Zonal Two Equation k-w Turbulence Models For Aerodynamic Flows

Free Turbulent Shear Flows, 1972

AIAA Journal, 1998

NOTES are short manuscripts describing new developments or important results of a preliminary nature. These Notes cannot exceed 6 manuscript pages and 3 gures; a page of text may be substituted for a gure and vice versa. After informal review by the editors, they may be published within a few months of the date of receipt. Style requirements are the same as for regular contributions (see inside back cover).

Journal of Aircraft, 1995

Four turbulence models are described and evaluated for transonic flows using the upwind code CFL3D and the central-difference code TL.NS3D. in particular, the effects of recent modijications to the half-equation model of Johnson-King are explored in detail. and diflerent versions of the model are compared. ?his model can obtain good results for both two-dimensional (2-0) and three-dimensional (3-DJ separatedflows. The one-equation models of Baldwin-Barrh and Spalarr-Allmaras perform well for separared aiifoiipows, but can predict the shock roo far fonvard at the outboard stations o f a separated wing. The equilibrium model of Baldwin-Lomax predicts the shock locarion roo far afl for both 2-D and 3-0 separared flows, as erpected. in general, all models perform well for attached or mildly separated flows.

Symmetry, 2021

The Reynolds stress equations for two-dimensional and axisymmetric turbulent shear flows are simplified by invoking local equilibrium and boundary layer approximations in the near-wall region. These equations are made determinate by appropriately modelling the pressure–velocity correlation and dissipation rate terms and solved analytically to give a relation between the turbulent shear stress τ/ρ and the kinetic energy of turbulence (k=q2/2). This is derived without external body force present. The result is identical to that proposed by Nevzgljadov in A Phenomenological Theory of Turbulence, who formulated it through phenomenological arguments based on atmospheric boundary layer measurements. The analytical approach is extended to treat turbulent flows with external body forces. A general relation τ/ρ=a11−AFRiFq2/2 is obtained for these flows, where FRiF is a function of the gradient Richardson number RiF, and a1 is found to depend on turbulence models and their assumed constants. ...

Canadian Journal of Civil Engineering, 2010

A total of seven versions of two-equation turbulence models (four versions of low Reynolds number k-3 model, one k-u model and two versions of k-3 / k-u blended models) are tested against the direct numerical simulation (DNS) data of a one-dimensional oscillatory boundary layer with flat crested free-stream velocity that results from a steep pressure gradient. A detailed comparison has been made for cross-stream velocity, turbulent kinetic energy (TKE), Reynolds stress, and ratio of Reynolds stress and turbulent kinetic energy. It is observed that the newer versions of k-3 model perform very well in predicting the velocity, turbulent kinetic energy, and Reynolds stress. The k-u model and blended models underestimate the peak value of turbulent kinetic energy that may be explained by the Reynolds stress to TKE ratio in the logarithmic zone. The maximum bottom shear stress is well predicted by the k-3 model proposed by Sana et al. and the original k-u model.

An improved version of the k-kL two-equation turbulence model which predicts both free and nearwalljlows with a single set of model coef3cients is presented. The model variants previously employed by Ngfor near-wallflows and by Rodiforfreeflows are combined by introducing a gradient-dissipation term into the kL equation. The revised model is tested by application to a number of plane and axisymmetric flows of boundary layer type. The computed results for both mean and turbulence quantities are in fairly good agreement with existing measurements.

