Numerical modeling of the process of emplying a tank with a cryogenic liquid

Results of calculation of temperature and velocity fields in a cylindrical vessel with a cryogenic liquid (liquid hydrogen) upon its emptying are discussed. A problem is formulated for a viscous incompressible fluid at thermal boundary conditions of the first kind. Streamlines and isotherms for a variable fluid column are presented. Solutions are obtained for Rayleigh Ra = 10 ⁷ … 10 ¹⁰ and Reynolds Re = 10 ³ … 10 ⁴ numbers. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 70, No. 3, pp. 409–412, May–June, 1997.     

Flow of a non-Newtonian fluid past a wedge

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

Boson Inverse Operators and a New Family of Two-photon Annihilation Operators

Abstract

We introduce the inverse of the Hermitian operator (ââ ^?) and express the Boson inverse operators â ^?1 and â ^??1 in terms of the operators â, â ^? and (ââ ^?)^?1. We show that these Boson inverse operators may be realized by Susskind-Glogower phase operators. In this way, we find a new two-photon annihilation operator and denote it as â ²(ââ ^?)^?1. We show that the eigenstates of this operator have interesting non-classical properties. We find that the eigenstates of the operators (ââ ^?)^?1 â ², â(ââ ^?)^?1 â and â ²(ââ ^?)^?1 have many similar properties and thus they constitute a family of two-photon annihilation operators.     

On the linear stability of a compressible inviscid parallel shear flow

Summary By applying an approach similar to that used in the Miles-Howard theory [1], [2] we derive simple constraints on the phase speedc _r ^* of the neutral three-dimensional (3-D) monochromatic disturbances in an inviscid compressible parallel two-dimensional (2-D) shear flow. It is shown that for a boundary layer flow [a ₀ ^*(y ^*)]² —[U ₀ ^*(y ^*)—c _r ^*]² must have a zero in [y ₁ ^*,y ₂ ^*) for the neutral 2-D modes whose phase speedc _r ^* does not belong to the range ofU ₀ ^*(y ^*). For the unstable waves the argument of Chimonas [3] applies leading to the Howard semi-circle theorem. HereU ₀ ^*(y ^*) anda ₀ ^*(y ^*) are the dimensional base velocity and local sonic speed respectively. It is suggested that hypersonic flows possess vertically highly undulated unstable normal modes.     

Free convection effects on the oscillatory flow of a couple stress fluid through a porous medium

Summary Effects of free convection currents on the oscillatory flow of a polar fluid through a porous medium, which is bounded by a vertical plane surface of constant temperature, have been studied. The surface absorbs the fluid with a constant suction and the free stream velocity oscillates about a constant mean value. Analytical expressions for the velocity and the angular velocity fields have been obtained, using the regular perturbation technique. The effects of Grashof numberG; material parameters and ; Prandtl numberP; permeability parameterK and frequency parametern on the velocity and the angular velocity are discussed. The effects of cooling and heating of a polar fluid compared to a Newtonian fluid have also been discussed. The velocity of a polar fluid is found to decrease as compared to the Newtonian fluid.List of symbols C _p specific heat at constant pressure - g acceleration due to gravity - G Grashof number - K ⁺ permeability of the porous medium - K dimensionless permeability - P Prandtl number - t ⁺ time - t dimensionless time - T _w ⁺ mean temperature of the surface - T ⁺ temperature of the fluid - T ⁺ temperature of the fluid away from the surface - density of the fluid - viscosity - _r rotational viscosity - C _a ,C _d coefficients of couple stress viscosities - I a scalar constant of dimension equal to that of the moment of inertia of unit mass - x ⁺,y ⁺ coordinate system - u ⁺,v ⁺ velocity components in thex ⁺ andy ⁺ directions - u dimensionless velocity in thex ⁺-direction - ⁺ angular velocity component - dimensionless angular velocity - n ⁺ frequency of oscillations - n dimensionless frequency - perturbation parameter - U a constant velocity - u ₀ mean velocity - u ₁ fluctuating part of the velocity - ⁰ mean angular velocity - ¹ fluctuating part of the angular velocity - T ₀ mean temperature - T ₁ fluctuating part of the temperature - ⁰ coefficient of the volume expansion - kinematic viscosity - ^r rotational kinematic viscosity - , material parameters characterizing the polarity of the fluid - v ₀ suction velocity - density of the fluid far from the surface - y dimensionless coordinate normal to the surface     

