scholarly journals Improved Supersonic Turbulent Flow Characteristics Using Non-Linear Eddy Viscosity Relation in RANS and HPC-Enabled LES

Aerospace ◽  
2021 ◽  
Vol 8 (11) ◽  
pp. 352
Author(s):  
Kalyani Bhide ◽  
Kiran Siddappaji ◽  
Shaaban Abdallah ◽  
Kurt Roberts
Keyword(s):  
Turbulent Flow ◽  
Strain Rate ◽  
Linear Relationship ◽  
Eddy Viscosity ◽  
Flow Behavior ◽  
Preliminary Investigation ◽  
Flow Characteristics ◽  
Reynolds Stresses ◽  
Non Linear ◽  
Mean Strain

A majority of the eddy viscosity models for supersonic turbulent flow are based on linear relationship between Reynolds stresses and mean strain rate. The validity of these models can be improved by introducing non-linearity in relation as RANS models offer advantages in terms of reduced turnaround times typical of industry applications. With these benefits, the present work utilizes quadratic constitutive relation (QCR) with Menter’s k omega SST model to characterize the flowfield of rectangular jets. The sensitivity of this model with QCR, weighted towards diffusion, dissipation, and a combination of both, is addressed. Viscous large eddy simulations (LES) with WALE subgrid scale models are employed for qualitative comparisons using a commercial solver. Massively parallel LES are enabled by the new in-house 1088-core computing cluster at the University of Cincinnati and are also used for benchmarking. The nearfield results are validated with available experimental data and show good agreement in both fidelities. Flow characteristics, including the shear layer profiles, Reynolds stresses, and turbulence kinetic energy (TKE) and its production are compared. LES reveal higher TKE production in the regions with highest Reynolds stresses. It is comparatively lower in QCR RANS. As a special case of TKE analysis in jets, a preliminary investigation of retropropulsion is outlined for rectangular nozzles for the first time. Improved flow behavior by implementation of a non-linear relationship between Reynolds stresses and mean strain rate is demonstrated.

On the Constitutive Relation for the Reynolds Stresses and the Prandtl-Kolmogorov Hypothesis of Effective Viscosity in Axisymmetric Strained Turbulence

1999 ◽  
Vol 122 (1) ◽  
pp. 48-50 ◽  
Author(s):  
J. Jovanovic´ ◽  
I. Otic´
Keyword(s):  
Strain Rate ◽  
Stress Tensor ◽  
Reynolds Stress ◽  
Constitutive Relation ◽  
Effective Viscosity ◽  
Constitutive Relations ◽  
Reynolds Stresses ◽  
Reynolds Stress Tensor ◽  
The Mean ◽  
Mean Strain

The constitutive relation for the Reynolds stress tensor is considered for turbulence developing in axisymmetric strain fields. It is confirmed that the Reynolds stress tensor is aligned linearly with the mean strain rate. In contrast to the Prandtl-Kolmogorov, hypothesis, the effective viscosity is found to grow in proportion to the anisotropy of turbulence and the length scale based on the magnitude of the mean strain rate. Using invariant theory the effective viscosity is determined for the limiting states of turbulence. Additional analysis of the constitutive relations is supplemented for the dissipation and pressure-strain correlations. It is shown that analytical derivations are in excellent agreement with the data obtained from direct numerical simulations. [S0098-2202(00)02801-7]

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.

scholarly journals Spectral-Element Simulation of the Turbulent Flow in an Urban Environment

2021 ◽  
Author(s):  
Maxime Stuck ◽  
Alvaro Vidal ◽  
Pablo Torres ◽  
Hassan M. Nagib ◽  
Candace Wark ◽  
...  
Keyword(s):  
Turbulent Flow ◽  
Urban Environment ◽  
Good Description ◽  
Flow Behavior ◽  
Flow Characteristics ◽  
Mean Flow ◽  
Complex Flow ◽  
Turbulence Statistics ◽  
Experimental Database ◽  
The Impact

