Madhat Abdel-Jawad

New calibration technique for multiple-component stress wave force balances

The measurement of forces in hypervelocity expansion tubes is not possible using conventional techniques. The stress wave force balance technique can be applied in expansion tubes to measure forces despite the short test times involved. This article presents a new calibration technique for multiple-component stress wave force balances where an impulse response created using a load distribution is required and no orthogonal surfaces on the model exist. This new technique relies on the tensorial superposition of single-component impulse responses analogous to the vectorial superposition of the calibration loads. The example presented here is that of a scale model of the Mars Pathfinder, but the technique is applicable to any geometry and may be useful for cases where orthogonal loads cannot be applied.

Effects of direction decoupling in flux calculation in finite volume solvers

In a finite volume CFD method for unsteady flow fluxes of mass, momentum and energy are exchanged between cells over a series of small time steps. The conventional approach, which we will refer to as direction decoupling, is to estimate fluxes across interfaces in a regular array of cells by using a one-dimensional flux expression based on the component of flow velocity normal to the interface between cells. This means that fluxes cannot be exchanged between diagonally adjacent cells since they share no cell interface, even if the local flow conditions dictate that the fluxes should flow diagonally. The direction decoupling imposed by the numerical method requires that the fluxes reach a diagonally adjacent cell in two time-steps. To evaluate the effects of this direction decoupling, we examine two numerical methods which differ only in that one uses direction decoupling while the other does not. We examine a generalized form of Pullins equilibrium flux method (EFM) [D.I. Pullin, Direct simulation methods for compressible ideal gas flow, J. Comput. Phys. 34 (1980) 231-244] which we have called the true direction equilibrium flux method (TDEFM). The TDEFM fluxes, derived from kinetic theory, flow not only between cells sharing an interface, but ultimately to any cell in the grid. TDEFM is used here to simulate a blast wave and an imploding flow problem on a structured rectangular mesh and is compared with results from direction decoupled EFM. Since both EFM and TDEFM are identical in the low CFL number limit, differences between the results demonstrate the detrimental effect of direction decoupling. Differences resulting from direction decoupling are also shown in the simulation of hypersonic flow over a rectangular body. The computational cost of allowing the EFM fluxes to flow in the correct directions on the grid is minimal.

Stability Analysis of Beagle2 in the Free-Molecular and Transition Regimes

We present the results of a series of Direct Simulation Monte Carlo (DSMC) calculations to determine the aerodynamic coefficients of the Beagle2 aeroshell at selected points along its planned trajectory through the upper Martian atmosphere. The flow around the aeroshell can be characterized as free-molecular on first entry to the atmosphere, then transitional as Beagle2 descends towards the lower atmosphere. The aerodynamic coefficients were used as inputs for a dynamic stability analysis of the capsule over the first 25.4 seconds of its flight through the upper atmosphere. In the transition regime the stabilizing moments of the pressure forces were within 0.5% of the destabilizing moments due to the skin friction forces, leaving only a very small net stabilizing moment. The high spin rate of the aeroshell counteracted not only the destabilizing moments in the free molecular regime but also counteracted the small stabilizing moments in the transition regime. It is unlikely that the Beagle2 could have achieved its target zero angle of attack condition at time = 13.2s, or any subsequent time up to the 25.4s analyzed. Although our analysis does not extend to Beagle2’s path through the lower atmosphere, we suggest that the probable departure from zero angle of attack when Beagle2 entered the lower Martian atmosphere is a likely cause of the loss of the spacecraft.

Nonequilibrium reaction rates in the macroscopic chemistry method for direct simulation Monte Carlo calculations

