A STUDY OF CONVECTION IN CLEAR AIR AND IN WET AIR Technical Note No. 9 1943 by EDMOND.RUN French Committee for the Development of Aeronautical Research (G.R.A.) Translated by FREDERICK WEINER North American Aviation, Inc. April 1954

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FOREWORD This is a translation of one of several papers on aircraft icing which have been made available to the University of Michigan by Dr. Edmond Brun, professor at the Sorbonne, Paris, France. This translation is reproduced and distributed by the Engineering Research Institute of the University of Michigan for the convenience of Engiishspeaking persons who may be interested. ii

TABLE OF CONTENTS Page Nomenclature.................... 1 Chapter I. Description of the Apparatus... 2 Chapter II. Convection in Clear Air...... 8 Chapter III. Convection in Wet Air....... 15 Appendix......................20 iii

A STUDY OF CONVECTION IN CLEAR AIR AND IN WET AIR (Flow perpendicular to the axis of a heated tube) This report contains the following chapters: I. A description of the apparatus and the methods used. II. Results obtained in clear air. III.Results obtained in wet air. NOMENCLATURE: (Translator's Note - A list of the symbols used in the original French report and the symbols used in the present translation are listed here.) French Report: Translation Lateral surface area, cm2 s A Biot Number, dimensionless 63 Bi Constant, dimensionless C C Tube diameter, cm d D Water catch collection efficiency, dimensionless f Em Heat transfer coefficient of convection, cal/(m)2 (sec)(0C) h ho Heat transfer coefficient of convection in clear air, cal/(m) (sec)(~C) hc hc Heat transfer coefficient of convection in wet air, cal/(m)2(sec)) (0Ch hw Differential height, mm of alcohol 1 1 Flow rate of circulated hot water, gm/sec m m 1

NOMENCLATURE (cont' d) French Report Translat ion Heat release per unit length of wire, watts w q Ratio of convection coefficients in wet and in dry air, hw/hc, dimensionless r r Reynolds Number, dimensionless Re Temperature difference between tube surface and air, ~C 0 A t Temperature difference of circulated water, 0C t Atw Wind tunnel air velocity, cm/sec v U~ Galvanometer deflection, mm Mo x Time, min. m Kinematic viscosity, c.g.s. units I. A DESCRIPTION OF THE APPARATUS Two arrangements were used; the one. comprised a pipe with stationary fluid (the first setup); the other arrangement consisted of a pipe through which fluid was circulated (the second setup). Some interesting results were obtained with the first apparatus. We were not able to get as many results with the second arrangement because of equipment failures during the experiments. A concise description is given here for future use. 1. The First Arrangement a. Principles - A hollow metal tube filled with an insulating liquid spans the wind tunnel perpendicular to its axis. A constantan wire is set in the interior of the tube; an electric current is passed through it; in this manner energy can be transferred to the tube and can be precisely measured, The wind tunnel was put into operation and an electrical current passed through the constantan wire. Steady state was gradually established, in which the heat released by the electric current is dissipated by convection. Steady state was recognized by the fact that the temperature difference nt between the tube and the air in the wind tunnel remains constant. In the center region of the tube where conduction from the ends does not affect it, the energy, q, is transferred to the air from the lateral surface, A, per unit length of the tube. Consequently, the coefficient of convection hO at the tube surface is' = A A t

