Numerical study of nonequilibrium gas flow in a microchannel with a ratchet surface

The nonequilibrium gas flow in a two-dimensional microchannel with a ratchet surface and a moving wall is investigated numerically with a kinetic method [Guo et al., Phys. Rev. E 91, 033313 (2015)]. The presence of periodic asymmetrical ratchet structures on the bottom wall of the channel and the temperature difference between the walls of the channel result in a thermally induced flow, and hence a tangential propelling force on the wall. Such thermally induced propelling mechanism can be utilized as a model heat engine. In this article, the relations between the propelling force and the top wall moving velocity are obtained by solving the Boltzmann equation with the Shakhov model deterministically in a wide range of Knudsen numbers. The flow fields at both the static wall state and the critical state at which the thermally induced force cancels the drag force due to the active motion of the top wall are analyzed. A counterintuitive relation between the flow direction and the shear force is observed in the highly rarefied condition. The output power and thermal efficiency of the system working as a model heat engine are analyzed based on the momentum and energy transfer between the walls. The effects of Knudsen number, temperature difference, and geometric configurations are investigated. Guidance for improving the mechanical performance is discussed.

Figure 1

(a) Channel with ratchet surface. The top and bottom walls are maintained at different temperatures. (b) One segment (in the dashed line rectangle) of the periodical structures. The thick blue and red solid lines with hatched patterns represent diffusive solid walls maintained at different temperatures $T_b$ and $T_t$, respectively. The thick dashed green lines represent specularly reflective solid walls.

Figure 2

Isotherms and streamlines of the validation case ($\text{Kn}=0.1,U_w=0.01$). (a) Results obtained by the DUGKS. (b) Results obtained by DSMC method.

Figure 3

Shear stress $p_{xy}$ and normal heat flux $q_y$ along the top wall for the validation case ($\text{Kn}=0.1,U_w=0.01$) predicted by both DSMC method and the DUGKS.

Figure 4

Temperature $T$ and horizontal velocity $u_x$ profiles across the throat of the channel for the validation case ($\text{Kn}=0.1,U_w=0.01$) predicted by both DSMC method and the DUGKS.

Figure 5

Tangential force acted on the top wall against wall velocity at different Knudsen numbers ranging from 0.01 to 5.

Figure 6

Tangential force acted on the top wall against wall velocity for the case of $H=0.9$ and $B=0.1$ at $\text{Kn}=1$ and $\text{Kn}=10$.

Figure 7

Tangential force on a static wall (SWF in the body text) and shear-free wall velocity (SFV in the body text) at various Knudsen numbers.

Figure 8

Velocity fields with static top wall configuration, i.e., $U_w=0$ at different Knudsen numbers. (a) $\text{Kn}=0.01$. (b) $\text{Kn}=0.1$. (c) $\text{Kn}=1$. (d) $\text{Kn}=10$. Data have been interpolated to structured grids for better presentation.

Figure 9

Contours of the distribution function at three points near the top wall [marked in Fig. 8] when $\text{Kn}=10$.

Figure 10

Results of the case of $\text{Kn}=10, U_w=0$ using DSMC method. (a) Shear stress distribution at the top wall (the DUGKS solution has been included). (b) Velocity fields.

Figure 11

Velocity field at shear-free state, i.e., when $F=0$ at different Knudsen numbers. (a) $\text{Kn}=0.01$. (b) $\text{Kn}=0.1$. (c) $\text{Kn}=1$. (d) $\text{Kn}=10$. Data have been interpolated to structured grids for better presentation.

Figure 12

Static wall tangential force (a) and shear-free wall velocity (b) against temperature difference.

Figure 13

Temperature field and streamlines at two temperature configurations. (a) Hot-bottom case ($T_t=0.75, T_b=1.25$). (b) Hot-top case ($T_t=1.25, T_b=0.75$). In both cases, $\text{Kn}=0.1$ and $U_w=0$.

Figure 14

Shear stress along the top wall at two different temperature configurations. In the hot-bottom case, $T_t=0.75$ and $T_b=1.25$. In the hot-top case, $T_t=1.25$ and $T_b=0.75$. In both cases, $\text{Kn}=0.1$ and $U_w=0$.

Figure 15

Static wall tangential force (a) and shear-free velocity wall velocity (b) as functions of $H/L$ at various Knudsen numbers.

Figure 16

Static wall tangential force (a) and shear-free velocity wall velocity (b) as functions of $B/H$ at various Knudsen numbers.

Figure 17

Dependence of the power output on the wall velocity at various Knudsen numbers.

Figure 18

Maximum power output and thermal efficiency.