CALCULATION OF THE HEAT TRANSFER AND TEMPERATURE ON THE AIRCRAFT ANTI-ICING SURFACE

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1 7 TH INTERNATIONAL CONGRESS OF THE AERONAUTICAL SCIENCES CALCULATION OF THE HEAT TRANSFER AND TEMPERATURE ON THE AIRCRAFT ANTI-ICING SURFACE W. Dong, J. J. Zhu, X. H. Min Shool of Mehanial Engineering, Shanghai Jiaotong University, Shanghai 0040, CHINA Phone: ,Fax: Keywords: Anti-iing,Heat transfer,droplet impingement property,water film,energy balane Abstrat Ie aretion on the airraft wings, tails or any other key omponents may seriously hange the aerodynami harateristis of the airraft, ausing lift dereasing, drag inreasing, poorer operating quality, and a hazard of the flying safety. Anti-iing/deiing systems are widely used in airraft. Anti-iing or deiing systems an prevent ie aretion or remove the ie on the airraft surfae to a ertain extent, and onsequently ensure the flying safety. A numerial method of the heat transfer and temperature on the airraft anti-iing surfae is presented. An improved anti-iing model, whih taking into aount of the oupling effets of film layer and the air boundary layer, is developed. A film breaking up analysis method using a stability energy balane theory is introdued for alulating surfae wetness fator distribution. The oupling effets of heat transfer and mass transfer are onsidered in the surfae temperature alulation. Based on the modified model, a speial program is developed to alulate the surfae temperature of the antiiing airfoil, and the omputation results are ompared with the experiment results. 1 Introdution Ie aretions will our on the exposed omponents of an airraft suh as the windsreen, the wings, the tail and the engine inlet system when the airraft enter into louds whih ontain super-ooled droplets. Inflight iing may seriously affet the original aerodynami harateristis and result in handling diffiulties. For airraft engine, ie aretions on the inlet omponents an worsen the air ingestion harateristis. In addition, sheded ie may be suked into the engine and indues serious aident. In order to redue the hazards aused by in-flight iing, various methods of ie protetion system have been developed. These an be lassified in de-iing and anti-iing ategories. The anti-iing prevents ie aretion on partiular surfae either by evaporating or partially evaporating super-ooled droplets that impinge on the surfae. The partially evaporating anti-iing system allows the impinging liquid run bak to the unproteted area and form an tolerable ie layer. Most of airraft adopt thermal anti-iing system with ompressor bleed hot air as heating soure. In reent years, many omputational models of the ie aretion were developed to improve the design of ie protetion systems. Computational simulation odes of iing have been developed at ONEAR, DAR, NASA et al. These ie aretion simulation odes onsist of four basi steps[1]: omputation of aerodynami flow; determination of superooled droplet trajetories and loal olletion effiieny; thermal balane analysis of the air--ie-body system; determination of the shape of the ie aretion. For analysis of evaporating anti-iing systems, the step of iing shape predition an be eliminated as no ie is allowed to aumulate on the surfae of omponent. Flow field around the body an be obtained by solving Euler or Navier-Stokes equations and the onvetive heat transfer oeffiient on the iing surfae an be obtained at the same time. Super-ooled droplet 1

