Showing papers in "Flow Turbulence and Combustion in 1973"
TL;DR: In this paper, experiments have been made in the turbulent flow through a conduit of rectangular cross-section with large aspect ratio and one of the long walls has been made rough, except for a strip, located centrally.
Abstract: In continuation to an earlier publication, experiments have been made in the turbulent flow through a conduit of rectangular cross-section with large aspect ratio. One of the long walls has been made rough, except for a strip, located centrally. As shown in the earlier paper, secondary currents will occur in the regions of transition from smooth to rough wall-condition. The main purpose of the investigation was to check the admissibility of the simplifying assumptions made to the mechanical-energy balance equation. The results of the measurements indeed justified the neglect of unimportant terms of this equation, leading to the following rule. When in a localized region the production is much greater (smaller) than the viscous dissipation, there must be a secondary current that transports turbulence-poor fluid into (outwards) this region and turbulence-rich fluid outwards (into) the region.
97 citations
TL;DR: In this article, the analytical solution to the Graetz problem with uniform wall heat flux is extended by including the viscous dissipation effect in the analysis, which reduces to that of Siegel, Sparrow and Hallman neglecting viscous disipation as a limiting case.
Abstract: The analytical solution to Graetz problem with uniform wall heat flux is extended by including the viscous dissipation effect in the analysis. The analytical solution obtained reduces to that of Siegel, Sparrow and Hallman neglecting viscous dissipation as a limiting case. The sample developing temperature profiles, wall and bulk temperature distributions and the local Nusselt number variations are presented to illustrate the viscous dissipation effects. It is found that the role of viscous dissipation on thermal entrance region heat transfer is completely different for heating and cooling at wall. In the case of cooling at wall, a critical value of Brinkman number, Br
c=−11/24, exists beyond which (−11/24 B
b > T
0 indicating overall heating effect for the fluid. The numerical results for the case of cooling at wall Br < 0 are believed to be of some interest in the design of the proposed artctic oil pipeline.
69 citations
TL;DR: In this paper, the full Navier-Stokes equations describing flow through a sudden contraction are solved by an explicit finite-difference method, and Streamlines, vorticity distributions, velocity profiles, excess pressure drops and entrance lengths are calculated as functions of Reynolds number and radius ratio.
Abstract: The full Navier-Stokes equations describing flow through a sudden contraction are solved by an explicit finite-difference method. Streamlines, vorticity distributions, velocity profiles, excess pressure drops, and entrance lengths are calculated as functions of Reynolds number and radius ratio. The results are compared with existing experimental data and the limited theoretical work available.
59 citations
TL;DR: In this article, the diffraction pattern due to a plane H-polarized electromagnetic wave is investigated, when this wave is incident upon an infinitely long slit of finite width in an opaque screen of non-vanishing thickness.
Abstract: The diffraction pattern due to a plane H-polarized electromagnetic wave is investigated, when this wave is incident upon an infinitely long slit of finite width in an opaque screen of non-vanishing thickness. The screen is located between the plane boundaries of two media with different electromagnetic properties. A Green's function formulation of the problem is employed, leading to a system of four coupled integral equations in which the field distributions in the slit occur as unknowns. Numerical results are presented for the field just below the screen as well as for the far field pattern.
55 citations
TL;DR: In this article, various kinds of capillary viscometers have been used in the past, and the relation between the measured quantities and the viscosity of the fluid has been formulated.
Abstract: The purpose of this work is to analyze the various kinds of capillary viscometers that have been used in the past, and to formulate the relation between the measured quantities and the viscosity of the fluid. Three kinds of capillary viscometers are discussed: the steady-state capillary, two capillaries in tandem and the Rankine viscometer. Improved working formulae are derived for every case. Throughout the work the fluid is assumed to be incompressible. However, a short discussion of the correction for compressibility is also provided.
53 citations
TL;DR: In this paper, the relative motion of two spherical drops along their line of centers is considered and a general solution for creeping flow is presented, which may be used to predict the fractional achievement of terminal velocity of the particles.
