Vladimir Roussinov

Rayleigh–Bénard flow of a rarefied gas and its attractors. I. Convection regime

In this paper we investigate the long time behavior (final state) of the Rayleigh–Benard (RB) flow of a rarefied monatomic gas for a set of the nondimensional Knudsen and Froude numbers in the intervals Kn∈[1.0×10−3,4×10−2], Fr∈[1.0×10−1,1.5×103]. For the most part of the computations the third nondimensional parameter, the ratio of the cold and hot wall temperatures is fixed to Tc/Th=0.1, corresponding to a large temperature difference (Th serves as reference temperature), for which the RB system is believed to reach most of the possible final states (attractors). The low Knudsen numbers allow the problem to be investigated numerically by using two completely different methods: direct simulation Monte Carlo (DSMC) method (molecular approach) and finite difference (FD) method (continuum approach based on the model of compressible viscous heat conducting gas with state-dependent transport coefficients). As a result the effect of rarefaction on the onset of convection in the two-dimensional case is studied ...

Stability loss and sensitivity in hollow fiber drawing

Stability of hollow fiber drawing is studied, based on the quasi‐one‐dimensional equations of thin film dynamics. It is shown that the model isothermal drawing process is unstable when the draw ratio E (that of output to input velocities) exceeds the critical value E*=20.22 when the viscosity force is dominating. Under stable regimes with E<E*, the response of the as‐drawn fiber to external perturbations is studied (the sensitivity problem). In unstable situations with E≳E*, onset of the so‐called draw resonance regime with self‐sustained oscillations is predicted by using numerical simulation. The effects of the inertia, gravity, surface tension, and gas pressure differential are considered.

Rayleigh–Bénard flow of a rarefied gas and its attractors. II. Chaotic and periodic convective regimes

This second part of our study of the Rayleigh–Benard flow of a rarefied gas deals with the analysis of the convection regimes for near-continuum conditions at a Knudsen number Kn=0.001. Here a set of qualitatively new regimes and final states have been found for different Froude (Fr) numbers and a fixed temperature ratio Tc/Th=0.1. In contrast to paper I [Phys. Fluids 14, 2255 (2002)] where we were mainly interested in the long time behavior, or, in other words, in the flow attractors, in this paper we extend the analysis of the most interesting cases to the full transition period from the initial state to the established flow regime. Two transient periods (to a chaotic attractor found for Fr=1.0 and to a stable two-roll configuration for Fr=2.0) are computed by using two different approaches: a direct simulation Monte Carlo method (molecular approach) and a finite difference method solving the system of equations for a compressible viscous heat-conducting gas (continuum approach). The comparison of the s...

Rayleigh–Bénard flow of a rarefied gas and its attractors. III. Three-dimensional computer simulations

We investigate the three-dimensional Rayleigh–Benard flow for a set of different Knudsen and Froude numbers at a fixed temperature ratio r=0.1, as well as for different aspect ratios. We observe a variety of stable vortex structures in the form of rolls, squares, and more complicated polygonal patterns. For sufficiently low Knudsen numbers, the existence of irregular regimes was confirmed. Two numerical approaches (the direct simulation Monte Carlo method and a finite-difference method for the Navier–Stokes equation) are used and the results show a satisfactory agreement.

Stationary Cylindrical Couette Flow at Different Temperature of Cylinders: the Local Knudsen Number Effect

The stationary Couette gas flow between rotating inner cylinder and stationary outer one is studied using DSMC method and numerical solution of a continual model. Different cases were studied by varying the temperature of the stationary cylinder and the Knudsen number. The continuum model results are obtained by setting a local value of Knudsen number in the corresponding first order slip boundary conditions. The comparison results showed that the slip boundary conditions with local Knudsen number included improves the accuracy of the continual model.

Cylindrical Couette Flow of Rarefied Gas: Comparison between Navier‐Stokes and DSMC Computations

The cylindrical Couette flow of a rarefied gas is studied in the case of two cylinders rotating with different velocities. Velocity, density and temperature profiles are investigated by the Direct Monte Carlo Simulation method and a numerical solution of the Navier‐Stokes equations for compressible flow is found. We have obtained numerical results for gas velocity and temperature at the walls for different values of rotation velocities of the cylinders. The gas lags or outstrips in comparison with the walls or it has the elastic rigid body behavior. These results are important for applications in non‐planar microfluidic problems. The results obtained by both methods are in a good agreement at the smaller Knudsen number Kn = 0.02 and differs notably at the larger Kn = 0.1.

Modeling of Cylindrical Couette Flow of Rarefied Gas. The Case of Rotating Outer Cylinder

The cylindrical Couette flow of a rarefied gas is studied in the case when the outer cylinder is rotating while the inner cylinder is at rest. Velocity, density and temperature profiles are investigated by a Direct Monte Carlo Simulation method and a numerical solution of the Navier‐Stokes equations for compressible flow is found. The results obtained by both methods are: in an excellent agreement at a small Knudsen number Kn = 0.02; in a satisfactory agreement at Kn = 0.1 and they vastly differs each other at a moderate Kn = 0.5. The comparison shows that the continuum approach can be used successfully for calculations of non‐planar isothermal rarefied gas flows at small Knudsen numbers Kn<0.1. These results are important for applications in non‐planar microfluidic problems.

The Attractors of the Rayleigh‐Bénard Flow of a Rarefied Gas

We have studied the Rayleigh‐Benard flow of a rarefied gas for Kn ∈ [1.0 × 10−3, 4 × 10−2] , Fr ∈ [1.0 × 10−1, 1.5 × 103] and a fixed temperature ratio Tc/Th = 0.1. The calculations are performed by both the DSMC and the numerical solution of Navier‐Stokes equations, with a remarkable agreement between the methods. We exhibit chaotic behavior and also a hysteresis cycle.