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– model often claimed to give the best predictive performance among low-Re k– 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.     

Separation-induced boundary layer transition: Modeling with a non-linear eddy-viscosity model coupled with the laminar kinetic energy equation

We present an effort to model the separation-induced transition on a flat plate with a semi-circular leading edge, using a cubic non-linear eddy-viscosity model combined with the laminar kinetic energy. A non-linear model, compared to a linear one, has the advantage to resolve the anisotropic behavior of the Reynolds-stresses in the near-wall region and it provides a more accurate expression for the generation of turbulence in the transport equation of the turbulence kinetic energy. Although in its original formulation the model is not able to accurately predict the separation-induced transition, the inclusion of the laminar kinetic energy increases its accuracy. The adoption of the laminar kinetic energy by the non-linear model is presented in detail, together with some additional modifications required for the adaption of the laminar kinetic energy into the basic concepts of the non-linear eddy-viscosity model. The computational results using the proposed combined model are shown together with the ones obtained using an isotropic linear eddy-viscosity model, which adopts also the laminar kinetic energy concept and in comparison with the existing experimental data.     

A new physics-based γ–kL transition model

A new physics-based γ–k_L transition model is proposed for the first time in this paper where γ is the intermittency and k_L is the laminar kinetic energy. Unlike the correlation-based γ–Re_θ model, the transport equations of the γ–k_L model are constructed based on basic physical mechanisms and their interactions. The relationship among γ, k_L and k enhances the coupling mechanism between transition and turbulence. The derivation of the γ-equation, following the definition of γ in terms of k_L and k, is presented here in detail. The shear-sheltering effect is also taken into account to damp or promote the influence of bypass transition mechanism. To account for the transitional effects on the mean flow, the γ–k_L model is readily coupled to the shear stress transport k–ω turbulence model via the production and destruction terms of the k-equation without any modification to the turbulence model. The ERCOFTAC test cases of T3AM, T3A and T3B are employed to validate this γ–k_L model. It is found that the γ–k_L model can predict the natural and bypass transitions better than the k_L model and as accurately as the γ–Re_θ model.     

Separation-Induced Transition to Turbulence: Second-Moment Closure Modelling

The paper presents some results of application of a low-Re-number second-moment closure (SMC) to modelling the laminar-to-turbulent transition induced by a separation bubble. The same model, tested earlier in a number of low and high-Re-number flows, was found also to reproduce reasonably well several cases of bypass transition, as well as cyclic sequence of laminarization and turbulence revival in oscillating flows at transitional Re numbers, without any artificial transition triggering. The focus of the paper is on separation-induced transition in flow over a flat plate with a circular leading edge, and on a plane surface on which a laminar separation bubble was generated by imposed suction on the wall-opposite boundary. The results show acceptable agreement with available experimental data, large-eddy and direct numerical simulations (LES, DNS). The importance of applying higher-order discretization schemes for reproducing both the bubble and the transition is also discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Transition of Energy to a Nonlinear Localized Mode in a Highly Asymmetric System of Two Oscillators

Redistribution of energy in a highly asymmetric system consisting ofcoupled linear and highly nonlinear damped oscillators isinvestigated. Special attention is paid to the excitation of a nonlinearnormal mode while the energy is initially stored in other modes of thesystem. The transition proceeds via the mechanism of subharmonicresonance which is possible because of the strong nonlinearity of thesystem. The conditions of the energy transition to NNM being effectiveare revealed and guidelines to design such a systems are formulatedin detail.     

Bifurcations of Nonlinear Normal Modes of Linear Oscillator with Strongly Nonlinear Damped Attachment

Linear oscillator coupled to damped strongly nonlinear attachment with small mass is considered as a model design for nonlinear energy sink (NES). Damped nonlinear normal modes of the system are considered for the case of 1:1 resonance by combining the invariant manifold approach and multiple scales expansion. Special asymptotical structure of the model allows a clear distinction between three time scales. These time scales correspond to fast vibrations, evolution of the system toward the nonlinear normal mode and time evolution of the invariant manifold, respectively. Time evolution of the invariant manifold may be accompanied by bifurcations, depending on the exact potential of the nonlinear spring and value of the damping coefficient. Passage of the invariant manifold through bifurcations may bring about destruction of the resonance regime and essential gain in the energy dissipation rate.     

Use of Higher-Order Frequency Response Functions for Identification of Nonlinear Adsorption Kinetics: Single Mechanisms under Isothermal Conditions

The concept of higher-order frequency response functions(FRFs), which is based on Volterra series expansion of nonlinearfunctions, is used for analysis of kinetics of nonlinear adsorptionsystems. Four different kinetic mechanisms: Langmuir kinetics, filmresistance control, micropore diffusion control and pore-surfacediffusion control were analyzed and the results were compared. It wasshown that, contrary to the linear frequency response characteristicfunctions, the higher-order FRFs corresponding to different mechanismsdiffer in shape. This result offers great potential for theidentification of the adsorption-diffusion mechanism governing theprocess. It is shown that the second order FRFs give sufficientinformation for distinguishing different mechanisms.     

