A Velocity and Length Scale Approach to k–ε Modeling

1996 ◽  
Vol 118 (4) ◽  
pp. 857-863 ◽  
Author(s):  
O. Kwon ◽  
F. E. Ames
Keyword(s):  
Reynolds Number ◽  
Kinetic Energy ◽  
Turbulent Flows ◽  
Dissipation Rate ◽  
Eddy Viscosity ◽  
Normal Component ◽  
Transport Equations ◽  
Length Scale ◽  
Wall Region ◽  
Wide Range

This paper describes a velocity and length scale approach to low-Reynolds-number k–ε modeling, which formulates the eddy viscosity on the normal component of turbulence and a length scale. The normal component of turbulence is modeled based on the dissipation and distance from the wall and is bounded by the isotropic condition. The model accounts for the anisotropy of the dissipation and the reduced length of mixing in the near wall region. The kinetic energy and dissipation rate were computed from the k and ε transport equations of Durbin (1993). The model was tested for a wide range of turbulent flows and proved to be superior to other k–ε based models.

Turbulent kinetic energy production and flow structures in flows past smooth and rough walls

2019 ◽  
Vol 866 ◽  
pp. 897-928 ◽  
Author(s):  
P. Orlandi
Keyword(s):  
Reynolds Number ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Turbulent Flows ◽  
Energy Production ◽  
Compressive Strain ◽  
Turnover Time ◽  
Flow Structures ◽  
Wall Region ◽  
Rate Of Dissipation

Data available in the literature from direct numerical simulations of two-dimensional turbulent channels by Lee & Moser (J. Fluid Mech., vol. 774, 2015, pp. 395–415), Bernardini et al. (J. Fluid Mech., 742, 2014, pp. 171–191), Yamamoto & Tsuji (Phys. Rev. Fluids, vol. 3, 2018, 012062) and Orlandi et al. (J. Fluid Mech., 770, 2015, pp. 424–441) in a large range of Reynolds number have been used to find that $S^{\ast }$ the ratio between the eddy turnover time ($q^{2}/\unicode[STIX]{x1D716}$, with $q^{2}$ being twice the turbulent kinetic energy and $\unicode[STIX]{x1D716}$ the isotropic rate of dissipation) and the time scale of the mean deformation ($1/S$), scales very well with the Reynolds number in the wall region. The good scaling is due to the eddy turnover time, although the turbulent kinetic energy and the rate of isotropic dissipation show a Reynolds dependence near the wall; $S^{\ast }$, as well as $-\langle Q\rangle =\langle s_{ij}s_{ji}\rangle -\langle \unicode[STIX]{x1D714}_{i}\unicode[STIX]{x1D714}_{i}/2\rangle$ are linked to the flow structures, and also the latter quantity presents a good scaling near the wall. It has been found that the maximum of turbulent kinetic energy production $P_{k}$ occurs in the layer with $-\langle Q\rangle \approx 0$, that is, where the unstable sheet-like structures roll-up to become rods. The decomposition of $P_{k}$ in the contribution of elongational and compressive strain demonstrates that the two contributions present a good scaling. However, the good scaling holds when the wall and the outer structures are separated. The same statistics have been evaluated by direct simulations of turbulent flows in the presence of different types of corrugations on both walls. The flow physics in the layer near the plane of the crests is strongly linked to the shape of the surface and it has been demonstrated that the $u_{2}$ (normal to the wall) fluctuations are responsible for the modification of the flow structures, for the increase of the resistance and of the turbulent kinetic energy production.

