Unsteady MHD Flow on a Rotating Cone in a Rotating Fluid

Unsteady flow over an infinite permeable rotating cone in a rotating fluid in the presence of an applied magnetic field has been investigated. The unsteadiness is induced by the time-dependent angular velocity of the body, as well as that of the fluid. The partial differential equations governing the flow have been solved numerically by using an implicit finite-difference scheme in combination with the quasi-linearization technique. For large values of the magnetic parameter, analytical solutions have also been obtained for the steady-state case. It is observed that the magnetic field, surface velocity, and suction and injection strongly affect the local skin friction coefficients in the tangential and azimuthal directions. The local skin friction coefficients increase when the angular velocity of the fluid or body increases with time, but these decrease with decreasing angular velocity. The skin friction coefficients in the tangential and azimuthal directions vanish when the angular velocities of fluid and the body are equal but this does not imply separation. When the angular velocity of the fluid is greater than that of the body, the velocity profiles reach their asymptotic values at the edge of the boundary layer in an oscillatory manner, but the magnetic field or suction reduces or suppresses these oscillations.     

Experimental Determination of Lagrangian Velocity Statistics in Turbulent Pipe Flow

The calculation of Lagrangian statistics out of experimentally determined data from homogeneously seeded inhomogeneous turbulent flows is far from straightforward since statistical properties are position-dependent, necessitating local sampling. Two solutions for the preferential sampling of faster particles at a certain position in the flow are proposed. The performance of both methods was tested using DNS calculations for turbulent pipe flow. Both methods show a good performance for various statistical properties, thus providing two reliable ways to analyze experimental data from inhomogeneous turbulent flows.     

The Problems of the Turbulent Burning Velocity

The paper reviews the practical problems in measuring a turbulent burning velocity that gives the mass rate of burning. These largely centre on identifying an appropriate flame surface to associate with the turbulent burning velocity, u _t , and the density of the unburned mixture. Such a flame surface has been identified, in terms of the mean reaction progress variable, $\bar {c}$ , for explosive flame propagation in a fan-stirred bomb. Measurement of $\bar {c}$ makes possible an estimation of the flame surface density, ??, from the relationship ${\it \Sigma} =k\bar {c}\left( {1-\bar {c}} \right)$ . It is shown that in such explosions, mass rates of burning derived from the measured total flame surface area agreed well with those found from the measured turbulent burning velocity. Flamelet considerations identify appropriate dimensionless correlating parameters for u _t . As a result, correlations of turbulent burning velocity divided by the effective rms turbulent velocity, are plotted against the turbulent Karlovitz stretch factor, K, for different values of the Markstein number for flame strain rate, Ma_sr. These plots cover a wide range of variables, including pressure and fuels, and are indicative of different regimes of turbulent combustion. At the lower values of K, there is some evidence of increases in u _t and k due to high-frequency flame surface wrinkling arising from flame instabilities. These increase as Ma_sr becomes more negative. It is found from the developed value of the mean flame surface density throughout the flame brush that, to a first approximation, an increase in u _t for a given mixture is accompanied by a proportional increase in the volume of the brush. The analysis shows that the volume fraction of the turbulent flame brush that is reacting is quite small.     

Experimental Determination of the Burning Velocity of Mixtures of n-Heptane and Toluene in Engine-like Conditions

Although the burning velocities of fuel-air mixtures have been extensively studied at room temperature and pressure, there is relatively little experimental information available for elevated temperatures and pressures (the so-called engine like conditions). Therefore, the main aim of the present work is to generate accurate experimental burning velocities valid over a range of high unburned gas temperatures and pressures of a variety of mixtures of n-heptane and toluene, varying its proportion by 25% in volume each time. Two experimental combustion facilities have been used and their results compared. One facility consists of a constant volume cylindrical bomb in which Schlieren images can be recorded and used to calculate the flame front development. The second facility is a spherical combustion bomb with centred ignition in which burning velocities are calculated from pressure records by means of a two-zone model. In order to check that the pressure method is reliable, experiments with n-heptane at room temperature and pressure for different equivalence ratios carried out in the spherical combustion bomb were compared with the ones obtained at the same conditions in the cylindrical vessel equipped with the Schlieren technique. Once the validity has been checked, extensive experiments have been carried out for widely varying initial conditions of pressure between 0.3 and 0.7?MPa, temperature between 363?K and 453?K and equivalence ratios from 0.8 to 1.1. Over the ranges studied, by removing the influence of the ignition energy at the earliest stages of combustion and the quenching effects at the later ones, the burning velocities are fitted by a correlation of type $ Cc=Cc_{r}\cdot (T_{ub}/T_{r})^{\varepsilon }\cdot (P/P_{r})^{\beta } $ , where Cc _r , ?? and ?? depend on the equivalence ratio. The ranges of validity of the correlations obtained cover from 370?K to 700?K, from 0.3?MPa to 4.5?MPa, and from 0.8 to 1.1 equivalence ratio. A comparison with previous predicted values is also given.     

