Modified partially averaged Navier–Stokes model for turbulent flow in passages with large curvature

2020 ◽  
Vol 34 (23) ◽  
pp. 2050239
Author(s):  
Weixiang Ye ◽  
Xianwu Luo ◽  
Ying Li
Keyword(s):  
Turbulent Flow ◽  
Turbulent Flows ◽  
Turbulence Model ◽  
Navier Stokes ◽  
Small Scale ◽  
Bounded Region ◽  
Rectangular Duct ◽  
Reynolds Stresses ◽  
Curvature Effects ◽  
Text Model

This study presents a partially averaged Navier–Stokes model, MSST PANS, based on a modified SST [Formula: see text] turbulence model to predict turbulent flows with large streamline curvature. The model was validated for turbulent flow in a [Formula: see text] curved rectangular duct (Re = 224,000) to assess the MSST PANS capabilities. The predictions are compared against flow simulations for the same curved rectangular duct using four turbulence models including the standard [Formula: see text] model, SST [Formula: see text] model, [Formula: see text] PANS model and SST [Formula: see text] PANS model. Comparisons among those numerical results and available experimental data show that the MSST PANS model more accurately predicts the velocity components in all three directions, especially in the wall-bounded region than the other models. The study also shows the advantages of the MSST PANS model for predicting the Reynolds stresses, vorticity, and smaller scale turbulent structures in the wall-bounded region not only qualitatively but quantitatively. Furthermore, the MSST PANS model requires fewer computations than the SST PANS model, indicating that this turbulence model, which takes large streamlines curvature effects into consideration, is an effective alternative for capturing the small-scale turbulence flow structures. This turbulence model is expected to be very useful for engineering applications, especially for flows in turbomachinery.

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.

BEM Based Solution of Turbulent Flow Over Periodic Hills With Heat Transfer

2011 ◽  
Author(s):  
Leopold Sˇkerget ◽  
Jure Ravnik
Keyword(s):  
Heat Transfer ◽  
Turbulent Flow ◽  
Turbulent Flows ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Small Scale ◽  
Test Case ◽  
Turbulent Structures ◽  
Eddy Simulation ◽  
Turbulent Models

Detached turbulent flows are difficult to predict numerically and often serve as benchmark cases for developing new numerical schemes and new turbulent models. Turbulent flow over periodic hills is one such examples, since the flow exhibits separation and reattachment on a smoothly and/or sharp curved geometry, strong pressure gradients and fluctuation of the separation point in time. These cases have been chosen by many authors for testing different turbulence simulation approaches. When the bottom wall is heated, the complexity of the problem increased, since convective heat transfer is defined by small scale turbulent structures close to the wall. We developed a Reynolds-Averaged Navier-Stokes and Large Eddy Simulation solver based on the velocity-vorticity formulation of Navier Stokes equations. RANS equations are coupled by a low-Reynolds number turbulent model, while Smagorinsky subgrid model is used for LES. The governing equations are solved with a numerical solution algorithm, which is based on the boundary element method. The pressure field is computed in a post processing step by solving a Poisson equation. The single domain as well as domain decomposition approaches are applied. The developed method was validated using flow over periodic hills test case.

Feedback Control of Turbulence

1994 ◽  
Vol 47 (6S) ◽  
pp. S3-S13 ◽  
Author(s):  
Parviz Moin ◽  
Thomas Bewley
Keyword(s):  
Feedback Control ◽  
Turbulent Flows ◽  
Systems Approach ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Small Scale ◽  
Flow Equations ◽  
Active Feedback ◽  
Active Feedback Control ◽  
Mathematical Techniques

A brief review of current approaches to active feedback control of the fluctuations arising in turbulent flows is presented, emphasizing the mathematical techniques involved. Active feedback control schemes are categorized and compared by examining the extent to which they are based on the governing flow equations. These schemes are broken down into the following categories: adaptive schemes, schemes based on heuristic physical arguments, schemes based on a dynamical systems approach, and schemes based on optimal control theory applied directly to the Navier-Stokes equations. Recent advances in methods of implementing small scale flow control ideas are also reviewed.

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 Self-consistent triple decomposition of the turbulent flow over a backward-facing step under finite amplitude harmonic forcing

2019 ◽  
Vol 475 (2225) ◽  
pp. 20190018
Author(s):  
E. Yim ◽  
P. Meliga ◽  
F. Gallaire
Keyword(s):  
Turbulent Flow ◽  
Finite Amplitude ◽  
Navier Stokes ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Backward Facing Step ◽  
Eddy Viscosity Model ◽  
Coherent Interaction ◽  
Self Consistent ◽  
The Mean

We investigate the saturation of harmonically forced disturbances in the turbulent flow over a backward-facing step subjected to a finite amplitude forcing. The analysis relies on a triple decomposition of the unsteady flow into mean, coherent and incoherent components. The coherent–incoherent interaction is lumped into a Reynolds averaged Navier–Stokes (RANS) eddy viscosity model, and the mean–coherent interaction is analysed via a semi-linear resolvent analysis building on the laminar approach by Mantič-Lugo & Gallaire (2016 J. Fluid Mech. 793 , 777–797. ( doi:10.1017/jfm.2016.109 )). This provides a self-consistent modelling of the interaction between all three components, in the sense that the coherent perturbation structures selected by the resolvent analysis are those whose Reynolds stresses force the mean flow in such a way that the mean flow generates exactly the aforementioned perturbations, while also accounting for the effect of the incoherent scale. The model does not require any input from numerical or experimental data, and accurately predicts the saturation of the forced coherent disturbances, as established from comparison to time-averages of unsteady RANS simulation data.

