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l ,, -. # -’.,*: .... A. -s. .,, 4° .+O . . ,, ..,.. ,,, ,., ,.. ,,, .,.,,, , _,. ‘TECHNICAL !JEMORA?!JDUMS ,.,,., “, ... —., ....,, NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS - ~ NO. 1028 .. THE ICIITG 03?,AIRCRAYT By M. Robitzsch Beitrge zur Physik der freien Atmosph&e . 01. 18, NO. .,. -.,,, ., . . . . .: :’.,. ,>. :,!.. ,,,:, .!,1..’.. LANGuzY&mMOW AERONI+,UTIC& ‘,,... . . 4, 1932 ~.;,. ~..’ ...$ ‘. !).! ..: NACALBWY ... .;:,,.” K-JW3mTORY (’ .-. =.. . . . . . ,, ,.. ,, Washington September !, w FieM#vf& “ .,, 1942

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~Illlllilllllllflimlnfilllllllllllllli 31176014404942 - ‘———.— _ ._ ..__ : —. .-= — .--, COMMITTEE FOR. AERONAUTICS ‘NATIONAL ADVISORY MEMORANDUM NO. 1028 TECHNICAL ... .,,. . . . THE ICING 03’ AIRCRAFT* By M. Robitzsch The subject of the present article has already been discussed repeatedly ‘from purely practical points of view (reference 1) . All the more, it seems necessary to analyze the problem theoretically, since a study of the processes accompanying the formation of ice on solid bodies of itself comprises all factors involved and makes it possible to weigh the effect of each against the total effect. The problem is to be treated from the very beginning. Assume two air masses A and B separated by a boundary area G. Air mass A has a temperature !!21;in it the partial pressure of water vapor el prevails. For air mass B the corresponding values of these quantities which are to change abruptly on surface G, are of air A has a total heat T2 and ea. The unit mass content Wl, built up additively from two components: !eat content J .I which is propor- The perceptible tional to the absolute temperature TI of A. The proportionality factor is the specific heat Cp of (moist) air; as the Cp value differs dry air, it is introduced at The latent heat content very little for moist or (Cp = 241 cal/kg). Then Will which is proportional to the specific moisture of air sl (or, expressed in g/kg) * %=c: where c = 622 indicates the vapor referred to air = 1000, el specific weight of water B the barometric pressure - *llUber die Vereisung von Luftfahrzeugen. fi Beitrge zur ~hysik der freien Atmosphere, PP l 235-241. vol. 18, no. 4, 1932,

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I ‘2 NACA ‘Technical Nem’orandurn Iio. 1028 measure as el. The proportionality expressed in the same factor is the heat of evaporation of the water, L = 606 cal/g; hence Then the total heat content ,5s WI =~J+lll=cp,T1+ ‘per unit mass of moist air WI el Lc el Lc— .— B= Cp ‘1 + Cp B 1 [ J The bracketed quantity defines the equivalent temperatures 61 mass. The same derivations hold of the analyzed air B; it affords for the unit mass of air mass m mGves from 3 toward A Next we assume that air through the unit surface E that the same air mass m moves The continuity stipulates of boundary area G. back from A toward B. Supposing this also takes place through the surface element total heat cntent of unit E. This process changes the mass A in a well-defined manner. With WI denoting this quantity after the interchange, we get form - with respect to time - Xxpressed in differential this formula can be written r ~ ~= ~ CP TI + dt dt -L( CP or, after regrouping of the as , Lc” ez Ta-—7 )-( )] B CP terms, as M=.m Cp (Tl -T2)+@L dt dt dt B(eX-e2)

