Effect of the gas flow geometry and turbulence on the hydrodynamic drag of a body in the flow

The effect of the incoming flow geometry on the hydrodynamic drag of a body is investigated in a numerical experiment simulating a free gas flow past a sphere as well as flows in cylindrical tubes of various radii, in a confuser, and a diffuser. The results of calculations lead to the conclusion that the confinement of the flow by the tube walls, its contraction and expansion may change the hydrodynamic force and the drag acting on the body insignificantly (not more than by 30%). This cannot explain the early drag crisis, in which the values of these quantities decrease by 4–7 times for Reynolds numbers on the order of 100. This phenomenon is explained theoretically by the effect of strong turbulence of the incoming flow to the body.     

Calculation of the flow about a sphere and the drag of the sphere under laminar and strongly turbulent conditions

To investigate the influence of a strongly turbulent incoming flow on the hydrodynamic drag of a body and occurrence of the early crisis of drag, a numerical experiment is conducted in which a free gas flow about a sphere is simulated for two cases, namely, for a laminar flow and for a strongly turbulent flow. Turbulence is simulated by assuming a high kinematic coefficient of turbulent viscosity. Calculation data lead us to conclude that the early crisis of drag at Reynolds numbers near 100, which shows up as a considerable (four-to sevenfold) decrease in the hydrodynamic force and the drag coefficient of the body, can be explained by the strong turbulence of the incoming flow.     

等离子体气动激励机理数值研究

基于介质阻挡与准直流电弧放电的物理过程, 分析了它们的气动激励机理, 建立了各自的气动激励模型, 并分别研究了它们对低速和超声速流动的激励效果. 结果显示: 介质挡板放电等离子体气动激励机理是改变了连续流体中的三种力, 即由牛顿内摩擦引起的剪切应力、由电动力学引起的体积力及由压力突变引起的冲击力, 其中基于电动力学的体积力效应占主导地位; 临近空间环境中体积力的作用效果更强, 诱导速度更大; 超声速来流下准直流电弧放电气动激励机理主要是等离子体的热阻塞效应, 本文所建立的爆炸丝传热模型可以用于仿真其控制激波的过程; 热电弧对于超声速来流而言就像一个具有一定斜坡角度的虚拟突起, 可用于高超声速飞行器前体激波的控制.     

Pressure variation by a magnetohydrodynamic method at the surface of a body placed in a supersonic flow

This study is aimed at investigating the possibility of pressure variation near the surface of a body placed in a supersonic flow as a model of an aerofoil or the nose of an aircraft by organizing a surface gas discharge in a magnetic field transverse to the flow. The flow parameters and pressure are mainly affected by the ponderomotive Lorentz force acting on the gas in the direction orthogonal to the direction of the organized discharge current and leading to the removal or compression of the gas at the surface of the body and, hence, a variation of pressure. Experimental data on the visualization of the flow and on the pressure at the surface of the body are considered for various configurations of the current and intensities of the gas discharge and magnetic field; it is demonstrated that such configurations of the current and magnetic field near the surface of the body under investigation can be organized in such a way that the pressure at the front part as well as the upper and lower surfaces of the body under investigation can be increased or decreased, thus changing the aerodynamic drag and the aerofoil lift. Such a magnetohydrodynamic control over aerodynamic parameters of the aircraft can be used during takeoff and landing as well as during steady-state flight and also during the entrance into dense atmospheric layers. This will considerably reduce the thermal load on the surface of the body in the flow.     

Mechanism of Electromagnetic Flow Control Enhanced by Electro-Discharge in Water

Pulsed discharge utilized to achieve large current density in the electromagnetic flow control is numerically studied. A mathematic discharge model is established to calculate the plasma channel, and an actuator is designed to generate the Lorentz force in the micro plasma channel. During the discharge process, the resistance in the channel decreases rapidly and a large current density appears between the discharge electrodes. After the actuator is applied in the leading edge of a flat plate, the separation region and downstream turbulent boundary layer on the plate disappear. Meanwhile, a skin-friction drag force reduction is achieved.     

