1、RESEARCH MEMORANDUM EXPERIMENTAL HEXT -TRANSFER AND FRICTION COEFFICIENTS FOR AIR FLOWING THROUGH STACKS OF PARALLEL FLAT PLATES By Eldon W. Sams and Walter F. Weiland, Jr. Lewis Flight Propulsion Laboratory C leveland, Ohio NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS WASHINGTON August 19, 1954 Prov
2、ided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-WCA RM E54Fl.l N ATION AEFiONAUTICS FOR AIR FLOWING TELROUCIH STACKS OF PARAILEL FLAT PLATES By Eldon W. Sams and Walter F. Weiland, Jr. An investigation is being conducted at the NACA Leuis laboratory to o
3、btain forced-convection heat-transfer and pressure-drop data for flaw d I of air between electrically heated parallel flat plates stacked to form 5 passages of short.length-to-effective-dia?neter ratio. Two such stacks of plates were alined in series in the direction of air flow, with a 1/4-inch spa
4、cing between plates in each stack. Data were obtahed for three gap spacings betweeri stacks of 1/32, l/8, and 1/4 inch, as well as for various degrees of plate misalinement between stacks, and also with the upstreamstack removed frm the tugnel. The primary purpose of the investigation is to determin
5、e the interference effects of the upstream stack of platee on the heat-transfer and friction character- istics of the downstream stack. Data were obtained over a range of Reynolds number frm 15,000 to 80,000, average surface temperatures fram 661 to 683 R, heat fluxes up to 8080 Btu per hour per squ
6、are foot, inlet air temperature of about 518O R, and inlet pressures up to 45 inches of mercury absolute, and with heat addition to the downstream stack only. The average and local heat-transfer coefficients obtained for the downstream stack with the two stacks alined were slightly higher than the v
7、alues predicted frm-established data on round tubes for the length-diameter ratio used herein. Also, the effects of changes in plate misalinement and gap spacing between stacks were found to be neg- ligible. The friction factors for the upstream stack, when fu,Uy cor- rected for nonfriction losses a
8、nd length-diameter ratio effects, were in good agreement with data for smooth round tubes; for the downstream stack, the friction factors were lower than those for smooth tubes when a uniform velocity profile at the entrance was assumed, and higher than those for smooth tubes when a fully developed
9、velocity profile at the entrance was assumed in the correction of the data for entrance effects. Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-2 NACA RM EWll The present investigation was undertaken heat-transfer and pressure-drop data for.fluw to
10、obtain forced-convection of air between electrically heated parallel flat plates forming passages of short length-to-effective- dimeter ratio. More specifically, the progrAuiwa6 designed to provide these data fpr successive stacks of plates herein the effects of such configuration variables as dista
11、nce between parallel plates, gap spacing between successive stacks, and degree af misalineaent between plates in successive stacks are to be evaluated for a range of Reynolds numbers, plate surface temperatures, and heat fluxes. These data are of interest in the design of heat exchangers of sim- ila
12、r geometries (and plain or interrupted surfaces), where advantage can be taken of the increased-heat transfer associated with flow in passages of short length-diaueter ratio. In addition to average heat-transfer values, the design of heat exchangers may require a more detailed knowl- edge of local s
13、urface-tenperatme gradients or limiting local tempera- tures, in which case recourse must be made to local heat-transfer values. Both local and average heat-transfer coefficlents a.re reported herein. In the present investigation, heat-transfer and pressure-drop data were obtained for two stacks of
14、parallel flat plates with a 1/4-inch spacing between plates in each stack, various de rees of plate misaline- ment, and various gap spacingsl1/32., .:i18, Fd 174 in. between stacks, as well as with the upstreari stack removed. %e data reported herein- were obtained with heat addition to the damstrea
15、m stack only. Data were obtsined over a range of Reynolds numbers from 15,000 to 80,000 , average surface temperatures from 661 to 683O R, heat fluxes up to 8080 Btu per how per square foot, an inlet air temperature of about 518O R, and inlet pressures up to 45“ inches of mercue-Xbsolute.- “- - . “.
