Exploring a Three-Equation R–k–ε Turbulence Model

1996 ◽  
Vol 118 (4) ◽  
pp. 795-799 ◽  
Author(s):  
U. C. Goldberg
Keyword(s):  
Experimental Data ◽  
Boundary Condition ◽  
Reynolds Number ◽  
Time Scale ◽  
Eddy Viscosity ◽  
Current Approach ◽  
Wall Distance ◽  
Wall Boundary Condition ◽  
Proposed Model ◽  
Arbitrary Flow

A low Reynolds number extension of the k–ε model is proposed and evaluated. This version has the following attributes: (a) it does not involve wall distance or normal-to-wall directionality; (b) it enforces time scale realisability by preventing it from falling below the Kolmogorov (dissipative eddy) scale, (ν/ε)1/2; (c) it employs a simple wall boundary condition for ε. The current approach requires an additional transport equation for the undamped eddy viscosity, R, thus the resulting model is of the three-equation variety. Since wall distance is not used, the proposed model is applicable to arbitrary flow topologies. Predictions using this model are compared with experimental data of several flow cases, with encouraging results.

Turbulent Flow Using a Modified V2f Turbulence Model

2004 ◽  
Author(s):  
Hanif Montazeri ◽  
Siamak Kazemzadeh Hannani ◽  
Bijan Farhanieh
Keyword(s):  
Boundary Condition ◽  
Turbulence Model ◽  
Flow Problem ◽  
Two Dimensional ◽  
Convergence Problem ◽  
New Model ◽  
Step Flow ◽  
Wall Boundary Condition ◽  
Proposed Model ◽  
Accuracy Of Results

An improved version of the V2f turbulence model has been examined in this paper. The objective was to overcome the convergence problem encountered in the original V2f model. The convergence problem is due to the commonly-used wall boundary condition, which therefore has been modified in the proposed model. To test the soundness of the new model, several two-dimensional cases such as Poiseuille flow, channel flow, and backward-step flow has been analyzed and the results are compared with the standard k-ε model, DNS, and in case of the backward flow problem, also with the original V2f model. Based on the comparison, the new model presents a promising approach both with respect to convergence as well as the accuracy of results.

On the Wall Boundary Condition for Computing Turbulent Heat Transfer With K–ω Models

2000 ◽  
Author(s):  
J. Bredberg ◽  
S.-H. Peng ◽  
L. Davidson
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Reynolds Number ◽  
Channel Flow ◽  
Turbulence Model ◽  
Turbulent Heat Transfer ◽  
Turbulent Heat ◽  
Wall Function ◽  
Wall Boundary Condition ◽  
Wall Boundary

Abstract A new wall boundary condition for the standard Wilcox’s k–ω model (1988) is proposed. The model combines a wall function and a low-Reynolds number approach, and a function that smoothly blends the two formulations, enabling the model to be used independently of the location of the first interior computational node. The model is calibrated using DNS-data for a channel flow and applied to a heat transfer prediction for a flow in a rib-roughened channel (Reb = 100 000). The results obtained with the new model are improved for various mesh sizes and are asymptotically identical with those of the standard k–ω turbulence model.

On the Grid Sensitivity of the Wall Boundary Condition of the k-ω Turbulence Model

2004 ◽  
Vol 126 (6) ◽  
pp. 900-910 ◽  
Author(s):  
L. Ec¸a ◽  
M. Hoekstra
Keyword(s):  
Boundary Condition ◽  
Turbulence Model ◽  
Eddy Viscosity ◽  
Solid Wall ◽  
Turbulence Models ◽  
Numerical Implementation ◽  
Two Dimensional ◽  
Grid Refinement ◽  
Wall Boundary Condition ◽  
Order Of Magnitude

This paper presents a study on the k-ω turbulence model with regard to the numerical implementation of the ω boundary condition at a solid wall, where ω tends to infinity. Three different implementations are tested in the calculation of a simple two-dimensional turbulent flow over a flat plate. Grid refinement studies in grids with different near-wall grid line spacings are performed to assess the numerical uncertainty of the predicted drag coefficient CD. The results are compared with the predictions of several alternative algebraic, one-equation, and two-equation eddy-viscosity turbulence models. For the same level of grid refinement, the estimated uncertainty of CD obtained with the k-ω model is one order of magnitude larger than for all the other models.

