Reynolds Number DeG/ f*f 2933,6 10-09.8 6009.3 661*0.2 7276.8 809U.7 8218,7 LO. Stanton Number (h/CpG) 0.0126U 0.01121 0.00778 0.00622 0.00617 O.O063U 0.005U5 LI. Heat transfer coefficient h B.t.u./(hr.)(sq.ft.)(°F) 1.965 2.U37 2.U08 2.126 2.309 2.588 2.301* L2. j h-factor 0.00986 0.0087U 0.00612 0.001*89 0.001*85 0.00500 0,001*28 FIGURE 6 . Direction of Thermocouple Travel F I G U R E 7. Temperature Profiles-CentraI Unit Cel 3$ d Re=63 3 190 17_6" 160 e G Re= 8 4 I 200 190 1.80 • 70 160 150 e <D G Re=9 8 8 2 0 0 I90_ 180 170 160 I5_0_ e -O-Re =115 2 190 180 170 !60_ I5_0_ 140 e 190 180 170 160. 150 f4_0_ J30-Re = 1862 O 1 72 /4 0 V4 >2 3/4 170 160 150 140 150 140 170 160 ISO 140 130 150 140 130 150 140 130 140 130 120 150 140 130 1.20 Re=2 9 34 Re=4 I I 0 Re = 6 0 0 9 e 0 G Re=6 6 4 0 G Re=7 2 7 7 e CD G Re=8 0 9 5 e (D Re=8 2! 9 © G 1  3/4 Jfc ^ 0 £j V2 3/4 Direction ofThermocouple Travel Distance from centre Thermocouple Positions e O Thermocouple position No. 15 814 H " 1 8 12 ii it ii 58 8 „ I I H 6 II II it 7 H II " '3 F I G U R E 8 . Summary of Results Resolt of Inayatov 8 Mikeev (8) Colburn line (2) Extrapoloted correlation of Miller et ol (j 2) from bulk temperature © j. from centre point " Q VI - DISCUSSION OF RESULTS In comparing the results of this work with those of Miller et a l and Inayatov and Mikeev, i t i s found, that each study has been done at a different Reynolds number range, though five runs from the present work overlap the data of Inayatov and Mikeev. The results of a l l three works are given i n Figure 8. While the present investi-gation includes part of the viscous range, assuming that the flow i s streamline below a hydraulic Reynolds number of 2100 for this set-up, the other studies have been limited to the turbulent region. A look at Figure 8, however, indicates that the general trend of the present data i s towards convergence with the values of Inayatov and Mikeev at higher Reynolds numbers. More runs have to be made i n the laminar region before any specific correlation can' be given. I t i s s t r i c t l y not correct to c a l l the factor reported i n this work as the true one for the central unit c e l l , since the Reynolds number was calculated using the equivalent diameter and the mass velocity for the entire heat exchanger. A true value corresponding to this Reynolds number would be based on the temperature profile for the entire heat exchanger, or alternately the Reynolds number should be based on the central unit c e l l alone. Furthermore, the calculations for the turbulent runs were not made using the bulk temperature i n the central unit c e l l , but using the centre-point temperature. A look at Figure 6, which shows the temperature profile across the heat exchanger sh e l l , indicates an apparent dissymmetry of temperature i n the two halves of the she l l . The recorded unsymmetrical 25 temperature distribution may be due to three factors: (a) non-uniform flow distribution (resulting i n non-uniform heating) due to heat exchanger design and construction, (b) non-uniform flow distribution caused by the presence of the thermocouple, and (c) faulty positioning of the thermocouple. Only the a i r side need be taken into consideration, since by a previous calculation (ref. Section IV (a).) i t has been shown that the resistance due to the steam condensate film and the metal wall i s negligible relative to that of the a i r film. The three factors that could cause the dissymmetry w i l l now be discussed. (a) While