Non-linear Eddy-viscosity Models Research Articles

K-1908 非線型乱流モデルによるエンジン定常吸気流の計算(S24-1 ガス流動,噴霧と混合気形成)(S24 燃料噴霧,ガス流動,混合気形成過程)

This paper presents discussions on predicting turbulent flows in simple model of engine intake port-valve-cylinder with three port-curvature ratios. The low-Reynolds-number linear k-ε, cubic nonlinear k-e and k-ε-A_2 turbulence models are applied to the flow field computation. The results suggest that the nonlinear eddy viscosity modelling of turbulence is very successful for predicting mass flow rate and in-cylinder velocity distributions.

Unsteady separated flows over manoeuvring lifting surfaces

Numerical simulations of dynamic–stall phenomena have been performed using an implicit unfactored Navier–Stokes solver and various turbulence closures, including linear and nonlinear low– Re eddy–viscosity models. The accuracy of the models has been assessed against a range of experimental data for ramping and oscillating aerofoils at subsonic and transonic conditions. The computations indicate that the nonlinear eddy–viscosity models better predict the shedding of the dynamic–stall vortex and the unsteady aerodynamic loads.

Turbulence modelling for separated flows with anisotropy-resolving closures

This paper discusses aspects of modelling turbulent flows, featuring curvature, impingement and separation, with statistical second–moment closure and nonlinear eddy–viscosity models. Both modelling approaches are first reviewed, with particular emphasis placed on the illumination of some of the mechanisms by which the alternative model forms capture the interactions between particular types of strain and the turbulence field. As part of the review, recent modelling developments, directed especially towards the prediction of physically complex flows, are presented and discussed. Finally, the predictive performance of selected models is illustrated by way of computational solutions and related comparisons with experimental data for five flows, three two dimensional and two three dimensional, all involving separation from continuous surfaces.

Numerical simulation of transonic buffet flows using various turbulence closures

The paper presents a numerical investigation of buffet flows using various turbulence models, including linear and non-linear low-Re eddy-viscosity models (EVM). The accuracy of the models is assessed against experimental data for transonic flows around the NACA-0012 aerofoil. The study shows that non-linear two-equation models in conjunction with functional cμ coefficient for the calculation of the eddy-viscosity (henceforth labelled NL-cμ), provide satisfactory results for transonic buffet flows. The computations also reveal that the Spalart–Allmaras one-equation model provides comparable results to the NL-cμ models, while larger inaccuracies are introduced by linear and non-linear models based on constant cμ coefficient. Moreover, the buffet onset boundaries are similarly predicted by the one-equation and NL-cμ models. The study has been performed using a second-order time accurate implicit-unfactored method which solves in a coupled fashion the Navier–Stokes and turbulence transport equations. The spatial discretisation of the equations is obtained by a Riemann solver in combination with a third-order upwind scheme.

CFD for aerodynamic turbulent flows: progress and problems

AbstractCurrent weaknesses in modelling the turbulent stresses arguably provide the main obstacle to relying on CFD predictions of complex aerodynamic flows. The paper reviews some recent strategies for obtaining more reliable models with especial focus on cubic non-linear eddy viscosity models and stress-transport schemes which comply with the two-component limit. Applications are shown for a broad range of test flows. Finally, important remaining weaknesses are considered.