Abstract: The relative motion of two spherical drops along their line of centres is considered and a general solution for creeping flow presented. The exact solution agrees with solutions previously published to certain limiting conditions and expressions for the drag force for these cases determined. Asymptotic solutions for large particle separations are also presented which may be used to predict the fractional achievement of terminal velocity of the particles.
52 citations
TL;DR: In this paper, a new model for the heat transfer in turbulent pipe flow is presented based on a modified form of the mixing length theory developed by Cebeci for boundary layer flow problems.
Abstract: A new model for the heat transfer in turbulent pipe flow is presented based on a modified form of the mixing length theory developed by Cebeci [1] for boundary layer flow problems. The model predicts the velocity and temperature distributions and the Nusselt number for fluids with low, medium and high Prandtl numbers (Pr=.02 to 15) and fits the available experimental data very accurately for values of Reynolds number exceeding 104. Expressions for the eddy conductivity and for the turbulent Prandtl number are presented and shown to be dependent upon the Reynolds number, the Prandtl number, and the distance from the tube wall.
37 citations
TL;DR: In this paper, the reflection and refraction of plane waves are used to construct a general solution in cylindrical coordinates for scattering by circular cylinders, which is given in terms of Bessel functions.
Abstract: The rotation of an elastic medium makes it act anisotropically and dispersively. The eigenvectors for plane wave propagation are in general complex and thus the waves are elliptically polarized. In general the waves are neither pure shear nor pure compressional waves, and their speeds depend on the ratio of rotational frequency of the medium and the angular frequency of the wave. The class of problems discussed here involves waves propagating perpendicularly to the axis of rotation and in particular we discuss plane strain modes. The reflection and refraction of plane waves is considered. The plane waves are used to construct a general solution in cylindrical coordinates. The solution is given in terms of Bessel functions. The cylindrical solution is applied to scattering by circular cylinders. The problem of free oscillations is mentioned briefly.
29 citations
TL;DR: In this paper, a numerical and experimental investigation of steady incompressible developing turbulent flow in smooth pipes is presented, where finite difference techniques are used to solve simultaneously the vorticity transport and stream function equations utilising a modified form of the Van Driest effective viscosity model.
Abstract: A numerical and experimental investigation of steady incompressible developing turbulent flow in smooth pipes is presented. Finite difference techniques are used to solve simultaneously the vorticity transport and stream function equations utilising a modified form of the Van Driest effective viscosity model. The numerical solutions are verified experimentally using air as a working fluid at pipe Reynolds 1 × 105, 2 × 105 and 3 × 105.
29 citations
TL;DR: In this paper, the vaporization or condensation rate of a motionless liquid droplet using the quasi-steady diffusion-controlled model was investigated. But the authors only considered a single component of the droplet and did not consider a series of pure hydrocarbon liquids.
Abstract: This theoretical investigation deals with the vaporization or condensation rate of a motionless liquid droplet using the quasi-steady diffusion-controlled model. A single-component liquid droplet is considered to be undergoing a phase change within a binary mixture of ideal gases (vapor plus noncondensable gas). Droplet vaporization rates corresponding to specified ambient conditions have been calculated by numerical solution of the variable-property governing equations. Results are presented for water and a series of pure hydrocarbon liquids for a range of ambient conditions of interest. A dimensionless correlation is given for the hydrocarbon vaporization and condensation rates. The pressure variation in the region surrounding a droplet undergoing vaporization or condensation has been investigated by numerical integration of the momentum equation. The resulting calculations indicate that the pressure decreases with increasing distance from the droplet for condensation as well as vaporization. Finally, criteria are given for estimating when the pressure gradient and viscous dissipation may be of significance in the energy equation.
28 citations
TL;DR: In this article, the mass transfer of oxygen to a rotating cone has been measured in a quiescent fluid with vertex angles of 19.2°, 30°, 60°, 90°, 120° and 180°.