the tubes were assembled inside the she l l the clearances between the tube bundle and the four shell walls were checked closely for uniformity. Significant excessive channeling of the a i r near any of the walls i s therefore unlikely. I t i s , however, possible that the distributor plates inside the heat exchanger do not completely prevent by-passing of a i r due to poor distribution from the four feed pipes, and i t i s also possible that there i s a slight flow through the clearance between the 1" o.d. tubes and the 1-1/32" diameter holes through which they pass. The clearances between the tubes and the tube plates may not be uniform, and because of t h i s , more air may leak through some of the clearances than through others. Area and flow calculations indicate, however, that the fraction of a i r that would leak through these clearances i s small relative to the total amount of a i r flowing, so that i t i s unlikely that this effect has much bearing on the temperature dissymmetry. (b) When the thermocouple i s introduced, there may be by-passing of some air because of the disturbance caused by the presence of the thermocouple tube. I t would be expected that this disturbance would manifest i t s e l f primarily downstream of the thin thermocouple tube. 26 However, i f there i s some disturbance on the same level as the thermocouple, the recorded temperature dissymmetry would be expected to show a uniform trend towards one side. As Figure 6 does not show this, i t i s concluded that the presence of the thermocouple i s not a major source of dissymmetry i n the direction of thermocouple travel. The possibility that sucking the small a i r sample from the flow could affect the flow pattern, thereby producting the dissymmetry, was investigated. I t was found that without suction the temperatures recorded were unsteady and lower than the corresponding temperatures recorded using suction, but that as long as some suction was applied, the same temperature was read at any point irrespective of the magnitude of the suction. The effect of increasing the suction was merely to decrease the time required to reach a steady temperature. I f the suction were responsible for significant change i n the flow regime and hence hot junction temperature, i t would be expected to increase this change with an increase i n i t s own magnitude. That i t does not do so means that the suction too cannot be blamed for the dissymmetry. (c) The most important and most probably the main reason for the apparent non-uniform heating may be the available play of the thermocouples i n the holes provided for their introduction. This play can move the hot junction of the thermocouple by as much as l/U". This means that i f the hot junction was moved towards the tube walls i t would read a higher temperature, and i n the opposite direction i t would read a lower temperature, than the true one for i t s assumed position. This play i n the thermocouple positions could not be controlled i n the present set-up even after stuffing the holes. Temperatures with a variation of up to 10°F were recorded i n some positions by deliberately playing the thermocouple at the extreme end from the wall through which the:.thermocouple was 27 introduced. Also, at some of the central unit c e l l positions, differences of U°F were recorded by deliberate play. This, more than any other factor, could account for the recording of unsymmetrical temperatures. A method for eliminating this thermocouple play i s recommended i n the next section. 