Session G37: Rarefield Fluids

On a Criterion for the Significance of Statistical Fluctuations in Rarefied Flows

Near the slip regime, the microscopic behavior within a gas becomes increasingly significant. As the characteristic length nears the mean free path, the flow shows great deviations from its equilibrium distribution and molecular-kinetic methods are employed. For rarefied gases, deterministic approaches are often limited by the required sample size to obtain accurate averages. We describe the influence of statistical fluctuations on models in the slip regime. Using numerical simulations, we demonstrate a relation between fluctuations in macroscopic flow properties and the number of simulated particles. The intersection between statistical fluctuations and the continuum limit is discussed and its implications on current algorithms are assessed. In particular, the break-down of statistical stability prior to reaching the continuum assumption is highlighted. We propose a criterion to predict the onset of statistical fluctuations in a dilute gas. Our derivations are supported by particle-based simulations, such as Direct Simulation Monte Carlo and molecular dynamics.

    

Enforcing Detailed Balance in the Borgnakke-Larsen Redistribution Method

It is often observed that Direct Simulation Monte Carlo (DSMC) simulations either fail or succeed to reach and maintain equilibrium depending on the choice of temperature dependent relaxation models for internal energy modes, with no clear consensus in the literature as to why. This work alleviates the ambiguity regarding the root cause of these failures by presenting a rigorous theoretical derivation of the requirement for satisfying detailed balance within the Borgnakke-Larsen method for energy redistribution, which is often used to implement relaxation models within DSMC. Specifically, it is shown that the Borgnakke-Larsen method maintains detailed balance if and only if the probability of internal-energy exchange during a collision depends only on collision invariants (e.g., total energy). The consequences of this result are explored in the context of several published relaxation models and definitions of relaxation temperature. The developed theory can be used when implementing existing or new relaxation models and will ensure detailed balance is satisfied.

    

Modeling of the pore diameter dependence of water evaporation from porous array membranes

The miniaturization and integration of power semiconductor devices necessitate cooling technologies capable of handling high heat fluxes beyond 1 kW/cm². To tackle this problem, cooling devices utilizing evaporation from porous membranes attract considerable attention. To optimize such devices, understanding non-equilibrium gas flows that determine mass flux is of prime importance. In addition, we should consider heat and mass transfer in liquid and solid phases. In this study, we show a simulation that combines the low-variance deviational simulation Monte Carlo method for the gas phase analysis and a continuum-based approach for the solid- and liquid-phase analyses. We connect the gas and liquid phase analyses by considering mass and energy conservation at the liquid-vapor interface. Using the coupled-simulation technique, we examine how liquid convection in porous membranes affects the evaporative heat flux. For various pore diameters, we quantify the evaporative heat flux as a function of the difference between the saturation vapor pressure and the pressure at the outer edge of the Knudsen layer. We construct simple models to predict the evaporative heat flux for two limiting cases, where the pore diameter is much smaller or larger than the mean free path of gas molecules.   

Computational Modeling of Dusty Gas Flows in DSMC-DEM Framework

In any space exploration mission during planetary descent, when a lander approaches towards the surface of an extraterrestrial body, the expanded supersonic plume from the nozzle exhaust of positioning rockets impinges on the planetary body’s soil or regolith, and interaction between plume and surface occurs. This high-speed and high-temperature plume produces a shock, fluidizes, and ejects granular particles from a surface. This creates one or more craters, and as a result, soil particles gain momentum. Consequently, this ejected matter would disperse dust and larger debris. The particles that are so dispersed have the potential to do severe damage. The present work aims to develop a high-fidelity simulation framework capable of modeling dusty gas flows encountered during plume surface interactions. The research work aims at performing dusty gas flow dynamics using a particle-based Lagrangian-Lagrangian computational framework. The solver that needs to be developed for dusty gas flows is by coupling the in-house DSMC flow solver with the in-house DEM solver.

    

Stability Analysis of a Rarefied Flow Around a Re-entry Vehicle Model

Flow and linear flow instability over the suborbital shuttle model designed by the AzimUTBM team is studied. The vehicle features an elongated fuselage and curved wingtips, and is placed at 30-degree angle of attack to the oncoming flow, density and temperature of which are chosen to model Mach 6 flight at an altitude of 120km. Rarefaction effects are captured by the Direct Simulation Monte Carlo (DSMC) approach, as implemented in the Sandia open source code SPARTA. Grid convergence is examined by performing simulation on two grids of different density, respectively run on 16384 and 32768 cores of the Archer2 supercomputing facility. Steady states are obtained after about 24 hours of wall clock time and about 200k samples are taken to reduce statistical noise and obtain fields of sufficient quality for stability analysis to be performed. The residuals algorithm and dynamic mode decomposition, both employed during linear decay, have revealed the leading global flow eigenmodes, which will be discussed in detail at the conference.