7th AIAA Theoretical Fluid Mechanics Conference, 2014

Recently a new one-equation turbulence model was proposed by Rahman, Agarwal and Siikonen; the model is known as the Rahman-Agarwal-Siikonen (RAS) model. It is an isotropic model which accounts for the low-Reynolds number (LRN) effects in the wall proximity. In the model, the turbulent kinetic energy k and the dissipation rate are evaluated using the R (= k 2 /˜ ) transport equation together with the Bradshaw and other empirical relations. The proposed eddy-viscosity formulation preserves the realizability constraints -the physically necessary conditions in developing a turbulence model. An anisotropic destruction coefficient is used to obtain a faster decaying behavior of turbulence destruction in the outer region of the boundary/shear layer, thereby precluding the free-stream dependency. In this paper, several improvements to the original RAS model are made which include the introduction of damping functions in the wall region. The improved model is validated against the well-documented turbulent flow cases, yielding predictions in excellent agreement with the direct numerical simulation (DNS) and the experimental data. A comparative assessment of the improved RAS model with the Spalart-Allmaras one-equation model and the shear stress transport k-ω model is made for non-equilibrium flows.

A new approach to Reynolds averaged turbulence modeling is proposed which has a computational cost comparable to two equation models but a predictive capability approaching that of Reynolds stress transport models. This approach isolates the crucial information contained within the Reynolds stress tensor, and solves transport equations only for these \reduced" variables. In this work, DNS data is used to analyze the nature of these newly proposed turbulence quantities and the source terms which appear in their respective transport equations. The physical relevance of these quantities is discussed and some initial modeling results for turbulent channel ow are presented.

2009

‫ﺑﺎﻟﺴﺮﻳﺎن‬ ‫اﻟﺘﻨﺒﺆ‬ ‫ﻓﻲ‬ ‫واﻟﻤﺴﺘﺨﺪﻣﺔ‬ ‫اﻟﻤﺨﺘﻠﻔﺔ‬ ‫اﻟﺮﻳﺎﺿﻴﺔ‬ ‫اﻟﻨﻤﺎذج‬ ‫ﻣﻦ‬ ‫ﻋﺪد‬ ‫ﻷداء‬ ‫ﻣﺴﺘﻔﻴﻀﺔ‬ ‫ﺑﺤﺜﻴﺔ‬ ‫دراﺳﺔ‬ ‫ﺗﻤﺖ‬ ‫اﻟﺒﺤﺚ‬ ‫هﺬا‬ ‫ﻓﻲ‬ ‫اﻟﻤﻌﺎدﻟﺘﻴﻦ‬ ‫ذو‬ ‫اﻟﻤﻌﺮوف‬ ‫اﻟﺮﻳﺎﺿﻲ‬ ‫اﻟﻨﻤﻮذج‬ ‫ﻋﻠﻰ‬ ً ‫أﺳﺎﺳﺎ‬ ‫واﻟﻤﻌﺘﻤﺪة‬ ‫اﻻﺿﻄﺮاﺑﻲ‬ (k-ε) . ‫ﺗﺤﺪﻳﺪ‬ ‫اﻟﺪراﺳﺔ‬ ‫هﺬﻩ‬ ‫ﻓﻲ‬ ‫ﺗﻢ‬ ‫ﻋﻠﻰ‬ ‫واﻟﻤﻌﺘﻤﺪة‬ ‫اﻻﺿﻄﺮاﺑﻲ‬ ‫ﻟﻠﺴﺮﻳﺎن‬ ‫رﻳﺎﺿﻴﺔ‬ ‫ﻧﻤﺎذج‬ ‫ﺛﻼﺛﺔ‬ ‫اﻟﺮﻳﺎﺿﻲ‬ ‫اﻟﻨﻤﻮذج‬

ISH Journal of Hydraulic Engineering , 2018

Due to the importance of channel flow characteristics in the water conveyance, the study of it is a noteworthy problem for hydraulics experts and much attempts has been accomplished for the modeling of the flow characteristics. One significant problem in this respect is the secondary flow cells and their effect on flow specifications. Widespread experimental and analytical investigations have been accomplished on this phenomenon. However, researchers are trying to replace the expensive and time-consuming experimental approaches and ad hoc analytical models with numerical simulation procedures using computational fluid dynamics (CFD). Selection of the proper turbulence model is one of the most important problems for this type of the numerical modeling. In the present study, after evaluating several turbulence models including k-ε, shear stress transport (SST) and three versions of the Reynolds stress model (RSM) (i.e. LRR-IP, LRR-QI, and SSG models), for the numerical simulation of the secondary flow cells and their effects on trapezoidal channels flow, the more efficient model was selected. Available experimental data and theoretical model was used to validate the selected turbulence model. The results were validated in terms of the free water surface, depth-averaged velocity, and boundary shear stress. The results confirmed the performance and efficiency of SSG version of the Reynolds stress model for the numerical modeling of the secondary flow cells.

