POF Nameplate
  • Volume/Page
  • Keyword
  • DOI
  • Citation
  • Advanced
   
 
 
 

Flickr Twitter iResearch App Facebook

SECTION LISTING

Search Issue | RSS Feeds RSS
Previous Issue

Dec 1972

Volume 15, Issue 12, pp. 2083-2451

Page 1 of 3 Pages Next Page | Jump to Page

Oscillating Cylinders and the Stokes' Paradox

Robert E. Williams and R. G. Hussey

Phys. Fluids 15, 2083 (1972); http://dx.doi.org/10.1063/1.1693839 (6 pages) | Cited 9 times

Online Publication Date: 31 July 2003

Full Text: | Download PDF


See Also: Erratum

Show Abstract
Measurements are reported of the inertia coefficient k and damping coefficient k′ for a circular cylinder (radius a) oscillating at angular frequency ω in a fluid of kinematic viscosity ν. Good agreement with the theory of Stokes is obtained throughout the range 0.286<(2ν/ωa2)1/2<4.13 even when the Reynolds number R and the relative amplitude are not small compared with 1. Stokes' theory is expressed in terms of modified Bessel functions, and values of k and k′ are tabulated for 0.001<(a2ω/4ν)1/2<0.5. The relation to Stokes' paradox is considered by examining the damping force in the limit (ωa2/ν)1/2≪1. The damping force for a cylinder, unlike that for a sphere, does not reduce to the low R drag in this limit. However, comparison with Lamb's solution of the Oseen equations suggests an expression that agrees well with drag measurements up to R  =  2.5.

Closed Streamlines Associated with Channel Flow over a Cavity

Vivian O'Brien

Phys. Fluids 15, 2089 (1972); http://dx.doi.org/10.1063/1.1693840 (9 pages) | Cited 26 times

Online Publication Date: 31 July 2003

Full Text: | Download PDF

Show Abstract
The viscous Stokes flow induced in a rectangular cavity by a parallel shear flow is calculated by a direct finite difference method. The separating streamline and the intensity of the circulation of the closed streamline flow within the cavity are shown as a function of cavity shape, relative channel size to cavity size, and the parallel velocity profile within the channel. Application of the results to viscous flow observations are indicated.

Numerical Solution of the Navier‐Stokes Equations by the Finite Element Method

Ralph Ta‐shun Cheng

Phys. Fluids 15, 2098 (1972); http://dx.doi.org/10.1063/1.1693841 (8 pages) | Cited 39 times

Online Publication Date: 31 July 2003

Full Text: | Download PDF

Show Abstract
Occurrences of viscous fluid flows in arbitrary internal passages are numerous, an analytical solution of the governing Navier‐Stokes equations cannot be obtained. Even a numerical approach faces difficulties arising from the nonlinearity and complexity of the geometry involved. To remedy these difficulties, the time‐dependent Navier‐Stokes equations are solved by the finite element method wherein a steady‐state solution is assumed when the time‐dependent solution becomes convergent. A family of locally constricted channels was considered in the computations, and in each case, the shear stress at the wall was found to be sharply increased at and near the region of constriction. Computations were carried out to Reynolds numbers when a separation eddy was established. The numerical scheme used seems to be fairly stable.

Perturbation Technique for the Study of Three‐Dimensional Separation

J. Buckmaster

Phys. Fluids 15, 2106 (1972); http://dx.doi.org/10.1063/1.1693842 (8 pages) | Cited 5 times

Online Publication Date: 31 July 2003

Full Text: | Download PDF

Show Abstract
The three‐dimensional boundary‐layer equations are studied close to separation and to a plane of symmetry. Perturbation about a one‐dimensional parabolic flow field leads to a sequence of linear equations which have eigensolutions, the first of which satisfies a nonlinear equation. This first eigensolution contains all the important information about the skin friction, and by appropriate choice of the perturbation problem the skin friction is shown to satisfy a first order nonlinear wave equation. The characteristics of this equation are the skin‐friction lines (surface stream lines), and their behavior is described close to separation. The description obtained is a global one (that is, not restricted to the neighborhood of a plane of symmetry) when the cross flow is small. The validity of the local solution is confirmed by a Goldstein‐type coordinate expansion.

