1、*” - ”* RESEARCH MEMORANDUM * MEASUREMENT OF HEAT-TRANSFER AND FRICTION COEFFICIENTS .- FOR FLOW OF AIR IN NONCIRCULAR DUCTS AT HIGH SURFACE TEMPERATURES By Warren H. Lowdermilk, Walter F. Weiland, Jr., and John N. B. Livingood Lewis Flight Propulsion Laboratory Cleveland, Ohio NATIONAL ADVISORY COM
2、MITTEE FOR AERONAUTICS WASHINGTON January 25, 1954 - Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA *FlM E53 507 * NATIONAL ADVISORY COMMITWZ FOR AERONAUTICS FOR FLOW QF AIR IN BONmULAR DUCTS AT HIGH By Warren E. Lardermilk, Walter F. Veiland,
3、Jr., and John N. B. Livingood 7 Measurements of average heat-transfer and friction coefficients 3 were obtained with air flawing through electricslly heated ducts square, rectangular (aspect ratio, 51, and triangulsr cross sections for a range of eurface terqerature from 5400 to 17800 R and Reynolds
4、 number frm lo00 to 330,000. The results indicate that the effect of heat flux on correlations s of the average heat-transfer and friction coefficients is similar to that obtained for circular tubes in a prevfous investigation and was - nearly eliminated by evaluating the physical properties md dens
5、ity of the air at a film temperature hEtlfway between the average surface and fluid bulk temgeratures. With the l?usselt and Reynolds numbers based on the hydraulic diameter of the ducts, the data for the non- circular ducts could. be represented by the same equations obtained in the previous invest
6、igation for circular tubes. Correlation of the average difference between the surface corner and midwall temperatures for the square duct was in agreement with predicted values from a previous analysis. However, for the rectangu- lar and triangular ducts, the measured corner temperature was greater
7、by approxima,tely 20 and 35 percent, respectively, than the values pre- dicted by analysis. An experimental investigation was imtituted at the NACA Lewis laboratory to obtain heat-transfer and related pressure-drop informa- tion for air flowing in tubes at hfgh surface and fluid temperatures. The ef
8、fects of such variables as surface temperature, inlet-air Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-2 NACA RM E53507 temperature, length-to-diameter ratio, and tube-entrance configuration on heat transfer and pressure drop in smooth round tube6
9、 are summarized in reference 1. The scope of the general investigation is extended herein to in- clude the effect of flow-passage shape on heat-transfer and friction coefficients for sir flowing through electrically heated square, tri- angular, and rectangular tubes at high heat-flux conditions. Dat
10、a were obtained for a range of Reynolds number fram 1000 to 330,000 and surface tenrperature frau 540 to 1780 R, and the results are compared with those of reference 1 for circular tubes. Arrangement of Apparatus A schematic diagram of the heater tubes and associated equipment is shown kl figure 1.
11、The experimentd. setup is the same as described in reference 1. Campressed air is supplied through a pressure- regulating valve, a cleaner, and a surge tank to a second pressure- regulating valve where the flow rate is controlled. From We valve, the air flaws through a bank of rotameters into a thre
12、e-gas6 mixing tank, through the test secticm, and into a second mixing tank frm which it is discharged to the atmosphere. . Electric power is supplied to the heater tube fram a 208-volt, 60- cycle supply line through an autotransformer and a 14:1 pawer trans- former. The low-voltage leads of the par
13、er transformer are connected to the heater-tube flanges by copper cables. The capacity of the elec- tric equipment is 15 kilovolt-amperes. d Three different 24-inch-long cross-sectianal shapes, a8 sham in figure 2 - square, equilateral triangle, and rectangle - were investi- gated, the inner dimensi
14、ons of wbich were as follows: shape in. Length to hydraulic- Hydraulic Peraeter, in. dim. ratio dim., Square 57 .42 3.0 Rectangle 53 .45 2.31 Equilateral 53 0.45 1.80 triangle N 3 D Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA RM E53J07 3 B T
15、he test sections were fabricated frm Inconel sheet stock with a thickness of 0.031 inch. The test-section sides were cut to the desired with a heliarc welder. The excess weld material was ground off so that the corner wall thickness did not exceed 1/32 inch. The inner corners of the test sections we
16、re shsrp and even along the entire length of the test section. Steel flanges welded to the test sections at each end provided electric contact with the transformer leads fran the parer supply. channels were milled in the outer faces of the flanges to min-fm-lze end heat losses, and the test sections
17、 were thermally Insulated. 4 dimensions and clamped on ground-steel forms; each corner was welded Eo . Outside-wall temperatures were measured at 13 stations along the length of the test sections (fig. 21 with chramel-alumel thermocouples and a self-balancing indicating potentiometer. At each statio
