Force-driven compressible plane Poiseuille flow by Onsager-Burnett equations

Abstract

The purpose of this work is to evaluate the recently derived Onsager-Burnett (OBurnett) equations [N. Singh, R. S. Jadhav, and A. Agrawal, “Derivation of stable Burnett equations for rarefied gas flows,” Phys. Rev. E 96, 013106 (2017)] for force-driven compressible plane Poiseuille flow. This classical internal flow problem depicts several non-equilibrium phenomena, for instance, non-constant pressure profile in the transverse direction and tangential heat flux, which are not captured by the classical Navier-Stokes-Fourier equations. The results of OBurnett equations for conserved and non-conserved variables are validated against the existing direct simulation Monte Carlo (DSMC) and molecular dynamics (MD) simulation results. These results suggest that the OBurnett equations are able to predict most of the variables well with respect to DSMC and MD simulation results. We find that the OBurnett equations predict a strictly monotonic pressure profile, in contrast to the bimodal profile predicted by the DSMC results and the conventional Burnett equations, but in agreement with the molecular dynamics simulation results. The equations also recover the non-zero tangential heat flux but fail to capture the peculiar temperature dip at the center, owing to its second order accuracy. These results suggest that the evaluated equations are accurate in predicting the non-equilibrium phenomena observed in the rarefied gas flows for the case considered.

Derivation of extended-OBurnett and super-OBurnett equations and their analytical solution to plane Poiseuille flow at non-zero Knudsen number

“…Additionally, a novel collision scheme, known as the simplified Bernoulli trial, has been introduced in Stefanov (2011). The DSMC technique has also been employed in Gavasane et al (2011Gavasane et al ( , 2017, Jadhav et al (2017), Shah, Agrawal & Bhandarkar (2018a, Shah et al (2018b) andJadhav, Gavasane & for different microchannel flow and shock wave problems. That is why we also resort to DSMC data to validate the analytical solution obtained above.…”

“…(2011, 2017), Jadhav et al. (2017), Shah, Agrawal & Bhandarkar (2018 a ), Shah et al. (2018 b ) and Jadhav, Gavasane & Agrawal (2021) for different microchannel flow and shock wave problems.…”

“…Readers are directed to the above-mentioned studies for a more detailed exploration of the differences and advantages of the OBurnett equations relative to the Burnett equations. This set of equations has been validated for several canonical problems involving non-equilibrium flow conditions (Jadhav, Singh & Agrawal 2017; Singh et al. 2017; Jadhav & Agrawal 2020 b , 2021; Yadav & Agrawal 2021); a consolidated account of the different validation cases can be found in Jadhav et al.…”

“…This set of equations has been validated for several canonical problems involving non-equilibrium flow conditions Singh et al 2017;Jadhav & Agrawal 2020b; a consolidated account of the different validation cases can be found in Jadhav et al (2023). Specifically, the validation of the OBurnett equations for the force-driven Poiseuille flow problem (Jadhav et al 2017) is particularly relevant in the context of wall-bounded flows in the late-slip/transition regime. However, as is the case with a large portion of the existing literature employing Burnett-type higher-order transport equations for this problem, Jadhav et al (2017) employ numerical methods to solve the resulting system of equations.…”

“…Specifically, the validation of the OBurnett equations for the force-driven Poiseuille flow problem (Jadhav et al 2017) is particularly relevant in the context of wall-bounded flows in the late-slip/transition regime. However, as is the case with a large portion of the existing literature employing Burnett-type higher-order transport equations for this problem, Jadhav et al (2017) employ numerical methods to solve the resulting system of equations.…”