Abstract: The mass transfer of oxygen to a rotating cone has been measured in a quiescent fluid. Cones with vertex angles of 19.2°, 30°, 60°, 90°, 120° and 180° (disks) were used in both laminar and turbulent flow at a Schmidt number of 400. The laminar flow mass transfer data is in agreement with an equation derived for cones at high Schmidt numbers. The turbulent flow mass transfer data for cones with vertex angles greater than 19.2° is in agreement with the high Schmidt number expression of Deissler. The 19.2° cone angle, however, results in experimental values for the mass transfer which are greater than the predicted values. Lastly, the values of the Reynolds number for transition from laminar to turbulent flow, as determined directly from the mass transfer data, are in agreement with previous results.
TL;DR: In this article, the moments of electric and magnetic dipoles whose far field is equivalent to the Rayleigh term in a given radiating electromagnetic field are expressed as integrals over an arbitrary closed surface of the near electromagnetic fields.
Abstract: Expressions are derived for the moments of electric and magnetic dipoles whose far field is equivalent to the Rayleigh term in the far field of a given radiating electromagnetic field. The equivalent dipole moments are expressed as integrals over an arbitrary closed surface of the near electromagnetic fields and simplification is achieved by rewriting these expressions in terms of the static potentials from which the near fields are derived. The results are valid regardless of the complexity of the field and the medium within the integration surface as long as the exterior is homogeneous, isotropic and source-free.
TL;DR: In this article, the axial velocity distribution of the three-dimensional laminar jet of an incompressible fluid with and without free stream has been analyzed and the accuracy of the method has been determined from the exact solutions of the two limiting cases of three dimensional jets, i.e., the two-dimensional and axisymmetric cases.
Abstract: Systematic numerical solutions of two-dimensional and axisymmetrical laminar jet of an incompressible fluid with and without free stream have been obtained. For the case without free stream, the exact numerical solutions have been obtained for different initial velocity profiles and compared with experimental results and similarity solutions. For the case with free stream, the numerical solutions have been compared with the linearized analytical solutions. An approximate numerical solution for the axial velocity distribution of the three-dimensional laminar jet is proposed. The accuracy of the method has been determined from the exact solutions of the two limiting cases of three-dimensional jets, i.e., the two-dimensional and axisymmetric cases.
TL;DR: In this article, a numerical solution using a combination of boundary vorticity method and line iterative relaxation method is presented for the hydrodynamically and thermally fully developed combined free and forced laminar convection with upward flow in inclined tubes subjected to the thermal boundary conditions of axially uniform wall heat flux and peripherally uniform wall temperature at any axial position.
Abstract: A numerical solution using a combination of boundary vorticity method and line iterative relaxation method is presented for the hydrodynamically and thermally fully developed combined free and forced laminar convection with upward flow in inclined tubes subjected to the thermal boundary conditions of axially uniform wall heat flux and peripherally uniform wall temperature at any axial position. The numerical solution converges up to a reasonably high value of the characteristic parameter where an asymptotic behaviour for flow and heat transfer resultsfalready appears, and further results can be obtained by a linear extrapolation. The tube inclination angle or body-force orientation effects on flow and heat transfer characteristics are clarified for upward laminar flow configuration, and show that in high Rayleigh number regime the tube orientation effect has considerable influence on the results in the neighborhood of horizontal direction. Typical graphical results for flow and heat transfer are presented, mainly to illustrate the effects of Rayleigh number and tube inclination. The numerical results show that the perturbation method is invalid for the present problem.
TL;DR: In this paper, it was shown that the inclusion of the boundary effects gives rise to frequency components in the transmitted signal which were not predicted by previous theories, and that the interference from boundary effects leads to frequency variations in the signal.
Abstract: Expressions are obtained for the electromagnetic fields transmitted through a time-varying dielectric layer when a plane wave is incident normally upon one interface. Solutions are obtained for the case when the dielectric constant is changed in a stepwise fashion, and also for the case when the dielectric constant varies slowly and continuously. It is found that the inclusion of the boundary effects gives rise to frequency components in the transmitted signal which were not predicted by previous theories.
TL;DR: In this paper, the volume ratios of the residual and detached parts of drops, determined experimentally are compared with those predicted theoretically by Lohnstein, and the results show that the residual ratios of drops are significantly larger than those predicted by the theoretical model.
Abstract: Volume ratios of the residual and detached parts of drops, determined experimentally are compared with those predicted theoretically by Lohnstein.
