scholarly journals Application of Different Turbulence Models for Duct Flow Simulation With Reduced and Full Navier-Stokes Equations

1995 ◽  
Author(s):  
Charles Hirsch ◽  
Andrei E. Khodak
Keyword(s):  
Reynolds Number ◽  
Reynolds Stress ◽  
Stokes Equations ◽  
Flow Simulation ◽  
Turbulence Models ◽  
Navier Stokes ◽  
Duct Flow ◽  
Mean Velocity ◽  
Navier Stokes Equations ◽  
Wall Functions

An S-shaped diffusing duct flow is analysed with various turbulence models: standard high-Reynolds-number k-ε model with wall functions, a low-Reynolds-number k-ε model, and an explicit non-linear algebraic Reynolds stress closure model (ASM). In addition, computations were obtained with parabolic and partially-parabolic approximations along with solutions of the full Navier-Stokes equations. Results of the numerical simulation are compared with LDA measurements of the turbulent flow as reported by Whitelaw and Yu (1993). Detailed comparisons of mean velocity and Reynolds stress distributions are presented. It is shown that the partially-parabolic approach gives a significant improvement over parabolic approximation in predicting mean velocities and pressure distributions. However, the turbulence models used are still not able to reproduce all the observed flow features, although the ASM results appear to be slightly but consistently closer to the experimental data.

scholarly journals Model-based scaling of the streamwise energy density in high-Reynolds-number turbulent channels

2013 ◽  
Vol 734 ◽  
pp. 275-316 ◽  
Author(s):  
Rashad Moarref ◽  
Ati S. Sharma ◽  
Joel A. Tropp ◽  
Beverley J. McKeon
Keyword(s):  
Reynolds Number ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Low Rank ◽  
Navier Stokes ◽  
Mean Velocity ◽  
Navier Stokes Equations ◽  
Self Similar ◽  
The Mean ◽  
High Reynolds

AbstractWe study the Reynolds-number scaling and the geometric self-similarity of a gain-based, low-rank approximation to turbulent channel flows, determined by the resolvent formulation of McKeon & Sharma (J. Fluid Mech., vol. 658, 2010, pp. 336–382), in order to obtain a description of the streamwise turbulence intensity from direct consideration of the Navier–Stokes equations. Under this formulation, the velocity field is decomposed into propagating waves (with single streamwise and spanwise wavelengths and wave speed) whose wall-normal shapes are determined from the principal singular function of the corresponding resolvent operator. Using the accepted scalings of the mean velocity in wall-bounded turbulent flows, we establish that the resolvent operator admits three classes of wave parameters that induce universal behaviour with Reynolds number in the low-rank model, and which are consistent with scalings proposed throughout the wall turbulence literature. In addition, it is shown that a necessary condition for geometrically self-similar resolvent modes is the presence of a logarithmic turbulent mean velocity. Under the practical assumption that the mean velocity consists of a logarithmic region, we identify the scalings that constitute hierarchies of self-similar modes that are parameterized by the critical wall-normal location where the speed of the mode equals the local turbulent mean velocity. For the rank-1 model subject to broadband forcing, the integrated streamwise energy density takes a universal form which is consistent with the dominant near-wall turbulent motions. When the shape of the forcing is optimized to enforce matching with results from direct numerical simulations at low turbulent Reynolds numbers, further similarity appears. Representation of these weight functions using similarity laws enables prediction of the Reynolds number and wall-normal variations of the streamwise energy intensity at high Reynolds numbers (${Re}_{\tau } \approx 1{0}^{3} {\unicode{x2013}} 1{0}^{10} $). Results from this low-rank model of the Navier–Stokes equations compare favourably with experimental results in the literature.

Experimental and Numerical Investigation of Two-Dimensional Parallel Jets

2001 ◽  
Vol 123 (2) ◽  
pp. 401-406 ◽  
Author(s):  
Elgin A. Anderson ◽  
Robert E. Spall
Keyword(s):  
Good Accuracy ◽  
Stokes Equations ◽  
Numerical Models ◽  
Symmetry Plane ◽  
Turbulence Models ◽  
Turbulent Jets ◽  
Navier Stokes ◽  
Mean Velocity ◽  
Navier Stokes Equations ◽  
The Mean

The flowfield of dual, parallel planar turbulent jets is investigated experimentally using an x-type hot-wire probe and numerically by solving the Reynolds-averaged Navier-Stokes equations. The performance of both differential Reynolds stress (RSM) and standard k-ε turbulence models is evaluated. Results show that the numerical models predict the merge and combined point characteristics to good accuracy. However, both turbulence models show a narrower width of the jet envelope than measured by experiment. The predicted profiles of the mean velocity along the symmetry plane agree well with the experimental results.

