Full report

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NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS ~;~7-~~L2 WWNEDFRO}tiL;37i REMCWZD FF?OM f.,]‘3Ww ————————— No. 1054 ——— —_____ HEAT TRANSFER AND HYDRAULIC FLOW RESISTANCE FOR STREAliS OF HIGH ‘VELOCITY By V. L. Lelchuk Journal of Technical Physics vol. IX, Noa 9, 193q Washington December 1943

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: Illlllllllllillmmilllllllllll 31176014415120 ——. ____ NATIONAL ADVISORY -COMMITTEE FOR AERONAUTICS ~ ——. — !l!EGHNIG~- MEMORANDUM N(3* 1054 - .“ -—-. . .. , ,. — ., ,., . AfiD ‘HYDRAULIC, ., FLOW RESI STANCE HiAT TRANSFER’ .J - ,, FOR,. STREAMS OF HIGH VELOCITY* -, ., By Vc L- Lelchuk “ ‘ ,. >- ., SUMMARY -, -“’ Problems of hydraulic flow resistance and heat transfer for streams with velocities comparable with acoustic have present great importance for various -’ fields of technical science. Especially, they have great importance for the field of heat transfer in designing and constructing boilers.of the ~Veloxll type. In this article a description results as ‘regards definition of experiments and their of the laws of heat transfer in differential form for high velocity air streams inside smooth tubes are given, ,, ,, EXPERIMENTAL APPARATUS AND PROOIIDURE ,, !. -’General Scheme of Experimental Apparatus ; ‘ ., . and Experimental .’ .. Section ,.. The general scheme of experimental apparatus is shown in figure 16 The air came in from” the compressor into the apparatus through the large surge tank B, which has the purpose of, removing the pulsations and separating the water fog. The orifice D was installed to’ measure the air flow rate and the air passing through .,, was directed into’ a zig zag conduit P inside of which there was an electric heater. The heated air passed through the mixing section of the pipe G into the ex- ‘ perimental tube A“ where it lost a ‘part of its heat to ..,.;. . .,.. .. ,,., .A — .. =s--...—--.— ----- ——-. --— .— ..-— “*Jour. ~echt ~hys.( USSR), vol. .1X, no. 9, ,lq39, pp. 808-818. NOTE: Translation receivqd from Massachusett s, Institute of ~Technology, “Cambridge, Massh. ‘ :.

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‘, , ‘NACA “Techn’ic(alMemorandum No. 1054. 2 cooling water which fl’owed”through” the casing around the experimental tube, losing its pressure and expanding up atmospheric exhaust pressure. The air to the limit of discharged from the experimental section at high velocity which approached acoustic velocity- The experimental secti’on is shown in figure 2. A l+millimeter inside diameter and smooth copper tube of 16-millimeter outside diameter by 1431–millimeter length was placed axially inside a brass tube 19,8-millimeter inside diameter, The heated air flowed with high velocity through the inside tube and the cooling water flowed in the annular space. Transition from the large pipe to the experirr.ental tube was accomplished smoothly%y means nozzle, A length of 21 millimeters of a slowly converging at the exhaust end of the experimental tube was given a diverging oonic shapes considered as a nozzle, Thus the experimental tube may be first converging and then after a long narrow throat, enlarging again. li’lowvelocities as hfgh as acoustic velocity and corresponding pressure relations were achieved the cylindrical section at the point of transition from to the conic section. By this means the opportunity to make relatively easy all measurements, including even those in the acoustic region were obtained. The air pressure was measured at a number of experimental section. !l?hetemperatures points al,ong tbe of the inside wall of the air tube as well as those of the cooling watie,r,wer,ealso measured along the flow. In the experimental tube 9 static pressure tops of 0c08-millimeter diameter were loc:ated to measure the changes in static pressure as the fluid flowed through the tube, In order to eliminate roughness formed by boring the pressure tas a special drill by which side the tube was made, ,the burrs were cut off from in- ., Af$er the holes were-made and the pressure taps attacked. the transverse section of the tube and its vari-ati-on all along the length..was measured by gradually filling,.th,e tube with mercury in the section between two pres-sune taps and weighing the .roercur.y.-.The measurements’ showed that the diameter uniform all along. The of the tube was sufficiently average ,inside area of a tran-sverse section of t,he tube-was 155.3 square millimeters ‘and the me-an diameter 14*O7 mill.imetersa A% seven oints in- the outside wall’ o’f the c’opper tube thermocouples were inserted to measure tlie tube-wall temperatve an,d.their variation along the tube- . Yor this purpose. small grooves

