EFFECTS OF AIRFLOW PARAMETERS ON AIRCRAFT ICING CHARACTERISTICS

Transcription

1 Proeedins o the Asian Conerene on Thermal Sienes 7, st ACTS Marh -, 7, Jeju Island, Korea EFFECTS OF AIRFLOW PARAMETERS ON AIRCRAFT ICING CHARACTERISTICS Xuan Zhan, Jinhun Min *, Xiaomin Wu Tsinhua University, Tsinhua Park Haidian Distrit, Beijin, China Presentin Author: thuzhanxuan@mail.om * Correspondin Author: minj@mail.tsinhua.edu.n ACTS-P ABSTRACT An improved one-dimensional model has been developed to desribe the airrat iin proess, hih is divided into to staes: the dry and et mode iin staes. Rime ie orms on airrat skin at the dry mode iin stae hile laze ie ros on the rime ie and ater ilm develops on the laze ie at the et mode iin stae. The model diers rom the traditional iin models in its assumption that the rime ie is a kind o porous medium and its physial properties are initially aeted by airlo parameters and then vary linearly ith the rime ie thikness. Further, it inludes the runbak ater eet by assumin that Couette lo exists in the ater ilm on the laze ie. Calulations are perormed to analyze the ie aretion harateristis, and the results are ompared ith those iven by the model ith property-onstant rime ie. The eets o airlo parameters on the dierenes beteen these models are investiated. As the liquid ater ontent, airlo veloity, olletion eiieny, and airlo temperature derease, the dierenes in the ie thikness beteen these the models ith property-variable and property-onstant rime ie beome more onspiuous. Criterion assoiated ith the airlo parameters is provided or seletion o the airrat iin model that onsiders both the rime ie property variability and runbak ater eet. KEYWORDS: Airrat iin model; Property-variable rime ie; Runbak ater; Ie aretion; Airlo. INTRODUCTION Airrat iin inreases dra and redues lit, even leads to serious lihidents []. Developments o theoretial models or airrat iin an help improve the auray o ie aretion predition, hih may inreasein the liht saety. Most theoretial and numerial models or airrat iin start rom the lassial Messiner iin model []. Researhers [, ] modiied the Messiner model [] that onsiders only the enery balane beteen the latent heat release and heat transer at as/liquid interae but they inored the heat ondutions in the ie layer and ater ilm. Myers el. [] took into aount the existene o rime ie as ell as the eet o runbak ater in their models but they simpliied the rime ie as property-onstant laze ie. We suests in our previous researh [] that rime ie as atually a kind o porous medium and its eetive properties (suh as the volume ration, density, and thermal ondutivity) ere initially inluened by the airlo parameters and then varied ith the rime ie thikness, hih aets the ie aretion harateristis as shon in Fi.. We urther provide an improved airrat iin model onsiderin both the rime ie property variability and runbak ater eet [7]. z Air Glaze Ie A Pixel 7 z v Water Rime Ie Horizontally Averaed Gray Value z t m Glaze ie Cylinder z r O t s t p Skin t Rime ie r, r Fi. Iin model: Variation o ray value ith ie thikness, Physial iin model. [, 7]

