Showing papers in "Flow Turbulence and Combustion in 1970"
TL;DR: In this article, the authors considered viscous flow in a circular cylindrical tube containing an infinite line of rigid spheroidal particles equally spaced along the axis of the tube.
Abstract: Viscous flow in a circular cylindrical tube containing an infinite line of rigid spheroidal particles equally spaced along the axis of the tube is considered for (a) uniform axial translation of the spheroids (b) flow past a line of stationary spheriods and (c) flow of the suspending fluid and spheroids under an imposed pressure gradient. The fluid is assumed to be incompressible and Newtonian. The Reynolds number is assumed to be small and the equations of creeping flow are used. Two types of solutions are developed: (i) an exact solution in the form of an infinite series which is valid for ratios of the spheroid diameter to the tube diameter up to 0.80, (ii) an approximate solution using lubrication theory which is valid for spheroids which nearly fill the tube. The drag on each spheroid and the pressure drop are computed for all cases. Both prolate and oblate spheroids are considered. The results show that the drag and pressure drop depend on the spheroidal diameter perpendicular to the axis of tube primarily and the effects of the spheroidal thickness and spacing are secondary. The results are of interest in connection with mechanics of capillary blood flow, sedimentation, fluidized beds, and fluid-solid transport.
54 citations
TL;DR: In this article, the authors investigated the structure of shock waves in liquids containing gas bubbles and showed that the overall thickness of the shock appears to be determined by the dispersion effect.
Abstract: The structure of shock waves in liquids containing gas bubbles is investigated theoretically. The mechanisms taken into account are the steepening of compression waves in the mixture by convection and the effects due to the motion of the bubbles with respect to the surrounding fluid. This relative motion, radial and translational, gives rise to dissipation and to dispersion caused by the inertia of the radial flow associated with an expanding or compressed bubble. For not too thick shocks the dissipation by radial motion around the bubbles dominates over the dissipation by relative translational motion, in mixtures with low gas content. The overall thickness of the shock appears to be determined by the dispersion effect. Dissipation, however, is necessary to permit a steady shock wave. It is shown that, analogous to undular bores, a stationary wave train may exist behind the shock wave.
52 citations
TL;DR: In this paper, the authors extended the Graetz problem in heat transfer to the analysis of mass transfer in circular ducts for the cases where wall resistance is included and where non-Newtonian fluids that obey Casson's equation are considered.
Abstract: The Graetz problem in heat transfer is extended to the analysis of mass transfer in circular ducts for the cases where wall resistance is included and where non-Newtonian fluids that obey Casson's equation are considered. The eigenvalues and fluid bulk coefficients are presented for the fluid between the extremes of Newtonian and slug flow. It is found that for fluids which are only slightly non-Newtonian, such as blood, which is closely approximated by Casson's equation, the mass transfer rate can be predicted by Newtonian fluid analysis without appreciable error. Some experimental results give support to the theory.
49 citations
TL;DR: In this paper, an explanation for a phenomenon observed e.g. in a wall jet in a small region near the maximum velocity is given, where the turbulence shear stress is expressed as the sum of two terms, proportional to the first and second derivative of the mean velocity, respectively.
Abstract: An explanation is given for a phenomenon observed e.g. in a wall jet in a small region near the maximum velocity. The turbulence shear stress is expressed as the sum of two terms, proportional to the first and the second derivative of the mean velocity, respectively. Use is made of the nonsymmetric flow pattern around the maximum velocity, and of the nonuniform distribution of the intensity of the lateral turbulence velocity component. The coefficient of the second derivative of the mean velocity is shown to contain the first derivative of this turbulence velocity component. Since the second derivative of the mean velocity is negative around its maximum, a positive turbulence intensity gradient as observed in the region concerned in the wall jet, results in a negative contribution to the shear stress. Hence, in this region the shear stress can have a sign opposite to the positive — though very small — gradient of the mean velocity. Consequences with respect to the mechanical energy balance of the mean flow and of the turbulence are discussed.
