Direct Simulation Monte Carlo Method Technique with Application to Multiple Interacting High-Speed Jets

Transcription

1 Stony Brook Seawulf Cluter Application for additional reource Direct Simulation Monte Carlo Method Technique with Application to Multiple Interacting High-Speed Jet Wenhai Li & Foluo Ladeinde Department of Mechanical Engineering Stony Brook Univerity Summary The goal of thi project i to invetigate the dynamic of multiple interacting high peed jet. To thi end, a parallel three-dimenional direct imulation Monte Carlo (DSMC) code i developed. An iterative flux method i ued to implement the preure oundary condition in DSMC. Jet expanding into a vacuum and into a pecified preure ackground are invetigated, a i the influence of the ackground ga on the interacting jet. Empirical model will e developed. In the pat year, the code ha een uccefully parallelized and executed in Seawulf Cluter, uing domain decompoition with the MPI protocol. Code validation i in progre, for which a one-dimenional hock tue prolem with Mach numer up to ha een invetigated. Preliminary reult for three-dimenional interacting jet have alo een otained uing the parallel code.. Background With the rapid development of pace technology, a lot of emphai ha een placed on the tudy of the interaction etween rarefied free jet. Variou jet interaction phenomena exit in the deign of pacecraft, one example eing multi-nozzle rocket. The rocket are uually equipped with two or more nozzle, to provide large impule and taility. Becaue of the high altitude, the preure i low, which caue the plume from each nozzle to have a large radial extent. Therefore, an interaction etween neighoring plume may occur. Another application i the pacecraft' Oriter Reaction Control Sytem (RCS), which comprie of many primary and vernier engine. The RCS can provide the thrut for altitude maneuver and mall velocity change (along the oriter axi) y firing the elected engine. If adjacent engine are fired imultaneouly, an interaction etween the two jet can occur. The jet interaction phenomena alo can e een in a atellite' Altitude Control Sytem (ACS). Thi ytem i generally formed y an array of mall thruter. Becaue the ize of the atellite i relatively mall and the plume ize i large in high altitude, jet interaction etween the adjacent plume can e oerved. The interaction etween multiple plume i receiving attention alo

2 ecaue of the development of micropacecraft, which can ignificantly lower farication and launch cot ecaue of it maller ize and lower weight compared to conventional pacecraft. Many deign of micro-propulion ytem involve the ue of thruter array for orital maneuver, uch a attitude control and orit riing. The thruter array can e atch faricated uing Microelectromechanical Sytem (MEMS) technique. They can alo increae the flexiility for micropacecraft ince thruter can e fired in pecific equence or imultaneouly to get deired impule profile and thrut level for a particular maneuver. In thruter array, the ditance etween the thruter i alway very mall, enhancing interaction etween the plume. Interaction etween the jet can have everal effect on pacecraft operation, uch a change in the thrut impule profile, the dynamic of jet impingement, heat flux and preure force on pacecraft urface, contamination, taility, and ound generation. Thee phenomena can caue a lot of difficultie in the deign of a pacecraft. For example, a ackflow region i generated in the interaction region when the interaction effect are trong. The ackcattered molecule can make the occurance of contamination more likely and can alo lead to relatively high heat flux and preure force on pacecraft urface. Finally, it i noted that noie reduction could e a ide effect of multiple jet interaction, 5 a i the dynamic preure that exceed the fatigue failure limit for metallic aircraft tructure.. Ojective of the Project Undertanding the phyic of underexpanded interacting jet i the focu of thi work, a three-dimenional parallel direct imulation Monte Carlo (DSMC) code i eing developed to imulate the flow field. An iterative flux method 7 i invetigated for the implementation of the preure oundary condition. Both jet expanding into vacuum and thoe expanding into a pecified preure ackground are eing invetigated. The influence of the ackground ga on the interacting jet are eing tudied and a rarefaction parameter will e developed to evaluate thi influence. The 'primaryecondary' cell hock tructure (Fig. ) will e reproduced for the dual interacting jet in the near continuum regime, and an empirical expreion will e developed for the poition of the Mach dik in the econdary cell, with guidance from the numerical imulation reult. The heat flux and preure force at the orifice plane will alo e invetigated.. Computational Method The implemented DSMC algorithm i uilt around the ame phyical concept a decried y Bird. A a particle imulation method, DSMC doe not olve the Boltzmann equation directly. Rather, the equation i olved y mimicking the phyical nature of the (ga) molecular motion and intermolecular colliion, where imulated molecule are ued in place of real molecule. (A imulated molecule can e regarded a a group of real molecule.) DSMC i alo a tatitical method. It i the colliion tatitical proaility that determine whether or not a pair of molecule will collide, not

