Computation of three-dimensional transonic flow using a cell vertex finite volume method for the Euler equations

Summary A cell vertex finite volume method for the solution of the three dimensional Euler equations has been developed. The computations can be carried out block-wise after dividing the computational domain into smaller blocks to reduce the memory requirement for a single processor computer and also to facilitate parallel computing. A five stage Runge-Kutta scheme has been used to advance the solution in time. Enthalpy damping, implicit residual smoothing, local time stepping, and grid sequencing are used for convergence acceleration. The solution procedure has been studied in detail by computing transonic flow over the ONERA M-6 wing, using both C-H and O-H type structured grids. The effects of changing the artificial viscosity parameters and the distance of the far field boundary are also investigated.     

Computation of transonic potential flow past wing-body configurations

Summary A simple approach has been developed to use the two dimensional grid generation method by solving elliptic partial differential equations to generate the three dimensional grid for wingfuselage configurations. This simple method can be applied to generate grids for arbitrary fuselage fitted with any swept wing with dihedral. Three dimensional transonic analysis code TWING, with approximate factorization (AF2) scheme has been suitably used as a flow solver. As an example, RAE-WING-A with body-B2 configuration has been considered. The results obtained have been compared with available numerical and experimental results. It has been observed in the present computations that AF2 scheme is not sensitive to grid stretching.     

Computation of transonic viscous flow over airfoils with control by an elastic membrane and comparison with control by passive ventilation

Summary The performance of transonic wings can be influenced by control of the shock/boundary layer interaction (SBLI) using an adaptive surface in the shock region. This is achieved by inserting a cavity into the airfoil and covering it with an elastic membrane. The theoretical methods for the computation of transonic viscous flow around airfoils with control are presented. The zonal solution method consists of numerical and analytical parts. The influence of the adaptive wall on the flow field over a modern transonic airfoil has been investigated. The flow parameters have been varied up to off-design conditions to understand the physical effects of the control. Previous investigations of a second way of control, the passive ventilation, allow a comparison of these two methods.     

A large-scale three-dimensional finite element analysis of incompressible viscous fluid flow

An efficient finite element scheme for large-scale three-dimensional flow analysis is proposed. Focus of attention is placed on the time integration algorithm and some techniques for the reduction of the storage requirement, including the one-point quadrature technique and an iterative matrix solver. Application to large-scale three-dimensional problems is given to demonstrate the feasibility of the proposed scheme.     

Inverse method for viscous flow design using stream-function coordinates

In the paper, a new inverse method for viscous 2D laminar flows is developed. The method is based on incompressible Navier–Stokes equations transformed to the stream-function coordinate system (von Mises coordinates). The flow design problem with appropriate boundary conditions is formulated and solved numerically. The geometrical shape of the boundary is obtained through the integration along streamlines. The method may be coupled with a flow analysis solver to model the influence of known parts of geometry. Results for two analytically solvable cases (the Poiseuille and the Jeffery–Hamel flows) are presented. Then, the foil design problem is considered as an example. Potential applications and developments towards axisymmetric and 3D flows are discussed.     

Computation of the velocity profile for nonlinearly viscous fluid flow in spiral channels with low reynolds numbers

Two methods are presented for solving the problem of nonlinear viscous fluid flow in spiral channels of arbitrary transverse section in the Stokes approximation, variational and iterational.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 55, No. 4, pp. 581–589, October, 1988.     

Finite element computation of unsteady viscous transonic flows past stationary airfoils

Results are presented for computations of unsteady viscous transonic flows past a stationary NACA0012 airfoil at various angles of attack. The Reynolds number, based on the chord-length of the airfoil, is 10,000 and the Mach number is 0.85. Stabilized finite-element formulations are employed to solve the compressible Navier-Stokes equations. The equation systems, resulting from the discretization, are solved iteratively by using the preconditioned GMRES technique. Time integration of the governing equations is carried out for large values of the non-dimensional time to understand the unsteady dynamics and long-term behavior of the flows. The results show interesting flow patterns and a complex interaction between the boundary/shear layers, shock/expansion waves and the lateral boundaries of the computational domain. For transonic flow past an airfoil at various angles of attack in a narrow channel/wind-tunnel one can observe solutions that are qualitatively different from each other. At low angles of attack an unsteady wake is observed. At moderate angles of attack the interaction between the shock system and the lateral walls becomes significant and the temporal activity in the wake decreases and eventually disappears. At high angles of attack a reflection shock is formed. Hysteresis is observed at an angle of attack 8^∘. For the flow in a domain with the lateral boundaries located far away, the unsteadiness in the flow increases with an increase in the angle of attack. Computations for a Mach 2, Re 106 flow past an airfoil at 10^∘ angle of attack compare well with numerical and experimental results from other researchers     