Crossing Rate Analysis with a Non-Gaussian Closure Method for Nonlinear Stochastic Systems

The mean upcrossing rate of the stationary responses of nonlinear stochastic system excited by white noise is analyzed based on the assumption that the probability density function (PDF) of the responses is a linear superposition of basic functions. The Gaussian PDFs are used as the basic functions of which the coefficients are the reciprocal of the number of the basic functions. The Gaussian closure method is a special case of the proposed method. Based upon the approximate PDF, the explicit expression for the mean upcrossing rate (MCR) is given. Numerical results show that the approximate MCRs approach the exact ones in the tails of the MCR curves as the number of the basic functions increases.     

Nonlinear Energy Transfer over the Wave Spectrum in Water Covered by Solid Ice

On the basis of the hydrodynamic equations for nonlinear elastic-gravity waves beneath a solid ice cover and their Hamiltonian representation, a three-wave kinetic equation for the time evolution of the wave spectrum is formulated. The properties of the kernel of the kinetic integral describing the nonlinear interactions between wave triplets are investigated. An algorithm for numerically calculating the kinetic integral is developed. The rate of nonlinear energy transfer over the wave spectrum is estimated quantitatively and its most important characteristics are found.     

Modelling of Unsteady Transition in Low-Pressure Turbine Blade Flows with Two Dynamic Intermittency Equations

A transition model for describing wake-induced transition is presented based on the SST turbulence model by Menter and two dynamic equations for intermittency: one for near-wall intermittency and one for free-stream intermittency. In the Navier-Stokes equations, the total intermittency factor, which is the sum of the two, multiplies the turbulent viscosity computed by the turbulence model. The quality of the transition model is illustrated on the T106A test cascade for two Reynolds numbers, using experimental results by Stieger and Hodson for transition mainly due to kinematic wake impact on a separation bubble. The quality of the model is also revealed on the T106D test cascade using experimental results from Hilgenfeld, Stadtmuller and Fottner for wake turbulence induced transition. The test cases differ in pitch to chord ratio, Reynolds number and inlet free-stream turbulence intensity, causing different transition mechanisms. The unsteady results are presented in space-time diagrams of shape factor and wall shear stress on the suction side. The results show the capability of the model to capture the physics of unsteady transition in separated state. Inevitable shortcomings are revealed as well.     

Energy Pumping with Various Nonlinear Structures: Numerical Evidences

Numerical investigations are carried out on a linear structure, weakly coupled to a small nonlinear attachment. The essential nonlinearity of the attachment enables it to resonate with any of the linearized modes of the structure leading to energy pumping, i.e. passive, one-way, irreversible transfer of energy from the structure to the attachment. Different nonlinear structures (piecewise linear system, chaotic system) and efficiency of energy pumping are studied in each case in order to be able to apply it to civil engineering. As a specific application, attenuation of vibrations of a building is studied with two building models. In particular, the case of stochastic excitations is analyzed to examine if it is possible to process energy pumping when a seism occurs and an indicator of efficiency has been introduced.     

Energy Method for Computing Periodic Solutions of Strongly Nonlinear Autonomous Systems with Multi-Degree-of-Freedom

In this paper with the use of conservation of average energy, a newmethod for computing the periodic solutions of strongly nonlinearautonomous systems with multi-degree-of-freedom is suggested. Thismethod cannot only decide the existence, but also give the approximateexpressions of the periodic solutions.     

The Existence Stability and Approximate Expressions of Periodic Solutions of Strongly Nonlinear Nonautonomous Systems with Multi-Degree-of-Freedom

Based upon the conservation of average energy a theorem about the periodic solutions of strongly nonlinear nonautomous systems with multi-degree-of freedom is proved. This theorem can not only decide the existence and stability of the periodic solutions, but at the same time can also give their first-order and second-order approximate expressions.     

逆压梯度边界层未分离情况下的湍流模式适用性研究Turbulence model applicability for boundary layer flow with adverse pressure gradient in attached case

边界层逆压梯度作用下的流动是许多工程中的一个基础问题,由于逆压梯度作用,流动形态复杂,使得数值模拟有很大的难度。基于雷诺平均纳维‐斯托克斯RANS（Reynolds Averaged Navier‐Stokes）方程对二维平板逆压梯度边界层作数值计算研究,选取6种代表性的湍流模式,得到局部摩擦系数的数值解,与实验值比较,发现k‐ω模式具有很好的精度。基于该湍流模式,给出了湍动能分布,该结果有助于认识逆压梯度边界层流动的复杂特征。