The mean flow and turbulence statistics of the flow through a simplified urban environment, which is an active research area in order to improve the knowledge of turbulent flow in cities, is investigated. This is useful for civil engineering, pedestrian comfort and for health concerns caused by pollutant spreading. In this work, we provide analysis of the turbulence statistics obtained from well-resolved large-eddy simulations (LES). A detailed analysis of this database reveals the impact of the geometry of the urban array on the flow characteristics and provides for a good description of the turbulent features of the flow within a simplified urban environment. The most prominent features of this complex flow include coherent vortical structures such as the so-called arch vortex, the horseshoe vortex and the roof vortex. These structures of the flow have been identified by an analysis of the turbulence statistics. The influence of the geometry of the urban environment (and particularly the street width and the building height) on the overall flow behavior have also been studied. Finally, the well-resolved LES results were compared with the experimental database from Monnier et al. to discuss differences and similarities between the respective urban configurations.

Numerical investigation of semifilled-pipe flow

2021 ◽  
Vol 932 ◽  
Author(s):  
Julian Brosda ◽  
Michael Manhart
Keyword(s):  
Shear Stress ◽  
Free Surface ◽  
Wall Shear Stress ◽  
Turbulent Flow ◽  
Pipe Flow ◽  
Flow Characteristics ◽  
Streamwise Vorticity ◽  
Reynolds Stresses ◽  
Data Set ◽  
Wall Shear

This study describes turbulent flow in a semifilled pipe with a focus on its secondary currents. To the authors’ knowledge, we provide the first highly resolved data-set for semifilled-pipe flow using direct numerical simulation. The flow parameters range from $Re_\tau =115$ , just maintaining turbulence, to moderate turbulent flow at $Re_\tau =460$ . Some of the main flow characteristics are in line with previously published results from experiments, such as the velocity-dip phenomenon, the main secondary flow and the qualitative distribution of the Reynolds stresses in the core of the flow. We observe some flow phenomena which have not yet been reported in the literature so far for this type of flow. Among those is the inner secondary cell in the mixed corner between the free surface and the pipe's wall, which plays a major role in the distribution of the wall shear stress along the perimeter. We observe that the position and extension of the inner vortex scale with the wall shear stress and those of the outer vortex scale with outer variables. For the first time, we present and discuss distributions of the complete Reynolds stress tensor and its anisotropy which gives rise to the generation of mean streamwise vorticity in a small region in the mixed corners of the pipe. Mean secondary kinetic energy, however, is generated at the free surface around the stagnation point between the inner and outer vortices. This generation mechanism is in line with a vortex dynamics mechanism proposed in the literature.

Heat Transfer in a Suddenly Expanded Turbulent Flow Past a Porous Insert Using Linear and Non-Linear Eddy-Viscosity Models

2002 ◽  
Author(s):  
Marcelo J. S. de Lemos ◽  
Marcelo Assato
Keyword(s):  
Heat Transfer ◽  
Turbulent Flow ◽  
Eddy Viscosity ◽  
Control Volume ◽  
Numerical Technique ◽  
Turbulence Models ◽  
Wall Functions ◽  
Porous Insert ◽  
Flow Past ◽  
Non Linear

This work presents numerical results for heat transfer in turbulent flow past a backward-facing-step channel with a porous insert using linear and non-linear eddy viscosity macroscopic models. The non-linear turbulence models are known to perform better than classical eddy-diffusivity models due to their ability to simulate important characteristics of the flow. Parameters such as porosity, permeability and thickness of the porous insert are varied in order to analyze their effects on the flow pattern, particularly on the damping of the recirculating bubble after the porous insertion. The numerical technique employed for discretizing the governing equations is the control-volume method. The SIMPLE algorithm is used to correct the pressure field. Wall functions for velocity and temperature are used in order to bypass fine computational close to the wall. Comparisons of results simulated with both linear and non-linear turbulence models are presented.

scholarly journals On the relationship between strain rate and seismicity in the India-Asia collision zone: Implications for probabilistic seismic hazard

