michael macrossan | The University of Queensland, Australia (original) (raw)

Papers by michael macrossan

Journal of Computational Physics, Apr 1, 2008

In a finite volume CFD method for unsteady flow fluxes of mass, momentum and energy are exchanged... more 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. In order 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 Pullin's Equilibrium Flux Method (EFM) [1] 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.

We consider some scale model experiments in which the forces on rowing blades were measured [Capl... more We consider some scale model experiments in which the forces on rowing blades were measured [Caplan and Gardner, J. Sport Sciences, 25(6), 653-650, 2007]. The experiments were conducted in a flume at a single flow velocity which corresponded to a Froude number, based on the depth dimension of the blade, very close to the critical value of unity. For real rowing, the blade moves at speeds corresponding to Froude numbers in the range of approximately 0.3 to 3.5. We use a computational fluid dynamics (CFD) analysis to investigate the Froude and Reynolds number effects on the forces on a flat plate 'blade', as well as the effects of the flume size relative to the model size in the experiments. We consider only one orientation of the plate to the flow velocity and we consider only idealized steady flow. We find that the flume in the experiments was probably too shallow, so that the measured force coefficients could be 6% higher than for rowing in deep water. Using a series of calculations for fluids with different densities, we show that the force coefficient is independent of the Reynolds number for the range of Reynolds numbers characteristic of real rowing, but is a strong function of the Froude number. There is a sudden decrease of some 30% in the force coefficient as the Froude number changes from sub-critical (less than 1) to super-critical (greater than 1). For Froude numbers greater than 2 the force coefficient increases steadily with Froude number.

Science & Engineering Faculty, 2006

We describe the X-series impulse facilities at The University of Queensland and show that they ca... more We describe the X-series impulse facilities at The University of Queensland and show that they can produce useful high speed flows of relevance to the study of high temperature radiating flow flields characteristic of atmospheric entry. Two modes of operation are discussed: (a) the expansion tube mode which is useful for subscale aerodynamic testing of vehicles and (b) the non-reflected shock tube mode which can be used to emulate the nonequilibrium radiating region immediately following the bow shock of a flight vehicle.

International Journal for Numerical Methods in Fluids, 2003

In the direct simulation Monte Carlo (DSMC) method for simulating rarefied gas flows, the velocit... more In the direct simulation Monte Carlo (DSMC) method for simulating rarefied gas flows, the velocities of simulator particles that cross a simulation boundary and enter the simulation space are typically generated using the acceptance-rejection method that samples the velocities from the theoretical velocity distribution. This paper analyses an alternative technique, where the velocities of entering particles are obtained by extending the simulation procedures to a region adjacent to the simulation space, and considering the movement of particles generated within that region during the simulation time step. The alternative method may be considered as a form of acceptance-rejection technique. The number flux obtained using the alternative method is slightly lower than the theoretical number flux, due to a depleted population of high velocities. Methods of obtaining the correct number flux are presented. The alternative method allows acceptance of all possible velocities, and represents an improvement over the acceptance-rejection method where some velocities are excluded to improve computational efficiency. For upstream boundaries in high speed flows, the alternative method is more computationally efficient than the acceptance-rejection method. However, for downstream boundaries, the alternative method is extremely inefficient. The alternative method, with the correct theoretical number flux, should therefore be used in favour of the acceptance-rejection method only for upstream boundaries in DSMC computations.

Nucleation and Atmospheric Aerosols, 2005

We test the recently developed macroscopic approach to modeling chemistry in DSMC, by simulating ... more We test the recently developed macroscopic approach to modeling chemistry in DSMC, by simulating the flow of rarefied dissociating nitrogen over a blunt cylinder. In this macroscopic method, chemical reactions are decoupled from the collision routine. Molecules are chosen to undergo dissociation at each time step, after the collisions are calculated. The required number of reaction events is calculated from macroscopic reaction rate expressions with macroscopic information taken from the time-averaged cell properties. One advantage of this method is that "state-of-the-art" macroscopic information about reaction rates can be used directly in DSMC in the same way as in continuum codes. Hybrid Navier-Stokes/DSMC codes can therefore easily use the same chemical models in both rarefied and continuum flow regions. Here we show that the macroscopic method can capture dissociation-vibration (DV) coupling, which is an important effect in vibrationally cold blunt body flows because it results in increased surface heat fluxes. We use the macroscopic method with Park's two-temperature rate model, often used in continuum studies, to capture DV coupling in DSMC. This produces a flowfield in reasonable agreement with that calculated using the conventional collision-based threshold line dissociation model.