16、 . “ “ The results are presented herein in the form of curves of average values of a Nusselt-Prandtl number relation (Nu/Prom4) against Reynolds number, of local heat-transfer coefficients and plate temperatures against distance from leading edge of plate, apd of average friction factors against Rey
17、nolds numher. - . . . . . . . .“ “ APPARATUS Air and Electrical Systems A schematic diagram of the test section and related components of the air and electrical systems used in this investigation is shown in figure 1. . Provided by IHSNot for ResaleNo reproduction or networking permitted without lic
18、ense from IHS-,-,-NACa RM E54FU. 3 04 0 3 0 P cd Air system. - As indicated in figure 1, air at IlO pounds per square inch gage passed through a pressure-regulating valve, a filter, and an orifice run consisting of an air straightener and an A.S.M.E. type flat-plate orifice where the air flaw was me
19、asured before entering the test section. The air then passed through the test section which consisted of an approach section, the two stack8 of electrically heated flat plates, and a three-pass mixing tank having a thermally insulated approach, after which the air discharged to the atmosphere A wind
20、ow and light source were provided upstream of the test section for visual observation of the flat plates during testing. The temperature of the air entering the test section was measured by an iron-constantan thermocouple upstream of the approach section; the temperature of the air learing the test
21、section was stmilarly measured by two themocouples just dawnstreem of the mixing screens in the mixing tank. Electrical system. - Provisions were made for electrically heating both stacks of flat plates, although only the damstream stack was heated for the data reported herein, the electrical system
22、 for each stack being separate and independently controlled (see fig. I). Electric power was supplied to each stack through a variable transformer and a pmr trans- former, the latter being connected by flexible cables to bus bars which were fastened to the two outer plates (top and bottam) of each s
23、tack; the plates in each stack were connected in series. The capacity of the electrical equipment for each stack was 12 kilovolt-amperes at a maximum of 12 volts across the stack. Test Section Installation figure 2(a). The in a steel tunnel . - A schematic diagram of the test section is sham in two
24、stacks of flat plates were independently mounted provided with micrometer screws to permit vertical movement of the stacks for plate alinement and misalinement between stacks. The two stacks could be separated by 1/32-, 1/8-, or 1/4-inch- thick transite spacers having a 2- by 3-inch opening in the c
25、enter. Similar spacers of 3/4-inch thickness were provided before the upstream stack and after the downstream stack, with a high-temperature rubber gasket recessed into the spacer to provide an air seal between stack and spacer. Transite plates (not shown) running the length of both stacks were prov
26、ided between the stack and tunnel side walls with sufficient clearance to allow vertical movement of the stacks; these transite plates were grooved vertically to allow plate instrumentation leads to be brought up the side of the stack. A wooden approach section (24 in. long with 2- by 3-in. opening)
27、 ha- a rounded entrance was located before the upstream stack. A three-pass mixing tank was located after the downstream stack; the mixing-tank approach section was,thermally Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-4 NACA RM E54FU . insulated
28、 and contacted a rubber gasket in the rear spacer. Two screens were provided in the mixing tank center passage for thorough mixing of air ahead of the exit air thermocouples. * The two stacks of plates tested were identical, one such stack being shm in more detail in figure 2(b). The stack consisted
29、 of nine flat plates stacked vertically with a 0.25-inch spacing between plates. This spacing was provided by either one 1/4-inch or two 1/8-inch spacer strips running the length of the plates along either side. The strips (conductors or insulatwrs) were Btacked in such a manner as to provide . an e
30、lectrical 6eries connection between plates. An insulator plate and a steel support plate were provided Over the two outside plates in the stack (fig. 2(a), the entire stack being clamped together by four in- sulated bolts through the stack. The bus bars supplying electrical pow- er to the plates wer
31、e silver-soldered to the conductor strips of the two outside plates in the stack. Bosses which were provided on the bottom support plate of the stack-rested on micrameter -screws fastened to the bottom tunnel wall, thereby pr it also provided seals for the bus bars leavtng the tunnel and fittings fo
32、r insertion of probes into the spacer openings. Evaluation of average plate and stack temperature. - As previously indicated in figure 2(c), thermocouples were located down the center line of the plate at Wrlous distances from the plate leading edge with a similar row of thermocouples dong a line 3/
