Numerical solution of 2D and 3D backward facing step flows

The work deals with numerical modelling of flow through 2-dimensional (2D) and 3-dimensional (3D) backward facing step. In laminar case, we apply several higher order upwind and central discretizations and compare numerical results with measurements. The turbulent regime is considered in 2D as well as in 3D and influence of secondary flow is observed. Different modifications of low-Re two equation turbulence models and an explicit algebraic Reynolds stress model (EARSM) are considered. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Investigation of secondary flow instability on an infinite yawed cylinder with 15 per cent. Thick joukowski profile as section

This paper contains a theoretical investigation of the secondary flow instability in the incompressible boundary layer on an infinite yawed cylinder with chordwise section as Joukowski profile of 15 per cent. thickness at zero incidence and with homogeneous suction, the suction mass flow coefficient being equal to 0·2085. Values of the instability criterion are obtained at different points of the wing section and for various angles of sweepback. It is found that the values of the criterion increase with the increasing sweepback whether the pressure gradient is favourable or adverse. The effect of adverse pressure gradient on the variation of the criterion is more pronounced than that of a favourable pressure gradient. At some points in adverse pressure gradients, there are two values of the criterion for a given sweepback. It is also found that the flow is intermittently laminar and turbulent for low values of the chordwise free stream Reynolds number and consists of an irregular sequence of laminar and turbulent regions.     

Eddy cascade of instabilities and transition to turbulence

Numerical simulation is used to investigate a shear layer influenced by a constant external forcing in the theory of turbulence (Kolmogorov’s problem). The dynamics of flows developing in the case of various initial streamwise velocity profiles are studied. The transition from a two-dimensional laminar flow to a three-dimensional turbulent flow is considered. It is shown that developing hydrodynamic instabilities give rise to an eddy cascade, which, in the transition of the flow to a turbulent stage, corresponds to an eddy cascade developing in the energy and, then, inertial ranges.     

Interactive computing methods for aeroelastic analysis of turbomachinery

An interaction viscous‐inviscid method for efficiently computing steady and unsteady viscous flows is presented. The inviscid domain is modeled using a finite element discretization of the full potential equation. The viscous region is modeled using a finite difference boundary layer technique. The two regions are simultaneously coupled using the transpiration approach. A time linearization technique is applied to this interactive method. For unsteady flows, the fluid is assumed to be composed of a mean or steady flow plus a harmonically varying small unsteady disturbance. Numerically exact nonreflecting boundary conditions are used for the far field conditions. Results for some steady and unsteady, laminar and turbulent flow problems are compared to linearized Navier‐Stokes or time‐marching boundary layer methods. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Heat Transfer in Rotor/Rotor and Rotor/Stator Cavity: Physics,Correlations and Numerical Modeling

The transitional and turbulent flow in the near wall sublayer is now mostly modeled based on the existing knowledge of simple 2D flows. To determine the effect of three dimensionality on the turbulent flow structures and turbulent heat transfer in the near wall areas the authors investigate numerically (SVV) turbulent flow in rotor/stator and rotor/rotor flows (with and without axial throughflow). These simple model flows contain most of the phenomena that are needed to understand more complex, 3D transitional and turbulent flows. Attention is focused on the turbulent characteristics which should have more universal character. To stabilize calculations for high Reynolds numbers (up to Re=800 000) the SVV operator is introduced into the Navier-Stokes and energy equations solver for cylindrical coordinate system without using complex numbers. Code optimization and parallelization have speeded up computations 20 times. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Laminar-turbulent reactive flows in porous media

We state some recent results concerning liquid-vapor phase transitions for a fluid flow through a porousmedium. The focus is on the friction exerted by the porous medium, which is modeled in such a way to include both laminar and turbulent flows. In this way we obtain a hyperbolic system of three balance laws with a forcing term that is discontinuous in the state variables. Existence, uniqueness and qualitative behavior of traveling waves is proved by a novel regularization technique.     