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. NACA Technical.’M6morandum No: 1“054 3 .,w.exe.,rnadg.+.$.e tube wall, ”*he”Jtwo thermocople wires were inserte~ in “the g200tQ”$’and -so=l-&ered.ov-er flu-srh with the tube wall; ‘In order to detect, any asymmetry of cooling of the tube which might ‘have occurred during the experiment, four thermocouples were inserted along a line parallel to the tube axis and t.lireealternate couples diametrically’ opposite- The diswere placed along a line tances between the thermocouples can be seen in figure 1. To measure the temperature of the cooling water at points along the flow inside, thermocouples of wire of 062--milli– meter diameters were placed in the annular space. The diameter of the smoothed soldered junctions was 1.0 millimeter., Each thermocouple was tied by a thin wire close to the’ experimental tube so that the free end of the couple was slightly above the tube surfacea A thermocouple installed in this manner with relatively large thickness of junction equal to one–half the crack width assured measurement of the bulk temperature of the water flowing at this points There were six such thermocouples along the tube in addition to two others to measure the inlet and exit temperatures of the water, These thermocouples were distributed similarly to the tube-wall thermocouples. All the thermocouples for measurement of the wall and water temperatures were carefully insulated by a special varnish and calibrated The water thermocouple distribution in the annular space is shown in figure 1, In making up the experimental section it was necesse– ry t’0 keep the experimental tube centered inside the casing to insure symmetrical flow of cooling medium. This was done by using, as spacers, three small wires 20-millimeters long and of diameter equal to the crack width soldered to the tube wall at each of these pointse Besides, this, centering rings were soldered on each end of the “experimental tube ‘and the ends of the casing were then sol– dercd to these rings. In order to avoid any deformation, of the experimental section because of the differences in ther+::i mal expansion of experimental tube and casin&, the latter was cut transversely in the, middle into two sections, The ends of the casing could then move freely inside a metal ring placed over the cut in the casing: Tightening of the joint was accomp.lisherd.by use of a rubber tube placed over the ring and wired to both ends of the cut c’as’ing;’thus the rubber served to absorb all the deformation resulting “ from thermal expansion of tube and casingO The thermocouple leads were brought out through small holes in the casing. Short tubes of 3 millimeters outside-diameter were carefully soldered to the pressure. taps in the test

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4 .NACA Technical section, These tubes were : r: Yiemorandum No; ”,1O54 brpughk out through holes made . in the casing as shown in.figure 2 by”short$ thick–walled, metal-armored rubber tuties placed over the small tubes. A tube passin-g through and soldered to the casing was in– end. of the rubber. Thus there was serted into the outer assured the necessary compactness and elasticity of the joints to the manometer and pressure of the air. To the measurement of the static outside wall of the casing al”l ‘possible security in there w,a=e also soldered five’ thermocouples to measure the casing temperature along the experimental section. The bestos to avoid heat loss, casing,was insulated with as- .Ilxperimental Erocedure and Measurements Before the experiment was begun the air and the cooling water were started flowing in the apparatus and the electric heater was turned operations After the desired and to reach steady-state on to heat the vhole apparatus flow conditions were reached, the experiment was started. experiment steady. air flow rates Before and during the wer-e maintained by continuous observation of the ‘level of the differential water manometer on the orifice and by valve B, The duration of one careful regulation of the experiment varied from 15 to 30 minutes. During this time all data were taken three times. Some of the exper– iments were repeated from two to three times under the same conditions. Because the air f-low rates were regulated, the pressure in the experimental tube varied insignificantly during the experiment- In order to assure even distribution of cooling water around the anhular space, artificial turbulence was introduced into the water flow by admixture of compressed air which was put into the water line before the water entered the casing. The well–mixed air-water emulsion passed through the annular space at high velocity and thus during the experiments uniform smooth curves of thermocouple readings were obtained for the cooling water and the experimental tubeQ The inevitable inaccuracy in heat quantities due to the air in the water is insignificant even if the volume of the air were three times that actually used. In our experiments counter-current flow of air and cooling emulsionwere used. With parallel fl’ow the main portion of the change in water flow would occur in the first portion of the experimental section and this first section inter– ests us least because it represents only the beginning of