2021 ◽  
Author(s):  
V L Stevens ◽  
J-P Avouac
Keyword(s):  
Seismic Hazard ◽  
Strain Rate ◽  
Linear Relationship ◽  
Active Tectonics ◽  
Probabilistic Seismic Hazard ◽  
Maximum Magnitude ◽  
Collision Zone ◽  
Geodetic Strain Rate ◽  
Non Linear ◽  
Geodetic Strain

Summary The increasing density of geodetic measurements makes it possible to map surface strain rate in many zones of active tectonics with unprecedented spatial resolution. Here we show that the strain tensor rate calculated from GPS in the India-Asia collision zone represents well the strain released in earthquakes. This means that geodetic data in the India-Asia collision zone region can be extrapolated back in time to estimate strain buildup on active faults, or the kinematics of continental deformation. We infer that the geodetic strain rates can be assumed stationary through time on the timescale needed to build up the elastic strain released by larger earthquakes, and that they can be used to estimate the probability of triggering earthquakes. We show that the background seismicity rate correlates with the geodetic strain rate. A good fit is obtained assuming a linear relationship ($\dot{N} = \lambda \ \cdot \dot{\epsilon }$ where $\dot{N}$ is the density of the rate of Mw ≥ 4 earthquakes, $\dot{\epsilon }$ is strain rate and λ = 2.5 ± 0.1 × 10−3 m−2), as would be expected from a standard Coulomb failure model. However, the fit is significantly better for a non-linear relationship ($\dot{N} = \gamma _1 \cdot \dot{\epsilon }^{\gamma _2}$ with γ1 = 2.5 ± 0.6 m−2 and γ2 = 1.42 ± 0.15). The b-value of the Gutenberg-Richter law, which characterize the magnitude-frequency distribution, is found to be insensitive to the strain rate. In the case of a linear correlation between seismicity and strain rate, the maximum magnitude earthquake, derived from the moment conservation principle, is expected to be independent of the strain rate. By contrast, the non-linear case implies that the maximum magnitude earthquake would be larger in zones of low strain rate. We show that within areas of constant strain rate, earthquakes above Mw4 follow a Poisson distribution in time and and are uniformly distributed in space. These findings provide a framework to estimate the probability of occurrence and magnitude of earthquakes as a function of the geodetic strain rate. We describe how the seismicity models derived from this approach can be used as an input for probabilistic seismic hazard analysis. This method is easy to automatically update, and can be applied in a consistent manner to any continental zone of active tectonics with sufficient geodetic coverage.

Turbulent flow characteristics responsible for current-induced scour around a complex pier

2021 ◽  
Author(s):  
Priyanka Gautam ◽  
T I Eldho ◽  
B. S. Mazumder ◽  
M. R. Behera
Keyword(s):  
Reynolds Number ◽  
Spectral Analysis ◽  
Turbulent Flow ◽  
Vortex Shedding ◽  
Flow Characteristics ◽  
Acoustic Doppler Velocimeter ◽  
Reynolds Stresses ◽  
Velocity Data ◽  
Pile Cap ◽  
Upward Moving

This study investigates the turbulent flow characteristics around a complex pier (CP) with elliptical pile cap, for understanding the mechanics of flow responsible for current-induced scour. The velocity data are recorded using an acoustic Doppler velocimeter (ADV) for a Reynolds number of 67,745. This study gives mean velocities in horizontal and vertical planes, Reynolds stresses, turbulent kinetic energy, and spectral analysis around the CP, which are not addressed earlier. The streamwise spectra with vortex-shedding frequencies and corresponding Strouhal numbers are focused on three distinct regions generated by CP. The elliptical pile-cap shields the downward flow at the upstream of the column, and the upward-moving wakes at the downstream of the CP, responsible for the sediment entrainment around a pier. On comparison, the effect of perturbed flow around the CP is considerably less than that of the simple pier (SP), resulting in less scour around the CP with identical flow situations.

