Modelling of Compressibility Effects in Mixing Layer

2002 ◽  
Author(s):  
Bertrand Aupoix
Keyword(s):  
Mixing Layer ◽  
Turbulence Models ◽  
Spreading Rate ◽  
Compressible Turbulence ◽  
Navier Stokes ◽  
Rate Reduction ◽  
Boundary Layer Flows ◽  
Turbulence Effects ◽  
Self Similar ◽  
Compressibility Effects

The ability of turbulence models to predict self-similar mixing layers is investigated. The influence of velocity is well captured but no model reproduces the sensitivity of the mixing layer to density differences. A correction proposed for boundary layer flows hardly affects mixing layer predictions. A correction is proposed but is not satisfactory. At last, compressible turbulence effects are investigated. Without corrections, models cannot predict the spreading rate reduction. Standard corrections predict too weak a reduction. The sonic eddy concept is validated whatever the turbulence model. A form suitable for Navier-Stokes codes is proposed.

scholarly journals Reynolds-Averaged Navier-Stokes Modeling of Turbulent Rayleigh-Taylor, Richtmyer-Meshkov, and Kelvin-Helmholtz Mixing Using a Higher-Order Shock-Capturing Method

2019 ◽  
Author(s):  
Oleg Schilling
Keyword(s):  
Sulfur Hexafluoride ◽  
Mixing Layer ◽  
Turbulence Models ◽  
Shock Capturing ◽  
Navier Stokes ◽  
Weno Reconstruction ◽  
Third Order ◽  
Central Difference ◽  
Reynolds Averaged Navier Stokes ◽  
Good Agreement

Abstract A numerical implementation of a large number of Reynolds-averaged Navier–Stokes (RANS) models based on two-, three-, four-equation, and Reynolds stress turbulence models (using either the turbulent kinetic energy dissipation rate or the turbulent lengthscale) in an Eulerian, finite-difference shock-capturing code is described. The code uses third-order weighted essentially nonoscillatory (WENO) reconstruction of the advective fluxes, and second- or fourth-order central difference derivatives for the computation of spatial gradients. A third-order TVD Runge–Kutta time-evolution scheme is used to evolve the fields in time. Improved closures for the turbulence production terms, compressibility corrections, mixture transport coefficients, and a consistent initialization methodology for the turbulent fields are briefly summarized. The code framework allows for systematic comparisons of detailed predictions from a variety of turbulence models of increasing complexity. Applications of the code with selected K–ε based models are illustrated for each of the three instabilities. Simulations of Rayleigh–Taylor unstable flows for Atwood numbers 0.1–0.9 are shown to be consistent with previous implicit LES (ILES) results and with the expectation of increased asymmetry in the mixing layer characteristics with increasing stratification. Simulations of reshocked Richtmyer–Meshkov turbulent mixing corresponding to experiments with light-to-heavy transition in air/sulfur hexafluoride and incident shock Mach number Mas = 1.50, and heavy-to-light transition in sulfur hexafluoride/air with Mas = 1.45 are shown to be in generally good agreement with both pre- and post-reshock mixing layer widths. Finally, simulations of the seven Brown–Roshko Kelvin–Helmholtz experiments with various velocity and density ratios using nitrogen, helium, and air are shown to give mixing layer predictions in good agreement with data. The results indicate that the numerical algorithms and turbulence models are suitable for simulating these classes of inhomogeneous turbulent flows.

Numerical Simulation of Dynamic Stall Around an Airfoil in Darrieus Motion

1999 ◽  
Vol 121 (1) ◽  
pp. 69-76 ◽  
Author(s):  
A. Allet ◽  
S. Halle´ ◽  
I. Paraschivoiu
Keyword(s):  
Stokes Equations ◽  
Turbulence Models ◽  
Dynamic Stall ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Eddy Viscosity Model ◽  
Minimum Residual ◽  
Turbulence Effects ◽  
Numerical Solver ◽  
Naca 0015

The objective of this study is to investigate the two-dimensional unsteady flow around an airfoil undergoing a Darrieus motion in dynamic stall conditions. For this purpose, a numerical solver based on the solution of the Reynolds-averaged Navier-Stokes equations expressed in a streamfunction-vorticity formulation in a non-inertial frame of reference was developed. The governing equations are solved by the streamline upwind Petrov-Galerkin finite element method (FEM). Temporal discretization is achieved by second-order-accurate finite differences. The resulting global matrix system is linearized by the Newton method and solved by the generalized minimum residual method (GMRES) with an incomplete triangular factorization preconditioning (ILU). Turbulence effects are introduced in the solver by an eddy viscosity model. Our investigation centers on an evaluation of the algebraic Cebeci-Smith model (CSM) and the nonequilibrium Johnson-King model (JKM). In an effort to predict dynamic stall features on rotating airfoils, first we present some testing results concerning the performance of both turbulence models for the flat plate case. Then, computed flow structure together with aerodynamic coefficients for a NACA 0015 airfoil in Darrieus motion under dynamic stall conditions are presented.

