Experimental Investigation of the Transverse Self-Oscillations of Circular Cylinders Mounted with a Narrow Clearance in a Plane Channel

The results of an investigation of the flow past and the behavior of free bluff bodies mounted in pipes and channels with a narrow clearance, conducted in the Institute of Mechanics of Moscow State University, are presented. The drag of circular cylinders of different size and mass in a circulation-free water flow in a plane channel of rectangular cross-section was studied in the transverse self-oscillation regime. The experiments were conducted for Reynolds numbers based on the cylinder diameter 1.7 ? 10⁴ ≤ Re ≤ 7.2 ? 10⁴, relative clearances \(\bar S\) based on a cross-sectional area ranging from 0.76 to 0.9, and cylinder-to-water density ratios ρ _c /ρ ranging from 1.29 to 8.2. Only the case of intense transverse self-oscillations accompanied by impact interaction with the channel wall was considered. The dependence of the period-average cylinder drag coefficient C _x on the basic dimensionless relevant parameters is obtained. The dependence of the dimensionless self-oscillation frequency determined in [1] is refined. The kinematic and dynamic features of the flows past spheres in cylindrical pipes and cylinders in plane channels are compared in the transverse self-oscillation regime.     

Supersonic Flow Past an Obstacle with a Clearance at the Base

The supersonic air flow structure and the pressure distribution in the vicinity of a vertical cylinder suspended over the surface of a plate with a turbulent boundary layer are studied experimentally. The effects of the free-stream Mach number and the width of the clearance between the cylinder base and the surface on the dimensions of the separated flow region and the pressure distribution in the latter are examined.     

Application of Differing Forcing Function Models on Simulated Flow Past an Oscillating Cylinder in a Uniform Low Reynolds Number Flow

A Computational Fluid Dynamics (CFD) model is presented for the uniform viscous two dimensional flow past an oscillating cylinder at low Reynolds number. Numerical simulations are made to study the effect of differing forced induced oscillation mechanisms with a large range of cylinder forcing frequencies. In the first case sinusoidal velocity slip boundary conditions are adopted for the cylinder surface to simulate cylinder oscillation. The implication suggests that no modification or additional term need to be added to the Navier-Stokes equations. In the second case this time extra body force terms which are assumed to account for velocity effects due to cylinder movement are included in the Navier-Stokes equations with the imposition of same boundary conditions. Drag and lift coefficients are extracted from present numerical results and other detailed computations of these coefficients are made at a Reynolds number of 80 and an amplitude-to diameter ratio 0.14. The results are found to be in agreement with each other at low force driving frequencies below and near lock-in. However, differences are found at higher frequencies above lock-in. Agreement are also found with experimental results at some frequency ranges.     

Comparison of the Calculated Results for Hypersonic Flow Past Blunt Bodies with the OREX Flight Test Data

The physico-chemical hypersonic air flow model is verified for the conditions of the experimental vehicle OREX reentry path over the altitude range H = 84 –105 km. The calculations are performed on the basis of both the viscous shock layer equations and the complete system of Navier-Stokes equations. The temperature and chemical component concentration fields calculated within the framework of the two models are in good agreement for H 100 km (Re 300). The numerical results for the heat flux at the stagnation point and the electron concentration agree well with the flight test data over the entire altitude range considered.     

Numerical Simulation of a Turbulent Flow in a Channel with Surface Mounted Cubes

In this paper we report on a fourth-order, spectro-consistent simulation of a complex turbulent flow. A spatial discretization of a convection-diffusion equation is termed spectro-consistent if the spectral properties of the convective and diffusive operators are preserved, i.e. convection skew-symmetric; diffusion symmetric positive definite. We consider a fully developed flow in a channel, where a matrix of cubes is placed at a wall of the channel. The Reynolds number (based on the channel width and the mean bulk velocity) is equal to Re = 13,000. The three-dimensional flow around the surface mounted cubes has served at a test case at the 6th ERCOFTAC/IAHR/COST workshop on refined flow modeling (Delft, June 1997). Here, mean velocity profiles as well as Reynolds stresses at various locations in the channel have been computed without using any turbulence models. The results agree well with the available experimental data.     

Investigation of Dynamic Stability Regimes for Axisymmetric Bodies in Supersonic Flow

The problem of supersonic flow past a slender blunt cone with allowance for the reverse boundary-layer effect on the outer flow is solved with the aim of studying the influence of the boundary layer on the damping coefficient of axisymmetric body oscillations. It is assumed that the body executes plane angular, both low-amplitude and low-velocity, oscillations about a center of rotation. A modified version of the method [1] is applied for calculating the time-dependent flow past a body with the viscosity effect taken into account. The high accuracy of the flow parameter determination provided by this technique is confirmed by wind- tunnel experiments on a large-scale cone model (L1 m) at Mach numbers M=4 and 6. The agreement between the calculated and measured data forms the basis for the numerical investigation of the blunt-cone damping coefficient over a wide range of freestream Mach (M=4–20) and Reynolds (Re _L =10⁶–10⁸) numbers. At moderate freestream Mach numbers (M=4 and 6) an appreciable Re _L effect on the damping coefficient was not detected. However, on the hypersonic range this effect manifests itself more strongly, especially when there is gas injection into the boundary layer from the vehicle surface.     