2 W. DONG, J. J. ZHU,X. H. MIN trajetories an be traked using a Lagrangian approah[,3,4] and subsequently the loal olletion effiieny on the surfae an be alulated. Another approah for determining the mass of droplets impinging on the surfae is Eulerian approah, whih solves flow field and the droplet equation of motion using the same grid and numerial tehniques. Bourgault et al.[5] have developed a ode using Eulerian approah to alulate impat loads on omplex geometries. Both of Lagrangian approah and Eulerian approah an give satisfied droplet impingement results. Most ie aretion odes ompute the surfae temperature and predit the ie growth rate using heat and mass balane model given by Messinger[6]. The heat balane model is important for prediting ie aretion proess and ie shape. The physis mehanism for iing problem is not well known and the models are improved ontinuously in order to solve this omplex problem more aurately. Al-Khalil[7] utilizes the breakup of a uniformly thin liquid film into individual streams or rivulets to more aurately desribe the physis of runbak. Al-Khalil et al.[8,9]developed the heat transfer and film models for the runbak in numerial simulation thermal anti-iing system. Yi X[10] modified the thermodynami iing model and finished numerial simulations of rime, glaze and mixed ie aretion on the airfoil surfae. Silva et al. [11,1] developed a thermal model onsidering oupled and mass transfer effets for anti-iing numerial simulation. Al-Khalil et al. [13] validated transient eletrothermal de-iing and anti-iing simulations ode LEWICE and steady state hot gas and eletrothermal anti-iing simulations ode ANTICE by results of an experimental program. Whalen E A et al. [14] investigated the aerodynamis phenomenon of the runbak ie aretions using boundary-layer measurements and fluoresent-oil flow visualization. The present study onsists of an improved anti-iing model onsidering the effet of runbak and the oupling effet of film layer and the air boundary layer. A film breaking up analysis method using stability energy balane theory is introdued for alulating the surfae wetness fator distribution, heat transfer oeffiient and the surfae temperature. Colletion effiieny alulation The Super-ooled droplet trajetories and loal olletion effiieny are alulated by Lagrangian approah and the flow veloities around the body are obtained from numerial simulation. The equation of motion for droplets is formulated with the following assumption: the droplets remain spherial; the droplets do not affet the flow field. The equation is, = D+ P+ Gw d U m (1 w dt D is the drag fore on the droplet, P is the pressure differene fore, G w is gravity fore on the droplet, mw, d U U and are its mass, dt veloity and aeleration. the pressure differene fore is small, so it an be ignored. The drag fore D is, 1 D = Cd ρ a V U Aw ( ρ a and V are air density and veloity, Aw is frontal area of the droplet, C d is the drag oeffiient and an be omputed using experiene equation as follows, C d Re = Re Re (3 Re is relative Reynolds number and is defined as, ρ d r ( V U a Re = (4 μ a r

3 CALCULATION OF THE HEAT TRANSFER AND TEMPERATURE ON THE AIRCRAFT ANTI-ICING SURFACE d is diameter of the droplet, μa is air visosity. Loal olletion effiieny β is defined as the ratio of the area of impingement to the area through whih the passes at some distane upstream of the airfoil. 3 Mass balane and Energy balane model The anti-iing omponent surfae will form a film, and the film will runbak due to aerodynami fores. An improved energy balane and mass balane model is developed. This model treats runbak film layer and the air boundary layer as two related regions, the veloity gradient and enthalpy transport are taken into aount shown in Fig.1. The heat ondution of solid ll is also onsidered. Fig.1 Runbak Water Film on the Surfae 3.1 Mass balane on the surfae For the ontrol volume, the mass balane equation is, m & + = + (5 in imp out evap The terms of in, imp, out, evap represent the inlet mass rate, droplets impingement mass rate, outlet mass rate and evaporation mass rate respetively. Sine loal olletion effiieny has been obtained, the mass flow rate of droplet impingement an be easily alulated by, = V v β A LWC (6 imp ht Aht is impingement surfae area of the ontrol volume, LWC is the liquid ontent. 0.6Ih pv, p air v, e evap = FAht ( (7 p p p, e v, Where p v refers to the loal saturated vapor pressure, whih is a funtion of temperature; p e is the loal pressure. F is Wetness fator, whih s defined as the ratio of wet region area to the total area. The following volume s inlet fae is the urrent volume s outlet fae, and in the stagnation point, there is no mass flow rate through the inlet fae, so we an obtain mass flow rate of the eah inlet and outlet surfae volume by volume. 3. Energy balane on the surfae Aording to the energy onversation law, the energy balane equation an be written as, T h v Qanti ie + k ll All + (1 F r s = Fh Aht ( Tll T + (1 F h A ( T T air ht ll re air e p, air A ht (8 The terms of the left side of Eq.(8 represent the energy of anti-iing heating, ondution and aerodynami heating respetively. The terms of the right side of Eq.(8 represent onvetion heat transfer between ll and and onvetion heat transfer between ll and air respetively. Condution is only onsidered in s diretion, while ondution in y diretion is negleted. k ll is thermal ondutivity of the solid, p is speifi heat, r is reovery fator, T re is the air reovery temperature, an be alulated as follows, T re k 1 Tre = (1 r Te + rte (1 + Me (9 Where k is the ratio of speifi heats. Energy balane equation for the film an be given as:, Fh out = Fh ( T T air A ht ( T out Aht ( T T ll in T + imp T + i] re + ( in v [ + evap p, p, [ T ( T p, in T (10 3

