Turbulent flow simulation based on the IDDES approach using the code zFlare
DOI:
https://doi.org/10.7242/1999-6691/2023.16.2.18Keywords:
gas dynamics, hybrid simulation methods, URANS, IDDES, TsAGI code zFlare, numerical implementation, verification testsAbstract
The experience gained in scale-resolving simulations of turbulent flows using the in-house code zFlare developed at the Central Aerohydrodynamic Institute (TsAGI) is described. The code allows simulating the three-dimensional unsteady flows of arbitrary geometry on the basis of either unsteady Reynolds equations or a hybrid scale-resolving approach. The capabilities of the code zFlare concerning its applicability to the three-dimensional turbulent flows of a single-component gas with a constant heat capacity are discussed. To close the equations of turbulent motion, the following models are used: the Menter turbulence model based on the Boussinesq hypothesis and its analogue for the hybrid scale-resolving approach, and two non-Boussinesq turbulence models: the Cécora et al. model and its original analogue for the hybrid scale-resolving approach. A full description of non-Boussinesq models is provided. The numerical set-up of the test examples of scale-resolving simulations based on the code zFlare is presented: the isotropic turbulence decay; the developed turbulent flow in a plane channel; the turbulent flow in a smooth expanding channel with the boundary layer separation. The first two tests are used to adjust the coefficients of the models for hybrid simulations, and the third one is used to validate these models. The results obtained with the zFlare code (using the hybrid approach and based on the Reynolds equations) are compared with the known reference data for each test case and with the results of simulations by other authors. The test case concerning the subsonic flow in an expanding channel and the boundary layer separation shows that the new non-Boussinesq hybrid scale-resolving method predicts the average velocity field significantly better than the analogous hybrid simulation using the Boussinesq hypothesis-based model.
Downloads
References
Reynolds O. On the dynamical theory of incompressible viscous fluids and the determination of the criterion. Proc. R. Soc. Lond., 1894, vol. 56, pp.40-45. http://dx.doi.org/10.1098/rspl.1894.0075
Wilcox D.C. Turbulence modeling for CFD. DCW Industries, 2006. 544 p.
Engblom W.A., Georgiadis N.J., Khavaran A. Proc. of the 11th AIAA/CEAS Aeroacoustics Conference. Monterey, California, USA, May 23-25, 2005. 19 p. https://doi.org/10.2514/6.2005-3085
Troshin A.I. A turbulence model with variable coefficients for calculating mixing layers and jets. Fluid Dyn., 2012, vol. 47, pp. 320-328. https://doi.org/10.1134/S0015462812030052
Babulin A.A., Bosnyakov S.M., Vlasenko V.V., Engulatova M.F., Matyash S.V., Mikhailov S.V. Experience of validation and tuning of turbulence models as applied to the problem of boundary layer separation on a finite-width wedge. Comput. Math. and Math. Phys., 2016, vol. 56, pp. 1020-1033. https://doi.org/10.1134/S0965542516060051
Dolling D.S. High-speed turbulent separated flows: Consistency of mathematical models and flow physics. AIAAJ, 1998, vol. 36, pp. 725-732. https://doi.org/10.2514/2.460
Sagaut P. Large eddy simulation for incompressible flows: An introduction. Springer Science & Business Media, 2006. 558 p.
Mockett C., Fuchs M., Garbaruk A., Shur M., Spalart P., Strelets M., Thiele F., Travin A. Two non-zonal approaches to accelerate RANS to LES transition of free shear layers in DES. Progress in hybrid RANS-LES modeling, ed. S. Girimaji, W. Haase, S.-H. Peng, D. Schwamborn. Springer, 2015. Pp. 187-201. https://doi.org/10.1007/978-3-319-15141-0_15
Spalart P.R., Jou W., Strelets M., Allmaras S. Comments on the feasibility of LES for wings, and on a hybrid RANS/LES approach. Advances in DNS/LES, ed. C. Liu, Z. Liu. Greyden Press, Columbus, 1997. Pp. 137-147.