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}Lemorandurn No. ‘1054 5 NACA Technical int.eres.t, With counter–flow the the velocity range o-f., change in water temperature is more” ’uniform with insignificant -concavity toward the latter case the curve of water axis of length- ,In this tempe.ratur”e from inlet to exit of the casing is almost linear along the entire experimental section. This assured greater accuracy in differentiation of these curvese The distribution of air pressure along the flow was measured by a mercury differential manometer having 10 legs. A detailed description of this manometer is given in the work on measurement of hydr~ulic resistance. Nine legs of the manometer were attached to the pressure taps and the tenth point communicated to the atmosphere. Thus the differential manometer gave a distribution of mercury levels corresponding to the pressure gradient in the tube above atmospheric pressure. The air flow was measured by a standard orifice made of stainless steel placed in a 7&millimeter inside—diameter electric heater. The orifice pipe upstream from the diameter was 21 millimeters. The pressure drop across the orifice was measured by a U-tube manometer filled with colored waterm The absolute pressure upstream from the orifjce was measured by a precision Bourclon gage to six atmospheres with a scale graduated to 0-03 atmosphere. The from the orifice was measured The quantity of heat Q air temperature upstream by a thermocouple. (per unit time) lost by the air in the test section was determined by measuring the weight rate of flow of cooling water and temperature rise of the water. In addition, the curve of water temperature against length of test section differentiation of this curve heat transfer could be determineddQ CG at6 ~L=dLwhere was measured so that by the instantaneous rate of (1) G6 mass flow rate of water, kg/hr dt6/dL* derivative of water temperature tg with respect to length, deg.C/meter ————__————— ——— ——.———_ -—- *1 was changed to L in translation to facilitate reading the typewritten text,

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6 NACA Technical Memorandum No. 1054 ., dQ/dL derivative of Q with respect to length in cal/(m](hr) : c water = 1 cal/(g)(°C) specific heat of The entire heat loss from the air along the test from measurement of air flow section was also computed rates and inlet and exit temperature af;d ,pressure for the test section, With these mass flow raLes and the same inlet and exit pressures and temperatures obtained in the 3-inch sections preceding and following the test section. the heat losp from 3-inch inside-diameter pye the air was measured in a (where changes in kinetic negligible). The two independent energy of the air were measurements of Q checked in 5 percent. EXPERIMENTAL DATA In all our experiments that te,erat?e ,~~ ,ttainedo tube acoustic velocity at -Table I shows the complete in our experiments to with- AND THIIIR MEANING at the exhaust end of the mozsu:ed data fcr all experiments. From these data plots cJf measured quantities were made. Figure 3 shows curves of the pressure distribution. The abscissa is marked as ditance in millimetersfrorn the section and the ordinate as the presentrance of the test water. !YLJreach experiment plots sure in millimeters of of temperatures of inside w,I1;.f test section, cooling water temperatures and casing wai- temperature have been made and these are shown in f’lgure .!, The motion of a compressible gas is described by the following formulas: (1)’ Conservation of matter (2) Equation of state pV = RT (3) (2)

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/ Memorandum No; 1054 7 NACA Technical (3) Energy ”balance .. ., ,, W. 2 A< + Cp T + Q= QpTo+A— (4) . ,2g .,.. where .- 2g “ --- G air flow rate, mass per unit time l?’ transvers.-e”ar”ea of tube “ w flow velocity ., v specific volume P absolute pressure T absolute temperature w, v, P, T mean values over the section* Cp specific heat at constant pressure R gas contant A thermal equivalent of mechanical work ~ acceleration of gravity Q heat output per kilogram of air in the test section from the inlet to the section in question Subscript: o inlet section If started at the large tube before the test section the initial kinetic energy A {wo2/2g) relative to Cp Te can be neglected. In the authoris experiments the quanti– ties G/F and p were measured directly. In the large tube preceding the experimental section the inlet temperature of the air was measured by a resistance thermometer. _____________________________________________________ *For’,the laws of averaging of the authors work on hydraulic L— — the separate quantities, see resistance for high velocities,