Similarity in non-rotating and rotating turbulent pipe flows

1999 ◽  
Vol 379 ◽  
pp. 1-22 ◽  
Author(s):  
MARTIN OBERLACK
Keyword(s):  
Reynolds Number ◽  
Scaling Laws ◽  
Stokes Equations ◽  
Scaling Law ◽  
Navier Stokes ◽  
Invariant Solutions ◽  
Mean Velocity ◽  
Navier Stokes Equations ◽  
Pipe Flows ◽  
The Mean

The Lie group approach developed by Oberlack (1997) is used to derive new scaling laws for high-Reynolds-number turbulent pipe flows. The scaling laws, or, in the methodology of Lie groups, the invariant solutions, are based on the mean and fluctuation momentum equations. For their derivation no assumptions other than similarity of the Navier–Stokes equations have been introduced where the Reynolds decomposition into the mean and fluctuation quantities has been implemented. The set of solutions for the axial mean velocity includes a logarithmic scaling law, which is distinct from the usual law of the wall, and an algebraic scaling law. Furthermore, an algebraic scaling law for the azimuthal mean velocity is obtained. In all scaling laws the origin of the independent coordinate is located on the pipe axis, which is in contrast to the usual wall-based scaling laws. The present scaling laws show good agreement with both experimental and DNS data. As observed in experiments, it is shown that the axial mean velocity normalized with the mean bulk velocity um has a fixed point where the mean velocity equals the bulk velocity independent of the Reynolds number. An approximate location for the fixed point on the pipe radius is also given. All invariant solutions are consistent with all higher-order correlation equations. A large-Reynolds-number asymptotic expansion of the Navier–Stokes equations on the curved wall has been utilized to show that the near-wall scaling laws for at surfaces also apply to the near-wall regions of the turbulent pipe flow.

RANS Predictions in an Idealized Lower-Plenum Model

2006 ◽  
Author(s):  
Joshua D. Hodson ◽  
Robert E. Spall ◽  
Barton L. Smith
Keyword(s):  
Stokes Equations ◽  
Turbulence Models ◽  
Navier Stokes ◽  
Mean Velocity ◽  
Navier Stokes Equations ◽  
Pressure Losses ◽  
Pressure Loss Coefficient ◽  
The Mean ◽  
Recirculation Length

The two-dimensional, unsteady, Reynolds-averaged Navier-Stokes equations have been solved for the flow across a row of confined cylinders with a pitch-to-diameter ratio of 1.7, a configuration which was designed to model a next generation nuclear plant lower-plenum. Four different turbulence models were used: k–ε, k–ω, v2–f, and differential Reynolds-stress transport. Comparisons with available experimental data were made for pressure losses, recirculation lengths, and mean velocity profiles. The results indicate that all models did a reasonable job of predicting the pressure loss coefficient. However, in terms of the mean velocities and recirculation length, the determination of which model performed best is not clear.

scholarly journals Simulation of turbulent flow over the hill

2021 ◽  
Vol 2094 (2) ◽  
pp. 022045
Author(s):  
A Y Kurbanaliev ◽  
A B Turganbaeva ◽  
K T Berdibekova ◽  
K A Bokoev
Keyword(s):  
Turbulent Flow ◽  
Stokes Equations ◽  
Turbulence Models ◽  
Numerical Data ◽  
Numerical Calculations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Wall Functions ◽  
Hilly Area ◽  
The Hill

Abstract An airflow around a hilly area is simulated by numerically solving the Reynolds-averaged Navier-Stokes equations within the open OpenFOAM 2006 package. To simulate turbulence, standard turbulence models implemented in OpenFOAM 2006 were used together with wall functions. The results of numerical calculations were compared to the numerical data obtained using the CFL3D and FUN3D packages.

A note on the solution of the Navier-Stokes equations for a spherically symmetric expansion into a very low pressure

1973 ◽  
Vol 59 (2) ◽  
pp. 391-396 ◽  
Author(s):  
N. C. Freeman ◽  
S. Kumar
Keyword(s):  
Shock Wave ◽  
Reynolds Number ◽  
Stokes Equation ◽  
Stokes Equations ◽  
Low Pressure ◽  
Navier Stokes ◽  
Spherically Symmetric ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
Type Flow

It is shown that, for a spherically symmetric expansion of a gas into a low pressure, the shock wave with area change region discussed earlier (Freeman & Kumar 1972) can be further divided into two parts. For the Navier–Stokes equation, these are a region in which the asymptotic zero-pressure behaviour predicted by Ladyzhenskii is achieved followed further downstream by a transition to subsonic-type flow. The distance of this final region downstream is of order (pressure)−2/3 × (Reynolds number)−1/3.