4 W. DONG, J. J. ZHU,X. H. MIN From left to right, the terms of above equation represent onvetion heat transfer between film and ll, the inrease of film s enthalpy, kineti energy ontribution of the impinging droplets, onvetion heat transfer between film and air, heat loss by evaporation, respetively. Subsript represent freestream. T in and T out are the temperatures at the inlet and the outlet. i is the latent heat of. T is the average temperature of the film on the surfae, whih is defined as, T & & mint in + moutt out = (11 Where is the average mass of the film on the surfae, m & = + / (1 ( in out In the mass and energy equations, onvetion heat transfer oeffiients are needed. They an be approximately got by using the experiential expressions or obtained from the results of CFD omputation. For the leading edge, the experiened onvetion heat transfer oeffiient an be alulated using the following equation: hd θ 3 Nu D = = 1.14 Re D Pr [1 ( ] k 90 (13 ( θ 80 D refers to the leading edge s diameter. Other loations Nusselt number an be alulated using the following equation, Nu = Pr (14 S Re S Where the subsript s refers to the urve length from the stagnation point to the loal position. 4 Wetness fator distribution analysis Surfae wetness fator distribution is obtained using stability minimum total energy riteria from the film breaking up model. The total energy of the runbak film shown in Fig. is given as, 1 3 E film total + ll 1 = mv lδx + ll air + air ( L l Δx lδx Fig. Water Film Breaking up Model (15 The terms of the right side of Eq.(15 represent kineti energy, interfaial energy of film and air, interfaial energy of film and ll surfae, interfaial energy of air and ll surfae respetively. Aording to the theory of physial hemistry, the three surfae tension oeffiients have the following relationship, = ll air osθ 0 (16 ll air + Where θ 0 is the stati ontat angle of and ll. m = ρ ld Δx (17 V y 1 = 0 y V dy (18 Hene, the total energy equation of film is, m y E = Vdy + y 0 m air (1 osθ 0 ρ be, + y ll air LΔx (19 When the film breaks up, there should E( y = 0 y= d y (0 Assuming the veloity distribution of film in y diretion is liner, the ritial thikness and mass flow rate an be obtained as, 4

5 CALCULATION OF THE HEAT TRANSFER AND TEMPERATURE ON THE AIRCRAFT ANTI-ICING SURFACE d ρ (, = 1.44[ τ = bρ μ 1/ 3 Where, air ρ 0 d V / 3 air (1 osθ τ ( μ 0 1/ 3 ] dy = 1.04b (1 osθ / 3 0 (1 ( V, e τ = μ (3 y When the mass flow rate of film is less than the ritial mass flow rate, runbak film will break up, and the wetness fator an be alulated as, F = (4, impinging area and the wet fator is equal to unit. Table 1 Heaters Loations and Power Densities Heater Loation (s/ Heater Element Power Density (kw/m Start End F D B A C E G Considering flow is unstable in the impingement region, the wet fators in this region are assumed to be unit. 5 Results and disussion 5.1 Referene ase and alulation results Based on the modified model, a speial program is developed to alulate the droplet impingement harateristis and the surfae temperature distributions. One ase is hosen to run, and then the obtained surfae temperature is ompared with the experiment result. The veloity and temperature of freestream is 44.7m/s and -7.6, MVD is 0 μ m, LWC is 0.78g/m 3, attak angle is 0. The sizes of the test airfoil are shown in Fig.3, the power density distributions of the heaters are listed in Table 1 and other test onditions are mentioned in Ref.13. Fig.4 shows the omparison of loal olletion effiieny alulated by the program and ONERAD. In this ase, the heating energy is so large that most of droplets evaporate as they reah the surfae. The wet region falls into the Fig.3 Struture and Size of the Test Component Fig.4 Loal Colletion Effiieny Calulation Fig.5 shows the surfae temperature results alulated by the program using experiened onvetion heat transfer oeffiient. There is some differene between this result and experimental result in dry regions. It seems that in dry regions, the onvetion heat transfer 5

