The determination of turbulence-model statistics from the velocity–acceleration correlation

2014 ◽  
Vol 757 ◽  
Author(s):  
Stephen B. Pope
Keyword(s):  
Turbulent Flows ◽  
Turbulence Model ◽  
Stokes Equations ◽  
Turbulence Models ◽  
Variable Density ◽  
Navier Stokes ◽  
Reynolds Stresses ◽  
Constant Property ◽  
Langevin Model ◽  
High Reynolds

AbstractFor inhomogeneous turbulent flows at high Reynolds number, it is shown that the redistribution term in Reynolds-stress turbulence models can be determined from the velocity–acceleration correlation. It is further shown that the drift coefficient in the generalized Langevin model (which is used in probability density function (PDF) methods) can be determined from the Reynolds stresses and the velocity–acceleration correlation. These observations are valuable, since the second moments of velocity and acceleration can be measured in experiments, in direct numerical simulations and in well-resolved large-eddy simulations (LES), and hence these turbulence-model quantities can be determined. The redistribution is closely related to the pressure–rate-of-strain, and the unknown in the PDF equation is closely related to the conditional mean pressure gradient (conditional on velocity). In contrast to the velocity–acceleration moments, these pressure statistics are much more difficult to obtain, and our knowledge of them is quite limited. It is also shown that the generalized Langevin model can be re-expressed to provide a direct connection between the drift term and the fluid acceleration. All of these results are first obtained using the constant-property Navier–Stokes equations, but it is then shown that the results are simply extended to variable-density flows.

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.

Multigrid Computation of Incompressible Flows Using Two-Equation Turbulence Models: Part I—Numerical Method

1997 ◽  
Vol 119 (4) ◽  
pp. 893-899 ◽  
Author(s):  
X. Zheng ◽  
C. Liao ◽  
C. Liu ◽  
C. H. Sung ◽  
T. T. Huang
Keyword(s):  
Turbulent Flows ◽  
Turbulence Model ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Turbulence Models ◽  
Numerical Approach ◽  
Navier Stokes ◽  
Strongly Coupled ◽  
Acceleration Techniques ◽  
Model Equations

A highly efficient numerical approach based on multigrid and preconditioning methods is developed for modeling 3-D incompressible turbulent flows. The incompressible Reynolds-averaged Navier-Stokes equations are written in pseudo-compressibility from, then a preconditioning method is used to reduce the wave speed disparity. The k-ω and k-ε turbulence models are used to estimate the effects of turbulence. The model equations are solved together with the N-S equations in a strongly-coupled way, and all the acceleration techniques originally developed for N-S equations are also used for the turbulence model equations. A point-implicit technique is developed to improve the efficiency of the solution of the turbulence model equations.

Simulation of the Transitional Flow in a Low Pressure Gas Turbine Cascade With a High-Order Discontinuous Galerkin Method

2013 ◽  
Vol 135 (7) ◽  
Author(s):  
A. Ghidoni ◽  
A. Colombo ◽  
S. Rebay ◽  
F. Bassi
Keyword(s):  
Discontinuous Galerkin ◽  
Turbulence Model ◽  
Stokes Equations ◽  
Time Integration ◽  
High Order ◽  
Transitional Flow ◽  
Navier Stokes ◽  
Implicit Time ◽  
Turbine Cascade ◽  
High Reynolds

In the last decade, discontinuous Galerkin (DG) methods have been the subject of extensive research efforts because of their excellent performance in the high-order accurate discretization of advection-diffusion problems on general unstructured grids, and are nowadays finding use in several different applications. In this paper, the potential offered by a high-order accurate DG space discretization method with implicit time integration for the solution of the Reynolds-averaged Navier–Stokes equations coupled with the k-ω turbulence model is investigated in the numerical simulation of the turbulent flow through the well-known T106A turbine cascade. The numerical results demonstrate that, by exploiting high order accurate DG schemes, it is possible to compute accurate simulations of this flow on very coarse grids, with both the high-Reynolds and low-Reynolds number versions of the k-ω turbulence model.