30 citations
TL;DR: In this article, the shape of the phase boundary of two fluids in systems with a rotational symmetry, and particularly the level of the liquid in a rotating vessel, is studied, and the solutions of these equations, taking into account the boundary conditions, are discussed.
Abstract: The shape of the phase boundary of two fluids in systems with a rotational symmetry, and particularly the level of the liquid in a rotating vessel, is studied. The knowledge of the shape of the surface of such a liquid is necessary for centrifugal moulding of optical surfaces. The dimensionless surface equations are formulated, and the solutions of these equations, taking into account the boundary conditions, are discussed.
20 citations
TL;DR: In this paper, the method of group invariance under an infinitesimal transformation is applied to a class of nonlinear partial differential equations, yielding a large number of known forms of self-similar solutions.
Abstract: The method of group invariance under an infinitesimal transformation is applied to a class of nonlinear partial differential equations. Besides yielding a large number of known forms of self-similar solutions, the method also gives new types of solutions.
20 citations
TL;DR: In this paper, the maximum torque on the rotor and the corresponding surface resistance were determined under the condition that the amplitude of the ac voltages on the electrodes is constant and that the phase-shifted voltage amplitude is constant.
Abstract: For an electrostatic motor consisting of a rotor of insulating material covered with a slightly conducting surface layer, and a ring of electrodes fed with phase-shifted ac voltages that generate a rotating electric field acting on the rotor, the maximum torque on the rotor and the corresponding surface resistance are determined theoretically under the condition that the amplitude of the ac voltages on the electrodes is constant
16 citations
TL;DR: In this article, the phase velocity of a wave at the edge of a thick plate under initial stress is derived, and the frequency equation for the phase velocities of the wave in a thin and an infinite-thick plate is derived.
Abstract: The frequency equation giving the phase velocity of a wave at the edge of a thick plate under initial stress is obtained. Some particular cases are discussed to derive (a) the velocity of edge waves in a thin plate and (b) the velocity of Rayleigh waves in a plate of infinite thickness under initial stress.
16 citations
TL;DR: In this paper, a perturbation away from infinite conductivity is proposed, which allows the solution of electrodynamics problems to be calculated to any order of accuracy in the quantity (ωe/σ)1/2 for some important cases.
Abstract: The electrodynamics of wave reflection from conducting media lead to difficult mathematical problems because of the matching conditions which must be met at the interface between conductors and nonconductors. Simplified boundary conditions have been proposed by Leontovitch and others which considerably simplify certain of the mathematical problems. We discuss the Leontovitch condition together with certain of its shortcomings and present a new method which overcomes some of the difficulties of the Leontovitch condition. The new method is a perturbation away from infinite conductivity which allows the solution of electrodynamics problems to be calculated to any order of accuracy in the quantity (ωe/σ)1/2 for some important cases. An instance in which the perturbation method fails is also discussed.
13 citations
TL;DR: In this article, the trictional force and torque on the reference sphere were computed for the particular case when two spheres move in a direction perpendicular to their line of centers symmetrically placed about the axis of a circular cylinder.
Abstract: Numerical values are provided which enable the trictional force and torque on the reference sphere to be computed for the particular case when two spheres move in a direction perpendicular to their line of centers symmetrically placed about the axis of a circular cylinder. Results for this motion are also expressed in terms of the ratio of frictional forces experienced by 1) a body of arbitrary shape in a bounded fluid with another particle and 2) the body now moving alone with the same speed and orientation in the same but unbounded fluid. The computation furnishes the interaction and wall corrections correct to the first order in the ratios of characteristic particle dimension to characteristic distance of the particle from another object.
9 citations
TL;DR: The linear stability of the flat plate boundary layer with surface blowing and suction was investigated by the application of numerical techniques in this article, and the universal stability bound of Joseph was evaluated and compared with the corresponding numerically exact neutral stability curve.