Drag and Lift Forces Acting on a Sphere in Shear Flow of Power-Law Fluid

Laminar flow of a power-law fluid over a sphere is considered for unbounded shear flow. The Navier–Stokes equations with power-law viscosity are solved numerically using an in-house developed CFD package. Vorticities structures downstream of particle are suppressed for powerlaw fluid. The shear rate influence on drag force is negligible for power index close to unit, and the drag force appreciably decreases with falling power index. For small Reynolds numbers, the lift force coefficient monotonically decreases against the power index and exhibits an opposite behavior for moderate values of Reynolds numbers. The results of the parametric studies are used to derive correlations for the drag force and to detect the hydrodynamic differences from uniform flow. The investigation parameters varied within the following ranges: power-law index 0.3 ≤ n ≤ 1, Reynolds number 0 < Re ≤ 150, and dimensionless shear rate 0.05 ≤ s ≤ 0.4.     

The influence of the thermal wake due to pulsating optical discharge on the aerodynamic-drag force

The influence of a thermal wake due to gas injection and due to a pulsating optical discharge (POD) on the aero-dynamic-drag force of a body in a supersonic air flow with Mach number M = 1.45 are experimentally examined. With the help of a single-component aerodynamic balance, the influence of the injected subsonic jet and the thermal wake produced by POD on the aerodynamic drag of a hemisphere-on-cylinder model was studied. It is shown that the observed aerodynamic-force reduction phenomenon can be made more pronounced by increasing the laser power and pulse repetition frequency, or by decreasing the distance between the model and the pulsating optical discharge. The maximum aerodynamic-force reduction (up to 15%) due to the thermal-wake action was observed at a maximum laser-radiation power of W = 2.3 kW and at a pulse rate of f = 90 kHz. The joint effect due to the argon jet and due to the POD caused an aerodynamic-drag force reduction reaching 30%.     

Dense granular flow around a penetrating object: experiment and hydrodynamic model

We present in this Letter experimental results on the bidimensional flow field around a cylinder penetrating into dense granular matter, together with drag force measurements. A hydrodynamic model based on extended kinetic theory for dense granular flow reproduces well the flow localization close to the cylinder and the corresponding scalings of the drag force, which is found to not depend on velocity, but linearly on the pressure and on the cylinder diameter and weakly on the grain size. Such a regime is found to be valid at a low enough "granular" Reynolds number.     

Incorporation of smooth spherical bodies in the Lattice Boltzmann method

A method to simulate bodies suspended in a Lattice Boltzmann solvent is proposed. It is based on a generalized reaction force that enforces no-slip boundary conditions at the fluid–body interface as the limiting case of an iterative procedure. A smooth version of the Heaviside function allows to treat spherical particles of arbitrary size and produces smooth hydrodynamic forces as particles move in the continuum. Numerical tests demonstrate the accuracy of the method in reproducing the hydrodynamic field around a single particle and the fluid-mediated forces between pairs of particles. The drag force experienced by a particle moving in a straight channel and at various Reynolds numbers is studied as a non-trivial testcase.     

Translational oscillations of a microsphere in superfluid helium

The translational motion of a microsphere (radius 100 μm) in liquid helium is investigated. The sphere is levitating inside a superconducting capacitor and oscillates about its equilibrium position. The velocity amplitude and the resonance frequency are measured as a function of driving force and temperature (0.35 K up to 2.2 K). By increasing the driving force we first find a linear regime (laminar flow) which changes abruptly into a nonlinear one (turbulent flow). For temperatures below 0.7 K the linear drag is given by ballistic roton and phonon scattering whereas for temperatures above 1.1 K the hydrodynamic force on the sphere is described by Stoke's solution. In the turbulent regime, above a temperature independent threshold velocity, we find the drag force to be given by turbulence in the superfluid component plus an essentially laminar drag by the normal component.     