Spatial Stability of Stagnation Water Boundary Layer with Heat Transfer

A. R. Wazzan, Gerlina Keltner, T. T. Okamura, and A. M. O. Smith

Phys. Fluids 15, 2114 (1972); http://dx.doi.org/10.1063/1.1693843 (5 pages) | Cited 13 times

Online Publication Date: 31 July 2003

Full Text: | Download PDF

Show Abstract
Neglecting temperature fluctuations, assuming viscosity is only temperature dependent, and assuming all other fluid properties are constant, the two‐dimensional linearized parallel flow stability problem is adequately treated by modifying the Orr‐Sommerfeld equation to include viscosity variations with temperature. The resulting equation is used to study the spatial stability of stagnation water boundary layer with heat transfer. The mean flow with free‐stream temperature T∞  =  60°F and wall temperature Tw ranging from 32 to 200°F is computed numerically, from the boundary layer equations with variable fluid properties. It is found that heating stabilizes the boundary layer and cooling destabilizes it. At Tw ≅ 196°F the neutral curve degenerates to a singular point at frequency ω  =  5×10−7 and Reynolds number Rδ*  =  30.7×103. All disturbances become completely damped for Tw>196°F. It appears that the effect of viscosity μ is larger than the effect of its first derivative μ′ on stability, and that the effect of μ″ is negligible compared with the effect of μ′.

Temperature Field Structure in Strongly Heated Buoyant Thermals

Shao‐Chi Lin, Leslie Tsang, and C. P. Wang

Phys. Fluids 15, 2118 (1972); http://dx.doi.org/10.1063/1.1693844 (11 pages) | Cited 15 times

Online Publication Date: 31 July 2003

Full Text: | Download PDF

Show Abstract
Laboratory measurements on the temperature field structure in rising turbulent thermals are presented. The relatively small size (about 10 cm initial diameter), but strongly heated thermal bubbles are generated by pulsed arc discharges of about 103 J energy in otherwise undisturbed air. Temperature field measurements are made by stationary and rotating fine‐wire thermometers which probe through the rising bubble. The thermal front is found to be sharp at the top and around the side of the bubble, but become diffused near the bottom, suggesting thermal wake formation. The large amplitude fluctuation, strong gradient, and rich harmonic content of the interior temperature field indicate that the mass entrainment process penetrates deeply into the bubble, and turbulent mixing proceeds at all depths. By invoking passive scalar mixing theories and assuming local equilibrium spectral transfer, the averaged turbulence kinetic energy dissipation rate within the bubble ϵ can be estimated from the diffusive cutoff wavenumber apparent in these preliminary experiments to be of the order of 0.03 (U3/D), where U and D are, respectively, the instantaneous rise velocity and mean diameter of the bubble.

Characteristics of the Unsteady Shock‐Induced Laminar Boundary Layer on a Flat Plate

William J. Cook and Gary T. Chapman

Phys. Fluids 15, 2129 (1972); http://dx.doi.org/10.1063/1.1693845 (11 pages) | Cited 2 times

Online Publication Date: 31 July 2003

Full Text: | Download PDF

Show Abstract
The unsteady shock‐induced laminar boundary layer on a flat plate is theoretically studied for shock speeds ranging from 1.12 to 9 km/sec. Boundary layer flows for real air, assumed to be in thermochemical equilibrium, are analyzed by extending Lam's work on shock‐induced laminar boundary layers to equilibrium dissociated and ionized flows. A complete description of the unsteady nature of the boundary layer is presented in terms of heat transfer and several boundary layer thickness quantities as functions of a single time‐position variable. Boundary layer development is considered for two points of view. Time‐dependent boundary layer development and approach to steady state for any fixed position on the plate is described, as is the configuration of the boundary layer with position on the plate at any point in time. Quantities presented in graphical form permit accurate values for descriptive boundary layer quantities to be easily obtained for post shock pressures at or near 1 atm. Results indicate that in shock‐tube experiments where observations of the flow are made through a boundary layer that influences experimental measurements, it is desirable to employ a flat plate to generate a boundary layer that minimizes the boundary layer thickness and diminishes or eliminates boundary layer unsteadiness.