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.

Turbulent Flow Velocity Between Rotating Co-Axial Disks of Finite Radius

1989 ◽  
Vol 111 (3) ◽  
pp. 333-340 ◽  
Author(s):  
J. F. Louis ◽  
A. Salhi
Keyword(s):  
Turbulent Flow ◽  
Turbulence Model ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Finite Radius ◽  
Navier Stokes Equations ◽  
Rotating Cavity ◽  
Tangential Wall ◽  
Frictional Forces

The turbulent flow between two rotating co-axial disks is driven by frictional forces. The prediction of the velocity field can be expected to be very sensitive to the turbulence model used to describe the viscosity close to the walls. Numerical solutions of the Navier–Stokes equations, using a k–ε turbulence model derived from Lam and Bremhorst, are presented and compared with experimental results obtained in two different configurations: a rotating cavity and the outflow between a rotating and stationary disk. The comparison shows good overall agreement with the experimental data and substantial improvements over the results of other analyses using the k–ε models. Based on this validation, the model is applied to the flow between counterrotating disks and it gives the dependence of the radial variation of the tangential wall shear stress on Rossby number.

Numerical Simulations of Turbulent Flow Through a 90° Elbow

2019 ◽  
Author(s):  
Ravon Venters ◽  
Brian Helenbrook ◽  
Goodarz Ahmadi
Keyword(s):  
Turbulent Flow ◽  
Cross Section ◽  
Navier Stokes ◽  
Mean Square ◽  
Reynolds Stresses ◽  
Streamline Curvature ◽  
Secondary Motion ◽  
Flow Through ◽  
The Mean ◽  
Flow Transitions

Abstract Turbulent flow in an elbow has been numerically investigated. The flow was modeled using two approaches; Reynolds Averaged Navier-Stokes (RANS) and Direct Numerical Simulation (DNS) methods. The DNS allows for all the scales of turbulence to be evaluated, providing a detailed depiction of the flow. The RANS simulation, which is typically used in industry, evaluates time-averaged components of the flow. The numerical results are accompanied by experimental data, which was used to validate the two methods. Profiles of the mean and root-mean-square (RMS) fluctuating components were compared at various points along the midplane of the elbow. Upstream of the elbow, the predicted mean and RMS velocities from the RANS and DNS simulations compared well with the experiment, differing slightly near the walls. However, downstream of the elbow, the RANS deviated from the experiment and DNS, showing a longer region of flow re-circulation. This caused the mean and RMS velocities to significantly differ. Examining the cross-section flow field, secondary motion was clearly present. Upstream secondary motion of the first kind was observed which is caused by anisotropy of the reynolds stresses in the turbulent flow. Downstream of the bend, the flow transitions to secondary motion of the second kind which is caused by streamline curvature. Qualitatively, the RANS and DNS showed similar results upstream of the bend, however downstream, the magnitude of the secondary motion differed significantly.

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.

Direct simulations of low-Reynolds-number turbulent flow in a rotating channel

1993 ◽  
Vol 256 ◽  
pp. 163-197 ◽  
Author(s):  
Reidar Kristoffersen ◽  
Helge I. Andersson
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Complete Suppression ◽  
Reynolds Stresses ◽  
Mean Velocity ◽  
Computational Mesh ◽  
Developed Pressure ◽  
Rotating Channel

Direct numerical simulations of fully developed pressure-driven turbulent flow in a rotating channel have been performed. The unsteady Navier–Stokes equations were written for flow in a constantly rotating frame of reference and solved numerically by means of a finite-difference technique on a 128 × 128 × 128 computational mesh. The Reynolds number, based on the bulk mean velocity Um and the channel half-width h, was about 2900, while the rotation number Ro = 2|Ω|h/Um varied from 0 to 0.5. Without system rotation, results of the simulation were in good agreement with the accurate reference simulation of Kim, Moin & Moser (1987) and available experimental data. The simulated flow fields subject to rotation revealed fascinating effects exerted by the Coriolis force on channel flow turbulence. With weak rotation (Ro = 0.01) the turbulence statistics across the channel varied only slightly compared with the nonrotating case, and opposite effects were observed near the pressure and suction sides of the channel. With increasing rotation the augmentation and damping of the turbulence along the pressure and suction sides, respectively, became more significant, resulting in highly asymmetric profiles of mean velocity and turbulent Reynolds stresses. In accordance with the experimental observations of Johnston, Halleen & Lezius (1972), the mean velocity profile exhibited an appreciable region with slope 2Ω. At Ro = 0.50 the Reynolds stresses vanished in the vicinity of the stabilized side, and the nearly complete suppression of the turbulent agitation was confirmed by marker particle trackings and two-point velocity correlations. Rotational-induced Taylor-Görtler-like counter-rotating streamwise vortices have been identified, and the simulations suggest that the vortices are shifted slightly towards the pressure side with increasing rotation rates, and the number of vortex pairs therefore tend to increase with Ro.

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