Physics of Fluids, Sep 24, 2003

Mott-Smith's approximate theory of plane 1D shock structure (Phys. Rev., 82, 885-92, 1951; Phys. ... more Mott-Smith's approximate theory of plane 1D shock structure (Phys. Rev., 82, 885-92, 1951; Phys. Rev., 5, 1325-36, 1962) suggests, for any intermolecular potential, the average number of collisions undergone by a molecule as it cross the shock quickly approaches a limit as the Mach number increases. We check this with DSMC calculations and show that it can be used to estimate the gas viscosity at high temperatures from measurements of shock thickness. We consider a monatomic gas (γ = 5/3) for five different collision models and hence five different viscosity laws µ = µ (T). The collision models are: the variable hard sphere, σ ∝ 1/g 2υ , with three values of υ; the generalized hard sphere; and the Maitland-Smith potential. For shock Mach numbers M 1 4.48, all these collision models predict a shock thickness ∆ = 11.0λ s , where λ s is a suitably defined 'shock length scale', with a scatter ≈ 2.5% (2 standard deviations). This shock length depends on the upstream flow speed, downstream density and a collision cross-section derived from the viscosity of the gas at a temperature T g , characteristic of the collisions at relative speed g = u 1 − u 2 between upstream and downstream molecules. Using ∆ = 11λ s and the experimental measurements of shock thickness in argon given by Alsmeyer (J. Fluid Mech. 74, 498-513, 1976), we estimate the viscosity of argon at high values of T g. These estimated values agree with the viscosity of argon recommended by the CRC Handbook of Chemistry and Physics (2001) at T ≈ 1, 500 K. For T 2, 000 K, for which there appears to be no reliable direct measurements of viscosity, our estimated values lie between the extrapolated values recommended by the CRC Handbook and those predicted by the simple power law µ = µ ref (T /T ref) 0.72 , with T ref = 300 K and µ ref = 2.283 × 10 −5 Pa.s. Taking the error in the experimental measurements of ∆ as the scatter in the results of Alsmeyer (± 2%), we estimate the uncertainty in the viscosity deduced from the shock thickness measurements as less than ± 5%. To this accuracy, our results agree with the power law predictions and disagree with the CRC Handbook values, for T 3,000 K.

The Total Collision Energy (TCE) model is used to simulate chemical reactions in the Direct Simul... more The Total Collision Energy (TCE) model is used to simulate chemical reactions in the Direct Simulation Monte Carlo method. Colliding particle pairs with total collision energy (translational plus internal energy) greater than an activation energy are accepted for reaction with a probability which depends on the amount of the collision energy in excess of the activation energy. Constants in the probability function are adjusted to match experimentally determined rates in an Arrhenius form under thermal equilibrium conditions. The model thus attempts to extrapolate equilibrium reaction rates to non-equilibrium conditions by using microscopic based information from colliding particle pairs. However, the number of active 'degrees of freedom' (DOF) in the vibrational energy mode contributing to the total collision energy must be specified for each collision pair; various methods have been proposed for this. It is shown that the different calculation methods can alter the equilibrium reaction rate returned by the TCE model, and can have significant effects throughout non-equilibrium flowfields. If we assume, as is usual, that all of the internal energy is available for the reaction, we consider that the most consistent and physically intuitive approach is to determine the number of active DOF from the local macroscopic temperatures in the cell.

The complexity of the collision term in the Boltzmann equation for rarefied flows is such that it... more The complexity of the collision term in the Boltzmann equation for rarefied flows is such that it is often replaced by a model equation such as the Bhatnagar-Gross-Krook (BGK) model [5]. To solve the BGK equation numerically a number of different advection equations-one for each molecular velocity range which is included in the numerical method-must be solved in parallel. For a fixed time step, the CFL numbers for these different advection equations can differ by an order of magnitude or more. For a feasible time-step, and a reasonable computational time, it becomes necessary to solve at least some of these linear advection equations with a CFL number much greater than 1. It is the purpose of this work to provide the groundwork for solving the BGK method by presenting a fast, accurate solution to the linear advection equation that is stable for CFL numbers greater than 1.

A new arbitrarily high order method for the solution of the model Boltzmann equation for micro-ch... more A new arbitrarily high order method for the solution of the model Boltzmann equation for micro-channel flows in the transitional regime is presented. The Bhattnagar-Gross-Krook approximation of the Boltzmann collision integral is implemented, with Shakhov's modification, and the resulting system of equations solved by a discrete ordinate method. The method approximates velocity space using a truncated Hermite polynomial expansion of arbitrary order and performs the associated integration by Gauss-Hermite quadrature. This approach conserves mass, momentum and energy during relaxation of the discretised velocity space towards equilibrium. Physical space is discretised by discontinuous Legendre polynomial expansions with both the spatial representation and conservative flux calculation being of arbitrary order. Owing to the high order spatial representation of the discretised velocity space the BGK-Shakhov relaxation process is carried out in a 'continuous in space' manner. New high order boundary conditions of the inviscid slip wall and no-slip wall are implemented. A new fully diffuse reflection boundary condition, built on the high order spatial information available in the method, is also proposed. Results are presented for low speed planar Couette flow and non-linear channel flow.