Compressibility effects on the structure of supersonic mixing layers: experimental results

1994 ◽  
Vol 259 ◽  
pp. 47-78 ◽  
Author(s):  
S. Barre ◽  
C. Quine ◽  
J. P. Dussauge
Keyword(s):  
Mixing Layer ◽  
Spreading Rate ◽  
Turbulent Friction ◽  
Radiated Noise ◽  
Supersonic Mixing ◽  
Diffusion Scheme ◽  
Supersonic Mixing Layer ◽  
Compressibility Effects ◽  
Supersonic Mixing Layers ◽  
Convective Mach Number

An experiment in a supersonic mixing layer at convective Mach number Mc = 0.62 was performed to study the evolution of a flow from a turbulent boundary layer to a fully developed mixing layer. Turbulence measurements were taken and are interpreted with a diffusion model, which is well adapted to these flows. These measurements show that the level of turbulent friction varies with Mc proportionally to the spread rate. Our measurements appear to be consistent with the spreading rate of the layer and suggest that compressibility does not significantly alter the diffusion scheme at Mc = 0.62. This is also confirmed by a review of the existing data. Moreover, in the present flow, the anisotropy of the turbulent stresses seems to be affected by compressibility. The evolution of the radiated noise shows an increase corresponding to the developed part of the layer. Quantitative assessments of compressibility effects on turbulent quantities are given and are related to modifications in the structure of the flow.

scholarly journals A Compressible Turbulence Model for Pressure—Strain

Fluids ◽  
2022 ◽  
Vol 7 (1) ◽  
pp. 34
Author(s):  
Hechmi Khlifi ◽  
Adnen Bourehla
Keyword(s):  
Mach Number ◽  
Shear Flow ◽  
Turbulent Flows ◽  
High Speed ◽  
Turbulence Models ◽  
Mixing Layers ◽  
Compressible Turbulence ◽  
Homogeneous Shear ◽  
Homogeneous Shear Flow ◽  
Compressibility Effects

This work focuses on the performance and validation of compressible turbulence models for the pressure-strain correlation. Considering the Launder Reece and Rodi (LRR) incompressible model for the pressure-strain correlation, Adumitroaie et al., Huang et al., and Marzougui et al., used different modeling approaches to develop turbulence models, taking into account compressibility effects for this term. Two numerical coefficients are dependent on the turbulent Mach number, and all of the remaining coefficients conserve the same values as in the original LRR model. The models do not correctly predict the compressible turbulence at a high-speed shear flow. So, the revision of these models is the major aim of this study. In the present work, the compressible model for the pressure-strain correlation developed by Khlifi−Lili, involving the turbulent Mach number, the gradient, and the convective Mach numbers, is used to modify the linear mean shear strain and the slow terms of the previous models. The models are tested in two compressible turbulent flows: homogeneous shear flow and the newly developed plane mixing layers. The predicted results of the proposed modifications of the Adumitroaie et al., Huang et al., and Marzougui et al., models and of its universal versions are compared with direct numerical simulation (DNS) and experiment data. The results show that the important parameters of compressibility in homogeneous shear flow and in the mixing layers are well predicted by the proposal models.

Development of A Two-Equation Turbulence Model for Hypersonic Shock Wave and Turbulent Boundary Layer Interaction

2011 ◽  
Vol 66-68 ◽  
pp. 1868-1873
Author(s):  
Jing Yuan Liu ◽  
Chun Hian Lee
Keyword(s):  
Turbulent Flows ◽  
Stokes Equations ◽  
Single Point ◽  
Turbulence Models ◽  
Compressible Turbulence ◽  
Navier Stokes ◽  
Tvd Scheme ◽  
Navier Stokes Equations ◽  
Boundary Layer Interaction ◽  
Artificial Diffusion