Travin A., Shur M., Strelets M., Spalart P. Detached-eddy simulations past a circular cylinder. Flow, Turbulence and Combustion, 2000, vol. 63, pp. 293-313. https://doi.org/10.1023/A:1009901401183
Gritskevich M.S., Garbaruk A.V., Schütze J., Menter F.R. Development of DDES and IDDES formulations for the k-ω shear stress transport model. Flow Turbulence Combust., 2012, vol. 88, pp. 431-449. https://doi.org/10.1007/s10494-011-9378-4
Bosnyakov S.M., Vlasenko V.V., Engulatova M.F., Zlenko N.A., Matyash S.V., Mikhaylov S.V. Programmnyy kompleks dlya sozdaniya geometrii LA, sozdaniya mnogoblochnoy 3-kh mernoy raschetnoy setki, polucheniya poley techeniya pri pomoshchi resheniya sistemy uravneniy Eylera i sistemy uravneniy Nav’ye-Stoksa, osrednennykh po vremeni obrabotka rezul’tatov rascheta (EWT) [Software package for creating the geometry of the aircraft, creating a multi-block 3 dimensional computational grid, obtaining flowfields by solving the system of Euler equations and the time-averaged system of Navier Stokes, processing of calculation results (EWT)]. Certificate of state registration of the computer code No. 2008610227 dated 09.01.2008. Register of computer codes, 2008.
Neyland V., Bosniakov S., Glazkov S., Ivanov A., Matyash S., Mikhailov S., Vlasenko V. Conception of electronic wind tunnel and first results of its implementation. Progr. Aero. Sci., 2001, vol. 37, pp. 121-145. https://doi.org/10.1016/S0376-0421(00)00013-0
Mikhaylov S.V. Programma, realizuyushchaya zonnyy podkhod, dlya rascheta nestatsionarnogo obtekaniya vyazkim potokom turbulentnogo gaza slozhnykh aerodinamicheskikh form, vklyuchaya krylo s mekhanizatsiyey (ZEUS) [A code implementing a zone approach for calculating the unsteady flow of a viscous turbulent gas around complex aerodynamic shapes, including a wing with mechanization (ZEUS)]. Certificate of state registration of the computer code No. 2013610172 dated 12.11.2012. Register of computer codes, 2012.
Mikhaylov S.V. Ob”yektno-oriyentirovannyy podkhod k sozdaniyu effektivnykh programm, realizuyushchikh parallel’nyye algoritmy rascheta [Object-oriented approach to the creation of effective codes implementing parallel calculation algorithms]. Trudy TsAGI, 2007, iss. 2671, pp. 86-108.
Vlasenko V.V., Mikhaylov S.V., Molev S.S., Troshin A.I., Shiryaeva A.A. Programma dlya chislennogo modelirovaniya trekhmernykh techeniy s goreniyem v kanalakh pryamotochnykh vozdushno-reaktivnykh dvigateley v ramkakh podkhodov URANS i DES s primeneniyem modeley vzaimodeystviya turbulentnosti s goreniyem, tekhnologii drobnogo shaga po vremeni i metoda pristenochnykh funktsiy (zFlare) [A code for numerical simulation of three-dimensional flows with combustion in the ducts of ramjet engines within the URANS and DES approaches using models of turbulence interaction with combustion, fractional time step technology and the method of wall functions (zFlare)]. Certificate of state registration of the computer code No. 2019610822 dated 18.01.2019. Register of computer codes, 2019.
Menter F.R. Two-equation eddy-viscosity turbulence models for engineering applications. AIAAJ, 1994, vol. 32, pp. 1598 1605. https://doi.org/10.2514/3.12149
Menter F.R., Kuntz M., Langtry R. Ten years of industrial experience with the SST turbulence model. Turbulence, heat and mass transfer, 2003, vol. 4, pp. 625-632.
Boussinesq J. Essai sur la théorie des eaux courantes [Essay on the theory of running waters]. Imprimerie nationale, 1877. 744 p.
