Subsonic Viscous Flow Research Articles

Computation of subsonic viscous and transonic viscous-inviscid unsteady flow

A new viscous-inviscid interaction scheme is introduced, which implicitly couples the unsteady Euler and the boundary-layer equations. The adequacy of an integral formulation of the viscous flow equations for use in unsteady flows is shown in comparison with experimental results and finite-difference computations, and an explanation is worked out which traces back the unsteady response of the mean and turbulence field due to the external unsteadiness to a quasi-steady behaviour. The interaction computations of transonic airfoil flows by means of the Euler-boundary-layer technique are compared with the steady and unsteady experimental data sets for the RAE 2822 and the NLR 7301 supercritical airfoils, respectively.

Viscous subsonic flow computation for wings with flaps for high-lift

A computing method for calculation of the subsonic, viscous flow around clean wings of moderate to high aspect ratio and low swep has been extended to analyse wings with deployed high-lift systems, that is,wings with deflected leading and/or trailing edge flaps. The overall method.is an iterative procedure combining a 3-d inviscid lifting surface theorywith a 2-d multi-element airfoil analysis procedure including boundary layer effects and a model for rear separation. Also, the ground effects are included by means of reflected image technique and the final solution is improved using a curved basic flow analysis. In this report the total method is briefly described giving the - salient features of the procedure. The results of numerical studies regarding the convergence of the iterations, and validation of the current method against experi mental results are included along with a discussion about present limitations and possible future work

An Analysis Methodology for Internal Swirling Flow Systems With a Rotating Wall

This paper presents an analysis methodology for the calculation of the flow through internal flow components with a rotating wall such as annular seals, impeller cavities, and enclosed rotating disks. These flow systems are standard components in gas turbines and cryogenic engines and are characterized by subsonic viscous flow and elliptic pressure effects. The Reynolds-averaged Navier-Stokes equations for turbulent flow are used to model swirling axisymmetric flow. Bulk-flow or velocity profile assumptions aren’t required. Turbulence transport is assumed to be governed by the standard two-equation high Reynolds number turbulence model. A low Reynolds number turbulence model is also used for comparison purposes. The high Reynolds number turbulence model is found to be more practical. A novel treatment of the radial/swirl equation source terms is developed and used to provide enhanced convergence. Homogeneous wall roughness effects are accounted for. To verify the analysis methodology, the flow through Yamada seals, an enclosed rotating disk, and a rotating disk in a housing with throughflow are calculated. The calculation results are compared to experimental data. The calculated results show good agreement with the experimental results.

A semi-elliptic analysis for 2-D viscous flows through cascade configurations

A semi-elliptic formulation, termed the interacting parabolized Navier-Stokes (IPNS) formulation, is developed for the analysis of a class of subsonic viscous flows for which streamwise diffusion is negligible but which are significantly influenced by upstream interactions. A two-step alternating-direction-explicit numerical scheme is developed to solve the resulting governing equations efficiently. The quasi-linearization and discretization of the equations are carefully examined so that no artificial viscosity is added externally to the scheme. Various simple channel and cascade flow configurations are examined for several values of Re, thickness ratio and Mach number, in order to establish the applicability of the IPNS model for these flows. With this model, solutions to compressible as well as nearly incompressible flows are obtained without any modification either in the analysis or in the solution procedure.

Numerical investigation of unsteady subsonic viscous gas flows in a plane channel with a sudden expansion

The nonlinear processes of development of instability in an unsteady subsonic viscous gas flow in a plane channel with a sudden expansion are investigated numerically with allowance for acoustico-vortex interaction over a broad interval of the characteristic parameters. Effects associated with the acoustic self-excitation of the jet flowing into the wider part of the channel are determined. Approximate relations are obtained for the resonance conditions of self-excitation. The effect of the inlet mean-velocity profiles on the evolution of the flow is estimated. The processes of formation and subsequent interaction of the coherent structures are analyzed.

Airfoil design using quasisolutions of inverse boundary-value problems

A mathematically rigorous approach to the solution of inverse boundary-value problems of aerohydrodynamics — problems in which the airfoil contour is found from the given distribution of the velocity as a function of the arc abscissa – is proposed. The approach is based on the notion of a quasisolution in the theory of improperly posed problems and involves a controlled modification of the initial data for the purpose of obtaining a unique solution in a given class of contours. The approach is explained with reference to the problem of designing an isolated airfoil in a plane steady ideal incompressible flow and is extended to the cases of subsonic gas flow and viscous incompressible flow. Some numerical results illustrating the possibilities of the method are also presented.