For hypersonic compressible turbulence, the correlations with respect to the density fluctuation must not be neglected. A Reynolds averaged K-ε model is proposed in the present paper to include these correlations, together with the Reynolds averaged Navier-Stokes equations to describe the mean flowfield. The K-equation is obtained from Reynolds averaged single-point second moment equations which are deduced from the instantaneous compressible Navier-Stokes equations. Under certain hypotheses and scales estimation of the compressible terms, the K-equation is simplified. The correlation terms of the fluctuation field appearing in the resulting K-equation, together with a conventional form of the ε-equation, are thus correlated with the variables in the average field. The new modeling coefficients of closure terms are optimized by computing the hypersonic turbulent flat-plate measured by Coleman and Stollery [J. Fliud Mech., Vol. 56 (1972), p. 741]. The proposed model is then applied to simulate hypersonic turbulent flows over a wedge compression corner angle of 34 degree. The predicting results compare favorably with the experimental results. Also, comparisons are made with other turbulence models. Additionally, an entropy modification function of Harten-Yee’s TVD scheme is introduced to reduce artificial diffusion near boundary layers and provide the required artificial diffusion to capture the shockwaves simultaneously.

scholarly journals Challenging Mix Models on Transients to Self-Similarity of Unstably Stratified Homogeneous Turbulence

2016 ◽  
Vol 138 (7) ◽  
Author(s):  
Benoît-Joseph Gréa ◽  
Alan Burlot ◽  
Jérôme Griffond ◽  
Antoine Llor
Keyword(s):  
Isotropic Turbulence ◽  
Turbulence Models ◽  
Homogeneous Turbulence ◽  
Navier Stokes ◽  
Late Time ◽  
Data Set ◽  
Long Range Correlations ◽  
Transient Flows ◽  
Transient Regimes ◽  
Self Similar

The present work aims at expanding the set of buoyancy-driven unstable reference flows—a critical ingredient in the development of turbulence models—by considering the recently introduced “Unstably Stratified Homogeneous Turbulence” (USHT) in both its self-similar and transient regimes. The previously established accuracy of an anisotropic Eddy-Damped Quasi-Normal Markovian Model (EDQNM) on the USHT has allowed us to: (i) build a data set of well defined transient flows from Homogeneous Isotropic Turbulence (HIT) to late-time self-similar USHT and (ii) on this basis, calibrate, validate, and compare three common Reynolds-Averaged Navier–Stokes (RANS) mixing models (two-equation, Reynolds stress, and two-fluid). The model calibrations were performed on the self-similar flows constrained by predefined long range correlations (Saffman or Batchelor type). Then, with fixed constants, validations were carried out over the various transients defined by the initial Froude number and mixing intensity. Significant differences between the models are observed, but none of them can accurately capture all of the transient regimes at once. Closer inspection of the various model responses hints at possible routes for their improvement.

scholarly journals Assessment of Numerical Methods for Plunging Breaking Wave Predictions

2021 ◽  
Vol 9 (3) ◽  
pp. 264
Author(s):  
Shanti Bhushan ◽  
Oumnia El Fajri ◽  
Graham Hubbard ◽  
Bradley Chambers ◽  
Christopher Kees
Keyword(s):  
Solitary Wave ◽  
Wave Breaking ◽  
Large Scale ◽  
Turbulence Models ◽  
Navier Stokes ◽  
Wave Crest ◽  
Breaking Wave ◽  
Rans Turbulence Models ◽  
Run Up ◽  
Better Than

This study evaluates the capability of Navier–Stokes solvers in predicting forward and backward plunging breaking, including assessment of the effect of grid resolution, turbulence model, and VoF, CLSVoF interface models on predictions. For this purpose, 2D simulations are performed for four test cases: dam break, solitary wave run up on a slope, flow over a submerged bump, and solitary wave over a submerged rectangular obstacle. Plunging wave breaking involves high wave crest, plunger formation, and splash up, followed by second plunger, and chaotic water motions. Coarser grids reasonably predict the wave breaking features, but finer grids are required for accurate prediction of the splash up events. However, instabilities are triggered at the air–water interface (primarily for the air flow) on very fine grids, which induces surface peel-off or kinks and roll-up of the plunger tips. Reynolds averaged Navier–Stokes (RANS) turbulence models result in high eddy-viscosity in the air–water region which decays the fluid momentum and adversely affects the predictions. Both VoF and CLSVoF methods predict the large-scale plunging breaking characteristics well; however, they vary in the prediction of the finer details. The CLSVoF solver predicts the splash-up event and secondary plunger better than the VoF solver; however, the latter predicts the plunger shape better than the former for the solitary wave run-up on a slope case.

