Comparative analysis of turbulence models for calculating a near-wall boundary layer

The integral relations, the algebraic model, and the family of differential turbulence models widely used in theoretical and practical boundary layers studies are considered. The differential turbulence models are analyzed for fully developed incompressible-fluid flow in three regions: the viscous sublayer, the logarithmic layer, and the flow core. Numerical results are compared with analytical and experimental dependences. The numerical results for the boundary layer in a liquid rocket engine (LRE) nozzle, where compressibility, the temperature factor, and flow acceleration are significant, are presented. Recommendations on the applicability of the turbulence models considered are given. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 44–58, January–February, 1998. The work received financial support from the Russian Foundation for Fundamental Research (project No.96-01-00260).     

Investigation of intermittency measurement methods for transitional boundary layer flows

Three turbulent intermittency methods, namely the , TERA (turbulent energy recognition algorithm), and M-TERA (modified turbulent energy recognition algorithm) methods, for identifying the intermittent flow characteristics associated with boundary layer transition from laminar to turbulent were considered and compared. The data used were obtained from hot-wire measurements in transitional boundary layer flows on a concave surface with a 2-m radius of curvature and on a flat plate. Comparisons show that the and TERA methods are more sensitive to the choice of threshold constants than the M-TERA method. In terms of the intermittency distribution across the boundary layer, the values obtained by the and TERA methods are unrealistically high in the near-wall region, while those obtained by the M-TERA method are more realistic. In the outer boundary layer region and outside the boundary layer, the and M-TERA methods give reasonable intermittency values, whereas the TERA method produces unrealistically high values in the region outside the boundary layer. In addition, the M-TERA method provides a sharper definition of theend of transition.     

Near-wall model for boundary layer turbulence

The evolution of an intermittently created isolated three-dimensional turbulent eddy near a wall is followed in space and time on the assumption that its structure evolves on three separate time scales, a shear interaction one, a viscous one, and a nonlinear one. The large-time limit of the solution for the shear interaction stage shows many of the observed features of the near-wall turbulence structure such as the formation of shear layers, of streaks, and of streamwise vortices. It also provides initial conditions for the viscous and nonlinear stages showing viscous decay of convected structures and the possibility of a singularity in the nonlinear development. The eddy model is also used to construct a new model for the turbulent shear stress showing strong similarity to Prandtl's mixing-length model.     

Structure of turbulence in a boundary layer

The transient vortical model of turbulent flow introduced in a preceding article [1] on the basis of an idea originally proposed in [2] is used in order to derive an analytical expression for the longitudinal component of the liquid velocity due to primary turbulence (i.e., ejections) alone. Stepped functions are employed instead of continuous functions in solving the problem. This article is concerned with the problem of finding the field of pulsation velocities on the basis of the earlier model.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 8–13, January–February, 1975.     

The effect of Reynolds number on boundary layer turbulence

A new facility for studying high Reynolds number incompressible turbulent boundary layer flows has been constructed. It consists of a moderately sized wind tunnel, completely enclosed by a pressure vessel, which can raise the ambient air pressure in and around the wind tunnel to 8 atmospheres. This results in a Reynolds number range of about 20:1, while maintaining incompressible flow. Results are presented for the zero pressure gradient flat plate boundary layer over a momentum thickness Reynolds number range 1500–15?000. Scaling issues for high Reynolds number non-equilibrium boundary layers are discussed, with data comparing the three-dimensional turbulent boundary layer flow over a swept bump at Reynolds numbers of 3800 and 8600. It is found that successful prediction of these types of flows must include length scales which do not scale on Reynolds number, but are inherent to the geometry of the flow.     

Finite element implementation of two‐equation and algebraic stress turbulence models for steady incompressible flows

The main purpose of this paper is to describe a finite element formulation for solving the equations for k and ε of the classical k–ε turbulence model, or any other two‐equation model. The finite element discretization is based on the SUPG method together with a discontinuity capturing technique to deal with sharp internal and boundary layers. The iterative strategy consists of several nested loops, the outermost being the linearization of the Navier–Stokes equations. The basic k–ε model is used for the implementation of an algebraic stress model that is able to account for the effects of rotation. Some numerical examples are presented in order to show the performance of the proposed scheme for simulating directly steady flows, without the need of reaching the steady state through a transient evolution. Copyright © 1999 John Wiley & Sons, Ltd.     

Step-induced turbulence in a high-velocity boundary layer

The fact that the stability of the boundary layer on smooth plane bodies (in particular, on a flat plate) at Mach numbers M>5 is very high and laminar-turbulent transition takes place at points fairly distant from the leading edge of the model has given rise to the question: how difficult is it to induce transition (in particular, by means of a step) in a laminar boundary layer at M>5. The present article is devoted to the solution of this problem.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 176–179, January–February, 1989.The authors are grateful to Yu. A. Safronov for assistance with the flow visualization.     

Spanwise propagation of turbulence in a boundary layer

The process of spanwise propagation of turbulence in a laminar boundary layer on a plate is numerically investigated. Three well-known turbulence models are considered. It is shown that the calculated values of the "turbulent wedge" angle are several times less than that observed experimentally. The reason for the deviation of the calculated and experimental data is analyzed. Moscow, Seattle. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 77–84, May–June, 1998. The work was financially supported by the Russian Foundation for Basic Research (project No. 95-01-00251a) and the Moscow Boeing Science-Technology Center.     