Journal of Computational Physics, Aug 1, 2016

The 'Restricted Collision List' (RCL) method for speeding up the calculation of DSMC Vari... more The 'Restricted Collision List' (RCL) method for speeding up the calculation of DSMC Variable Soft Sphere collisions, with Borgnakke-Larsen (BL) energy exchange, is presented. The method cuts down considerably on the number of random collision parameters which must be calculated (deflection and azimuthal angles, and the BL energy exchange factors). A relatively short list of these parameters is generated and the parameters required in any cell are selected from this list. The list is regenerated at intervals approximately equal to the smallest mean collision time in the flow, and the chance of any particle re-using the same collision parameters in two successive collisions is negligible. The results using this method are indistinguishable from those obtained with standard DSMC. The CPU time saving depends on how much of a DSMC calculation is devoted to collisions and how much is devoted to other tasks, such as moving particles and calculating particle interactions with flow boundaries. For 1-dimensional calculations of flow in a tube, the new method saves 20% of the CPU time per collision for VSS scattering with no energy exchange. With RCL applied to rotational energy exchange, the CPU saving can be greater; for small values of the rotational collision number, for which most collisions involve some rotational energy exchange, the CPU may be reduced by 50% or more.

AIP Conference Proceedings, 2012

Results obtained by numerically solving the discrete Boltzmann equation, using the Bhattnagar-Gro... more Results obtained by numerically solving the discrete Boltzmann equation, using the Bhattnagar-Gross-Krook (BGK) relaxation approximation with Shakhov target distribution, are compared to those obtained by the Direct Simulation Monte-Carlo (DSMC) method. The relaxation dynamics of the BGK-Shakhov system are also compared to DSMC results. The method is of arbitrary order with velocity and physical space discretized according to truncated series of Hermite and Legendre polynomials respectively. The polynomial based physical space discretization is shown to allow the implementation of the relaxation operator in a continuous-in-space manner. Results show a high degree of similarity with DSMC solutions with little numerical dissipation and no statistical scatter.

We present a new scheme for modeling rotational energy exchange with the direct simulation Monte ... more We present a new scheme for modeling rotational energy exchange with the direct simulation Monte Carlo (DSMC) method. The new scheme is fundamentally different from conventional Borgnakke-Larsen (BL) procedures, in which energy exchange is performed at the time of collision. In the new scheme, all collisions are performed elastically. Rotational energy exchanged is performed after the collision routine, in an independent step. The rotational energy of all particles in each cell is adjusted by a factor, to satisfy the desired macroscopic relaxation behavior. To conserve total energy in a cell, the thermal velocities of all particles in the cell are adjusted. DSMC calculations of shock structure show that the new scheme gives results in reasonable agreement with those provided by conventional BL procedures. The new scheme has a potential advantage over BL procedures - it is easy to use with any DSMC collision model.

In high altitude flight the average spacing between the molecules of the flow gas is not negligib... more In high altitude flight the average spacing between the molecules of the flow gas is not negligible compared to a typical dimension of the flow field. In this case, the gas does not behave like a continuum and its discrete particle nature must be considered. The continuum assumption ‘breaks down ’ and the Navier-Stokes equations can, in theory, no longer be shown to be valid, particularly for high speed flight. The fundamental equation describing the flow at the particle level is the Boltzmann equation, from which the Euler equations, the Navier-Stokes equations and more accurate Burnett equations may be derived under various assumptions. Various scaling parameters have been suggested to identify the regimes in which these different equations are valid, ranging from the Knudsen number, Tsein’s (1946) parameter Cheng’s rarefaction parameter (1961), Bird’s breakdown parameter (1971), and a form of the viscous interaction parameter derived from shock-boundary layer theory. All these de...

The Direct Simulation Monte Carlo (DSMC) method is used to simulate the flow of rarefied gases. I... more 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 r...

Regardless of the angle the oar makes to the forward direction during a rowing stroke, there is n... more Regardless of the angle the oar makes to the forward direction during a rowing stroke, there is negligible loss of energy between the oar and the gate. However, it does not follow from this that there is no decrease in oar efficiency at the extreme oar angles necessary for a very long catch. The loss of energy from the oar occurs, not at the gate, but at the blade. The water which is moved by the blade, against the water reaction force on the blade, absorbs mechanical energy from the oar. Calculations, experimental data and “on-water” measurements of rowing show that the energy efficiency of the oar is generally lowest for oar angles less than 55 degrees to the boat-forward direction (i.e. in the early part of the stroke).

Journal of Computational Physics, Apr 1, 2008

Science & Engineering Faculty, 2006

International Journal for Numerical Methods in Fluids, 2003

Nucleation and Atmospheric Aerosols, 2005

Physics of Fluids, Sep 24, 2003

Journal of Computational Physics, Aug 1, 2016

AIP Conference Proceedings, 2012