The Direct Simulation Monte Carlo (DSMC) method is used to simulate the flow of rarefied gases. In the Macroscopic Chemistry Method (MCM) for DSMC, chemical reaction rates calculated from local macroscopic flow properties are enforced in each cell. Unlike the standard total collision energy (TCE) chemistry model for DSMC, the new method is not restricted to an Arrhenius form of the reaction rate coefficient, nor is it restricted to a collision cross-section which yields a simple power-law viscosity. For reaction rates of interest in aerospace applications, chemically reacting collisions are generally infrequent events and, as such, local equilibrium conditions are established before a significant number of chemical reactions occur. Hence, the reaction rates which have been used in MCM have been calculated from the reaction rate data which are expected to be correct only for conditions of thermal equilibrium. Here we consider artificially high reaction rates so that the fraction of reacting collisions is not small and propose a simple method of estimating the rates of chemical reactions which can be used in the Macroscopic Chemistry Method in both equilibrium and non-equilibrium conditions. Two tests are presented: (1) The dissociation rates under conditions of thermal non-equilibrium are determined from a zero-dimensional Monte-Carlo sampling procedure which simulates ‘intra-modal’ non-equilibrium; that is, equilibrium distributions in each of the translational, rotational and vibrational modes but with different temperatures for each mode; (2) The 2-D hypersonic flow of molecular oxygen over a vertical plate at Mach 30 is calculated. In both cases the new method produces results in close agreement with those given by the standard TCE model in the same highly nonequilibrium conditions. We conclude that the general method of estimating the non-equilibrium reaction rate is a simple means by which information contained within non-equilibrium distribution functions predicted by the DSMC method can be included in the Macroscopic Chemistry Method.

Multiple reactions and trace species in the Direct Simulation Monte Carlo Macroscopic Chemistry Method

The Macroscopic Chemistry Method is a technique for modeling chemical reactions in the Direct Simulation Monte Carlo (DSMC) method. The approach differs from conventional DSMC chemistry methods in that the change in the number of each species over a time step is calculated from the overall macroscopic cell parameters, rather than on a collision pair basis. The Macroscopic Chemistry Method (MCM) can be applied in flows where the collision rate is highly nonequilibrium and has previously been applied to model dissociation-recombination reactions of a symmetrical diatomic gas. Here we propose a procedure for applying MCM to a multiple species reaction set that includes exchange reactions, as well as a method by which trace species can be modeled without the need for variable weighting factors. The procedure is tested in constant volume reservoir relaxation simulations of a high-temperature gas and quasi-one-dimensional expansion of a high-speed, high-temperature gas. Initial compositions are chosen to resemb...

Energetics for gas separation in microporous membranes

Gas separation by inorganic membranes has proven to be effective at laboratory scales, but is now facing challenges in developing for industrial scales. A particular type of inorganic membrane is the class of porous molecular sieves formed by sol-gel method deposited on ceramic substrates. These molecular sieve silica (MSS) membranes are ideally suited to high temperature He, H2, CO2 and CH4 separation, but one of the major understandings lacking is energy modelling enabling industrial level simulations for technology potential forecasting. In this paper we report experimental results of high quality membranes and use as a basis for predicting the exergetic efficiency of mixture separation. A specifically exergetic analysis was derived and successfully implemented. The more selective two-step membrane offered better exergetic efficiency for widely different gas molecule pair sizes like He/CH4, but lower improvement to less different pair sizes like H2/CH4. For instance, at 10 bar pressure difference, He/CH4 exergetic efficiency was around 54% while being around 35% for H2/CH4. Likewise, the higher CO2/CH4 selectivity of the single-step membrane leads to better exergetic efficiency prediction. This technique has therefore provided a working method to evaluate membrane unit performance for optimal industrial outcomes. Permselectivities were shown to correlate to exergetic efficiencies leading to a practical analysis of membrane performance.

Sonic line location in reacting flows

Superorbital re-entry vehicles involve blunt configurations, and are designed to operate near to the limits of stability in order to produce the best possible aerodynamic characteristics. The location of the sonic line is as an important factor in determining windward pressure distributions, and changes to that location have been correlated to potential instabilities for several flight conditions. The chemical changes associated with high speed flight cause perturbations to the local temperature and sound speed in the shock layer, leading to a shift in the sonic line. This paper presents an analysis based on Newtonian surface pressure and thin shock layer assumptions which enables the location of the sonic line to be approximated for any given post-shock gas composition and any blunt cone geometry. We outline two approaches for the calculation of the location of the sonic line. The first relies on a prescribed chemical composition, while the second is a full non-equilibrium calculation of the shocklayer. The primary determining parameters on shock layer Mach number for the prescribed chemistry model are seen to be the flow turning angle, and the distribution of the associated transfer of kinetic energy to thermal and chemical forms. This enables flight regimes in which there may be a high sensitivity of sonic line location to changes in velocity and altitude to be easily identified, allowing more detailed numerical and experimental studies to focus on conditions which are likely to produce instabilities. The analysis is presented for a binary dissociating gas (Nitrogen) but has general applicability to more complex reacting mechanisms and angles of attack.