Mixed convection turbulent film condensation on a sphere

The present paper reports a research on condensation heat transfer of an isothermal sphere with an external flow of vapor. The high tangential velocity of the vapor flow is determined from potential flow theory. The transition criterion of the onset turbulence has been given in the local film Reynolds number (Re_Γ). An eddy diffusivity model along with an expression by [H. Kato, N.N. Shiwaki, M. Hirota, On the turbulent heat transfer by free convection from a vertical plate, Int. J. Heat Mass Transfer, 11(1968) 1117–1125] is used to model turbulence. And the local liquid–vapor interfacial shear which occurs for high velocity vapor flow across a sphere surface is defined by the Colburn analogy. The paper then presents analytical analysis for the local dimensionless film thickness and heat transfer characteristics for the film condensation. And a comparison with those generated by previous theoretical of laminar condensation is discussed. The comparison shows the heat transfer coefficient of turbulent film condensation is higher than laminar film condensation under the high vapor velocity.     

Vortex breakdown in turbulent pipe flows

In many technical applications turbulent flows with embedded slender vortices exist. Depending on the boundary conditions vortex breakdown can occur. The purpose of this work is to develop and implement a solution scheme for large‐eddy simulations of vortex breakdown in turbulent pipe flows. One of the main problems in this simulation is the formulation of the inflow boundary condition for a fully developed turbulent flow with an embedded vortex. For that purpose a rescaling technique is developed in which a solution at a downstream location is inserted at the inflow boundary after an appropriate rescaling. To determine rescaling laws for pipe flows with an embedded vortex, analytical velocity profiles of swirling flows are first prescribed in a laminar flow. From the spatial development of the vortex a scaling law is deduced. In a next step this procedure is to be transferred to turbulent flows.     

Numerical solution of turbulent jet flows

The work deals with numerical modelling of several turbulent 3D jet flows: steady impinging jet, steady free jet in cross–flow, synthetic free jet (unsteady) and synthetic impinging jet (unsteady). The numerical method is based on artificial compressibility method with dual time extension for unsteady cases. Space discretization uses cell–centered finite volume method with third order accurate upwind approximation for convection, the time discretisations are implicit. Turbulence is modelled using two–equation eddy viscosity models and by explicit algebraic Reynolds stress model (EARSM by Wallin and Hellsten). The results of first three cases are compared with measurements. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Performance and limitations of the unsteady RANS approach

Turbulent flows in complex geometries often exhibit an oscillating behavior of large coherent structures, even in the case of steady state boundary conditions. Recently, numerous efforts have been made to resolve these oscillations by means of numerical simulations. Unfortunately, large-eddy simulations are often very time- and memory-consuming in the case of complex flows. Therefore, the unsteady RANS (URANS) approach is an attractive alternative, especially when numerical simulations are used as a design and optimization tool. Here, two complex flow situations are presented, the tundish flow and a jet in a crossflow. For these flows, relationships between the Strouhal number and important flow parameters are known from experiments. In the paper, URANS models are applied to resolve those relationships also numerically. The evaluation of the numerical results demonstrates the abilities and the limitations of the URANS approach when resolving the dynamics of large coherent structures in complex flows. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Direct numerical simulation of turbulent flows in eccentric pipes

A numerical algorithm was developed for solving the incompressible Navier-Stokes equations in curvilinear orthogonal coordinates. The algorithm is based on a central-difference discretization in space and on a third-order accurate semi-implicit Runge-Kutta scheme for time integration. The discrete equations inherit some properties of the original differential equations, in particular, the neutrality of the convective terms and the pressure gradient in the kinetic energy production. The method was applied to the direct numerical simulation of turbulent flows between two eccentric cylinders. Numerical computations were performed at Re = 4000 (where the Reynolds number Re was defined in terms of the mean velocity and the hydraulic diameter). It was found that two types of flow develop depending on the geometric parameters. In the flow of one type, turbulent fluctuations were observed over the entire cross section of the pipe, including the narrowest gap, where the local Reynolds number was only about 500. The flow of the other type was divided into turbulent and laminar regions (in the wide and narrow parts of the gap, respectively).     

The development and substantiation of the kinetic theory of gases in the twentieth century

A new kinetic theory that is close to dynamic processes is constructed. A system of M integro-differential equations and a system of M partial differential equations are obtained. The theory is demonstrated using the examples of the calculation of the structure of intense shock-waves and by calculating turbulent flows in a plane channel. It is shown that the theory of the structure of high-intensity shock-waves agrees with remarkable accuracy with numerous experimental data. Calculations of turbulent flow approximate quite well to experimental data, but it is remarkable that a single theory can describe both the turbulent core at the centre of the channel and the laminar sublayer on the wall so well.     

