Viscous–inviscid interactions in transonic flows through slender nozzles

Considering the miniaturization trend in technical applications, the need of a slender nozzle theory for such conventional, that is ideal-gas-like, fluids, which accounts for a strong boundary-layer interaction with the core region, arises in quite a natural way as the dimensions of the flow device are successively reduced. Moreover, a number of modern technological processes (e.g. organic Rankine cycles) involve fluids with high molecular complexity, some of which are expected to exhibit embedded regions with negative values of the fundamental derivative in the vapour phase commonly termed Bethe–Zel'dovich–Thompson (BZT) fluids. Linked to it, unconventional Laval nozzle geometries are needed to transform subsonic to supersonic internal flows. In the present paper, the transonic flows through nozzles of short length scales located in a channel of constant cross-section so slender that the flow in the inviscid core region is one-dimensional are considered. Rapid streamwise changes of the flow field caused by the nozzle then lead to a local breakdown of the classical hierarchical boundary-layer approach, which is overcome by the triple-deck concept. Consequently, the properties of the inviscid core and the near-wall (laminar) boundary-layer regions have to be calculated simultaneously. The resulting problem is formulated for both regular (ideal-gas-like) fluids and dense gases. Differences and similarities of the resulting flow pattern with respect to the well-known classical Laval nozzle flow are presented for perfect gases, and the regularizing influence of viscous–inviscid interactions, is examined. Furthermore, the analogous problem is considered for BZT fluids in detail as well. The results indicate that the passage through the sonic point in the inviscid core is strongly affected by the combined influence of nozzle geometry and boundary-layer displacement effects suggesting in turn an inverse Laval nozzle design in order to obtain the desired flow behaviour.

On the suppression of shock-induced separation in Bethe–Zel'dovich–Thompson fluids

We consider the reflection of oblique compression waves from a two-dimensional, steady, laminar boundary layer on a flat, adiabatic plate at free-stream pressures such that dense-gas effects are non-negligible. The full Navier–Stokes equations are solved through use of a dense-gas version of the Beam–Warming implicit scheme. The main fluids studied are Bethe–Zel'dovich–Thompson (BZT) fluids. These are ordinary gases which have specific heats large enough to cause the fundamental derivative of gasdynamics to be negative for a range of pressures and temperatures in the single-phase vapour regime. It is demonstrated that the unique dynamics of BZT fluids can result in a suppression of shock-induced separation. Numerical tests performed reveal that the physical mechanism leading to this suppression is directly related to the disintegration of any compression discontinuities originating in the flow. We also demonstrate numerically that the interaction of expansion shocks with the boundary layer produces no adverse effects.

Supersonic flows of dense gases in cascade configurations

We examine the steady, inviscid, supersonic flow of Bethe-Zel'dovich–Thompson (BZT) fluids in two-dimensional cascade configurations. Bethe-Zel'dovich–Thompson fluids are single-phase gases having specific heats so large that the fundamental derivative of gasdynamics, Γ, is negative over a finite range of pressures and temperatures. The equation of state is the well-known Martin–Hou equation, and the numerical scheme is the explicit predictor-corrector method of MacCormack. Numerical comparisons between BZT fluids and lighter fluids such as steam are presented. It was found that the natural dynamics of BZT fluids can result in significant reductions in the adverse pressure gradients associated with the collision of compression waves with neighbouring turbine blades. A numerical example of an entirely isentropic supersonic cascade flow is also presented.