Numerical Prediction of Turbulent Wakes Behind a Square Cylinder

1998 ◽  
Vol 14 (1) ◽  
pp. 23-29
Author(s):  
Robert R. Hwang ◽  
Sheng-Yuh Jaw
Keyword(s):  
Stokes Equations ◽  
Numerical Study ◽  
Navier Stokes ◽  
Wall Region ◽  
Square Cylinder ◽  
Mean Velocity ◽  
Navier Stokes Equations ◽  
Turbulent Vortex Shedding ◽  
Model Equations ◽  
Good Agreement

ABSTRACTThis paper presents a numerical study on turbulent vortex shedding flows past a square cylinder. The 2D unsteady periodic shedding motion was resolved in the calculation and the superimposed turbulent fluctuations were simulated with a second-order Reynolds-stress closure model. The calculations were carried out by solving numerically the fully elliptic ensemble-averaged Navier-Stokes equations coupled with the turbulence model equations together with the two-layer approach in the treatment of the near-wall region. The performance of the computations was evaluated by comparing the numerical results with data from available experiments. Results indicate that the present study gives good agreement in the shedding frequency and mean drag as well as in some phase profiles of the mean velocity.

Free-stream coherent structures in parallel boundary-layer flows

2014 ◽  
Vol 752 ◽  
pp. 602-625 ◽  
Author(s):  
Kengo Deguchi ◽  
Philip Hall
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Coherent Structures ◽  
Free Stream ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Homotopy Continuation ◽  
Boundary Layer Flows ◽  
Navier Stokes Equations ◽  
High Reynolds

AbstractOur concern in this paper is with high-Reynolds-number nonlinear equilibrium solutions of the Navier–Stokes equations for boundary-layer flows. Here we consider the asymptotic suction boundary layer (ASBL) which we take as a prototype parallel boundary layer. Solutions of the equations of motion are obtained using a homotopy continuation from two known types of solutions for plane Couette flow. At high Reynolds numbers, it is shown that the first type of solution takes the form of a vortex–wave interaction (VWI) state, see Hall & Smith (J. Fluid Mech., vol. 227, 1991, pp. 641–666), and is located in the main part of the boundary layer. On the other hand, here the second type is found to support an equilibrium solution of the unit-Reynolds-number Navier–Stokes equations in a layer located a distance of $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}O(\ln \mathit{Re})$ from the wall. Here $\mathit{Re}$ is the Reynolds number based on the free-stream speed and the unperturbed boundary-layer thickness. The streaky field produced by the interaction grows exponentially below the layer and takes its maximum size within the unperturbed boundary layer. The results suggest the possibility of two distinct types of streaky coherent structures existing, possibly simultaneously, in disturbed boundary layers.

Measurement and Calculation of Nozzle Guide Vane End Wall Heat Transfer

1998 ◽  
Author(s):  
Neil W. Harvey ◽  
Martin G. Rose ◽  
John Coupland ◽  
Terry Jones
Keyword(s):  
Heat Transfer ◽  
Stokes Equations ◽  
Guide Vane ◽  
Correction Method ◽  
Navier Stokes ◽  
Design Data ◽  
Navier Stokes Equations ◽  
Wall Functions ◽  
Transfer Rates ◽  
Nozzle Guide

A 3-D steady viscous finite volume pressure correction method for the solution of the Reynolds averaged Navier-Stokes equations has been used to calculate the heat transfer rates on the end walls of a modern High Pressure Turbine first stage stator. Surface heat transfer rates have been calculated at three conditions and compared with measurements made on a model of the vane tested in annular cascade in the Isentropic Light Piston Facility at DERA, Pyestock. The NGV Mach numbers, Reynolds numbers and geometry are fully representative of engine conditions. Design condition data has previously been presented by Harvey and Jones (1990). Off-design data is presented here for the first time. In the areas of highest heat transfer the calculated heat transfer rates are shown to be within 20% of the measured values at all three conditions. Particular emphasis is placed on the use of wall functions in the calculations with which relatively coarse grids (of around 140,000 nodes) can be used to keep computational run times sufficiently low for engine design purposes.

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