Stokes drag on a disk sedimenting edgewise toward a plane wall

For comparison with the results of current experiments, a concise analytical method is developed to describe the non-axisymmetric flow generated by the edgewise sedimentation of a disk toward a plane wall. Since all Fourier modes contribute to the flow, the use of Abel transforms in earlier work must be suitably extended in order to again obtain integral equations of the second kind. By expanding the wall effects in powers of D^–1, where D is the distance from the disk axis to the wall, the dimensionless drag coefficient is found to order D^–5 without having to solve the flow problem beyond the second Fourier mode.     

Spin-up and spin-down of a viscous fluid over a heated disk rotating in a vertical plane in the presence of a magnetic field and a buoyancy force

Summary The hydromagnetic spin-up and spin-down of an incompressible electrically conducting fluid on a heated infinite disk rotating in a vertical plane in the presence of a magnetic field and a buoyancy force have been studied. The flow is non-axisymmetric due to the imposition of the buoyancy force. We have considered the situation where there is an initial steady state which is perturbed by suddenly changing the angular velocity of the disk. By using suitable transformations the Navier-Stokes and energy equations with four independent variables (x, y, z, t) are reduced to a system of partial differential equations with two independent variables (,t ^*). Also, these transformations uncouple the momentum and energy equations, resulting in a primary axisymmetric flow with an axial magnetic field, in an energy equation dependent on the primary flow and in a buoyancy induced secondary cross flow dependent on both primary flow and energy.The results indicate that the effect of the step-change in the angular velocity of the disk is more pronounced on the primary flow than on the secondary flow and the temperature field. For both spin-up and spin-down cases the surface shear stress in the non-axial direction normal to gravity for the primary flow and the surface shear stresses for the secondary flow increase with the magnetic parameter, whilst the surface shear stress in the vertical direction and the heat transfer at the surface decrease as the magnetic parameter increases. Also, the secondary flow near the disk dominates the primary flow. We have also developed an asymptotic analysis for large magnetic parameters which complements well the numerical results obtained in the lower magnetic parameter range.     

Fluid flow induced by a rotating disk of finite radius

The boundary-layer equations outside a rotating disk of radius a have been solved. It is shown that it is unnecessary to take special precautions for the sudden change in boundary conditions at the edge of the disk except if one is interested in the flow at distances which are smaller than about 10^–3 a from the edge. The behaviour of the flow at large distances from the disk is investigated analytically with results which are confirmed by the numerical computations.     

Domain Walls Due to Anisotropic Diffusion in 3.8% 3He-4He Solutions

Nonlinear anisotropic spin diffusion is considered in ³He-⁴He solutions at the ³He concentration 3.8% where spin-rotation effects are absent. For large anisotropy D _∥ D _⊥ it is shown that a long-lived domain wall solution exists in which transverse magnetization is confined in a tube between two reservoirs of up and down spins, as in a longitudinal spin diffusion experiment. This is possible when D _∥ D _⊥ because diffusion of the transverse magnetization away from the domain wall is balanced by longitudinal diffusion toward the wall. Furthermore, the spin current between the up- and down-spin reservoirs is reduced because the spins must diffuse through the domain wall via transverse diffusion. The decay rate of the wall due to small external and demagnetizing field gradients is also calculated.     

The Stewartson layer of a rotating disk of finite radius

It is shown that if a disk of finite radius and the surrounding medium rotate coaxially with slightly different angular velocities, an axial layer in the form of a cylindrical shell exists at the edge of the disk. This shell of thickness O(E ^1/3) has length O(E ^–1) in axial direction, where E is the Ekman number. Its most characteristic element is the axial velocity of O(E ^1/6) which is larger than everywhere else in the field. We calculate the velocity components and the pressure in this layer.     

On the dynamic susceptibility of the bulging domain wall model of polycrystalline magnetic oxides

The static initial magnetic susceptibility due to domain wall motion in a polycrystalline magnetic oxide has been explained by Globuset al. [3] using a model of a bulging domain wall inside grains of uniform diameter,D. The present work deals with the dynamic response of this model by solving the equation of motion of such a wall. The resultant solution reproduces Globus' relation for the static case and further shows that the dispersion frequency is D ^–1 for small grainsizes and D ^–2 for large grain sizes.     