3 the ditance etween the two molecule. Thi i the main difference from the Molecular Dynamic (MD) method, which, on the other hand, i a determinitic method.. Current Statu of Simulation Work The DSMC code aed on Bird equential algorithm 8 ha een parallelized uing domain decompoition and the MPI meage paing protocol. Preliminary reult have een otained. Particle movement and colliion are calculated in each domain. Communication etween procee occur only when computational particle cro domain oundarie. The parallel algorithm of the parallel DSMC code i hown in Fig.. The code i written in Fortran 9 where dynamic memory allocation technique i ued to ave on memory. (A linked lit data tructure i ued to tore particle information.) Fig. how a egment of code that end particle to neighoring procee. Non-locking receive i ued to receive particle from neighoring procee. Fig. how a egment of code that receive particle from neighoring procee. Tale compare the computation time for the argon normal hock wave (Mach ) imulation uing procee. It how that y uing non-locking communication algorithm, the computation peed increae y approximately %. The one-dimenional (D) DSMC code ha een uccefully parallelized and executed on the Seawulf cluter. The D hock tue prolem ha een ued to validate the code. Some reult are hown elow. Fig. 5 through 7 compare the olution (denity, tranlational temperature, and rotational temperature profile of an nitrogen normal hock wave at Mach ) for equential and parallel imulation, uing,, and procee. Agreement etween the equential and parallel imulation i evident. The reult are alo compared with the experimental data y Almeyer 9 in Fig. 8, where agreement etween the two reult i alo evident. Fig. 9 i a plot of the hock wave reciprocal thickne for different Mach numer. The DSMC value are maller than the experimental reult. Load alancing i an important iue for parallel application. Proper load-alancing can, to firt order, e achieved y uing an equal numer of particle in each proceor. A dynamic domain decompoition method i ued to ditriute an equal numer of computational particle to each proce. The technique ha alo een uccefully implemented in the D hock tue code. Fig. i the imulation reult ( procee) for an argon normal hock wave at Mach with equal decompoed lock. Fig. i the imulation reult for the ame cae ut with dynamic domain decompoition. Thu, the particle are uccefully equally ditriuted etween the procee. The computation time performance for thee two cae i compared in Tale. It how that y uing dynamic domain decompoition, the computation time i reduced y approximately 5%. The three-dimenional DSMC code ha alo een parallelized. The imulation of dual interacting jet

4 expanding into vacuum i reported. Fig. how the computation domain for the imulation. Fig. and are the denity contour in the x z and x y ymmetry plane for =., L/ D= and =., L/ D=, repectively, where i the tagnation uden numer, L i the ditance etween two orifice, and D i the diameter of the orifice. For further information on thi project contact: Profeor Foluo Ladeinde Department of Mechanical Engineering Stony Brook Univerity Stony Brook, NY, foluo.ladeinde@uny.edu 5. Significance of Seawulf Cluter for the project Since DSMC i a very expenive technique, and the prolem i threedimenional, intenive computational reource are needed. Tale lit the imulation cae propoed for the project. The lat column in the tale how the completion tatu for each cae uing the Seawulf Cluter. It i clear that thi project would not have een poile without the maive parallelization capaility that i availale in Seawulf Cluter. The etimated CPU hour needed for the computation are hown y adding the CPU Hour column in the tale, we ee that thi project require approximately, CPU hour.