Rough Surface Wall Function Treatment With Single Equation Turbulence Models

2017 ◽  
Vol 139 (8) ◽  
Author(s):  
U. Goldberg ◽  
P. Batten
Keyword(s):  
Heat Transfer ◽  
Kinetic Energy ◽  
Distance Function ◽  
Eddy Viscosity ◽  
Rough Surfaces ◽  
Turbulence Models ◽  
Single Equation ◽  
Current Approach ◽  
Wall Function ◽  
Wall Distance

Most literature in the area of turbulent flow over rough surfaces discusses methods for turbulence models based on two or more transport equations, one of which is that for turbulence kinetic energy which supplies k that is heavily used for the rough wall treatment. However, many aeronautical engineers routinely use single equation turbulence models which solve directly for eddy viscosity and do not involve k. The present work proposes methods by which such one-equation models can predict flow cases which include multiple rough surfaces. The current approach does not impose changes to the wall distance function, should such a function be necessary. Several examples show that the proposed method is able to produce good predictions of both skin friction and heat transfer along rough surfaces. While results are not always as accurate as those predicted by turbulence models which solve for k, especially if detached or wake-like flow regions exist, accompanied by a significant increase in eddy viscosity, the single-equation models are able to provide predictions at least good enough for preliminary studies.

Dual Release Model to Evaluate Dissolution Profiles from Swellable Drug Polyelectrolyte Matrices

2020 ◽  
Vol 17 (6) ◽  
pp. 511-522 ◽  
Author(s):  
Alicia Graciela Cid ◽  
María Verónica Ramírez-Rigo ◽  
María Celeste Palena ◽  
Elio Emilio Gonzo ◽  
Alvaro Federico Jimenez-Kairuz ◽  
...  
Keyword(s):  
Experimental Data ◽  
Drug Release ◽  
Inflection Point ◽  
Release Profile ◽  
Experimental Point ◽  
Extended Model ◽  
Release Process ◽  
Proposed Model ◽  
Dual Release ◽  
Release Model

Background: Mathematical modeling in modified drug release is an important tool that allows predicting the release rate of drugs in their surrounding environment and elucidates the transport mechanisms involved in the process. Objective: The aim of this work was to develop a mathematical model that allows evaluating the release profile of drugs from polymeric carriers in which the swelling phenomenon is present. Methods: Swellable matrices based on ionic complexes of alginic acid or carboxymethylcellulose with ciprofloxacin were prepared and the effect of adding the polymer sodium salt on the swelling process and the drug release was evaluated. Experimental data from the ciprofloxacin release profiles were mathematically adjusted, considering the mechanisms involved in each stage of the release process. Results: A proposed model, named “Dual Release” model, was able to properly fit the experimental data of matrices presenting the swelling phenomenon, characterized by an inflection point in their release profile. This entails applying the extended model of Korsmeyer-Peppas to estimate the percentage of drug released from the first experimental point up to the inflection point and then a model called Lumped until the final time, allowing to adequately represent the complete range of the drug release profile. Different parameters of pharmaceutical relevance were calculated using the proposed model to compare the profiles of the studied matrices. Conclusion: The “Dual Release” model proposed in this article can be used to predict the behavior of complex systems in which different mechanisms are involved in the release process.

scholarly journals Fibre-induced drag reduction

2008 ◽  
Vol 602 ◽  
pp. 209-218 ◽  
Author(s):  
J. J. J. GILLISSEN ◽  
B. J. BOERSMA ◽  
P. H. MORTENSEN ◽  
H. I. ANDERSSON
Keyword(s):  
Experimental Data ◽  
Numerical Simulation ◽  
Reynolds Number ◽  
Drag Reduction ◽  
Elastic Layer ◽  
Turbulent Drag Reduction ◽  
Rigid Polymer ◽  
Fibre Concentration ◽  
Induced Drag ◽  
Turbulent Drag

We use direct numerical simulation to study turbulent drag reduction by rigid polymer additives, referred to as fibres. The simulations agree with experimental data from the literature in terms of friction factor dependence on Reynolds number and fibre concentration. An expression for drag reduction is derived by adopting the concept of the elastic layer.

Comparison of LES of Steady Transitional Flow in an Idealized Stenosed Axisymmetric Artery Model With a RANS Transitional Model

2011 ◽  
Vol 133 (5) ◽  
Author(s):  
F. P. P. Tan ◽  
N. B. Wood ◽  
G. Tabor ◽  
X. Y. Xu
Keyword(s):  
Experimental Data ◽  
Turbulence Intensity ◽  
Eddy Viscosity ◽  
Flow Analysis ◽  
Wall Turbulence ◽  
Transitional Flow ◽  
Navier Stokes ◽  
Turbulence Structures ◽  
Eddy Simulation ◽  
Accurate Treatment