TL;DR: In this article, the Stokes problems of an incompressible, viscous, conducting fluid with embedded small spherical particles over an infinite plate, set into motion in its plane by impulse and by oscillation, in the presence of a transverse magnetic field, are studied.
Abstract: The Stokes problems of an incompressible, viscous, conducting fluid with embedded small spherical particles over an infinite plate, set into motion in its plane by impulse and by oscillation, in the presence of a transverse magnetic field, are studied. The velocities of the fluid and of the particles and the wall shear stress are obtained. The stress is found to increase due to the particles and the magnetic field, with the effect of the particles diminishing as the field strength is increased.
TL;DR: In this paper, the authors investigated the scattering of a plane electromagnetic wave by a perfectly conducting elliptic cylinder, based upon the expansion of the scattered wave functions in terms of Mathieu functions.
Abstract: The scattering of a plane electromagnetic wave by a perfectly conducting elliptic cylinder is investigated theoretically. The calculations are based upon the expansion of the scattered wave functions in terms of Mathieu functions. Both E- and H-polarized waves are considered. Numerical results, in particular for the scattering cross-section, are presented for cylinders the cross-sectional dimensions of which are up to many wavelengths (e.g. distance between the focal lines up to 20 wavelengths).
TL;DR: In this paper, the shape of the shoulder of a forming, filling and closing machine is calculated, based on geometrical considerations, first for a circular and subsequently for a rectangular (superelliptic) section.
Abstract: The shape of the shoulder of a forming, filling and closing machine is calculated, based on geometrical considerations, first for a circular and subsequently for a rectangular (superelliptic) section. It appears to be possible to formulate a feasible solution for a model represented by a flat triangular region in the centre, which connects two truncated cones; for each cone one half of the intersection of shoulder and cylinder acts as the directrix of the cone. The solutions are formulated in terms which permit direct application in machine construction. Verification of the theory with the help of paper models and with real shoulders on machines shows a very good agreement between theory and practice. In addition practical tests produce excellent results as well.
TL;DR: In this article, slow and steady viscous fluid flow in a pipe whose cross-section is bounded by an ellipse and a circle is considered and the method used is in deriving general solutions independently on the two boundaries using one or two conformal mapping functions and an attempt is made to make the complex potentials continuous in the doubly connected region.
Abstract: Slow and steady viscous fluid flow in a pipe whose cross-section is bounded by an ellipse and a circle is considered. The method used is in deriving general solutions independently on the two boundaries using one or two conformal mapping functions and an attempt is made to make the complex potentials continuous in the doubly connected region. Numerical results are found and compared with those for the case of concentric circles and the case of concentric ellipses.
TL;DR: The maxima and minima of the power reflection coefficient as a function of the wave frequency of an electromagnetic wave obliquely incident on isotropic and uni-axial plasma slabs are discussed in this paper.
Abstract: The maxima and minima of the power reflection coefficient as a function of the wave frequency of an electromagnetic wave obliquely incident on isotropic and uni-axial plasma slabs are discussed.
TL;DR: In this paper, the exact solution of the equation of motion of a circular disk accelerated along its axis of symmetry due to an arbitrarily applied force in an otherwise still, incompressible, viscous fluid of infinite extent is obtained.
Abstract: The exact solution of the equation of motion of a circular disk accelerated along its axis of symmetry due to an arbitrarily applied force in an otherwise still, incompressible, viscous fluid of infinite extent is obtained. The fluid resistance considered in this paper is the Stokes-flow drag which consists of the added mass effect, steady state drag, and the effect of the history of the motion. The solutions for the velocity and displacement of the circular disk are presented in explicit forms for the cases of constant and impulsive forcing functions. The importance of the effect of the history of the motion is discussed.
TL;DR: In this article, a flow of conducting liquid through two porous nonconducting infinite circular cylinders rotating with various angular velocities for some time in the presence of a radial magnetic field was investigated.
Abstract: In this note the author has investigated some problems of a flow of conducting liquid through two porous non-conducting infinite circular cylinders rotating with various angular velocities for some time in the presence of a radial magnetic field.