General Nonlocal Model Describing the Laminar and Turbulent Flows of Viscous and Nonlinear Viscous Fluids and Its Investigation

A general nonlocal model describing the flows of viscous and nonlinear viscous fluids for both laminar and turbulent flows is introduced and studied. For this model, the viscosity of the fluid depends on the second invariant of the rate of the strain tensor and on a nonlocal (integral) characteristic of the flow. This characteristic is a vector that, in the simplest case, is an analog of the Reynolds number. For slow flows, the model turns into the Navier–Stokes equations or into the equations of a nonlinear viscous fluid. Problems on steady and nonsteady flows with mixed boundary conditions when velocities and surface forces are prescribed on different parts of the boundary are studied. Existence results without restrictions on the smallness of data and on the length of the interval of time are proved.     

固液两相流中的K-ε双方程湍流模式*

建立了固液两相流中更一般的K-ε双方程湍流模式。模化了固相和液相的连续方程、动量方程及K方程和ε方程。该湍流模型考虑了固液两相间速度的滑移,颗粒间的作用及相间作用。使用本文所建立的湍流模型,数值预测了一管湍流中的沙水混合流动,其预测结果与实验结果比较一致。     

Investigation of secondary flow and the related instability on an infinite yawed cylinder with Schubauer’s ellipse as section

This paper presents the principal results of a theoretical investigation of the secondary flow and the related instability performed in the laminar incompressible boundary layer on an infinite uniform yawed solid cylinder with Schubauer’s ellipse of axial ratio 2·96:1 as the section normal to the leading edge. The secondary flow profiles and the value of the instability criterion are obtained at different points of the wing section and for various angles of sweepback. It is found that in favourable pressure gradients and at pressure minimum, the secondary flow profiles have negative values. In regions of adverse pressure gradients after the pressure minimum the secondary flow changes sign from negative to positive values and have points of inflexion. The change of sign starts from the surface and extends to the edge of the boundary layer downstream. At some points in adverse pressure gradients the secondary flow profiles have double points of inflexion and values of both signs simultaneously. It is found that an adverse pressure gradient produces more powerful secondary flow than a favourable pressure gradient of the same strength. It is also found that the values of the instability criterion increase with the increasing sweepback whether the pressure gradient is favourable or adverse. At every point of the wing section, there are two values of the criterion for a given sweepback. The effect of adverse pressure gradient on the variation of the criterion is much more pronounced than that of a favourable pressure gradient. It is also seen that the flow is intermittently laminar and turbulent for low values of the chordwise free stream Reynolds number and for low values of sweepback and consists of an irregular sequence of laminar and turbulent regions.     

Local and instantaneous turbulence modification induced by small spherical bubbles

The paper provides insight into the local and instantaneous turbulence modification induced by small spherical bubbles in an upward directed turbulent channel flow. This is accomplished by analyzing each term of the transport equation of the local and instantaneous kinetic energy for bubbly flows and dedicated flow visualizations are provided to address the mechanisms involved in the turbulence modification. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modelling dispersion in laminar and turbulent flows in an open channel based on centre manifolds using 1D-IRBFN method

Centre manifold method is an accurate approach for analytically constructing an advection–diffusion equation (and even more accurate equations involving higher-order derivatives) for the depth-averaged concentration of substances in channels. This paper presents a direct numerical verification of this method with examples of the dispersion in laminar and turbulent flows in an open channel with a smooth bottom. The one-dimensional integrated radial basis function network (1D-IRBFN) method is used as a numerical approach to obtain a numerical solution for the original two-dimensional (2-D) advection–diffusion equation. The 2-D solution is depth-averaged and compared with the solution of the 1-D equation derived using the centre manifolds. The numerical results show that the 2-D and 1-D solutions are in good agreement both for the laminar flow and turbulent flow. The maximum depth-averaged concentrations for the 1-D and 2-D models gradually converge to each other, with their velocities becoming practically equal. The obtained numerical results also demonstrate that the longitudinal diffusion can be neglected compared to the advection.     

On the flow resistance of wide surface structures

The possibility of skin-friction drag reduction in channel flows due to surface structures is investigated numerically. In this context, surface structures with a high width to height ratio compared to the typical dimensions of riblets are studied in the laminar as well as in the turbulent flow regime. In general, it is found that a reduction of the flow resistance is possible in both flow regimes. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)