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Memorandum No. 1028 3 NACA Technical The heat flow ~ also consists accordingly of two components: dt ., ,- . ,..-. h,..,--,-,...,,..-.,,,,.,e-. dP . dm ., .... . .,,.,.., ,_-., The first, - Cp (Tl - Ta) ~ dt is sus’taiqed throughout the existence of a temperature difference TI - !r between A and B. ture transport. g=L&(el The second component at It is unessential for mois- .. - ea) comdtB prises the heat transport resulting from a flow of latent vapor heat’; It is determinant moisture of the air masses A for the interchange of and B. Next, assume that air mass A forms the fltransitional layerl! of a moist body the moist surface of which continu- OUSly gives off so muoh water vapor on th,e transitional layer that the partial pressure of water vapor in this transitional layer maintains the average value el. Air mass B is to tie so larga that its specific partial pressure of water vapor ez is not changed by the inflow of the water vapor from A. Then 1 dQ -— L dt is the quantity of water ‘V passing through the transi- E tional layer per unit surface per unit time, that is, the volume of water evaporating per unit surface of body per unit time., The formula reads If e2> el condensation must occur oil the body sur$ace. The amount of water condensed. on the unit surface of the body in unit time is then given by ,.. ....

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4 NACA Technical “Meti.orandum3io.”’’lO28 If water sublimates On the s“urfa.ce of the body, the evaporation heat L is replaced by the quantity L + S, heat of water (8O cal/g). so, s denoting the freezing dif:ferenee .e~ - ez the ratio of by equal, vaor.. pressure condensed to sublimated water is given by the fraction ,, . L+’S =— 686 L 606 So far, no asumptions have = 1.13 : been made concerning quantity and ez.. Naturally, in the event of condensation, el el saturation pressure El of the must he replaced bj the water ’vapor at the temperature of the body surface. In the case of sublimation El a quantity representing the vapor above ice. dealing with icing on aircraft; In the present case, automatically changes to ‘~l, saturation pressure of water that is,, solid bodies in the atmosl?here$ the sublimation formula 1 dV du 1 .dmc -— .=— d.t dt 3 1.13 dt must be interpreted. —- (ea -Zl) The amount of ice sublimated per unit surface of the body in unit time is proportional to the l’ventilation factoru ~ (reference 2). BY definition, this quantity is the air mass dm passing into and out of the transidifferential dt through the tional layer in the time unit surface. quantity, besides being a function of This the speed of the ventilation body form, the surface condition, stantially decided by the strean. Its determination is and the direction of the more of an aerodynamic than an airplane, for instance, dm flow, is at the same time suba meteorological problem. On the effect of the local variation of is such that the ice deposit is not of the z same thickness everywhere; the deposition prefers the lexposedl parts of the structure. mass is, i& addition, inversely The sublimating ice momentary barometric pressure. Hence proportional to the

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NACA Technical Memorandum No. 1028. 5 the sublimating ice mass is, other ‘things being equal, . ,. greater .in..higher,atrnospher.ic layers than near the ground, ,or the same ice mass su-~~~ma’tek-”ihhigher atmospheric. .. layers at a much lower vapor pressure difference than necessary in ground proximity. The simplest method of estimating the vapor pressure difference A = ea - El is to take its amount from one of the conventional tables. But it can be much more clearly expressed if represented in relation to the following elements familiar to the meteorologist: air temperature, degrees Centigrade ‘2 ez partial pressure of water vapor in air E~ saturation pressure of water vapor referred to water at temperature T2 R2=~ saturation ratio in air E2 surface temperature of body in deg C; in the case in ‘1 in point -- sublimation processes - it is always negative El saturation pressure of water vapor referred to water at temperature -r 1 El saturation pressure of water vapor referred to ice at temperature TI R1 = *“ saturation ratio of air referred to ice at the 1 temperature of the body .9?hen ez = E2Ra = %lR1, by definition, and .A = “e2 -%1 =15111-131=~1 (RI -1) In this formula for A, %1 appears as pure function of the surface temperature TI of the body; while R..z is a complex function of the above enumerated single elements. This quantity must be eliminated. For this purpose we put II IIIImmm III ,—.,8 -