2023

Prediction of the sediment transport in streams requires an accurate estimation of bed shear stress (for bed load) and eddy viscosity (for suspended load). In general, shallow water models employ empirical relationships to estimate the bottom shear stress. However, with the advancement of computing systems, the utilization of advanced turbulence models is getting common. In this paper, a number of model versions are reviewed based on their predictive abilities against the well-known bottom boundary layer properties in open channels and computational economy. Qualitative and quantitative comparisons have been made to infer that the choice of model versions should be based on the field application. For example, the bottom shear stress is very well predicted by the k- model whereas the cross-stream velocity profile and turbulent kinetic energy are predicted more efficiently by k- model versions. This study may be useful for researchers and practicing engineers in selecting a suitable two-equation model for calculating various bottom boundary layer properties.

AIAA Journal, 2006

Three two-equation turbulence models developed specifically to improve prediction of jet flowfields are investigated. These models are the Tam-Ganesan k-ε formulation, a standard k-ε model employing a modification for heated jets referred to as the PAB temperature correction, and a standard k-ε model employing variable diffusion for the k and ε equations. Two standard two-equation models are also investigated for comparison with the modified formulations. The standard models are the Chien k-ε and Menter Shear Stress Transport (SST) formulations. All of the models are investigated for a reference nozzle producing heated and unheated jets at a low acoustic Mach number of 0.5 to avoid complications of large compressibility effects. The primary deficiency of the standard models was the delayed initial jet mixing rate relative to experimental data. All of the modified turbulence model formulations provided improved mean flow predictions relative to the standard models. The improved mixing rate enabled by the Tam-Ganesan model and the variable diffusion correction was the result of increased turbulent diffusion enabled by both models. While the Tam-Ganesan model and PAB temperature correction improved predictions of mean axial velocities for the heated jet, the calculated turbulent kinetic energy fields produced by these models did not improve upon those from the standard models.

Turbulence models are developed by supplementing the renormalization group (RNG) approach of Yakhot & Orszag with scale expansions for the Reynolds stress and production of dissipation terms. Th, additional expansion parameter,, (---K/ i) is the ratio of the turbulent to mean strain time scale. While 'low-order expansions appear to provide an adequate description for the Reynolds stress, no finite truncation of the expansion for the production of dissipation term in powers of ;r sufficesterms of all orders must be retained. Based on these ideas, a new two-equation model and Reynolds stress transport model are developed for turbulent shear flows. The models are tested for homogeneous shear flow and flow over a backward facing step. Comparisons between the model predictions and experimental data are excellent. Aceos2:,a Y-r •~~~~ r aIIon e "' Iji-'ty CcdO8

Journal of Fluid Mechanics, 1972

The paper provides a model of turbulence which effects closure through approximated transport equations for the Reynolds stress tensor $\overline{u_iu_j}$ and for the turbulence energy-dissipation rate ε. In its most general form the model thus entails the solution of seven transport equations for turbulence quantities but contains only six constants to be determined by experiment. It is demonstrated that the proposed approximation to the pressure-rate-of-strain correlations leads to satisfactory predictions of the component stress levels in plane homogeneous turbulence, including the non-equality of the lateral and transverse normal-stress components.For boundary-layer flows a simpler version of the model is derived wherein transport equations are solved only for the shear stress $-\overline{u_1u_2}$ the turbulence energy κ and ε. This model has been incorporated in the numerical solution procedure of Patankar & Spalding (1970) and applied to the prediction of a number of boundary-...