Investigation of the rarefied gas flow around a circular cylinder in stationary and oscillatory regimes

Numerically, on the basis of the Krook kinetic equation, the rarefied gas flow around a circular cylinder is investigated in stationary and oscillatory regimes. The flows around a rotating cylinder and a cylinder with a nonuniformly heated surface are considered. The Knudsen numbers at which the lift force acting on the rotating cylinder changes sign are calculated. It is shown that at low Knudsen numbers a lift force acts on the nonuniformly heated cylinder.     

Effect of the accommodation coefficient on transfer processes in a supersonic rarefied gas flow around a transversely aligned cylinder

A supersonic flow around a cylinder is studied by the direct statistical Monte Carlo method in a wide range of rarefaction: from regimes close to continuum to free-molecular flow. The effect of the accommodation coefficient on the flow near the cylinder and on heat transfer between the gas and the cylinder is examined. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 3, pp. 64–72, May–June, 2008.     

A multi-dimensional time-marching method of characteristics for viscous and heat-conducting flows

Summary A numerical scheme is presented which employs the characteristic surfaces in space-time for solving Navier-Stokes equations for compressible fluid flow. We consider the general case of a three-dimensional flow, a simplification of which yields the equations of the two-dimensional case. Emphasis is put on the method itself. We apply it to simulate a laminar hypersonic flow around a circular cylinder of a five-components gas mixture of nitrogen and oxygen with thermally perfect constituents and at chemical nonequilibrium. First, the partial differential equations are transformed into a standard form with directional derivatives, enabling to attain the compatibility conditions, including the viscosity terms. These conditions are discretized by approximating their integrals along the corresponding characteristic surfaces. The result is an explicit time-marching numerical scheme. Using a grid fitted between the shock and the cylinder, and starting from roughly estimated initial conditions, a steady solution is searched. A comparison is made with the solution obtained under the assumption of a perfect gas. Received 6 April 1999; accepted for publication 13 May 1999     

Effect of a Dispersed Admixture on the Flow Pattern and Heat Transfer in a Supersonic Dusty-Gas Flow Around a Cylinder

A mathematical model of two-phase (gas-solid particle) flow which takes into account particle-particle collisions and the feedback effect of the admixture on the gas parameters is proposed. The dispersed phase is described by a kinetic equation of the Boltzmann type and the carrier gas by modified Navier-Stokes equations. Using this model, a supersonic uniform dusty-gas flow past a cylinder is calculated. The fields of the macroparameters of the admixture and the carrier medium are obtained. The dependence of the heat transfer at the stagnation point on the relative particle size and the free-stream admixture concentration is studied in detail. The ranges of these parameters on which particle collisions and the feedback effect of the admixture on the carrier-gas flow are important are found.     

Kinetic analysis of longitudinal Couette flow between coaxial cylinders

On the basis of a model kinetic equation, the rarefied gas flow between coaxial circular cylinders, of which the outer one is at rest while the inner one travels along its symmetry axis at a constant velocity, is studied. The problem is solved numerically in both the linear and nonlinear formulations by an implicit conservative method of second-order accuracy. The effect of the rarefaction, the cylinder radius ratio, and the inner cylinder velocity on the flow parameters is investigated. The limits of applicability of the linearized kinetic equation are established.     

Direct Statistical Simulation of a Supersonic Flow of a Binary Mixture of Rarefied Gases around a Transversely Positioned Cylinder

A supersonic flow of a binary mixture of gases in a wide range of rarefaction (from a flow with a Knudsen number K _n = 0.1 to a free-molecular flow) around a cylinder is studied by means of direct statistical Monte Carlo simulations (DSMC method). The influence of a small fraction of heavy particles in a light gas flow on the region of significant nonequilibrium near the cylinder and on the heat flux is considered.__________Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 5, pp. 53–59, September–October, 2005.     

Experimental study of heat and mass transfer from a horizontal cylinder in downward air-water mist flow with blockage effect

An experimental study was made on convective heat and mass transfer from a horizontal heated cylinder in a downward flow of air-water mist at a blockage ratio of 0.4. The measured local heat transfer coefficients agree fairly well with the authors' numerical solutions obtained previously for the front surface of a cylinder over the ranges mass flow ratio 0–4.5×10⁻², a temperature difference between the cylinder and air 10–43 K, gas Reynolds number (7.9–23)×10³, Rosin-Rammler size parameter 105–168 μm, and dispersion parameter 3.4–3.7. Heat transfer augmentation, two-pahse to single-phase of greater than 19 was attained at the forward stagnation point. For heat transfer in the rear part of the cylinder, an empirical formula is derived by taking into account the dimensionless governing variables, that is, coolant-feed and evaporation parameters.     

