The necessity of correcting differential semiempirical turbulence models to calculate circulating fl ows of an incompressible viscous fl uid is discussed. Approaches to taking account of the infl uence of the curvature of streamlines on turbulence characteristics arereviewed. Experience gained in modeling numerically twodimensional separated fl ows in a square and a cylindrical cavity on the wall of a plane-parallel channel is analyzed; an additional semiempirical constant in the expression for vortex viscosity of a modifi ed shear-stress-transfer model is substantiated.Introduction. The signifi cant difference in results of numerical modeling of circulating fl ow in the circular cavity on the wall of a rotating channel [1] from the corresponding data obtained with the Doppler laser velocimeter on the experimental setup in Southampton [2] increasingly draws attention to the idea of correction of semiempirical turbulence models used to close Reynolds-averaged Navier-Stokes equations [3] with account of the infl uence of the streamline curvature.In this connection, the present work seeks to analyze experience gained in modeling numerically separated fl ows with turbulence models, in particular, with the frequently used semiempirical turbulence model, i.e., the Mentershear-stresstransfer k-ω model (MSST) in the versions of the year 1993 (MSST1993) and of the year 2003 (MSST2003) [4, 5]. Also, the present work seeks to substantiate the semiempirical constant in the expression for vortex viscosity in the MSST 2003 version [5] using, as examples, the calculations of experimental analogs of separated fl ows of an incompressible viscous medium in a square and a cylindrical cavity on the wall of a plane-parallel channel.Historical Review of Investigations into the Correction of Semiempirical Turbulence Models with Account of the Infl uence of the Streamline Curvature. It is common knowledge that semiempirical models of closure of Reynoldsaveraged Navier-Stokes equations [3, 6] have been constructed for calculation of wall fl ows. In any event, calibration of the constants for them is based on measurements that have been performed on special test beds for model fl ows [7]. Turbulence models are not universal. Thus, the turbulent Prandtl number for the boundary layer is equal to 0.9, and for the jet fl ow, to 0.6 [8]. At the same time, in intricate wall fl ow, one cannot, in practice, single out jet fl ows and, in modeling them using package technologies, takes the turbulent Prandtl number as constant and equal to 0.9 [9]. Also, it should be noted that algebraic turbulent models for calculation of fl ows in curvilinear channels include curvature corrections in expressions for a turbulence scale [3]. Rotation corrections seem even more signifi cant as far as their infl uence, primarily, on velocity profi les is concerned [10].

No abstract

Vortex dynamics and heat transfer in a viscous incompressible fluid flow past shallow and deep trenches on a plane wall are studied methodically within the framework of the multiblock approach to solution of steadystate Reynolds equations closed by the Menter and Spalart-Allmaras turbulence models and the energy equation.A detached flow of viscous fluid in the vicinity of a trench on a plane wall has drawn the attention of hydromechanicians [1]. Trenches as well as protrusions on a washed wall are of interest to them first of all from the point of view of the contribution of the mentioned elements of roughness to the total resistance of bodies of complex geometry. Simultaneously, thermal physicists consider trenches or grooves as elements of enhancement of heat-transfer processes in near-wall flows [2,3].In many respects, interest in investigation of vortex dynamics and heat transfer in flow past a trench on a plane wall is also predetermined by the fact that lunes are a three-dimensional analog of trenches. As is known (see, e.g., [4]), lune technologies are a very promising tool of heat and mass transfer enhancement with very low hydraulic losses for pumping of a heat-transfer agent. Therefore, in order to analyze the governing mechanism of self-generation of vortex structures in concavities, thorough measurements of the parameters of flow past spherical lunes and two-dimensional trenches with a generatrix that copies the shape of the lune in the middle cross section were conducted at the N. E ′ . Bauman Moscow Higher Technical School at the beginning of the 1990s [5]. We should also mention a series of experimental works performed at the Institute of Thermophysics of the Siberian Branch of the Russian Academy of Sciences [6] with an emphasis on the effect of a three-dimensional character of flow in trapezoidal short trenches.The genesis of numerical simulations of an incompressible viscous fluid flow past trenches, as well as of the whole computational fluid dynamics (CFD), is closely related to the progress made in computer technology, the development of methods of solution of the Navier-Stokes equations, and improvement of semiempirical models of turbulence. It should be emphasized that the problem under consideration ranks among the classical problems, and its numerical solution for a laminar flow is quite satisfactory and has long been known. Of course, problems still remain, which are related, first of all, to interpretation of unsteady flows past bodies. However, the calculations of turbulent detached flows always presented the greatest difficulties. In the 1970-80s, a two-parameter dissipative model of turbulence or the Launder-Spalding k-ε model was widely used to close the Reynolds equations [7]. In the standard highReynolds variant it was supplemented by near-wall functions, since it was inapplicable in the immediate vicinity of the wall. Within this approach, detached flows with a fixed detachment point in the neighborhood of a recess [8] and technological joint [9] were calculated; in the latter ca...

No abstract

No abstract