The turbulence structure of drag-reduced boundary layer flow

The structure of turbulence in a drag-reduced flat-plate boundary layer flow has been studied with particle image velocimetry (PIV). Drag reduction was achieved by injection of a concentrated polymer solution through a spanwise slot along the test wall at a location upstream of the PIV measurement station. Planes of velocity were measured parallel to the wall (x–z plane), for a total of 30 planes across the thickness of the boundary layer. For increasing drag reduction, we found a significant modification of the near-wall structure of turbulence with a coarsening of the low-speed velocity streaks and a reduction in the number and strength of near-wall vortical structures.     

自然对流边界层中湍流的发生

自然对流边界层中从层流到湍流的转捩经历了浮力振型、无摩擦振型和黏性振型的三重流动不稳定性相继产生的前转捩过程,以及近壁迅速出现强湍流源,随之平缓地向自模拟的湍流边界层过渡的热转捩过程.浮力振型在修正Grashof数G>40时开始失稳并成为主要振型,在振幅分布中3种振型的临界层位置处出现3个峰值;在G>100时浮力振型消失,无摩擦振型失稳并成为主要振型,振幅分布中在近壁区还出现黏性振型的峰值;在G>170时无摩擦振型经非线性演化在外层形成较弱的湍流,但内层黏性应力仍远高于湍流应力,振幅分布中仅有与黏性振型相应的峰值,在频谱中黏性振型的基频、第一、第二、第三阶亚谐频随G的增加相继出现,此时黏性不稳定波的高频成分已转化为湍流,但低频成分仍按线性规律增长,直至湍流惯性子区开始形成;至G>800时黏性振型消失,并在G=850附近时近壁区出现强湍流源,湍流应力、湍能产生项和近壁湍流热流率剧增.在热转捩后期,湍流应力和湍能产生项明显下降,流动在内外层趋于平衡.     

On the boundary conditions for differential turbulence models

The distinctive features of the formulation of boundary conditions at the outer edge of a boundary layer and near a wall are considered. Approximate wall functions of turbulence parameters are proposed for three turbulence models.     

Two-phase turbulence models for simulating dense gas-particle flows

The two-fluid model is widely adopted in simulations of dense gas-particle flows in engineering facili- ties. Present two-phase turbulence models for two-fluid modeling are isotropic. However, turbulence in actual gas-particle flows is not isotropic. Moreover, in these models the two-phase velocity correlation is closed using dimensional analysis, leading to discrepancies between the numerical results, theoretical analysis and experiments. To rectify this problem, some two-phase turbulence models were proposed by the authors and are applied to simulate dense gas-particle flows in downers, risers, and horizontal channels; Experimental results validate the simulation results. Among these models the USM-O and the two-scale USM models are shown to give a better account of both anisotropic particle turbulence and particle-particle collision using the transport equation model for the two-phase velocity correlation.     

Effect of turbulence on propagation of a coherent beam in the boundary layer and mixing layer

A semi-empirical model is developed to study distortions of the phase function of a coherent beam, which are induced by turbulent fluctuations of flow parameters. Large eddy simulations of the boundary-layer and mixing-layer flows and also of related aero-optical effects are performed. Results of numerical calculations are compared with results of physical experiments and with data obtained by solving the Reynolds-averaged Navier—Stokes equations.     

Longitudinal vortex pair imbedded in a turbulent boundary layer: Comparative performances of several turbulence models

Four turbulence models, namely, the basic and nonlinear stress-transport models and the basic and anisotropick-ε models, have been tested in the case of interaction between a longitudinal vortex pair and a flat-plate boundary layer. The results of their predictions were compared with Mehta and Bradshaw's measurements. In this paper, part of the results involving those of the nonlinear stress-transport model and anisotropick-ε model are presented and discussed. The project supported by the National Natural Science Foundation of China under Contract No. 19132012     

Influence of jet turbulence on flow in the boundary layer near the wall

Results are presented of an experimental investigation of the interaction of a subsonic axisymmetric jet, within the initial section, and a flat plate mounted parallel to the jet axis. Relations are obtained for the mean and fluctuating velocities in the wall boundary layer, and the friction stress on the plate is also given.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 77–82, November–December, 1972.     

Leading-edge receptivity of boundary layer to three-dimensional free-stream turbulence

The laminar-turbulent transition has always been a hot topic of fluid mechanics. Receptivity is the initial stage and plays a crucial role in the entire transition process. The previous studies of receptivity focus on external disturbances such as sound waves and vortices in the free stream, whereas those on the leading-edge receptivity to the three-dimensional free-stream turbulence(FST), which is more general in the nature,are rarely reported. In consideration of this, this work is devoted to investigating the receptivity process of three-dimensional Tollmien-Schlichting(T-S) wave packets excited by the three-dimensional FST in a flat-plate boundary layer numerically. The relations between the leading-edge receptivity and the turbulence intensity are established, and the influence of the FST directions on the propagation directions and group velocities of the excited T-S wave packets is studied. Moreover, the leading-edge receptivity to the anisotropic FST is also studied. This parametric investigation can contribute to the prediction of laminar-turbulent transition.     

Interaction of a laminar boundary layer with external turbulence

Transition in the boundary layer on a flat plate in a turbulent flow is investigated experimentally and theoretically. It is established that over a broad range of flow conditions (variation of the intensity and scale of the external turbulence, the angle of attack, the shape of the leading edge, etc.) transition takes place without the formation of Tollmien-Schlichting waves, and its initial stages, including the amplification of disturbances, are described by the linearized unsteady three-dimensional boundary layer equations without a pressure gradient.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 55–65, September–October, 1989.The authors are grateful to N. F. Polyakov, V. S. Kosorygin, and O. S. Ryzhov for useful discussions and to N. N. Bychkov and O. N. Konstantinovskii for assisting with the experiments.