28 VII - RECOMMENDATIONS FOR FUTURE WORK From the previous section i t can be seen that some improvements must be made in order to get dependable results from this equipment. Enlarging the a i r distributor holes would cut down the leakage around the tubes by causing an even greater proportion of the air to flow through these holes. This would also increase the capacity of the set-up using the given blower and decrease the entrance and exit calming lengths necessary for a f u l l development of the flow regime. The fraction of the free flow area occupied by the distributor holes i s at present only 0.158, as compared to 0.UU3 i n the equipment of Mil l e r et a l (12) and 1.000 i n the set-up used by Inayatov and Mikeev (8). Estimation of an optimum value should be looked into. I f the equipment i s operated at considerably higher Reynolds Numbers, obtained by using larger o r i f i c e diameters, the a i r film coefficient could conceivably go to as high as 100(B,t,u,/(hr.)(sq.ft.)(°F).), i n which case the steam condensate film resistance would not be negligible. It would then be worth while making arrangements for the dropwise condensation of steam inside the tubes, either by coating the inside with benzyl mercaptan or oleic acid, or by the introduction of these compounds with the steam, or by any other suitable method. With reference to the thermocouple measurements, a longer thermocouple tube that goes through and rests on opposite walls i s suggested. This tube would have a.hole near the hot junction so that as the tube i s moved, the hole also moves to different positions i n the heat exchanger, thereby sensing different point temperatures. Suction would be used i n this case aleo. This method would eliminate any dissymmetry i n the 29 direction of thermocouple travel due to the flow obstruction caused by thermocouple tube. Also, since the thermocouple tube would rest at two positions 12" apart, i t i s estimated that the play of the hot junction could be reduced i n this manner to less than 1/32". A measurement of the velocity profiles at different levels i n the heat exchanger would throw considerable light on the flow pattern, allow rational evaluation of bulk temperature from temperature profiles, and i n the viscous region, provide a rigorous empirical test of Emersleben's solution of the Navier-Stokes equations. The same equipment, with slight modifications, could be used to study f l u i d f r i c t i o n i n flow parallel to tube bundles, but a viscous liq u i d would have to be used, since the pressure drop for gases or for liquids of low viscosity would be too small to measure adequately. Since the tubes can be removed easily by slipping off the 0-rings, different l a t t i c e arrangements can be b u i l t and inserted with relative ease. The effect of l a t t i c arrangements and fractional free area on heat transfer and f l u i d f r i c t i o n can therefore be studied. Even i f the velocity profile measurements are not made, the f l u i d f r i c t i o n study i n the viscous region would afford a chance to check experimentally the pressure drop form of Emersleben's solution of the Navier-Stokes equations. Finally, the analogy between momentum and heat transfer i n turbulent flow can also be studied. 30 NOMENCLATURE a - tube pitch between centres, f t . A - heat transfer area, sq.ft. A - heat transfer area of the a i r film, sq.ft. a A - heat transfer area of the steam film, sq.ft. s A^ - heat transfer area of the tube wall, sq.ft. C - constant i n equation (1) C ~ - heat capacity, B.t.u./(lb.)