Theory of nonsteady propellant combustion. Combustion in the presence of harmonically varying pressure

It is shown that in order to construct a theory of nonsteady propellant combustion it is necessary to know the steady-state dependences of the burning rate u₀ °, surface temperature T_s °, and flame temperature T_F ° on the external parameters and the initial temperature of the propellant. The combustion processes in an unbounded space, when one of the external parameters varies according to a harmonic law, are examined within the framework of such a theory.Translated from Zhumal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 60–69, September–October, 1971.     

Unsteady flow of a viscous gas between two solid walls,one of which is free and vibrating at high frequency

The pressure field is investigated in a thin layer of a viscous compressible gas between two walls, one of which is free and executing high-frequency harmonic vibrations. Asymptotic methods are applicable to the case in which one wall vibrates at high frequencies [1]. The motion of the gas, as shown in [2], can be assumed to be nearly isothermal, and the influence of the inertial terms in the equation of motion for the gas can be neglected.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 111–116, March–April, 1971.     

The photoelastic determination of the stresses in vibrating cantilevered beams

A method of determining the dynamic stresses in vibrating cantilevered beams using photoelasticity is presented. The method uses the basic principles of photomechanics and the optic-stress laws. A high-intensity strobe light is timed with the frequency of vibration so that the beam image appears to be stationary. Data are recorded with a camera and analyzed to provide an experimental solution. The theoretical solution is derived from the Bernoulli-Euler equation of motion. Two basic types of beams were investigated, an aluminum beam coated with a birefringent material to simulate an actual structural member and a birefringent model that was dynamically similar to the aluminum beam. The feasibility of extending the technique to more complicated shapes is suggested by this investigation. The experimental results and feasibility of the concept are verified by close correlation with the analytical solution.     

Normal stress measurements

A review of the methods for obtaining the normal stress differences in simple shear flow from force measurements on the walls of apparatus in which curvilinear shear flows are generated is given. Indirect methods, for example the flow birefringence method, are considered. Some new work on normal stress measurement using cone and plate, parallel plate pressure distribution and total thrust measurements in conjunction with flow birefringence methods are reviewed. The difficulties found in obtaining consistant results are discussed.Paper presented at the Conference on Experimental Rheology, University of Bradford, April 17–19, 1968. — Original paper published in Rheo. Acta,7, 368 (1968).     

The distribution function of atomic level populations in a plasma

An analytic form is obtained for the population distribution function in an atomic plasma as a series in successive time derivatives of the population of the first level. The first approximation includes the well-known method of a stationary sink. The quasistationary distribution obtained for hydrogen agrees well with numerical calculations of recombination and ionization, and for lithium, helium, and argon the quasistationary distribution gives qualitative agreement with numerical calculations.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 18–26, July–August, 1972.We should like to thank B. F. Gordiets for a helpful discussion.     

Two-dimensional adiabatic forced convection at low péclet number

This paper deals with heat transfer to two-dimensional laminar Poiseuille flow with arbitrary heat fluxes specified on the walls. The solution is first obtained for fluxes which are symmetric and antisymmetric delta functions and from these the general solution is obtained by integration. The solutions include the effects of axial conduction and also of preheating of the incoming fluid. Detailed solutions are given for the cases Pé=1 and Pé=.5.     

A sensitive and rapid bridge for the study of magnetic susceptibilities at frequencies from 200 to 106 Hz

Summary A new piece of equipment is described for measuring / ₀ and / ₀ as a function of field (0 to 4250 Oe), temperature (1.2°K to room temperature) and frequency (200 Hz to 1 MHz). It is about ten times more sensitive than the Hartshorn bridge used in Leiden²⁾ and it is more convenient to operate as the measuring procedure is automatic after initial adjustments have been made. The main component is a bridge circuit of four inductors, built as closely similar to each other as possible. The output from the bridge goes to two phase sensitive detectors which monitor the two outputs, one inphase, one /2 out of phase, of the bridge. A heterodyne system is used where the input signal to the bridge is obtained by mixing the output from a variable frequency oscillator with that from a 1.5 MHz oscillator and taking the difference frequency, which is phase locked to a master oscillator. The output from the bridge, after preamplification, is mixed with a second output from the variable oscillator and the difference taken again. This gives a 1.5 MHz signal modulated by the magnetic effects in the bridge which is used in the two phase-sensitive detectors. Their output is recorded on an x–y writer. The bridge needs only be balanced to an output of about 50 mV because the sample is moved between two coils and the difference voltage is measured. The use of the same equipment to measure relaxation times longer than 100 ms is also described.Communication No. 349a from The Kamerlingh Onnes Laboratorium, Leiden, The Netherlands     

Torsional oscillations of an infinite plate in an elastico-viscous fluid

Summary The equations of motion of an infinite plate performing torsional oscillations in Walters elastico-viscous liquid B have been solved by expanding the velocity profile in powers of the amplitude of oscillation of the plate. The first order solution consists of a transverse velocity and the second-order solution gives a radial-axial flow composed of a steady part and a fluctuating part. The steady part of the radial flow does not vanish outside the boundary layer and hence the equations are solved by another approximate method for the steady part of the flow. The effects of the non-Newtonian term is to increase the non-dimensional boundary layer to start with and subsequently to decrease it and to increase the shearing stress at the plate. The steady radial and the steady axial velocities fall short of the inelastic flow in the beginning but later on their values lie above.     

Exact solutions of the kinetic-moment equations of a mixture of monatomic gases

An extension is given of the class of exact solutions of the kinetic-moment equations for a monatomic gas in the absence of external forces [1] to the case of a mixture of monatomic Maxwellian gases with account for external forces. Very simple solutions of this class are obtained which are examples of the normal solutions of the Boltzmann equations in the Chapman-Enskog sense [2]. Conclusions are summarized concerning the applicability of the various methods of solving the Boltzmann equations and their properties, obtained on the basis of an analysis of the indicated exact solutions.The author wishes to thank M. N. Kogan and A. A. Nikol'skii for their interest in the study.     

A model of the steady-state motion of suspensions

The authors examine the steady-state one-dimensional motions of suspensions whose particles have a density equal to that of the corresponding dispersion medium. As a whole, the mechanical behavior of such suspensions is described by equations of motion that coincide in form with the Navier-Stokes equations for a certain incompressible fluid whose viscosity is a known function of the particle concentration in the suspensions. To close these equations, the authors postulate a principle of minimum energy dissipation for steady-state motion, which plays the paxt of an equation of state for the suspension. This new equation permits the determination of the spatial distribution in the concentration of solids. Exact solutions are presented for certain variational problems associated with the Poiseuille flow of a fluid of this kind in circular tubes and Couette flows between concentric cylinders and parallel planes. It is shown that in most cases separation of the suspension takes place.