Filippo Sabetta

Compressibility Correction for the Spalart-Allmaras Model in Free-Shear Flows

A correction of the Spalart-Allmaras turbulence model to account for the compressibility effects in mixing-layer flows is presented. Unlike other corrections proposed for the K-e model, the present correction does not need the knowledge of the turbulent Mach number and, therefore, can be applied to those turbulence models, like the Spalart-Allmaras one, which do not integrate directly the turbulent kinetic energy equation. To explore the validity of the proposed correction, four mixing-layer flows and four supersonic backward-facing step flows, covering a wide range of flow conditions, were selected and computed using both the standard and the corrected Spalart-Allmaras model. The analysis of the numerical results and their comparison with the experimental data show that the proposed correction produces a significant improvement of the numerical predictions.

Transition between open and closed wake in 3D linear aerospike nozzles

Linear aerospike nozzles are envisaged as a possible device able to improve launcher engine performance. One of the most interesting properties of these nozzles is the possibility of a good integration with the vehicle. To improve the knowledge of the flow-field and performance of aerospike nozzles, they are studied numerically, with particular attention to the dierences between the basic two-dimensional nozzle, usually considered in the design phase, and the more realistic three-dimensional nozzle. The study considers dierent plug lengths and ambient pressures to assess the role of the linear plug side truncation on the base pressure behavior. Numerical tests are carried out at supersonic flight Mach number.

Nonequilibrium hypersonic inviscid steady flows

A numerical method for the solution of nonequilibrium flows about blunt bodies is presented. The method is based on the splitting in two parts of the reactive Euler equations: the gasdynamic operator (mass and momentum equations) and the chemical operator (energy and species conservation equations). The gasdynamic operator is discretized on a body- and shock-litted grid, and integrated in diagonalized form by means of a semi-implicit technique. The chemical operator is integrated along the streamlines by means of an implicit technique with variable step size

Numerical simulation of hypersonic flows past three-dimensional blunt bodies through a unstructured shock-fitting solver

Owing to the maturity nowadays reached by computational geometry, shock-fitting, i.e. treating shock waves as true surfaces of discontinuity may no longer be prohibitively complex, as commonly believed by CFD practitioners. In this paper we report on some newly implemented features and algorithmic improvements of an unstructured, shock-fitting algorithm for threedimensional flows that has been recently proposed by the authors. The shock wave is described using a double-sided triangulated surface which is allowed to float over a background tetrahedral grid while obeying to the Rankine-Hugoniot jump relations. A constrained, Delaunay tetrahedralization is applied in the neighbourhood of the shock-front to make sure that the triangular faces that make up the shock surface are part of the tetrahedral mesh that covers the entire computational domain. A shockcapturing, vertex-centred solver is used to discretise the governing PDEs ∗Associate Professor, AIAA member †Post-doctoral research assistant ‡Associate Professor, AIAA member §Professor ¶Post-doctoral research assistant ‖Professor, AIAA member

Performance analysis of an infinite array linear clustered plug nozzle

I N the challenge of realizing a new generation of space launchers, either single or two stage to orbit, an important role is played by the performance of the engine expansion system working in a varying pressure environment. In this framework a great interest has been devoted to the linear plug nozzle, which has been the subject of several studies in the last decade [1–6]. The plug nozzle is an external-expansion nozzle that yields self-adaptation of the exhaust jet to varying ambient pressure ratios, in a certain range of the launcher trajectory. This self-adapting capability allows high nozzle expansion ratios while avoiding the risks of flow separation that would exist in equivalent bell nozzles. The plug nozzle is made of a primary internal expansion nozzle, which is a conventional supersonic nozzle, and an external-expansion ramp, referred to as the plug surface. Most of the different engineering solutions proposed for plug nozzles have the following common feature: the primary expansion is made through a cluster of bell nozzles (or modules) exhausting onto a common linear plug surface [7–9]. The primary nozzle partitioning allows easier manufacturing, lower thermal loads, easier cooling and higher thrust vector capability. However, clustering causes additional performance losses due to three-dimensional flow inside the modules and to the interaction of jets exhausting from adjacent modules. For these reasons the three-dimensional features have to be studied in depth to better predict the engine performance and the expected mechanical and thermal loads for nominal operating conditions both at sea level and altitude and for differentially throttled modules as well. In fact, the thrust vectoring could be achieved by differential throttling of modules and, when thrust requirement is reduced in the final part of the ascent, some of the modules could be intentionally shut down. To this goal, the present paper studies by numerical simulation, the three-dimensional flowfield generated by themodules on a reference linear plug surface. The attention is focused on the effects of the three-dimensional flow features that take place when two different kind of modules are considered: the first module is obtained by dividing the reference two-dimensional primary nozzle by vertical walls and the second one is a full three-dimensional round-to-square nozzle. The performance analysis of these different module configurations allows weighing separately the role of clustering (i.e., just divide the primary nozzle into modules with infinitely thin flat walls) and the role of module design. A further subject of this study is the analysis of the effects produced by the shut down of a module of the cluster, for both module configurations. The analysis of the different configurations is made by comparing the thrust losses with the reference two-dimensional solution.