Calculation of High-Lift Cascades in Low Pressure Turbine Conditions Using a Three-Equation Model

2010 ◽  
Vol 133 (3) ◽  
Author(s):  
Roberto Pacciani ◽  
Michele Marconcini ◽  
Atabak Fadai-Ghotbi ◽  
Sylvain Lardeau ◽  
Michael A. Leschziner
Keyword(s):  
Reynolds Number ◽  
Kinetic Energy ◽  
Eddy Viscosity ◽  
Low Reynolds Number ◽  
Low Pressure ◽  
Equation Model ◽  
Bypass Transition ◽  
High Lift ◽  
Wide Range ◽  
Low Reynolds

A three-equation model has been applied to the prediction of separation-induced transition in high-lift low-Reynolds-number cascade flows. Classical turbulence models fail to predict accurately laminar separation and turbulent reattachment, and usually overpredict the separation length, the main reason for this being the slow rise of the turbulent kinetic energy in the early stage of the separation process. The proposed approach is based on solving an additional transport equation for the so-called laminar kinetic energy, which allows the increase in the nonturbulent fluctuations in the pretransitional and transitional region to be taken into account. The model is derived from that of Lardeau et al. (2004, “Modelling Bypass Transition With Low-Reynolds-Number Non-Linear Eddy-Viscosity Closure,” Flow, Turbul. Combust., 73, pp. 49–76), which was originally formulated to predict bypass transition for attached flows, subject to a wide range of freestream turbulence intensity. A new production term is proposed, based on the mean shear and a laminar eddy-viscosity concept. After a validation of the model for a flat-plate boundary layer, subjected to an adverse pressure gradient, the T106 and T2 cascades, recently tested at the von Kármán Institute, are selected as test cases to assess the ability of the model to predict the flow around high-lift cascades in conditions representative of those in low-pressure turbines. Good agreement with experimental data, in terms of blade-load distributions, separation onset, reattachment locations, and losses, is found over a wide range of Reynolds-number values.

Calculation of Developing Turbulent Flows in a Rotating Pipe

1991 ◽  
Vol 113 (1) ◽  
pp. 34-41 ◽  
Author(s):  
G. J. Yoo ◽  
R. M. C. So ◽  
B. C. Hwang
Keyword(s):  
Turbulent Flows ◽  
Reynolds Stress ◽  
Circumferential Strain ◽  
Three Dimensional ◽  
Wall Region ◽  
Boundary Layer Flows ◽  
Viscous Effects ◽  
Wide Range ◽  
Turbulence Closures ◽  
Rotating Boundary

Internal rotating boundary-layer flows are strongly influenced by large circumferential strain and the turbulence field is anisotropic. This is especially true in the entry region of a rotating pipe where the flow is three dimensional, the centrifugal force due to fluid rotation is less important, and the circumferential strain created by surface rotation has a significant effect on the turbulence field near the wall. Consequently, viscous effects cannot be neglected in the near-wall region. Several low-Reynolds-number turbulence closures are proposed for the calculation of developing rotating pipe flows. Some are two-equation closures with and without algebraic stress correction, while others are full Reynolds-stress closures. It is found that two-equation closures with and without algebraic stress correction are totally inadequate for this three-dimensional flow, while Reynolds-stress closures give results that are in good agreement with measurements over a wide range of rotation numbers.

scholarly journals Dissipation rate of turbulent kinetic energy in stably stratified sheared flows

2018 ◽  
Author(s):  
Sergej Zilitinkevich ◽  
Oleg Druzhinin ◽  
Andrey Glazunov ◽  
Evgeny Kadantsev ◽  
Evgeny Mortikov ◽  
...  
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Turbulent Flows ◽  
Atmospheric Chemistry ◽  
Dissipation Rate ◽  
Stable Stratification ◽  
Turbulence Closure ◽  
Atmospheric Measurements ◽  
Precise Knowledge ◽  
Budget Equation

Abstract. Over the years, the problem of dissipation rate of turbulent kinetic energy (TKE) in stable stratification remained unclear because of the practical impossibility to directly measure the process of dissipation that takes place at the smallest scales of turbulent motions. Poor representation of dissipation causes intolerable uncertainties in turbulence-closure theory and, thus, in modelling stably stratified turbulent flows. We obtain theoretical solution to this problem for the whole range of stratifications from neutral to limiting stable; and validate it via (i) direct numerical simulation (DNS) immediately detecting the dissipation rate and (ii) indirect estimates of dissipation rate retrieved via the TKE-budget equation from atmospheric measurements of other components of the TKE-budget. The proposed formulation of dissipation rate will be of use in any turbulence-closure models employing the TKE budget equation and in problems requiring precise knowledge of the high-frequency part of turbulence spectra in atmospheric chemistry, aerosol science and microphysics of clouds.