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8 NACA Technical Memorandum Nom 1054 The quantity Q may be calculated up to any section by the water mass flow rate and the temperature rise of the waters Yrom the plot of Q and the initial air temperature, the quantity so-called “stagnation temperature Tm and its change almng the test section have been computed Tm =A-~~+T=To-~ cp2g (5) Cp A solution of equations (2) and (4) gives a quadratic equation for the flow temperature To calculate T from equation (6) a graphical solution based on methods is descri%ed in the work on flow resist– ante. The magnitude of flow velocity is computed from the difference between stagnation and actual temperatures. :— ——.-. (7) From the experiment fridtion factors have been cal– culated under conditions with heat flow- The Bernoulli equation for flow of compressible fluids wdw —-–---.--~dp_ g W2 dL k— (8) 2g D together with equation (2) determines the friction factor ~ for compressible flow. 5 =-2D d(p + PW2) (9) dLpw2

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Memorandum No. 1054 9 NACA Technical where ,,- ,,, , P l/Tg = air density D tube diameter With very low ve~ocities .. . aa and p W2 << p or W2<< gyV=-k- (a acoustic velocity, k adiabatic exponent) - that is, .“ with velocities far below acoustic, equation (9) heaomes the ordinary relation for ~ fluids. The quantity (p + p w’) for flow’of incompressible .’ varied all along the tube in the experiment much less than did the quantities p and impact pressure separately. Therefore in cal– thepe;~eriments the curves of (p+p W2) culating ~ from against tube length were differentiated. The values of ‘( have been calculated for the 1250, and 1360 millimeters. sections L = 700, 900, 1100, In figure 5 the experimental values of ~asa fu-nction of Peynolds number, calculated on the mean stagnation temperature in a given section are shown as small circles. The curve fits the Nikuradse equation K = 0.0032 So it is seen that the actual 0.221 + —-— (10) Re0.237 experiments with heat transfer occurring confirm the previous conclusion made for adiabatic streams - that is, that the Nikuradse relation for ~ is applicable to streams of high velocity. In the same sections where the friction factors were determined, loaal heat transfer coefficients from the equation for heat flow for a tube surface element of diameter D and length dL were also computed &q = CL (Tm —— Tcm)mD dL (11) where Tcm is the absolute temperature of the tube wall,

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—. 10 NACA Technical Memorandum No.. 1054 The values of dQ were calculated from experimental data by use of equation (1). The utility of reckoning hbat transfer coefficient’s, not on actual fluid temperature but on stagnation temperature, has already been well founded by Vittgeo (reference 2), M. l?. Shirokov (reference 4), and Jung (reference 5). Calculation’ of transfer H was.made for to L = 1.250M. The curves of water tube length approximated the mean coefficient of heat tule ‘sections L = 0.7 (L/D=50) and wall temperatures against straight lines in the section up to L = 1*250M; therefore for stagnation temperature and for Q, there also is, in this section, approximate linear dependency on length according to equations (3) and (1), To determine the mean E according to equation (11} . L 1 L 1 dQ a=- adL.— (12) L J o Substituting ‘dQ = G dL, b, To are constant, and or nDL J Tm - Tcm 0 Tin-- Tcm =-TO-Y bL, where ‘-”a, after integration (13) where T = Tm — Tcm ‘5s the temperature potential in a given section and —.— .——‘L - T= To - To in ~L .

