Rarefied gas flow in a rectangular enclosure induced by non-isothermal walls

Abstract

The flow of a rarefied gas in a rectangular enclosure due to the non-isothermal walls with no synergetic contributions from external force fields is investigated. The top and bottom walls are maintained at constant but different temperatures and along the lateral walls a linear temperature profile is assumed. Modeling is based on the direct numerical solution of the Shakhov kinetic equation and the Direct Simulation Monte Carlo (DSMC) method. Solving the problem both deterministically and stochastically allows a systematic comparison and verification of the results as well as the exploitation of the numerical advantages of each approach in the investigation of the involved flow and heat transfer phenomena. The thermally induced flow is simulated in terms of three dimensionless parameters characterizing the problem, namely, the reference Knudsen number, the temperature ratio of the bottom over the top plates, and the enclosure aspect ratio. Their effect on the flow configuration and bulk quantities is thoroughly examined. Along the side walls, the gas flows at small Knudsen numbers from cold-to-hot, while as the Knudsen number is increased the gas flows from hot-to-cold and the thermally induced flow configuration becomes more complex. These flow patterns with the hot-to-cold flow to be extended to the whole length of the non-isothermal side walls may exist even at small temperature differences and then, they are enhanced as the temperature difference between the top and bottom plates is increased. The cavity aspect ratio also influences this flow configuration and the hot-to-cold flow is becoming more dominant as the depth compared to the width of the cavity is increased. To further analyze the flow patterns a novel solution decomposition into ballistic and collision parts is introduced. This is achieved by accordingly modifying the indexing process of the typical DSMC algorithm. The contribution of each part of the solution is separately examined and a physical interpretation of the flow configuration, including the hot-to-cold flow close to the side walls, in the whole range of the Knudsen number is provided.

Predicting the Knudsen paradox in long capillaries by decomposing the flow into ballistic and collision parts

“…The authors claim that at small pressures the rate of reduction of the first flow is larger than the rate of increase of the second one and therefore the total flow must initially decrease with pressure. A further increase in pressure stimulates the overall drift velocity that in turn, from that point on, monotonically increases the entire flow through the tube.Recently, the concept of decomposing the solution into two parts, as described above, has been accordingly implemented in the typical DSMC algorithm by introducing a suitable particle indexation process [21,22]. In the present work the same DSMC decomposition is implemented to investigate the Knudsen paradox in a precise manner with quantitative arguments.…”

“…Recently, the concept of decomposing the solution into two parts, as described above, has been accordingly implemented in the typical DSMC algorithm by introducing a suitable particle indexation process [21,22]. In the present work the same DSMC decomposition is implemented to investigate the Knudsen paradox in a precise manner with quantitative arguments.…”

Thermally induced rarefied gas flow in a three-dimensional enclosure with square cross-section

“…The recent study in Ref. [20] shows that the overall agreement between the flow fields predicted using the Shakhov model equation and the DSMC method of for the thermally driven flow can be quite good even the temperature field varies significantly in space. Details of the numerical method will be explained in the following section.…”

“…The Shakhov model equation is appropriate for thermally driven flow as has been demonstrated by numerous applications in the literature, such as Refs. [19,20,[32][33][34], to name a few. It should be noted that to match the realistic gas viscosity [35,36] in a wide temperature range, the power-law index ω will vary significantly.…”

Continuum Analysis of Rarefaction Effects on a Thermally Induced Gas Flow

“…Streamlines and temperature contours comparison for 0 = 0.9 ⁄ and = 0.1 between R13 (right) and DSMC method[Vargas et al 2014] (left) adapted to the Vargas's problem (vertical, top-to-down, linearly heated cavity).…”