An Asymptotic Analysis of Compressible Base Flow and the Implementation into Linear Plug Nozzles

Abstract

The major technical challenge the development of next-generation launchers is facing today, is to achieve complete reusability in two stages to orbit or ultimately in one single stage. These Two-Stage-To-Orbit (TSTO) or Single-Stage-To-Orbit (SSTO) Reusable Launch Vehicles (RLV) may reduce payload cost by a factor of ten or more. The challenge, however, can only be met by the design of special propulsion systems equipped with so called altitude-adaptive nozzles. The most promising altitude-adaptive concept is that of the linear plug nozzle, a conventional bell nozzle turned inside out and arranged in a linear configuration. Advantages of this type of nozzle are: adaptability to varying ambient pressure; simplicity and reliability, because there are no movable parts; low engine weight, because of ease in vehicle integration and distributed thrust loads; built-in Thrust Vector Control (TVC) by throttling modular engines; and, cheap manufacturing of high-performance nozzles, because the nozzle is divided in multiple equivalent segments. The adaptability of the concept, however, ceases to exist around and beyond transonic velocities. The problem is related to the development of a lowpressure planar compressible base flow, located behind the vehicle base in the region between the separated external flow and the separated exhaust jet. Compressible base flow is a well-known fluid-dynamic phenomenon, which has been studied and analysed for many years, especially during the onset of rocketry in the late 1950s and 1960s. However, a satisfying description of the physical processes driving the base flow has as yet not been determined. Nevertheless, a proper understanding of these processes is essential for the development of a linear plug nozzle resisting external-flow effects, and is critical for the realisation of single-stage-to-orbit vehicles in general. The complexity of compressible base flow lies in the composition and interaction of multiple processes. For every separate process that can be identified in the complex flow around launch-vehicle nozzles, the local Reynolds number may be assumed high, even though corresponding length scales may be relatively small; this is a result of rather high velocities, densities and launch-vehicle sizes, and rather low viscosities. Consequently, an asymptotic approach is allowed in which the different elements of compressible base flow are treated separately. The asymptotic approach enables the analytical proof of existence and quantification of driving base-flow phenomena, such as upstream influence, isentropic compression before reattachment, and interaction of the developing shear layer with the expanded boundary layer and circulatory region. From this analysis two limiting base-flow solutions are identified. One is the well-known Chapman limit, in which the boundary-layer thickness is assumed to be negligible in comparison with the shear-layer thickness. The other is a newly-identified limit, in which the shear-layer thickness is assumed to be negligible in comparison with the boundary-layer thickness. The corresponding solution methods have been adjusted to cope with asymmetric base-flow conditions (allowing the exchange of mass and energy between the two flows), adiabatic and non-adiabatic base bleed, base heating, and the use of different species. The asymptotic solution method has been further adjusted to cope with the base flow downstream of the actual plug nozzle as well. The shear layer, developed in between the jet exhaust and this base flow, is generally redirected by reflecting expansion waves. Optimal base-bleed percentages for the plug-nozzle base flow have been determined for maximal specific impulse. Subjecting the vehicle base flow solution to a parameter-variation analysis, reveals that real exhaust gases will produce significantly higher base pressures and temperatures than cold gases (air). Clarifying the problem of base flow enables one to diminish or even avoid the negative consequences of base flow by application of a well-considered and well-shaped after body. For the case of inviscid flow the optimal conventional boat-tail shape is found to be linear. The Ventilated Trailing-Edge Cavity (VTEC), attached to the vehicle base, moreover avoids the low base pressures by relocating the reattachment point farther downstream, so that the exhaust jet still retains the ability to fulfil its altitude-adaptive tasks at supersonic flight speeds.