Nonplanar Relativistic Flow

Peter G. Eltgroth

Phys. Fluids 15, 2140 (1972); http://dx.doi.org/10.1063/1.1693846 (5 pages) | Cited 8 times

Online Publication Date: 31 July 2003

Full Text: | Download PDF

Show Abstract
The equations for nonplanar relativistic flow are solved by similarity analysis for a restricted set of problems. The relativistic equation of state p  =  ⅓ E is used. The solutions obtained are for flow resulting from a point source of energy at the origin, having a power law time dependence. The results are applied to the problem of spherical shock propagation into a medium and to the problem of cosmic ray generation from supernovae. It is found that the predicted spectrum of cosmic rays is somewhat steeper than is actually observed.

First‐Order Perturbation Theory for the Distribution Functions of a Dense Fluid

S. W. Brelvi and J. P. O'Connell

Phys. Fluids 15, 2145 (1972); http://dx.doi.org/10.1063/1.1693847 (5 pages) | Cited 2 times

Online Publication Date: 31 July 2003

Full Text: | Download PDF

Show Abstract
A first‐order expansion of the Percus‐Yevick functional is derived for the properties of a real fluid as a perturbation about a hard‐sphere reference fluid. The resulting expression is an integral equa ion relating the real fluid distribution functions and intermolecular potential to those of the reference fluid. Use of a realistic approximation in calculating the integral in the Ornstein‐Zernike equation leads to real‐fluid distribution functions that are in closer agreement with molecular dynamics results than those of the usual first‐order Percus‐Yevick equation.

Radiating‐Conducting Thick‐Transparent Normal Shock Solution

Leland A. Carlson

Phys. Fluids 15, 2150 (1972); http://dx.doi.org/10.1063/1.1693848 (3 pages) | Cited 1 time

Online Publication Date: 31 July 2003

Full Text: | Download PDF

Show Abstract
An approximate solution for the radiating and conducting flowfield behind hypervelocity normal shock waves is presented. The solution is used to investigate the effects of conduction and uncertainty in radiative properties upon the flowfield enthalpy variation.

Radiative Decay behind Strong Shocks

Alan Oppenheim

Phys. Fluids 15, 2153 (1972); http://dx.doi.org/10.1063/1.1693849 (2 pages) | Cited 8 times

Online Publication Date: 31 July 2003

Full Text: | Download PDF

Show Abstract
The effect of radiation on the state of a gas behind a strong shock is studied with a different radiation model than used by Koch and Gross. The formalism and assumptions are otherwise the same as in their paper.

Initial Free‐Surface Motion of an Impulsively Loaded Half‐Space

William J. Rae

Phys. Fluids 15, 2155 (1972); http://dx.doi.org/10.1063/1.1693850 (4 pages) | Cited 1 time

Online Publication Date: 31 July 2003

Full Text: | Download PDF

Show Abstract
Some results are presented which describe the motion of layers near the surface of a half‐space, caused by an explosion or high‐speed particle impact at a nearby point. These results are found from a known closed‐form solution for the flow field near the point where the shock wave propagating into the half‐space intersects the free surface. Trajectories, calculated for a layer of particles which initially lie at a shallow depth beneath the surface, show the influence of the primary shock wave and subsequent expansion fan on the motion.

