SHOCK LAYERS FOR TURBULENCE MODELS

2008 ◽  
Vol 18 (08) ◽  
pp. 1443-1479 ◽  
Author(s):  
CHRISTOPHE BERTHON ◽  
FRÉDÉRIC COQUEL
Keyword(s):  
Turbulent Flows ◽  
Traveling Wave ◽  
Stokes Equations ◽  
Turbulence Models ◽  
Traveling Wave Solutions ◽  
Conservative System ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Wave Solutions ◽  
Systems Of Conservation Laws

The present work is devoted to an extension of the Navier–Stokes equations where the fluid is governed by two independent pressure laws. Several turbulence models typically enter this framework. The striking novelty over the usual Navier–Stokes equations stems from the impossibility to recast equivalently the system of interest in full conservation form. Opposing to systems of conservation laws, where the end states of the viscous shock are completely characterized by jump relations, the lack of conservation implies the absence of jump relations. We analyze the traveling wave behaviors according to the ratio of viscosities, and we show that the traveling wave solutions of our system tend to the traveling wave solutions of a fully conservative system. This result is used to exhibit asymptotic expansions of the end states. Such an asymptotic behavior achieves a deep physical interpretation when illustrated in the case of compressible turbulent flows.

Traveling Wave Solutions of the Nonlocal Brenner Hydrodynamic Models

2014 ◽  
Vol 24 (11) ◽  
pp. 1450135
Author(s):  
Skurativskyi Sergiy
Keyword(s):  
Traveling Wave ◽  
Stokes Equations ◽  
Traveling Wave Solutions ◽  
Homoclinic Solutions ◽  
Navier Stokes ◽  
Hydrodynamic Models ◽  
Navier Stokes Equations ◽  
Wave Solutions ◽  
Nonlocal Models ◽  
Section Technique

This paper deals with the nonlocal hydrodynamic models based on Brenner's modification of Navier–Stokes equations. Traveling wave solutions of the nonlocal models are studied in more detail. The models are shown to admit the multiperiodic, chaotic, as well as homoclinic solutions. The influence of spatiotemporal nonlocalities upon the solutions' features is studied by the Poincaré section technique.

Multigrid Computation of Incompressible Flows Using Two-Equation Turbulence Models: Part II—Applications

1997 ◽  
Vol 119 (4) ◽  
pp. 900-905 ◽  
Author(s):  
X. Zheng ◽  
C. Liao ◽  
C. Liu ◽  
C. H. Sung ◽  
T. T. Huang
Keyword(s):  
Turbulent Flows ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Turbulence Models ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Time Stepping ◽  
Grid Algorithm ◽  
High Reynolds

In this paper, computational results are presented for three-dimensional high-Reynolds number turbulent flows over a simplified submarine model. The simulation is based on the solution of Reynolds-Averaged Navier-Stokes equations and two-equation turbulence models by using a preconditioned time-stepping approach. A multiblock method, in which the block loop is placed in the inner cycle of a multi-grid algorithm, is used to obtain versatility and efficiency. It was found that the calculated body drag, lift, side force coefficients and moments at various angles of attack or angles of drift are in excellent agreement with experimental data. Fast convergence has been achieved for all the cases with large angles of attack and with modest drift angles.

Simulation of the Turbulent Flow Inside the Combustion Chamber of a Reciprocating Engine With a Finite Element Method

1994 ◽  
Vol 116 (2) ◽  
pp. 363-369 ◽  
Author(s):  
Y. Mao ◽  
M. Buffat ◽  
D. Jeandel
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Turbulent Flows ◽  
Stokes Equations ◽  
Numerical Procedure ◽  
Turbulence Models ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Numerical Precision ◽  
Element Method

This paper presents numerical simulations of turbulent flows during the intake and the compression strokes of a model engine. The Favre average Navier-Stokes equations are solved with a k-ε turbulence model. The numerical procedure uses a time dependent semi-implicit scheme and a finite element method with a moving mesh (Buffat, 1991, Mao, 1990). Results of 2-D axisymmetrical calculations with and without inlet swirl are presented and compared to experimental data (Lance et al., 1991). The influence of different turbulence models and the numerical precision of the simulations are also discussed.

