scholarly journals Development of a Nonlinear k-ε Model Incorporating Strain and Rotation Parameters for Prediction of Complex Turbulent Flows

2015 ◽  
Vol 2015 ◽  
pp. 1-15 ◽  
Author(s):  
Md. Shahjahan Ali ◽  
Takashi Hosoda ◽  
Ichiro Kimura
Keyword(s):  
Turbulent Flows ◽  
Eddy Viscosity ◽  
Model Performance ◽  
Quadratic Term ◽  
Vortex Center ◽  
Compound Channel ◽  
Turbulent Structures ◽  
Fundamental Properties ◽  
Rotation Parameters ◽  
Basic Equations

The standard k-ε model has the deficiency of predicting swirling and vortical flows due to its isotropic assumption of eddy viscosity. In this study, a second-order nonlinear k-ε model is developed incorporating some new functions for the model coefficients to explore the models applicability to complex turbulent flows. Considering the realizability principle, the coefficient of eddy viscosity (cμ) is derived as a function of strain and rotation parameters. The coefficients of nonlinear quadratic term are estimated considering the anisotropy of turbulence in a simple shear layer. Analytical solutions for the fundamental properties of swirl jet are derived based on the nonlinear k-ε model, and the values of model constants are determined by tuning their values for the best-fitted comparison with the experiments. The model performance is examined for two test cases: (i) for an ideal vortex (Stuart vortex), the basic equations are solved numerically to predict the turbulent structures at the vortex center and the (ii) unsteady 3D simulation is carried out to calculate the flow field of a compound channel. It is observed that the proposed nonlinear k-ε model can successfully predict the turbulent structures at vortex center, while the standard k-ε model fails. The model is found to be capable of accounting the effect of transverse momentum transfer in the compound channel through generating the horizontal vortices at the interface.

INCREASE OF HEAT TRANSFER AND NEGATIVE EDDY VISCOSITY IN TURBULENT FLOWS INFLUENCED BY A MAGNETIC FIELD

1990 ◽  
Author(s):  
C. Henoch ◽  
Martin Hoffert ◽  
A. Baron ◽  
D. Klaiman ◽  
Semion Sukoriansky ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Turbulent Flows ◽  
Eddy Viscosity

scholarly journals Optimal nonlinear eddy viscosity in Galerkin models of turbulent flows

2015 ◽  
Vol 766 ◽  
pp. 337-367 ◽  
Author(s):  
Bartosz Protas ◽  
Bernd R. Noack ◽  
Jan Östh
Keyword(s):  
Turbulent Flows ◽  
High Speed ◽  
Eddy Viscosity ◽  
Broad Class ◽  
Constitutive Relations ◽  
Body Height ◽  
Mixing Layer ◽  
The Body ◽  
Stream Velocity ◽  
Initial Vorticity

AbstractWe propose a variational approach to the identification of an optimal nonlinear eddy viscosity as a subscale turbulence representation for proper orthogonal decomposition (POD) models. The ansatz for the eddy viscosity is given in terms of an arbitrary function of the resolved fluctuation energy. This function is found as a minimizer of a cost functional measuring the difference between the target data coming from a resolved direct or large-eddy simulation of the flow and its reconstruction based on the POD model. The optimization is performed with a data-assimilation approach generalizing the 4D-VAR method. POD models with optimal eddy viscosities are presented for a 2D incompressible mixing layer at $\mathit{Re}=500$ (based on the initial vorticity thickness and the velocity of the high-speed stream) and a 3D Ahmed body wake at $\mathit{Re}=300\,000$ (based on the body height and the free-stream velocity). The variational optimization formulation elucidates a number of interesting physical insights concerning the eddy-viscosity ansatz used. The 20-dimensional model of the mixing-layer reveals a negative eddy-viscosity regime at low fluctuation levels which improves the transient times towards the attractor. The 100-dimensional wake model yields more accurate energy distributions as compared to the nonlinear modal eddy-viscosity benchmark proposed recently by Östh et al. (J. Fluid Mech., vol. 747, 2014, pp. 518–544). Our methodology can be applied to construct quite arbitrary closure relations and, more generally, constitutive relations optimizing statistical properties of a broad class of reduced-order models.