Atomic Oxygen Formation Times Obtained from Measurements of Electron Density Profiles behind Shock Waves in Air

J. Stricker and W. Low

Phys. Fluids 15, 2159 (1972); http://dx.doi.org/10.1063/1.1693851 (5 pages) | Cited 1 time

Online Publication Date: 31 July 2003

Full Text: | Download PDF

Show Abstract
Microwave attenuation and neutral gas density profiles were measured behind shock waves in air, at an initial pressure of 5 Torr in the shock Mach number range of 8‐10. From these data and with the assumptions that the ionization cross section Qion is reasonably constant during the O2 dissociation process and the atomic nitrogen concentration is approximately equal to the equilibrium value during this process, the formation times of atomic oxygen and ionization relaxation times were obtained. It is shown that the formation time of atomic oxygen and the ionization relaxation time agree well with different theoretical calculations. The electron peak density was found to be 2‐3 times higher than the values calculated for thermodynamic equilibrium. The neutral gas density was measured with the aid of a simple laser interferometer.

Diatomic Gasdynamic Lasers

Robert L. McKenzie

Phys. Fluids 15, 2163 (1972); http://dx.doi.org/10.1063/1.1693852 (11 pages) | Cited 13 times

Online Publication Date: 31 July 2003

Full Text: | Download PDF

Show Abstract
Predictions from a numerical model of the vibrational relaxation of anharmonic diatomic oscillators in supersonic expansions are used to show the extent to which the small anharmonicity of gases like CO can cause significant overpopulations of upper vibrational states. When mixtures of CO and N2 are considered, radiative gain on many of the vibration‐rotation transitions of CO is predicted. Experiments are described that qualitatively verify the predictions by demonstrating laser oscillation in CO‐N2 expansions. The resulting CO‐N2 gasdynamic laser displays performance characteristics that equal or exceed those of similar CO2 lasers.

Steady Nonlinear Ekman‐Hartmann Boundary Layers

Edward R. Benton and Julianna H. S. Chow

Phys. Fluids 15, 2174 (1972); http://dx.doi.org/10.1063/1.1693853 (8 pages) | Cited 4 times

Online Publication Date: 31 July 2003

Full Text: | Download PDF

Show Abstract
The steady, axially symmetric Ekman‐Hartmann boundary layer on a flat insulating surface is analyzed in its fully nonlinear form. Emphasis is placed on evaluation of Ekman pumping and induced Hartmann current as functions of Rossby number, magnetic interaction parameter, and magnetic Prandtl number. Significant quantitative departures from the estimates of linear theory are found. Yet, for some purposes (such as for predicting its influence on spin‐up) the strength of this hydromagnetic pump is shown to be adequately described by an analytic series solution truncated after the terms quadratic in Rossby number.

Nonlinear Thermal Convection in Conducting Fluids

D. P. Lalas and S. Carmi

Phys. Fluids 15, 2182 (1972); http://dx.doi.org/10.1063/1.1693854 (5 pages) | Cited 1 time

Online Publication Date: 31 July 2003

Full Text: | Download PDF

Show Abstract
The stability of an electrically conducting Boussinesq fluid subjected to a temperature gradient and a magnetic field is analyzed by the energy method. The mathematically rigorous results establish the existence of a region of certain stability near the origin of the parameter space (Ra, Re, Rm) where Ra, Re, and Rm are the Rayleigh, Reynolds, and magnetic Reynolds numbers, respectively. Furthermore, by using the calculus of variation methods, the region of certain stability is enlarged and the relevant Euler‐Lagrange equations are obtained. An exact solution for the stability limit is obtained for a motionless layer of fluid heated from below and subjected to a crossed horizontal magnetic field. The region of certain stability is delineated by Ra + Rm2<1708, Re  =  0. This result is compared with the results of linear theory. The pertinent regions for the design of future stability experiments are indicated.

Stability of an Electrical Discharge Surrounded by a Free Vortex

Chuen‐Yen Chow and Mahinder S. Uberoi

Phys. Fluids 15, 2187 (1972); http://dx.doi.org/10.1063/1.1693855 (6 pages) | Cited 2 times

Online Publication Date: 31 July 2003

Full Text: | Download PDF

Show Abstract
Analysis shows that the serious unstable disturbances on a fluid cylinder carrying an axial current can be suppressed by a coaxial vortex flow, in agreement with laboratory observation on electrical discharges. The result may provide an explanation for the electrical activities found in the funnel of tornadoes.