b. Description - The tube, made of copper, has an external diameter D, of 2.92 cm and a length equal to the width of the wind tunnel (120 crm). (See Figure 1). The air temperature remained continuously at about 150~C and the pressure about 600 mm of mercury; its kinematic viscosity ) was about 0.188 c.g.s. The Reynolds Number of the flow is then UpD 2.92 U, Re = -— = 0.188 = 15.5 U0 c.g.s. The tube was filled with mineral oil. This liquid has an advantage over water, being an electrical insulator and having a lower specific heat (this property reduces the time to reach steady state). To permit expansion of the oil, two glass tubes were attached, with rubber joints, at the copper outlet tubes which were brazed on the upper ends of the tube. The constantan wire, 115 cm long, was suspended inside the tube below the axis so as to provide a uniform temperature inside the tube by natural convection. The electric resistance of the wire was about 14 ohms. In most of the experiments the current intensity in the wire was 5 amperes. The temperature difference 4 t between the surface of the tube and the air of the wind tunnel vs measured by means of a copper constantan thermocouple. To do this a copper wire, F, well insulated from the wall of the wind tunnel,was stretched across the tunnel. Then a constantan wire was soldered on one end to the copper wire (cold junction at the temperature of the air) and on the other end to-the surface of the copper tube (hot junction at the temperature of the tube wall). After calibration of the thermocouple itwas necessary only to connect the tube and the wire F to the terminals of a galvanometer to obtain the temperature difference between the two junctions. Actually, there exist three thermocouples reading the temperatureone in the center of the tube, and at two points symmetrical to the center and located toward the ends of the tube (Figure 2). In this way it is possible to control the uniformity of the temperature of the tube. It should be pointed out that there is always a certain temperature difference of at least 10~C existing between the tube ends during the course of operation. Finally, the results were obtained by consideration of the temperature of the central thermocouple. Calibration of the thermocouples was made on the spot. The tube, ventilated by a small current of air, was assumed to be at the temperature of the air stream. The cold junctions were kept in a liquid bath at a temperature different from the air stream. It was found that using the galvanometer at its least sensitivity, a deviation of 1 mm on a strip placed 1.50 m from a mirror corresponded to a temperature difference of 0.11850C. The air-stream velocity was measured by means of a Pitot tube located in front of and above the tube, in a vertical plane which included the central soldered joint. The pressure lines were connected to an alcohol manometer whose differential height, 1 mm, is proportional to the speed, U cm/sec. by the relation *H is not defined in the original French report (transl. note)

ineral oil copper tube glass tube rubber joint constantan wir,./ ——,z,,,,, side of the wind. tunnel insulation 115 cm 120 cm Figure 1. Set-up of the first arrangement.

tube ~/. /; /........... ~ thermocouples ard rubber plate wire stays l_________ l_____ _ |galvanom eter 6 v battery Figure 2. Installation of the first arrangement.

c. Experiment - With the wind tunnel in operation, electric current was passed into the heated filament. Steady state was attained after about 20 minutes, at a very low airspeed (20 m/sec). The following table presents the galvanometer deflections ( x mm) as a function of time (e minutes) for the center thermocouple, for a speed of 24.5/sec and a 5-ampere current.. (See Figure 3). e (min) 0 2 3 4 5 6 7 8 9 10 x (mm) 0 105 130 144 153 161 167 171 174 176 i 11 12 13 14 15 16 17 18 19 20 x 1 177 179 182 182 182 181 182 181 180 182 It can be seen that small variations of temperature occur when steady state was established; these are due either to variations in the air speed (which was low) or to variations in the external air temperature. These variations ate particularly important when the air is stirred by a breeze whose main direction lies predominantly along the wind tunnel axis. Because the voltage variation was: not insignificant, it was necessary to keep a strict watch on the amount of heat produced during the experiment. A rheostat served to keep the same value throughout the experiment. These variations of current cause abrupt variations in the operation of the wind tunnel; it was also necessary to control the indication of the pitot tube constantly even for a calm atmosphere. It was during a period only slightly disturbed that simultaneous readings of the temperature difference At and the air speed were made. 2. The Second. Arrangement a. Principles - In order that the tube temperature would be uniform in all directions, another arrangement was designed in which the tube was uniformly heated by hot water circulation. As shown previously, a hollow metal tube was placed across the wind tunnel perpendicular to its axis. Hot water circulated through the tube with a flow of m gmn/sec. A thermocouple gave the difference, A tw, between the water entrance and exit temperatures. At steady state the tube transferred an energy equal to m tw calories to the wind tunnel air. If, as before, the temperature difference 4t between the surface of the tube and the air is measured, it is possible to calculate the heat transfer coefficient of convection, ho. b. Description - The diameter of the copper tube is 3.24 cm and thus is slightly larger than the first tube. The temperature difference A t between the tube surface and the air was measured with the same apparatus used previously. 6

200 150 rd. 0 o 0 0 10 20 30 time, e, min Figure 3 Variation of the temperature difference (proportional to measured voltage ), as a function of time.

