Showing papers in "Flow Turbulence and Combustion in 1971"
TL;DR: In this paper, the effects of angular velocity variation on the shock velocity were shown graphically, and it was found that an increase in the initial angular velocity leads to a decrease in the velocity.
Abstract: Similarity solutions describing the flow behind a diverging strong cylindrical shock wave, advancing into a nonuniform gas having solid body rotation, are studied. The effects of the angular velocity variation on the shock velocity are shown graphically. It is found that an increase in the initial angular velocity leads to a decrease in the shock velocity.
71 citations
TL;DR: In this article, the reflection of a monochromatic plane electromagnetic wave by an electrically perfectly conducting grating is investigated, and the vectorial electromagnetic problem is reduced to two separate scalar problems: those corresponding to E- and H-polarization respectively.
Abstract: The reflection of a monochromatic plane electromagnetic wave by an electrically perfectly conducting grating is investigated. The vectorial electromagnetic problem is reduced to two separate scalar problems: those corresponding to E- and H-polarization respectively. A Green's function formulation of the problem is employed. For both cases an integral equation of the second kind for the remaining unknown function on the surface of the grating is derived. A numerical solution of this integral equation is obtained with the aid of either a (discrete) Fourier transform or a cubic spline approximation. Some numerical results of both the echellette grating and the sinusoidal grating are presented.
65 citations
TL;DR: In this article, the steady flow in a parallel plate channel rotating with an angular velocity Ω and subjected to a constant transverse magnetic field is analyzed and an exact solution of the governing equations is obtained.
Abstract: The steady flow in a parallel plate channel rotating with an angular velocity Ω and subjected to a constant transverse magnetic field is analysed. An exact solution of the governing equations is obtained. The solution in the dimensionless form contains two parameters: the Hartmann number, M2, and K2 which is the reciprocal of the Ekman number. The effects of these parameters on the velocity and magnetic field distributions are studied. For large values of the parameters, there arise thin boundary layers on the walls of the channel.
43 citations
TL;DR: In this paper, a finite difference technique is used for the evaluation of the rate of heat transfer in the thermal entrance region of ducts with axial conduction, and the velocity profile is fully developed and flow in a tube and between parallel plates is studied.
Abstract: A finite difference technique is used for the evaluation of the rate of heat transfer in the thermal entrance region of ducts with axial conduction. The velocity profile is fully developed and flow in a tube and between parallel plates is studied. Local and average Nusselt numbers and mixing temperatures are presented as a function of the Peclet number. A criterion is also established which proves useful for predicting the conditions under which axial conduction may be ignored.
26 citations
TL;DR: In this paper, the general case of a fully developed pipe flow of a suspension in a turbulent fluid with electrically charged particles or with significant gravity effect, or both, and for any inclination of the pipe with the direction of gravity, is formulated.
Abstract: The general case of a fully developed pipe flow of a suspension in a turbulent fluid with electrically charged particles or with significant gravity effect, or both, and for any inclination of the pipe with the direction of gravity, is formulated. Parameters defining the state of motion are: pipe flow Reynolds number, Froude number, electro diffusion number, diffusion response number, momentum transfer number and particle Knudsen number. Comparison with experimental results is made for both gas-solid and liquid-solid suspensions. It is shown that the gravity effect becomes significant in the case of large pipe diameters and large particle concentrations.
22 citations
TL;DR: In this paper, the roughness-induced mean velocity in terms of the spectral density of roughness and an influence function is calculated in an integral form using the known values of modified Hankel functions of order 1/3 and their integrals.
Abstract: Flow past a rough wall is examined. Calculations are made to find the roughness-induced mean velocity which is expressed in an integral form in terms of the spectral density of the roughness and an influence function. Values of the influence function are tabulated using the known values of the modified Hankel functions of order 1/3 and their integrals. The first order change in lower critical Reynolds number due to the roughness-induced change in profile is calculated; the stability of the profile is increased due to the presence of roughness.