Numerical Analysis of Magnetohydrodynamic Instabilities by the Finite Element Method

Tatsuoki Takeda, Yasuo Shimomura, Mitsuru Ohta, and Masaji Yoshikawa

Phys. Fluids 15, 2193 (1972); http://dx.doi.org/10.1063/1.1693856 (9 pages) | Cited 20 times

Online Publication Date: 31 July 2003

Full Text: | Download PDF

Show Abstract
A finite‐element method has been applied to the analysis of magnetohydrodynamic instabilities in a cylindrical current‐carrying plasma embedded in a strong longitudinal magnetic field. To examine the applicability of the finite‐element method to the stability analysis, the growth rate of instabilities has been calculated numerically using an electronic computer. It has been shown that the numerical results, for which corresponding analytical results are available, are in good agreement with them. Several examples of the analysis of low‐m mode instabilities with various current distributions are demonstrated. It is concluded that the finite‐element method is a powerful tool for the study of magnetohydrodynamic instabilities in the cylindrical plasma as well as, possibly, plasmas with more complex geometries.

Scattering of Light by Relativistic Electrons

Gray Ward and R. E. Pechacek

Phys. Fluids 15, 2202 (1972); http://dx.doi.org/10.1063/1.1693857 (9 pages) | Cited 4 times

Online Publication Date: 31 July 2003

Full Text: | Download PDF

Show Abstract
The differential scattering cross section for the interaction of optical photons with relativistic electrons is calculated from quantum electrodynamics. The cross section is confirmed by scattering monochromatic electromagnetic radiation from 50‐keV electrons. The classical calculation of the differential scattering cross section which agrees with the quantum electrodynamic calculation and with experiment is one which takes into account the fact that scattering electrons enter and leave the scattering volume during the period of observation. These results are important for the proper intepretation of laser scattering measurements of plasma distribution functions when electron temperatures are ≥  10 keV.

Effect of Field Asymmetry on Neoclassical Transport in a Tokamak

R. D. Hazeltine and M. N. Rosenbluth

Phys. Fluids 15, 2211 (1972); http://dx.doi.org/10.1063/1.1693858 (7 pages) | Cited 15 times

Online Publication Date: 31 July 2003

Full Text: | Download PDF

Show Abstract
The effect on transport of a local increase (“bump”) in the confining field of a large aspect ratio tokamak is studied in the small collision frequency regime, in which trapped particles—particles reflected by the bump—make a dominant contribution. From solution of the drift‐kinetic equation with boundary conditions appropriate to trapped and untrapped particles, explicit expressions for the cross‐field particle and energy fluxes are obtained; the density, temperature, and potential gradients, and a parallel electric field, are considered as driving terms. While the diffusion and energy fluxes have an easily anticipated form, similar to superbanana transport, the influence of the bump on the Ware flux, resulting from the parallel electric field, is surprisingly large.

Self‐Consistent Finite Amplitude Wave Damping

I. H. Oei and D. G. Swanson

Phys. Fluids 15, 2218 (1972); http://dx.doi.org/10.1063/1.1693859 (4 pages) | Cited 21 times

Online Publication Date: 31 July 2003

Full Text: | Download PDF

Show Abstract
An approximate self‐consistent damping rate for a finite amplitude wave is obtained. In the limit of γLτ0≫1 and γLτ0≪1, where γL is the linear Landau damping coefficient and τ0 is the bounce period of the particles in the wave potential well, the linear Landau damping rate and O'Neil damping coefficient, respectively, are recovered from the generalized result, which is in the form of an integral equation. By the technique of numerical iteration, the damping coefficients for different values of γLτ0 ranging from 0.1 to 1 have been obtained. Damped wave amplitudes are also plotted which show semiquantitative agreement with the experimental data of Malmberg and Wharton.

