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.

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

2020 ◽  
Author(s):  
Huang Chen ◽  
Yuanchao Li ◽  
Subhra Shankha Koley ◽  
Joseph Katz
Keyword(s):  
Strain Rate ◽  
Reynolds Stress ◽  
Suction Side ◽  
Reynolds Stresses ◽  
Flow Rates ◽  
Tip Leakage ◽  
Anisotropy Tensor ◽  
Stress Models ◽  
Turbomachine Rotor ◽  
Mean Strain

Abstract Challenges in predicting the turbulence in the tip region of turbomachines include anisotropy, inhomogeneity, and non-equilibrium conditions, resulting in poor correlations between the Reynold 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 evolution of turbulence in the tip region of an axial turbomachine with and without axial casing grooves, and for two flow rates. The semi-circular axial grooves are skewed by 45° in the positive circumferential direction, similar to that described in Müller et al. [1]. Comparison to results obtained for an untreated endwall includes differences in the distributions of turbulent kinetic energy (TKE), Reynolds stresses, anisotropy tensor, and dominant terms in the TKE production rate. The evolution of TKE at high flow rates for blade sections located downstream of the grooves is also investigated. Common features include: with or without casing grooves, the TKE is high near the tip leakage vortex (TLV) center, and in the shear layer connecting it to the blade suction side tip corner. The turbulence is highly anisotropic and inhomogeneous, with the anisotropy tensor demonstrating shifts from one dimensional (1D) to 2D and to 3D structures over small distances. Furthermore, the correlation between the mean strain rate and Reynolds stress tensor components is poor. With the grooves, the flow structure, hence the distribution of Reynolds stresses, becomes much more complex. Turbulence is also high in 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 production rates of normal Reynolds stress components, the grooves increase the axial and reduce the radial velocity fluctuations compared to the untreated endwall. These findings introduce new insight that might assist the future development of Reynolds stress models suitable for tip flows.

Intergranular Stress Corrosion Cracking Damage Model: An Approach and Its Development for Alloy 600 in High-Purity Water

CORROSION ◽  
1986 ◽  
Vol 42 (2) ◽  
pp. 99-105 ◽  
Author(s):  
Y. S. Garud ◽  
A. R. McIlree
Keyword(s):  
Strain Rate ◽  
Stress Corrosion ◽  
Stress Corrosion Cracking ◽  
High Purity ◽  
Corrosion Cracking ◽  
Model Parameters ◽  
Alloy 600 ◽  
Intergranular Stress Corrosion ◽  
Film Rupture ◽  
Intergranular Stress Corrosion Cracking

Abstract A logical approach to quantitative modeling of intergranular stress corrosion cracking (IGSCC) is presented. The approach is based on the supposition (supported partly by experimental and field observations, and by a related plausible underlying mechanism) that strain rate is a key variable. The approach is illustrated for the specific case of NiCrFe Alloy 600 in high-purity water. Model parameters are determined based on the constant stress IGSCC data (between 290 and 365 C) assuming a power law relation between the damage and the nominal strain rate. The model may be interpreted in terms of a film rupture mechanism of the corrosion process. The related mechanistic considerations are examined for the specific case. Resulting calculations and stress as well as temperature dependence are shown to be in good agreement with the data. More data are needed for further verification under specific conditions of interest.

Transferability of the Gurson Damage Model Parameters with Charpy and Tensile Tests with Different Constrain Level

2009 ◽  
Vol 65 ◽  
pp. 19-31
Author(s):  
Ruben Cuamatzi-Melendez ◽  
J.R. Yates
Keyword(s):  
Strain Rate ◽  
Damage Model ◽  
Rolling Direction ◽  
Fracture Initiation ◽  
Tensile Tests ◽  
Model Parameters ◽  
Gurson Model ◽  
Finite Element Program ◽  
Element Program ◽  
Gurson's Model

Little work has been published concerning the transferability of Gurson’s ductile damage model parameters in specimens tested at different strain rates and in the rolling direction of a Grade A ship plate steel. In order to investigate the transferability of the damage model parameters of Gurson’s model, tensile specimens with different constraint level and impact Charpy specimens were simulated to investigate the effect of the strain rate on the damage model parameters of Gurson model. The simulations were performed with the finite element program ABAQUS Explicit [1]. ABAQUS Explicit is ideally suited for the solution of complex nonlinear dynamic and quasi–static problems [2], especially those involving impact and other highly discontinuous events. ABAQUS Explicit supports not only stress–displacement analyses but also fully coupled transient dynamic temperature, displacement, acoustic and coupled acoustic–structural analyses. This makes the program very suitable for modelling fracture initiation and propagation. In ABAQUS Explicit, the element deletion technique is provided, so the damaged or dead elements are removed from the analysis once the failure criterion is locally reached. This simulates crack growth through the microstructure. It was found that the variation of the strain rate affects slightly the value of the damage model parameters of Gurson model.