19 citations
TL;DR: In this article, the Rayleigh and Marangoni types of instability of completely and partially confined fluid columns are considered and appropriate differential systems are reformulated in a form that fully accounts for the presence of the surrounding solid and free surfaces as well as for the surface-tension variations in the latter.
Abstract: Rayleigh and Marangoni types of instability of completely and partially confined fluid columns are considered The appropriate differential systems are reformulated in a form that fully accounts for the presence of the surrounding solid and free surfaces as well as for the surface-tension variations in the latter The present work is carried out under the assumption that the free surface, if present, is constrained to stay horizontal It is shown that if this assumption and the principle of exchange of stabilities hold the differential systems for both open and closed containers, govern no less than four dependent variables
11 citations
TL;DR: In this article, upper and lower bounds for the mass flow rate for the steady flow of a conducting liquid along a pipe of arbitrary cross section under the influence of a uniform transverse magnetic field are obtained.
Abstract: Upper and lower bounds are obtained for the mass flow rate for the steady flow of a conducting liquid along a pipe of arbitrary cross section under the influence of a uniform transverse magnetic field. The extrema are constructed by first establishing an identity which is then used in some simple inequalities. It is shown how these bounds can be used to derive an asymptotic expansion for the flow rate at large Hartmann number. Two illustrations are included.
10 citations
TL;DR: In this article, the scattering of a plane electromagnetic wave by a dielectric lens which behaves like a metal reflector is considered and the leading term of the backscattered field cannot be determined entirely through simple geometrical optics considerations; instead, it is obtained by means of a modified Watson transformation of the exact solution.
Abstract: The scattering of a plane electromagnetic wave by a dielectric lens which behaves like a metal reflector is considered. At short wavelengths, the leading term of the backscattered field cannot be determined entirely through simple geometrical optics considerations; instead, it is obtained by means of a modified Watson transformation of the exact solution. The difficulties that arise in applying this technique to other lenses are discussed.
10 citations
TL;DR: In this paper, the influence of a vertical magnetic field on the stability of a compressible, inviscid fluid of variable density is investigated and an approximate solution for the fluid of exponentially varying density, confined between two planes is obtained.
Abstract: The influence of a vertical magnetic field on the stability of a compressible, inviscid fluid of variable density is investigated. The solution is characterized by a variational principle. Based on it an approximate solution for the fluid of exponentially varying density, confined between two planes is obtained. The magnetic field is found to have a stabilizing influence on the unstable arrangement. Also the effect of a magnetic field on the angular frequency of oscillations of the waves generated in stable arrangement is considered.
10 citations
TL;DR: The steady two-dimensional laminar flow of an incompressible conducting fluid between two parallel circular disks in the presence of a transverse magnetic field was investigated in this article.
Abstract: The steady two-dimensional laminar flow of an incompressible conducting fluid between two parallel circular disks in the presence of a transverse magnetic field is investigated. A solution is obtained by perturbing the creeping flow solution and it is valid only for small suction or injection Reynolds numbers. Expressions for velocity, induced magnetic field, pressure, and shear stress distribution are determined and are compared with the creeping flow and hydrodynamic solutions. It is found that the overall effect of the magnetic field on the flow is the same as that in the Hartmann flow.
TL;DR: In this article, the effect of a uniform external magnetic field on the laminar, incompressible rarefied gas flow along an infinite porous flat plate is studied under the following conditions: 1) there is uniform suction, 2) the external flow velocity varies periodically with time in magnitude but not in direction, 3) the magnetic Reynolds number is small and 4) the current occurs under slip flow boundary conditions.
Abstract: The effect of a uniform external magnetic field on the laminar, incompressible rarefied gas flow along an infinite porous flat plate is studied under the following conditions: 1) there is uniform suction, 2) the external flow velocity varies periodically with time in magnitude but not in direction, 3) the magnetic Reynolds number is small and 4) the current occurs under slip flow boundary conditions. Expressions for the velocity and temperature fields in the boundary layer are obtained. The response of skin friction, and heat transfer to the fluctuating stream is studied for variations in the rarefaction parameter h
1, the magnetic field parameter M, and the frequency of the fluctuating stream.