TL;DR: In this article, general expressions for fully developed temperature profiles and Nusselt numbers are obtained for heat transfer to non-Newtonian fluid flow between parallel plates and through circular pipes subjected to a uniform wall heat flux.
Abstract: General expressions for fully developed temperature profiles and Nusselt numbers are obtained for heat transfer to non-Newtonian fluid flow between parallel plates and through circular pipes subjected to a uniform wall heat flux. The effect of viscous dissipation is taken into account since it may often be significant in the flow of non-Newtonian fluids. Asymptotic Nusselt numbers for three widely used models, i.e. the power law fluid, the Bingham plastic, and the Ellis fluid are obtained as specific results.
TL;DR: In this paper, approximate solutions of the Navier-Stokes equations are derived through the Laplace transform for two dimensional, incompressible, elastico-viscous flow past a flat porous plate.
Abstract: Approximate solutions of the Navier-Stokes equations are derived through the Laplace transform for two dimensional, incompressible, elastico-viscous flow past a flat porous plate. The flow is assumed to be independent of the distance parallel to the plate. General formulae for the velocity distribution, skin friction and displacement thickness as functions of the given free stream velocity and suction velocity are obtained.
TL;DR: In this article, the effect of inclination on laminar film condensation over and under isothermal flat plates is investigated analytically and the complete set of Navier Stokes equations in two dimensions is considered.
Abstract: The effect of inclination on laminar film condensation over and under isothermal flat plates is investigated analytically. The complete set of Navier Stokes equations in two dimensions is considered. Analysed as a perturbation problem, the zero-order perturbation represents the boundary layer equations. First and second order perturbations are solved to bring about the leading edge effects. Corresponding velocity and temperature profiles are presented. The results show decrease in heat transfer with larger ∥inclinations∥ from the vertical. Comparison with experimental data of Gerstmann and Griffith indicates a closer agreement of the present results than the analytical results of the same authors.
TL;DR: In this article, the authors presented accurate numerical data concerning the creeping flow in curved annular channels with rectangular cross sections of which the outer wall is rotating with constant angular velocity, and the results of the theoretical analysis were also expressed in terms of the flow rate correction factors widely used in calculating the pumping efficiency of screw-pumps, agitators and extruders.
Abstract: The object of this paper is to present accurate numerical data concerning the creeping flow in curved annular channels with rectangular cross sections of which the outer wall is rotating with constant angular velocity. Dimensionless expressions for velocity profiles, flow rates and friction factors are obtained analytically for both the “drag” and “pressure” flow contributions. Numerical data were obtained on a digital computer and are presented in tabular and graphical form. The results of the theoretical analysis are also expressed in terms of the flow rate correction factors widely used in calculating the pumping efficiency of screw-pumps, agitators and extruders. This enables to estimate the effect of flight curvature on the pumping capacity.
TL;DR: In this paper, the Monte Carlo method was used to study the statistics of electromagnetic rays in a random medium and to trace the path of a ray in a 2D random surface with prescribed correlation functions.
Abstract: Statistics of electromagnetic rays in a random medium are studied numerically by the Monte Carlo method. Two dimensional random surfaces with prescribed correlation functions are used to simulate the random media. Rays are then traced in these sample media. Statistics of the ray properties such as the ray positions and directions are computed. Histograms showing the distributions of the ray positions and directions at different points along the ray path as well as at given points in space are given. The numerical experiment is repeated for different cases corresponding to weakly and strongly random media with isotropic and anisotropic irregularities. Results are compared with those derived from theoretical investigations whenever possible.
TL;DR: In this article, the cooling effect of liquid droplets introduced into a hot gas stream flowing in an adiabatic duct is analyzed, and the coupled interaction between the changes in the droplets and in the surrounding gas conditions is examined as a result of droplets vaporization.
Abstract: The cooling effect of liquid droplets introduced into a hot gas stream flowing in an adiabatic duct is analysed. The coupled interaction between the changes in the droplets and in the surrounding gas conditions is examined as a result of droplets vaporization. It was found that the use of liquid sprays as a rapid cooling process for a hot gas discharge is quite effective.