scholarly journals An enhanced set of displacement parameter restraints in CRYSTALS

2018 ◽  
Vol 51 (4) ◽  
pp. 1059-1068 ◽  
Author(s):  
Pascal Parois ◽  
James Arnold ◽  
Richard Cooper
Keyword(s):  
Structural Model ◽  
Rigid Bodies ◽  
Model Parameters ◽  
Coordinate Systems ◽  
Principal Axes ◽  
Anisotropic Displacement Parameters ◽  
Set Up ◽  
Meaningful Relationships ◽  
Parameter Values ◽  
Total Model

Crystallographic restraints are widely used during refinement of small-molecule and macromolecular crystal structures. They can be especially useful for introducing additional observations and information into structure refinements against low-quality or low-resolution data (e.g. data obtained at high pressure) or to retain physically meaningful parameter values in disordered or unstable refinements. However, despite the fact that the anisotropic displacement parameters (ADPs) often constitute more than half of the total model parameters determined in a structure analysis, there are relatively few useful restraints for them, examples being Hirshfeld rigid-bond restraints, direct equivalence of parameters and SHELXL RIGU-type restraints. Conversely, geometric parameters can be subject to a multitude of restraints (e.g. absolute or relative distance, angle, planarity, chiral volume, and geometric similarity). This article presents a series of new ADP restraints implemented in CRYSTALS [Parois, Cooper & Thompson (2015), Chem. Cent. J. 9, 30] to give more control over ADPs by restraining, in a variety of ways, the directions and magnitudes of the principal axes of the ellipsoids in locally defined coordinate systems. The use of these new ADPs results in more realistic models, as well as a better user experience, through restraints that are more efficient and faster to set up. The use of these restraints is recommended to preserve physically meaningful relationships between displacement parameters in a structural model for rigid bodies, rotationally disordered groups and low-completeness data.

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.

scholarly journals Measurements and Characterization of Turbulence in the Tip Region of an Axial Compressor Rotor

2017 ◽  
Vol 139 (12) ◽  
Author(s):  
Yuanchao Li ◽  
Huang Chen ◽  
Joseph Katz
Keyword(s):  
Strain Rate ◽  
Shear Layer ◽  
Turbulent Flows ◽  
Reynolds Stress ◽  
Suction Side ◽  
Stress And Strain ◽  
Spatial And Temporal Variability ◽  
Mean Flow ◽  
The Mean ◽  
Stress And Strain Rate

Modeling of turbulent flows in axial turbomachines is challenging due to the high spatial and temporal variability in the distribution of the strain rate components, especially in the tip region of rotor blades. High-resolution stereo-particle image velocimetry (SPIV) measurements performed in a refractive index-matched facility in a series of closely spaced planes provide a comprehensive database for determining all the terms in the Reynolds stress and strain rate tensors. Results are also used for calculating the turbulent kinetic energy (TKE) production rate and transport terms by mean flow and turbulence. They elucidate some but not all of the observed phenomena, such as the high anisotropy, high turbulence levels in the vicinity of the tip leakage vortex (TLV) center, and in the shear layer connecting it to the blade suction side (SS) tip corner. The applicability of popular Reynolds stress models based on eddy viscosity is also evaluated by calculating it from the ratio between stress and strain rate components. Results vary substantially, depending on which components are involved, ranging from very large positive to negative values. In some areas, e.g., in the tip gap and around the TLV, the local stresses and strain rates do not appear to be correlated at all. In terms of effect on the mean flow, for most of the tip region, the mean advection terms are much higher than the Reynolds stress spatial gradients, i.e., the flow dynamics is dominated by pressure-driven transport. However, they are of similar magnitude in the shear layer, where modeling would be particularly challenging.

