基于自适应非结构嵌套网格的旋翼流场模拟
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摘要
针对直升机旋翼CFD仿真的复杂性,提出了改进的适合于格心格式求解器的非结构嵌套网格算法。采用自适应网格技术在旋翼流场仿真的整个过程中进行网格的自适应加密和疏化操作,以更好地捕捉桨尖涡等流动细节。对于频繁的自适应过程中产生的大量重复点和无用点,采用了高效的交替数字树算法(Alternating digital tree,ADT)和标记-删除-移动算法(Mark,delete,move,MDM)进行删除,节约了不必要的存储。针对格心格式的求解器,采用了基于梯度的网格间插值方式,简化了网格间数值传递的复杂性,同时不降低求解器的精度。对Caradonna&Tung旋翼悬停算例和HLISHAPE 7A旋翼悬停算例进行了模拟验证,计算值与实验值吻合,表明本文建立的方法具有良好的鲁棒性和有效性。最后,与未采用自适应时求解器对桨尖涡的捕捉效果进行了对比,结果表明本文所采用的方法可以明显地提高求解器对桨尖涡的捕捉。
In order to deal with the fluid simulation of the rotor,an algorithm for overset mesh system based on unstructured grids is built.It is suitable for the CFD solver of cell-centred scheme.To capture the blade vortex,the Cartesian grid is adapted all the time during the fluid simulation of the rotor.Alternating digital tree(ADT)algorithm and make,delete,move(MDM)algorithm are used to delete amounts of unused and repeated points generated in every adaptive process.An interpolation method based on gradient is adopted,which greatly simplifies the complexity of the numerical transmission between grids and can satisfy the requirement of accuracy.For Caradonna&Tung and HLISHAPE 7 Arotors,calculation in hovering state is conducted and the results are corresponding with the experimental data.It indicates that the algorithm is robust and efficient.After that,the results about capturing blade tip vortex are compared with the simulation without utilizing adaptive gird.It shows that the algorithm can significantly improve the resolution of capturing the blade tip vortex.
In order to deal with the fluid simulation of the rotor,an algorithm for overset mesh system based on unstructured grids is built.It is suitable for the CFD solver of cell-centred scheme.To capture the blade vortex,the Cartesian grid is adapted all the time during the fluid simulation of the rotor.Alternating digital tree(ADT)algorithm and make,delete,move(MDM)algorithm are used to delete amounts of unused and repeated points generated in every adaptive process.An interpolation method based on gradient is adopted,which greatly simplifies the complexity of the numerical transmission between grids and can satisfy the requirement of accuracy.For Caradonna&Tung and HLISHAPE 7 Arotors,calculation in hovering state is conducted and the results are corresponding with the experimental data.It indicates that the algorithm is robust and efficient.After that,the results about capturing blade tip vortex are compared with the simulation without utilizing adaptive gird.It shows that the algorithm can significantly improve the resolution of capturing the blade tip vortex.
引文
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[21]COIRIER W J,POWELL K G.Adaptively refined Euler and Navier-Stokes solutions with a Cartesian-cell based scheme[C]//ICASE/LaRC Workshop on Adaptive Grid Methods.[S.l.]:[s.n.],1995:153-161.
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[24]BONET J,PERAIRE J.An alternating digital tree(ADT)algorithm for 3Dgeometric searching and intersection problems[J].International Journal for Numerical Methods in Engineering,1991,31(1):1-17.
[25]MENTER F R.Two-equation eddy-viscosity turbulence models for engineering applications[J].AIAA Journal,1994,32(8):1598-1605.
[26]JAMESON A,TURKEL E.Implicit schemes and MYMLUMYM decompositions[J].Mathematics of Computation,1981,37(156):385-397.
[27]WILCOX D C.Turbulence modeling for CFD[M].California,USA:DCW Industries,2006:363-367.
[28]CARADONNA F X,TUNG C.Experimental and analytical studies of a model helicopter rotor in hover[J].Vertica,1981,5(1):149-161.
[29]STEIJL R,BARAKOS G N,BADCOCK K J.A CFD framework for analysis of helicopter rotors[C]//17th AIAA Computational Fluid Dynamics Conference.Toronto,Ontario,Canada:AIAA,2005.
[2]徐国华,招启军.直升机旋翼计算流体力学的研究进展[J].南京航空航天大学学报,2003,35(3):338-344.XU Guohua,ZHAO Qijun.Advances in computational fluid dynamics of helicopter rotor[J].Journal of Nanjing University of Aeronautics&Astronautics,2003,35(3):338-344.
[3]赵国庆,招启军,吴琪.旋翼非定常气动特性CFD模拟的通用运动嵌套网格方法[J].航空动力学报,2015,30(3):546-554.ZHAO Guoqing,ZHAO Qijun,WU Qi.A universal moving-embedded grid method for CFD simulation of unsteady aerodynamic characteristics of rotot[J].Journal of Aerospace Power,2015,30(3):546-554.
[4]李亚波.基于自适应网格方法的倾转旋翼流场数值模拟[D].南京:南京航空航天大学,2013.LI Yabo.Numerical simulations for flowfield of tiltrotor based on adaptive grid method[D].Nanjing:Nanjing University of Aeronautics and Astronautics,2013.