Shape optimization of a split-and-recombine micromixer by the local energy dissipation rate

2020 ◽  
Vol 234 (3) ◽  
pp. 243-251
Author(s):  
Eshaq Ebnereza ◽  
Kamran Hassani ◽  
Mahmoud Seraj ◽  
Katayoun Gohari Moghaddam
Keyword(s):  
Reynolds Number ◽  
Energy Dissipation ◽  
Objective Function ◽  
Dissipation Rate ◽  
Computation Time ◽  
Energy Dissipation Rate ◽  
Local Energy ◽  
Number Range ◽  
Design Variables ◽  
Wide Range

A passive split-and-recombine micromixer was developed based on the concept of lamellar structure and advection mixing type for a serpentine structure. The flow patterns and mixing performance were analyzed using numerical simulation in Reynolds number range of 10≤ Reynolds ≤170. Two design variables, defining the shape of the split-and-recombine branch, were optimized by the local energy dissipation rate as the objective function. The reduction of computation time and the absence of numerical diffusion were the advantages of using the energy dissipation rate as the objective function. At each Reynolds number, 64 sample data was generated on the design space uniformly. Then a model was used based on the Radial basis neural network for the prediction of the objective function. The optimum values of the design variables within the constraint range were found on the response surface. The optimization study was performed at five Reynolds numbers of 10, 50, 90, 130, 170 and the mixing index was improved 0.156, 0.298, 0.417, 0.506, and 0.57, respectively. The effect of design variables on the objective function and the concentration pattern was presented and analyzed. Finally, the mixing characteristic of the split-and-recombine micromixer was studied in a wide range of Reynolds number and the flow was categorized to stratify and show the vortex regime based on the Reynolds number. The optimized split-and-recombine micromixer could be integrated by any system depending on the desired velocity and Reynolds number.

Improved Form of the k-ε Model for Wall Turbulent Shear Flows

1987 ◽  
Vol 109 (2) ◽  
pp. 156-160 ◽  
Author(s):  
Y. Nagano ◽  
M. Hishida
Keyword(s):  
Reynolds Number ◽  
Turbulent Flows ◽  
Plate Boundary ◽  
Wall Turbulence ◽  
Turbulent Shear ◽  
Committee Report ◽  
Low Reynolds Number Flows ◽  
Diffuser Flow ◽  
Wide Range ◽  
Predicted Values

An improved k-ε turbulence model for predicting wall turbulence is presented. The model was developed in conjunction with an accurate calculation of near-wall and low-Reynolds-number flows to meet the requirements of the Evaluation Committee report of the 1980–1981 Stanford Conference on Complex Turbulent Flows. The proposed model was tested by application to turbulent pipe and channel flows, a flat plate boundary layer, a relaminarizing flow, and a diffuser flow. In all cases, the predicted values of turbulent quantities agreed almost completely with measurements, which many previously proposed models failed to predict correctly, over a wide range of the Reynolds number.

scholarly journals Turbulent boundary layers over permeable walls: scaling and near-wall structure

2011 ◽  
Vol 687 ◽  
pp. 141-170 ◽  
Author(s):  
C. Manes ◽  
D. Poggi ◽  
L. Ridolfi
Keyword(s):  
Turbulent Flows ◽  
Laser Doppler Anemometry ◽  
Wall Turbulence ◽  
Shear Instability ◽  
Wall Structure ◽  
Wall Region ◽  
Mean Velocity ◽  
Wide Range ◽  
Permeable Walls ◽  
Near Wall