LES Investigation of Boussinesq Constitutive Relation Validity in a Corner Separation Flow

2018 ◽  
Author(s):  
Jean-François Monier ◽  
Nicolas Poujol ◽  
Mathieu Laurent ◽  
Feng Gao ◽  
Jérôme Boudet ◽  
...  
Keyword(s):  
Strain Rate ◽  
Stress Tensor ◽  
Reynolds Stress ◽  
Constitutive Relation ◽  
Strain Rate Tensor ◽  
Separation Flow ◽  
Compressor Cascade ◽  
Corner Separation ◽  
Reynolds Stress Tensor ◽  
Mean Strain

The present study aims at analysing the Boussinesq constitutive relation validity in a corner separation flow of a compressor cascade. The Boussinesq constitutive relation is commonly used in Reynolds-averaged Navier-Stokes (RANS) simulations for turbomachinery design. It assumes an alignment between the Reynolds stress tensor and the zero-trace mean strain-rate tensor. An indicator that measures the alignment between these tensors is used to test the validity of this assumption in a high fidelity large-eddy simulation. Eddy-viscosities are also computed using the LES database and compared. A large-eddy simulation (LES) of a LMFA-NACA65 compressor cascade, in which a corner separation is present, is considered as reference. With LES, both the Reynolds stress tensor and the mean strain-rate tensor are known, which allows the construction of the indicator and the eddy-viscosities. Two constitutive relations are evaluated. The first one is the Boussinesq constitutive relation, while the second one is the quadratic constitutive relation (QCR), expected to render more anisotropy, thus to present a better alignment between the tensors. The Boussinesq constitutive relation is rarely valid, but the QCR tends to improve the alignment. The improvement is mainly present at the inlet, upstream of the corner separation. At the outlet, the correction is milder. The eddy-viscosity built with the LES results are of the same order of magnitude as those built as the ratio of the turbulent kinetic energy k and the turbulence specific dissipation rate ω. They also show that the main impact of the QCR is to rotate the mean strain-rate tensor in order to realign it with the Reynolds stress tensor, without dilating it.

Evaluation of Creep Constitutive Equations for Type 304 Stainless Steel Under Repeated Multiaxial Loading

1982 ◽  
Vol 104 (3) ◽  
pp. 159-164 ◽  
Author(s):  
Y. Ohashi ◽  
N. Ohno ◽  
M. Kawai
Keyword(s):  
Stainless Steel ◽  
Strain Rate ◽  
Strain Hardening ◽  
Deviatoric Stress ◽  
304 Stainless Steel ◽  
Multiaxial Loading ◽  
Mixed Hardening ◽  
Principal Axes ◽  
Type 304 ◽  
Type 304 Stainless Steel

Four kinds of creep constitutive models, i.e., strain-hardening, modified strain-hardening, kinematic-hardening, and mixed-hardening theory, are evaluated on the basis of creep-test results on type 304 stainless steel at 650°C under repeated multiaxial loading. The predictions of the four models are compared with the experimental results. It is shown that substantial differences appear among these predictions under large rotations of the principal axes of the deviatoric stress tensor, and that none of them can describe with sufficient accuracy the transient increase of strain-rate and the noncollinearity between the deviatoric stress and creep strain-rate vectors which are observed just after the stress-rotations.

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.

scholarly journals Effects of Turbulent Reynolds Number on the Displacement Speed Statistics in the Thin Reaction Zones Regime of Turbulent Premixed Combustion

2011 ◽  
Vol 2011 ◽  
pp. 1-19 ◽  
Author(s):  
Nilanjan Chakraborty ◽  
Markus Klein ◽  
R. S. Cant
Keyword(s):  
Reynolds Number ◽  
Strain Rate ◽  
Surface Density ◽  
Three Dimensional ◽  
Flame Surface ◽  
Tangential Strain ◽  
Turbulent Reynolds Number ◽  
Qualitative Nature ◽  
Displacement Speed ◽  
Turbulent Premixed

The effects of turbulent Reynolds number on the statistical behaviour of the displacement speed have been studied using three-dimensional Direct Numerical Simulation of statistically planar turbulent premixed flames. The probability of finding negative values of the displacement speed is found to increase with increasing turbulent Reynolds number when the Damköhler number is held constant. It has been shown that the statistical behaviour of the Surface Density Function, and its strain rate and curvature dependence, plays a key role in determining the response of the different components of displacement speed. Increasing the turbulent Reynolds number is shown to reduce the strength of the correlations between tangential strain rate and dilatation rate with curvature, although the qualitative nature of the correlations remains unaffected. The dependence of displacement speed on strain rate and curvature is found to weaken with increasing turbulent Reynolds number when either Damköhler or Karlovitz number is held constant, but the qualitative nature of the correlation remains unaltered. The implications of turbulent Reynolds number effects in the context of Flame Surface Density (FSD) modelling have also been addressed, with emphasis on the influence of displacement speed on the curvature and propagation terms in the FSD balance equation.

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