C. A. Langer

Structure-based turbulence modeling for wall-bounded flows

Abstract The performance of Reynolds stress transport (RST) models in non-equilibrium flows is limited by the lack of information about two dynamically important effects: the role of energy-containing turbulence structure (dimensionality) and the breaking of reflectional symmetry due to strong mean or frame rotation. Both effects are fundamentally non-local in nature and this explains why it has been difficult to include them in one-point closures like RST models. Information about the energy-containing structure is necessary if turbulence models are to reflect differences in dynamic behavior associated with structures of different dimensionality (nearly isotropic turbulence vs turbulence with strongly organized two-dimensional structures). Information about the breaking of reflectional symmetry is important whenever mean rotation is dynamically important (flow through axisymmetric diffuser or nozzle with swirl, flow through turbomachinery, etc.). Here we present a new one-point model that incorporates the needed structure information, and show a selection of results for homogeneous and inhomogeneous flows.

Structure and scales in turbulence modeling

The enstrophy of the large-scale energy-containing turbulence is proposed as the second turbulence scale for use, in conjunction with the turbulence energy, in two-scale one-point engineering turbulence models. Its transport equation is developed in general and modeled for homogeneous turbulence in terms of the two scales and our new one-point structure tensors. The model produces the correct behavior of the scales for both two- and three-dimensional turbulence. Constants in the high Reynolds number model are evaluated only by reference to asymptotic analysis for decaying turbulence in stationary and rotating frames, and this model is then shown to provide an excellent prediction of homogeneous turbulent shear flow when used with the structure tensors for that flow. The low Reynolds number constant in the model is evaluated using the asymptotic decay rate for isotropic turbulence at zero Reynolds number, and numerical simulations of decay for intermediate Reynolds numbers are used to establish one remaining constant, the value of which does not affect high Reynolds number predictions.

ASBM-BSL: An Easy Access to the Structure Based Model Technology

The Algebraic Structure Based Model (ASBM) offers unique features to represent the Reynolds stress tensor from the underlying turbulent structures. It is usually coupled with a non standard length scale equation. A way of coupling it with the more popular BSL ω equation is proposed here. Only a minor modification of the ω equation is required to obtain a realistic turbulent kinetic energy profile and thus achieve fair predictions.

Rapid shear of initially anisotropic turbulence in a rotating frame

In the present study, we investigate, using inviscid rapid distortion theory, the evolution of sheared turbulence in a rotating frame as a function of the rotation rate (including stable, transitional, and unstable regimes), and examine the sensitivity of the results for various nonisotropic initial conditions. Analytical solutions are derived for the evolution of the stresses and the structure dimensionality tensor components for three one-dimensional and three two-dimensional initializations. From these solutions, we calculate the asymptotic states of the turbulence, which are compared to the exact numerical solution of the three-dimensional initially isotropic case. From the investigation it is shown that the qualitative characteristics of the isotropic solution in the unstable regime are represented quite accurately when the initial turbulence is dependent at least on the axis of the rotation of the frame. For the transitional and the stable regimes, though, the initial dependence of the turbulence on...

Diagnostic Properties of Structure Tensors in Turbulent Flows

The behavior of turbulence structure tensors based on Large-Eddy Simulations (LES) in a wide range of turbulent channel flows is presented. The structure tensors provide significant physical information on the character of turbulent flows, since they provide an accurate description of the energy containing turbulence structure. LES is ideally suited for their computation since these tensors are quantities representing the larger – energy containing – turbulent scales. The basic aims of the present work are to (i) demonstrate the diagnostic properties of structure tensors in turbulent flows, (ii) report turbulence quantities which would be useful to develop and assess structure-based turbulence models, (iii) demonstrate the capability of LES to accurately compute structure tensors in a variety of flows. Structure tensors have been computed in the presence of complicated physical phenomena like frame rotation or MHD effects. Comparisons with available DNS solutions, confirm the capability of LES to accurately predict such quantities with fundamental significance in turbulent flows.

Rapidly sheared homogeneous stratified turbulence in a rotating frame

Rapid distortion theory is applied to stratified homogeneous turbulence that is sheared in a rotating frame. Insight into the stabilizing and destabilizing effects of the combined stratification and frame rotation is gained by considering initial fields that are two-dimensional, with the axis of independence aligned with the flow direction. For these conditions, we derive solutions for the Fourier components of the flow variables, and for one-point statistics in physical space. The analytical results are in qualitative agreement with the exact numerical solution for initially isotropic homogeneous turbulence, and they could be a reference point for the development of turbulence models.

An analytical solution for rapidly distorted turbulent shear flow in a rotating frame

In this study we apply rapid distortion theory to the case of nonstratified homogeneous turbulence that is sheared in a frame that counter-rotates at a rate that matches in magnitude the rotation associated with the mean shear. In the inviscid case, analytical solutions are worked out for the evolution of the components of the Reynolds stresses and the structure dimensionality tensor, and these are shown to equal each other. The results are compared to direct numerical simulations data with which they proved to be in good agreement, especially in terms of the Reynolds shear stress and of the dimensionless tensor components. Finally, the development of the structure of a passive scalar field with a constant mean gradient is investigated, and remarkable analogies are shown to exist between this case and the case of shear in a fixed frame.

Nonuniversality of sublayer streaks in turbulent flow

Coefficients of series expansions of turbulent velocity fluctuations in the viscous wall region are used to generate an arbitrary but quantitative measure of the time‐average strength of the near‐wall quasi‐streamwise vortices, which appear as ‘‘streaks’’ in flow visualization. Existing databases from direct numerical simulations of wall bounded turbulence are used to compute some estimates. The results show that the strength of the streaks is Reynolds‐number‐dependent, even in simple flows, as well as flow‐dependent, contrary to traditional law‐of‐the‐wall arguments.

On the linear stability of turbulent plane strain flow in a rotating frame

We apply inviscid rapid distortion theory to the limiting hyperbolic case of turbulent plain strain flow in a rotating frame and investigate the dependence of the evolution of the turbulent kinetic energy on the frame rotation rate. We derive an analytical two-dimensional solution that, unlike previous oversimplified pressureless analyses, allows for an accurate approximation of the three-dimensional initially isotropic problem. From the analytical solutions, we determine the correct stability criterion for the evolution of the turbulent kinetic energy in this flow. Also, we calculate the asymptotic states of the turbulence, in terms of the normalized Reynolds stresses and structure dimensionality tensor components, which coincide with the exact three-dimensional numerical results.

Application of a New Algebraic Structure-Based Model to Rotating Turbulent Flows

ABSTRACT A primary goal of RANS based modeling is to determine the Reynolds stress tensor in order to close the turbulence problem at the mean velocity level. However, the Reynolds stresses alone do not characterize adequately the turbulence, especially in presence of rotation; the structure of the turbulence is also important. Here hypothetical turbulent eddies are used to bring awareness of turbulence structure into the turbulence model. Averaging over an ensemble of eddies produces a set of one-point statistics, representative of the eddy field, and a set of equations of state relating the Reynolds stresses to these statistics. An algebraic model for the eddy statistics is constructed in terms of the local mean deformation and two turbulence scales; the turbulent kinetic energy and the large-scale enstrophy (LSE). Contrary to existing ad-hoc definitions of the second scale equation, the LSE equation has a fundamental background; it is derived from the large-scale vorticity equation. The algebraic model is further sensitized to the presence of walls, ensuring proper asymptotic behavior. The complete model has been found to produce very good results for a set of channel flows in fixed frames and in spanwise-rotating frames of reference.