Abstract: The linear stability of the flat plate boundary layer with surface blowing and suction is investigated by the application of numerical techniques. Complete neutral stability curves, critical Reynolds numbers and wave numbers, and other stability characteristics are determined for a wide range of surface mass transfer intensities. The critical Reynolds number, based on the displacement thickness, is found to vary from 59 to 32500 between the extreme limits of blowing and suction that are investigated. Comparisons are made between the present results and available linear stability information for boundary layers with surface mass transfer and with free-stream pressure gradients. The universal stability bound of Joseph is evaluated and compared with the corresponding numerically exact neutral stability curve.
TL;DR: In this article, an analysis for the combined forced and free convective magnetohydrodynamic flow in a vertical, finite rectangular channel that is subjected simultaneously to a pressure gradient and a temperature gradient is presented.
Abstract: An analysis is presented for the combined forced and free convective magnetohydrodynamic flow in a vertical, finite rectangular channel that is subjected simultaneously to a pressure gradient and a temperature gradient. Exact solutions are found for electrically nonconducting channel walls and perfectly conducting walls. In particular, the case of heating from below is examined and discussed.
TL;DR: In this paper, the effects of radiative heat transfer and injection or suction on the surface of the plate have been studied and numerical examples for velocity and temperature profiles are given.
Abstract: Unsteady laminar boundary layers on an infinite plate including the effects of radiative heat transfer and injection or suction on the surface of the plate have been studied Similar solutions for the velocity and for the temperature are analyzed Numerical examples for velocity and temperature profiles are given The effectiveness of transpiration cooling decreases with increasing radiation parameter R
F The peak temperature in the boundary layer is suppressed if R
F is high enough
TL;DR: In this article, the Coriolis acceleration in the frequencies of inplane vibrations of a rotating disk is calculated and it is shown that when disks are spun at ultra high speeds, such as exceeding the one that corresponds with one-tenth of the lowest natural frequency of a stationary disk, the effect does become significant.
Abstract: The changes effected by the Coriolis acceleration in the frequencies of inplane vibrations of a rotating disk are calculated. It is shown that the current practice to neglect this effect in everyday engineering calculations is quite justified. It is also shown that when disks are spun at ultra high speeds, say exceeding the one that corresponds with one-tenth of the lowest natural frequency of a stationary disk, the effect does become significant.
TL;DR: In this paper, the reflection of water waves by a semi immersed cylinder having a symmetric cross section is studied for both Dirichlet and Neumann boundary conditions on the cylinder.
Abstract: The reflection of water waves by a semi immersed cylinder having a symmetric cross section is studied for both Dirichlet and Neumann boundary conditions on the cylinder. The method of conformal transformations as utilized by Ursell and by Tasai for the radiation problem is adapted to the present diffraction problem. The problem is solved by expansions of the reflected wave potential using nonorthogonal functions (wave free potentials). These functions are not complete, and an additional source and a dipole are required. Infinite systems of linear equations are obtained for the unknown expansion coefficients and the unknown strengths of the source and the dipole terms. Numerical results are obtained for the reflection coefficient, transmission coefficient, horizontal force on cylinder, vertical force on cylinder. In the long wave region analytical approximations are obtained for these functions when the cross section is circular. The reflection and transmission coefficients are very different for the two boundary conditions in the long wave region, the Dirichlet reflection coefficient being much larger than the corresponding Neumann coefficient. This behavior is similar to acoustic and electromagnetic diffraction problems in two dimensions.
TL;DR: In this paper, the effects of an applied magnetic field on the steady, laminar, low speed plane Couette flow of a slightly rarefied and electrically conducting gas are studied.
Abstract: The effects of an applied magnetic field on the steady, laminar, low speed plane Couette flow of a slightly rarefied and electrically conducting gas are studied. Consideration is given to the slip-flow regime, wherein the gas rarefaction begins to play its important role. The generally accepted method of analysis for slip flows is utilized, i.e. the continuum magnetohydrodynamic equations of motion are used throughout the gas, together with the first and the second order slip velocity and temperature jump boundary conditions. Considerations are further given to (1) the case of zero electric field and (2) the case of a nonconducting channel in which the net current across the channel is zero.