TL;DR: In this article, the authors investigated the effect of frequency on the sensitivity and the temperature distribution of a hot wire to the ambient airflow, and provided a short review of some complicating factors not included in the linear theory.
Abstract: The aim of the investigation was primarily the computation of the dynamical corrections on the static calibration curve. A brief account is given of the available analytical expressions for the heat transfer of a hot wire to the ambient airflow. The appropriate form is inserted in the small perturbation energy equation giving, with constant values of the characteristic parameters, a linear second order differential equation. A number of numerical examples was computed from the exact solution yielding the influence of frequency on the sensitivity and the temperature distribution along the wire. The analysis is supplemented by a short review of some complicating factors not included in the linear theory.
TL;DR: In this paper, the theory of temperature variation at any point in an infinitely extending medium containing an infinitely long thin conducting wire, heated periodically, is applied to a probe having finite dimensions and thermal properties.
Abstract: The theory of temperature variation at any point in an infinitely extending medium containing an infinitely long thin conducting wire, heated periodically, is applied to a probe having finite dimensions and thermal properties. The conditions for a minimal effect due to finite dimension of the medium and contact resistance between the probe and medium are discussed. The results of thermal conductivity and diffusivity, thus obtained, are reported. The thermal probe method under periodic conditions gives satisfactory results.
TL;DR: In this paper, a method for numerical reduction of transient matrix heat transfer test data resulting from single blow experiments is described, which permits in the entire practical N tu-range the numerical reduction.
Abstract: A method is described which permits in the entire practical N tu-range the numerical reduction of transient matrix heat transfer test data resulting from single blow experiments. Two particular cases are analyzed in detail: (1) the idealized case where the upstream fluid temperature follows a step change, and (2) the more realistic case where the upstream fluid temperature follows a decreasing exponential function, which is an acceptable assumption whenever a fast response electrical heater is employed to produce the upstream fluid temperature change. Discrete direct curve matching as formulated in this paper consists of minimizing a suitable distance function defined on discrete sets of data points. In an appendix to the present paper, the implementation of a direct curve matching method is presented for the more general case of an “arbitrary” upstream fluid temperature change.
TL;DR: In this article, the authors measured the concentration diffusion coefficient, D12, for the equimolar mixtures of Ne-Ar, Ne-Xe, NE-H2, Xe-H 2, H2-N2 and H2O2 binary gas systems in a two-bulb metal apparatus in the temperature range 0 C to 100 C.
Abstract: The concentration diffusion coefficient, D12, is measured for the equimolar mixtures of Ne-Ar, Ne-Xe, Ne-H2, Xe-H2, H2-N2 and H2-O2 binary gas systems in a two-bulb metal apparatus in the temperature range 0 C to 100 C. These values are compared with the existing data on these systems and with the predictions of the kinetic theory in conjunction with the modified Buckingham exp-six potential. Unlike the thermal diffusion coefficient, with the simple theory it is possible to predict D12 within a few percent even for systems involving polyatomic gases. The smoothed experimental D12 values are also used to obtain data for the coefficients of viscosity and thermal conductivity at round temperatures and compositions for these systems.
TL;DR: In this article, the nonlinear static behavior of a linearly elastic cantilever subjected to a nonconservative force of the follower type is formulated and examined, and exact solutions are found.
Abstract: The nonlinear static behavior of a linearly elastic cantilever subjected to a nonconservative force of the follower type is formulated and examined. The formulation allows for finite rotations with small strains (the elastica). Exact solutions are found. The investigation is greatly facilitated by means of a phase plane analysis in which the phase plane variables are related to slope angle and bending moment. Some of the interesting and unusual effects occurring in this system are discussed and illustrated with a set of deflection curves for a typical case.
TL;DR: In this paper, the torque on the inner cylinder of a second order fluid in the supercritical regime is calculated using the energy method, and it is shown that when the second normal stress difference is negative, the flow is more stable than for a Newtonian fluid and the torque is reduced.