(°F) P D - diameter, f t . Dg - orifice diameter, inches D Q - hydraulic diameter, f t . - inside diameter of tubes, f t . DQ - outside diameter of tubes, f t . G - mass velocity, lb./(hr.)(sq.ft.) h - heat transfer coefficient, B.t.u./(hr.)(sq.ft.)(°F) h a - ai r film coefficient, B.t.u./(hr.)(sq.ft.)(°F) h s - steam film coefficient, B.t.u./(hr.)(sq.ft.)(°F) 1^ - orifice differential pressure, inches of water 2/3 j h - " j - factor" for heat transfer = St.Pr ' , dimensionless k - thermal conductivity, B.t.u./(hr.)(sq.ft.)(°F/ft.) k - thermal conductivity.of tube wall, B.t.u./(hr.)(sq.ft.)(°F/ft.) K - orifice discharge coefficient, dimensionless K Q - a function of Reynolds Number i n equation (6a) L - length of tube or rod bundle, f t . p - pressure drop i n tube or rod bundle, (lb.force/sq.ft.) Pr - Prandtl Number, dimensionless, (Cp//k) heat transferred, B.t.u./hr. radius of tube, f t , resistance to heat transfer, (°F)(hr.)/B.t.u. Reynolds Number, DG/ , dimensionless cross sectional flow area of central unit c e l l , sq.ft, cross sectional flow area of heat exchanger, sq.ft, Stanton Number, h/CpG, dimensionless air i n l e t temperature to test section, °F air outlet temperature from test section, °F temperature i n the air inl e t section, °F temperature i n the a i r outlet section, °F bulk temperature, °F tube wall temperature, °F average velocity, ft./hr, local velocity, ft./hr. weight rate of flow, lbs./hr, weight rate of condensate, lbs./hr. distance i n the x - direction from a tube centre, inches thickness of the tube wall, f t . distance i n the y - direction from a tube centre, inches orifice expansion factor based on absolute static pressure at the upstream pressure tap, dimensionless orif i c e area multiplier for the thermal expansion of metal i n which the orifice plate i s made, dimensionless constant i n equation (12) unknown term i n equation (6) viscosity, lb./ft.nr. C - density of air at ori f i c e upstream pressure tap conditions, lbs./cu.ft. I"* - mass rate of flow of condensate on the condensing surface, divided by the perimeter, lb./(hr.)(ft.) X - latent heat of steam, B.t.u./ l b . Subscripts; f - a i r film, based on a i r film temperature f 1 - steam condensate fi l m , based on steam film temperature i - local values, average values of areas i n Figure h» REFERENCES Chemcial Engineers' Handbook, 3rd ed,, McGraw H i l l , New York, p 1*73, 1950. Colburn, A.P., Trans. Am. Inst. Chem. Engrs., 29, 1?U (1933). Dittus, F.¥., and L.M.K. Boelter, Univ. Calif., Pubs. Eng., 2, 1*1*3 (1930). Donohue, D. A., Ind. Eng. Chem., 1*1, 21*99 (19U9). Eckert, E.R.G., "Introduction to the Transfer of Heat and Mass", Fi r s t Edition, McGraw H i l l , New York, 1950. Emersleben, 0., Physik Z., 26, 601 (1925). Heinrich, E., and R. Stuckle, Ver. deut. Ing,, Mitt. Forsch. Gebiete Ingenieurw., Heft 271 (1925) Inayatov, A. Ya., and MiA. Mikeev, Toploenergetika, U,No.3,U8 (1957) Jakob, M., "Heat Transfer", Vol .1, John Wiley and Sons, New York 1953 Vol.11, John Wiley and Sons, New York 1957. Kern, D. Q., "Process Heat Transfer", F i r s t Edition, McGraw H i l l , New York, 1950. McAdams, W. H., "Heat Transmission", Third Edition, McGraw H i l l , New York, 195U. M i l l e r , P., J.J. Byrnes, and D.M. Benforado, J. Am. Inst. Chera.Engrs. 