Turbulence in Compressible Mixing Layers

1998 ◽  
Vol 120 (1) ◽  
pp. 48-53 ◽  
Author(s):  
Foluso Ladeinde ◽  
Wei Liu ◽  
Edward E. O’Brien
Keyword(s):  
Reynolds Stress ◽  
Turbulent Mixing ◽  
Turbulence Modeling ◽  
Mixing Layers ◽  
Correlation Tensor ◽  
Triple Correlation ◽  
Anisotropy Tensor ◽  
Homogeneous Shear Flow ◽  
Short Time ◽  
Grid Independence

The direct numerical simulation (DNS) of two-dimensional compressible turbulent mixing layers is reported in this paper for convective Mach numbers Mc = 0.5, 0.8 and 1.0. All scales of flow are resolved with a 2562 grid, although results are also obtained for 642, 962 and 1282 grids for the purpose of determining the effective accuracy and grid-independence of our calculations. The effect of Mach number is also reported for all the Reynolds stress tensor components and for the “shear” components of the anisotropy tensor, the dissipation tensor, pressure-strain, and the triple correlation tensor. The short-time behaviors of some of these quantities are similar to those reported by Sarkar (1995) for homogeneous shear flow, in spite of the differences in the problem type and initial and boundary conditions. The relative magnitudes and signs of the unclosed terms in the Reynolds stress equations provide information on those that have to be retained for turbulence modeling as well as the sense of their contribution.

Effects of Axial Casing Grooves on the Structure of Turbulence in the Tip Region of an Axial Turbomachine Rotor

2021 ◽  
pp. 1-46
Author(s):  
Huang Chen ◽  
Yuanchao Li ◽  
Subhra Shankha Koley ◽  
Joseph Katz
Keyword(s):  
Reynolds Stress ◽  
Turbulence Modeling ◽  
Suction Side ◽  
Vortex Center ◽  
Reynolds Stresses ◽  
Tip Leakage ◽  
Stress Components ◽  
Anisotropy Tensor ◽  
Stress Models ◽  
Turbomachine Rotor

Abstract Challenges in turbulence modeling in the tip region of turbomachines include anisotropy, inhomogeneity, and non-equilibrium conditions, resulting in poor correlations between Reynolds stresses and the corresponding mean strain rate components. The geometric complexity introduced by casing grooves exacerbates this problem. Taking advantage of a large database collected in the refractive index-matched liquid facility at JHU, this paper examines the effect of axial casing grooves on the distributions of turbulent kinetic energy (TKE), Reynolds stresses, anisotropy tensor, and TKE production rate in the tip region of an axial turbomachine. Comparisons are performed at flow rates corresponding to prestall and best efficiency points of the untreated machine. Common features include high TKE near the tip leakage vortex center, and in shear layer connecting it to the blade suction side tip corner. The turbulence is highly anisotropic and inhomogeneous, with the anisotropy tensor shifting from one dimensional (1D) to 2D and to 3D structures over small distances. With the grooves, the flow structure, hence the distribution of Reynolds stresses, becomes more complex. Additional sites with elevated turbulence include the corner vortex that develops at the entrance to the grooves, and in the flow jetting out of the grooves into the passage. Consistent with trends of the production rates of normal Reynolds stress components, the grooves increase the axial but reduce the radial velocity fluctuations as the inflow and outflow from the groove interacts with the passage flow. These findings might assist the development of Reynolds stress models suitable for tip flows.

Properties of the Turbulent Mixing Layer in a Spherical Implosion

2017 ◽  
Vol 140 (5) ◽  
Author(s):  
Ismael Boureima ◽  
Praveen Ramaprabhu ◽  
Nitesh Attal
Keyword(s):  
Turbulent Mixing ◽  
Turbulence Modeling ◽  
Mixing Layer ◽  
Three Dimensional ◽  
Turbulent Mixing Layer ◽  
Anisotropy Tensor ◽  
Problem Description ◽  
Atomic Mixing ◽  
Rt Instability ◽  
Quantities Of Interest

We describe the behavior of a multimode interface that degenerates into a turbulent mixing layer when subjected to a spherical implosion. Results are presented from three-dimensional (3D) numerical simulations performed using the astrophysical flash code, while the underlying problem description is adopted from Youngs and Williams (YW). During the implosion, perturbations at the interface are subjected to growth due to the Richtmyer–Meshkov (RM) instability, the Rayleigh–Taylor (RT) instability, as well as the Bell–Plesset (BP) effects. We report on several quantities of interest to the turbulence modeling community, including the turbulent kinetic energy (TKE), components of the anisotropy tensor, density self-correlation, and atomic mixing, among others.

scholarly journals Reynolds averaged turbulence modelling using deep neural networks with embedded invariance