Numerical outflow boundary condition for Navier-Stokes flow calculations by a line iterative method

THIS study investigates the use of explicit/implicit, step/linear space extrapolation as numerical outflow boundary conditions for turbulent flow calculations. The emphasis is on the interplay between the use of curvilinear coordinate systems for complex flow calculation and the semiimplicit line iterative procedure. Both a planar singlechanneled and an annular multichanneled flow configuration were used as test models. It was found that implicit linear space extrapolation needs more computing time and may not yield a unique solution. On the other hand, explicit zero-order space extrapolation appears to be a robust outflow boundary condition since it has the largest stability limit with respect to underrelaxation factors and initial conditions. Contents The present study investigates the use of outflow boundary condition for subsonic viscous flow calculations. The emphasis is on the complex geometry configuration arising from, e.g., modeling gas turbine combustor flows. Modeling these flows requires the use of the curvilinear body-fitted coordinate system to allow proper treatment of the near-wall region as well as to reduce the skewness between the streamlines and the coordinate lines, as discussed in Refs. 1 and 2. This study concentrates on one category of outflow boundary condition, extrapolation in space, since it is easier to implement into a computer code. The merits between the explicit and implicit implementation with respect to the iteration level are investigated. Both single- and multichanneled geometry configurations are used for the numerical experiments. Four outflow boundary conditions have been implemented and tested: 1) Explicit step space extrapolation—using an explicit onesided difference to approximate a zero first derivative along the main flow direction, i.e.,

Application of finite element methods to viscous subsonic flow

A finite element numerical procedure, called the General Interpolants Method (GIM), is briefly described. It has been derived using the Method of Weighted Residuals. Choosing weight functions which are orthogonal to the shape functions, an explicit Petrov-Galerkin scheme is obtained in non-orthogonal curvilinear coordinates. Calculations are performed using a two-step forward-backward operator to produce a second-order time-accurate pseudo-centered algorithm. Several applications are presented and discussed: (1) thermocapillary convection in a rectangular container; (2) crystal growth fluid behavior under low gravity conditions; and (3) exhaust manifold flow in the fuel turbopump of the Space Shuttle Main Engine. Numerical results for the thermocapillary convective flow are shown to agree with those predicted analytically, and the results for the turbopump exhaust gas manifold flow are found to be in basic agreement with experimental data. By changing the geometry of the flow path, improved flow conditions in the turbopump exhaust manifold are predicted.

Multiple-grid convergence acceleration of viscous and inviscid flow computations

A multiple-grid algorithm for use in efficiently obtaining steady solutions to the Euler and Navier-Stokes equations is presented. The convergence of a simple, explicit fine-grid solution procedure is accelerated on a sequence of successively coarser grids by a coarse-grid information propagation method which rapidly eliminates transients from the computational domain. This use of multiple-gridding to increase the convergence rate results in substantially reduced work requirements for the numerical solution of a wide range of flow problems. Computational results are presented for subsonic and transonic inviscid flows and for laminar and turbulent, attached and separated, subsonic viscous flows. Work reduction factors as large as eight, in comparison to the basic fine-grid algorithm, have been obtained. Possibilities for further performance improvement are discussed.

Calculation of subsonic viscous gas flows in plane channels and wakes

THE PROBLEM of tha laminar flow of a viscous gas in plane channels of constant cross-section and finite length, formed by a lattice of plates, and in the wakes behind the plates, is considered, using the complete Navier-Stokes equations. The case of the subsonic flows flows of gas is investigated when a direct condensation jump occurs at the channel input. The calcularions are carried out in the range of Reynolds numbers Re = 20 to 200. The wall temperature is assumed to be equal to the stagnation temperature. The data of the calculations confirm the features of the flow of a viscous gas in long channels revealed by the approximate treatment of the problem.

Model for the Solution of Supersonic Viscous Interaction Effects on Blunted Cones

over the past decade. The practical application of such investigations: space vehicle re-entry and high altitude flight, has initiated the development of numerous analytical and numerical models to accurately predict the viscous inviscid interaction and its effect on fluid properties, particularly pressure distribution. A proper assessment of the effects of interaction on blunted surfaces can only be accomplished by a theory which allows for both pressure and vorticity interaction phenomena for the high Mach number, low Reynolds number flows of practical interest. Previous investigations by the authors13'14 have attempted to establish a model which allows for the inclusion of all interaction effects directly, i.e., by solving the entire viscous and inviscid flowfield at the same time and establishing unique solutions. The model's main features are: its inclusion of viscous transports in the characteristic equations, the matching of the subsonic viscous flow (solved by a second-order, implicit CrankNicholson scheme) to the supersonic flow in the transonic zone, the inclusion of the normal momentum equation (thus allowing for transverse pressure gradients, whose importance is increased in thick, high curvature boundary layers), and the solution of the entire interaction problem by a marching technique. It is shown herein that the model's predictions of pressure distribution and heat transfer for high Mach number, low Reynolds number, flows over blunted cones are in excellent agreement with experimental data, whereas other interaction models do not exhibit such accuracy.

Subsonic and transsonic viscous gas flow in the wake of a two-dimensional body

Subsonic and transsonic viscous gas flow in the wake of a two-dimensional body