33、4 inch from the center line toward either side of the plate. The plate temperature gradients normal to the direction of air flow were found to be small campared to gradients in the flaw direction; therefore, the temperature gradient for the plate ch be well represented by plotting the plate center l
34、ine tem- perature against distance frm-the leading edge. The gradients for each plate in the stack were plotted in tMs manner; where center line ther- mocouples were not available (see fig. 2( c , the average of the two side row thermocouples was used. The average temperature for each plate was then
35、 obtained by dividing the measured area under the curve of the plate center line temperature against distance from leading edge by the plate length. The average surface teqerature for the entire stack was then taken as the arithmetic average of the various average plate tem- peratures weighted accor
36、ding to the surface area exposed to flow. (The two outside plates were exposed to flow on one side only.) Average heat-tranefer coefficients. - The average heat-transfer co- efficient for the stack was computed from the relation (symbols me de- fined in appendix A : The average bulk temperature %,av
37、 was taken as the arithmetic average of the inlet-air and exit-air total temperatures, TI and T4, respec- tively. The heat-transfer surface area S was taken as the total sur- face area of the plates exposed to flow. The exposed surface area con- tributed by the spacer strips between plates is not In
38、cluded, but would have a negligible effect on h. The values for physical properties of air used herein are presented in figure 4. Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-6 NACA RM E54Ell Local heat-transfer coefficients. - Local heat-transfer
39、 coeffi- cients for the center plate (plate 5) in the stack were evaluated in the following manner. The local heat-transfer coefficient at any dis- tance fram the leading edge was .taken as Tb, Z was assumed to vary linearly with X (distance from plate leading- edge) between T1 and T4; Ts, was obtai
40、ned from the plot of local plate temperature against X as explained in the previous section. This curve was also used to evaluate Pz/Pav in equation (Z in the following manner: Inasmuch as the voltage drop across the plate is es- sentially constant at any distance franleading edge X, and since heat
41、conduction along the plate cm be neglected, the local parer generatian at any point X is given by - . “, I . . . . pZ = E/R; = C/rt That is, the local power generation at .any point (distance X from leading edge) in the plate is inversely proportional to- the electrfcal resistivity r at the point; h
42、ence frm a curve of electrical resis- tivity r against temperature for the plate material. ad the curve of cr plate. By gFaphically integrating this . curve to obtain l/rav, the ratio of l/rZ to l/rav (which also represents Pi/Pav) was then plotted against distance from leading edge X. The local hea
43、t-transfer coefficients hz for the number 5 phte could-then be camputed fram equation (2) and plotted against X. *s, 2 against X, a curve of l/rz against X was plotted for the , - . . - . - Average friction coefficients. - The method used for computing the average friction coefficients for the ndivl
44、dii stacks is as follows: The friction coefficients. are based .on measure and QCom = while for complete misalinement, the upstream stack was moved by one-half the distance between plates. - . “. RESULTS AND DISCUSSION Plate Tenperature Gradient6 Typical plate temperature gradients obtained for the
45、dawnstream stack are presented in figure 5, where local surface temperature T,b is plotted against distance from plate leading edge X. The plates are numbered from top to bottam of the stack, but are listed in an order of smetry starting from the center.plate and movtng toward the outer top and Eott
46、om plates. The curves for the three ten- termost plates are essentially coincident, while the next two plates on either side of the three centermost plates show slightly higher terqpeya- tures at the trailing edges. The curves for the two outside plates fall considerably above the other curves, part
47、icularly at the trailing edge; this would be expected inasmuch as the top and bottom plates are cooled on one side only ( se6 fig. 2 (a) ) . The dashed lines, for the four outer- most plates, represent an approximation of-the temperature gradient, since thermocouples were located only at the leading
48、 axid trailing edges of these plates. The average plate and stack temperatures were obtained from these curves as indicated in the section METBaD OF CALCULATIOR. i -. d “ - - . .“ . Heat-Transfer Data Average heat-transfer caefficients for- stack - The .average heat- transfer coefficients obtaFned f
49、or the dawnstream stack are presented in figure 6 where tbe Nusselt-Prhdtl mer - relation -. . NU/P. is L plotted against Reynolds number DeG/pb. Included for comparison is “ . . .“ . .- Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA RM E54Fll 9 the McAdams line (solid) which was found to best represent the data of various investigators (ref.