Characterization of Geometrical and Temporal Properties of Large-scale Motions in Turbulent Flows

2021 ◽  
Author(s):  
Christina Tsai ◽  
Kuang-Ting Wu
Keyword(s):  
Turbulent Flow ◽  
Turbulent Flows ◽  
Coherent Structures ◽  
Large Scale ◽  
Streamwise Velocity ◽  
Turbulent Structures ◽  
Temporal Properties ◽  
Turbulent Statistics ◽  
Spatial Locations

<p>It is demonstrated that turbulent boundary layers are populated by a hierarchy of recurrent structures, normally referred to as the coherent structures. Thus, it is desirable to gain a better understanding of the spatial-temporal characteristics of coherent structures and their impact on fluid particles. Furthermore, the ejection and sweep events play an important role in turbulent statistics. Therefore, this study focuses on the characterizations of flow particles under the influence of the above-mentioned two structures.</p><div><span>With regard to the geometry of turbulent structures, </span><span>Meinhart & Adrian (1995) </span>first highlighted the existence of large and irregularly shaped regions of uniform streamwise momentum zone (hereafter referred to as a uniform momentum zone, or UMZs), regions of relatively similar streamwise velocity with coherence in the streamwise and wall-normal directions.  <span>Subsequently, </span><span>de Silva et al. (2017) </span><span>provided a detection criterion that had previously been utilized to locate the uniform momentum zones (UMZ) and demonstrated the application of this criterion to estimate the spatial locations of the edges that demarcates UMZs.</span></div><div> </div><div>In this study, detection of the existence of UMZs is a pre-process of identifying the coherent structures. After the edges of UMZs are determined, the identification procedure of ejection and sweep events from turbulent flow DNS data should be defined. As such, an integrated criterion of distinguishing ejection and sweep events is proposed. Based on the integrated criterion, the statistical characterizations of coherent structures from available turbulent flow data such as event durations, event maximum heights, and wall-normal and streamwise lengths can be presented.</div>

A Three-Equation Eddy-Viscosity Model for Reynolds-Averaged Navier–Stokes Simulations of Transitional Flow

2008 ◽  
Vol 130 (12) ◽  
Author(s):  
D. Keith Walters ◽  
Davor Cokljat
Keyword(s):  
Boundary Layer ◽  
Turbulent Flows ◽  
Eddy Viscosity ◽  
Flow Behavior ◽  
Applied Pressure ◽  
Plate Boundary ◽  
Low Frequency ◽  
Transitional Flow ◽  
Test Cases ◽  
Eddy Viscosity Model

An eddy-viscosity turbulence model employing three additional transport equations is presented and applied to a number of transitional flow test cases. The model is based on the k-ω framework and represents a substantial refinement to a transition-sensitive model that has been previously documented in the open literature. The third transport equation is included to predict the magnitude of low-frequency velocity fluctuations in the pretransitional boundary layer that have been identified as the precursors to transition. The closure of model terms is based on a phenomenological (i.e., physics-based) rather than a purely empirical approach and the rationale for the forms of these terms is discussed. The model has been implemented into a commercial computational fluid dynamics code and applied to a number of relevant test cases, including flat plate boundary layers with and without applied pressure gradients, as well as a variety of airfoil test cases with different geometries, Reynolds numbers, freestream turbulence conditions, and angles of attack. The test cases demonstrate the ability of the model to successfully reproduce transitional flow behavior with a reasonable degree of accuracy, particularly in comparison with commonly used models that exhibit no capability of predicting laminar-to-turbulent boundary layer development. While it is impossible to resolve all of the complex features of transitional and turbulent flows with a relatively simple Reynolds-averaged modeling approach, the results shown here demonstrate that the new model can provide a useful and practical tool for engineers addressing the simulation and prediction of transitional flow behavior in fluid systems.

On Anisotropy of Turbulent Flows in Regions of “Negative Eddy Viscosity”

2007 ◽  
pp. 85-88 ◽  
Author(s):  
A. Liberzon ◽  
B. Lüthi ◽  
M. Guala ◽  
W. Kinzelbach ◽  
A. Tsinober
Keyword(s):  
Turbulent Flows ◽  
Eddy Viscosity

Structural Parameters and Prediction of Adverse Pressure Gradient Turbulent Flows: An Improved k-ε Model

