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Chinese Journal of Aeronautics 2024年第3期37卷 34-48页

作者： Fanzhi ZENG Tianxin ZHANG Denggao TANG Jinping LI Chao YAN School of Aeronautic Science and Engineering Beihang UniversityBeijing 100191China School of Aeronautical Engineering Air Force Engineering UniversityXi’an 710038China

Accurate prediction of Shock-Wave/Boundary Layer Interaction(SWBLI)flows has been a persistent challenge for linear eddy viscosity models.A major limitation lies in the isotropic representation of the Reynolds stress,as assumed under the Boussinesq approximation.Recent studies have shown promise in improving the prediction capability for incompressible separation flows by perturbing the Reynolds-stress anisotropy tensor.However,it remains uncertain whether this approach is effective for SWBLI flows,which involve compressibility and discontinuity.To address this issue,this study systematically quantifies the structural uncertainty of the anisotropy for oblique SWBLI flows.The eigenspace perturbation method is applied to perturb the anisotropy tensor predicted by the Menter Shear–Stress Transport(SST)model and reveal the impacts of anisotropy on the prediction of quantities of interest,such as separation and reattachment positions,wall static pressure,skin friction,and heat flux.The results demonstrate the potential and reveal the challenges of eigenspace perturbation in improving the SST model.Furthermore,a detailed analysis of turbulent characteristics is performed to identify the source of uncertainty.The findings indicate that eigenspace perturbation primarily affects turbulent shear stress,while the prediction error of the SST model is more related to turbulent kinetic energy.

关键词： Shock-wave/boundary layer interaction(SWBLI) turbulence models Uncertainty analysis Eigenspace perturbation Anisotropy

Effect of turbulence models on predicting convective heat transfer to hydrocarbon fuel at supercritical pressure

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Chinese Journal of Aeronautics 2016年第5期29卷 1247-1261页

作者： Tao Zhi Cheng Zeyuan Zhu Jianqin Li Haiwang National Key Laboratory of Science and Technology on Aero-Engine Aero-Thermodynamics School of Energy and Power Engineering Beihang University

A variety of turbulence models were used to perform numerical simulations of heat transfer for hydrocarbon fuel flowing upward and downward through uniformly heated vertical pipes at supercritical pressure. Inlet temperatures varied from 373 K to 663 K, with heat flux rang- ing from 300 kW/m2 to 550 kW/m2. Comparative analyses between predicted and experimental results were used to evaluate the ability of turbulence models to respond to variable thermophysical properties of hydrocarbon fuel at supercritical pressure. It was found that the prediction performance of turbulence models is mainly determined by the damping function, which enables them to respond differently to local flow conditions. Although prediction accuracy for experimental results varied from condition to condition, the shear stress transport （SST） and launder and sharma models performed better than all other models used in the study. For very small buoyancy-influenced runs, the thermal-induced acceleration due to variations in density lead to the impairment of heat transfer occurring in the vicinity of pseudo-critical points, and heat transfer was enhanced at higher temperatures through the combined action of four thermophysical properties： density, viscosity, thermal conductivity and specific heat. For very large buoyancy- influenced runs, the thermal-induced acceleration effect was over predicted by the LS and AB models.

关键词： Buoyancy effect Hydrocarbon fuel Supercritical pressure turbulence models Variable properties

Numerical study of corner separation in a linear compressor cascade using various turbulence models

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Chinese Journal of Aeronautics 2016年第3期29卷 639-652页

作者： Liu Yangwei Yan Hao Liu Yingjie Lu Lipeng Li Qiushi Collaborative Innovation Center of Advanced Aero-Engine Beihang UniversityBeijing 100083China National Key Laboratory of Science and Technology on Aero-Engine Aero-ThermodynamicsSchool of Energy and Power EngineeringBeihang University

Three-dimensional corner separation is a common phenomenon that significantly affects compressor performance. turbulence model is still a weakness for RANS method on predicting corner separation flow accurately. In the present study, numerical study of corner separation in a linear highly loaded prescribed velocity distribution （PVD） compressor cascade has been investigated using seven frequently used turbulence models. The seven turbulence models include Spalart Allmaras model, standard k-e model, realizable k-e model, standard k-to model, shear stress transport k co model, v2-fmodel and Reynolds stress model. The results of these turbulence models have been compared and analyzed in detail with available experimental data. It is found the standard k-1： model, realizable k-e model, v2-f model and Reynolds stress model can provide reasonable results for predicting three dimensional corner separation in the compressor cascade. The Spalart-Allmaras model, standard k-to model and shear stress transport k-w model overesti- mate corner separation region at incidence of 0°. The turbulence characteristics are discussed and turbulence anisotropy is observed to be stronger in the corner separating region.