Steady Flow of a Navier-Stokes Fluid Around a Rotating Obstacle

Let ? be a body immersed in a Navier-Stokes liquid ? that fills the whole space. Assume that ? rotates with prescribed constant angular velocity ω. We show that if the magnitude of ω is not “too large”, there exists one and only one corresponding steady motion of ? such that the velocity field v(x) and its gradient grad?v(x) decay like |x|^?1 and |x|^?2, respectively. Moreover, the pressure field p(x) and its gradient grad?p(x) decay like |x|^?2 and |x|^?3, respectively. These solutions are “physically reasonable” in the sense of Finn. In particular, they are unique and satisfy the energy equation. This result is relevant to several applications, including sedimentation of heavy particles in a viscous liquid.     

Numerical Investigation of the Flow Past a Rotating Golf Ball and Its Comparison with a Rotating Smooth Sphere

Large-eddy simulations are conducted for a rotating golf ball and a rotating smooth sphere at a constant rotational speed at the subcritical, critical and supercritical Reynolds numbers. A negative lift force is generated in the critical regime for both models, whereas positive lift forces are generated in the subcritical and supercritical regimes. Detailed analysis on the flow separations on different sides of the models reveals the mechanism of the negative Magnus effect. Further investigation of the unsteady aerodynamics reveals the effect of rotating motion on the development of lateral forces and wake flow structures. It is found that the rotating motion helps to stabilize the resultant lateral forces for both models especially in the supercritical regime.     

The Velocity Variance Tensor in a Plane Seepage Flow

In the second-order perturbation theory approximation, the longitudinal and transverse components of the velocity variance tensor are calculated for a plane flow through a randomly heterogeneous porous medium with a log-normal conductivity distribution.     

锥体料斗内散料流动相对速度分布的实验研究

用示踪法进行了散粒体在圆锥料斗内不同出口直径条件下流动时相对速度分布的试验，并以此对Jenike轴向应力和共轴理论进行了实验验证，发现有些散料与Jenike轴向应力和共轴理论符合较好，而有些与之偏差较大。分析了内摩擦角、壁面摩擦角对最大主应变率方向的影响。     

Strain Measurement Within a Single-lap Joint Using Embedded Strain Gages

Experimental Techniques -     

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).     

An Experimental Investigation of Permeability Measurement of Water Flow in Crushed Rocks

Due to the high permeability of water flow in crushed rocks, flow catastrophes and water inrush accidents are apt to take place in the broken zones of aquifers in coal mining engineering. The pore, crack and fracture geometries needed for water transport are strongly influenced by grains diameter size and axial displacement conditions. In order to inspect and quantify the influence, we designed and manufactured a water flow apparatus that can be connected to the electro-hydraulic servo-controlled test system MTS815.02 which provides loading pressure in the experiment. Using the apparatus and MTS system, we tested crushed mudstone, limestone and sandstone specimens and obtained the relationship between permeability and variable grain diameter of a (2.5–5 mm), b (5–10 mm), c (10–15 mm), d (15–20 mm) and e (mixed sizes) under variable axial displacement (10, 15, 20, 25, 30, 35 and 40 mm). In particular, the permeability calculation based on collection of water flow velocity and pore pressure gradient difference has involved the influence of non-Darcy flow. The results show that (1) The porosity decreases with the increase of axial displacement and decrease of bigger particle size, respectively. Particle crushing during compaction is a main cause of size 0–2.5 mm appearing, some fine particles be washed away is a main cause of weight loss because of the effect of water seepage. (2) Water flow properties of crushed rocks are found to be strongly influenced by axial displacement and grain diameter size; in general, the permeability decreases with the increase of axial displacement and the decrease of grain diameter, respectively. (3) The fluctuations of permeability–axial displacement are especially intense for mudstone and sandstone than that for limestone. The permeability of crushed rocks is not only related to loading levels but also to grain diameters, style of arrangement. (4) To each grain diameter sizes, the permeability change of sandstone has a greater value than that of mudstone and limestone. The permeability of crushed mudstone shows much less than that of limestone and sandstone.     