1995 ◽  
Vol 117 (3) ◽  
pp. 424-432 ◽  
Author(s):  
G. Chukkapalli ◽  
O¨. F. Turan
Keyword(s):  
Pressure Gradient ◽  
Turbulent Flows ◽  
Reynolds Stress ◽  
Eddy Viscosity ◽  
Structural Parameters ◽  
Adverse Pressure Gradient ◽  
Reynolds Stress Model ◽  
Model Representation ◽  
Stress Model ◽  
Kinetic Diffusion

A modified k-ε model is proposed to predict complex, adverse pressure gradient, turbulent diffuser flows. The need for an eddy viscosity is eliminated by using three structural parameters. A fuller treatment of the rate of kinetic diffusion terms is incorporated with a Reynolds stress model representation. A thorough evaluation is given of the three structural parameters in three decreasing and one increasing adverse pressure gradient diffuser flows leading to a three-layer representation. The results indicate the need for better modeling of the ε-equation.

Drag Reduction in Synthetic Seawater by Flexible and Rigid Polymer Addition Into a Rotating Cylindrical Double Gap Device

2015 ◽  
Vol 138 (2) ◽  
Author(s):  
Rafhael M. Andrade ◽  
Anselmo S. Pereira ◽  
Edson J. Soares
Keyword(s):  
Drag Reduction ◽  
Turbulent Flows ◽  
Salt Concentration ◽  
Polymer Concentration ◽  
Transient Behavior ◽  
Turbulent Structures ◽  
Polymer Addition ◽  
Rigid Polymer ◽  
Potential Applications ◽  
Poly Ethylene

Flexible and rigid long chain polymers in very dilute solutions can significantly reduce the drag in turbulent flows. The polymers successively stretch and coil by interacting with the turbulent structures, which changes the turbulent flow and further imposes a transient behavior on the drag reduction (DR) as well as a subsequent mechanical polymer degradation. This time-dependent phenomenon is strongly affected by a number of parameters, which are analyzed here, such as the Reynolds number, polymer concentration, polymer molecular weight, and salt concentration. This last parameter can dramatically modify the polymeric structure. The investigation of the salt concentration's impact on the DR is mostly motivated by some potential applications of this technique to ocean transport and saline fluid flows. In the present paper, a cylindrical double gap rheometer device is used to study the effects of salt concentration on DR over time. The reduction of drag is induced by three polymers: poly (ethylene oxide) (PEO), polyacrylamide (PAM), and xanthan gum (XG). These polymers are dissolved in deionized water both in the presence of salt and in its absence. The DR is displayed from the very start of the test to the time when the DR achieves its final level of efficiency, following the mechanical degradations. The presence of salt in PEO and XG solutions reduces the maximum DR, DRmax, as well as the time to achieve it. In contrast, the DR does not significantly change over the time for PAM solutions upon the addition of salt.

The Effects of Upstream Wall Roughness on Separated and Reattached Flows Over a Forward-Facing Step

2020 ◽  
Author(s):  
Sedem Kumahor ◽  
Xingjun Fang ◽  
William Ediger ◽  
Mark F. Tachie
Keyword(s):  
Correlation Coefficient ◽  
Turbulent Flows ◽  
Eddy Viscosity ◽  
Leading Edge ◽  
Step Height ◽  
Stream Velocity ◽  
Reynolds Stresses ◽  
Third Order ◽  
The Mean ◽  
Forward Facing Step

Abstract Separating and reattaching turbulent flows induced by a forward-facing step submerged in thick oncoming turbulent boundary layers developed over smooth and rough walls were investigated using time-resolved particle image velocimetry. Both smooth and fully rough upstream bottom wall conditions were examined and the resultant oncoming boundary layer thickness were 4.3 and 6.7 times the step height, respectively. The Reynolds number based on the step height and free-stream velocity was 7800. The mean velocities, Reynolds stresses analyzed in both Cartesian and curvilinear coordinate systems, eddy viscosity, correlation coefficient and third order moments are discussed. The results indicate that, due to the enhanced turbulence intensity and shear rate in the fully rough case, distinct elevated regions of vertical and shear Reynolds stresses are consistent upstream of the leading edge of the step while the magnitude of the Reynolds stresses are consistently higher than observed in the smooth case. The correlation coefficient, eddy viscosity and third order moments also show distinct elevated regions upstream of the leading edge of the step in the fully rough case. Above the step, distinct elevated regions of the Reynolds stresses, eddy viscosity and correlation coefficient are observed in both cases with the peak values at a vertical location corresponding to the maximum elevation of the mean separating streamline.

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