The water circuit (Figures 4 and 5) is composed of a pump, P, a water heater, C, where the power can be regulated to as much as 500 watts, another water heater, C', where the power dissipation is 50 watts, a water meter not shown in the figure, and the copper tube. The complete water circtuit was insulated (except of course the portion of copper tube located in the wind tunnel). The power was regulated in the water heater C according to the temperature desired. The water heater C' serves only to. maintain the water temperature constant; for this purpose a thermostat is placed in the water heater C' and it cuts in or out, keeping the temperature within a fraction of a degree of the desired value. The flow of water was about 0.1 liters/sec. The difference Atw between the entrance and exit water temperatures of the copper tube was again measured by a copper-constantan thermocouple, but as the thermocouple was only accurate to about 2 degrees, it was expedient to employ the galvanometer which had much greater sensitivity. An electrical device not described here permitted the reading of the temperature differences a t and Atw. The photograph of Figure 6 shows the tube with stationary liquid (upper tube) and the tube with hot water circulation (lower tube) installed in the wind tunnel. The three copper wires may also be easily seen. II. CONVECTION IN CLEAR AIR It should be pointed out right at first that it was anticipated that only relative measurements would be made with out apparatus; in fact the problem was to compare convection in dry air and in a fog (wet air). The apparatus was therefore not calibrated for absolute values until later, and the numbers which figure in the analysis and in the graphs represent only relative values. 1. Influence of the Temperature Difference,At, between the Heated Tube and the Air Right away we assured ourselves that the coefficient of convection, h0, was independent of the difference in temperature A t between the tube and the air. For this purpose, with air speed constant, different intensities of current were passed through the wire. In this way, for an airspeed of 24.6 m/sec, when the current intensities were in the ratio of 4 to 6, the temperature differences 4t were in the ratio of 103 and 231. It can be confirmed to better than 1 per cent that After several similar tests we no longer believed it necessary to vary the intensity of the current, which remained fixed at 5 amperes. 2. Effect of the Air SSpeed The speed of the air in the wind tunnel was allowed to vary only between 25 and 50 m/seco Five series of measurements were made in this speed range. The 8

J-C Figure 4. Part -of the &pplarat-; fsor ct h&e;cond. -a'ra-ngeet.

Figure 5. Partial photograph of the second arrangement. I0

II~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Figure 6. View of the tubes in the wind tunnel. - g -~~~~~~~~~~~'

last series, which appeared to us the most satisfactory, were as follows-, Us, r m/sec. 24.5 30.2 37-25 44.1 47.85 ho relative values 0.016 0.0181 0.0212 0.0242 0.0264 Putting the coefficient, hointo its usual form, o:=C U0 Log ho was graphed as a function of log Uoo(Figure 7). It is seen that the points fall upon a line whose slope is 0.66. Accordingly, x = 0.66, whereby o, 66 ho % CU a This formula is valid for air for Reynolds Numbers between 35,000 and 70,000. 3. Comparison of Several Series of Measurements Similar results were obtained for all the measurements. In Figure 8 are represen-ted-the values obtained for three different sets of measurements2* The solid line reproduces the results already given in Figure 7. The other two lines are seen to be parallel to the first line and show results which deviate the most from the average values. It is seen, in considering the values obtained in the different measu~rements, that the differences never exceed 5 per cent. Consequently, it appeared interesting to determine the value of the constant C and, for this purpose. to calibrate the electrical measuring apparatus. We will not be able to guarantee good precision in these calibrations which were made at Mt. Lachat under rather bad conditions. At any rate, measuring hho in cal/(m2)(sec)(oC),. we find the line of figure 7 can be represented. by the equation 1h = 3.1 UoA If ho is measured in ergs/(cm)2(sec)(oC) and UI in cm/sec, we find: ho = 6s0 s 4. Introduction of Dimensionless Numbers into the Formulas To compare the results obtained with those of other experimenters, and in order to generalize, it is convenient to introduce the Biot and Reynolds Nfinbers 12

2.500 O'H.-t o.H C) 0 (a) CH rH c 2.300 0 0 CQ _ 9i ) k-I 2,200 3.300 3.400 3.500 3.600 3.700 Wind-tunnel air velocity, log U,, cm/see Figure 7. Relative change of the heat-transfer coefficient of convection as a function of speed. C) O O " ok 0 (1)0 ~~~3 2.300 ~~ ~ ~ 0, CH 0 J O l"-' H 3.300 3.400 3.500 3.600 3.700 Figure 8. Comparison of measurements of several tests, 1O3