2 For onveniene, the abovementioned three models are reerred to as the PVRI-RW, PCRI-RW, and PVRI models, respetively, here PVRI expresses the property-variable rime ie, PCRI the property-onstant rime ie, and RW the runbak ater. As desribed in Res. [, 7], the initial stae durin hih a sublayer o rime ie orms is alled the dry mode iin stae and the later stae durin hih laze ie/ater ilm develop the et mode iin stae. The time hen the dry mode transits to the et mode is named the ritial time and the ie thikness at that time the ritial ie thikness. In the present paper, the eets o airlo parameters on the ie aretion harateristis and the dierenes beteen these models are investiated, this researh is based on our previous orks [, 7].. THEORETICAL MODEL Fi. shos the basi physial model that onsists o the rime ie layer, laze ie layer and ater ilm. Density varies linearly alon the rime ie thikness but remains onstant in the laze ie layer and ater ilm. Couette lo ours in the ater ilm, implyin thater los ith a linear veloity distribution as shon in Fi., throuh hih the runbak ater eet is onsidered. Some assumptions are made or the model as in Res. [, 7].. PHYSICAL PROPERTIES OF RIME ICE As desribed in our previous papers [, 7], the initial rime ie density at the skin surae, r,, is [], MVD V ( ) exp., S... r... S ( D) ta The initial volume ration and initial eetive thermal ondutivity o the rime ie, hih an be rearded as a kind o porous medium, are [] k k k k k k r, a a r, a r,, r, a k ka r, k ka Assumin that the rime ie properties vary linearly ith the rime ie thikness, the eetive thermal ondutivity is k k k k k k k k B z k B z z a r a r, r k r,, k, k ka z r k ka () () (). DRY MODE ICING AND CRITICAL POINT The ritial time and ritial ie thikness are the same as those in Res. [, 7] Bz r, r, k kr, k tm ts, z Z, Z = V B kln k / k V L r, + qsoure he tm ta (). WET MODE ICING Governin equations. In the ater ilm, the lo driven by the air luid is simpliied as one-dimensional Couette lo. The one-dimensional momentum and enery equations thereore are d v d t dv, k () Boundary onditions. At the rime ie/laze ie interae, the temperature, heat lux, and physial properties o the rime ie are equal to those o the laze ie. At the laze ie/ater interae and air/ater interae, the enery equations satisy t t L k k d z z, t k qon qev a qd qa qk () z zzi z Water ilm. At the rime ie/laze ie interae, the temperature, heat lux, and physial properties o the rime ie are equal to those o the laze ie. The veloity proile in ater ilm and the ater ilm thikness are

3 V V d FT G F z v z zi ; z FT FT FT V d Glaze ie. The relation beteen the laze ie thikness and time an be obtained as t t tm t p ta tm zft L k k k k d z z z z (7) () RESULTS AND DISCUSSION As stated in our previous papers [, 7], the Rune-Kutta method is used to numerially solve these nonlinear dierential equations and the results iven by our model arees ell ith the experimental data on the rime ie and ater ilm thiknesses, supportin the reliability o the model. We note that our papers [, 7] provide a more detailed disussion on the basi ie aretion harateristis, hih may serve as a useul supplement to the above analyses.. EFFECTS OF AIRFLOW PARAMETERS ON CRITICAL POINT As the liquid ater ontent, airlo veloity, olletion eiieny, and airlo temperature inrease, the mass o droplets impatin on the airoil per unit time inreases and so does the amount o latent heat released, hih ats to strenthen the trend that more ater remains liquid, ausin a redued ritial ie thikness and a shortened ritial time, as shon in Fi.. Sine the ritial ie beomes thinner, its thermal resistane dereases, hih in turns an mee release o more latent heat. Also, sine the ritial time beomes shorter, the reezin ration beins to deline earlier, hih in turns slos don the release o latent heat. In addition, the ritial ie thikness iven by the PVRI-RW model is smaller and the ritial time is shorter than those by the PCRI-RW model oin to the variations o rime ie physial properties. As the liquid ater ontent, airlo veloity, olletion eiieny, and airlo temperature derease, the dierenes in the ritial ie thikness and ritial time beteen these to models inrease. V= m,, = -C = /m,, = -C.... /(/m ) = /m, V = m, = -C V /(m) = /m, V = m, () (d) /C Fi. Eets o airlo parameters on ritial ie thikness and ritial time: Liquid ater ontent, Airlo veloity, () Colletion eiieny, (d) Airlo temperature. COMPARISON BETWEEN THE PVRI-RW AND PCRI-RW MODELS The airlo parameters aet not only the ritial ie thikness and ritial time bulso the entire iin proess. Fi. ompares the ie thiknesses enerated by the PVRI-RW and PCRI-RW models or various airlo parameters. As the liquid ater ontent, airlo veloity, olletion eiieny, and airlo temperature derease, the dierenes