2, No.2, 226 (1956) Short, B. E., Univ. Texas Pub., No.l*32l* (19U3). Sinelnikova, A.C., and M.A. Mikeev, Treatises 7io~SVS written 1, 1931. Stearns, R.F., R. R. Johnson, R.M. Jackson and C.A. Larson, "Flow Measurement with Orifice Meters", D.Von Nostrand Company, New York, 1951. 3k APPENDIX Room temperature Steam temperature Air i n l e t temperature Orifice upstream pressure Table I Data for Run No. 13 68°F 228°F 1$6°F U.2" Barometric pressure Steam pressure Air outlet temperature Orifice differential pressure 757.6 mm.Hg 5.5 psig 206o F U.2" CENTRAL UNIT CELL POSITIONS Thermocouple .tion No. Temperatures (°F) at distances from centre -1" - 3 A " •4/2" -l/U" 0 l/U" 1/2" 3/U" 1" 1 200.2 200.6 201.1 200.1 200.0 200.3 201.6 203.1 206.9 5 201.5 201.5 200.6 200.8 200.8 201.1 202.3 207.0 206.0 15 208.2 208.2 208.5 203.7 203.1 202.9 202.9 203.1 203.3: 12 17U.3 17U.3 176.7 176.7 176.9 177.3 175.9 175.5 175.9 8 177.5 178.1 178.1 175.6 175.6 175.6 175.1 175.9 17U.3 1U 178,1* 179.3 177.U 177.6 175.5 175.9 176.0 177.5 179.5 6 196.5 7 188,2 13 155.2 Room temperature Steam temperature Air i n l e t temperature Orifice upstream pressure Table I I Data for Run No. 12 228°F 1U6°F 7.1" Barometric pressure Steam pressure Air outlet temperature 75U.6 mm.Hg 5.5 psig 20i*°F Orifice differential pressure 7 .U" CENTRAL UNIT CELL POSITIONS Thermocouple .tion No. Temperatures (°F) at distances from centre -in - 3 A " -1/2" - i A n 0 l A " 1/2" 3 A " 1" 1L 196.1 195.5 195.U 19U.9 193.U 19U.U 19U.1 195.8 198,6 5 198.3 195.7 19U.7 19U.9 19U.0 19U.9 195.7 197.5 197.5 15 20iu3 203.1 199.1 195.7 19U.7 197.0 202.2 202.2 199.6 12 173.1 167.9 165.5 160.I 157.7 160.9 160.9 159.5 162,3 8 162.8 158.9 160.2 159.2 155.5 157.6 157.5 158.9 158.1 1U 16U.8 165.1 159.5 158.3 158.0 158.3 159.1 160.2 160.1 6 187.0 7 178.1 13 HOuO Room -temperature Steam temperature Air inlet temperature Orifice upstream pressure Table I I I Data for Run No. 11 72°F 228°F U|1°F 9.8" Barometric pressure 75U.O nm.Hg Steam pressure 5.5 psig Air outlet temperature 202°F Orifice differential pressure 10,2" CENTRAL UNIT CELL POSITIONS Thermocouple Position No, Temperatures (°F) at distances from centre -1" -3A" -1/2" -l/U" 0 l A " 1/2" 3A» 1" 1 191.U 192.7 191.7 191.1 190.8 190.3 190.8 192.0 195,6 5 195.7 195.0 191.1 191.5 191.2 191.5 193.0 193.0 193.0 15 201.9 201.3 198.6 19U.9 192.7 193.7 201.7 203.it 203.3 12 162.6 160.2 158.1 157.5 15U.0 15U.0 153.5 15U.9 155.1 8 157.3 157.3 156.3 15U.0 153.9 152.8 152.8 152.8 153.5 Hi 159.0 158.8 157.U 15U.3 15U.3 15U.8 156.6 155.7 157.8 6 183.0 7 170.5 13 1U0.1 Room temperature Steam temperature Air i n l e t temperature Orifice upstream pressure CENTRAL UNIT CELL POSITIONS Thermocouple Position No, Temperatures (°F) at distances from centre -1" - 3 A " -1/2" - l A " 0 l A " 1/2" 3 A n 1" 1 186.8 186.8 185.8 18U.7 185.1 185.1 186.9 186.5 188.1 5 193.7 191.0 187.1 181*. 7 181*.0 181*. 2 186.9 190.)4 190.6 15 19U.9 193.3 187.U 186.5 185.9 186.8 190.9 195.0 190.8 12 15U.6 156.1 152.1 152.1 1U9.9 Ui9.9 11*9.9 150.9 151.9 8 156.9 153.5 153.1 151.U 150.3 1U9.5 1U9.0 1U9.0 1U9.3 1U 158.5 157.5 153.5 152.6 lli9.5 1U9.3 1U9.9 150.7 153.9 6 172.9 7 163.8 13 135.6 • Table IV Data for Run No. 10 70°F Barometric pressure 755.0 mm.Hg 228°F Steam pressure 5.5 psig 136°F Air outlet temperature 200°F 13.2" Orifice differential pressure 13.7" Table V Data for Run No. 9 Room temperature Steam temperature Air i n l e t temperature Orifice upstream pressure 7i+°F 228°F 13U°F 0.6" Barometric pressure Steam pressure Air outlet temperature Orifice differential pressure 0.32" * * A draft gage was used. 758.7 mm.Hg 5.5 