Abstract: Using Stuart's energy method, the torque on the inner cylinder, for a second order fluid, in the supercritical regime is calculated. It is found that when the second normal stress difference is negative, the flow is more stable than for a Newtonian fluid and the torque is reduced. If the second normal stress difference is positive, then the flow is more stable and there is no torque reduction. Experimental data related to the present work are discussed.
TL;DR: In this article, an analysis for laminar source flow between parallel stationary porous disks with suction at one of the disks and equal injection at the other is presented in the form of an infinite series expansion about the solution at infinite radius.
Abstract: An analysis is presented for laminar source flow between parallel stationary porous disks with suction at one of the disks and equal injection at the other. The solution is in the form of an infinite series expansion about the solution at infinite radius, and is valid for all suction and injection rates. Expressions for the velocity, pressure, and shear stress are presented and the effect of the cross flow is discussed.
TL;DR: In this paper, an analytical continuum solution of the Rayleigh problem in slip flow with applied magnetic field is obtained using a modified initial condition and slip boundary conditions, and the results are uniformly valid for all times and show that the velocity slip and local skin friction coefficient remain almost unaffected by the imposition of the magnetic field for small times.
Abstract: An analytical continuum solution of the Rayleigh problem in slip flow with applied magnetic field is obtained using a modified initial condition and slip boundary conditions. The results are uniformly valid for all times and show that the velocity slip and the local skin friction coefficient remain almost unaffected by the imposition of the magnetic field for small times. They increase however with the magnetic field for large times. The present results reduce to the corresponding results of the hydrodynamic case when there is no magnetic field.
TL;DR: The results of an investigation of the plasma parameters generated by a large V-groove cathode discharge are presented in this paper, where the electron densities up to 2×1012 cm−3 have been obtained in the 12 inch diameter chamber.
Abstract: The results of an investigation of the plasma parameters generated by a large V-groove cathode discharge are presented. The cathode consists of a twelve inch aluminum plate into which V-grooves of 1/8th inch spacing and 60 deg angle are milled. With this cathode, a negative glow discharge is produced which yields a stable, steady-state plasma. Electron densities up to 2×1012 cm−3 have been obtained in the 12 inch diameter chamber. The electron temperature is about 1200 K and is independent of discharge current and gas pressure over the range, 0.3 to 0.9 Torr.
TL;DR: In this article, the acceleration covariance of an incompressible, viscous and conducting fluid is derived for isotropic, spatially homogeneous MHD turbulence, where the defining scalars α(r, t) and β(r, t) depend on the defined scalars of Qij, Hij, Πij and Sik, j.
Abstract: The present paper deals with the turbulent flow of an incompressible, viscous and conducting fluid which is isotropic, spatially homogeneous. The expression for acceleration covariance is derived. The obtained result shows that the defining scalars α(r, t) and β(r, t) of the acceleration covariance in MHD turbulence depend on the defining scalars of Qij, Hij, Πij and Sik, j.
TL;DR: In this article, hot wires of various design, operated by the constant resistance method, were calibrated by means of a plane sound wave of 2500 Hz, which was achieved by locating a small open resonance tube axially in a homogeneous incompressible airflow.
Abstract: Hot wires of various design, operated by the constant resistance method, were calibrated by means of a plane sound wave of 2500 Hz. This is achieved by locating a small open resonance tube axially in a homogeneous incompressible airflow. Its third harmonic is excitated by superimposing a coaxial, damped, progressive, plane wave on the main airstream. The hot wire to be calibrated is situated in an anti-node of the particle velocity. The amplitude at this station is known from the pressure gradient of the standing wave measured at two small holes in the wall by a probe microphone. This device in turn is calibrated in a specially developed “pistonphone”. Numerical results of the diverse designs are communicated; an absolute accuracy of ±2% is achieved.