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Memorandum No. “1054 31 I?ACA Technical is the logarithmic mean temperature di,ffe,rehce in the tube between two ransverse sections, - ~ :.’.’ ,,, ~ By use of equ’attion (13), values of ‘~ ‘ have been calculated for; a’11these experiments as’ well as the - dimensioness pa,rae’ters Nu the heat transfer,’ t ‘ ‘ 1, Nu =,? -!4 an’d Pe cha,ra’cter,izing .. . ,t’~ I ,, ..., (14) ~ ?--;cik ,! -’ , / -., wyCp D ~ ‘ ‘: Pe = —— ..- (15) A s’ Here A is the conductivity of the air. The Reynolds-Prandtl hydrodynamic theory of heat transfer predicates a transfer the core of the stream to the of heat and momentum from walls by’s process of turbulent eddy motion of the same stream particles. If, in this theory, the resistance to heat transf’er of the thin laminar films for gases in tubes is neglected, the following relation between a and .,” ~ .is obtained: ~ . :, ‘, ~ a = Wvcp - ‘ , or in dimensionless parameters, Pe 8 t. ! (16)- 8 “ As Shirokov has demonstrated,, the hydrodynamic theory of heat tansfe may be extended to streams, of ‘high veloc— ities if for’the transfeb,not ,only of the heat but also of equivalent kinetic energy from the core of the stream to the walls is allowed, Then equation (36) is valid if a is calculated on the temperature difference based on stagnation temperature, . . The &at’a ‘oi’t”hes+ ixperimenti ‘cO’rif:irm,t“hi~ relation and check with the ‘data of V-itfgeo (refererice 2). “r . .

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12 NACA Technical the abscissa is Nu/ P e and the In. fiigure 6 where Memorandum No. 1054 ordinate ins”“ 5 the experimental data for mean ,values along the test section are marked with small ciycles and the data of Vittgeo with triangles, the straight line is equation (16). It may be seen that drawn as required by over almost the whole range. of this investigation, the data correlates well with equation (16) except in the small region of high values of Pee values of Nu/Pe and [ are In figure 7 local marked. The solid straight line corresponds to equation was fitted to the experimental (16) and the dotted line least squares. The conclusion redata by the method of garding the dependency of Nu/Pe on’ ~ for mean values is also confirmed by figure 70 Usually for gases, heat transfer experiments are reported as I?u against Pe, because ~ depends on Re and Re = Pe/Pr for gases is directly proportional to Pe (the Prandtl criterion Pr depends only on the number of atcms in the gas). In figur’e 8 Pe values are on the absc’issa and Nu on. the ordinate and the data based on mean values are shown as small circles, The values of the physical constants in Nu and Pe are calculated on mean gas stag— nation temperature- It is to be noted that the data, calculated on stagnation temperature and not on limiting temperatures as is usually done in this field, fit well with the ten Bosch equation for air. Nu = 0.0364 Pe0*75 (17) This is shown graphically on the same plot by the solid curve, This equation is obtained by substitution in equation (16) for ~ by the relation of Blasius which fits the Ni.kuradse equation for Re ,< 100,000 and it is confirmed by multiple experiments at low velocities if the -physical properties are based on the wall temperature~ “’This is also shown in figure 9 where the small circles show the relation between the local values of Nu and Pe calculated on stagnation temperature and the solid curve corresponds to ‘the ten Bosch formulae It should be stated that these experiments have not shown any noticeable influence of temperature on m and

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— Techn’ic-al hemo-randum No. 1054 ’13 ‘ NACA ~ as has been reported by Jung on stack gases where the temperature variation of the gases was much greater than in-our experiments, .,! ., CONCLUSIONS ., ,, .,, ,’,. .’ 1. The relations for friction and heat transfer for cooling hot air streams to acoustic velocity ‘throuh flowin& at velocities up’ straight water–cooled tubes. have been studied experimentally. 2. The range of variables covered values of Nusselt numbers, —Nu from 200 to 500 Pecle’t numbers --Pe from 50,000 to 300,0002 and Reynolds numbers -Re from 70, 000 to 420,000; the air temperature varied from 4000 C at the inlet to 140° C at the exit, and the velocities reached the acoustic value (up to 4201ti/see) at the exit end of the tube, 7 It was found that within the limits of our experim~;ts, the calculation of heat transfer coefficients based on stagnation temperatures confirmed the relation, —-=Nu -L which is derived from the Reynolds-Prandtl Pe 8’ analogy. This is as well confirmed for mean values of Nu and Pe in the tube as for point values of NU and Pe and is by no means de]endent on the (Bairstow) Mach number (the ratio of stream velocity to acoustic velocity), 4. The values of ~. for flow with heat transfer fit t!le Nikuradse formula as well as 5 for streams without heat transfer. Translation by N. P. Vakar and G. C. Williams. . ,,,.,,,,,.,,,, !!!!.!! !!! .!!!.. . . . . . . . . . , . . ,. . . . . . . . . . . . . . . . . . . . . . . . . . . . —. .-. .-. -.. . .- . . . . . . -. . . . . . . . . . .