Cécora R.D., Radespiel R., Eisfeld B., Probst A. Differential Reynolds-stress modeling for aeronautics. AIAAJ, 2015, vol. 53, pp. 739-755. https://doi.org/10.2514/1.J053250
Speziale C.G., Sarkar S., Gatski T.B. Modelling the pressure–strain correlation of turbulence: An invariant dynamical systems approach. J. Fluid Mech., 1991, vol. 227, pp. 245-272. https://doi.org/10.1017/S0022112091000101
Launder B.E., Reece G.J., Rodi W. Progress in the development of a Reynolds-stress turbulence closure. J. Fluid Mech., 1975, vol. 68, pp. 537-566. https://doi.org/10.1017/S0022112075001814
Shur M., Strelets M., Travin A. High-order implicit multi-block Navier-Stokes code: Ten-year experience of application to RANS/DES/LES/DNS of turbulence. P. 5-7. https://cfd.spbstu.ru/agarbaruk/doc/NTS_code.pdf (accessed 14 June 2023)
Abalakin I.V., Gorobec A.V., Duben' A.P., Kozubskaja T.K., Bahvalov P.A. Parallel research code NOISEtte for large-scale CFD and CAA simulations. Vych. met. Programmirovaniye – Numerical Methods and Programming, 2012, vol. 13, no. 3, pp. 110-125.
Cheprasov S.A., Lyubimov D.A., Secundov A.N., Yakubovsky K.Y., Birch S.F. Computational modeling of the flow and noise for 3-D exhaust turbulent jets. Computational Fluid Dynamics 2010, ed. A. Kuzmin. Springer, 2011. Pp. 903-908. https://doi.org/10.1007/978-3-642-17884-9_121
Favre A. Equations des gaz turbulents compressibles. 2. Methode des vitesses moyennes; methode des vitesses macroscopiques ponderees par la masse volumique. Journal de mecanique, 1965, vol. 4, no. 3, pp. 391-421.
Shur M.L., Spalart P.R., Strelets M.K., Travin A.K. An enhanced version of DES with rapid transition from RANS to LES in separated flows. Flow Turb. Combust., 2015, vol. 95, pp. 709-737. https://doi.org/10.1007/s10494-015-9618-0
Daly B.J., Harlow F.H. Transport equations in turbulence. Phys. Fluids, 1970, vol. 13, pp. 2634-2649. https://doi.org/10.1063/1.1692845
Bell J.H., Mehta R.D. Development of a two-stream mixing layer from tripped and untripped boundary layers. AIAAJ, 1990, vol. 28, pp. 2034-2042. https://doi.org/10.2514/3.10519
Vlasenko V.V. O matematicheskom podkhode i printsipakh postroyeniya chislennykh metodologiy dlya paketa prikladnykh programm EWT TsAGI [On the mathematical approach and principles of constructing numerical methodologies for the EWT-TsAGI application software package]. Trudy TsAGI, 2007, iss. 2671, pp. 20-85.
Bosnyakov S., Kursakov I., Lysenkov A., Matyash S., Mikhailov S., Vlasenko V., Quest J. Computational tools for supporting the testing of civil aircraft configurations in wind tunnels. Progr. Aero. Sci., 2008, vol. 44, pp. 67-120. https://doi.org/10.1016/j.paerosci.2007.10.003
Bakhne S., Vlasenko V.V., Voloshchenko O.V., Zosimov S.A., Ivankin M.A., Kursakov I.A., Matyash S.V., Mikhaylov S.V., Molev S.S., Morozov A.N., Nikolaev A.A., Nozdrachev A.Yu., Sabelnikov V.A., Sysoev A.V., Troshin A.I., Shiryaeva A.A. Opyt testirovaniya i primeneniya programmy zFlare dlya chislennogo modelirovaniya techeniy s goreniyem v kanalakh [Experience in testing and using the zFlare code for numerical simulation of flows with combustion in ducts]. Trudy TsAGI, 2022, iss. 2810.
Kulikovskiy A.G., Pogorelov N.V., Semenov A.Yu. Matematichechkiye voprosy chislennogo resheniya giperbolicheskikh sistem uravneniy [Mathematical problems of numerical solution of hyperbolic equation systems]. Moscow, Fizmalit, 2001. 656 p.
Godunov S.K., Zabrodin A.V., Ivanov M.YA., Krayko A.N., Prokopov G.P. Chislennoye resheniye mnogomernykh zadach gazovoy dinamiki [Numerical solution of multidimensional problems of gas dynamics]. Moscow, Nauka, 1976. 400 p.
