An Eddy-Resolving Reynolds Stress Model for the Turbulent Bubbly Flow in a Square Cross-Sectioned Bubble Column

2014 ◽  
Author(s):  
Matthias Ullrich ◽  
Benjamin Krumbein ◽  
Robert Maduta ◽  
Suad Jakirlić
Keyword(s):  
Reynolds Stress ◽  
Bubble Column ◽  
Bubbly Flow ◽  
Three Dimensional ◽  
Reynolds Stress Model ◽  
Moment Closure ◽  
Numerical Code ◽  
Stress Model ◽  
Mean Flow ◽  
Second Moment Closure

An instability-sensitive, eddy-resolving Reynolds Stress Model of turbulence, employed in the Eulerian-Eulerian two-fluid framework, is formulated and validated by computing the gas-liquid bubble column in a three-dimensional square cross-sectioned configuration in the homogeneous flow regime. Interphase momentum transfer is modelled by considering drag, lift and virtual mass forces. The turbulence in the continuous liquid phase is captured by using a Second-Moment Closure model employed in the Unsteady Reynolds-Averaged Navier Stokes framework implying the solving of the differential transport equations for the Reynolds stress tensor and the homogeneous part of the inverse turbulent time scale ωh. This uiuj – ωh model is appropriately extended in accordance with the Scale-Adaptive Simulation proposal, enabling so the development of the fluctuating turbulence. The results obtained are analysed along with a reference experiment with respect to the evolution of the mean flow and turbulent quantities in both gas and liquid phases. The model described is implemented in the numerical code OpenFOAM.

scholarly journals Analysis of Separated Flows Inside an Annular Compressor Cascade Using a Low-Re-Number k-ϵ and an Algebraic Reynolds-Stress-Model

1997 ◽  
Author(s):  
Jürgen R. Lücke ◽  
Heinz E. Gallus
Keyword(s):  
Flow Field ◽  
Reynolds Stress ◽  
Three Dimensional ◽  
Separated Flow ◽  
Reynolds Stress Model ◽  
Stress Model ◽  
Mean Flow ◽  
Compressor Cascade ◽  
Production Term ◽  
Algebraic Reynolds Stress Model

The flow field inside an annular compressor cascade is numerically investigated. The mean flow features are complex three-dimensional zones of turbulent separation at hub and shroud at high inflow angles. The flow field is investigated with an implicit three-dimensional Navier-Stokes code. To predict turbulent effects the flow solver includes two different variants of a Low-Re-number k-ϵ-model and an algebraic Reynolds-stress-model. Using the Low-Re-number model the structure of the regions of separated flow are fairly well predicted. However, intensity and size of these zones are too small compared with the experimental data. Better results are produced using the anisotropic algebraic Reynolds-stress-model combined with a stagnation point modification of the turbulent production term. Stucture and intensity of the vortex systems are simulated in more detail. Static pressure distributions and loss contours are in a very good agreement with the experiments.

scholarly journals Three-Dimensional Navier-Stokes Computation of Turbine Nozzle Flow With Advanced Turbulence Models

1995 ◽  
Author(s):  
J. Luo ◽  
B. Lakshminarayana
Keyword(s):  
Reynolds Stress ◽  
Three Dimensional ◽  
Turbulence Models ◽  
Reynolds Stress Model ◽  
Navier Stokes ◽  
Nozzle Flow ◽  
Stress Model ◽  
Mean Flow ◽  
The Mean ◽  
Algebraic Reynolds Stress Model

A three-dimensional Navier-Stokes procedure has been used to compute the three-dimensional viscous flow through the turbine nozzle passage of a single stage turbine. A low Reynolds number k-ε model and a zonal k-ε/ARSM (algebraic Reynolds stress model) are utilized for turbulence closure. The algebraic Reynolds stress model is used only in the endwall region to represent the anisotropy of turbulence. A four-stage Runge-Kutta scheme is used for time-integration of both the mean-flow and the turbulence transport equations. For the turbine nozzle flow, comprehensive comparisons between the predictions and the experimental data obtained at Penn State show that most features of the vortex-dominated endwall flow, as well as nozzle wake structure, have been captured well by the numerical procedure. An assessment of the performance of the turbulence models has been carried out The two models are found to provide similar predictions for the mean flow parameters, although slight improvement in the prediction of some secondary flow quantities has been obtained by the ARSM model.

Three-Dimensional Navier–Stokes Computation of Turbine Nozzle Flow With Advanced Turbulence Models

1997 ◽  
Vol 119 (3) ◽  
pp. 516-530 ◽  
Author(s):  
J. Luo ◽  
B. Lakshminarayana
Keyword(s):  
Reynolds Stress ◽  
Three Dimensional ◽  
Turbulence Models ◽  
Reynolds Stress Model ◽  
Navier Stokes ◽  
Nozzle Flow ◽  
Stress Model ◽  
Mean Flow ◽  
The Mean ◽  
Algebraic Reynolds Stress Model

A three-dimensional Navier–Stokes procedure has been used to compute the three-dimensional viscous flow through the turbine nozzle passage of a single-stage turbine. A low-Reynolds-number k–ε model and a zonal k-ε/ARSM (algebraic Reynolds stress model) are utilized for turbulence closure. The algebraic Reynolds stress model is used only in the endwall region to represent the anisotropy of turbulence. A four-stage Runge–Kutta scheme is used for time integration of both the mean-flow and the turbulence transport equations. For the turbine nozzle flow, comprehensive comparisons between the predictions and the experimental data obtained at Penn State show that most features of the vortex-dominated endwall flow, as well as nozzle wake structure, have been captured well by the numerical procedure. An assessment of the performance of the turbulence models has been carried out. The two models are found to provide similar predictions for the mean flow parameters, although slight improvement in the prediction of some secondary flow quantities has been obtained by the ARSM model.