TL;DR: In this article, a capillary tube filled with water and air is subjected to a temperature varying linearly along its wall, the temperature is highest at the water-filled end, and the axis of the capillary may be placed horizontally or vertically.
Abstract: A capillary tube filled with water and air is subjected to a temperature varying linearly along its wall. The temperature is highest at the water-filled end. The axis of the capillary may be placed horizontally or vertically.
TL;DR: In this paper, the effect of injection on the laminar flow in the inlet region of a circular tube was investigated and shown graphically for a fourth degree velocity profile.
Abstract: Integral forms of the boundary layer equations, coupled with an assumed n-th degree boundary layer velocity profile, are used to study the effect of injection on the laminar flow in the inlet region of a circular tube. Results are illustrated graphically for a fourth degree velocity profile. It is found that the length of the inlet region decreases with the injection parameter and also that, at a given distance from the entry, the pressure drop in the inlet region increases with the injection parameter.
TL;DR: In this article, the authors propose a special construction of the chamber giving the tube the characteristic specific acoustic impedance at its terminal; the chamber is accordingly shunted to the ambient atmosphere by a narrow slit; the effect of the inertia of the slit is balanced by the capacity of the membrane chamber, the resistance constitutes the required real impedance.
Abstract: Measuring a fluctuating pressure at a discrete point in an air flow requires a narrow probe connected by a transmission tube (of arbitrary length) to the membrane chamber of a microphone. A correct transmission of the pressure in the tube is achieved by a special construction of the chamber giving the tube the characteristic specific acoustic impedance at its terminal. The chamber is accordingly shunted to the ambient atmosphere by a narrow slit; the effect of the inertia of the slit is balanced by the capacity of the chamber, the resistance constitutes the required real impedance.
TL;DR: In this article, the effects of radiation on the heat transfer in fully developed turbulent flow in a channel were investigated for both small optical depths and for the optically thin limit, using the total band absorptance.
Abstract: A study of the effects of radiation on the heat transfer in fully developed turbulent flow in a channel is carried out. The analysis is valid for both small optical depths and for the optically thin limit. Nongrey effects are included through use of the total band absorptance.
TL;DR: In this article, the conditions of magnetic self-striction in an arc of finite length, not confined laterally by walls, are investigated with a recently developed theory of ambipolar diffusion in a magnetic field, including all first order corrections.
Abstract: The conditions of magnetic self-striction in an arc of finite length, not confined laterally by walls, are investigated with a recently developed theory of ambipolar diffusion in a magnetic field, including all first order corrections. Indications are given of how numerical predictions can be made; the case of mercury vapor is treated as an example, using earlier measurements of cylindrical arcs.
TL;DR: In this article, a theoretical analysis is made to predict the load carrying capacity, flow requirement, and stiffness of an externally pressurized air-lubricated journal bearing with several supply holes.
Abstract: A theoretical analysis is made to predict the load carrying capacity, flow requirement, and stiffness of an externally pressurized air lubricated journal bearing with several supply holes. The load, flow, and stiffness, expressed in dimensionless parameters, are presented for various bearing design parameters and eccentricity ratios. The design procedure of one such bearing either for maximum load capacity or for maximum stiffness is indicated.
TL;DR: In this article, the authors apply group theory techniques for reducing the number of independent variables in systems of partial differential equations without assumptions about the functions of state which relate pressure, specific heat, viscosity, and thermal conductivity to the temperature and density.
Abstract: New results for an extensive class of real-gas compressible viscous flows are obtained by applying recent group theory techniques for reducing the number of independent variables in systems of partial differential equations. In particular, the results are obtained without assumptions about the functions of state which relate pressure, specific heat, viscosity, and thermal conductivity to the temperature and density.