4 in density beteen the rime ie and laze ie beome more onspiuous, hih enlares the dierenes in the ie roth rate beteen the to models throuhout the entire iin staes, as seen in Fi.. V = m,, = -C = /m,, = -C =. /m =. /m =. /m V = m V = m V = m = /m, V = m, = -C = /m, V = m, () (d) = -C = -C = -C Fi. Comparison o ie thiknesses enerated by the PVRI-RW and PCRI-RW models or various airlo parameters: Liquid ater ontent, Airlo veloity, () Colletion eiieny, (d) Airlo temperature The above analyses support that the airlo parameter eets on the ritial poinnd ie aretion harateristis obey the same rules: hen the results iven by the PVRI-RW and PCRI-RW models are obviously dierent, the variations o rime ie physial properties need to be onsidered; hen the results iven by the to models are nearly the same, the PCRI-RW model an be rearded as an approximation o the PVRI-RW model. In pratie, hen the rime ie is so thik that the results iven by these to models are obviously dierent, the PVRI-RW model should be adopted beause it an better desribe the real iin proess; hen the rime ie is neliibly thin, the PVRI-RW model an be simpliied as the PCRI-RW model. The dierenes beteen the results enerated by the to models are related losely to the parameter S in Eq. (), rom hih the rime ie density an be alulated. Fi. shos the variation o the ratio o the ritial ie thikness by the PCRI-RW model to that by the PVRI-RW model ith S. When S<, the ne PVRI-RW model is suested, beause it an provide better simulation results... Z /.... S Fi. Variation o the ratio o ritial ie thikness by the PCRI-RW model to that by the PVRI-RW model ith S. CONCLUSIONS With inlusion o the runbak ater eend assumption that the rime ie physial properties vary linearly ith the rime ie thikness, an improved airrat iin model named the PVRI-RW model has been developed, and the eets o the airlo parameters on the ie aretion harateristis are analyzed. The results are ompared ith those by the traditional PCRI-RW model. Folloin are the onlusions:

5 () The airlo parameters aet the rime ie physial properties and runbak ater eet, hih inluene the heat ondutions in the ie layer and ater ilm as ell as the ie aretion proess. () The airlo parameters aet the ritial poinnd ie aretion harateristis. As the liquid ater ontent, airlo veloity, olletion eiieny, and airlo temperature inrease, the ritial ie thikness and ritial time both derease. () The dierenes beteen the PVRI-RW and PCRI-RW models are dependent on the rime ie properties. As the liquid ater ontent, airlo veloity, olletion eiieny, and airlo temperature derease, the dierenes in the ie thiknesses beteen these to models beome more onspiuous. () When S<, the PVRI-RW model is reommended or simulatin the airrat iin proess. ACKNOWLEDGMENT This researh is unded by National Key Basi Researh Proram o China (No. CB7). NOMENCLATURE B equation oeiient MVD mean volumetri droplet diameter (μm) phase speed o surae aves (m) t temperature ( C) D airoil leadin ede diameter (m) v veloity (m) volume ration v mean veloity (m) F reezin ration V airlo veloity (m) i interaial rition ator V ater veloity at the air/ater (m) interae F interaial shear stress atin on the (N/m ) z thikness oordinate (m) T ater ilm at the air/ater interae k thermal ondutivity (W/m-K) ritial ie thikness iven by the (m) PVRI-RW model L latent heat o usion (J/k) Z ritial ie thikness iven by the (m) PCRI-RW model Greek Symbols olletion eiieny density, - k m (k/m ) liquid ater ontent (LWC) (k/m ) time, s (s) visosity, (N s/m ) Subsript a air i ie ritial r rime ie laze ie ater REFERENCE [] Y.H. Cao, Z.L. Wu, Y. Su, Z.D. Xu, Airrat liht harateristis in iin onditions, Pro. Aerosp. Si. 7 () -. [] B.L. Messiner, Equilibrium temperature o an unheated iin surae as a untion o air speed, J. Aeronaut. Si. () () -. [] T.G. Myers, Extension to the Messiner model or airrat iin, AIAA J. () () -. [] Y.X. Du, Y.W. Gui, C.H. Xiao, X. Yi, Investiation on heat transer harateristis o airrat iin inludin runbak ater, Int. J. Heat Mass Transer ( ) () [] T.G. Myers, C.P. Thompson, Modelin the lo o ater on airrat in iin onditions, AIAA J. () () -. [] X. Zhan, J.C. Min, X.M. Wu, Model or airrat iin ith onsideration o property-variable rime ie, Int. J. Heat Mass Transer 7 () -. [7] X. Zhan, X.M. Wu, J.C. Min, Airrat iin model onsiderin both rime ie property variability and runbak ater eet, Int. J. Heat Mass Transer (7) -. [] M. Rios, Iin simulations usin Jones' density ormula or areted ie, Reno, Nevada,. [] H.T. Aihlmayr, F.A. Kulaki, The eetive thermal ondutivity o saturated porous media, in: G.A. Greene, J.P. Hartnett Avram (Eds), Advanes in Heat Transer, Elsevier,, pp. 77-.