In our tests, diameter D is equal to 2.92 cm; the coefficient of thermal conductivity, k, of the air at 200C is equal to 2508 ergs/(cm)(sec)(OC); the coefficient of kinematic viscosity, ), of the air at 200C and 60 cm of mercury is equal to 0.188. Consequently one may write, in c.g.s. units, 0.66 06 or,1 (6 ()' (O 6 and thus Bj = 0.13 Re066 This gives, for extreme values of Reynolds numbers, for Re = 35,000, Bi = 130 for Re = 70,000 Bi = 205 5. Comparison to Other Experimental Results Few measurements have been taken of forced convection over.tubes and wires for flow perpendicular to their axis, for Reynolds Numbers greater than 10,000. However Reiher gives for Reynolds Numbers between 1000 and 100,000: Bi = 0 33 Re0'56 but this formula was obtained for the case of the current of air heating the cylinder. Nusselt obtained higher numbers for the case of air cooling the cylinder. Hilpert gives the following formula, for Reynolds Numbers between 4000 and 40, 000: Bi = 0.174 Re0'618 and, for Reynolds Numbers between 40,000 and 400,000: Bi = 0.0239 Re0 805 These formulas really constitute only empirical rules of interpolation; one can choose, for each region of Reynolds Numbers, the exponent which represents the results as well as possible-. The domain which we have explored (35,000<Re<70,000), being on both sides of the region corresponding to the two formulas of Hilpert, it is perfectly logical that the exponent found, 0.66, has a value lying in between those of Hilpert (0.618 and 0.805). A comparison of numerical values is given in the following tableo Re Reiher Hilpert Brun 35,000 115 112 130 70,000 170 190 1 205 14

The numbers which we obtained were much higher than those of Hilpert and Reiher. This is possibly due to the fact that we were operating with a heated tube, whereas the other experimenters used a refrigerated tube. Furthermore, let us point out that even though the results of Reiher and Hilpert agree very. well in the neighborhood of Re = 40,000, it is not so in the neighborhood of Re = 100,000 where the results of Hilpert approach our own. It is regrettable that, being pressed for time, we were not able to determine the degree of precision of the numerical constant. III CONVECTION IN WET AIR 1. Principle -of Measurements The experiments described here were made with the object of comparing convection in wet air (fog) with convection in clear air. For this purpose, with the wind tunnel operating at a certain speed, the coefficient of convection, hc, in clear air and the coefficient of convection, hw, in a fog were measured. The ratio for convection in wet air is defined as "r" where hw r with which it is necessary to multiply the coefficient of convection in clear air, at a speed U6o, to obtain the coefficient of convection in wet air at the same speed. The significant thing to determine is whether or not the factor r depends upon the speed, and how it varies with the characteristics of the fog. The determination of the factor r evidently necessitates only the relative measurements of the coefficients of convection. Experiments in clea r having been- repeated and verified a sufficient number of times, it is necessary to operate the wind tunnel for some time in a fog, and to determine the coefficient hw while taking measurements of the fog composition. 2. Summary of Result s During our stay from August 15 to September 15, the atmosphere at Mt. Lachat was generally clear. Fog was present only during the nights of September -4 and 6 and the day of September 7o Even then the stability of the fog was not sufficient to be able to study the influence of speed upon the ratio r. To make such a study it would be necessary that the fog not change its characteristica from one measurement to the other, something which could only be produced on very calm days. It appeared, nevertheless, that the ratio r had a tendency to increase with speed. In the following table observations (e) and (f) were obtained successively in a fog of nearly the same density; it can be seen that the ratio r is clearly much higher for a higher speed. In the observations shown in the table it is not necessary to consider the nature of the fog after all. To make the comparison simple, we have not followed a chronological order, but have classed the observations for a qualitative nature of the fogo 15

Item Appearance Liquid Water Average Speed Ratio r Content, g/n3m Drop Size m/seco Microns a Very light fog 47.6 1.25 b Light fog 0.15 6 37.3 1.7 c Light fog 6 38.15 1.7 d Average fog 0.2 10 47.5 1. 9 e Heavy fog 24.8 2.3 f Heavy fog 40.3 | 3 g'Mist 37.6 2.2 h Fine rain 1 37.6 2.6 The table shows that, except for a very light mist, the factor for convection in a fog was about 2, and it could become equal or larger than 3 in a heavy fog. The diverse observations are equally well summarized in Figure 9. The line represents, in logarithmic coordinates, the coefficients of convection in clear air, The points shown above the line are for coefficients of convection in a fog (circled points: fog; diamonds: rain). 3. Characteristics of the Fog It is evident that in any reasonable study of convection in a fog it is necessary to determine the characteristics of the fog. This is the reason for which I set up at Mt. Lachat a "Brun-Pauthenier" apparatus' to measure the waterdrop diameter and the liquid-water content. The limited stock of supplies allowed for only a rather elementary realization of.this apparatus. Because of lack of personnel, the measurements that were made at night did not permit determination of the characteristics of the fog. Thus, only in observations b, c, and d was a measurement of the drops taken, For cases b and c the average waterdrop diameter was 6 microns, whereas in case d the average waterd.op diameter was 10 microns. For case b the liquid-water content was 0.15 g/,m; for case d it was 0.2 g/m3. It is impossible to draw any conclusions from this small number of results. However, the preceding values allow an interesting calculation to be made. 16