Equilibrium and nonequilibrium modeling of hypersonic inviscid flows

Abstract Hypersonic flows about ellipses at high angles of attack are analyzed by means of nonequilibrium, equilibrium and inert gas models. It is shown that the technique proposed for the nonequilibrium model, based on a streamline integration of the chemical rate equations, provides accurate results and allows precise computation of the stagnation point conditions, where equilibrium must be attained. Compared with the nonequilibrium one, the equilibrium model underpredicts the bow shock stand-off distance and overpredicts the wall temperature, whereas the inert gas model can only be used as a crude approximation for evaluating the wall pressure.

Base-Pressure Experimental Investigation on a Space Launcher in Subsonic Regime

An experimental investigation of the space launcher base flow during the early ascent phases has been carried out in a subsonic wind tunnel. Specifically, this study has considered a simple launcher model formed by a circular cylinder with an ogival nose and a centered nozzle in the truncated base. Tests have been conducted generating subsonic streams in the wind-tunnel test section ranging from Mach 0.18 to 0.43 and an overexpanded Mach 3 cold jet through the nozzle. Static pressure probes located on the launcher side walls and base provided the pressure distribution data. The analysis of the experimental data features the “aspiration” effects caused by the supersonic jet on the external subsonic stream and on the base pressure.

Analysis of a three-dimensional flow generated by a linear aerospike

Linear aerospike nozzles are envisaged as a possible means to improve launcher engine performance. One of the most interesting properties of these nozzles is the possibility of a good integration with the vehicle. To improve the knowledge of the flow-field and performance of aerospike nozzles, they are studied numerically, with particular attention to the differences between the basic two-dimensional nozzle, usually considered in the design phase, and the more realistic three-dimensional nozzle. The study considers also the effect of flight condition, which cannot be neglected because of the characteristic external expansion of aerospike nozzles.

Reactive and Inert Inviscid Flow Solutions by Quasi-linear Formulations and Shock Fitting

The first part of this paper (Section 1) concerns the solution of inert flows on the double ellipse (Test cases 6.1.1. and 6.1.3.), while in Section 2 the solution method and the results are described for the nonequilibrium, equilibrium and γ = 1.2 flows on the simple ellipse (Test cases 6.2.1., 6.3.1., and 6.3.2.).

Turbulence Modeling of Base Drag on Launcher in Subsonic Flight

Experimental wind tunnel tests, conducted to reproduce the base flow past a space launcher during early ascent fight conditions, were numerically simulated by solving the steady Reynolds-averaged Navier–Stokes equations using two different versions of the Spalart–Allmaras model. The launcher model consisted of a cylinder with a circular cross section, an ogival nose, and a centered nozzle that issued a supersonic cold jet embedded in the external subsonic stream. A comparative analysis of the data obtained from the steady-state simulations and from the experimental tests indicated that the launcher base pressure was closely related to the turbulent shear stresses within the jet mixing layer; therefore, accurate modeling of the compressibility effects in the turbulent mixing layer plays an important role in improving the base drag estimates provided by the numerical simulations.