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6 NACA Technical Memorandum,No. 1028 which is a formula following from, the definition of the saturati.o~ ratio; EZ is expressed by which affords a satisfactory approximation for small temperature intervals. From this, follows or, after minor transformation: . R.-1= J. 1 dEl -1 Factor — — is constant over a wide temperature El dT range and has the numerical value 0.073, which, entered in the calculation, gives for the desired quantity A El and %1 are quantities which is given with T1. the functional connection of Hence A can be represented in a system of coordinates containing temperature TI as abscissa, and the between air and body surface T2+ T1 temperature difference . as ordinate, leaving the factor R2 freely disposable. The diagram shows two such representations side by side: gives A for R2 = 1, that on The one on the left the right for Ra = 2. The values. curves represent integral A The left side of the diagram, which stipulates air saturated with water vapor, the occurrence of sublimation able extent requires the air indicates that in this case processes of any considertemperature to be -—--m Im Immlmm Imlm-m m mm 1111IIInl m

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NACA Technical Memorandum No. 1028 ? ,. substantially-.-..... . higher than the temperature of the body surfacG. X% ‘l”ciirer-body’emperatur.es.ice. f,orm,ation is possible because of the vapor pressure difference” “E1-”-”YI, if the temperature of the body is above that of the air. In air supersaturated with water vapor the conditions are markedly different - as shown in the right-han’d side - for very’ high supersaturation. in order to bringout the effect more plainly. In supersaturated air sublimation processes can therefore still occur if theobody temperature is much higher than the air, temperature (’7 in the hypothetical case). If no temperature difference exists, sublimation processes already occur to an extent which in saturated air postulate temperature differences in excess of 6° between air and body. Without entering into a discussion as to whether such temperature differences occur, the forcible conclusion can be drawn that the formation of sublimation products is due supersaturated air. The study of temperature less to saturated than to effect on the formation of sublimation products can be undertaken by means of a representation which reproduces the difference values of the ‘ A quantities of the right and left hn.lf of the diagram in a congenerous coordinate system. But even without such a representation, it is readily seen that the maximum differences of this nature occur at high body surface temperatures Tl, that is, near the freezing point. Then it is seen that the formation of sublimation products occurs most abundantly in such air strata the temperature of which is close to the freezing point and supersaturated with water vapor. The representation would be incomplete without the icing processes which are a result of the water in the atmosphere frequently in liquid state - subcooled at temperatures below the freezing point. Such conditions offer the greatest poteitialities for icing. Aerologically, they are tied to air strata that form ,the exchange zones between damp cold air and equally damp warm air (wetting .. fog) l Concerning the water content w which the unit air mass contains in liquid state in, such cases, a number of measurements are available which afford some insight into the order of magnitude of this admixture. In any case, several grams per kil,ogiam of air are involved, although for the time being, a theoretical study of such cases is impossible. M 11 1Im 11mm 11mm ,-,- ,, ,,,.,! !

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/ 8 NACA Technical Memorandum No. 3028 Even so, our considerations can be’ completed to the extent that the sublimation formula must be complemented .by an additive term of the form where a , as before the air mass is a constant, exchanged in unit time through the unit surface of the dmw transitional layer; is the amount of water in liquid dt state entering per unit time per unit surface into the transitional layer, an admixture which with the simultaneously outflowing air is not all removed aga’in, because the partial amount a on the surface of the body freezes on striking it. Hence it can be seen that determinations of w have not merely a purely scientific; but also an eminently practical significance. The arguments are equally applicable in modified form to the process of formation of precipitation elements aggregation in the atmosphere, This of solid state of question is to be discussed elsewhere. Translation by J. Vanier, Natioilal Advisory Committee for Aeronautics. REl?ERI!lNCI!S 1. Noth, H.: Vereisungsgefahr bei I?lugzeugen. Die Die Arb. des Preuss. Aeron. Ohs., Bd. XVI, Heft G. r“ 2. Robitzsch, M,’: Ventilationsfaktor. Gerl. Beitr. Der z. Geophysik (irn Druck).

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NACMlTeohnical Memorandum No. 1028 02 a) E F la 0246 8 10 12 Figure 1 I rig. 1 \ 0 “246 8 10 12 .

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