Evaluation of the Field near a Cusp of a Caustic

The field in the neighbourhood of a cusp of a caustic can be expressed in terms of a function of two variables, P(X,Y), known as Pearcey's integral or the Pearcey function. In this paper we develop efficient algorithms for computing this function and its derivatives P/ X and P/ Y. They are based on a Taylor series expansion in a region close to the cusp at X = Y = 0, and on asymptotic approximations in regions far from the cusp. The asymptotic results are given in terms of contributions of isolated stationary points in regions far from the caustic, and in terms of the Airy integral function and its derivative in a region close to the caustic. Three terms in the asymptotic expansions are used, and they give an accuracy for P(X,Y) better than 0·006 in amplitude and 0·6° in phase at distances from the cusp greater than (X² +Y² )^1/2 = 4.     

Heating of a current filament and formation of constrictions in a pulsed vacuum discharge

It is shown that a rapid current rise in a pulsed vacuum discharge is accompanied by enhanced compression of the current filament by its self-induced magnetic field. As a result, a constriction forms at a distance L≃1 mm from the cathode and the electron temperature increases to 10²–10³ eV at currents of order 1 kA. This behavior explains the observed increase in the degree of ion charge and the appearance of x-rays as the current pulse length decreases. The criterion for a rapid rise is the condition τ<L/V≃10⁻²⁷ s, where τ is the characteristic current amplification time and V≃10⁶ is the velocity of the cathode plasma. Pis’ma Zh. Tekh. Fiz. 24, 50–56 (September 26, 1998)     

Elastodynamic Response of a Periodic Layer of Spherical Particles Containing Vacancies

This paper is concerned with the influence of vacancies on the elastodynamic response of a periodic (square) array of identical spherical elastic inclusions embedded in an unbounded elastic matrix. A response function of the array is defined as H ^* (ω)\equiv R ^* (ω)/T ^* (ω) , where R ^* (ω) and T ^* (ω) are, respectively, the reflection and transmission spectra of the lattice. H ^* (ω) was measured for a ``perfect lattice,' i.e., one without any vacancies, and was found to be characterized by lattice resonances. H ^* (ω) was also measured for lattices containing one and three vacancies within the 72 lattice site area insonified by the ultrasonic beam. A counter-intuitive observation is that the presence of even one vacancy significantly reduces the amplitude of the fundamental lattice resonance. Furthermore, in the case of the specimen containing three closely spaced vacancies, the reduction is not three times the reduction due to one vacancy; it is significantly less than that.     

Correlations for the Thermal Conductivity of Metals as a Function of Temperature

The objective of this work was to find a suitable correlation that best fits the thermal conductivity of metals as a function of temperature. It was found that a multiple linear regression model of the form k=aT ^b e ^cT e ^d/T gives the smallest deviations from experimental data among various models. The coefficient of determination, R ², lies between 0.97 and unity, except for thorium (R ²=0.86). The average of the absolute relative error, AARE, in the predicted data is less than 4.75%, except for iron (about 11.7%), and the overall AARE for all data points is about 1.4%.     

Source-sink flow in a rotating cylinder

Summary This paper describes the axisymmetric source-sink flow in a rapidly rotating cylinder. Relative fluid motion is induced by the presence of a sink in the bottom corner and a ring source located somewhere in the fluid, at some distance from the solid boundaries. In order to neglect nonlinear effects the volumetric flow rates are assumed to be small, i.e. O(E ^1/2), with E the Ekman number of the flow. The transport from the source to the sink is carried by Ekman layers at the end caps, and a Stewartson layer at the sidewall. At the ring source a free Stewartson layer arises, in which the injected fluid is transported towards the Ekman layers. This Stewartson layer consists of layers of thicknesses E ^1/4 and E ^1/3, which both contribute to the vertical O(E ^1/2) transport. The ring source is enveloped by a ring-shaped region of cross-sectional dimensions O(E ^1/2 × E ^1/2), in which the injected fluid is rearranged before erupting into the E ^1/3 layer. As E ^1/2 E ^1/3, this region appears as an isolated singularity in the E ^1/3 layer; in fact it consists of a combination of an upward and a downward directed source, the strengths of which can be determined by transport arguments. The paper presents an analysis of the E ^1/3-layer structure on the basis of a linear theory; it also describes how the analysis can be extended to the situation in which fluid is injected through an array of sources at different heights.     