Accuracy and robustness of nonlinear eddy viscosity models

Abstract Two nonlinear eddy viscosity models (EVMs) proposed by Shih et al. (Shih, T.H., Zhu, J., Lumley, J.L., 1995. Comput. Methods Appl. Mech. Engrg. 125, 287–302) and Craft et al. (Craft, T.J., Launder, B.E., Suga, K., 1996. Int. J. Heat Fluid Flow 17, 108–115) and one algebraic Reynolds stress model of Gatski and Speziale (Gatski, T.B., Speziale, C.G., 1993. J. Fluid Mech. 254, 59–78) are compared to the standard k–ϵ model and the Reynolds stress model of Launder et al. (Launder, B.E., Reece, G.J., Rodi, W., 1975. J. Fluid Mech. 68, 537–566) with respect to model accuracy and computational robustness. Three flow situations are considered to analyze the models' capabilities in flows with streamline curvature: A backward facing step flow (Driver, D.M., Seegmiller, H.L., 1985. AIAA J. 23, 163–171), a plane U-duct flow (Monson, D.J., Seegmiller, H.L., 1992. NASA Technical Memorandum, 103931) and a curved mixing layer (Castro, I.P., Bradshaw, P., 1976. J. Fluid Mech. 73, 265–304). Results indicate that an improved prediction of the flow fields especially for important flow features like recirculation zones can be obtained with the tested models compared to calculations with the standard k–ϵ model. The decrease of computational robustness compared to the calculations with the standard k–ϵ model is rather moderate once a quasi-linear form of the models is employed.

Modelling shock-affected near-wall flows with anisotropy-resolving turbulence closures

Abstract This paper reviews some recent research aiming to assess the performance of advanced forms of second-moment closure and non-linear eddy-viscosity models for compressible flows, with particular emphasis placed on strong shock-boundary-layer interaction involving separation. This topic is of particular relevance to high-speed aerospace and turbomachinery aerodynamics. Relevant closure forms and their merits, relative to simpler linear eddy-viscosity approximations, are reviewed first, mainly in qualitative terms. The performance of some particular models is then examined by reference to solutions for a range of 2D and 3D compressible flows.

Nonlinear eddy viscosity modelling for turbulence and heat transfer near wall and shear-free boundaries

Abstract New turbulence and turbulent heat flux models are proposed for capturing flow and thermal fields bounded by walls or free surfaces. The models are constructed using locally definable quantities only, without any recourse to topographical parameters. For the flow field, the proposed model is a cubic nonlinear k–e–A three equation eddy viscosity model. It employs dependence on Lumley's stress flatness parameter A, by solving its modelled transport equation as the third variable. Since A vanishes at two-component turbulence boundaries, introducing its dependency enables a turbulence model to capture the structure of turbulence near shear-free surfaces as well as wall boundaries. To close the modelled A equation, an up-to-date second-moment closure is applied. For the thermal field, an explicit algebraic second-moment closure for turbulent heat flux is proposed. The new aspect of this heat flux model is the use of nonlinear Reynolds stress terms in the eddy diffusivity tensor. This model complies with the linearity and independence principles for passive scalar. The proposed models are tested in fully developed plane channel, open channel and plane Couette–Poiseuille flows at several fluid Prandtl numbers. The results show the very encouraging performance of the present proposals in capturing anisotropic turbulence and thermal fields near both wall and shear-free boundaries in the range of 0.025⩽Pr⩽95.

Advanced Turbulence Modelling of Separated Flow in a Diffuser

The paper describes an investigation into the predictive performance of linear and non-linear eddy-viscosity models and differential stress-transport closures for separated flow in a nominally two-dimensional, asymmetric diffuser. The test case forms part of a broader collaborative exercise between academic and industrial partners. It is demonstrated that advanced turbulence models using strain-dependent coefficients and anisotropy-resolving closure offer tangible advantages in predictive capability, although the quality of their performance can vary significantly, depending on the details of closure approximations adopted. Certain features of the flow defy resolution by any of the closures investigated. In particular, no model resolves correctly the flow near the diffuser's inclined wall immediately downstream of the inlet corner, which may reflect the presence of a “flapping” motion associated with a highly-localised process of unsteady separation and reattachment.