2016 ◽  
Vol 807 ◽  
pp. 155-166 ◽  
Author(s):  
Julia Ling ◽  
Andrew Kurzawski ◽  
Jeremy Templeton
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Reynolds Stress ◽  
Network Architecture ◽  
Eddy Viscosity ◽  
Deep Neural Networks ◽  
Test Cases ◽  
Neural Network Architecture ◽  
Stress Anisotropy ◽  
Anisotropy Tensor

There exists significant demand for improved Reynolds-averaged Navier–Stokes (RANS) turbulence models that are informed by and can represent a richer set of turbulence physics. This paper presents a method of using deep neural networks to learn a model for the Reynolds stress anisotropy tensor from high-fidelity simulation data. A novel neural network architecture is proposed which uses a multiplicative layer with an invariant tensor basis to embed Galilean invariance into the predicted anisotropy tensor. It is demonstrated that this neural network architecture provides improved prediction accuracy compared with a generic neural network architecture that does not embed this invariance property. The Reynolds stress anisotropy predictions of this invariant neural network are propagated through to the velocity field for two test cases. For both test cases, significant improvement versus baseline RANS linear eddy viscosity and nonlinear eddy viscosity models is demonstrated.

A Robust Implementation of a Reynolds Stress Model for Turbomachinery Applications in a Coupled Solver Environment

2020 ◽  
Author(s):  
David Roos Launchbury ◽  
Luca Mangani ◽  
Ernesto Casartelli ◽  
Francesco Del Citto
Keyword(s):  
Reynolds Stress ◽  
Turbulence Modeling ◽  
Computational Cost ◽  
Reynolds Stress Model ◽  
Tip Vortex ◽  
Stability And Convergence ◽  
Stress Model ◽  
Robust Implementation ◽  
Flow Phenomena ◽  
The Stability

Abstract In the industrial simulation of flow phenomena, turbulence modeling is of prime importance. Due to their low computational cost, Reynolds-averaged methods (RANS) are predominantly used for this purpose. However, eddy viscosity RANS models are often unable to adequately capture important flow physics, specifically when strongly anisotropic turbulence and vortex structures are present. In such cases the more costly 7-equation Reynolds stress models often lead to significantly better results. Unfortunately, these models are not widely used in the industry. The reason for this is not mainly the increased computational cost, but the stability and convergence issues such models usually exhibit. In this paper we present a robust implementation of a Reynolds stress model that is solved in a coupled manner, increasing stability and convergence speed significantly compared to segregated implementations. In addition, the decoupling of the velocity and Reynolds stress fields is addressed for the coupled equation formulation. A special wall function is presented that conserves the anisotropic properties of the model near the walls on coarser meshes. The presented Reynolds stress model is validated on a series of semi-academic test cases and then applied to two industrially relevant situations, namely the tip vortex of a NACA0012 profile and the Aachen Radiver radial compressor case.

Numerical Simulations of Turbulent Mixing and Autoignition of Hydrogen Fuel at Reheat Combustor Operating Conditions

2011 ◽  
Author(s):  
Elizaveta Ivanova ◽  
Berthold Noll ◽  
Peter Griebel ◽  
Manfred Aigner ◽  
Khawar Syed
Keyword(s):  
Natural Gas ◽  
Numerical Simulations ◽  
Flue Gas ◽  
Turbulent Mixing ◽  
Turbulence Modeling ◽  
Numerical Study ◽  
Operating Conditions ◽  
Fuel Blend ◽  
Flow Configuration ◽  
Modeling Methods

Turbulent mixing and autoignition of H2-rich fuels at relevant reheat combustor operating conditions are investigated in the present numerical study. The flow configuration under consideration is a fuel jet perpendicularly injected into a crossflow of hot flue gas (T > 1000K, p = 15bar). Based on the results of the experimental study for the same flow configuration and operating conditions two different fuel blends are chosen for the numerical simulations. The first fuel blend is a H2/natural gas/N2 mixture at which no autoignition events were observed in the experiments. The second fuel blend is a H2/N2 mixture at which autoignition in the mixing section occurred. First, the non-reacting flow simulations are performed for the H2/natural gas/N2 mixture in order to compare the accuracy of different turbulence modeling methods. Here the steady-state Reynolds-averaged Navier-Stokes (RANS) as well as the unsteady scale-adaptive simulation (SAS) turbulence modeling methods are applied. The velocity fields obtained in both simulations are directly validated against experimental data. The SAS method shows better agreement with the experimental results. In the second part of the present work the autoignition of the H2/N2 mixture is numerically studied using the 9-species 21-steps reaction mechanism of O’Conaire et al. [1]. As in the reference experiments, autoignition can be observed in the simulations. Influences of the turbulence modeling as well as of the hot flue gas temperature are investigated. The onset and the propagation of the ignition kernels are studied based on the SAS modeling results. The obtained numerical results are discussed and compared with data from experimental autoignition studies.