Development of a flow field structure in the vicinity of a circular cylinder in the presence of a laminar-turbulent transition

The Reynolds equations and the two-parameter differentialq-Ω model of turbulence are used to investigate a flow past a circular cylinder with an isothermal surface (temperature factorT _w0 = 0.5) at the Mach numberM _∞ = 5 in the range of Reynolds numbers Re = 10⁴-10⁸. It is demonstrated that the turbulization of flow leads to a shift of the separation point downstream, a reduction and stabilization of the separation zone length, a decrease in the maximum velocity in the separation zone, and an increase in the heat flux at the rear stagnation point compared with its value at the forward stagnation point.     

Numerical solution of a fourth-order ordinary differential equation

Summary In this paper we have derived numerical methods of orderO(h ⁴) andO(h ⁶) for the solution of a fourth-order ordinary differential equation by finite differences. A method ofO(h ²) was earlier discussed by Usmani and Marsden [6]. Convergence of the fourth-order method is shown. Two examples are computed to show the superiority of our methods.     

The onset of motion in a toroidal thermosyphon

Summary The instability associated with the onset of motion in a toroidal natural-circulation loop has been studied theoretically. A one-dimensional model is used to investigate the problem of global flow initiation from a rest state. It is shown that a thermosyphonic flow is established when the modified Rayleigh number exceeds a critical value, R _c ^* or R _c , which depends on the modified Biot number B. For a loop heated by a uniform heat flux R _c ^* is between the limits of 1/4 and 2.816 for small and large B, respectively. For a loop heated by a prescribed constant wall temperature, R _c has a minimal value of 2 at B=1. These results were obtained by two methods: a direct solution of the steady-state problem and a stability analysis of the rest state. The latter shows that when R ^*>R _c ^* there is a single monotonously growing perturbation and there are always additional monotonously decaying disturbance modes.     

Slow motion of a bubble in a viscoelastic fluid

Summary The motion of a deformed spherical body in a fluid medium is significantly different from the motion of an undeformed spherical body in the same medium. It is shown in this work that a bubble moving in a viscoelastic fluid takes the shaper=a+U ₀₀/a( ₁– ₂)(180R ³+240R ²+816R+672)P ₂(cos)/960(1+R)³ and so one must expect the dynamics of a bubble moving in a non-Newtonian fluid to be significantly different from that of a bubble moving in a purely viscous fluid.     

Dissemination of units from a reference source of neutrons with energy of 14 MeV

A method for the dissemination of units from a standard neutron source with energy 14 MeV by means of activated detectors made of fluoroplastic and aluminum according to the reactions ¹⁹F(n, 2n)¹⁸F and ²⁷Al(n, α)²⁴Na is described.     

Performance characteristics of a plasma-type sputter ion source

A low-power, plasma-type sputter source for the production of positive ions of non-volatile elements has been constructed and tested. Argon and copper were employed as support gas and sample material, respectively. The source output was measured as a function of the discharge current, the axial magnetic field, the sputter voltage, the spacing between the sputter sample and the source exit, the diameter of the sputter sample, and the argon pressure. It was found that the Cu⁺ current, I_Cu, increases with increasing discharge current i_d as I_Cu ∝ i_dⁿ, where n 2. I_Cu increases with decreasing sample-to-exit spacing s. For not too small spacings, I_Cu ∝ s⁻². Cu⁺ currents of up to 6 μA were produced at a total power consumption of less than 60 W. The simultaneous prese nce of an intense Ar⁺ component in the beam causes space charge expansion which becomes significant at low energies and large ratios of the drift length to the beam-size defining apertures. Loss of target current may also be caused by neutralization of ions in charge-transfer collisions outside of the source.     