Investigation of nonlinear eddy-viscosity turbulence models in shock/boundary-layer interaction

Investigation of nonlinear eddy-viscosity turbulence models in shock/boundary-layer interaction

1121 非線形渦粘性モデルを適用したカプラン水車吸出し管の 3 次元ナビエ・ストークス解析

1121 非線形渦粘性モデルを適用したカプラン水車吸出し管の 3 次元ナビエ・ストークス解析

Progress in the use of non-linear two-equation models in the computation of convective heat-transfer in impinging and separated flows

The paper considers the application of the Craft et al. [6]non-linear eddy-viscosity model to separating and impinging flows. The original formulation was found to lead to numerical instabilities when applied to flow separating from a sharp corner. An alternative formulation for the variation of the turbulent viscosity parameterc μ with strain rate is proposed which, together with a proposed improvement in the implementation of the non-linear model, removes this weakness. It does, however, lead to worse predictions in an impinging jet, and a further modification in the expression for c μ is proposed, which both retains the stability enhancements and improves the prediction of the stagnating flow. The Yap [24] algebraic length-scale correction term, included in the original model, is replaced with a differential form, developed from that proposed by Iacovides and Raisee [10]. This removes the need to prescribe the wall-distance, and is shown to lead to superior heat-transfer predictions in both an abrupt pipe flow and the axisymmetric impinging jet. One predictive weakness still, however, remains. The proposed model, in common with other near-wall models tested for the abrupt pipe expansion, returns a stronger dependence of Nusselt number on the Reynolds number than that indicated by the experimental data.

Nonlinear eddy-viscosity turbulence model and its application

Nonlinear eddy-viscosity turbulence model and its application

Computational prediction of flow around highly loaded compressor-cascade blades with non-linear eddy-viscosity models

Abstract A computational study is presented which examines the predictive performance of two variants of a cubic low-Re eddy-viscosity model when applied to the flow around two highly loaded compressor-cascade blades. Particular challenges are posed by the transitional nature of the flow and the presence of laminar leading-edge separation in off-design conditions. Comparisons are presented for local as well as integral flow parameters, including turbulence intensity and losses. The study demonstrates that the cubic model is able to predict, in accord with experimental data and in contrast to a linear base-line model, the influential leading-edge separation preceding transition, due to the suppression of turbulence-energy generation in the impinging zone ahead of the leading edge. This attribute and a greater sensitivity to streamline curvature enable the model to give, in some flow conditions, a more realistic description of the development of the boundary layer after transition and a better prediction of the loss at off-design incidence. However, the model also exhibits predictive weaknesses, among them an inappropriate delay in reattachment and transition to fully developed turbulence, resulting in insufficient sensitivity to adverse pressure gradient once transition has occurred.

Non-linear eddy-viscosity modelling of transitional boundary layers pertinent to turbomachine aerodynamics

Abstract The predictive performance of three low-Reynolds-number turbulence models, one based on the linear (Boussinesq) stress-strain relationship and two adopting cubic forms, is examined by reference to transitional flat-plate boundary layers subjected to streamwise pressure gradient and moderate free-stream turbulence, the latter causing bypass transition. One of the cubic models involves the solution of two transport equations, while the other involves three equations, one of which relates to the second invariant of turbulence anisotropy. The investigation demonstrates that, for the conditions examined, the non-linear models return a more credible representation of transition than the linear variant, although none of the models may be said to be entirely satisfactory. Thus, while non-linear modelling shows promise and offers inherent advantages through the use of a more general stress-strain linkage and elaborate calibration, further refinement is needed in the present cubic variants for transitional flows.

B-62 非線形渦粘性モデルの室内気流解析への適用に関する研究 : その3 非線型渦粘性モデルによる3次元等温場の検討

B-62 非線形渦粘性モデルの室内気流解析への適用に関する研究 : その3 非線型渦粘性モデルによる3次元等温場の検討

Projection 2 Goes Turbulent - and Fully Implicit

We describe and demonstrate both our newest projection method (fully implicit) for the incompressible Navier-Stokes equations via the finite element method and our newest turbulence model - a somewhat sophisticated nonlinear (cubic) eddy viscosity model that does not employ wall functions or normal distances to walls - the combination providing a method and a model that is each applicable in arbitrary geometry. We demonstrate both via a flow simulation past an automobile-like body at a Reynolds number of 4.3 million.