5 Reference. Houhang, B. E., Jay Levine and Alan Kawaaki, Numerical Invetigation of Twin-Nozzle Rocket Plume Phenomenology, Journal of Propulion and Power, Vol., No.,, pp Dagum, L. and Zhu, S. H. K., DSMC Simultaion of the Interaction Between Rarefied Free Jet, AIAA Paper 9-87, 99. Koppenwallner, G., Scaling Law for Rarefied Plume Interaction with Application to Satellite Thruter, Proceeding of the th International Sympoium on Space Technology and Science, Tokyo, May 98, pp Ketdever, A., Selden,N., Gimelhein, S., Alexeenko, A., Vahchenkov, P., and Ivanov, M., Plume Interaction of Multiple Jet Expanding into Vacuum: Experimental Invetigation, AIAA Paper -8 Reonance, AIAA Paper Wu, j.-s., Lee, F., and Wong, S.-C., Preure Boundary Treatment in Micromechanical Device Uing the Direct Simulation Monte Carlo Method, JSME International Journal, Serie, Vol.,, pp. 9-5 () 8. Bird, G. A., Molecular Ga Dynamic and Direct Simultation of Ga Flow, t Ed., Oxford Univerity Pre, Oxford, H. Almeyer, Denity profile in argon and nitrogen hock wave meaured y the aorption of an electron eam, Journal of Fluid Mechanic, Vol. 7, 97, pp Clua, J. S., Wright, B. R., and Bowie, G. E., Twin Jet Noie Shielding for a Superonic Cruie Vehicle, AIAA Paper Seiner, J. M., Manning, J. C., and Pooton, M. K., Dynamic Preure Load Aociated with Twin Superonic Plume

6 Lit of Figure Firt cell Barrel hock Reflected hock Plume Mach dik of firt cell Plume Mach dik of econd cell Olique hock Second cell Jet oundary Slip line Fig. The chematic tructure of the flow field of dual interacting underexpanded jet.

7 Start Data Input Inialization Ditriution Data CPU CPU CPU CPU np- Enter New Particle Move Particle Domain Repartition Check Boundary Interaction Communicate Particle Data Meh Adaption Sort Particle Collide Particle Sample Flow Field Renumer Particle Load Balancing? Ye No Steady Flow? No Reet Sampling Meh Adaption Ye Sufficient Sampling? No Ye Output Reult Renumer Particle Ye Meh Adaption? No No Sufficient Iteration? End Ye Fig. Parallel algorithm for the DSMC code

8 n_end = particle_ptr => root_ending_particle do if(.not. aociated(particle_ptr)) exit n_end = n_end + call MPI_ADDRESS(particle_ptr,elmoffet(n_end),ierr) elmize(n_end) = particle_ptr => particle_ptr%next_ptr end do call MPI_TYPE_HINDEXED(n_end,elmize,elmoffet, & type_particle,particle_mg,ierr) call MPI_TYPE_COMMIT(particle_mg,ierr) call MPI_SEND(MPI_BOTTOM,,particle_mg,det,tag, & MPI_COMM_WORLD,ierr) call MPI_TYPE_FREE(type_mg,ierr) <deallocate all the particle which have een ent> Fig. Segment of code that end particle to neighoring procee i = do call MPI_IPROBE(MPI_ANY_SOURCE,MPI_ANY_TAG, & MPI_COMM_WORLD,flag,tatu,ierr) if (flag) then call MPI_GET_COUNT(tatu,type_particle,n,ierr) allocate(particle_recv(:n)) call MPI_RECV(particle_recv,n,type_particle,tatu(MPI_SOURCE), & tatu(mpi_tag),mpi_comm_world,tatu,ierr) <inert received particle to the particle linked lit> i = i+ end if if (i >= n_recv_mg) exit end do Fig. Segment of code that receive particle from neighoring procee

9 ..8 (ρ-ρ )/(ρ -ρ )... Sequential Procee Procee Procee X/λ Fig. 5. Normalized denity profile of nitrogen normal hock wave at Mach for the equential reult and parallel reult uing,, and procee.. (T tr -T )/(T -T ).8... Sequential Procee Procee Procee X/λ Fig.. Normalized tranlational temperature profile of nitrogen normal hock wave at Mach for the equential reult and parallel reult uing,, and procee

10 . (T rot -T )/(T -T ).8... Sequential Procee Procee Procee X/λ Fig. 7. Normalized rotational temperature profile of nitrogen normal hock wave at Mach for the equential reult and parallel reult or,, and procee.. ϕ n =(ϕ-ϕ )/(ϕ -ϕ ) ρ : DSMC T t : DSMC T r : DSMC ρ : Experiment T t : Experiment :Experiment T r x/λ Fig. 8. Normalized denity and temperature profile for nitrogen at Mach howing comparion with the experimental reult

11 .7..5 Expermient DSMC λ /L Ma Fig. 9. Normalized hock wave reciprocal thickne for nitrogen howing comparion with the experimental reult..9 Proce Proce 895 particle 7 particle Normalized Value Denity Temperature - - X/λ Fig.. Denity and temperature profile of argon normal hock wave at Mach with uing the equally decompoed domain.

