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.

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.

scholarly journals Weakly nonlinear modelling of a forced turbulent axisymmetric wake

2017 ◽  
Vol 814 ◽  
pp. 570-591 ◽  
Author(s):  
Georgios Rigas ◽  
Aimee S. Morgans ◽  
Jonathan F. Morrison
Keyword(s):  
Turbulent Flows ◽  
Bluff Body ◽  
Stokes Equations ◽  
Nonlinear Models ◽  
Navier Stokes ◽  
Turbulent Regime ◽  
Navier Stokes Equations ◽  
Weakly Nonlinear ◽  
Zero Net Mass Flux ◽  
High Reynolds

A theory is presented where the weakly nonlinear analysis of laminar globally unstable flows in the presence of external forcing is extended to the turbulent regime. The analysis is demonstrated and validated using experimental results of an axisymmetric bluff-body wake at high Reynolds numbers, $Re_{D}\sim 1.88\times 10^{5}$, where forcing is applied using a zero-net-mass-flux actuator located at the base of the blunt body. In this study we focus on the response of antisymmetric coherent structures with azimuthal wavenumbers $m=\pm 1$ at a frequency $St_{D}=0.2$, responsible for global vortex shedding. We found experimentally that axisymmetric forcing ($m=0$) couples nonlinearly with the global shedding mode when the flow is forced at twice the shedding frequency, resulting in parametric subharmonic resonance through a triadic interaction between forcing and shedding. We derive simple weakly nonlinear models from the phase-averaged Navier–Stokes equations and show that they capture accurately the observed behaviour for this type of forcing. The unknown model coefficients are obtained experimentally by producing harmonic transients. This approach should be applicable in a variety of turbulent flows to describe the response of global modes to forcing.

scholarly journals A Pressure-Correction Scheme for Rotational Navier-Stokes Equations and Its Application to Rotating Turbulent Flows

2011 ◽  
Vol 9 (3) ◽  
pp. 740-755 ◽  
Author(s):  
Dinesh A. Shetty ◽  
Jie Shen ◽  
Abhilash J. Chandy ◽  
Steven H. Frankel
Keyword(s):  
Boundary Conditions ◽  
Turbulent Flows ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Pressure Correction ◽  
Correction Scheme ◽  
Diagonalization Method ◽  
Pseudo Spectral

AbstractThe rotational incremental pressure-correction (RIPC) scheme, described in Timmermans et al. [Int. J. Numer. Methods. Fluids., 22 (1996)] and Shen et al. [Math. Comput., 73 (2003)] for non-rotational Navier-Stokes equations, is extended to rotating incompressible flows. The method is implemented in the context of a pseudo Fourier-spectral code and applied to several rotating laminar and turbulent flows. The performance of the scheme and the computational results are compared to the so-called diagonalization method (DM) developed by Morinishi et al. [Int. J. Heat. Fluid. Flow., 22 (2001)]. The RIPC predictions are in excellent agreement with the DM predictions, while being simpler to implement and computationally more efficient. The RIPC scheme is not in anyway limited to implementation in a pseudo-spectral code or periodic boundary conditions, and can be used in complex geometries and with other suitable boundary conditions.

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.

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.

Fluid-Inertia Effects in Radial Flow Between Oscillating, Rotating Parallel Disks

1981 ◽  
Vol 103 (1) ◽  
pp. 144-149
Author(s):  
D. K. Warinner ◽  
J. T. Pearson
Keyword(s):  
Turbulent Flows ◽  
Radial Flow ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Fluid Inertia ◽  
Rotating Disks ◽  
Spiral Flow ◽  
Navier Stokes Equations ◽  
Inertia Effects

An order-of-magnitude analysis is applied to the Navier-Stokes equations and the continuity equation for isothermal, radial fluid flow between oscillating and rotating disks. This analysis investigates the four basic cases of 1) steady, radial flow, 2) unsteady, radial flow, 3) steady, spiral flow, and 4) unsteady, spiral flow. It is shown that certain values of particular dimensionless parameters for general cases will reduce the Navier-Stokes equations to simplified forms and thus render them amenable to closed-form solutions for, say, the pressure distribution between oscillating, rotating disks. The analysis holds for laminar and turbulent flows and compressible and incompressible flows. The conditions that must be satisfied for one to reasonably neglect 1) rotation, 2) unsteady terms, and 3) convective terms are set forth. One result shown is that only rarely could one reasonably neglect the radial convective acceleration while retaining the radial local acceleration.

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