An explicit algebraic Reynolds-stress and scalar-flux model for stably stratified flows

2013 ◽  
Vol 723 ◽  
pp. 91-125 ◽  
Author(s):  
W. M. J. Lazeroms ◽  
G. Brethouwer ◽  
S. Wallin ◽  
A. V. Johansson
Keyword(s):  
Heat Flux ◽  
Kinetic Energy ◽  
Temperature Gradient ◽  
Reynolds Stress ◽  
Turbulent Heat Flux ◽  
Turbulent Heat ◽  
Homogeneous Shear ◽  
Self Consistent ◽  
The Mean ◽  
Homogeneous Shear Flow

AbstractThis work describes the derivation of an algebraic model for the Reynolds stresses and turbulent heat flux in stably stratified turbulent flows, which are mutually coupled for this type of flow. For general two-dimensional mean flows, we present a correct way of expressing the Reynolds-stress anisotropy and the (normalized) turbulent heat flux as tensorial combinations of the mean strain rate, the mean rotation rate, the mean temperature gradient and gravity. A system of linear equations is derived for the coefficients in these expansions, which can easily be solved with computer algebra software for a specific choice of the model constants. The general model is simplified in the case of parallel mean shear flows where the temperature gradient is aligned with gravity. For this case, fully explicit and coupled expressions for the Reynolds-stress tensor and heat-flux vector are given. A self-consistent derivation of this model would, however, require finding a root of a polynomial equation of sixth-order, for which no simple analytical expression exists. Therefore, the nonlinear part of the algebraic equations is modelled through an approximation that is close to the consistent formulation. By using the framework of a$K\text{{\ndash}} \omega $model (where$K$is turbulent kinetic energy and$\omega $an inverse time scale) and, where needed, near-wall corrections, the model is applied to homogeneous shear flow and turbulent channel flow, both with stable stratification. For the case of homogeneous shear flow, the model predicts a critical Richardson number of 0.25 above which the turbulent kinetic energy decays to zero. The channel-flow results agree well with DNS data. Furthermore, the model is shown to be robust and approximately self-consistent. It also fulfils the requirements of realizability.

Modelling of rapid pressure—strain in Reynolds-stress closures

1994 ◽  
Vol 269 ◽  
pp. 143-168 ◽  
Author(s):  
Arne V. Johansson ◽  
Magnus Hallbäck
Keyword(s):  
Strain Rate ◽  
Reynolds Stress ◽  
Sudden Change ◽  
Model Parameters ◽  
Rapid Distortion Theory ◽  
Flow Parameters ◽  
Turbulent Reynolds Number ◽  
Principal Axes ◽  
Anisotropy Tensor ◽  
Rapid Pressure

The most general form for the rapid pressure—strain rate, within the context of classical Reynolds-stress transport (RST) closures for homogeneous flows, is derived, and truncated forms are obtained with the aid of rapid distortion theory. By a classical RST-closure we here denote a model with transport equations for the Reynolds stress tensor and the total dissipation rate. It is demonstrated that all earlier models for the rapid pressure—strain rate within the class of classical Reynolds-stress closures can be formulated as subsets of the general form derived here. Direct numerical simulations were used to show that the dependence on flow parameters, such as the turbulent Reynolds number, is small, allowing rapid distortion theory to be used for the determination of model parameters. It was shown that such a nonlinear description, of fourth order in the Reynolds-stress anisotropy tensor, is quite sufficient to very accurately model the rapid pressure—strain in all cases of irrotational mean flows, but also to get reasonable predictions in, for example, a rapid homogeneous shear flow. Also, the response of a sudden change in the orientation of the principal axes of a plane strain is investigated for the present model and models proposed in the literature. Inherent restrictions on the predictive capability of Reynolds-stress closures for rotational effects are identified.

Anisotropy Invariants of Reynolds Stress Tensor in a Duct Flow and Turbulent Boundary Layer

1998 ◽  
Vol 120 (2) ◽  
pp. 280-284 ◽  
Author(s):  
A. Mazouz ◽  
L. Labraga ◽  
C. Tournier
Keyword(s):  
Surface Roughness ◽  
Turbulent Flow ◽  
Stress Tensor ◽  
Reynolds Stress ◽  
Pipe Flow ◽  
Duct Flow ◽  
Reynolds Stress Tensor ◽  
Entire Thickness ◽  
Anisotropy Tensor ◽  
Flow Turbulence

The present study shows that the Reynolds stress anisotropy tensor for turbulent flow depends both on the nature of the surface and the boundary conditions of the flow. Contrary to the case of turbulent boundary layers with k-type surface roughness, the measured anisotropy invariants of the Reynolds stress tensor over a series of spanwise square bars separated by rectangular cavities (k-type) in duct flows show that roughness increases the anisotropy. There is a similarity between the effect of roughness on channel flow turbulence and that on pipe flow turbulence. The present data show that the effect of introducing a surface roughness significantly perturbs the entire thickness of the turbulent flow.

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