T.200 1.100 7.ooo. 0.00 o v 2=ai o,@o ~ fog. oU.rain o 0 0D, 2. 2.700,~Od ~.60 0 O 0 L 2 74400 o 7.300 2.200 3.300 3.500 3.700 Wind-tunnel air velocity, log UO cm/sec Figure 9. Comparison of heat-transfer coefficients of convection in a fog and in clear air. 17

4. Calculation of the Fraction of Water Evaporated In case b, application of the formula ho = 3.4 U-0o66 shows that the coefficient of convection in clear air is 37.cal/(m)2(sec)(~C)o Since the ratio for convection in wet air is 1.7 the coefficient of convection has been increased in wet air by 37 x 0.7 = 26 cal/(m)2(sec)(~C)o The temperature difference between the tube and the air being 9~C throughout this eyperiment, the additional heat exchanged due to the fog is 26 x 9 = 234 cal/(m) (sec). If instead of referring to this heat exchanged per square meter of lateral area we refer to tfe area of the tube at the master thermocouple,* we obtain 234 x Tr = 735 cal/(m) (sec),** In addition, the water content contained in the fog which blows over a square meter at the master thermocouple* is 0.15 x 37.3 506 gn. Let us assume that a fraction, Em, of this water is deposited on the cylinder, In evaporating in contact with this surface, the water absorbs about 600 x 5.6 x Em 3360 Em cal/(m)2(sec) at the master thermocouple.* If we suppose that -'the deposit of the water droplets on the tube does not change the convection characteristics, we may calculate that the fraction of water c.aught by the cylinder is: It is usually taken for granted, without giving any good reason,: that the fraction of water caught is quite large (on the order of 0.4), but in an actual case the droplets are very fine and they probably follow the air streamlines quite easily without impinging on an object. This calculation, is interesting because it presents measurements of convection in a fog, in conjunction with measuring and weighing of the water droplets. Not only does it allow the establishing of conditions of cooling of airplane radiators in a fog and the consumption of energy of thermal deicing apparatus, but it also leads' to an evaluation of the water caught by an airfoil in diverse atmospheric conditions.. It could also be possible by studying the local heat losses by convection on certain parts of a section to calculate the distribution of the droplets *over the leading -edge and thus to draw useful conclusions. 5. Studies with Water Sprays Studies were made on September 11, 1942 in clear air with water sprays using a "Ventil" apparatus, on the very first day of its operation. The outside temperature was faijrly high (190C) and the humidity relatively low (0.5). Hence, the conditions were completely different fromfK that of a natural cloud, since the droplets were in the process of evaporating up to the point where they impinged upon the tube. The proof of this evaporation, increasing with speed, was given by the fact that for the same flow of water at lower speeds the surfaces of the wind tunnel and the tube were streaming with vater'whereas at higher sp.eeds the surfaces and the tube remained dry. * Original report reads "maitre-couple" (transl. note) o ** Author does not derive above relationship (transl. note). 18

The ratio for convection in wet air obtained during the course of these measurements was very large (on the order of 6, as shown by the two highest points of Figure 9). This was due not only to the abundance of liquid water introduced into the wind tunnel by the Ventil apparatus but also by the considerable chilling which was involved in the rapid evaporation of water in an atmosphere of low relative humidityo In general, in order that measurements of convection in wet air or tests of thermal de-icers can be made with water sprays, it is necessary that the relative humidity be around 1 (the condition by which an artificial cloud approaches a natural cloud). 19

APPENDIX (Translator's Note) The readers of this translation may be interested to know that two other French reports on icing by Dr. Brun have been translated by Frederick Weiner of North American Aviation, Inc., and reproduced through the courtesy of the Engineering Research Institute, University of Michigan. These are: 1. "Calculations for a Thermal Anti-icer," by Edmond Brun and Marcel Vasseur, French Academy for the Development of Aeronautrical Research (G.R.-A.), Report No. 49-150, 1946. Translated October, 1953. 2. "Thermal Anti-icing," by E. Brun, R. Caron, and M. Petit, French Academy for the Development of Aeronautical Research (G.R.A.) and the Aeronautical Technical Service (A.T.S.), Report No. 42-136, 1946. Translated January, 1954. 20

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