Shape optimization towards stability in constrained hydrodynamic systems

Hydrodynamic stability plays a crucial role for many applications. Existing approaches focus on the dependence of the stability properties on control parameters such as the Reynolds or the Rayleigh number. In this paper we propose a numerical method which aims at solving shape optimization problems in the context of hydrodynamic stability. The considered approach allows to guarantee hydrodynamic stability by modifying parts of the underlying geometry within a certain flow regime. This leads to a formulation of a shape optimization problem with constraints on the eigenvalues related to the linearized Navier–Stokes equations. In that context the eigenvalue problem is generally non-symmetric and may involve complex eigenvalues. To validate the proposed numerical approach we consider the flow around a body in a channel. The shape of the body is parameterized and can be changed by means of a discrete number of design variables. It is our aim to find a design which minimizes the drag force and ensures at the same time hydrodynamic stability while keeping the volume of the body constant. The numerical results show that a transition from an unstable design to a stable one is attainable by considering an adequate change of the body shape. The resulting bodies are long and flat which corresponds to common intuition.     

确定分布的展向Lorentz力调制下的槽道湍流涡结构

采用直接数值模拟方法,对槽道湍流中确定分布的Lorentz力的流动控制与减阻问题进行研究.讨论了Lorentz力作用于槽道湍流后,流场的特性和涡结构的特性,并对此类Lorentz力对槽道湍流的控制与减阻机理进行了讨论.研究发现:1)Lorentz力诱导的层流流场壁面附近存在梯度极大的展向速度剪切层,该剪切层容易形成流向涡结构;2)在给定合适参数的确定分布的Lorentz力作用下,湍流流场仅剩周期分布的准流向涡;3)与未控制流场相比,控制后的流场中,准流向涡的抬升高度大大降低,从而减小猝发强度,使壁面阻力下降.     

Optimization of supersonic flows past thin bodies by using external effects on the flow

Problems of optimization of flows past a thin body of revolution and a slender profile at a small angle of attack in the presence of local energy release zones and an external force acting on the flow near the surface are considered. Analysis is based on an analytic theory of supersonic flow past thin bodies presented in previous papers. The following problems are considered: drag reduction of a thin body of revolution, lift force enhancement of a profile with infinite aspect ratio, attenuation of acoustic noise generated by supersonic flows past bodies.     

Numerical simulation of the sedimentation of a sphere in a sheared granular fluid: a granular Stokes experiment

We study, computationally, the sedimentation of a sphere of higher mass in a steady, gravity-driven granular flow of otherwise identical spheres, on a rough inclined plane. Taking a hydrodynamic approach at the scale of the particle, we find the drag force to be given by a modified Stokes law and the buoyancy force by the Archimedes principle, with excluded volume effects taken into account. We also find significant differences between the hydrodynamic case and the granular case, which are highlighted.     

Effect of acceleration by internal and external force fields on particle motion in intermediate regimes between the hydrodynamic and free-molecular limits

The kinetic theory of gases is applied to analyze slow translational motion of low-concentration particles driven by an external force in a homogeneous gas. The analysis takes into account the diffusion due to the difference in acceleration between particles and molecules in internal and external force fields. A general expression is derived for the particle drag force in hydrodynamic, free-molecular, and intermediate regimes. This expression reduces to a simple relation between the drag force and its values in the hydrodynamic and free-molecular limits and the force of intermolecular interaction between particles and gas molecules. In the case of spherically symmetric potential of interaction between the particle and molecules, the drag force is the harmonic mean of its limit values.     