Limits of the Inertial Particle Deposition Regime and Heat Transfer in Supersonic Viscous-Dusty-Gas Flow Past Bodies

Supersonic steady dusty-gas flow past a blunt body at moderate and large Reynolds numbers Re is considered. Using the complete Navier-Stokes equations for the carrier phase, the effect of viscosity on the limits of the inertial particle deposition regime and the two-phase flow pattern near the frontal surface of the body is studied numerically for 10² Re 10⁵. The dependence of the limits of the inertial particle deposition regime on the phase velocity slip ahead of the bow shock is investigated. For large Re, the flow near the stagnation point is studied in the boundary layer approximation. On the basis of numerical calculations over a wide range of variation of the Reynolds number and the particle inertia parameter, the maximum increase in the heat fluxes at the stagnation point due to the presence of dispersed particles in the free-stream is estimated.     

Subsonic Compressible Flow Past a Body with Developed Cavitation

The essence of the Prandtl rule consists in the fact that in a flow at a Mach number M < 1 the transverse dimensions of a sharp-ended slender body must be reduced by a factor of 1/(1 - M²)^1/2 to conserve the same pressure distribution over the body surface as in a flow with the same velocity at M=0.Following Prandtl [1], the derivation is repeated with reference to axisymmetric flow with developed cavitation.     

Jet Flow Past a Plate with a Spoiler in the Presence of a Stagnation Zone

An exact analytical solution of the problem of the jet flow past a flat plate with a spoiler is obtained for the case in which there is a stagnation zone near the spoiler. The Chaplygin method of singular points and the theory of elliptic theta-functions are used to construct the solution. The pressure in the stagnation zone is determined from the Brillouin-Villat condition of smooth separation. It is found that the lift and drag coefficients, considered as functions of the stagnation zone length, have extrema at points corresponding to the smooth separation condition.     

Numerical Study of the Flow Behind a Rotary Oscillating Circular Cylinder

A numerical study is performed of flow behind a rotationally oscillating circular cylinder in a uniform flow by solving the two-dimensional incompressible Navier-Stokes equations. The flow behavior in lock-on regime and the timing of vortex formation from the oscillating cylinder are studied. When the frequency of excitation of the cylinder is in the vicinity of the natural vortex formation frequency, a lock-on vortex formation regime appears. As the excitation frequency being increased relative to the natural frequency the initially formed vorticity concentration switches to the opposite side of the cylinder. The effects of oscillating frequency and amplitude on the vortex structures formed in the near wake of the cylinder are also investigated. Based on the present calculated results, some complicated vortex patterns are identified and are consistent with the previous experimental visualizations.     

Steady Flow Generated by a Core Oscillating in a Rotating Spherical Cavity

Steady flow generated by oscillations of an inner solid core in a fluid-filled rotating spherical cavity is experimentally studied. The core with density less than the fluid density is located near the center of the cavity and is acted upon by a centrifugal force. The gravity field directed perpendicular to the rotation axis leads to a stationary displacement of the core from the rotation axis. As a result, in the frame of reference attached to the cavity, the core performs circular oscillation with frequency equal to the rotation frequency, and its center moves along a circular trajectory in the equatorial plane around the center of the cavity. For the differential rotation of the core to be absent, one of the poles of the core is connected to the nearest pole of the cavity with a torsionally elastic, flexible fishing line. It is found that the oscillation of the core generates axisymmetric azimuthal fluid flow in the cavity which has the form of nested liquid columns rotating with different angular velocities. Comparison with the case of a free oscillating core which performs mean differential rotation suggests the existence of two mechanisms of flow generation (due to the differential rotation of the core in the Ekman layer and due to the oscillation of the core in the oscillating boundary layers).     

DNS of a Laminar Separation Bubble in the Presence of Oscillating External Flow

A three-dimensional Direct Numerical Simulation (DNS) of a laminar separation bubble in the presence of oscillating flow is performed. The oscillating flow induces a streamwise pressure gradient varying in time. The special shape of the upper boundary of the computational domain, together with the oscillating pressure gradient causes the boundary layer flow to alternately separate and re-attach. When the inflow decelerates, the shear layer starts to separate and rolls up. Simultaneously the flow becomes 3D. After a transient period, the phase-averaged reverse flow inside the separation bubble reaches speeds ranging from 20 up to 150% of the free-stream velocity. During these phases, the flow is absolutely unstable and self-sustained turbulence can exist. When the inflow starts to accelerate, a spanwise roll of turbulent flow is shed from the shear layer. Shortly after this, the remainder of the separation bubble moves downstream and rejoins with the shed turbulent roll. During the flow-acceleration phase, a patch of laminar boundary layer flow is obtained. Along the flat plate, a series of turbulent patches of flow travelling downstream, separated by laminar flow can be observed, reminiscent of boundary layer flow in a turbine cascade with periodically appearing free-stream disturbances.     

