Overview of wall functions for compressible turbulent boundary layers
-
摘要: 以建立工程实用的高超声速湍流边界层模拟方法为目标，从湍流壁面函数是湍流边界层方程近似解的角度，梳理了相关文献的研究工作，得到如下认识：1）壁面函数与所求定解问题数值解的相容程度决定了壁面第一层网格允许放粗的程度，在流动分离点和再附点附近区域，目前壁面函数尚需进一步完善，而“子网格”壁面函数从理论上解决了相容性问题，尽管要耗费更多计算资源，但在目前计算资源相对充裕的条件下，仍不失为一个解决问题的途径；2）对于具有强压缩性和显著气动加热的高超声速湍流边界层流动而言，常用的解析形式并未充分考虑可压缩性和传热的影响，并在文中进行了重点探讨。最后，建议基于数据驱动技术和依托“子网格”壁面函数方法来发展更加普适的壁面函数。Abstract: Related studies about wall functions, which are approximate solutions to turbulent boundary layers, are surveyed to shed light on the development of a pragmatic simulation method for hypersonic turbulent boundary layers. This overview reveals the following understandings: 1) The consistency between wall functions and numerical solutions determines the mesh size of the wall-next cells. However, the consistency problem is not well solved by analytical wall functions, especially in separation and reattachment regions where the pressure gradient is strong. The sub-grid wall function, in contrast, theoretically solves this problem, which makes it to be a promising method when computational resources are abundant. 2) The effects of strong compressibility and significant heat transfer in hypersonic turbulent flows need to be adequately integrated into analytical wall functions. Finally, the development of a more universal wall function based on the data-driven methods and sub-grid wall functions is recommended.
-
Key words:
- hypersonic flow /
- turbulent boundary layer /
- turbulence model /
- wall function /
- compressibility
-
图 3 典型高超声速边界层平均速度分布ReL = 3.7×107 m−1, T∞ = 68.79 K, Tw = 300 K
Figure 3. The mean velocity profiles of typical hypersonic boundary layers ReL = 3.7×107 m−1, T∞ = 68.79 K, Tw = 300 K
图 4 典型高超声速边界层温度分布 ReL = 3.7×107 m−1, T∞ = 68.79 K, Tw = 300 K
Figure 4. The mean temperature profiles of typical hypersonic boundary layers ReL = 3.7×107 m−1, T∞ = 68.79 K, Tw = 300 K
-
[1] WANG M, MOIN P. Dynamic wall modeling for large-eddy simulation of complex turbulent flows[J]. Physics of Fluids, 2002, 14(7): 2043. DOI: 10.1063/1.1476668 [2] SMITS A J, DUSSUAGE J P. Turbulent shear layers in supersonic flow: Second Edition M]. Springer, 2011: 193-199. [3] MILLIKAN C B A. A critical discussion of turbulent flows in channels and circular tubes[C]// 5th International Congress of Applied Mechanics, 1938: 386-392. [4] TENNEKES H, LUMLEY J L. A first course in turbulence[M]. The MIT Press, 1972. doi: 10.7551/mitpress/3014.001.0001 [5] NICHOLS R. Development and validation of a two-equation turbulence model with wall functions for compressible flow[C]// 14th Applied Aerodynamics Conference, New Orleans, LA. Reston, Virginia: AIAA, 1996. doi: 10.2514/6.1996-2385 [6] VIEGAS J, RUBESIN M, HORSTMAN C. On the use of wall functions as boundary conditions for two-dimensional separated compressible flows[C]// 23rd Aerospace Sciences Meeting, Reno, NV. Reston, Virginia: AIAA, 1985. doi: 10.2514/6.1985-180 [7] SMITH B. The k-kl turbulence model and wall layer model for compressible flows[C]// 21st Fluid Dynamics, Plasma Dynamics and Lasers Conference, Seattle, WA. Reston, Virginia: AIAA, 1990. doi: 10.2514/6.1990-1483 [8] WILCOX D. Wall matching, a rational alternative to wall functions[C]// 27th Aerospace Sciences Meeting, Reno, NV. Reston, Virginia: AIAA, 1989. doi: 10.2514/6.1989-611 [9] SPALDING D B. A single formula for the “law of the wall”[J]. Journal of Applied Mechanics, 1961, 28(3): 455-458. DOI: 10.1115/1.3641728 [10] FRINK N T. Tetrahedral unstructured Navier-Stokes method for turbulent flows[J]. AIAA Journal, 1998, 36(11): 1975-1982. DOI: 10.2514/2.324 [11] SHIH T-H et al. Turbulent surface flow and wall function[C]// 35th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, 1999, AIAA- 99-2392. [12] NICHOLS R H, NELSON C