psig 197°F CENTRAL UNIT CELL POSITIONS .tion No,. Temperatures (°F) at distances from centre -1" -3/U" -1/2" -l/U" 0 1/1+" 1/2 m 3A" 1" 1 178,8 178,2 175.8 172.8 173.7 171.0 171.1+ 171.1+ 172.7 5 186,1 178.5 177.0 17U.5 17U.1 171+.5 179.3 185.2 185.2 15 189.0 185.2 177.0 17U.6 17U.5 175.0 178.6 189.5 193.8 12 150,2 151.1 H+7.7 li+7.9 11+8.0 11+7.1+ 11+7.2 11+8.2 11+8.8 8 15U.9 151+.1+ 150.0 11+8.0 11+6.8 11+7.0 11+7.2 11+U.5 11+1+.5 1U 162.8 160.2 157.5 153.9 150.0 150.0 11+9.1 150.2 11+9.1 6 170.0 7 160.2 1} 135.3 Table VI Data for Run Mo. 1 Room temperature 79°F Barometric pressure 757.5 mm.Hg Steam temperature 22$°F Steam pressure U.5 psig Air i n l e t temperature 128°F Air outlet temperature 192°F Orifice upstream pressure 1.05" Orifice differential pressure 1.7"1 CENTRAL UNIT CELL POSITIONS Thermocouple Position No. Temperatures (°F) at distances from centre -1" - 3 A " -1/2" -1/1*" 0 l A " 1/2" 3A" 1" 1 17U.2 175.9 172.2 169.7 168.5 168.0 166.9 169.6 172.3 5 169.5 168.2 168.0 167.1 167.1 167.3 167.5 169.3 170.2 15 175.8 173.7 '171.0 168.2 168.0 166.2 168.9 170.0 171.7 12 11*6.5 11*6.0 1U3.U 11*3.3 11*3.2 11*3.3 1UU.2 11*6.6 11*9.9 8 11*7.1* 11*5.9 1U5.0 11*3.8 11*2.8 11*3.3 11*2.0 11*2.0 11*3.0 1U 158.8 15U.6 11*9.9 150.2 11*5.8 11*5.5 11*3.3 11*3.3 11*2.3 Room temperature Steam temperature Air i n l e t temperature Orifice upstream pressure Table VII Data for Run No. 2 80°F 225°F 122°F 3.15" Barometric pressure Steam pressure Air outlet temperature Orifice differential pressure 755.0 mm.Hg U.5 psig 186QF 2.0" Thermocouple Position No. CENTRAL UNIT CELL POSITIONS Temperatures (°F) at distances from centre -1" -3/1*" -1/2" -1/i*" 0 1/1*" 1/2" 3/U" 1" 1 16U.7 170.0 167.0 161*.3 162.3 161.1* 161.8 161.1 162.0 5 163.9 163.2 161.8 160.5 160.2 160.2 162.0 162.8 163.1 15 168.8 166.9 163.2 162.0 161.2 160.8 161.3 162.6 161*.7 12 138.2 137.7 137.3 137.8 137.9 138.3 139.6 11*0.9 11*1.8 8 H i l . 8 11*1.3 11*1.3 138.9 137.5 136.9 136.3 137.0 137.0 Hi 120.0 119.2 118.7 117.2 116,8 116.8 117.1* 117.1 117.5 Room temperature Steam temperature Air i n l e t temperature Orifice upstream pressure Table VIII Data for Run No, it 82°F 225°F 122°F 6.6" Barometric pressure 75U.5 mm.Hg Steam pressure U.5 psig Air outlet temperature 180°F Orifice differential pressure U.l" CENTRAL UNIT CELL POSITIONS Thermocouple .tion No, Temperatures (°F) at distances from centre -1" -3/U" -1/2" - I / U " 0 . i A " 1/2" 3/U" 1" 1 155.0 155.8 156.2 155.6 155.6 153.6 152.9 152.9 152.9 5 161,8 161.8 157.7 156.5 156.1 155.6 157.1 15U.9 152.U 15 157.9 158.0 158.0 155.0 15U.6 155.6 156.U 161.8 157.5 12 137.8 137.8 138.6 138.2 137.9 137.8 138.8 138.U 139.1 8 lUU.5 1U2.0 U i l . l 138.8 137.6 137.U 136.5 136.5 137.3 lU 1UU.0 liA . 5 H|0.2 138.8 137.6 138. h 138.6 138.U 138.6 6 150.8 7 1U5.0 13 126.3 Table IX Data for Run No, 5 Room temperature 80°F Barometric pressure 75U.5 mm.Hg Steam temperature 22U°F Steam pressure U.25 psig Ai r i n l e t temperature 118°F' Air outlet temperature 179°F Orifice upstream pressure 8,0" Orifice differential pressure 5,0" CENTRAL UNIT CELL POSITIONS Thermocouple Position No,. Temperatures (°F) at distances from centre -1" -3/U" -1/2" -1/U" 0 l / U " 1/2" 3/U" 1" 1 153.1 153,2 153.2 152.0 151.2 151.2 150. u 150.U 152.1 5 157.9 157.0 15U.8 153.9 151.2 151.5 151.6 151.6 150.U 15 156.1; 155.0 15U.0 152.6 152.6 153.0 153.0 15U.U 15U.8 12 136.9 136.9 136.9 136.U 136.6 136.9 137.1 137.6 137.1 8 1U3.9 1U3.5 1U1.5 139.U 137.6 136.5 135.0 13U.6 133.0 1U 1UU.3 1U5.6 1U0.8 139.6 