Simulation of Gas-Solid Flow in Inlet Particle Separator on Probabilistic Restitution Model

Transcription

1 Intenational Foum on Enegy, Envionment Science and Mateials (IFEESM 15) Simulation of Gas-Solid Flow in Inlet Paticle Sepaato on Pobabilistic Restitution Model Ke-ke ZHANG1,a *, Hai-yang HU1 and Qiang WANG1 1 School of Enegy and Powe Engineeing, Beihang Univesity, Beijing , China a @qq.com Keywods: paticle ebound; paticle-wall collision; estitution atio; pobabilistic estitution; gas-solid flow; inlet paticle sepaato. Abstact. The pobabilistic estitution model was adopted by fitting pobability functions with Gauss-Hemite method fo the integal inlet sepaato paticle tajectoy simulation compaed with deteministic estitution model and elastic collision model. Result shows that the above thee bounce models pefom well in AC coase sand sepaation pediction. Fo C-spec sand, esults based on elastic collision model deviate fom test data seiously, and the deteministic estitution model ove pedicts its sepaation efficiency, especially fo the swiling inlet paticle sepaato, while the pobabilistic estitution model achieves an intemediate value which shows a good ageement with test data. Intoduction Integated inlet paticle sepaato IPS (Inlet Paticle Sepaato) is a kind of helicopte ai puification equipment, potecting the engine by emoving sand paticles fom the inlet ai [1,2]. With a smalle density than the ai phase, sand s movement mainly depends on ai dag foce, and is influenced by paticle estitution chaacteistics afte collision with wall [3]. Its chaacteistics is elated to sand s paticle shape, size, impact velocity, wall suface featues, etc. W. Tabakoff concluded, fom expeimental studies, that paticle ebound velocity and diection shows andom, but its estitution atio obtained fom multiple tests pesents a clea statistical law, which is a single-valued function of the impact angle [5,6]. Recent simulation methods fo paticle-wall collision (including mainsteam commecial softwae) ae based on the deteministic estitution model, which ignoes the ebound andomness [7,8,9]. A. Hamed founds that, fom a vaiety of expeimental and numeical studies, pobabilistic model pefoms bette than deteministic model in lage paticle size paticle tajectoy simulation and suface abasion chaacteistics pediction [3,10]. But the Monte Calo method, A. Hamed used, to obtain the statistical chaacteistics of local paticle ebound speed and angle by tacking the amount of andom obits is too computationally expensive to solve difficult engineeing calculations fo complex poblems. Theefoe, thee is a need fo an impoved, high efficiency method to descibe the pobabilistic model. The five-point Gauss-Hemite integal method was used hee by fitting the pobability density functions of paticle estitution coefficient. This method is used in the numeical simulation of the gas-solid flow in the two-dimensional non-swiling IPS and thee dimensional swiling IPS espectively. Analysis on the pos and cons of diffeent paticle-wall collision models was pefomed accoding to elevant expeimental data. Numeical Calculation Method All numeical calculation in this pape is based on ou own pogam. As sand concentation is small, the effects of paticles on ai is ignoed. Calculation of Reynolds-aveaged Navie-Stokes ( N-S ) equation [11] based on finite volume method is used to simulate the ai flow field. Paticle Movement Equation. The dag foce detemines how paticle and ai inteact in IPS [3]. Paticle movement is simulated by Lagangian Method [12], given as Eq The authos - Published by Atlantis Pess 637