Flow Analysis of the M151 Aircraft Model Using the Academic CFD Code Galatea

2017 ◽  
Author(s):  
Dimitrios A. Inglezakis ◽  
Georgios N. Lygidakis ◽  
Ioannis K. Nikolos
Keyword(s):  
Turbulent Flows ◽  
Stokes Equations ◽  
Flow Analysis ◽  
Three Dimensional ◽  
Turbulence Models ◽  
Navier Stokes ◽  
Research Association ◽  
Navier Stokes Equations ◽  
Aircraft Model ◽  
Short Period

CFD (Computational Fluid Dynamics) solvers have become nowadays an integral part of the aerospace manufacturing process and product design, as their implementation allows for the prediction of the aerodynamic behavior of an aircraft in a relatively short period of time. Such an in-house academic solver, named Galatea, is used in this study for the prediction of the flow over the ARA (Aircraft Research Association) M151/1 aircraft model. The proposed node-centered finite-volume solver employs the RANS (Reynolds-Averaged Navier-Stokes) equations, combined with appropriate turbulence models, to account for the simulation of compressible turbulent flows on three-dimensional hybrid unstructured grids, composed of tetrahedral, prisms, and pyramids. A brief description of Galatea’s methodology is included, while attention is mainly directed toward the accurate prediction of pressure distribution on the wings’ surfaces of the aforementioned airplane, an uncommon combat aircraft research model with forward swept wings and canards. In particular, two different configurations of M151/1 were examined, namely, with parallel and expanding fuselage, while the obtained results were compared with those extracted with the commercial CFD software ANSYS CFX. A very good agreement is reported, demonstrating the proposed solver’s potential to predict accurately such demanding flows over complex geometries.

Reynolds-Averaged Navier–Stokes Equations for Turbulence Modeling

2009 ◽  
Vol 62 (4) ◽  
Author(s):  
Giancarlo Alfonsi
Keyword(s):  
Turbulent Flows ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Nonlinear Models ◽  
Turbulence Models ◽  
Equation Model ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Linear And Nonlinear ◽  
Reynolds Averaged Navier Stokes

The approach of Reynolds-averaged Navier–Stokes equations (RANS) for the modeling of turbulent flows is reviewed. The subject is mainly considered in the limit of incompressible flows with constant properties. After the introduction of the concept of Reynolds decomposition and averaging, different classes of RANS turbulence models are presented, and, in particular, zero-equation models, one-equation models (besides a half-equation model), two-equation models (with reference to the tensor representation used for a model, both linear and nonlinear models are considered), stress-equation models (with reference to the pressure-strain correlation, both linear and nonlinear models are considered) and algebraic-stress models. For each of the abovementioned class of models, the most widely-used modeling techniques and closures are reported. The unsteady RANS approach is also discussed and a section is devoted to hybrid RANS/large methods.

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.

On Direct Numerical Simulation of Turbulent Flows

2011 ◽  
Vol 64 (2) ◽  
Author(s):  
Giancarlo Alfonsi
Keyword(s):  
Numerical Simulation ◽  
Direct Numerical Simulation ◽  
High Performance Computing ◽  
Turbulent Flows ◽  
High Performance ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Turbulent Shear ◽  
Navier Stokes Equations ◽  
Performance Computing

The direct numerical simulation of turbulence (DNS) has become a method of outmost importance for the investigation of turbulence physics, and its relevance is constantly growing due to the increasing popularity of high-performance-computing techniques. In the present work, the DNS approach is discussed mainly with regard to turbulent shear flows of incompressible fluids with constant properties. A body of literature is reviewed, dealing with the numerical integration of the Navier-Stokes equations, results obtained from the simulations, and appropriate use of the numerical databases for a better understanding of turbulence physics. Overall, it appears that high-performance computing is the only way to advance in turbulence research through the front of the direct numerical simulation.

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