Supersonic Flow Past a Circular Cylinder with an Isothermal Surface

Supersonic perfect-gas flow past a circular cylinder with an isothermal surface is investigated at the Mach number 5 and Reynolds numbers ranging from 30 to 500,000. It is shown that two branches of the numerical solution of the problem can exist. On the first branch the following flow patterns are successively realized as Re is increased: separationless flow, flow with formation of a local separation zone, and flow with formation of a global separation zone. On the second branch the flow pattern with a local separation zone is observed at all Reynolds numbers; at a certain value of Re this solution jumps to the first branch.     

Electrical Fracture Diagnostics for Metal Bodies in a Gas Flow

New results of studying the electrical aspects of metal body fracture in a gas flow are obtained. The basis of the investigations and the diagnostic method developed is a fundamentally new effect discovered by the authors: most of the microparticles formed when metal specimens (rods) fracture have the same (positive) electric charge. When the specimen is immersed in a gas flow, the charged particles formed are carried out by the flow into the ambient space and the electric field generated by the particles can be recorded by special probe-antennas. The electric signals produced by fracturing rods made of different metals immersed in a high-temperature jet of combustion products are measured. An approximate theoretical dependence of the total charge on the particles formed as a result of fracture on the strength characteristics of the rod material is obtained.     

Instability of an Oscillating Cylinder in a Circulation Flow of Ideal Fluid

The problem of the stability of a circular cylinder in a circulation flow is considered under the condition that the cylinder can perform both free (free cylinder) and forced oscillations (cylinder on a spring). It is shown that this simple system can be unstable in the presence of flow vorticity. Particular cases of vorticity distributions which make it possible to obtain an analytic solution are considered. The case of weak monotonically decreasing vorticity of an arbitrary form is analyzed for an arbitrary relation between the densities of the cylinder and the fluid. It turns out that the instability can develop only for a cylinder whose density is greater than that of the fluid. An approximate method of solving this problem based on consideration of the energy balance in the system is constructed. This makes it possible to obtain an expression for the growth rates and explain the physical mechanism realizing the instability, which is associated with the possibility of energy transfer from perturbations in the critical layer to the cylinder oscillations.     

Boundary-Layer Separation in the Two-Layer Flow Past a Cylinder in a Rotating Frame

Following on from the study by Brevdo and Merkine (1985), this paper examines the nature of boundary-layer separation in the two-layer flow past a cylinder in a rotating frame for the zero Froude number case and makes a comparison with that study. The full equations are solved numerically for the steady laminar flow throughout the region and then compared with the results of the study of Brevdo and Merkine, which solved the boundary-layer equations. This includes a comparison of radial-velocity profiles, cylinder shear stress and separation criteria. Good agreement was found between the two studies when the flow in the faster layer had not separated, however, the model of Brevdo and Merkine was no longer appropriate once the flow in the faster layer had separated. An interesting feature of this flow is that the flow in the slower layer can be reversed without separation taking place. Received 2 June 1997 and accepted 29 December 1997     

Numerical Simulation of the Unsteady Laminar Flow Past a Circular Cylinder with a Perforated Sheath

The unsteady two-dimensional laminar flow past a circular cylinder encased in a perforated sheath is numerically simulated. On the basis of the calculated results a technique for controlling the wake flow by diverting a portion of the flow from the forward stagnation point through internal ducts to orifices in the sheath located in the separation zone, is analyzed.     

A Limiting Solution for Flow Past a Delta Wing in the Presence of Supercritical Flow Regions

The flow past a planar delta wing is studied for strong interaction between the boundary layer and the outer supersonic flow. An analytic investigation is carried out using the Newtonian passage to the limit in which the specific heat ratio tends to unity and the Mach and Reynolds numbers to infinity. Possible flow regimes are classified for various wing aspect ratios. For determining the supercritical-subcritical flow transition line an analytic expression, correct to the second approximation, is obtained for flow past a cold wing with a fairly large aspect ratio in which the transverse boundary-layer flows are insignificant.     

Optimal Axisymmetric Noses of Bodies in a Flow. Calculations and Experiments

The distinctive features of directmethods for contouring axisymmetric noses of bodies in a supersonic flow are discussed. The nose of a body of revolution in a supersonic flow, optimal with respect to the wave drag, includes a forward-looking flat face adjoining through a bend a sloping region of given aspect ratio (length-to-base-radius ratio), which, in turn, adjoins, again through a bend, the main part of the body. The above-mentioned sloping region can have, depending on its length, some additional internal bends. The presence of bends in a contoured configuration can often be undesirable, owing to strength, thermal, or others restrictions. For this reason, in solving the optimal contouring problems by means of direct methods analytical approximations of the unknown contour are often used, which leads to an increase in the drag of the optimized configuration. The degree of the increase in the drag of the nose part of a body of revolution in the cases of the local smoothing of bends in the optimal configuration and the global variation of its shape on the basis of an analytical approximation is investigated. It is shown that an increase in the drag of the nose part of a body of revolution owing its ineffective approximation can be many times greater than the gain due to optimization. The results of calculations are confirmed by the experimental data obtained.