2 Intenational Foum on Enegy, Envionment Science and Mateials (IFEESM 15) 1 dk du k = (U U k ), U k =. dt τ Vk dt (1) whee U k is paticle velocity, and U is local ai velocity, and τ Vk is the paticle velocity elaxation time, which is solved on the dag foce model [13,]. Paticle Restitution Chaacteistics. W. Tabakoff poposed the concept of paticle estitution atio on the basis of expeimental studies, as shown in Fig. 1. Velocity estitution atio ev and angle estitution atio e ae defined as the following foms: Uk2 ev =, e = k 2. U (2) Uk 2 Uk 1 k 2 Fig.1 Paticle-wall collision nomenclatue whee U k 1, ae impact velocity and angle, U k 2, k 2 epesent paticle ebound velocity and angle. The mean values and standad deviations in tems of impact angle ae shown as Eq. 3[5,6] : ev0 = k k e = k σ = ev σ = e (3) whee σ ev, σ e ae coesponding standad deviations of mean estitution atios. Assumed that the paticle ebound velocity and ebound angle afte collision ae nomally distibuted espectively and they had nothing to do with each othe. Thei pobability density functions ae dsecibed as: pev,e 1 = pev pe = e 2πσ ev ( ev ev0 )2 2σ ev 2 1 e 2πσ e ( e e0 )2 2σ e 2. (4) Based on a five-point Gauss-Hemite integation, statistical mean value of any function F in tems of paticle estitution atio can be expessed as: F ( U, ) p p d d F (U k 2,i, k 2, j )wi w j. k 2 k 2 ev e ev e π i =1 j =1 whee U k 2,i = U (ev0 + 2σ e xi ), k 2, j = 1 (e0 + 2σ e x j ), and ( xi, wi ) is integal point and its weight facto [15]. 15. The authos - Published by Atlantis Pess 638 (5)

3 Intenational Foum on Enegy, Envionment Science and Mateials (IFEESM 15) When σ ev = σ e = 0 Eq. 5 degades into the mean estitution coefficient model. When σ ev and σ e ae both not 0, one paticle divides into 25, and its weight facto degades fom 1 to wi w j afte collision with the wall. To educe the amount of computation, paticle ebound chaacteistics is teated by mean estitution coefficient fom the thid paticle-wall collision, which means a paticle will split up to 625 tacks. Simulation of Gas-Solid Flow in Integal IPS Main IPS Pefomance Paametes. Total pessue loss of the ai is defined as: P = Pt1 Pt 2. (6) whee Pt1 is the total pessue of the inlet flow, Pt 2 is the total pessue of the outlet flow. Sepaation efficiency is defined as: η w = W p1 / (W p 0 + W p1 ) 100%. (7) whee W p 0 is the mass flow ate of sands out of the coe flow, and Wp1 is the mass flow ate of sands out of the scavenge flow. Scavenge coe atio (SCR) is defined as: SCR = Wa1 / Wa 0 100%. (8) whee Wa0 is the coe ai flow ate, Wa1 is the scavenge ai flow ate. Simulation of Gas-Solid Flow in Vaneless IPS. Typical vaneless IPS geomety model is established based on 5.0lb/s IPS configuation VI in efeence [,17]. Refe to the elevant IPS flow field simulation liteatue [,19], additional vetical shinkage is installed at the tail of the scavenge passage in case that eflux appeas on the bode, as shown in Fig. 2. Fig. 3 shows the mesh distibution fo this IPS model consisting of fluid elements. Vetical Shinkage Oute Wall Scavenge Flow Inlet Splitte Inne Wall Coe Flow Fig.2 Sketch of the vaneless IPS Fig.3 Two-dimensional mesh aangement fo the vaneless IPS Bounday condition: Inlet total pessue is set to Pa, and the mass flow ate of coe flow and scavenge flow is detemined by the test data. Testing sand size, C-spec sand, AC coase sand, obeys Rosin-Rammle distibution []. As the entance test model is equipped with hoizontal sand blowe, the aveage velocity of the inlet ai is set as sand initial velocity. Fig. 4 shows the velocity images of flow field in conditions of coe mass flow being 4.88lb/s and SCR being 17.15%. Thee is a clea eciculation egion nea the exit of the scavenge channel, and the total pessue loss of ai fom the inlet to the coe flow exit is 988Pa. The intuitive velocity distibution demonstates that the vetical contaction section ensues no eflux on the scavenge exit bode. The simulation esult of wall static pessue is showed in Fig. 5 with compaison with tests data, illustating the accuacy of the flow field calculation. 15. The authos - Published by Atlantis Pess 639