Dynamics of dislocations and disclinations of the field of a few-order optical fiber: I. Creation and annihilation of C ± disclinations

It is shown experimentally and theoretically that the interconversion dynamics of the field of the LP₁₁ mode combination of a few-mode optical fiber is determined by the interaction of circularly polarized pure edge C ⁺ and C ⁻ disclinations. The C ⁺ and C ⁻ disclinations correspond to characteristics of the field for which the right-or left-circularly polarized electric field goes to zero. During propagation the uniformly linear-polarized dislocations D _y break down into four C ⁺ disclinations travelling in opposite senses. When each pair of C ⁻ and C ⁺ disclinations meet they annihilate each other and form linear polarization. The field of the linearly polarized disclinations thus created sums up out of phase into the original field and forms a uniformly linearly polarized field with D _x dislocations. Pis’ma Zh. Tekh. Fiz. 23, 20–27 (January 26, 1997)     

The connection between Ekman and Stewartson layers for a rotating disk

When a disk of finite radius and the surrounding medium rotate coaxially with slightly different angular velocities, a so-called Stewartson layer exists at the edge of the disk. The properties of this layer outside the boundary layer of the disk have been given in a previous publication. In the present paper it is shown how the radial flow of the Ekman boundary layer turns into the axial flow of the Stewartson layer. This happens in a region of which both the radial and axial dimensions are O(E^1/2), where E is the Ekman number.     

Sand accumulation on a wall in flows around a near-wall circular cylinder

Summary The sand accumulation on a flat plate in flows around a near-wall circular cylinder has been mainly investigated by the method of numerical simulation at the sub-critical Reynolds number1200 (based on the diameter of the circular cylinder) and the gap ratio G/D (ratio of the gap between the circular cylinder and the plane wall to the diameter of the circular cylinder) 1.0, 0.5 and 0.25. The standard k− ε turbulent model and the vorticity-stream function formulation are adopted to analyze the wake characteristics. The lift and drag coefficients of the circular cylinder and the pressure pulsation on the wall are solved. The simulation of streak-lines for the flow visualization and PIV experiments are detailed carried out to analyze the sand accumulation phenomenon on the plane wall, and a possible mechanism has been proposed. Results of the numerical simulation indicate that the effect of the cylinder results in flow separation from the plane wall. Separations occur about 1 to 2 cylinder diameters behind the cylinder, where the particles in the flow near the plane wall accumulate gradually.     

Impact force on downstream bed of weir by free overfall flow

Abstract

According to previous experimental studies on free overfall, the main influencing factors of the local scour downstream of a drop structure were found to be the impact position of the nappe flow and the force striking on the channel bed. In this study, the pressure transducers and strain amplifiers, which did not disturb the flow field, were set up to measure the pressure distributions along the streamwise direction downstream of the weir. The data were recorded through an A‐D converter and compared with the data collected by Moore (1943) and Rand (1955). Expressions for the impact position and impact force of the flow nappe derived from the experimental results and the theoretical analysis. The relationship among weir height h, impact position of free overfall L_p , and drop number D were put into the following equation: L_p/h = 1.82D ^0.17.     

Two-phase flow regimes in round, square and rectangular tubes during condensation of refrigerant R134a

An experimental investigation of two-phase flow mechanisms during condensation of refrigerant R134a in six small diameter round (4.91 mm), square (D_h=4 mm, α=1), and rectangular (4×6 and 6×4 mm: D_h=4.8 mm, α=0.67 and 1.5; 2×4 and 4×2 mm: D_h=2.67 mm, α =0.5 and 2) was conducted. Unique experimental techniques and test sections were developed to enable the documentation of the flow mechanisms during phase change. For each tube under consideration, flow mechanisms were recorded over the entire range of qualities for five different refrigerant mass fluxes between 150 and 750 kg m⁻² s⁻¹. The flow mechanisms were categorized into four different flow regimes: intermittent flow, wavy flow, annular flow, and dispersed flow. In addition, the large amount of data enabled the delineation of several different flow patterns within each flow regime, which provides a clearer understanding of the different modes of two-phase flow. Transition lines between the respective flow patterns and regimes on these maps were established based on the experimental data. It was found that for similar hydraulic diameters, flow regime transitions are not very strongly dependent on tube shape or aspect ratio. These maps and the transition lines can be used to predict the particular flow pattern or regime that will be established for a given mass flux, quality and tube geometry.     