In this study, two different turbulence methodologies are investigated to predict transitional flow in a 75% stenosed axisymmetric experimental arterial model and in a slightly modified version of the model with an eccentric stenosis. Large eddy simulation (LES) and Reynolds-averaged Navier–Stokes (RANS) methods were applied; in the LES simulations eddy viscosity subgrid-scale models were employed (basic and dynamic Smagorinsky) while the RANS method involved the correlation-based transitional version of the hybrid k-ε/k-ω flow model. The RANS simulations used 410,000 and 820,000 element meshes for the axisymmetric and eccentric stenoses, respectively, with y+ less than 2 viscous wall units for the boundary elements, while the LES used 1,200,000 elements with y+ less than 1. Implicit filtering was used for LES, giving an overlap between the resolved and modeled eddies, ensuring accurate treatment of near wall turbulence structures. Flow analysis was carried out in terms of vorticity and eddy viscosity magnitudes, velocity, and turbulence intensity profiles and the results were compared both with established experimental data and with available direct numerical simulations (DNSs) from the literature. The simulation results demonstrated that the dynamic Smagorinsky LES and RANS transitional model predicted fairly comparable velocity and turbulence intensity profiles with the experimental data, although the dynamic Smagorinsky model gave the best overall agreement. The present study demonstrated the power of LES methods, although they were computationally more costly, and added further evidence of the promise of the RANS transition model used here, previously tested in pulsatile flow on a similar model. Both dynamic Smagorinsky LES and the RANS model captured the complex transition phenomena under physiological Reynolds numbers in steady flow, including separation and reattachment. In this respect, LES with dynamic Smagorinsky appeared more successful than DNS in replicating the axisymmetric experimental results, although inflow conditions, which are subject to caveats, may have differed. For the eccentric stenosis, LES with Smagorinsky coefficient of 0.13 gave the closest agreement with DNS despite the known shortcomings of fixed coefficients. The relaminarization as the flow escaped the influence of the stenosis was amply demonstrated in the simulations, graphically so in the case of LES.

scholarly journals The Tidally Averaged Momentum Balance in a Partially and Periodically Stratified Estuary

2010 ◽  
Vol 40 (11) ◽  
pp. 2418-2434 ◽  
Author(s):  
Mark T. Stacey ◽  
Matthew L. Brennan ◽  
Jon R. Burau ◽  
Stephen G. Monismith
Keyword(s):  
Water Column ◽  
Time Scale ◽  
Eddy Viscosity ◽  
Momentum Equation ◽  
Momentum Balance ◽  
Exchange Flow ◽  
Bed Stress ◽  
Turbulent Momentum ◽  
Stratified Estuary ◽  
Estuarine Exchange

Abstract Observations of turbulent stresses and mean velocities over an entire spring–neap cycle are used to evaluate the dynamics of tidally averaged flows in a partially stratified estuarine channel. In a depth-averaged sense, the net flow in this channel is up estuary due to interaction of tidal forcing with the geometry of the larger basin. The depth-variable tidally averaged flow has the form of an estuarine exchange flow (downstream at the surface, upstream at depth) and varies in response to the neap–spring transition. The weakening of the tidally averaged exchange during the spring tides appears to be a result of decreased stratification on the tidal time scale rather than changes in bed stress. The dynamics of the estuarine exchange flow are defined by a balance between the vertical divergence of the tidally averaged turbulent stress and the tidally averaged pressure gradient in the lower water column. In the upper water column, tidal stresses are important contributors, particularly during the neap tides. The usefulness of an effective eddy viscosity in the tidally averaged momentum equation is explored, and it is seen that the effective eddy viscosity on the subtidal time scale would need to be negative to close the momentum balance. This is due to the dominant contribution of tidally varying turbulent momentum fluxes, which have no specific relation to the subtidal circulation. Using a water column model, the validity of an effective eddy viscosity is explored; for periodically stratified water columns, a negative effective viscosity is required.

Wear of a Tool in Double-Disk Lapping of Silicon Wafers

2010 ◽  
Author(s):  
Adam Barylski ◽  
Mariusz Deja
Keyword(s):  
Experimental Data ◽  
Integrated Circuits ◽  
Tool Wear ◽  
Silicon Wafers ◽  
Silicon Ingot ◽  
Proposed Model ◽  
Tool Wear Prediction ◽  
Simulation Results ◽  
High Degree ◽  
Kinematical Parameters

Silicon wafers are the most widely used substrates for fabricating integrated circuits. A sequence of processes is needed to turn a silicon ingot into silicon wafers. One of the processes is flattening by lapping or by grinding to achieve a high degree of flatness and parallelism of the wafer [1, 2, 3]. Lapping can effectively remove or reduce the waviness induced by preceding operations [2, 4]. The main aim of this paper is to compare the simulation results with lapping experimental data obtained from the Polish producer of silicon wafers, the company Cemat Silicon from Warsaw (www.cematsil.com). Proposed model is going to be implemented by this company for the tool wear prediction. Proposed model can be applied for lapping or grinding with single or double-disc lapping kinematics [5, 6, 7]. Geometrical and kinematical relations with the simulations are presented in the work. Generated results for given workpiece diameter and for different kinematical parameters are studied using models programmed in the Matlab environment.

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