C. Wall function boundary conditions including heat transfer and compressibility[J]. AIAA Journal, 2004, 42(6): 1107-1114. DOI: 10.2514/1.3539. [13] WHITE F M, CHRISTOPH G H. A simple new analysis of compressible turbulent two-dimensional skin friction under arbitrary conditions: AFFDL-TR-70-133[R]. U. S. Air Force Flight Dynamics Lab, Wright-Patterson AFB: 1971. [14] GRANVILLE P S. A modified van driest formula for the mixing length of turbulent boundary layers in pressure gradients[J]. Journal of Fluids Engineering, 1989, 111(1): 94-97. DOI: 10.1115/1.3243606 [15] DURBIN P A, BELCHER S E. Scaling of adverse-pressure-gradient turbulent boundary layers[J]. Journal of Fluid Mechanics, 1992, 238: 699-722. DOI: 10.1017/s0022112092001873. [16] KNOPP T, ALRUTZ T, SCHWAMBORN D. A grid and flow adaptive wall-function method for RANS turbulence modelling[J]. Journal of Computational Physics, 2006, 220(1): 19-40. doi: 10.1016/j.jcp.2006.05.003. [17] GONCALVES E, HOUDEVILLE R. Reassessment of the wall functions approach for RANS computations[J]. Aerospace Science and Technology, 2001, 5(1): 1-14. DOI: 10.1016/S1270-9638(00)01083-X. [18] VIESER W, ESCH T, MENTER F. Heat transfer predictions using advanced two-equation turbulence models[EB/OL]. https://www.researchgate.net/publication/292730255_Heat_transfer_predictions_using_advanced_two-equation_turbulence_models, 2004. [19] KALITZIN G, MEDIC G, IACCARINO G, et al. Near-wall behavior of RANS turbulence models and implications for wall functions[J]. Journal of Computational Physics, 2005, 204(1): 265-291. DOI: 10.1016/j.jcp.2004.10.018. [20] 贺旭照, 赵慧勇, 乐嘉陵. 考虑可压缩与热传导的壁面函数边界条件及其应用[J]. 空气动力学学报, 2006, 24(4): 450-453. doi: 10.3969/j.issn.0258-1825.2006.04.010HE X Z, ZHAO H Y, LE J L. Application of wall function boundary condition considering heat transfer and compressibility[J]. Acta Aerodynamica Sinica, 2006, 24(4): 450-453. (in Chinese)DOI: 10.3969/j.issn.0258-1825.2006.04.010. [21] 贺旭照, 赵慧勇, 乐嘉陵. 吸气式高超声速飞行器气动力气动热的数值模拟方法及应用[J]. 计算物理, 2008, 25(5): 555-560. doi: 10.3969/j.issn.1001-246X.2008.05.006HE X Z, ZHAO H Y, LE J L. Aerodynamic force and heat of hypersonic laminar and turbulent flows[J]. Chinese Journal of Computational Physics, 2008, 25(5): 555-560. (in Chinese)DOI: 10.3969/j.issn.1001-246X.2008.05.006. [22] 吴晓军, 马明生, 邓有奇, 等. 两种湍流模型在跨声速绕流计算的应用研究[J]. 空气动力学学报, 2008, 26(1): 85-90. doi: 10.3969/j.issn.0258-1825.2008.01.016WU X J, MA M S, DENG Y Q, et al. Two turbulence models for the computation of transonic flow[J]. Acta Aerodynamica Sinica, 2008, 26(1): 85-90. (in Chinese)DOI: 10.3969/j.issn.0258-1825.2008.01.016. [23] 肖红林, 罗纪生. 大涡模拟中亚格子模型的改进及其在槽道湍流中的应用[J]. 航空动力学报, 2007, 22(4): 583-587. doi: 10.13224/j.cnki.jasp.2007.04.010XIAO H L, LUO J S. Improvement of sub-grid model in large eddy simulation and applications in turbulent channel flow[J]. Journal of Aerospace Power, 2007, 22(4): 583-587. (in Chinese)DOI: 10.13224/j.cnki.jasp.2007.04.010. [24] GAO Z X, JIANG C W, LEE C. Improvement and application of wall function boundary condition for high-speed compressible flows[J]. Science China Technological Sciences, 2013, 56(10): 2501-2515. DOI: 10.1007/s11431-013-5349-4. [25] TAO Z, WU H J, YOU R Q, et al. Turbulent characteristics and rotation correction of wall function in rotating channel with high local rotation parameter[J]. Chinese Journal of Aeronautics, 2018, 31(10): 1985-1999. doi: 10.1016/j.cja.2018.08.006. [26] LIU J, WU S P. Generalized wall function and its application to compressible turbulent boundary layer over a flat plate[J]. Journal of Physics: Conference Series, 2017, 822: 012017. DOI: 10.1088/1742-6596/822/1/012017. [27] FERNHOLZ H H, FINLEY P J. A critical commentary on mean flow data for two-dimensional compressible turbulent boundary layers[EB/OL]. 