Typical flow between enclosed corotating disks and its dependence on Reynolds number

Abstract

The flow in an enclosed co‐rotating disk pair is investigated by Laser Doppler Velocimetry (LDV) measurements and flow visualizations. First, the typical flow structure at Re = 5.25 × 10⁵ and S = 0.09 is clarified. The flow fields in the r – θ and the r – z planes are both investigated and then divided into several flow regions based on the distinct flow types observed. The flow regions found in the two different planes are also compared and integrated. Second, with S fixed, the dependence of the flow field structure upon the Reynolds number is discussed. Three regimes of the r – θ plane flow with different Reynolds numbers are identified based on the measured mean velocity and spectral intensity. When Re < 1.6 × 10⁵, no solid body region is found and the flow is in a laminar regime. In the range 1.6 × 10⁵ ≤ Re ≤ 2.0 × 10⁶, the solid body region and the outer region vortices coexist, and an empirical equation is developed to estimate the number of vortices. When Re > 2.0 × 10⁶, the flow becomes turbulent. As Re increases from 9.3 × 104 to 5.25 × 10⁵, the spectral intensity initially increases and then decreases before increasing again to an even higher level, resulting in an increasing sawtooth pattern.     

Flow of a non-Newtonian fluid past a wedge

Summary A pseudo-similarity solution has been obtained for the flow of an incompressible fluid of second grade past a wedge. The numerical method developed for this purpose enables computation of the flow characteristics for any value of the parametersK anda, whereK is the dimensionless normal stress modulus of the fluid, anda is related to the wedge angle. Results computed forKx ^wa varying from 0 to 200 show a marked decrease or increase in wall shear, depending upon the wedge angle, asx ^–2a /K increases from 0 to about 1; thereafter the change in wall shear stress is small. The present results match exactly with those from an earlier perturbation analysis forKx ^2a 0.01 but differ significantly asKx ^2a increases.     

An electron spin resonance study of Mn2+ doped calcium hydrazine carboxylate monohydrate

Single crystals of calcium hydrazine carboxylate, monohydrate have been studied by ESR of Mn²⁺ doped in the calcium sites. X-band ESR indicated a large crystal field splitting necessitating experiments at Q band. The analysis shows two magnetically inequivalent (but chemically equivalent) sites withg _xx = 2.0042±0.0038,g _yy=2.0076 ±0.0029,g _zz=2.0314±0.001,A _zz=0.0099±0.0002 cm⁻¹,A _xx=0.0092±0.0002 cm⁻¹,A _yy=0.0082±0.0002 cm⁻¹,D=3/2D _zz=0.0558±0.0006 cm⁻¹, andE=1/2 (D _yy−D _yy)=0.0127±0.0002 cm⁻¹. One of the principal components of the crystal field, (D _zz), is found to be along the Ca ↔ Ca direction in the structure and a second one, (D _xx), along the perpendicular to the plane of the triangle formed by three neighbouring calciums. TheA tensor is found to have an orientation different from that of theg andD tensors reflecting the low symmetry of the Ca²⁺ sites.     

Convective heat transfer in the entrance region of a rectangular duct with two indented sides

This study presents a numerical solution to convective heat transfer in laminar flow in the thermal entrance region of a rectangular duct with two indented sides. The flow is considered to be hydrodynamically fully developed and thermally developing laminar flow of incompressible, Newtonian fluids with constant thermal properties. The ducts are subjected to a constant wall temperature. An algebraic technique is used to discretize the solution domain and a boundary-fitted coordinate system is numerically developed. The governing equations in the boundary-fitted coordinates are solved by the control volume-based finite difference method. Distribution of the bulk temperature and the Nusselt number along the direction of flow is calculated and presented graphically. Also calculated is the thermal entrance length of the rectangular ducts with two indented sides. The parameters, such as the friction factor times the Reynolds number, and the Nusselt number for the fully developed flow and thermally developing flow are obtained.List of symbols a half-width of duct [m] - A cross-sectional area [m²] - b half-height of duct [m] - C _p specific heat [kJ kg^-1 K^-1] - D _h hydraulic diameter [m] - f skin friction factor = - h _z local heat transfer coefficient [Wm^–2 K^–1] - h _T asymptotic heat transfer coefficient [Wm^–2 K^–1] - J Jacobian matrix of transformation, Eq. (20) - k thermal conductivity [Wm^–1 K^–1] - L thermal entrance length [m] - L ^* dimensionless thermal entrance length =L/D _h RePr - L1 maximum number of grids in direction - M1 maximum number of grids in direction - Nu _T asymptotic Nusselt number =h _T D _h /k - p pressure [n m^–2] - P circumferential length [m] - Pr Prandtl number = /_T - Re Reynolds number =w _m D _h / - T temperature [K] - T _b bulk temperature [K] - T _i inlet temperature - T _w circumferential duct wall temperature [K] - w velocity [ms^–1] - w _m mean velocity [ms^–1] - W dimensionless velocity = – - W _m dimensionless mean velocity - x, y transveral coordinates [m] - X,Y dimensionless transversal coordinates =      