AbstractThis paper presents an experimental study devoted to investigating the effects of permeability on wall turbulence. Velocity measurements were performed by means of laser Doppler anemometry in open channel flows over walls characterized by a wide range of permeability. Previous studies proposed that the von Kármán coefficient associated with mean velocity profiles over permeable walls is significantly lower than the standard values reported for flows over smooth and rough walls. Furthermore, it was observed that turbulent flows over permeable walls do not fully respect the widely accepted paradigm of outer-layer similarity. Our data suggest that both anomalies can be explained as an effect of poor inner–outer scale separation if the depth of shear penetration within the permeable wall is considered as the representative length scale of the inner layer. We observed that with increasing permeability, the near-wall structure progressively evolves towards a more organized state until it reaches the condition of a perturbed mixing layer where the shear instability of the inflectional mean velocity profile dictates the scale of the dominant eddies. In our experiments such shear instability eddies were detected only over the wall with the highest permeability. In contrast attached eddies were present over all the other wall conditions. On the basis of these findings, we argue that the near-wall structure of turbulent flows over permeable walls is regulated by a competing mechanism between attached and shear instability eddies. We also argue that the ratio between the shear penetration depth and the boundary layer thickness quantifies the ratio between such eddy scales and, therefore, can be used as a diagnostic parameter to assess which eddy structure dominates the near-wall region for different wall permeability and flow conditions.

Modeling Reynolds-Number Effects in Wall-Bounded Turbulent Flows

1996 ◽  
Vol 118 (2) ◽  
pp. 260-267 ◽  
Author(s):  
R. M. C. So ◽  
H. Aksoy ◽  
S. P. Yuan ◽  
T. P. Sommer
Keyword(s):  
Reynolds Number ◽  
Turbulent Flows ◽  
Reynolds Stress ◽  
Strain Tensor ◽  
Reynolds Numbers ◽  
Turbulence Statistics ◽  
Wide Range ◽  
Peak Shear Stress ◽  
Reynolds Number Effects ◽  
Near Wall

Recent experimental and direct numerical simulation data of two-dimensional, isothermal wall-bounded incompressible turbulent flows indicate that Reynolds-number effects are not only present in the outer layer but are also quite noticeable in the inner layer. The effects are most apparent when the turbulence statistics are plotted in terms of inner variables. With recent advances made in Reynolds-stress and near-wall modeling, a near-wall Reynolds-stress closure based on a recently proposed quasi-linear model for the pressure strain tensor is used to analyse wall-bounded flows over a wide range of Reynolds numbers. The Reynolds number varies from a low of 180, based on the friction velocity and pipe radius/channel half-width, to 15406, based on momentum thickness and free stream velocity. In all the flow cases examined, the model replicates the turbulence statistics, including the Reynolds-number effects observed in the inner and outer layers, quite well. Furthermore, the model reproduces the correlation proposed for the location of the peak shear stress and an appropriately defined Reynolds number, and the variations of the near-wall asymptotes with Reynolds numbers. It is conjectured that the ability of the model to replicate the asymptotic behavior of the near-wall flow is most responsible for the correct prediction of the Reynolds-number effects.

Assessment of Simple RANS Turbulence Models for Stall Delay Applications at Low Reynolds Number

2017 ◽  
Vol 863 ◽  
pp. 260-265
Author(s):  
M. Arif Mohamed ◽  
Y. Wu ◽  
Martin Skote
Keyword(s):  
Reynolds Number ◽  
Wind Tunnel ◽  
Kinetic Energy ◽  
Dissipation Rate ◽  
Radial Flow ◽  
Turbulence Models ◽  
Energy Dissipation Rate ◽  
Rotating Blade ◽  
Rans Turbulence Models ◽  
Delay Phenomenon

This paper assesses the performance of three two-equation turbulence models viz. the SST k-ω, the RNG and realizable k-εfor the simulations of a rotating blade in a wind tunnel experiment where k, ε and ω are turbulent kinetic energy, dissipation rate and specific dissipation respectively. The experiments showed the stall-delay phenomenon at the inboard of the rotating blade at a Reynolds number of 4800. This trend of suction peaks was captured by all three turbulence models albeit not matching the experimental coefficient of pressure accurately. All three models also showed radial flow at the inboard which is consistent with the experiments while the SST predicted the least k at low wall values.

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