4 Intenational Foum on Enegy, Envionment Science and Mateials (IFEESM 15) 1. 1 Ps / b a I nne I nne Wa l l - - Ca l c u l a t i o n Wa l l - - Te s t Da t a i n Re f. Ou t e Wa l l - - Ca l c u l a t i o n Ou t e Wa l l - - Te s t Da t a i n Re f Z F o m Sp l i t t e L e a d i n g Ed g e / m Fig.4 Axial velocity (m/s) vaiation Fig.5 Wall static pessue Fig. 6 shows the sepaation efficiency esults of AC coase and C-spec unde diffeent SCR and the compaison with expeimental data. Value deviations of AC coase sand sepaation efficiency fom expeimental data based on the thee ebound models ae close. Calculation esults of C-spec sand sepaation efficiency on deteministic estitution model, eaching moe than 95%, is obviously highe than test data (The sand enteing the coe flow value amounts to half of the expeimental value), and the pediction esults of elastic collision model was too low. In contast, the simulation esults on pobabilistic estitution model is ight between the above values as shown in the figue, closest to test esults On P o ba b i l i s t i c Re bo un d Mod el On Det e mi n i s i t i c Bou nc e Mod el On El a s t i c Co l l i s i o n Mo de l Te s t Dat a i n Ref ηw/ % 1 00 ηw/ % 100 On P o ba bi l i s t i c Reb ou nd Mod el On Det e mi ni s i t i c Bo un c e Mod el On El a s t i c Col l i s i on Mod el Te s t Dat a i n Ref (a) Fo Coase Sand (b) Fo C-spec Sand Fig.6 Compaison of analytical and expeimental sepaation efficiency esults fo AC coase sand (a) and C-spec sand (b) Fig. 7 shows pat of 3μm paticle tajectoies based on pobabilistic estitution model. The 3-µm paticle is mainly influenced by ai dag foce and does not ente the eciculation zone with no collision to the wall. The othe two ebound models each the same esults. Fig.7 Paticle tacks based on pobabilistic estitution model fo 3-μm sand Fig. 8 shows pat of 83-μm paticle tajectoies on pobabilistic estitution model and its local amplification. Afte the fist collision with the wall, one paticle splits into 25 ebounding in five diffeent diections, and thee ae five paticles with diffeent speeds in each diection. Unde diffeent 15. The authos - Published by Atlantis Pess 640

5 Intenational Foum on Enegy, Envionment Science and Mateials (IFEESM 15) dag foces, these paticles in the same diection gadually sepaate. To facilitate the mapping, the figue only shows thee paticles tajectoies with diffeent speed in each ebound diection afte the fist collision (amount 15 tajectoies), and shows 4 paticle tajectoies in thee diections afte the second collision. To save computing esouces, paticle tajectoy no longe divides fom the thid collision and ae calculated on deteministic model. Fig. 9 shows paticle tajectoies based on the othe bounce models. Paticles, on elastic collision model, ebound away easily fom the oute suface with a high nomal velocity, and flow into the coe channel. In contast, paticles moving on deteministic model have a lowe estitution coefficient, with obviously declined ebound velocity and angle, and gathe nea the oute wall into the scavenge channel. The calculation esult on pobabilistic model is ight between the above two ones. Fig.8 Paticle of 83-μm tacks on pobabilistic estitution model Fig.9 Paticle tacks of 83-μm based on deteministic estitution model and on elastic collision model Fig. 10 shows paticle sepaation efficiency esult calculated on the above thee bounce models fo diffeent diamete, concluding that these bounce models have no diffeence in sepaation efficiency calculation fo less than 30-μm paticles, and they have fo lage paticles. It mainly lies in that the small paticle moves unde the influence of the ai dag, and lage paticle s movement is affected by paticle-wall collision chaacteistics. Thee is a basically same esult in the liteatue [3] ηw% 40 0 On P o ba b i l i s t i c Re s t i t ut i o n Mod e l On De t e mi n i s i t i c Re s t i t u t i on Mo d e l On El a s t i c Co l l i s i o n Mo de l Pa t i c l e Di a me t e / µm Fig.10 Analytical sepaation efficiency fo diffeent paticle sizes based on the above thee bounce models Simulation of Gas-Solid Flow in Swiling IPS. The swiling IPS geomety model is established accoding to configuation V of 5.0lb/s IPS in the liteatue [-17], containing 9 swil blades and 9 deswil blades. The peiodic bounday is used in the nomal section, coveing 40 cicumfeence (including a swil blade and a deswil blade). The mesh distibution fo this IPS model is shown in Fig. 11, consisting of fluid elements. 15. The authos - Published by Atlantis Pess 641