Dimension reduction method for ODE fluid models

We develop a new dimension reduction method for large size systems of ordinary differential equations (ODEs) obtained from a discretization of partial differential equations of viscous single and multiphase fluid flow. The method is also applicable to other large-size classical particle systems with negligibly small variations of particle concentration. We propose a new computational closure for mesoscale balance equations based on numerical iterative deconvolution. To illustrate the computational advantages of the proposed reduction method, we use it to solve a system of smoothed particle hydrodynamic ODEs describing single-phase and two-phase layered Poiseuille flows driven by uniform and periodic (in space) body forces. For the single-phase Poiseuille flow driven by the uniform force, the coarse solution was obtained with the zero-order deconvolution. For the single-phase flow driven by the periodic body force and for the two-phase flows, the higher-order (the first- and second-order) deconvolutions were necessary to obtain a sufficiently accurate solution.     

Mechanism of controlling turbulent channel flow with the effect of spanwise Lorentz force distribution

A direct numerical simulation(DNS) is performed to investigate the control effect and mechanism of turbulent channel flow with the distribution of spanwise Lorentz force. A sinusoidal distribution of constant spanwise Lorentz force is selected, of which the control effects, such as flow characters, mean Reynolds stress, and drag reductions, at different parameters of amplitude A and wave number k_x are discussed. The results indicate that the control effects vary with the parameter A and k_x. With the increase of A, the drag reduction rate D_r first increases and then decreases rapidly at low k_x,and slowly at high k_x. The low drag reduction(or even drag increase) is due to a weak suppression or even the enhancements of the random velocity fluctuation and mean Reynolds stress. The efficient drag reduction is due to the quasi-streamwise vortex structure induced by Lorentz force, which contributes to suppressing the random velocity fluctuation and mean Reynolds stress, and the negative vorticity improves the distribution of streamwise velocity. Therefore, the optimal control effect with a drag reduction of up to 58% can be obtained.     

Submicron particle removal in post-oxide chemical–mechanical planarization (CMP) cleaning

Particle removal models for soft-pad buffing (the second-step polishing with DI water) and mechanical brush-cleaning processes are proposed and the removal forces are evaluated and compared with the average particle adhesion force to the oxide wafer surface resulting from the primary polishing (the first-step polishing with slurry). The hydrodynamic force due to the fluid flow is too small to remove slurry particles by itself and particles are most likely removed from the surfaces by the pad or brush asperity contact forces and the hydrodynamic drag force together. This conclusion is consistent with the experimental observations. Received: 25 January 1999 / Accepted: 18 May 1999 / Published online: 8 September 1999     

Turbulent Boundary Layer Control via a Streamwise Travelling Wave Induced by an External Force

Turbulent boundary layer control via a streamwise travelling wave is investigated based on direct numerical simulation of an incompressible turbulent channel flow. The streamwise travelling wave is induced on one side wall of the channel by a spanwise external force, e.g., Lorenz force, which is con~ned in the viscous sublayer. As the control strategy used in this study has never been examined, we pay our attention to its efficiency of drag control. It is revealed that the propagating direction of the travelling wave, i.e., the downstream or upstream propagating direction with respect to the streamwise flow, has an important role on the drag control, leading to a significant drag reduction or enhancement for the parameters considered. The coherent structures of turbulent boundary layer are altered and the underlying mechanisms are analysed. The results obtained provide physical insight into the understanding of turbulent boundary layer control.     

Drag reduction in turbulent channel flow using bidirectional wavy Lorentz force

Turbulent control and drag reduction in a channel flow via a bidirectional traveling wave induced by spanwise oscillating Lorentz force have been investigated in the paper. The results based on the direct numerical simulation (DNS) indicate that the bidirectional wavy Lorentz force with appropriate control parameters can result in a regular decline of near-wall streaks and vortex structures with respect to the flow direction, leading to the effective suppression of turbulence generation and significant reduction in skin-friction drag. In addition, experiments are carried out in a water tunnel via electro-magnetic (EM) actuators designed to produce the bidirectional traveling wave excitation as described in calculations. As a result, the actual substantial drag reduction is realized successfully in these experiments.