6 W. DONG, J. J. ZHU,X. H. MIN oeffiient using experiential expressions may result in lower temperature on the surfae. (b MVD=40 μ m Fig.5 Surfae Temperature Calulation 5. The effet of MVD in droplet impingement For different droplet mean volume diameters (MVD, the impingement harateristis are different. In this paper, the impingement harateristis of different MVDs are alulated. The results of loal olletion effiieny are shown in Fig.6 and the impinging trajetories are shown in Fig.7. ( MVD=50 μ m (d MVD=70 μ m Fig.7 Water Droplet Impingement Trajetories of Different MVDs Fig.6 Loal Colletion Effiieny of Different MVDs (a MVD=0 μ m The above pitures show that both the loal olletion effiieny and the impinging area inrease when the droplet MVD inrease. So when airrafts pass through louds whih ontain large droplets, more anti-iing energy is needed. 5.3 The effet of heat transfer oeffiient The oeffiient may influene the results of the temperature on the surfae. The oeffiients alulated by CFD are also given in this paper. The results are shown in Fig.8, and the surfae temperature alulated using the heat transfer oeffiient omputed by CFD is shown in Fig.9. Obviously, the results using the oeffiients whih alulated by CFD are muh loser to the 6

7 CALCULATION OF THE HEAT TRANSFER AND TEMPERATURE ON THE AIRCRAFT ANTI-ICING SURFACE experimental data. The omputation results show that heat transfer oeffiient is one of the key parameters in the alulation of surfae temperature. Fig.10 Surfae Temperature with Different LWCs Fig.8 Comparison of Convetion Heat Transfer Coeffiient Fig.11 Surfae Water Mass Flow Rate with Different LWCs Fig.9 Comparison of Surfae Temperature 5.4 The effet of LWC LWC is another key parameter whih an affet the surfae temperature. In this paper the freestream ondition of LWC=0.9g/m 3 is also alulated. The results of surfae temperature distribution and mass flow rate of film are shown in Fig.10 and Fig.11 omparing with LWC=0.78g/m 3. Fig.10 and Fig.11 show that LWC=0.78g/m 3 and LWC=0.9g/m 3 don t affet the impingement region surfae temperature seriously under this omputation ondition, beause eah kind of heat flux in this region doesn t hange greatly as LWC hanges. But in some other regions, higher LWC will result in lower surfae temperature. 5.5 The effet of MVD Large MVD will lead to the inrease of the loal olletion effiieny and impinging area and derease the surfae temperature. The results of surfae temperature using MVD=0 μm and MVD=40 μ m at LWC=0.78g/m 3 are shown in Fig.1. Computation results show that the surfae temperature dereases when the MVD inreases. Fig.1. Surfae Temperature with Different MVDs 7

8 W. DONG, J. J. ZHU,X. H. MIN Fig.13. Wet Fator on the Surfae MVD=40 μ m Fig.13 shows the wet fator on the surfae when MVD=40 μ m at LWC=0.78g/m 3. Out of the impinging region, the wet fator is very small, whih means the runbak mass flow rate is less than the ritial mass flow rate. Under this ondition, the runbak flow should be rivulet flow. Considering of the probable inauray of the wet fator assuming unit in wet region, it is needed to do further researh. 5.6 Analysis of different heat flux It is neessary to find out the heat transfer proess in anti-iing surfae. The heat flux perentages of heating or ooling the surfae are given, the results are shown in Fig.13 and Fig.14. Fig.14 Heat Flux Perentages of Heating the Surfae Fig.15 Heat Flux Perentages of Cooling the Surfae. Fig.14 shows that the heat flux of aero heating and droplet impingement an be negleted. The film on the surfae an absorb some energy and bring the energy to downstream. Fig.15 shows that the two largest heating flux terms are the evaporating and onvetion heat transfer. The rest is mostly taken ay by heating the droplets. Runbak absorbs and stores the energy and takes it to downstream. 6 Conlusion Based on the analysis of droplets movement equation and energy balane on the surfae, an improved anti-iing model onsidering the oupling effets of film layer and the air boundary layer is developed. A film break- up analysis method using stability energy balane theory is introdued for alulating surfae wetness fator distribution. Using the modified model, a speial program is developed to alulate the surfae temperature of the antiiing wings, and the omputation results are ompared with the experiment results. Furthermore, the perentages of the different heat flux on the surfae are analyzed and the effet fators on surfae temperature in alulation are also given. The results show that onvetion heat transfer oeffiient is a very important parameter in surfae temperature alulations. MVD of droplets make a notable impat on surfae temperature, beause larger MVD 8