Flow Bifurcations in a Thin Gap Between Two Rotating Spheres

This paper presents the use of a parameter continuation method and a test function to solve the steady, axisymmetric incompressible Navier–Stokes equations for spherical Couette flow in a thin gap between two concentric, differentially rotating spheres. The study focuses principally on the prediction of multiple steady flow patterns and the construction of bifurcation diagrams. Linear stability analysis is conducted to determine whether or not the computed steady flow solutions are stable. In the case of a rotating inner sphere and a stationary outer sphere, a new unstable solution branch with two asymmetric vortex pairs is identified near the point of a symmetry-breaking pitchfork bifurcation which occurs at a Reynolds number equal to 789. This solution transforms smoothly into an unstable asymmetric 1-vortex solution as the Reynolds number increases. Another new pair of unstable 2-vortex flow modes whose solution branches are unconnected to previously known branches is calculated by the present two-parameter continuation method. In the case of two rotating spheres, the range of existence in the (Re ₁ , Re ₂ ) plane of the one and two vortex states, the vortex sizes as a function of both Reynolds numbers are identified. Bifurcation theory is used to discuss the origin of the calculated flow modes. Parameter continuation indicates that the stable states are accompanied by certain unstable states. Received 26 November 2001 and accepted 10 May 2002 Published online 30 October 2002 Communicated by M.Y. Hussaini     

Flow of a Nonlinearly Viscous Fluid over the Surface of a Rotating Flat Disk

The flow of a nonlinearly viscous (power-law) fluid over the surface of a rotating flat disk is investigated. A solution form which makes it possible to reduce the complete system of partial differential equations to a system of ordinary differential equations is found. This system is integrated using the Runge-Kutta method and reduction to a Cauchy problem on the basis of Newton's method. The velocity and pressure fields in a power-law fluid film flowing over the surface of a rotating flat disk are found numerically.     

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     

Experimental study of coating flows in a partially-filled horizontally Rotating cylinder

 We describe a number of different phenomena seen in the free-surface flow inside a partially filled circular cylinder which is rotated about its horizontal axis of symmetry. At low angular velocities the flow settles into a steady two-dimensional flow with a front where the coating film coalesces with the pool at the bottom of the cylinder. This mode becomes unstable at higher angular velocities, initially to a sloshing mode on the rising side of the coating film and then to an axial instability on the front. The undulations that appear on the front grow into large-amplitude stationary patterns with cusp-like features for some parameter values. At still higher angular velocities and volume fractions, a number of different inertial instabilities and patterns appear. We present a phase diagram of the various transitions and characterize some of the more prominent instabilities and patterns in detail, along with some possible mechanisms for the observed behaviour. Received: 13 April 1996 / Accepted: 13 June 1996     

Similarities of Patterns in Fluid and Granulated Flow Inside a Horizontally Rotating Cylinder

The formation of flow patterns in liquid and granulated media is studied experimentally. Many phenomena such as segregation of particles different in dimensions, surface properties, and density are observed only in granulated media. However, there exist many effects typical of flows in both liquid and granulated media in a horizontal circular cylinder rotating about its axis. Eight classes of the following similar patterns in fluids and granulated mixtures were studied experimentally: vortex-like patterns, deformation of the trailing and leading edges of a layer, shark-teeth patterns, fish-like patterns, formation of rotating layers, ring-like patterns, and cellular patterns     

On the Flow Induced by Centrifugal Buoyancy in a Differentially-Heated Rotating Cylinder

We consider the nature of thermally stratified flow in a closed cylinder rotating about the direction of gravity under conditions appropriate for terrestrial laboratory experiments. Motion is driven by centrifugal buoyancy, with outflow near the cold disk and inflow near the hot disk. Although similarity solutions for the infinite disk open-geometry problem exist and are easily found, even analytically in certain limits, there remain questions about the applicability of these spatially simplified models in a closed geometry with a vertical sidewall. This paper compares theoretical self-similar core solutions with computational simulations constructed to satisfy a wide range of sidewall thermal boundary conditions; insulating, conducting (with a linear temperature profile up the wall), hot (isothermal), or cold. The width of penetration of sidewall influence in toward the axis of rotation depends on the sidewall thermal boundary condition. However, as the cylinder radius is increased for a fixed height, a substantial region of the container about the axis is accurately described by the thermocline solutions of the theory. The non-self-similar region at large radius can include separation of the lower outflow boundary layer, a feature not evident in previous studies of this problem. Received 8 June 1999 and accepted 12 December 1999-->     

Passive Scalar in a Turbulent Channel Flow with Wall Velocity Disturbances

Direct Numerical Simulations (DNS) of a passive scalar in a turbulent channel flow with a normal velocity disturbance on the lower wall are presented for high and low Reynolds numbers. The aim is to reproduce the complex physics of turbulent rough flows without dealing with the geometric complexity. In addition, isothermal walls that cannot be easily assigned in an experiment, are considered. The paper explains the increase of heat transfer through the changes of the velocity and thermal structures. As in real rough flows, the transpiration produces an isotropization of the turbulence near the wall.