138.2 138.0 137.6 138.2 138.1 6 150,8 7 1UU.2 13 126,0 Table X Data for Run No. 7 Room temperature 80°F Steam temperature 22U°F Air inlet temperature 118°F' Orifice upstream pressure 9.6" Barometric pressure Steam pressure Air outlet temperature Orifice differential pressure 75U.O mm.Hg U.5 psig 178°F 6.0" CENTRAL UNIT CELL POSITIONS .tion No© Temperatures (°F) at distances from centre -1" -3/U" -1/2"- -1/1+" 0 1/1+" 1/2" 3/U" 1" 1 11+7.0 1U8.5 11+8,5 11+8.2 11+7.1+ li+6.8 1U6.U 1U6.0 1U7.U 5 151.9 151.0 150.0 11+8.6 11+8.9 - 11+6.1+ H+7.5 1U7.5 1U7.3 15 11+9.9 11+9.9 11+8.7 11+7.3 li+7.3 11+7.8 11+8.2 1U8.U 1U8.8 12 131.2 131.2 133.0 133.0 132.2 132.2 132.1 132.1 132.U 8 ll+O.O 139.1 135.2 133,5 132.1+ 131.U 131.2 131.2 131.2 11+ 132.7 133.6 133.1+ 133.5 133.6 133.6 133.6 133.5 133.6 6 11+5.0 7 11+1.0 13 125.8 Room Temperature Steam temperature Air i n l e t temperature Orifice upstream pressure Table XI Data for Run No. 8 78°F 222°F 112°F Barometric pressure Steam pressure Air outlet temperature 752.8 mm.Hg U.O psig 17U°F Orifice differential pressure 7.1" CENTRAL UNIT CELL POSITIONS Thermocouple Position No. Temperatures (°F) at distances from centre -1" -3/U" -1/2" -1/U" 0 1/U" 1/2" 3/U" 1" 1 11+1.2 11+1.1 138.9 138.9 138.9 138.3 139.2 139.7 1U0.8 5 1U5,0 ll+U.7 li+2.0 ll+U.7 139.2 139.3 139.3 139.3 139.3 15 1UU.5 llt2.lt 11+1.9 11+1.3 1UU.2 11+1.0 11+1.6 11+1.6 11+1.7 12 12U.D 123.0 122.0 121.9 121.9 123,2 123.0 12U.1 12U.1 8 126.0 125,1 125.2 125.7 123.3 122*5 122,5 122.5 122.9 l U 127.0 127.0 125.1+ 125.U 126.1 12U,8 123,7 123.5 123.1 6 136.8 7 131.0 13 117.3 Room temperature Steam temperature Air inlet temperature Orifice upstream pressure Table XII Data for Run No. 6 8l°F 22U°F 1160F 12.2" Barometric pressure Steam pressure Air outlet temperature 75U.0 mm.Hg U.3 psig 177°F Orifice differential pressure 7.7" Thermocouple Position No. CENTRAL UNIT CELL POSITIONS Temperatures (°F) at distances from centre -1" - 3 A " -1/2" - l / U " 0 l A " 1/2" 3/U" l " 1 1UU.0 1UU.9 1UU.6 11*5.2 lUU.7 H*l*,7 H*5.o 1U5.0 1U5.0 5 150.0 1U9.2 11*7.2 11*7.2 11*5.3 11*5.1 il*5.o 1U5.0 1U5.0 15 1U9.6 11*8,7 11*7. U 11*7.1* 11*6.1 11*6.1 ll*7.U 1U7.U 1U7.U 12 130.5 130.7 131.0 131.0 131.0 131.0 132.2 131.7 131.7 8 138.3 138.2 137.2 13U.8 131*. 7 133.1 131.6 130.8 131.0 111 13U.0 133.1* 133.1 133.1 132.9 132.0 133.1 133.1 132.5 6 11*3.5 7 138.0 13 125.0 Table XIII Data for Run No. 8 to check Symmetry across Heat Exchanger Thermocouple Position No, -5-3A" -5" -k" -3" -2" -1" 1 11*5.8 151.0 11*5.0 11*1.0 11*1.0 156.1 2 ll*6.l 11*7.3 11*9.8 160.5 153.1 162.8 3 11*7.5 151.2 151.2 157.0 151.6 150.8 1* 15U.1 159.9 156.1 156.1 150.2 11*7.1 5 160.2 16U.8 159.6 159.0 15U.0 152.0 6 155.7 162.2 159.8 155.1 152.1 11*9.0 7 152.9 158.0 151.5 152.6 11*5.3 11*2.3 8 11*9.8 159.0 150.2 151.2 137.0 133.5 9 11*0.8 11*1.9 11*1.7 139.3 131*. 7 130.9 10 135.8 137.3 137.6 138.0 138.0 136.6 11 131.7 132.5 132.6 135.1* 131+.7 138.0 12 131*. 0 135.0 130.0 127.9 121*. 0 122.0 13 129.7 130.9 125.6 123.0 119.0 120.2 Ik 138.7 139.5 139.9 11*1.5 137.0 136.8 15 11*8.5 152.9 153.7 11*9.8 11*9.8 11*1*. 9 0 1" 2" 3" 1*" 5" 5-3/U1 11*3.7 11*1*. 