18、n, ther- mocouples were located at the center of each side, except for the rec- tanguhr test section, where the themocauples were dtted on the short sides. Thermocouples were also.located at each corner at the three sta- tions located 3, 12, and 21 inches fram the entrance. Static-pressure tap were
19、located 1/8 inch from the entrance and exit of each test section, and each section was fitted with a long- radius nozzle the throat dlmensions of which matched the cross-sectional dimensions of the test section. Range of Conditions * Heat-transfer and associated pressure-drop data were obtained with
20、 the square, the equilateral triangular, and the rectangular test sec- tions with rounded entrances over a range of Reynolds number from loo0 to 330,000, average outside-wall temperatures fram 540 to 1780 R, and heat-flux densities up to 120,000 Btu per hour per square foot of heat- transfer area. S
21、YMBOLS The following symbols are used in this report: A cross-sectional area, sq ft cp specific heat, Btu/(lb)f?F) 1 D inside hydraulic diameter, Perimeter, 4A ft- E voltage drap across test section, v b Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-
22、,-4 f ff G Q h I k k* L NU Pr P 4 82 R Re S 8* T % Tf TS NACA RM E53J07 average friction coefficient modified film friction coefficient mass velocity, lb/(hr) (sq ft) acceleration due to gravity, 4.17X108 ft/hr2 average heat-transfer coefficient, Btu/(hr) (sq ft) (9) current flaw through test sectio
23、n, amp thermal conductivity, Btu/(hr) (sq ft)(%/ft ratio of thermal conductivity of wall material to coolant length of test section, ft Nusselt number, hD/k Prasdtl number, cpp/k static pressure, lb/sq ft abs over-all static-pressure drop acrdss test section, lb/sq ft heat loss from test section ta
24、surroundings, Btu/hr gas constant, 53.35 ft-lb/(lb) (?El) Reynolds number, pVD/p heat-transfer area of test section, sq ft ratio of wall thickness to hydraulic diameter total temperature, OR average fluid bulk temperature, average fluid film temperature, average surface temperature, T, n Y “ Provide
25、d by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NaCA RM E53507 5 t static temperature, OR v velocity, ft/w w flow rate, r ratio of specific heats r) cr absolute viscosity, lb/(hr) (ft 0, I+ m P density, lb/cu ft Subscripts: av average b bulk (when applied t
26、o properties, indicates evaluation at average bulk temperature, % 1 C peripheral location at corner of test section f film (when applied to properties, indicates evaluation at average fihn temperature, rf) fr friction m peripheral location midway between corners of test section S surface (when appli
27、ed to properties, indicates evaluation at average surface tqerature, T,) 1 test-section entrance 2 test-section exit RESULTS AND DISCUSSION Heat Balances Heat balances for each test section are shown in figure 3, where the electric heat input minus the heat loss determined for condition of no air fl
28、ow through the test section is plotted against the rate of heat transferred to the air as determined by air-flow rate and temperature measurements. The heat balances obtained at low heat in- puts and correspondingly low flow rates were very poor. In this re- gion the air temperature at the exit of t
29、he test section could not Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-6 NACA RM E53507 be measured accurately, because the very law velocities in the outlet temgerature mixing tank prevented the attninmeat of equilibrium cod- tims in the mixing t
30、ank. The heat balances- imprcwed rapidly with increase in flow rate, and for values correspond.lng to turbulent flow in the test sections the data are in agreement wlth the match line (solid). The heat-transfer coefficients presented in reference 1 for round tubes, with which the present data are co
31、mpared, were calculated from the flow rate and tem- perature rise of the air measurements; hence, for consistency the pre- eent data are calculated in a similar manner for flow ratee correspond- ing to Reynolds numbers of 10,000 or greater. For lower flow rates, the electric heat-input and heat-lOSS
32、 measurements were belleved to be more accurate than the measured outlet-air temperature. Therefore, the heat-transfer coefficients for Reynolds*nunibers less than l0,OOO are calculated from the electric heat-input and heat-loss measurements. Correlation of Heat-Transfer Coefficients The average hea
33、t-traasfer coefficient h was ccmrputed frm the experimental data by the relation where (3.415EI - Q,) T2 = T1 + CP,b for %I T1 Reynolds numbers less than 10,000. The bulk tenrgerature of the air was taken as the arithmetic mean of the temgeratures at the entrance and the exit T2 of the teat sections