关键词： Compressor cascade Corner separation Turbomachinery CFD turbulence anisotropy turbulence models

Assessment of Two turbulence models and Some Compressibility Corrections for Hypersonic Compression Corners by High-order Difference Schemes

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Chinese Journal of Aeronautics 2012年第1期25卷 25-32页

作者： TU Guohua DENG Xiaogang MAO Meiliang State Key Laboratory of Aerodynamics China Aerodynamics Research and Development CenterMianyang 621000China

The Spalart-Allmaras （S-A） turbulence model, the shear-stress transport （SST） turbulence model and their compressibility corrections are revaluated for hypersonic compression comer flows by using high-order difference schemes. The compressibility effect of density gradient, pressure dilatation and turbulent Mach number is accounted. In order to reduce confusions between model uncertainties and discretization errors, the formally fifth-order explicit weighted compact nonlinear scheme （WCNS-E-5） is adopted for convection terms, and a fourth-order staggered central difference scheme is applied for viscous terms. The 15° and 34° compression comers at Mach number 9.22 are investigated. Numerical results show that the original SST model is superior to the original S-A model in the resolution of separated regions and predictions of wall pressures and wall heat-flux rates. The capability of the S-A model can be largely improved by blending Catris＇ and Shur＇s compressibility corrections. Among the three corrections of the SST model listed in the present paper, Catris＇ modification brings the best results. However, the dissipation and pressure dilatation corrections result in much larger separated regions than that of the experiment, and are much worse than the original SST model as well as the other two corrections. The correction of turbulent Mach number makes the separated region slightly smaller than that of the original SST model. Some results of low-order schemes are also presented. When compared to the results of the high-order schemes, the separated regions are smaller, and the peak wall pressures and peak heat-flux rates are lower in the region of the reattachment points.

关键词： aerodynamics high-order weighted compact nonlinear scheme hypersonic compression comers turbulence models compressibility corrections shock/boundary layer interactions shock waves

Comparative Experimental and Numerical Study of Wave Loads on A Monopile Structure Using Different turbulence models

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China Ocean Engineering 2021年第4期35卷 554-565页

作者： ZENG Xin-meng SHI Wei Constantine MICHAILIDES WANG Kai LI Xin DeepWater Engineering Research Centre Dalian University of TechnologyDalian 116024China State Key Laboratory of Coastal and Offshore Engineering Dalian University of TechnologyDalian 116024China Civil Engineering and Geomatics Cyprus University of TechnologyLimassol 2026Cyprus School of Marine Engineering and Technology Sun Yat-Sen UniversityZhuhai 51900China

This study numerically and experimentally investigates the effects of wave loads on a monopile-type offshore wind turbine placed on a 1:25 slope at different water depths as well as the effect of choosing different turbulence models on the efficiency of the numerical model.The numerical model adopts a two-phase flow by solving Unsteady Reynolds-Averaged Navier−Stokes(URANS)equations using the Volume Of Fluid(VOF)method and three differentk-􀀀ωturbulence models.Typical environmental conditions from the East China Sea are studied.The wave run-up and the wave loads applied on the monopile are investigated and compared with relevant experimental data as well as with mathematical predictions based on relevant theories.The numerical model is well validated against the experimental data at model scale.The use of different turbulence models results in different predictions on the wave height but less differences on the wave period.The baseline k-􀀀ωturbulence model and Shear-Stress Transport(SST)k-􀀀ωturbulence model exhibit better performance on the prediction of hydrodynamic load,at a model-scale water depth of 0.42 m,while the laminar model provides better results for large water depths.The SST turbulence model performs better in predicting wave run-up for water depth 0.42 m,while the laminar model and standard k-􀀀ωmodel perform better at water depth 0.52 m and 0.62 m,respectively.

关键词： hydrodynamic loads turbulence models Morison equation wave run-up numerical wave tank monopile structure

Evaluation of turbulence models in Predicting Hypersonic and Subsonic Base Flows Using Grid Adaptation Techniques

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Chinese Journal of Aeronautics 2012年第3期25卷 325-334页

作者： YOU Yancheng BUANGA Bjorn HANNEMANN Volker LUDEKE Heinrich Institute of Aerodynamics and Flow Technology German Aerospace Center (DLR) Braunschweig 38108 Germam Institute of Aerodynamics and Flow Technology German Aerospace Center (DLR) Gottingen 37073 Germany Department of Aeronautics Xiamen University Xiamen 361005 China

The flows behind the base of a generic rocket, at both hypersonic and subsonic flow conditions, are numerically studied. The main concerns are addressed to the evaluation of turbulence models and the using of grid adaptation techniques. The investigation focuses on two configurations, related to hypersonic and subsonic experiments. The applicability tests of different turbu- lence models are conducted on the level of two-equation models calculating the steady state solution of the Reynolds-averaged Navier-Stokes（RANS） equations. All used models, the original Wilcox k-co, the Menter shear-stress transport （SST） and the ex- plicit algebraic Reynolds stress model（EARSM） formulation, predict an asymmetric base flow in both cases caused by the support of the models. A comparison with preliminary experimental results indicates a preference for the SST and EARSM results over the results from the older k-co model. Sensitivity studies show no significant influence of the grid topology or the location of the laminar to turbulent transition on the base flow field, but a strong influence of even small angles of attack is reported from the related experiments.