Parameter Extension Simulation of Turbulent Flows in a Compressor Cascade With a High Reynolds Number

2020 ◽  
Author(s):  
Yan Jin
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
Turbulent Flows ◽  
Stokes Equations ◽  
Simulation Method ◽  
Potential Method ◽  
Navier Stokes ◽  
Reference Solution ◽  
Compressor Cascade ◽  
High Reynolds

Abstract The turbulent flow in a compressor cascade is calculated by using a new simulation method, i.e., parameter extension simulation (PES). It is defined as the calculation of a turbulent flow with the help of a reference solution. A special large-eddy simulation (LES) method is developed to calculate the reference solution for PES. Then, the reference solution is extended to approximate the exact solution for the Navier-Stokes equations. The Richardson extrapolation is used to estimate the model error. The compressor cascade is made of NACA0065-009 airfoils. The Reynolds number 3.82 × 105 and the attack angles −2° to 7° are accounted for in the study. The effects of the end-walls, attack angle, and tripping bands on the flow are analyzed. The PES results are compared with the experimental data as well as the LES results using the Smagorinsky, k-equation and WALE subgrid models. The numerical results show that the PES requires a lower mesh resolution than the other LES methods. The details of the flow field including the laminar-turbulence transition can be directly captured from the PES results without introducing any additional model. These characteristics make the PES a potential method for simulating flows in turbomachinery with high Reynolds numbers.

scholarly journals Three-Dimensional Turbulent Vortex Shedding From a Surface-Mounted Square Cylinder: Predictions With Large-Eddy Simulations and URANS

2014 ◽  
Vol 136 (6) ◽  
Author(s):  
B. A. Younis ◽  
A. Abrishamchi
Keyword(s):  
Experimental Data ◽  
Turbulence Model ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Large Eddy Simulations ◽  
Navier Stokes ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Navier Stokes Equations ◽  
Large Eddy

The paper reports on the prediction of the turbulent flow field around a three-dimensional, surface mounted, square-sectioned cylinder at Reynolds numbers in the range 104–105. The effects of turbulence are accounted for in two different ways: by performing large-eddy simulations (LES) with a Smagorinsky model for the subgrid-scale motions and by solving the unsteady form of the Reynolds-averaged Navier–Stokes equations (URANS) together with a turbulence model to determine the resulting Reynolds stresses. The turbulence model used is a two-equation, eddy-viscosity closure that incorporates a term designed to account for the interactions between the organized mean-flow periodicity and the random turbulent motions. Comparisons with experimental data show that the two approaches yield results that are generally comparable and in good accord with the experimental data. The main conclusion of this work is that the URANS approach, which is considerably less demanding in terms of computer resources than LES, can reliably be used for the prediction of unsteady separated flows provided that the effects of organized mean-flow unsteadiness on the turbulence are properly accounted for in the turbulence model.

An Assessment of Turbulence Models for Predicting the Fluid Flow in Spiral Casing of a Hydraulic Turbomachine Using SUPG-Finite Element Method

2013 ◽  
Author(s):  
N. Parameswara Rao ◽  
K. Arul Prakash
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Turbulence Models ◽  
Navier Stokes ◽  
Spatial Discretisation ◽  
High Reynolds ◽  
Spiral Casing ◽  
Element Method

Numerical simulation of complex three-dimensional flow through the spiral casing has been studied using a finite element method. An explicit Eulerian velocity correction scheme has been employed to solve the Reynolds averaged Navier-stokes equations. The simulation has been performed to describe the flow in high Reynolds number (106) regime and two k-ε turbulence models (standard k-ε and RNG k-ε) have been used for computing the turbulent flow. A streamline upwind Petrov Galerkin technique has been used for spatial discretisation. The velocity field and the pressure distribution inside the spiral casing has been studied. It has been observed that very strong secondary flow is evolved on the cross-stream planes.

scholarly journals The emergence of localized vortex–wave interaction states in plane Couette flow

2013 ◽  
Vol 721 ◽  
pp. 58-85 ◽  
Author(s):  
Kengo Deguchi ◽  
Philip Hall ◽  
Andrew Walton
Keyword(s):  
Reynolds Number ◽  
Turbulent Flows ◽  
High Reynolds Number ◽  
Stokes Equations ◽  
Wave Interaction ◽  
Critical Layer ◽  
Navier Stokes ◽  
Turbulent Spots ◽  
Navier Stokes Equations ◽  
High Reynolds