34、. The average surface tem- perature Ts was taken as the arithrmetic mean of the average outside corner temperature and the average outside midwall temperature. The temperature drop through the wall was neglected. The physical properties of air used in calculating the Nusselt, Reynolds, and Prandtl n
35、umbers are the sane 8s those used in reference 1, wherein the viscosity and specific heat were baaed on values reported in reference 2, and the thermal conductivity was assumed to vary a0 the square root of temperature. The results presented in reference 1 for turbulent flow in circular tubes indica
36、te that the average Nusselt number decreases progressively Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA RM E53J07 7 as the ratio of surface to fluid bulk temperature increases when the effect of the ratio of surface to bulk temperature was el
37、iminated by evaluating the prcqerties of the air, including the density term in the Reynolds number at the film temperature, defined a6 the arithmetic average of the surface and bulk tqeratures. The data for Reynolds numbers greater than 10,000 were well represented by the following relation: .I flu
38、id properties are evaluated at the fluid bulk temperature. The The average heat-transfer coefficients obtained herein for square, rectangular, aSa triangular ducts for a range of Reynolds nmiber from lo00 to 200,000 and ratios of surface to bulk temperature from 1.2 to 2.3 are correlated accordingly
39、 in figure 4. A solid line representing data obtained in reference 1 with a circular test section having a length-to-diameter ratio of 60 for similar conditions is included for line represents equation (2); for der Reynolds nunibers the refer- ence line represents the data of reference 1 reccaquted
40、on the basis of the electric heat-input and heat-loss measurements for purposes of camparison. The data for the square tube (fig. 4(a) agree well with the reference line for all surface to bulk tmrperature ratios and Reynolds nmibers. For the rectangulsr duct hang an aspect ratio of 5, the data (fig
41、. 4(b) are considerably higher than the reference -e for Reynolds numbers fm 1000 to l0,OOO are represented by equa- tion (2) for Reynolds nllnibers above 2500. The higher dues are in agreement WJth data obtained for noncircular ducts at lower heat fluxes by other Fwestigators. These data indicate t
42、hat use of the hydraulic diameter does not result In correlation of data for various passage shapes in the laminar and transition flow regions. For Reynolds nu- bers abwe 40, OOO the data fall slightly belaw the reference line. ccrmparison. For Reynolds nunibers greater than 10,000, the reference m.
43、 In figure 4(c), the average heat-transfer coefficients for the trimgular duct vary similarly to those obtained far the square duct. For Reynolds numbers abwe 10,OOO the data were lmer than the reference a slope of 0.78 rather than 0.8. This difference in slope is also noticeable in figure 4(b) for
44、the data of the rectangular duct for n line by 5 to 15 percent and could best be represented by a line having “ high Reynolds nmibers. This variation in slope could be eliminated Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-8 NACA RM E53307 by def
45、ining the average surface temgerature as the midwall temperature instead of as the arithmetic average of the corner and midwall tempera- tures. For example (as is shown in fig. 7), the difference between the average Surface and the average midwall teqeratures for the triangular tube is 3 percent of.
46、the difference between the average midwall tempera- ture and the fluid bulk temperature for a Reynolds number of lO,OOO, and ll percent for a Reynolds nuniber of 100,000. Evduating the average heat-transfer coefficient on the basis of the difference between the midwall and fluid bulk temperatures wo
47、uld result in a correspondfng increase in the average heat-transfer coefficient and, hence, would bring the data into agreement with the reference line for circular tubes. Measurements of the variation in rate of heat transfer around the periphery of noncircular ducts are required in order to define
48、 the average surface temperature for evaluating the average heat-transfer coefficient. Correlation of Friction Coefficients The method of calculating the average friction coefficient is es- sentially the same as described in reference 1, wherein where 4fr ff = D a3 L pfvb2 4“ and The subscripts 1 an
49、d 2 refer to positions xi.- the ducts, located 1/8 inch from the entrance and exit end8 of the ducts, respectively. For Reynolds numbers less than 10,000 the exit static temperature t2 is based on the value of the exit total temperature T2 determined from the electric heat-input and heat-lose measurements, as ms men- tioned in the precedhg section. f Pro
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