关键词： base flows turbulence models steady calculation grid adaptation numerical simulation

Rotational Forms of Large Eddy Simulation turbulence models:Modeling and Mathematical Theory

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Chinese Annals of Mathematics,Series B 2021年第1期42卷 17-40页

作者： Luigi C.BERSELLI Roger LEWANDOWSKI Dinh Duong NGUYEN Universita di Pisa Dipartimento di MatematicaVia Buonarroti 1/c1-56127 Pisa Italy IRMAR UMR CNRS 6625University of Rennes 1 and FLUMINANCE TeamINRIA RennesFrance

In this paper the authors present a derivation of a back-scatter rotational Large Eddy Simulation model,which is the extension of the Baldwin&Lomax model to nonequilibrium problems.The model is particularly designed to mathematically describe a fluid filling a domain with solid walls and consequently the differential operators appearing in the smoothing terms are degenerate at the boundary.After the derivation of the model,the authors prove some of the mathematical properties coming from the weighted energy estimates,which allow to prove existence and uniqueness of a class of regular weak solutions.

关键词： Fluid mechanics turbulence models Rotational Large Eddy Simulation models Navier-Stokes equations

Temporal power spectral models of angle of arrival fluctuations for optical waves propagating through weak non-Kolmogorov turbulence

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Chinese Optics Letters 2013年第11期11卷 5-8页

作者：崔林艳薛斌党朱文越白相志曹晓光周付根 Key Laboratory of Atmospheric Composition and Optical Radiation Chinese Academy of Sciences School of Astronautics Beihang University

Analytical expressions of the temporal power spectral models of angle of arrival （AOA） fluctuations are derived using the generalized exponential spectral model for optical waves propagating through weak non- Kolmogorov turbulence. Compared with expressions of temporal power spectral models derived from the general non-Kolmogorov spectral model, the new expressions consider the influences of the inner and outer scales of finite turbulence. Numerical calculations show that large outer scales of turbulence increase the value of the temporal power spectrum of AOA fluctuations in low-frequency regions.

关键词： turbulence models

Accurately predicting hypersonic transitional flow on cone via a symmetry approach

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Chinese Journal of Aeronautics 2023年第7期36卷 337-347页

作者： Weitao BI Kexin ZHENG Zhou WEI Zhensu SHE State Key Laboratory for turbulence and Complex Systems and Department of Mechanics and Engineering Science College of EngineeringPeking UniversityBeijing 100871China State Key Laboratory of Aerodynamics and Computational Aerodynamics Institute China Aerodynamics Research and Development CenterMianyang 621000China

A new algebraic transition model is proposed based on a Structural Ensemble Dynamics(SED)theory of wall turbulence,for accurately predicting the hypersonic flow heat transfer on cone.The model defines the eddy viscosity in terms of a two-dimensional multi-regime distribution of a Stress Length(SL)function,and hence is named as SED-SL.This paper presents clear evidence of precise predictions of transition onset location and peak heat flux of a wide range of hypersonic Transitional Boundary Layers(TrBL)around straight cone at zero incidence,to an unprecedented accuracy as validated by over 70 measurements for varying five crucial influential factors(Mach number,temperature ratio,cone half angle,nose Reynolds number and noise level).The results demonstrate the universality of the postulated multi-regime similarity structure,in characterizing not only the spatial non-uniform distribution of the eddy viscosity in hypersonic TrBL on cone,but also the dependence of the transition onset location on the five influential factors.The latter yields a novel correlation formula for transition center Reynolds number which takes similar functional form as the SL function within the symmetry approach.It is concluded that the SED-SL model simulates TrBL around cone with uniformly high accuracy,and then points out to an optimistic alternative way to construct hypersonic transition model.

关键词： Cones Heat flux Hypersonic boundary layers Transition flow turbulence models

Superimposed orbital angular momentum mode of multiple Hankel–Bessel beam propagation in anisotropic non-Kolmogorov turbulence

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Chinese Optics Letters 2016年第8期14卷 6-11页

作者：武光辉童创明程明建彭鹏 Air and Missile Defense College Air Force Engineering UniversityXi'an 710051China State Key Laboratory of Millimeter Waves Nanjing 210096China School of Physics and Optoelectronic Engineering Xidian UniversityXi'an 710071China

Mathematical models for the superimposed orbital angular momentum （OAM） mode of multiple Hankel-Bessel （HB） beams in anisotropic non-Kolmogorov turbulence are developed. The effects of anisotropic turbulence and source parameters on the mode detection spectrum of the superimposed OAM mode are analyzed. Anisotropic characteristics of the turbulence in the free atmosphere can enhance the performance of OAM-based communi- cation. The HB beam is a good source for mitigating the turbulence effects due to its nondiffraction and self-focusing properties. turbulence effects on the superimposed OAM mode can be effectively reduced by the ap- propriate allocation of OAM modes at the transmitter based on the reciprocal features of the mode cross talk.

关键词： Angular momentum Anisotropy Crosstalk Electromagnetic wave propagation turbulence models