Recirculating Turbulent Flows of Thixotropic Fluids

2001 ◽  
Author(s):  
Américo S. Pereira ◽  
Fernando T. Pinho
Keyword(s):  
Turbulent Flow ◽  
Turbulent Flows ◽  
Aqueous Suspension ◽  
Flow Characteristics ◽  
Shear Thinning ◽  
Sudden Expansion ◽  
Reynolds Stresses ◽  
Hydrodynamic Behaviour ◽  
Inlet Conditions ◽  
High Reynolds

Abstract An aqueous suspension of 1% by weight laponite was investigated in terms of its rheology and hydrodynamic behaviour in a sudden expansion flow. The fluid was shear-thinning, thixotropic and had an yield stress which was measured by direct and indirect methods. The oscillatory tests showed that the elasticity of the 1% Laponite suspension was very small. The high Reynolds number turbulent flow downstream of a sudden expansion, with fully-developed inlet conditions, showed no major difference in relation to the flow of water. There were no differences between the laponite and water mean and turbulent flow characteristics upstream and downstream of the expansion plane, except for a small anticipation of the loci of maximum Reynolds stresses with the suspension, but this had no further consequence. In conclusion, although the laponite suspension was thixotropic, shear-thinning and viscoplastic, its hydrodynamic behaviour in a sudden expansion was akin to that of water, a result which could not be anticipated.

Perturbed turbulent flow, eddy viscosity and the generation of turbulent stresses

1974 ◽  
Vol 63 (4) ◽  
pp. 673-693 ◽  
Author(s):  
Russ E. Davis
Keyword(s):  
Boundary Layer ◽  
Turbulent Flow ◽  
Eddy Viscosity ◽  
Constant Stress ◽  
Constitutive Law ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Dynamical Equations ◽  
Mean Velocity ◽  
Taylor’S Hypothesis

The perturbation of a turbulent flow by an organized wavelike disturbance is examined using a dynamical, rather than phenomenological, approach. On the basis of the assumption that an infinitesimal perturbation results in a linear change in the statistics of the turbulence, and that the turbulence is either weak or that the turbulent perturbations are quasi-Gaussian, a method for predicting the perturbation turbulent Reynolds stresses is developed. The novel aspect of the analysis is that all averaging is delayed until the dynamical equations have been solved rather than attempting to find, apriori, equations for averaged quantities. When applied to long-wave perturbations the analysis indicates that the perturbation shear stress is of primary dynamical importance, and that this stress is determined by the principal component of mean shear through a relation which depends on the spectrum of the turbulent velocity component parallel to the gradient of the undisturbed mean velocity (the component perpendicular to the wall in a turbulent boundary layer). Theoretical arguments and observations are used to estimate the form of this spectrum in a constant stress shear layer. This results in a prediction of the constitutive law relating turbulent stress and the mean flow. The law is visco-elastic in nature, and is in agreement with the known constitutive relation for stress perturbations to a constant stress boundary layer; it resembles the eddy viscosity relation used successfully by others in describing perturbations in turbulent flows. The details of the constitutive law depend on how well the turbulence obeys Taylor's hypothesis that phase velocity equals mean flow velocity, and some insight into this question is given.

Some Solutions of the Plane Turbulent Impinging Jet

1970 ◽  
Vol 92 (4) ◽  
pp. 915-922 ◽  
Author(s):  
M. Wolfshtein
Keyword(s):  
Reasonable Agreement ◽  
Eddy Viscosity ◽  
Order Differential Equation ◽  
Impinging Jet ◽  
Experimental Information ◽  
Length Scale ◽  
Reynolds Stresses ◽  
Finite Difference Technique ◽  
The Mean ◽  
Mean Strain

The impinging jet problem is solved by an iterative finite-difference technique. Reynolds stresses are assumed to be related to the mean strain by a scalar eddy viscosity. The eddy viscosity is assumed to depend on the level of energy fluctuations and a length scale. The level of energy fluctuations is obtained from a second-order differential equation, while the length scale of turbulence is prescribed on the basis of experimental information. The solutions show reasonable agreement with experiment.

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