[5]田书玲.基于非结构网格方法的重叠网格算法研究[D].南京:南京航空航天大学,2008.TIAN Shuling.Investigation of overset unstructured grids algorithm[D].Nanjing:Nanjing University of Aeronautics and Astronautics,2008.
[6]许和勇,叶正寅,王刚,等.基于非结构嵌套网格的旋翼前飞流场计算[J].西北工业大学学报,2006,24(6):763-767.XU Heyong,YE Zhengyin,Wang Gang,et al.Improving numerical simulation of rotor forward flight flow field with unstructured dynamic overset grids[J].Journal of Northwestern Polytechnical University,2006,24(6):763-767.
[7]许和勇,叶正寅,史爱明.基于非结构嵌套网格的旋翼-机身干扰流场数值模拟[J].西北工业大学学报,2010,28(6):814-817.XU Heyong,YE Zhengyin,SHI Aiming.An effective method for numerically simulating helicopter rotor-fuselage aerodynamic interference using unstructured overset grids[J].Journal of Northwestern PolytechnicalUniversity,2010,28(6):814-817.
[8]SHAW S T,HILL J L,VILLAMARIN C E M.A priori grid adaptation for helicopter rotor wakes using unstructured and structured-unstructured hybrid grids[C]//43rd AIAA Aerospace Science Meeting and Exhibit.Reno,Nevada:AIAA,2005.
[9]叶靓.基于非结构网格的直升机旋翼流场及噪声研究[D].南京:南京航空航天大学,2009.YE Liang.Research on the flowfield and noise of helicopter rotors based on unstructured mesh[D].Nanjing:Nanjing University of Aeronautics and Astronautics,2009.
[10]WISSINK A M,KAMKAR S,PULLIAM T H,et al.Cartesian adaptive mesh refinement for rotorcraft wake resolution[C]//28th AIAA Applied Aerodynamics Conference.Chicago,Lllinois:AIAA,2010.
[11]WISSINK A M,JAYARAMAN B,DATTA A,et al.Capability enhancements in version 3of the helios high-fidelity rotorcraft simulation code[C]//50th AIAA Aerospace Science Meeting Including the New Horizons Forum and Aerospace Exposition.Nashville,Tennessee:AIAA,2012.
[12]WISSINK A M,KATZ A J,SITARAMAN J.Validation of 3DRANS-SA calculations on Strand/Cartesian meshes[C]//52nd Aerospace Sciences Meeting.National Harbor,Maryland:AIAA,2014.
[13]AIAA.An efficient adaptive cartesian vorticity transport solver for rotorcraft flowfield analysis[C]//AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition.[S.l.]:AIAA,2010.
[14]PERON S,BENOIT C.Automatic off-body overset adaptive Cartesian mesh method based on an octree approach[J].Journal of Computational Physics,2013,232(1):153-173.
[15]MCMORRIS H,KALLINDERIS Y.Octree-advancing front method for generation of unstructured surface and volume meshes[J].AIAA Journal,1997,35(6):976-984.
[16]LOHNER R.Applied computational fluid dynamics techniques[M].Chichester,UK:John Wiley&Sons Ltd,2008.
[17]TUCKER P G,RUMSEY C L,BARTELS R E,et al.Transport equation based wall distance computations aimed at flows with time-dependent geometry[R].NASA/TM-2003-212680,2003.
[18]WIGTON L.Research in computational aeroscience applications implemented on advanced parallel computing systems[R].NASA/CR-96-206062,1996.
[19]NAKAHASHI K,TOGASHI F,SHAROV D.An inter grid-boundary definition method for overset unstructured grid approach[J].AIAA Journal,2000,38(11):2077-2084.
[20]WANG Z J,CPHEN R F,HARIHARAN N,et al.A 2N tree bases automated viscous Cartesian grid methodology for feature capturing[J].AIAA Journal,1999:99-3300.
[21]COIRIER W J,POWELL K G.Adaptively refined Euler and Navier-Stokes solutions with a Cartesian-cell based scheme[C]//ICASE/LaRC Workshop on Adaptive Grid Methods.[S.l.]:[s.n.],1995:153-161.
[22]COIRIER W J.An adaptively-refined,Cartesian,cell-based scheme for the Euler and Navier-Stokes equations[D].Ann Arbor:The University of Michigan,1994.
[23]招启军,徐国华.直升机计算流体动力学基础[M].北京:科学出版社,2016:120-128.
[24]BONET J,PERAIRE J.An alternating digital tree(ADT)algorithm for 3Dgeometric searching and intersection problems[J].International Journal for Numerical Methods in Engineering,1991,31(1):1-17.
[25]MENTER F R.Two-equation eddy-viscosity turbulence models for engineering applications[J].AIAA Journal,1994,32(8):1598-1605.
[26]JAMESON A,TURKEL E.Implicit schemes and MYMLUMYM decompositions[J].Mathematics of Computation,1981,37(156):385-397.
[27]WILCOX D C.Turbulence modeling for CFD[M].California,USA:DCW Industries,2006:363-367.
[28]CARADONNA F X,TUNG C.Experimental and analytical studies of a model helicopter rotor in hover[J].Vertica,1981,5(1):149-161.
[29]STEIJL R,BARAKOS G N,BADCOCK K J.A CFD framework for analysis of helicopter rotors[C]//17th AIAA Computational Fluid Dynamics Conference.Toronto,Ontario,Canada:AIAA,2005.