2 11*5.9 166.0 155.1 169.3 152.2 150.1 166.5 11*9.0 161.0 li*U.O 138.8 139.9 11*5.1 11*5.6 11*1.0 11*5.0 11*1.9 139.6 138,0 11*1.7 11*1.0 11*0.3 11*2.5 11*0.5 11*2.8 11*1.1* 1U1+.8 11*1.7 11*1.0 ll*l*.0 11*2.5 11*5.0 11*1.0 11*2.9 138.5 137.5 138.5 139.7 139.7 139.5 136.0 132.9 131.6 132.1* 133.9 133,9 131.0 128.1 128.1 125.5 125.5 127.5 127.5 127.5 126.9 126.9 126.2 129.8 129.8 126.2 126.2 130.8 130.3 132.0 135.U 132.1* 130.2 129.8 133.2 11*8.8 133.1 11*7.3 13U. 2 132.3 131.6 123.1* 126.9 130.9 135.0 136.1 136.5 135.9 117.6 118.3 123.0 136.0 135.3 135.0 133.5 128.1 125.8 125.8 128.0 128.8 133.8 133.5 l l * l* . l 11*5.5 11*2.0 11*2.1* 11*2.8 11*7.0 11*6.3 Table XIV Data for Run No. 9 to check Symmetry across Heat Exchanger Thermocouple Position No. Temperatures (°F) at distances from centre - 5 - 3 A " -5.. -1*» -3" -2" -in 0 1" 211 3" i*» 5" 5-3A' 1 171.9 186.9 180.1 180.1 176.2 177.0 nk.k 172.6 171.5 180.9 178.1 182.1 177.7 2 17U.6 178.1* 17U.7 186.2 182.7 189.7 185.0 190.1 185.7 187.9 179.8 172.9 170.0 3 179.6 198.0 182.7 196.5 183.8 198.1 180.8 198.1* 181+.0 199.0 180.8 179.2 173.9 1* 179.3 183.9 183.3 186.0 , 177.9 177.9 176.7 180.0 176.7 183.2 176.9 189.2 176.8 5 181.1 190.1 186.0 187.0 181.8 182.2 17U.0 172.8 170.0 176.9 175.3 179.2 17U.0 6 177.7 182.0 180.7 183.5 177.9 178.1 169.9 165.0 162.0 168.8 168.8 171.9 171.9 7 170.6 nk.k 17U.6 177.5 170.9 170.5 I60.I* 159.8 155.8 159.8 160.6 161.0 162.0 8 157.5 I59.il 162.7 173.1 163.1 158.5 11*9.5 11*7.5 11*5.5 159.5 157.5 167.0 162.8 9 15U.0 15U.6 160.0 167.O 156.8 151.3 11*9.5 153.5 153.5 160.3 159.5 159.3 158.1* 10 161.9 167.0 162.1 166.0 16U.1 163.O 161.3 166.1 163.0 177.7 167.9 175.0 165.0 11 173.2 165.0 161.1 162.0 166.0 171.5 171.5 175.U 168.0 171.6 166.2 162.0 161.2 12 165.9 171.8 163.8 157.0 151.6 152.9 150.1* 151*. 0 155.8 160.6 161.8 161.8 162.0 13 156.0 165.1 159.0 153.0 l l * l * . 0 11*6.0 135.3 136.0 11*1.9 161.2 157.8 159.8 159.8 Ik 159.6 159.6 160.6 168.6 158.1* 162.9 150.0 150.0 150.1* 15U.0 I 6 i . 0 168,9 165.0 15 175.6 179.5 177.0 192.9 175.0 189.0 17U.9 193.8 176.7 181.3 178.5 193.6 180,3 Table XV Data for Run No. 13 to check Symmetry across Heat Exchanger Thermocouple Position No, Temperatures (°F) at distances from centre -5-3/1*" -5.. -1*« -3" -2" -1" 0 1" 2" 3" 1*" 5" 5-3/1* 1 189.2 198.2 197.7 199.0 197.U 200.1 199.8 206.9 202.9 209.1 203.2 202.1* 197.1* 2 193.6 191.1* 19l*.l* 199.0 199.2 199.6 199.1* 201.1 202.2 202.8 201.2 194.0 189.0 3 190.0 198.9 198.0 203.1* 199.5 205.8 203.2 209.0 203.1 211.0 208.0 202.2 198.0 1* 191.5 198.9 198.9 205.1 200.2 200.2 199.0 201*. 5 202.8 207.9 206.0 207.8 199.9 5 190.0 198.0 196.1 203.2 200.2 201.0 199.2 207.0 203.0 209.7 201+.1* 208.5 200.5 6 182.7 187.2 192.0 195.0 196.8 196.5 196.5 195.3 195.0 198.0 199.0 200.8 200.1* 7 180.1* 185.2 189.0 19U.7 192.9 191.1 188.2 188.7 186,1 188.7 189.5 189.9 186.1 8 175.2 180.5 182.3 189.1* 180.6 180.0 175.1 175.1 173.5 189.2 169.2 163.7 162.5 9 17U.5 176.6 180.5 186.5 176.9 175.2 178.5 180.3 176.2 176.6 I69.O 166.1 161*.8 10 179.0 182.7 178.7 182.7 181.3 178.7 181.3 190.8 183.0 191.0 185.8 185.3 175.0 11 182.5 178.2 176.9 175.0 181.0 181.1* 187.0 186.0 186.8 182.5 178.7 170.1 171.8 12 179.3 185.7 180.8 181.8 178.3 180.0 177.8 179.0 177.3 185.1 179.7 181.5 175.1 13 169.0 171.2 163.9 165.9 159.2 168.7 155.2 155,2 158.0 177.0 175.0 178.6 173.9 l l * 167. 1* 170.8 175.8 189.2 177.1 178.3 175.1 179.5 177.2 180.5 180.0 190.0 183.1 15 187.0 191.0 196.1 205.9 201.8 208.2 203.0 203.3 200.2 202.9 199.9 208.9 202.5 50 F I G U R E 4, Plot of J2L0L Vflyg .05Q_a • L503I L2725 1.4033 0.7912 1.0777 1.2600 0.4436 0.8604 1.1077 0.1313 0.6833 0.9902 1.5709 12 1.5389 10 1.4491 inches 0.6140 0.9454 -> 8 10 12, 8 1.3221 6 1.1894 4 1.0886 2 1.0509 0 / 12 12 F I G U R E 5 . Correlation of d a t a of I n a y a t o v 8» M i k e e v (8) 

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