1980. [28] VAN DRIEST E R. Turbulent boundary layer in compressible fluids[J]. Journal of the Aeronautical Sciences, 1951, 18(3): 145-160. DOI: 10.2514/8.1895. [29] SCHÜLEIN E. Optical skin friction measurements in short-duration facilities (invited)[C]// 24th AIAA Aerodynamic Measurement Technology and Ground Testing Conference, Portland, Oregon. Reston, Virigina: AIAA, 2004. doi: 10.2514/6.2004-2115 [30] KUSSOY M I, HORSTMAN K C. Documentation of two- and three-dimensional shock-wave/turbulent-boundary-layer interaction flows at Mach 8.2[R]. NASA Technical Memorandum 103838, 1991. [31] MARVIN J G, BROWN J L, GNOFFO J G. Experimental database with baseline CFD solutions: 2-D and axisymmetric hypersonic shock-wave/turbulent boundary-layer interactions: NASA TM-2013-216604[R]. NASA Langley Research Center, 2013. [32] HUANG P G, BRADSHAW P, COAKLEY T J. Skin friction and velocity profile family for compressible turbulent boundary layers[J]. AIAA Journal, 1993, 31(9): 1600-1604. DOI: 10.2514/3.11820. [33] KADER B A. Temperature and concentration profiles in fully turbulent boundary layers[J]. International Journal of Heat and Mass Transfer, 1981, 24(9): 1541-1544. DOI: 10.1016/0017-9310(81)90220-9. [34] STRATFORD B S. An experimental flow with zero skin friction throughout its region of pressure rise[J]. Journal of Fluid Mechanics, 1959, 5(1): 17-35. DOI: 10.1017/s0022112059000027. [35] WHITE F M. Viscous fluid flow[M]. McGraw-Hill Inc., 1974. [36] TIDRIRI M D. Domain decomposition for compressible Navier-Stokes equations with different discretizations and formulations[J]. Journal of Computational Physics, 1995, 119(2): 271-282. doi: 10.1006/jcph.1995.1135. [37] SPALART P, ALLMARAS S. A one-equation turbulence model for aerodynamic flows[C]// 30th Aerospace Sciences Meeting and Exhibit, Reno, NV. Reston, Virginia: AIAA, 1992. doi: 10.2514/6.1992-439. [38] LAUNDER B E, SPALDING D B. The numerical computation of turbulent flows[J]. Computer Methods in Applied Mechanics and Engineering, 1974, 3(2): 269-289. DOI: 10.1016/0045-7825(74)90029-2. [39] MENTER F R. Two-equation eddy-viscosity turbulence models for engineering applications[J]. AIAA Journal, 1994, 32(8): 1598-1605. DOI: 10.2514/3.12149. [40] CRAFT T J, GERASIMOV A V, IACOVIDES H, et al. Progress in the generalization of wall-function treatments[J]. International Journal of Heat and Fluid Flow, 2002, 23(2): 148-160. DOI: 10.1016/S0142-727X(01)00143-6. [41] IACOVIDES H, LAUNDER B E. PSL—an economical approach to the numerical analysis of near-wall, elliptic flow[J]. Journal of Fluids Engineering, 1984, 106(2): 241-242. DOI: 10.1115/1.3243109. [42] CRAFT T J, GANT S E, IACOVIDES H, et al. A new wall function strategy for complex turbulent flows[J]. Numerical Heat Transfer, Part B: Fundamentals, 2004, 45(4): 301-318. DOI: 10.1080/10407790490277931. [43] CHOI H, MOIN P. Grid-point requirements for large eddy simulation: Chapman's estimates revisited[J]. Physics of Fluids, 2012, 24(1): 011702. DOI: 10.1063/1.3676783. [44] LARSSON J, KAWAI S, BODART J, et al. Large eddy simulation with modeled wall-stress: recent progress and future directions[J]. Mechanical Engineering Reviews, 2016, 3(1): 15-00418. DOI: 10.1299/mer.15-00418. [45] 吴霆, 时北极, 王士召, 等. 大涡模拟的壁模型及其应用[J]. 力学学报, 2018, 50(3): 453-466. doi: 10.6052/0459-1879-18-071WU T, SHI B J, WANG S Z, et al. Wall-model for large-eddy simulation and its applications[J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(3): 453-466. (in Chinese)DOI: 10.6052/0459-1879-18-071. [46] BOSE S T, PARK G I. Wall-modeled large-eddy simulation for complex turbulent flows[J]. Annual Review of Fluid Mechanics, 2018, 50: 535-561. doi: 10.1146/annurev-fluid-122316-045241 -
下载:
点击查看大图
图(6)
计量
- 文章访问数: 322
- HTML全文浏览量: 106
- PDF下载量: 73
- 被引次数: 0