6 Intenational Foum on Enegy, Envionment Science and Mateials (IFEESM 15) Bounday condition: Inlet total pessue is set to Pa. Coe tunnel mass flow is set to 0.252kg/s, and scavenge mass flow is set to kg/s (accoding to SCR 17.92% ) Fig. 12 shows the calculated axial ai velocity (W) distibution in the IPS, thee is an obvious eflux zone nea the sepaato oute wall in the scavenge channel. Fig. 13 shows the total pessue loss calculation esults of the coe flow fo diffeent SCR, which agee with expeimental values well. Fig.11 Thee-dimensional mesh aangement Fig.12 Axial velocity (m/s) distibution in swiling IPS Pt / k Pa Ai To t al P es s u e Lo s s - - Ca l c u l at i o n Tes t Dat a i n Re f Fig.13 Compaison of analytical and expeimental coe pessue losses fo the swiling IPS Fig. shows the simulation esults of paticle concentation distibution in the swiling IPS based on pobabilistic estitution model and deteministic estitution model. Fo 4.5-µm paticles, the concentation distibution based on the above two models seems no diffeence. Fo 455-µm paticles, the concentation distibution based on deteministic model shows clea paticle tajectoies. Afte impact with the fome pat of inne wall, the latte pat of oute wall and the lip of splitte, most paticles ebound into the scavenge tunnel. In contast, paticle concentation image calculated on pobabilistic model seems moe unifom. Thee is a clea paticle steam into the coe flow and no appaent paticle tajectoy. Fig. Sand density (kg/m3) vaiation fo the swiling IPS fo paticles of diffeent size Fig. 15 shows sepaation efficiency of AC coase and C-spec sands fo diffeent SCR on the above thee bounce models. Fo AC coase sand, the esults on the thee models ae close, and agee with expeimental values well. Fo C-Spec sand with lage diamete, the esults on deteministic model is 15. The authos - Published by Atlantis Pess 642

7 Intenational Foum on Enegy, Envionment Science and Mateials (IFEESM 15) significantly highe than test data (the sand flowing into coe channel amount to less than half of the test data, and this deviation gows with the SCR). Elastic collision model achieves a lowe value than test data. The sepaation efficiency on pobabilistic model is ight between the above two esults, closest with the test data On P o babi l i s t i c Res t i t ut i on Model On Det e mi ni s i t i c Res t i t ut i on Model On El a s t i c Col l i s i on Model Tes t Dat a i n Ref On P o b a b i l i s t i c Re s t i t u t i o n Mo d e l On De t e mi n i s i t i c Re s t i t u t i o n Mo d e l ηw/ % ηw/ % On El a s t i c Co l l i s i o n Mo d e l Te s t Da t a i n Re f (a) Fo AC coase sand (b) Fo C-spec sand Fig. 15 Compaison of analytical and expeimental Sepaation efficiency fo the swiling IPS fo AC coase sand (a) and C-spec sand (b) Conclusion The aticle caies a compaative analysis of the effect exeted by pobabilistic estitution model of paticle-wall collision with the othe two conventional collision models, deteministic estitution model and elastic collision model, on the simulation accuacy of IPS paticle sepaation efficiency, and eaches the following conclusions: 1) The tack esults based on these thee impact models fo 30-μm paticle show baely no diffeence, as it is mainly affected by dag foce. Fo lage paticle, tajectoy simulated on deteministic estitution model is close to the IPS oute wall than on pobabilistic estitution model, while elastic collision model shows an opposite phenomenon, that paticle tack is obviously away fom the collision wall suface. 2) Fo both vaneless IPS and swiling IPS, the sepaation efficiency of small size AC coase sand is mainly influenced by the flow field chaacteistics. Simulation esults on the above thee bounce models has no diffeence, and show good ageement with the expeimental data. 3) Fo lage size C-Spec sand, paticle bounce model shows a significant effect on the pediction accuacy of sepaation efficiency. The pediction on elastic model is fa lowe than the expeimental value, and deteministic estitution model ove-pedicts the sepaation function fo both vaneless IPS and swiling IPS, while the esults on pobabilistic estitution model shows the best ageement with test data. Pobability ebound model s advantage in the swiling IPS is moe obvious, and eason is that paticle otates with the otating ai, and will collide easie with the IPS oute wall than inne wall. Theefoe, the ebound paticle s capacity of moving away fom the oute wall becomes the decisive facto of whethe it flow into the scavenge channel o the coe flow. Refeences [1] Stallad P. Helicopte engine potection, J. Pefusion. 12,4 (1997) [2] Chief Edit Committee, Inlet Device, in: The Aicaft Engine Design Manual, seventh book, aviation industy pess, Beijing, 00, pp In Chinese [3] A. Hamed, Y. D. Jun, J. J. Yeuan, Paticle dynamics simulations in inlet sepaato with an expeimentally based bounce model, J. Jounal of Populsion and Powe. 11,2 (1995) The authos - Published by Atlantis Pess 643