12 ..9 Proce Proce 88 particle 8 particle Normalized Value Denity Temperature - - X/λ Fig.. Denity and temperature profile of argon normal hock wave at Mach with uing the dynamic domain decompoition technique. z orifice plane downtream oundary orifice ymmetry plane Fig.. Computation geometry for dual jet interaction x

13 5 a) Y/D X/D Level ρ/ρ ) Z/D X/D Level ρ/ρ Fig.. Normalized denity contour in (a) x z and () x y ymmetry plane for =. and L/ D= a) Z/D X/D Level ρ/ρ ) Y/D X/D Level ρ/ρ Fig.. Normalized denity contour in (a) x z and () x y ymmetry plane for =. and L/ D=

14 Lit of Tale Receive Type CPU Time (ec) Uing general locking receive Uing non-locking receive 5 Tale. Computation time comparion for the parallel imulation of argon normal hock wave at Mach y uing procee. Decompoition Type Static domain decompoition (domain i equally decompoed) Dynamic domain decompoition (particle are equal ditriuted) CPU Time (ec) 89 5 Tale. Computation time comparion for two domain decompoition type in the parallel imulation of argon normal hock wave at Mach y uing procee.

15 Project Catalogue D parallel code development and deug D code validation: D hock tue prolem D code parallel efficiency and calaility tet: D hock tue prolem D parallel code development and deug D parallel code validation: ingle under-expanded jet Simulation Cae Numer Etimated Progre of CPU ( = done) Procee Hour Fortran 9 code development -- 5 Parallelization with general locking communication -- 5 Non-locking communication -- 5 Adaptive meh -- 5 Dynamic domain decompoition -- 5 Nitrogen Ma = Nitrogen Ma = Nitrogen Ma = Nitrogen Ma = Nitrogen Ma = Nitrogen Ma = Nitrogen Ma = 8 Argon Ma = (locking communication) Argon Ma = (non-locking communication) Argon Ma = (tatic equally domain decompoition) Argon Ma = (dynamic domain decompoition) Argon Ma = x Argon Ma = x Argon Ma = 5 x Argon Ma = x Argon Ma = x Fortran 9 code development -- 5 Code parallelization -- 5 Adaptive meh -- 5 Dynamic domain decompoition -- 5 Preure oundary condition implementation -- 5 Tet the implemented preure oundary condition -- x Tet the hock cell tructure -- x =. Vacuum x =. P / P = 8 8 x =. Vacuum x =. P / P = 8 x

16 D parallel code imulation: dual interacting jet expanding into vacuum D parallel code imulation: dual interacting jet expanding into ackground with pecified preure =. Vacuum 8 8 x =. P / P = 5 x =. P / P = x =.5 Vacuum x =.5 P / P = 5 x =.5 P / P = x =. Vacuum x =. P / P = x =. P / P = 5 x =. P / P = 5 x =. Vacuum x =. P / P = x =. P / P = 5 5 x =. P / P = 8 x =. L/ D=. 5 x =. L/ D= x =. L/ D= x =. L/ D=. 5 x =. L/ D= x =. L/ D= x =. L/ D= x =. L/ D= 8 8 x =. L/ D= 8 8 x =. L/ D=. 5 x =. L/ D= x =. L/ D= x =. L/ D=. 5 x =. L/ D= x =. L/ D= x =. L/ D= P / P = 5 x =. L/ D= P / P = x =. L/ D= P / P = 5 x =. L/ D= P / P = 5 x =.5 L/ D= P / P = 5 x

17 D parallel code imulation: three =.5 L/ D= P / P = 8 x =. L/ D= P / P = x =. L/ D= P / P = 5 8 x =. L/ D= P / P = x =. L/ D =.5 P / P = 5 8 x =. L/ D =.5 P / P = x =. L/ D= P / P = 5 8 x =. L/ D= P / P = x =. L/ D= P / P = 5 x =. L/ D= P / P = x =. L/ D= Vacuum 5 x interacting jet =. L/ D= P / P = 5 x =. L/ D= P / P = 5 x D parallel code =. L/ D= Vacuum 5 x imulation: four interacting jet =. L/ D= P / P = 5 x =. L/ D= P / P = 5 x Continuum CFD =. L/ D= Vacuum x code: dual jet interaction. =. L/ D= P / P = 5 x = L/ D= P / P = x Tale. Lit of imulation cae and the etimation of CPU hour needed.