scholarly journals Comparative Study of Different Turbulence Models for Cavitational Flows around NACA0012 Hydrofoil

2021 ◽  
Vol 9 (7) ◽  
pp. 742
Author(s):  
Minsheng Zhao ◽  
Decheng Wan ◽  
Yangyang Gao
Keyword(s):  
Angle Of Attack ◽  
Large Angle ◽  
Turbulence Models ◽  
Navier Stokes ◽  
Specific Information ◽  
Cloud Cavitation ◽  
Eddy Simulation ◽  
Large Eddy ◽  
Shedding Frequency ◽  
Reynolds Average

The present work focuses on the comparison of the numerical simulation of sheet/cloud cavitation with the Reynolds Average Navier-Stokes and Large Eddy Simulation(RANS and LES) methods around NACA0012 hydrofoil in water flow. Three kinds of turbulence models—SST k-ω, modified SST k-ω, and Smagorinsky’s model—were used in this paper. The unstable sheet cavity and periodic shedding of the sheet/cloud cavitation were predicted, and the simulation results, namelycavitation shape, shedding frequency, and the lift and the drag coefficients of those three turbulence models, were analyzed and compared with each other. The numerical results above were basically in accordance with experimental ones. It was found that the modified SST k-ω and Smagorinsky turbulence models performed better in the aspects of cavitation shape, shedding frequency, and capturing the unsteady cavitation vortex cluster in the developing and shedding period of the cavitation at the cavitation number σ = 0.8. At a small angle of attack, the modified SST k-ω model was more accurate and practical than the other two models. However, at a large angle of attack, the Smagorinsky model of the LES method was able to give specific information in the cavitation flow field, which RANS method could not give. Further study showed that the vortex structure of the wing is the main cause of cavitation shedding.

Multiscale Partially Averaged Navier Stokes Approach for the Prediction of Flow in Linear Compressor Cascade With Moving Casing

2011 ◽  
Author(s):  
Domenico Borello ◽  
Giovanni Delibra ◽  
Franco Rispoli
Keyword(s):  
Turbulence Models ◽  
Navier Stokes ◽  
Test Case ◽  
Compressor Cascade ◽  
Preliminary Assessment ◽  
Linear Compressor ◽  
Tip Leakage ◽  
Experimental Campaign ◽  
Elliptic Relaxation ◽  
Linear Compressor Cascade

In this paper we present an innovative Partially Averaged Navier Stokes (PANS) approach for the simulation of turbomachinery flows. The elliptic relaxation k-ε-ζ-f model was used as baseline Unsteady Reynolds Averaged Navier Stokes (URANS) model for the derivation of the PANS formulation. The well established T-FlowS unstructured finite volume in-house code was used for the computations. A preliminary assessment of the developed formulation was carried out on a 2D hill flow that represents a very demanding test case for turbulence models. The turbomachinery flow here investigated reproduces the experimental campaign carried out at Virginia Tech on a linear compressor cascade with tip leakage. Their measurements were used for comparisons with numerical results. The predictive capabilities of the model were assessed through the analysis of the flow field. Then an investigation of the blade passage, where experiments were not available, was carried out to detect the main loss sources.

Numerical Simulation of Turbine Blade Boundary Layer and Heat Transfer and Assessment of Turbulence Models

1997 ◽  
Vol 119 (4) ◽  
pp. 794-801 ◽  
Author(s):  
J. Luo ◽  
B. Lakshminarayana
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Reynolds Number ◽  
Low Reynolds Number ◽  
Turbulence Models ◽  
Navier Stokes ◽  
Bypass Transition ◽  
Boundary Layer Development ◽  
Low Reynolds ◽  
Layer Development

The boundary layer development and convective heat transfer on transonic turbine nozzle vanes are investigated using a compressible Navier–Stokes code with three low-Reynolds-number k–ε models. The mean-flow and turbulence transport equations are integrated by a four-stage Runge–Kutta scheme. Numerical predictions are compared with the experimental data acquired at Allison Engine Company. An assessment of the performance of various turbulence models is carried out. The two modes of transition, bypass transition and separation-induced transition, are studied comparatively. Effects of blade surface pressure gradients, free-stream turbulence level, and Reynolds number on the blade boundary layer development, particularly transition onset, are examined. Predictions from a parabolic boundary layer code are included for comparison with those from the elliptic Navier–Stokes code. The present study indicates that the turbine external heat transfer, under real engine conditions, can be predicted well by the Navier–Stokes procedure with the low-Reynolds-number k–ε models employed.

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