Experimental Performance of a Single Stage Superfluid Stirling Refrigerator Using a Small Plastic Recuperator

The experimental performance of the first superfluid Stirling refrigerator (SSR) to use a plastic recuperator is reported. This SSR is a single stage machine, has a total internal volume of 83 cm ³ , and uses a 3 cm ³ Kapton heat exchanger. Operating from a high temperature of 1.0 K and with a 1.5% ³ He– ⁴ He mixture, this SSR achieves a low temperature of 344 mK and delivers net cooling powers of 1.86 mW at 750 mK, 358 W at 500 mK, and 97 W at 400 mK. Cooling power versus cold piston temperature for various frequencies of operation and for two piston stroke configurations are provided.     

The interaction of a relativistic dipole particle with a flat surface

The electromagnetic interaction of a flat solid surface with a relativistic dipole molecule moving parallel to the surface is studied for the first time. It is demonstrated that the first nonvanishing correction to the stopping force acting upon the particle is proportional to V ²/c ². In the nonrelativistic limit, the proposed formula coincides with the known result.     

Transverse Optical Resonance of Wigner Solid as a Sensitive Probe of Liquid Helium Surface

The formation of the Wigner Solid in the sheet of Surface Electrons (SE) on liquid helium leads to change in the plasmon dispersion relation of the system. As a result the coupled phonon-ripplon (CPR) modes appear in the spectrum of SE. The transverse optical (TO) CPR mode is scarcely dispersive, and consequently convenient for precise determination of the resonance frequency. In our experiments we have shown that the frequency of TO CPR resonance can be used to obtain the absolute value of liquid helium surface tension. The measurements have been gained for pure ³ He and for weak solution ³ He (0.5 ppm) in ⁴ He. The modification of weak ⁴ He- ³ He mixture surface tension in respect of pure ⁴ He data was observed. This behaviour can be explained by the filling of the Andreev's levels with ³ He atoms that results in the formation of the 2D Fermi-liquid on the surface of ⁴ He. The TO CPR resonance of SE can be proposed as a sensitive and convenient method for study of surface properties of liquid ⁴ He, ³ He and their mixtures.     

Inelastic Interaction of an Electron with a C60 Cluster

The method of intersecting beams of C₆₀ fullerene clusters and of electrons is used to investigate the production of C ₆₀ ⁺ and C ₆₀ ^– ions and the radiation in the wavelength range from 300 to 800 nm for the electron energy E _e ranging from zero to 100 eV. The absolute values of the ionization and electron-attachment cross sections [⁺(E _e ) and ^–(E _e ), respectively] are determined. A maximum of ⁺(E _e ) of 0.53 nm²is observed at E _e = 52 eV. For a C₆₀ cluster excited by electron impact, delayed (150 s) ionization initiated by collision with the surface and ionization due to thermionic emission (its characteristic time at E _e = 60 eV is 6 s) is observed. It is found that, for E _e < 0.4 eV, the formation of C ₆₀ ^– is defined by the polarization capture of an s-electron (^– E _e ^–1 ), and a formula is suggested for determining ^–(E _e ). In the region of E _e from 1 to 6 eV, the cross section ^–(E _e ) shows only slight variations about ^–(E _e ) = 0.36 ± 0.03 nm². For E _e > 7.5 eV, C ₆₀ ^– ions proved to be unstable to electron autodetachment. In the region of intersection of C₆₀ and electron beams, radiation of a quasicontinuous spectrum described by a modified Planck formula for the thermal emission of spherical particles of diameter d is recorded. For E _e > 47 eV, the brightness temperature proved to be 3150 ± 50 K. It is found that this radiation is emitted predominantly by hot C ₆₀ ^+* ions produced as a result of thermionic emission from C ₆₀ ^* . The rate of radiation loss of energy by a C ₆₀ ^+* ion and the cross section for the formation of radiating C ₆₀ ^+* ions are found to be, respectively, 5.5 × 10⁵ eV/s at T = 3150 K and 2 × 10^–2 nm² at E _e = 60 eV.