Hybrid Continuum-Rarefied Solver

Graduate Students: Sruti Chigullapalli

Non-equilibrium flows are encountered in high-altitude flight, vacuum technology and in microscale devices. Moreover further development of high-frequency microsystems such as resonators, RF MEMS, microturbines and pulsed-detonation microengines require improved understanding of unsteady gas dynamics at the microscale. Accurate computational simulation of such flows demands new approaches beyond the conventional formulations based on either continuum or rarefied gas dynamics methods. This is due to the breakdown of the continuum hypothesis in the presence of significant non-equilibrium and rarefaction because of large gradients and small scales, respectively. Hybrid continuum-rarefied simulations, in turn, require a continuum breakdown parameter for switching between the two types of governing equations. In the past a number of breakdown parameters have been proposed such as the gradient-length Knudsen number and the viscous dissipation energy parameter.Though such parameters provide a usable indication of the onset of rarefaction, they do not have a direct relation to the physics of non-equilibrium on the level of the velocity distribution function.

Figure 1: Peaks in entropy generation Figure 2: Non-dimensional x-velocity and entropy contours

rate in a 1D shock tube of length 1m for a planar shock tube at P1/P4=10.

The main goal of this research is the investigation and application of coupling schemes and continuum breakdown parameters within a hybrid Boltzmann Kinetic/Navier-Stokes framework.

Entropy generation rate, being a high-order moment of the velocity distribution function, is extremely sensitive to the flow gradients. The use of entropy considerations in rarefied flow simulations has been investigated for normal shocks, Riemann and two-dimensional shock tube problems. The numerical method consists of a finite volume discretization in physical space and discrete velocity method in the velocity space. Figure 1 shows the instantaneous locations of shock, contact discontinuity and rarefaction wave in a 1D shock tube as identified by the increase in entropy generation. The maps of x-velocity and entropy in a 2D shock tube of width h are shown in Fig. 2 at two instants of time. As time progresses, the extent of the expanding zone of non-equilibrium can be found from the entropy profiles.

REFERENCES:

1) S. Chigullapalli, A. Venkattraman, M.S. Ivanov, and A.A. Alexeenko, "Entropy Considerations in Numerical Simulation of Non-Equilibrium Rarefied Flows”,accepted to Journal of Computational Physics, November 2009.

2) S. Chigullapalli, A. Venkattraman, A. Alexeenko, and M.S. Ivanov, "Non-Equilibrium Flow Modeling Using High-Order Schemes for the Boltzmann Model Equations", AIAA Paper 2008-3929, 40th Thermophysics Conference, Seattle, Washington, June 23-26, 2008.

3) S. Chigullapalli, A. Venkattraman, and A. Alexeenko, " Modeling of Viscous Shock Tube Using ES-BGK Model Kinetic Equations ", AIAA-2009-1317, 47th AIAA Aerospace Sciences Meeting and Exhibit, Orlando, Florida in Jan 2009.