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14 NACA” Technical Jiemorandum No. 1054 REFERENCES - 1, Lelchuk, V. L.: Jour. 1826, 1937. ,, Tech. Phys. (USSR), VO1. 7, 2* Vittgeo: Jour. Tech. Phys. (USSR), vol. 5, no. 10, 1935. 3. Jung, Ingvar: Transmission of Heat and Frictional Resistance by Gas ??1ow in Pip:es at High Velocities. Forschungsheft 380, vol. 7,. 1936. 4. Shirokov, h. F.: Bull. ‘3?ederal Heat Science Institute. No. 9, 107, 1935. ,. .

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Table I Static air pressure in mm H@ At dietance of Before test Air temperature in ‘C Mass Ma8a rate rate of of flow of flow cooling of efore )ehind water Run 8ec- 953.5 1203.5 1353.5 1394.0 1404 1410 air teet teet in 203.5 453,5 703.5 tion . mm from pipe inlet ! kg/~ec sec- Bec- kg/see tion tion 1 24,740 19,187 17,926 16,489 14,807 12,706 9,682 9,153 8,285 0.0486 341 171 0.0306 10,739 2 24,900 19,323 18,062 16,611 14,916 9,736 9,221 8,340 .0486 345 175 .0306 12,706 10,780 3 24,900 19,296 18,048 16,597 14,889 12,773 10,753 9,709 9,092 8,326 .0486 353 178 .0302 4 21,075 16,028 14,970 13,777 M3,326 10,539 8,855 7,987 7,529 6,875 .0393 381 190 .0278 J 5 21,075 16,353 15,323 14,062 12,598 8,190 7,743 7,092 ,0395 392 193 .0282 10,780 9,072 P 6 ------ 22,?40 21,276119,608 17,628 15,201 12,774 11,540 10,957 .0582 338 182 9,940 .0411 5! + 7 42,800 33:358 31,382 88,869 25,995 22,428 16,923 15,987 14,523 .0893 254 149 .0417 18,808 8 43,000 33,846 31,800 29,236 26,279 22,632 18,888 16,950 15,974 14,550 .0894 247 145 .0406 9 49,500 39,039 36;612 33,738 30,392 26,225 21,832 19,581 18,523 16,828 .1042 140 .0382 231 10 49,700 39,388 37,019 34,063 30,673 26,429 21,927 19,649 18,577 16,869 .1047 140 231 .0375 11 50,100 38,036 35,731 33,046 29,805 19,432 18,428 16,746 .102E 231 142 .0382 25,707 21,615 12 50,10C 36,775 34,456 31,785 28,666 24,643 20,571 18,388 17,425 15,838 .099E 231 142 .0389 13 36,80C 28,828 26,971 24,882 22,397 19,336 16,162 14,730 39,953 12,620 .073e .0413 284 155

