Maurizio Pandolfi

Computation of steady supersonic flows by a flux-difference/splitting method

Abstract A “flux-difference splitting” method has been conceived for the numerical solution of hyperbolic problems and successfully implemented for unsteady flows. It aims to describe the propagation of waves and to respect the domains of dependence. Shock waves are captured numerically very neatly. Here an extension is proposed for the prediction of two-dimensional or axisymmetric steady supersonic flows. Numerical examples are shown to validate the capabilities of the method.

On the “Flux-Difference Splitting” Formulation

The present paper refers to the numerical prediction of the inviscidi compressible flows described by the Euler equations. We will focus our attention on unsteady flows (time marching), but any concept can be easily translated in terms of steady supersonic flows (space marching).

Nonequilibrium hypersonic flows over corners

The hypersonic nonequilibrium flow of air over concave and convex corners is investigated. The description of the flowfield is based on the Euler equations and a chemical model that accounts for the finite rate reactions. An upwind formulation and the related space-marching technique are developed in order to achieve the numerical solution of the fluid dynamical and chemical equations, coupled together. The attention is focused on the effects of nonequilibrium chemistry on fluid dynamics.

Supersonic flow about elliptic cones with large semiaxis ratio

Large attention has bean paid at the numerical investigation of the supersonic flow about elliptic cones. By looking at the literature, many approaches have been used. Different formulations of the problem, sets of variables and coordinate systems have been selected. Nevertheless no solutions and reliable numerical results have been achieved for very thin coneS, namely for the ratio (R) of the semiaxis of the crossSection ellipse greater than 3.3 3.7. In this paper I would like to show how the supersonic flow about elliptic cones with very lar~ ratio R (R = i0) may be computed by using a proper set of variables and coordinate system, different from those assumed in other investigations.

An Upwind Numerical Method for the Prediction of Ideal MHD High Speed Flows

An upwind numerical method for predicting ideal MHD high speed flows is presented. It is based on a flux-difference splitting procedure with an approximate solver for the solution of the Riemann problem. The method is used for investigating numerically the admissibility of discontinuities that satisfy the jump conditions of the 1D planar problem. Fast and slow magnetic shock waves are numerically predicted and also particular shocks, which result from the merging of a slow and a fast magnetic compression waves. Moreover, compound waves are computed where a compression shock is attached to a rarefaction fan of the same family. Both slow and fast compound waves are predicted numerically, as well as transitional compound waves which represent the limiting case of a fast and a slow rarefaction fans attached each other through a compression shock.

PERFORMANCES OF "UPWIND" METHODS IN PREDICTING SHEAR LIKE FLOWS

Upwind methods are considered as the most appropriate numerical tools for predicting high speed flows. However, disturbing problems may arise in dealing with shear-like flows such as boundary layers. Here, the fluid dynamics is dominated by the diffusion processes and the convective terms, which are estimated through an upwind method, have to play a secondary and almost negligible role. Unfortunately, the presence of density and velocity gradients inside boundary layers introduces, in some upwind method, purely numerical effects. In some methods, the boundary layer region may grow, unphysically, beyond the correct thickness because of a spurious dissipation generated by an incorrect evaluation of the convective terms. In other methods, pressure oscillations may appear inside the boundary layer. Such situations, well known in the scientific community, can be properly analyzed by developing a linearized form of the first order scheme for the Euler conservation laws in a particular problem, with the evaluation of the fluxes made as dictated by the formulation of each upwind method. This analysis provides suggestions and hints useful to understand and predict the behavior of an upwind method in simulating shear-like flows.

A Contribution to the Prediction of Hypersonic Non-Equilibrium Flows

We contribute to this Workshop by presenting computations of hypersonic flows about simple and double ellipses. Since we assume inviscid the flow, the fluid dynamics is described by the Euler equations. As regards the real gas effects, we neglect the ionization, we assume the vibrational energy at the local equilibrium level, and we consider in non-equilibrium the chemical processes. These real gas effects are described on the base of the model provided in [1]. We have performed computations for this kind of non-equilibrium flows, as well as for the inert perfect gas (at γ = 1.4 and 1.2) and for the real gas in local chemical equilibrium.

A Physically Consistent Time-Dependent Method for the Solution of the Euler Equations in Transonic Flow

The central theme of this GAMM Workshop is the comparison of the respective performance of various computing procedures in current use today for the numerical solution of inviscid steady transonic flow.

PHYSICAL ASPECTS OF HYPERSONIC FLOW: FLUID DYNAMICS AND NON-EQUILIBRIUM PHENOMENA

The high speeds in hypersonics make available a large amount of energy, that prompts variations in the physical nature of the gas. In the lower part of the regime (high supersonic) energy is transfered to the vibrational excitation of biatomic molecules. At higher speeds, these molecules dissociate and generate new different species. On the upper limit of hypersonics, ionization can occur. Each of these phenomena presents a typical time of relaxation and the hypothesis of equilibrium flow can not be accepted. Therefore, proper equations have to be considered to describe these non-equilibrium phenomena.

A Contribution on the Numerical Prediction of Transonic Flows

This paper deals with a numerical method for the prediction of transonic flows. We consider here the inviscid, compressible, rotational and unsteady flow which is described by the Euler equations. The unsteady terms are taken into account in order to predict real transient phenomena, as well as for achieving steady flow configurations through a time-dependent technique. The numerical method is founded on a finite-differences approximation of the space- and time-derivatives.