Viscous drag in steady state gas flow between rotating cylinders

We consider the rarefied cylindrical Couette flow. The inner cylinder rotates at the constant angular velocity and the outer cylinder is at rest. We investigate the momentum and energy fluxes transferred to the cylinders and show that this flow is fundamentally different from the rarefied Couette flow with the fixed inner cylinder. For the free molecular mode, we derive the explicit analytical expressions for the fluxes. We find that momentum and energy fluxes transferred to the inner cylinder have a maximum with respect to the ratio of radii. The influence of the rarefaction on the energy and momentum transfer in the transitional regime is studied using the direct simulation Monte Carlo method. The shear stress and energy flux transferred to the inner cylinder increase with an increase in the angular velocity of the inner cylinder rather than tend to zero at high velocities, as in the Couette flow with the fixed inner cylinder with an increase in the angular velocity of the outer cylinder. In the transitional mode, for the flow with the fixed outer cylinder, the absolute value of the normal momentum flux transferred to the inner cylinder has a minimum as a function of the angular velocity of the inner cylinder. On the other hand, in the Couette flow with the fixed inner cylinder, this flux tends to zero at high angular velocities of the outer cylinder. The fundamental difference between these two flows at high velocities is associated with the degree of influence of dissipation on the flows.

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Rarefied cylindrical Couette problem: Effect of a very sharp transition from weakly rarefied flow near the inner cylinder to free molecular flow at very low average Knudsen numbers

Abramov,

Butkovskii,

Buzykin

2024

Physics of Fluids

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We consider the rarefied cylindrical Couette flow. The outer cylinder rotates at a constant angular velocity, and the inner one is at rest. The Knudsen number, calculated from the average gas density, is much less than one. To find the fluid dynamic variables and fluxes, the direct simulation Monte Carlo method (DSMC) is used. We find the effect of a very sharp decrease in shear stress and energy fluxes transferred to the cylinders if the Knudsen number is sufficiently low and the rotation speed of the outer cylinder is sufficiently high. We show that when the average Knudsen number is sufficiently low, if the velocity is initially high and increases slightly further, the weakly rarefied flow regime near the inner cylinder transitions abruptly to a free molecular flow regime. Thus, the flow abruptly separates from the inner cylinder. We compare the fluxes obtained by solving the Navier–Stokes equations and by the DSMC method. It turns out that the solutions of the Navier–Stokes equations with slip boundary conditions also change abruptly at certain critical values, and these critical values are close to the appropriate DSMC values.

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Viscous drag in steady state gas flow between rotating cylinders

Cited by 3 publications

References 17 publications

Transient heat transfer in viscous rarefied gas between concentric cylinders. Effect of curvature

Transient heat transfer in viscous rarefied gas between concentric cylinders. Effect of curvature

Cylindrical Couette flow with fixed outer cylinder: Rarefied effects

Rarefied cylindrical Couette problem: Effect of a very sharp transition from weakly rarefied flow near the inner cylinder to free molecular flow at very low average Knudsen numbers

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