Low‐Frequency Beam‐Plasma Interactions in a Finite‐Sized Plasma

V. P. Bhatnagar and W. D. Getty

Phys. Fluids 15, 2222 (1972); http://dx.doi.org/10.1063/1.1693860 (9 pages) | Cited 4 times

Online Publication Date: 31 July 2003

Full Text: | Download PDF

Show Abstract
Results are presented for an experimental and theoretical investigation of low‐frequency waves in a beam‐generated plasma. Waves are excited at frequencies immediately above the ion‐plasma frequency by sinusoidally modulating the electron beam current. The study is aimed at obtaining ion heating at the lower‐hybrid resonant frequency. An electron beam of 400‐1000 V energy and a few milliamperes of current is used to generate plasmas with densities in the range of 109 cm−3 in a magnetic field of a few hundred gauss. Hydrogen, argon, deuterium, and neon gases are used. The rf electric field is probed as a function of r, z, and frequency, and energetic ions are detected by a gridded probe. Two or three resonances are found in the probe response above ωpi, and are shown to be multiple half‐wavelength resonances of standing plasma waveguide axisymmetric modes. A normal‐mode analysis is used to calculate the probe responses and is found to correctly predict the effects of varying beam voltage, plasma density, ion mass, and dc axial magnetic field. The excited wave may be viewed as an electrostatic wave propagating at an angle very close to 90 deg from the magnetic field.

Intermittent Behavior of a Plasma Discharge in Turbulent Gas Flow

A. M. Levine, V. L. Granatstein, and M. Rhinewine

Phys. Fluids 15, 2231 (1972); http://dx.doi.org/10.1063/1.1693861 (9 pages) | Cited 1 time

Online Publication Date: 31 July 2003

Full Text: | Download PDF

Show Abstract
A new model to describe an arc discharge struck in a turbulent pipe flow is discussed. In this model, a randomly twisted column is convected down the pipe producing an intermittent signal on electrostatic probes. A theoretical and experimental analysis of these signals is presented. The analysis provides information about discharges in rapidly flowing gases and also develops techniques useful in studying intermittent phenomena.

Spatial Distributions of Plasma Density in a High‐Frequency Discharge with a Superimposed Static Magnetic Field

Edward P. Szuszczewicz and Hans Oechsner

Phys. Fluids 15, 2240 (1972); http://dx.doi.org/10.1063/1.1693862 (7 pages) | Cited 9 times

Online Publication Date: 31 July 2003

Full Text: | Download PDF

Show Abstract
An experimental investigation has been carried out on the spatial distribution of charged‐particle density in an inductively‐coupled, cylindrical high‐frequency plasma discharge with a superimposed perpendicular magnetic field. The studies were performed at and near conditions of electron‐cyclotron‐wave resonance and consideration was given to the influence of magnetic field and high‐frequency power levels. It is shown that high‐frequency power levels have relatively little influence on the volume distribution of charge, but that very unique distributions result under conditions of electron‐cyclotron‐wave resonance. Characteristic distributions are presented and discussed in the context of plasma anisotropy resulting from the superimposed magnetic field.

Numerical Calculations of Off‐Resonance Heating

J. C. Sprott

Phys. Fluids 15, 2247 (1972); http://dx.doi.org/10.1063/1.1693863 (7 pages) | Cited 5 times

Online Publication Date: 31 July 2003

Full Text: | Download PDF

Show Abstract
The off‐resonance heating that is observed in hot‐electron plasmas is explained in terms of harmonic resonances, appropriately modified to include relativistic and Doppler effects. A theoretical expression for the heating rate is proposed and is found to agree with the results of a computer simulation over a range of parameters. The theoretical heating rate is evaluated numerically for several special cases, including a uniform magnetic field, a mirror field with a 2:1 mirror ratio, and a large‐aspect ratio bumpy torus. The enhanced axial loss observed experimentally with heating below the cyclotron frequency is explained by absorption at harmonics of the electron bounce frequency.
Page 1 of 3 Pages Next Page | Jump to Page
Close

Google Calendar

ADVERTISEMENT

Go to AIP Home   © AIP Publishing LLC
close