TL;DR: In this paper, a line shape matching procedure based on least squares analysis is described, and the limits of reliability of the parameters found in this way are also calculated, based on a digital computer.
Abstract: A line shape matching procedure, programmed for a digital computer, is described. Based upon a least squares analysis the procedure enables one to select a line shape of a suitable analytical form and determine its parameters for the representation of an experimental single line absorption spectrum. The limits of reliability of the parameters found in this way are also calculated.
TL;DR: In this paper, the effect of radial diffusion on the performance of a liquid-liquid displacement process is considered in fluid flow between porous parallel plates and through a porous tube, as examples of a two-zone problem in unsteady-state mass transfer.
Abstract: The effect of radial diffusion on the performance of a liquid-liquid displacement process is considered in fluid flow between porous parallel plates and through a porous tube, as examples of a two-zone problem in unsteady-state mass transfer. The double Laplace transformation is applied to the system equations. In obtaining the inversion of the Laplace transformed equations the first inversion (with respect to the transformed dimensionless axial distance) is performed by use of the residue method, and then the second inversion (with respect to the transformed dimensionless time) is performed by use of the numerical Laplace transform technique advanced by Bellman et al. A numerical example is shown and discussed.
TL;DR: In this article, an analytical study of the conductivities and the wave propagation phenomenon in a colloidal plasma is presented, where a rigorous kinetic approach is used to obtain the expression for the current density.
Abstract: This paper presents an analytical study of the conductivities and the wave propagation phenomenon in a colloidal plasma. A rigorous kinetic approach is used to obtain the expression for the current density. Variations of dc and microwave conductivities, refractive index, attenuation, and reflection coefficients are studied as a function of relevant colloidal plasma parameters.
TL;DR: In this article, the first order magnetic self-striction in a low pressure arc with remote walls was investigated and a method for adding the Gvosdover effect (reduction in electron mobility by ion-electron scattering) was proposed.
Abstract: This paper continues the calculations of a preceding one (Theoretical investigation of the first order magnetic self-striction in a low pressure arc with remote walls) and indicates a method for adding the Gvosdover effect (reduction in electron mobility by ion-electron scattering) to the corrections introduced in that paper. The case of mercury vapor is, again, treated as an example.
TL;DR: In this paper, a small elastic inclusion is bonded to a large cylindrical shaft to ensure continuous displacements and tractions across the surface of the inclusion, and the shear modulus is assumed to be μ 0 exp(−1/2β2r2).
Abstract: Stresses are calculated for a small elastic inclusion bonded (in a way to ensure continuous displacements and tractions across the surface of the inclusion) to a large circular cylindrical shaft. The inclusion considered is inhomogeneous and of spherical shape. The shear modulus of the inclusion is assumed to be μ0 exp(−1/2β2r2). Some special cases are also discussed.
TL;DR: In this paper, the authors considered the two-dimensional solidification of forced viscous flow over a semi infinite flat plate and determined the growth of the solid layer as a function of time and position along the plate.
Abstract: Two-dimensional solidification of forced viscous flow over a semi infinite flat plate is considered. The plate is initially maintained at a constant temperature above the freezing point of the liquid. At time t>0, heat is removed from the plate so that the liquid freezes. The continuity equation and the two-dimensional, nonsteady, momentum and energy equations in the liquid and solid phases are solved numerically. The growth of the solid layer as a function of time and position along the plate is determined.
TL;DR: In this paper, a simple polynomial form is chosen to represent the deflection configuration of clamped parallelogrammic panels with variable thickness, and Galerkin's variational procedure is then used to yield an approximate solution to the governing differential equation of such panels under uniform lateral load.
Abstract: A simple polynomial form is chosen to represent the deflection configuration of clamped parallelogrammic panels with variable thickness. Galerkin's variational procedure is then used to yield an approximate solution to the governing differential equation of such panels under uniform lateral load. A fair agreement is shown between the theoretical results and those found from tests on a Plexiglas plate model.