Physicochemical Model of Hypersonic Rarefied Gas Flow past Bodies

The effect of the internal molecular degrees of freedom on the flow field and heat transfer in hypersonic rarefied gas flow past a cylinder or sphere is investigated using the direct statistical simulation (Monte-Carlo) method. The variable-diameter rough spherical molecule model (VRS-model) is generalized to include the case of energy exchange between the translational and vibrational degrees of freedom. The interaction between diatomic molecules with allowance for vibrational degrees of freedom is simulated as the interaction of classical or quantum-mechanical harmonic and anharmonic oscillators in the external force approximation. A model of the dissociation of a diatomic gas is proposed.     

Calculating liquid droplets settling on a cylinder in gas-liquid spray flow

Adding atomized liquid to air flowing around a cylinder gives an appreciable increase in heat transfer by forming a liquid film on the cylinder surface. The heat transfer coefficient depends upon the amount of liquid forming the film, which is limited by two phenomena: droplet deflection from the liquid film on the surface and droplets not striking the cylinder. This paper presents a method of calculating the quantity of liquid droplets settling on a cylinder surface in a gas-liquid spray flow. A coefficient $\text{k}$, the volume ratio of the liquid entering the film to the amount of liquid directed at the cylinder, is introduced. $\text{k}$ values were calculated by means of numerical computation and the theory verified experimentally. The calculation method permits estimation of the dependence of the amount of liquid settling on a cylinder on the droplet diameter distribution parameters and on the linear gas velocity     

On the orbital motion of a rotating inner cylinder in annular flow

In this paper, numerical calculations have been performed to analyse the influence of the orbital motion of an inner cylinder on annular flow and the forces exerted by the fluid on the inner cylinder when it is rotating eccentrically. The flow considered is fully developed laminar flow driven by axial pressure gradient. It is shown that the drag of the annular flow decreases initially and then increases with the enhancement of orbital motion, when it has the same direction as the inner cylinder rotation. If the eccentricity and rotation speed of the inner cylinder keep unchanged (with respect to the absolute frame of reference), and the orbital motion is strong enough that the azimuthal component (with respect to the orbit of the orbital motion) of the flow‐induced force on the inner cylinder goes to zero, the flow drag nearly reaches its minimum value. When only an external torque is imposed to drive the eccentric rotation of the inner cylinder, orbital motion may occur and, in general, has the same direction as the inner cylinder rotation. Under this condition, whether the inner cylinder can have a steady motion state with force equilibrium, and even what type of motion state it can have, is related to the linear density of the inner cylinder. Copyright © 2006 John Wiley & Sons, Ltd.     

Free convection of a dusty‐gas flow along a semi‐infinite vertical cylinder

An analysis is performed to study the free convection of a dusty‐gas flow along a semi‐infinite isothermal vertical cylinder. The governing equations of the flow problem are transformed into non‐dimensional form and the resulting nonlinear, coupled parabolic partial differential equations have been solved numerically using an implicit finite difference scheme of Crank–Nicholson type. The flow variables such as gas–velocity, dust‐particle velocity and temperature, shearing stress and heat transfer coefficients are calculated numerically for various parameters occurring in the problem. It is observed that due to the presence of dust particles, the gas velocity is found to decrease. Copyright © 2009 John Wiley & Sons, Ltd.     

侧柱与串列双柱绕流之间的干扰

本文给出了关于串列双柱与创柱间流动干扰的实验研究结果。当三个圆柱排成等边三角形并靠得很近时，由于三圆柱间强烈的缝隙流动，大大地改变了绕流其中的串列双圆柱的流态。特别，当三圆柱中心距等于二倍圆柱直径时，在串列双柱的前、后柱之间形成了强烈的偏斜的缝隙流，出现了独特的压力分布以及要比单柱高出三倍以上的旋涡脱落频率。     

Investigation of slow monatomic gas flows past a circular cylinder

Slow low-Knudsen-number monatomic-gas flow past a circular cylinder is numerically investigated on the basis of a model kinetic equation. The gas flow is described by a new kinetic equation, from which the continuum equations for slow nonisothermal gas flows containing temperature stresses follow rigorously. It is shown that a closed convective-flow region arises near a nonuniformly heated cylinder in a slow gas flow if the flow impinges on the hot side of its surface. Using a new model of the Boltzmann equation makes it possible to study gas flows both in continuum and rarefied flow regimes.     

Direct Monte Carlo Simulation of Transverse Supersonic Rarefied Gas Flow around a Cylinder

Supersonic flow around a cylinder is investigated using the direct simulation Monte Carlo method over a wide rarefaction range: from the Knudsen number Kn = 0.1 to free-molecular flow. The effect of the cylinder temperature on the region of sharp nonequilibrium near the cylinder and the heat flux is studied.     