Guseva E.K., Garbaruk A.V., Strelets M.K. An automatic hybrid numerical scheme for global RANS-LES approaches. J. Phys.: Conf. Ser., 2017, vol. 929, 012099. https://doi.org/10.1088/1742-6596/929/1/012099
Vlasenko V.V. Raschetno-teoreticheskiye modeli vysokoskorostnykh techeniy gaza s goreniyem i detonatsiyey v kanalakh [Computational and theoretical models of high-speed gas flows with combustion and detonation in ducts]. DSc Dissertation, Central Aerohydrodynamic Institute, Zhukovsky, 2017. 487 p.
Petrov I.B., Lobanov A.I. Lektsii po vychislitel′noy matematike [Lectures on computational mathematics]. Moscow, Internet-University of Information Technologies; BINOM. Laboratory of knowledge, 2006. 523 p.
Ortega J.M. Introduction to parallel and vector solution of linear systems. Springer Science & Business Media, 2013. 305 p.
https://nasa.github.io/CFL3D/ (accessed 14 June 2023)
https://fun3d.larc.nasa.gov/ (accessed 14 June 2023)
https://turbmodels.larc.nasa.gov/flatplate.html (accessed 14 June 2023)
https://turbmodels.larc.nasa.gov/bump.html (accessed 14 June 2023)
Chumakov S.G., Rutland C.J. Dynamic structure subgrid‐scale models for large eddy simulation. Int. J. Numer. Meth. Fluid., 2005, vol. 47, pp. 911-923. https://doi.org/10.1002/fld.907
Zhou Z., He G., Wang S., Jin G. Subgrid-scale model for large-eddy simulation of isotropic turbulent flows using an artificial neural network. Comp. Fluids, 2019, vol. 195, 104319. https://doi.org/10.1016/j.compfluid.2019.104319
Bakhne S. Comparison of convective terms’ approximations in DES family methods. Math Models Comput Simul., 2022, vol. 14, pp. 99-109. https://doi.org/10.1134/S2070048222010057
Matjash S.V. Nekotoryye aspekty metodicheskoy raboty po ispol′zovaniyu solverov v promyshlennykh raschёtakh. Trudy TsAGI, 2022, iss. 2810.
Hinze J.O. Turbulence. McGraw-Hill Publishing Co., 1975. 790 p.
Zhang R., Zhang M., Shu C.W. On the order of accuracy and numerical performance of two classes of finite volume WENO schemes. Comm. Comput. Phys., 2011, vol. 9, pp. 807-827. https://doi.org/10.4208/cicp.291109.080410s
Suresh A., Huynh H.T. Accurate monotonicity-preserving schemes with Runge–Kutta time stepping. J. Comput. Phys., 1997, vol. 136, pp. 83-99. https://doi.org/10.1006/jcph.1997.5745
Gottlieb S., Shu C.-W., Tadmor E. Strong stability-preserving high-order time discretization methods. SIAM Rev., 2001, vol. 43, pp. 89-112. https://doi.org/10.1137/S003614450036757X
Lee M., Moser R.D. Direct numerical simulation of turbulent channel flow up to Reτ ≈ 5200. J. Fluid Mech., 2015, vol. 774, pp. 395-415. https://doi.org/10.1017/jfm.2015.268
Yang X.I., Park G.I., Moin P. Log-layer mismatch and modeling of the fluctuating wall stress in wall-modeled large-eddy simulations. Phys. Rev. Fluids, 2017, vol. 2, 104601. https://doi.org/10.1103/PhysRevFluids.2.104601
Keating A., Piomelli U. A dynamic stochastic forcing method as a wall-layer model for large-eddy simulation. Journal of Turbulence, 2006, vol. 7, N12. https://doi.org/10.1080/14685240612331392460
Bentaleb Y., Lardeau S., Leschziner M.A. Large-eddy simulation of turbulent boundary layer separation from a rounded step. Journal of Turbulence, 2012, vol. 13, N4. https://doi.org/10.1080/14685248.2011.637923
https://turbmodels.larc.nasa.gov/Other_LES_Data/curvedstep.html (accessed 14 June 2023)
Zhang S., Zhong S. Proc. of the 5th Flow Control Conference. Chicago, Illinois, USA, 28 June-1 July, 2010. 16 p. https://doi.org/10.2514/6.2010-4582
Downloads
Published
Issue
Section
License
Copyright (c) 2023 Computational Continuum Mechanics
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.