Modeling of carbon dioxide condensation in the high pressure flows using the statistical BGK approach

Abstract

In this work, we propose a new heat accommodation model to simulate freely expanding homogeneous condensation flows of gaseous carbon dioxide using a new approach, the statistical Bhatnagar-Gross-Krook method. The motivation for the present work comes from the earlier work of Li et al. [J. Phys. Chem. 114, 5276 (2010)] in which condensation models were proposed and used in the direct simulation Monte Carlo method to simulate the flow of carbon dioxide from supersonic expansions of small nozzles into near-vacuum conditions. Simulations conducted for stagnation pressures of one and three bar were compared with the measurements of gas and cluster number densities, cluster size, and carbon dioxide rotational temperature obtained by Ramos et al. [Phys. Rev. A 72, 3204 (2005)]. Due to the high computational cost of direct simulation Monte Carlo method, comparison between simulations and data could only be performed for these stagnation pressures, with good agreement obtained beyond the condensation onset point, in the farfield. As the stagnation pressure increases, the degree of condensation also increases; therefore, to improve the modeling of condensation onset, one must be able to simulate higher stagnation pressures. In simulations of an expanding flow of argon through a nozzle, Kumar et al. [AIAA J. 48, 1531 (2010)] found that the statistical Bhatnagar-Gross-Krook method provides the same accuracy as direct simulation Monte Carlo method, but, at one half of the computational cost. In this work, the statistical Bhatnagar-Gross-Krook method was modified to account for internal degrees of freedom for multi-species polyatomic gases. With the computational approach in hand, we developed and tested a new heat accommodation model for a polyatomic system to properly account for the heat release of condensation. We then developed condensation models in the framework of the statistical Bhatnagar-Gross-Krook method. Simulations were found to agree well with the experiment for all stagnation pressure cases (1-5 bar), validating the accuracy of the Bhatnagar-Gross-Krook based condensation model in capturing the physics of condensation.

Simulation of homogeneous condensation of small polyatomic systems in high pressure supersonic nozzle flows using Bhatnagar–Gross–Krook model

“…18,19 In particular, 19 it was found that the sticking coefficient for the small polyatomic system of water was invariant for cluster sizes above 10 and for temperatures of the order of 100 K. Once the cluster growth rate is estimated in a cell, the rest of the procedure is straight-forward. For each cluster growth event, a cluster of size j is randomly chosen from the cell and increased in size to j + 1.…”

“…Therefore, the postcollisional velocities and temperatures of cluster can be calculated using Eqs. (18) and (19). From the evaporation rate relationship, Eq.…”

An adaptive procedure for the numerical parameters of a particle simulation

“…As previously stated, most DSMC simulations of axisymmetric flows are at least conducted with radially varying weights [2,8,9] with values that increase with the distance to the centerline. This is performed to increase particle counts close to the centerline while preventing an excessive number of particles in cells further removed from it as their volume scales with y.…”

“…These drawbacks inherent to the DSMC method have led to a number of modifications to the basic DSMC algorithm that are in ubiquitous use today. The first is the use of spatially varying weights, particularly for axisymmetric simulations, such as in (amongst many others) [7,8] where the cell volume scales with the distance to the centerline, that allows enough particles to be present close to the centerline while reducing their number further away from it. The second improvement is the use of a spatially varying time step, and an adaptive procedure to calculate the optimum time step field as in, e.g., [9][10][11].…”

BGK and MD Simulations of H2O Supersonic Condensed Jets

“…The BGK model assumes that sufficient collisions have taken place in the flow such that individual collisions do not have to be simulated because the flow relaxes to a known velocity distribution. Kumar et al 11 developed a comprehensive homogeneous condensation model to simulate supersonic expansion of CO 2 from small nozzles into near-vacuum conditions in the context of the BGK approach taking into the account of nucleation, cluster-monomer sticking and non-sticking collisions, cluster evaporation, and cluster-cluster coalescence. A new model was proposed to redistribute the heat released in a BGK or DSMC (for low enough pressures) computational cell due to the exothermic processes of nucleation and cluster growth by monomer addition.…”