Improved Prediction of Turbomachinery Flows Using Near-Wall Reynolds-Stress Model

2001 ◽  
Vol 124 (1) ◽  
pp. 86-99 ◽  
Author(s):  
G. A. Gerolymos ◽  
J. Neubauer ◽  
V. C. Sharma ◽  
I. Vallet
Keyword(s):  
Experimental Data ◽  
Turbulent Flows ◽  
Reynolds Stress ◽  
Turbulence Models ◽  
Reynolds Stress Model ◽  
Stress Model ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Flow Equations ◽  
Near Wall

In this paper an assessment of the improvement in the prediction of complex turbomachinery flows using a new near-wall Reynolds-stress model is attempted. The turbulence closure used is a near-wall low-turbulence-Reynolds-number Reynolds-stress model, that is independent of the distance-from-the-wall and of the normal-to-the-wall direction. The model takes into account the Coriolis redistribution effect on the Reynolds-stresses. The five mean flow equations and the seven turbulence model equations are solved using an implicit coupled OΔx3 upwind-biased solver. Results are compared with experimental data for three turbomachinery configurations: the NTUA high subsonic annular cascade, the NASA_37 rotor, and the RWTH 1 1/2 stage turbine. A detailed analysis of the flowfield is given. It is seen that the new model that takes into account the Reynolds-stress anisotropy substantially improves the agreement with experimental data, particularily for flows with large separation, while being only 30 percent more expensive than the k−ε model (thanks to an efficient implicit implementation). It is believed that further work on advanced turbulence models will substantially enhance the predictive capability of complex turbulent flows in turbomachinery.

A Numerical Study of Vortex Breakdown in Turbulent Swirling Flows

1999 ◽  
Vol 122 (1) ◽  
pp. 179-183 ◽  
Author(s):  
Robert E. Spall ◽  
Blake M. Ashby
Keyword(s):  
Reynolds Stress ◽  
Stokes Equations ◽  
Vortex Breakdown ◽  
Numerical Study ◽  
Reynolds Stress Model ◽  
Navier Stokes ◽  
Stress Model ◽  
Mean Flow ◽  
Navier Stokes Equations ◽  
The Mean

Solutions to the incompressible Reynolds-averaged Navier–Stokes equations have been obtained for turbulent vortex breakdown within a slightly diverging tube. Inlet boundary conditions were derived from available experimental data for the mean flow and turbulence kinetic energy. The performance of both two-equation and full differential Reynolds stress models was evaluated. Axisymmetric results revealed that the initiation of vortex breakdown was reasonably well predicted by the differential Reynolds stress model. However, the standard K-ε model failed to predict the occurrence of breakdown. The differential Reynolds stress model also predicted satisfactorily the mean azimuthal and axial velocity profiles downstream of the breakdown, whereas results using the K-ε model were unsatisfactory. [S0098-2202(00)01601-1]

Robust Implicit Multigrid Reynolds-Stress Model Computation of 3-D Turbomachinery Flows

2006 ◽  
Author(s):  
G. A. Gerolymos ◽  
I. Vallet
Keyword(s):  
Reynolds Stress ◽  
Time Integration ◽  
Computational Cost ◽  
Turbulence Models ◽  
Reynolds Stress Model ◽  
Finite Volume Scheme ◽  
Stress Model ◽  
Mean Flow ◽  
Approximate Factorization ◽  
Flow Equations

The purpose of this paper is to present a numerical methodology for the computation of complex 3-D turbomachinery flows using advanced multiequation turbulence closures, including full 7-equation Reynolds-stress transport models. A general frame-work describing the turbulence models and possible future improvements is presented. The flow equations are discretized on structured multiblock grids, using an upwind biased (O[Δx3] MUSCL reconstruction) finite-volume scheme. Time-integration uses a local-dual-time-stepping implicit procedure, with internal subiterations. Computational efficiency is achieved by a specific approximate factorization of the implicit subiterations, designed to minimize the computational cost of the turbulence-transport-equations. Convergence is still accelerated using a mean-flow-multigrid full-approximation-scheme method, where multigrid is applied on the mean-flow-variables only. Speed-ups of a factor 3 are obtained using 3 levels of multigrid (fine + 2 coarser grids). Computational examples are presented using several Reynolds-stress model variants (and also a baseline k–ε model), for various turbomachinery configurations, and compared with available experimental measurements.

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