AbstractThe recently understood relationship between high-Reynolds-number vortex–wave interaction theory and computationally generated self-sustaining processes provides a possible route to an understanding of some of the underlying structures of fully turbulent flows. Here vortex–wave interaction (VWI) theory is used in the long streamwise wavelength limit to continue the development found at order-one wavelengths by Hall & Sherwin (J. Fluid Mech., vol. 661, 2010, pp. 178–205). The asymptotic description given reduces the Navier–Stokes equations to the so-called boundary-region equations, for which we find equilibrium states describing the change in the VWI as the wavelength of the wave increases from $O(h)$ to $O(Rh)$, where $R$ is the Reynolds number and $2h$ is the depth of the channel. The reduced equations do not include the streamwise pressure gradient of the perturbation or the effect of streamwise diffusion of the wave–vortex states. The solutions we calculate have an asymptotic error proportional to ${R}^{- 2} $ when compared to the full Navier–Stokes equations. The results found correspond to the minimum drag configuration for VWI states and might therefore be of relevance to the control of turbulent flows. The key feature of the new states discussed here is the thickening of the critical layer structure associated with the wave part of the flow to completely fill the channel, so that the roll part of the flow is driven throughout the flow rather than as in Hall & Sherwin as a stress discontinuity across the critical layer. We identify a critical streamwise wavenumber scaling, which, when approached, causes the flow to localize and take on similarities with computationally generated or experimentally observed turbulent spots. In effect, the identification of this critical wavenumber for a given value of the assumed high Reynolds number fixes a minimum box length necessary for the emergence of localized structures. Whereas nonlinear equilibrium states of the Navier–Stokes equations are thought to form a backbone on which turbulent flows hang, our results suggest that the localized states found here might play a related role for turbulent spots.

scholarly journals On the analysis of a geometrically selective turbulence model

2020 ◽  
Vol 9 (1) ◽  
pp. 1402-1419 ◽  
Author(s):  
Nejmeddine Chorfi ◽  
Mohamed Abdelwahed ◽  
Luigi C. Berselli
Keyword(s):  
Turbulent Flows ◽  
Turbulence Model ◽  
Large Scale ◽  
Stokes Equations ◽  
A Priori ◽  
Strong Solutions ◽  
Navier Stokes ◽  
Smagorinsky Model ◽  
Navier Stokes Equations ◽  
Velocity Pressure

Abstract In this paper we propose some new non-uniformly-elliptic/damping regularizations of the Navier-Stokes equations, with particular emphasis on the behavior of the vorticity. We consider regularized systems which are inspired by the Baldwin-Lomax and by the selective Smagorinsky model based on vorticity angles, and which can be interpreted as Large Scale methods for turbulent flows. We consider damping terms which are active at the level of the vorticity. We prove the main a priori estimates and compactness results which are needed to show existence of weak and/or strong solutions, both in velocity/pressure and velocity/vorticity formulation for various systems. We start with variants of the known ones, going later on to analyze the new proposed models.

Numerical Integration Procedure for the Steady State Navier-Stokes Equations

1969 ◽  
Vol 11 (5) ◽  
pp. 445-453 ◽  
Author(s):  
A. K. Runchal ◽  
M. Wolfshtein
Keyword(s):  
Stokes Equations ◽  
Computing Time ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Square Cavity ◽  
Constant Property ◽  
Navier Stokes Equations ◽  
High Reynolds ◽  
Very High ◽  
Numerical Integration Procedure

A procedure is proposed for the integration of the full Navier-Stokes equations for constant-property two-dimensional flows. In contrast with earlier procedures, the present one is capable of dealing with cases of very high Reynolds number. The power of the new procedure is demonstrated in two cases: (1) the square recirculating eddy, for which no solution was previously available for Reynolds numbers larger than about 400, and (2) an impinging jet, for which no solution was available previously. The procedure has also been applied to the square cavity at Reynolds numbers below 400; it gives results of an accuracy comparable with that of previous solutions, but with a smaller computing time.

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.

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