TL;DR: In this paper, the flow of a dipolar fluid between two parallel plates with and without heat transfer is studied, and the following cases are discussed, without and with heat transfer:
Abstract: The flow of a dipolar fluid between two parallel plates with and without heat transfer is studied. The following cases are discussed:
TL;DR: In this paper, the authors analyzed the scattering of a low frequency electromagnetic wave by a metallic cone, whose base is part of a spherical surface centered on the apex of the cone, using a mode matching technique.
Abstract: The scattering of a low frequency electromagnetic wave by a metallic cone, whose base is part of a spherical surface centered on the apex of the cone, is analyzed using a mode matching technique. The dipole contributions to the scattering are obtained in complete generality, and numerical results are presented for a wide range of cone angles. Comparisons of the computed data with the predictions of an empirical formula for the scattering reveal both the strengths and weaknesses of the latter.
TL;DR: In this paper, a method of successive approximations is utilized to analyze the potential flow field around freely rising collapsing bubble trains, and an infinite series solution is obtained and the truncation errors are quantitatively analyzed.
Abstract: A method of successive approximations is utilized to analyze the potential flow field around freely rising collapsing bubble trains. For simplicity, the analysis is confined to a two bubble column. An infinite series solution is obtained and the truncation errors are quantitatively analyzed.
TL;DR: In this article, the authors applied the method of discrete ordinates, in conjunction with the modified half-range quadrature, to the study of heat transfer in rarefied gas flows.
Abstract: The method of discrete ordinates, in conjunction with the modified “half-range” quadrature, is applied to the study of heat transfer in rarefied gas flows. Analytic expressions for the reduced distribution function, the macroscopic temperature profile and the heat flux are obtained in the general n-th approximation. The results for temperature profile and heat flux are in sufficiently good accord both with the results of the previous investigators and with the experimental data.
TL;DR: In this article, the optimal control of a heat exchanger having internal heat sources from a reference steady state to a desired value was investigated under certain constraints inherent in the operating conditions and physical limitations.
Abstract: This paper investigates the optimum control of a heat exchanger having internal heat sources from a reference steady state to a desired value. Both the wall and coolant are treated as distributed-parameter systems. Under certain constraints inherent in the operating conditions and physical limitations of the heat exchanger, the control function of the system, i.e. the heat generation rate which minimizes the deviation of the temperature distribution from an assigned pattern at a given time, is found through the use of a linear programming method. The effects of physical parameters on the optimal control function and the temperature response and distribution are examined. Experimental results are presented which compare favorably with the theoretical analysis. Heat exchangers to which these results apply include the electrical heater, a chemical reactor in which a chemical reaction occurs within the solid walls and a heterogeneous nuclear reactor.
TL;DR: In this article, a simple model of rigid dumbbells suspended in a Newtonian fluid with Brownian motion included is represented by a simple macromolecular solution, and the ultimate shear recovery S∞ is developed as a power series in κ−, the shear rate prior to the cessation of the steady shear flow.
Abstract: A macromolecular solution is represented by the simple model of rigid dumbbells suspended in a Newtonian fluid with Brownian motion included. Hydrodynamic interaction is not taken into account. It is found that for this model there will be recoil after the cessation of steady shearing flow. The ultimate shear recovery S∞ is developed as a power series in κ−, the shear rate prior to the cessation of the steady shear flow:
$$S_\infty = (\theta _0 /2\eta _0 ) \kappa ^\user1{ - } + O(\kappa ^\user1{ - } )^3$$
where η0 and θ0 values of the viscosity and primary normal stress functions respectively at zero-shear rate. The coefficient of the term in (κ−)3 is calculated. In addition, the behavior of the normal stresses during the recoil process is found; during recoil τ22−τ33 has the opposite sign from τ11−τ22.
TL;DR: In this article, the coupled problem whereby a solid heat generating cylinder is being cooled in steady state by a coolant in potential flow is investigated, and an analytical technique for determining the temperature distributions in the solid and the fluid is presented.
Abstract: The coupled problem whereby a solid heat generating cylinder is being cooled in steady state by a coolant in potential flow is investigated. An analytical technique for determining the temperature distributions in the solid and the fluid is presented. Numerical studies for six Peclet numbers (0.9