Singularities of viscous flow

Summary The force and torque on a slender body in Stokes flow is obtained by using a distribution of singularities along the centreline and the required image system to satisfy the no-slip condition and the plane boundary. It is found that the force on a slender body increases rapidly as it approaches within a body length of the boundary, but not the torque. To rule out “wall effects”, experiments on slender bodies, such as flagellated or ciliated micro-organisms, should be carried out a distance of many body lengths (not radii!) from all boundaries. The ratio of normal to tangential resistance coefficients is found to be greater than 2 (the maximum in an infinite fluid) in the presence of walls.     

Computation of the velocity profile in the flow of an anomalously viscous liquid in cylindrical channels of arbitrary cross section

A method is proposed for computing the velocity profile in the flow of an anomalously viscous liquid in cylindrical channels of arbitrary cross section as a function of the pressure drop, the dimensions of the transverse cross section, and the rheological characteristics of the liquid.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 34, No. 6, pp. 1081–1084, June, 1978.     

Combined single domain and subdomain BEM for 3D laminar viscous flow

A subdomain boundary element method (BEM) using a continuous quadratic interpolation of function and discontinuous linear interpolation of flux is presented for the solution of the vorticity transport equation and the kinematics equation in 3D. By employing compatibility conditions between subdomains an over-determined system of linear equations is obtained, which is solved in a least squares manner. The method, combined with the single domain BEM, is used to solve laminar viscous flows using the velocity vorticity formulation of Navier–Stokes equations. The versatility and accuracy of the method are proven using the 3D lid driven cavity test case.     

Squeezing flow of fibre-reinforced viscous fluids

A relatively simple continuum model is described for the viscous flow of highly anisotropic materials such as fibre-reinforced resins. The theory is applied to the flow of such a fluid when squeezed between two rigid platens.     

The decay of slow viscous flow

A weak force acts within a viscous fluid for a finite time leading to a slow flow with negligible viscous effects; the force then ceases so that the fluid returns steadily to a state of the rest under the action of diffusion. In the model developed, the force is equivalent in time to a delta function mathematically, having the form of a pulse physically; singular solutions such as rotlets and skokeslets are introduced to simplify the calculations and their use can be justified as representing solid bodies. Here we solve the transient Stokes flow equations to fins the behaviour in a number of different situations, the rates of decay are computed, and the nature of the final motion described. A number of general conclusions are deduced from these examples.     

Computation of laminar viscous fluid flows in arbitrary axisymmeric channels

A finite-difference method is proposed for computing flows in axisymmetric channels of arbitrary configuration in the presence of a swirling stream.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 8, No. 1, pp. 42–49, January, 1990.     

A variable-domain variational theory using Clebsch variables for hybrid problems of 2-D transonic rotational flow

Summary By means of functional variations with variable domain the variational principles of [7], [8] are extended to inverse and hybrid flow problems.     

Identification of self-organizing structures by the numerical simulation of laminar three-dimensional flow around a crater on a plane by a flow of viscous incompressible fluid

Three-dimensional steady-state vortex structures which undergo self-organization during flow around a deep spherical crater on a plane are analyzed by using a factorized finite-volume method to solve the Navier-Stokes equations in a simplified approach based on an analytic definition of metric coefficients. Pis’ma Zh. Tekh. Fiz. 24, 6–12 (March 26, 1998)     

Computation of hypersonic flow and radiation of viscous chemically reacting gas in a channel modeling a section of a scramjet

This work is devoted to a consideration of flow and combustion of a hydrogen-air mixture in a channel modeling a section of a supersonic combustion ramjet (scramjet). Fields of concentrations, pressure, and temperature are obtained. Based on them, the thermal radiation of gas within a scramjet combustor is computed. The density of the radiative heat flux to the chamber wall is computed by two methods, i.e., in a P1 approximation of the spherical harmonics method and in an approximation of the plane layer. It has been shown that the radiative heat flux contribute significantly to the total heating of the jet wall.     

Calculation of a three-dimensional flow of a viscous incompressible liquid in the neighborhood of a shallow well on a flat surface

A three-dimensional flow in the neighborhood of a shallow well on a plane was simulated numerically on the basis of a solution of the Reynolds equations written in curvilinear nonorthogonal coordinates and closed by a two-parametric dissipative model of turbulence.The work has been financed by the Russian Basic Research Foundation (Grant No. 94-02-04092 a).Civil Aviation Academy, St. Petersburg, Russia. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 67, Nos. 5–6, pp. 373–378, November–December, 1994.