9 CALCULATION OF THE HEAT TRANSFER AND TEMPERATURE ON THE AIRCRAFT ANTI-ICING SURFACE leads to larger loal olletion effiieny and impinging area. The heat flux perentages of heating or ooling the surfae show that the two largest heating flux terms are the evaporating and onvetion heat transfer. In addition, the energy of heating impingement liquid annot be negleted. Using the film break-up model developed in this paper, the results of the wet fator is very small at out of the impinging region under the omputation flow ondition. Further researh of this problem is needed. Referenes [1] Kind R J, Potapzuk M G, Feo A, Golia C, Shah A D. Experimental and omputational simulation of inflight iing phenomena. Progress in Aerospae Siene. Vol.34, pp , [] Potapzuk M G. A review of NASA Lewis development plans for omputational simulation of airraft iing. AIAA , 1999 [3] Tran P, Brahimi M T, Tezok F, Parashivoiu I. Numerial simulation of ie aretion on multiple element onfigurations. AIAA ,1996 [4] Hou Y ZH, Mehanism study on heat transfer and flow of hot air anti-iing for guide vane. M.S. Thesis, Shanghai Jiaotong Univ., Shanghai, 009. [5] Bourgault Y, Habashi W G, Dompierre J, Boutanios Z, Di Bartolomeo W. An Eulerian approah to superooled droplets impingement alulations. AIAA , [6] Messinger B L. Equilibrium temperature of an unheated iing surfae as a funtion of air speed. Journal of the Aeronautial Sienes, Vol.0, pp [7] Al-Khalil K M, Numerial simulation of an airraft anti-iing system inorporating a rivulet model for the runbak. Ph.D Thesis, Univ. of Toledo, Toledo, OH,1991. [8] Al-Khalil K M, Keith T G, DeWitt K J, Nathman J K and Dietrih D A. Thermal analysis of engine antiiing systems. Journal of Propulsion and Power. Vol.6,No.5, pp , [9] Al-Khalil K M, Keith T G, DeWitt K J. New onept in runbak modeling for anti-ied airraft surfaes. Journal of Airraft. Vol.30, No.1, pp.41-49, [10] Yi X. Numerial omputation of airraft iing and study on iing test saling law. Ph.D Thesis, China Aerodynamis Researh and Development Center Mianyang, 007. [11] Silva G A L, Silvares O M, Zerbini E J G J. Numerial Simulation of Airfoil Thermal Anti-Ie Operation Part 1: Mathematial Modeling. Journal of Airraft. Vol.44, No., pp , 007. [1] Silva G A L, Silvares O M, Zerbini E J G J. Numerial Simulation of Airfoil Thermal Anti-Ie Operation Part : Implementation and Results. Journal of Airraft. Vol.44, No., pp , 007. [13] Al-Khalil K M, Horvath C, Miller D R and Wright W. Validation of NASA Thermal Ie Protetion Computer Codes Part 3:Validation of ANTICE. NASA TM , Cleveland, OH, May 001. [14] Whalen E A, Broeren A P, Bragg M B. Aerodynami of saled runbak ie aretions. Journal of Airraft. Vol.45, No., pp , 008. Copyright Statement The authors onfirm that they hold opyright on all of the original material inluded in this paper. The authors also onfirm that they have obtained permission, from the opyright holder of any third party material inluded in this paper, to publish it as part of their paper. The authors onfirm that they give permission, or have obtained permission from the opyright holder of this paper, for the publiation and distribution of this paper as part of the ICAS010 proeedings or as individual off-prints from the proeedings. Aknowledgements The authors would like to reognize people who made this researh program possible. The authors at Shanghai Jiaotong University were supported by the National Natural Siene Foundation of China under Grant No