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— Table I-Continued Coollng water temperaturein ‘C Temperatureof test section of Temperatureof outer wall outer pipe wall in ‘C jacket in ‘C - I distance of at.distance of at distance of at I+3%) I :% 416 1670 , 913 1173 1330 1406 2.$ 416 667 ’912 1177 1335 1375 1406 673.5 829.5 1083.5 1293.5 I -... —.-1X)L -,. mm from pipe inlet 40 mm from pipe inlet mm from pipe inlet — 1 75.3 53*3 45.0 28.6 20.0 13.6 13.8 7.8 66.0 49.0 37.9 30.0 22.0 19.2 19.4 52.0 39.0 27.4 16.8 9.2 2 73.1 54.1 46.5 29.8 20.8 14.2 14.2 8.4 66.1 50.0 38.6 32.0 22.8 20.0 20.3 54.0 41.1 27.7 16.9 9.9 3 75:6 55.8 48.8 31.8 22.2 15.5 16.0 9.6 68.8 52.8 41.6 33.4 24.4 21.6 22.2 55.1 40.7 28.4 17.6 9.7 4 75.5 57.2 49.0 32.5 22.6 15.8 16.2 9.8 71.0 55.0 42.5 33.5 24.2 21.7 22.5 58.4 42.8 30.0 18.6 11.0 5 77.8 59.0 49.2 32.4 22.9 15.8 16.8 9.8 70.0 53.1 41.4 34,4 124.422.0 21.8 59.1 44.1 31.6 19.6 11.0 6 64.7 47.1 39.6 26.4 19.2 13.9 14.1 9.4 60.8 43.8 33.6 28.4 ‘21.419.0 19.0 48.4 36.6 26.4 17.4 11.0 7 63.0 47.7 40.0 26.3 19.2 13.2 13.6 8.8 59.7 44.4 34.5 28.2 22.0 19.0 18.6 47.9 36.5 26.0 16.8 10.2 8 63.4 48.6 41.3 27.2 19.9 13.8 14.0 9.0 61.1 45.2 35.8 29.2 22.6 19.3 18.8 49.6 37.6 26.7 13.6 11.1 9 68,4 51.7 43.8 29.2 21.2 14.5 14.7 9.1 64.2 47.6 37.6 31.1 ~23.820.2 19.8 53.4 40.7 29.0 18.8 11.2 10 66.5 52.0 44.2 29.0 21.5 14.7 14.8 9.0 64.7 48.0 38.6 31.3 ,24.020.0 19.8 53.5 40.8 29.5 19.0 11.6 11 64.8 50.4 43.4 29.0 20.8 14.1 14.5 8.8 62.2 46.8 37.3 31.0 123.720.1 20.0 52.1 28.9 18.8 11.4 40.2 12 64a 49.2 41.7 27.9 20.0 13.6 14.0 8.8 61.2 45.8 36.2 29.8 23.1 20.0 19.6 50.5 38.6 28.0 18.4 11.2 l 13 63.0 43.8 38.1 22.6 21.6 13.1 15.6 8.0 64.6 46.8 46.0 39.4 30.2 24.0 23.5 45.0 31.3 21.7 14.2 10.3

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B t/Df l==- Water — r— . ) El\ Figure 1.- Scheme of experimentalapparatus.

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Water ! ..,,. . / ,. Vv: ,. lfa’~~””’‘;;’’’’””’’””’”~ /, J ——I ‘*:-!!!h.ernocouple ‘,,, lfater 1 I Figure 2.- Scherneof experimentaltube. N

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. . . . . . . ----- ~TACA Technical Memorandum No. 1054 40000 $30000 ~ g 20000 .- ~ ~oooo a) k . ... . .--. ——- .-.._- -. . Figs. 3,4,5 o 250 500 1000 1250 1500 750 mm Fiogure3.- Tressure distribution along experimental tube. Oc \ Run No. 3 300 > “ \ - l-Stagnation temperature of air 2-Air temperature,200 3-Temperature of walls of experimental tube 100 &Water temperature 5-Temperature of ——. I 4. ~ ,1 - \ . L \ \ 12 ~ - ~ —. \ \ \ ;3 ~ -9=— ~ — ~ — — ~ ‘Q-S? I o .4 .6 ,,.8 1.0 1*2 1.4 casing walls .2 M Figure 4.- Temperature distribution along experimental tube. 104 t 200 160 120 80 40 0 I -— l OO03?e oooRe Figure 5

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NACA Tectiical Memord No. 1o54 105 ~ 3000 2000 0*L . L/ n o. Gt b b+ — 1000 0 0 140 160 180 200 220 ...- . Figure 6 3006 2000 - y&a_+4Jf- %’-3’-Jm-;~o ‘%- - _ L A!7XEQ0 =%b== = loof&— ‘ -L-..3----- 160 180 lo$ Figure 7 Nu .— 400 ,$f ‘ao 2 0 r, C@ R . 0 -o A@’ 200 AF % / / I Figs. 6,’7,8,9 .-. 200 220 Nu 600 / 400 ~ ,58---- / OH ,- 200 Y“s 0 100000 200000 300000 Pe Figure 8 /0 ~. — 9 I o 50000 300000 150000 200000 250000 30dOO0 Pe Figure 9