Effects of an airfoil and shock waves on vortex shedding process behind a square cylinder

Summary Effects of an airfoil and shock waves on vortex shedding process behind a square cylinder have been examined experimentally at a Mach number of about 0.91 and at a Reynolds number (based on the side lengthD of the square cylinder) of about 4.2×10⁵. The main experimental parameter is the spacing ratioL/D, and is varied from 1.125 to 5.5, whereL is the spacing between the square cylinder and the airfoil.It is found that similarly to the case at subcritical Mach numbers at the supercritical Mach number there exist three patterns of the flow around the square cylinder and airfoil arranged in tandem depending upon the spacing ratioL/D: In the first flow pattern with small spacing ratio, the downstream airfoil is enclosed completely in the vortex formation region of the square cylinder. In the second flow pattern, the shear layers separating from the square cylinder reattach to the airfoil. In the third flow pattern with large spacing the shear layers roll up upstream of the airfoil. The Strouhal number at the supercritical Mach number is higher than that at the subcritical Mach numbers. Shock waves hasten the vortex shedding behind the square cylinder by decreasing the area of asymmetrical part of the vortex formation region with respect to the wake axis, and let the streamwise length of the separating shear layers longer than otherwise.With 8 Figures     

Thermal interaction between laminar film condensation and forced convection along a conducting wall

Summary A theoretical analysis is presented to investigate the thermal interaction between laminar film condensation of a saturated vapor and a forced convection system separated by a heat conducting wall. In this work, the effect of the wall thermal resistance is considered. It is assumed that the countercurrent boundary layer flow is formed on the two sides. Governing boundary layer equations together with their corresponding boundary conditions for film condensation and forced convection are all cast into dimensionless forms by using the non-similarity transformation. The resulting system of equations is solved by using the local non-similarity method in conjunction with the fourth order Runge-Kutta method in conjunction with the Nachtsheim-Swigert iteration scheme. The total heat flux through the wall and the wall temperature distribution are determined. The present results show that the effect of the forced convection Prandtl number Pr _c is not negligible for large values of the thermal resistance ratioA ^*, and the effect ofA ^* and Pr _c on the overall heat transfer through the wall is more pronounced than that of the Jakob number and film Prandtl number.     

The superflow state of 3He-B at a diffusive wall. Quasiclassical calculations

We report on first computations considering effects of a rough wall on the counterflow state in superfluid ³He-B for high flow velocities. Using the quasiclassical Green's-function formalism supplemented by the boundary conditions for a diffusive wall, we calculate the order-parameter field and the supercurrent near a container wall for various pressures and temperatures. One of our results is that the current density at the wall as a function of the flow has a maximum at the velocity which is about half of the pair breaking velocity.     

Free-convective heat transfer within a differentially heated vertical plane during additional heat supply through a bottom wall

This work presents results of a numerical investigation of the structure of flow and heat exchange in a vertically closed interlayer with various relative heights A = H/L = 4–16 during variation in heat supply to its bottom. The vertical walls were isothermic; top wall, bottom wall, heat flow was supplied uniformly. The nonstationary Navier-Stokes equations were solved numerically in the two-dimensional formulation for the laminar flow. At small Rayleigh numbers (Ra ≈ 10³), when conductive heat transfer prevails within the interlayer, the effect of heat supply from below results in a change of heat transfer only in an immediate vicinity of the bottom. As the Rayleigh number and supplied heat increase, flow destabilization is observed, which results in strong heterogeneity of the density of heat flow along the wall height. At the same time, the heat flow at the hot vertical wall at defined Rayleigh numbers and heating from below may change the sign to the opposite one.     

Scanning Kerr Microscopy of the Spin Hall Effect in <Emphasis Type="Italic">n</Emphasis>-Doped GaAs with Various Doping Concentration

We investigated the doping concentration (N _D) dependence of the extrinsic spin Hall effect (SHE) in n-doped GaAs with N _D raging from 3×10¹⁶ cm⁻³ to 5×10¹⁷ cm⁻³. By using scanning Kerr microscopy (SKM) measurements, we observed the Kerr rotation signal due to the spin accumulation near the channel edges in all the samples with different N _D. Moreover, the position and in-plane magnetic field dependence of the Kerr rotation signal are found to vary with N _D. We analyzed the N _D dependence of the spin Hall conductivity by taking account of the N _D-dependent spin lifetime based on the typical drift-diffusion model.