应用小干扰柱体控制角区马蹄涡结构的实验研究

本文提出一种简单的抑制和控制角区马蹄涡的被动控制方法.即在角区平板上游放置一个远小于主柱体的小干扰柱体,用其产生的弱马蹄涡来抑制和控制角区的马蹄涡结构.目的是使角区原来的马蹄涡结构由强变为弱、由大变为小、由多变为少、由非定常变为定常,以获得减小冲刷、抑制湍流、降低噪声、避免振动的工程效果.作者在风洞中采用烟线法和激光片光流动显示的方法开展研究,实验表明,在平板上游适当位置放置小干扰柱体的确可以有效抑制和控制角区马蹄涡结构.实验发现,当小干扰柱体放置在原角区马蹄涡生成区时,其抑制和控制效果最佳;当小干扰柱体放置在上游区或下游区时,控制效果不好.本文讨论了小干扰柱体控制角区马蹄涡的机理.此外,实验还研究了小干扰柱体相对尺度和截面形状对角区马蹄涡结构抑制和控制的影响.     

The direct simulation Monte Carlo method using unstructured adaptive mesh and its application

The implementation of an adaptive mesh‐embedding (h‐refinement) scheme using unstructured grid in two‐dimensional direct simulation Monte Carlo (DSMC) method is reported. In this technique, local isotropic refinement is used to introduce new mesh where the local cell Knudsen number is less than some preset value. This simple scheme, however, has several severe consequences affecting the performance of the DSMC method. Thus, we have applied a technique to remove the hanging node, by introducing the an‐isotropic refinement in the interfacial cells between refined and non‐refined cells. Not only does this remedy increase a negligible amount of work, but it also removes all the difficulties presented in the originals scheme. We have tested the proposed scheme for argon gas in a high‐speed driven cavity flow. The results show an improved flow resolution as compared with that of un‐adaptive mesh. Finally, we have used triangular adaptive mesh to compute a near‐continuum gas flow, a hypersonic flow over a cylinder. The results show fairly good agreement with previous studies. In summary, the proposed simple mesh adaptation is very useful in computing rarefied gas flows, which involve both complicated geometry and highly non‐uniform density variations throughout the flow field. Copyright © 2002 John Wiley & Sons, Ltd.     

非定常不可压N-S方程的最小二乘算子分裂有限元法数值求解

采用最小二乘算子分裂有限元法求解非定常不可压N-S(Navier-Stokes)方程,即在每个时间层上采用算子分裂法将N-S方程分裂成扩散项和对流项,这样既能考虑对流占优特点又能顾及方程的扩散性质。扩散项是一个抛物型方程,时间离散采用向后差分格式,空间离散采用标准Galerkin有限元法。对流项的时间项采用后向差分格式,非线性部分用牛顿法进行线性化处理,再用最小二乘有限元法进行空间离散,得到对称正定的代数方程组系数矩阵。采用Re=1000的方腔流对该算法的有效性进行检验,表明其具有较高的精度,能够很好地捕捉流场中的涡结构。同时,对圆柱层流绕流进行了数值研究,通过流线图、压力场、阻力系数、升力系数及斯特劳哈数等结果的分析与对比,表明本文算法对于模拟圆柱层流绕流是准确和可靠的。     

Heat transfer promotion with a cylinder array located near the wall

Heat transfer from a flat plate has been investigated when a cylinder array is located near the wall. Each cylinder in the cylinder array was positioned normal to the flow direction and parallel to the flat plate surface. Measurements of the heat transfer coefficient and the optimum value for the cylinder pitch and spacing between the cylinders and the flat plate surface were obtained. A comparison of the heat transfer mechanism in this flow system with that obtained previously for the case when a single cylinder is inserted in the boundary layer was made.     

Gas flow in rotary kilns

This paper describes an experimental investigation on the flow characteristics within a rotating cylinder containing a rolling bed of sand. The axis of the cylinder was horizontal and there was no axial bulk flow of particles. The velocity field of the gas flowing through the cylinder was measured by hot-wire anemometry. The measurements indicate that the velocity field is asymmetric with respect to a diameter perpendicular to the granular bed. CFD calculations confirm this finding. The gas velocity profiles are crucial in determining heat transfer from gas to solid.     

High-order overset grid method for detecting particle impaction on a cylinder in a cross flow

An overset grid method was developed to investigate the interaction between a particle-laden flow and a circular cylinder. The method is implemented in the Pencil Code, a high-order finite-difference code for compressible flow simulation. High-order summation-by-parts operators were used at the cylinder boundary, and both bi-linear Lagrangian and bi-quadratic spline interpolation were used to communicate between the Cartesian background grid and the body-conformal cylindrical grid. The performance of the overset grid method was assessed to benchmark cases of steady and unsteady flows past a cylinder. Results show high-order accuracy and good agreement to the literature. Particle-laden flow simulations were performed, with inertial point particles impacting on a cylinder. The simulations reproduced results from the literature at a significantly reduced cost. Further, an investigation into blockage effects on particle impaction revealing that the previously published DNS data is less accurate than assumed for particles with very small Stokes numbers.