Prediction of Solid/Free-Surface Juncture Boundary Layer and Wake of a Surface-Piercing Flat Plate at Low Froude Number

Results are reported of a RANS simulation investigation on the prediction of turbulence-driven secondary flows at the free-surface juncture of a surface-piercing flat plate at low Froude numbers. The turbulence model combines a nonlinear eddy viscosity model and a modified version of a free-surface correction formula. The different elements of the model are combined and the model constants calibrated based on the premises that the anisotropy of the normal stresses is mainly responsible for the dynamics of the flow in the juncture region, and an accurate modeling of the normal-stress anisotropy as obtained from the data is a primary requirement for the successful prediction of the overall flow field. The predicted mean velocity, streamwise vorticity, turbulent kinetic energy, and other quantities at the juncture are then compared with data and analyzed with regard to findings of related studies. In agreement with the experimental observations, the simulated flow at large depths was essentially two-dimensional and displayed all the major features of zero pressure gradient boundary layer and wake, including the anisotropy of normal stresses in the near-wall region. In the boundary-layer free-surface juncture region, the major features of interest that were predicted include the generation of secondary flows and the thickening of the boundary layer near the free surface. In the wake free-surface juncture region, even though secondary flows and a thickening of the wake width near the free surface were predicted in accordance with the experimental observations, the overall comparison with the experiment was not as satisfactory as the boundary-layer juncture. This is partly due to the lack of a strong coherent flow structure in the wake juncture and the presence of possible wave effects in the wake in the experiments. An examination of the terms in the Reynolds-averaged streamwise vorticity equation reconfirmed the importance of the anisotropy of the normal Reynolds stresses in the production of streamwise vorticity. The free-surface wave elevations were negligible for the present model problem for the nonzero Froude number studied. Finally, concluding remarks are presented with regards to extensions for practical geometries such as surface ship flows.

Modelling shock/boundary-layer interaction with nonlinear eddy-viscosity closures

An investigation is reported of several nonlinear eddy-viscosity models, both from a fundamental point of view and as a basis for resolving turbulence transport in transonic flows, with particular emphasis placed on shock-induced separation. The models are first analyzed by reference to a homogeneous shear flow and a plane channel flow, after which they are applied to two transonic flows with strong shock-wave/boundary-layer interaction including separation. The computational results demonstrate that nonlinear models with coefficients appropriately sensitized to strain and vorticity invariants, yield results which are superior to a “standard” linear low-Re k–e model often claimed to give the best predictive performance among low-Re k–e models which do not contain ad-hoc corrections. While this superior performance is partly associated with the functional dependence of the linear coefficient on strain and vorticity, this cannot be separated from the role of at least some nonlinear terms which interact with that coefficient, especially in complex strain fields featuring large streamline curvature and irrotational straining.

Predicting noninertial effects with linear and nonlinear eddy-viscosity, and algebraic stress models

Three types of turbulence models which account for rotational effects in noninertial frames of reference are evaluated for the case of incompressible, fully developed rotating turbulent channel flow. The different types of models are a Coroiolis-modified eddy-viscosity model, a realizable nonlinear eddy-viscosity model, and an algebraic stress model which accounts for dissipation rate anisotropies. A direct numerical simulation of a rotating channel flow is used for the validation of the turbulence models. This simulation differs from previous studies in that significantly higher rotation numbers are investigated. Flows at these higher rotation numbers are characterized by a relaminarization on the cyclonic or suction side of the channel, and a linear velocity profile on the anticyclonic or pressure side of the channel. The predictive performance of the three types of models are examined in detail, and formulation deficiencies are identified which cause poor predictive performance for some of the models. Criteria are identified which allow for accurate prediction of such flows by algebraic stress models and their corresponding Reynolds stress formulations.