8 Intenational Foum on Enegy, Envionment Science and Mateials (IFEESM 15) [4] W. Tabakoff, C. Balan, A study of the suface deteioation due to eosion, J. J. Eng. Powe. 105,4 (1983) [5] W. Tabakoff, M. F. Malak, A Hamed, Lase measuements of solid-paticle ebound paametes impacting on 24 aluminum and 6a1-4v titanium alloys, J. Aiaa Jounal. 25,5 (1987) [6] W. Tabakoff, A. Hamed, D. M. Muugan, Effect of taget mateials on the paticle estitution chaacteistics fo tubomachiney application, J. Jounal of Populsion and Powe. 12,2 (1996) [7] M. E. Taslim, S. Sping, A numeical study of sand paticle distibution, density, and shape effects on the scavenge efficiency of engine inlet paticle sepaato systems, J. Jounal of the Ameican Helicopte Society. 55,2 (10) [8] Heng-gang Wu, Numeical Simulation of the Integal Paticle Sepaato, Nanjing Univesity of Aeonautics and Astonautics, Nanjing, 07. In Chinese [9] Zhi Huang, Expeimental Study and Numeical Simulation of Gas-Solid Flow in Split Channel, Shanghai Jiao Tong Univesity, Shanghai, 08. In Chinese [10] A. Hamed, T. P. Kuhn, Effects of vaiational paticle estitution chaacteistics on tubomachiney eosion, J. Jounal of Engineeing fo Gas Tubines and Powe. 117,3 (1995) [11] John D. Andeson (Edito). Song-ping Wu, Zhao-miao Liu (Tanslato), Numeical equations of fluid mechanics, in: Foundation and application of computational fluid dynamics, China machine pess, Beijing, 07, pp In Chinese [12] Dan Yang, Numeical Simulation of Gas-Solid Flow in Rocket Engine, Habin Engineeing Univesity, Habin, 06. In Chinese [13] Chales B Hendeson, Dag coefficients of sphees in continuum and aefied flows, J. Ameican Institute of Aeonautics and Astonautics.,6 (1976) [] Qing Shang, Qing Shen, Fenggan Zhuang, Aeodynamics analysis and aeodynamic heating and vapoization of supesonic flow simplification fo tiny doplets, C. Poceedings of the thid National Confeence on Hypesonic Technology. Chinese society, Wuxi, (10) In Chinese [15] Qingjin Yan, Numeical integation, in: Numeical Analysis, thid ed., Beijing Univesity of Aeonautics and Astonautics Pess, Beijing, 12, pp In Chinese [] GE Aicaft Engine Goup, Integal engine inlet paticle sepaato, volume 1-technology pogam, R. //USAAMRDL-TR-75-31A (1975). [17] J D Robet, S Bemnad, Integal engine inlet paticle sepaato, volume 2-design guide, R. //USAAMRDL -TR-75-31B (1975). [] A. Ghenaiet, S C Tan, Numeical study of an inlet paticle sepaato, C. //Tubo Expo Volume 2. Vienna, Austia, (04) [19] Floian Paoli, Tong Wang, Numeical study of intenal flow field and flow passage impovement of an inlet paticle sepaato, J. Fonties in Enegy. 5,4 (11) The authos - Published by Atlantis Pess 644