M. Di Giacinto

Propellant trade-off analysis for upper stage solid rocket motors performance

Aim of this paper is to perform a propellant trade-off analysis in order to determine the propellant formulation able to maximize solid rocket motor performance for upper stage solid rocket motors (SRMs). The study is performed with the use of a 0D quasi-steady model of SRM internal ballistics developed on this purpose, which assumes the chemicalequilibrium in the combustion chamber up to the nozzle throat, frozen flow conditions in the nozzle divergent, and takes into account the nozzle throat erosion using a validated semi-empirical correlation of the throat recession rate. Three different upper stage SRM configurations are selected for the propellant trade-off analysis. The SRM configurations are inspired in terms of design to the available data in the open literature of three Zefiro family SRMs: Zefiro 23 and Zefiro 9A, second and third stage of VEGA launcher, and Zefiro 40, candidate for the evolution of Zefiro 23. Results indicate that, with respect to the baseline propellant HTPB 1912 (19 % aluminum 12 % HTPB), a gain in the performance can be obtained for propellant formulation with a higher aluminum loading and roughly the same HTPB mass fraction. The optimum aluminum loading increases with respect to the baseline formulation for SRM configurations characterized by high nozzle throat erosion.

Propellant effects on SRM upper stage internal ballistics and performance with nozzle erosion characterization

Nozzle throat erosion is inherently present in high performance solid rocket motors because of high operative pressures and long combustion times. Whereas for large SRM boosters, operating in atmosphere, it does not represent a strong limit to obtain high performance, for upper stage SRMs it brings to relevant losses in the speci c impulse and, hence, less e cient design of the solid rocket motor due to the nozzle throat erosion e ects on both the operative pressure and speci c impulse. This paper discusses the e ects on the performance of an upper stage SRM of di erent kinds of aluminized propellants, compared to the baseline propellant HTPB 1912. The reference con guration is Ze ro 9A, third stage of the European launcher VEGA, recently quali ed with its rst maiden ight. The analysis is performed with the use of the complete coupling of the following models: a 3D grain burnback model, GREG, a full Navier-Stokes simulation of the nozzle throat erosion and a Q1D model of the SRM internal ballistic.

Performance prediction for oblique detonation wave engines (odwe)

Abstract The aim of this paper is to present a mathematical model to predict the overall performance of an oblique detonation wave engine (ODWE). The model of the propulsive system accounts for the four main components of a vehicle propelled by an ODWE, the air intake, a mixing device, the ODW-based combustor and a supersonic nozzle. The combustion modeling of the ODW accounts explicitly for the finite-rate kinetics of the combustible mixture as opposed to the simpler models adopted in the previous studies which are based either on modified Rankine–Hugoniot relations with a prescribed heat addition or on the assumption of CJ equilibrium conditions behind the detonation wave. All the relevant performance parameters of the engine can be estimated together with a first guess of the geometry of the vehicle. Therefore, the model can be easily incorporated into a more global optimization procedure involving the vehicle weights and the overall mission profile.

Two approaches for condensed-phase modeling in solid rocket motor flows

Modeling of the condensed phase in a solid rocket motor engine is typically accomplished via a two-fluid Eulerian approach or a direct Lagrangian approach. Each approach has its advantages and intrinsic disadvantages in terms of describing a polydispersed population of aluminum particles while it burns and convects within the carrier flow. A more unconventional approach is the Population Balance Equation (PBE) approach which solves a convection equation for a number density field, representative of the particulate phase. In the most general case the PBE is an integro-differential equation and can account for aerodynamic drag on particles, their combustion, breakage and agglomeration, via representative constitutive models. Here we will describe the PBE approach and will adopt it to simulate the aluminum particulate phase in a solid rocket engine. The results will be compared to those yielded by a more conventional Lagrangian approach. While the Lagrangian approach is spatially 3-dimensional, the PBE approach will adopt a quasi 1-dimensional assumption, leaving the extra two dimensions available for ”internal” particle coordinates such as particle radius and velocity. The characterization of the two-phase flow in a heterogeneous solid-propellant rocket chamber and nozzle is crucial in ballistic/performance predictions, aeroacoustic studies, erosion analyses, slag accumulation rate estimates, predictions of thermal loads, plume analyses etc. In particular, aluminum particles initially embedded within the binder and injected in the flow during the burning of the grain, undergo mechanical and chemical interactions with the flow itself, and constitute a principal component of the condensed phase. Among the numerous techniques used to model the solid phase a Lagrangian approach 2,3,7 - coupled to an Eulerian formalism for the continuous phase - is possibly the most widely accepted. In the latter, also known as a ’discrete element’ model, the kinematics of each particle is solved in parallel with the fluid flow by integrating a large system of ODE’s. Such formulation has the advantage of attempting a direct numerical simulation of the two-phase flow thereby avoiding the requirement of any additional constitutive laws for the dispersed phase. Typically in such context only larger particles are modeled via the Lagrangian setting, whereas the very small particles (aluminum oxide smoke) are modeled as a continuum . 3,7 The individual motion of the large particles is tracked by integrating their momentum equation which couples to the continuous phase through an aerodynamic drag term evaluated from the fluid field properties at the particle location. Similarly, the combustion of aluminum particles is modeled through burn rate relations which depend both on the particle and on the surrounding fluid field states. Complete two-way coupling between solid and gas phase is achieved by ad-hoc source terms in the gas phase equations supplying the continuous phase with mass and energy from the condensed phase. The combustion process also produces

Numerical Simulation of High Speed Reactive Flows with Adaptive Mesh Refinement

The adaptive mesh refinement technique proposed by the authors [13] is applied to the solution of the unsteady, ID, reactive Euler equations. Special emphasis is devoted to the analysis of perturbations caused by the nonlinear source terms at the junctions of grids with different resolution, and to the formulation of refinement criteria to monitor physical processes of different nature. Results for the initiation of a planar detonations will be presented and compared with those obtained with uniform grids.

Adaptive Mesh Refinement for Unsteady, Nonequilibrium, High Speed Flows

An adaptive mesh refinement technique using embedded patches is presented. The technique is especially oriented to the numerical simulation of high speed reactive flows in unsteady regimes. Structured, uniform, orthogonal subgrids of increasing resolution are obtained by means of a recursive, modular procedure. The main merits of the technique are (i) the low computational overhead for subgrid generation and management, (ii) the general formulation of the space-time conditions at the subgrid interfaces, (iii) a suitable formulation of the refinement criterium for unsteady problems, (iv) the straightforward applicability to multidimensional problems. The performances of the method are analyzed in onedimensional test cases with special attention to the accuracy obtainable in the description of propagation phenomena.

Fast moving sub-subsonic shocks in closed-end tubes

Abstract The problem of the detection, formation, and propagation of a fast moving shock in a wholly subsonic environment inside a closed-end tube is solved by a finite-difference integration method belonging to the family of shock-fitting techniques. The shock is fitted by locally combining the method of characteristics with the Rankine-Hugoniot relations, while the regions of smooth flow are solved via a λ scheme. A special attention is devoted to the problems related to shock detection and formation and to the treatment of the reflection of the shock at the boundaries. The pressure oscillation data demonstrate that the shock transition remains sharp and oscillation-free even after many wave cycles. The spectral analysis performed on these data shows that the energy distribution among modes is in good agreement with the analytical solution. These results point out the characteristics of low dissipation and dispersion of the method. For these reasons, the proposed integration technique is particularly well suited for the study of nonlinear axial mode instabilities (usually referred to as “triggered instabilities”) in combustion chambers.