Unsteadiness of Flow Separation and End-Effects Regime in a Thrust-Optimized Contour Rocket Nozzle

Turbulent flow separation in over-expanded rocket nozzles is investigated experimentally in a sub-scale model nozzle fed with cold air and having a thrust-optimized contour. Depending upon the pressure ratio either a free shock separation (FSS) or a restricted shock separation (RSS) is observed with a significant hysteresis between these two flow regimes. It is shown that the RSS configuration may involve several separated regions. Analysis of wall pressure fluctuations give quantitative information on the fluctuating pressure field directly connected with the occurrence of significant side loads. Direct measurements of the evolution of the side loads with respect to the pressure ratio show the occurrence of three distinct peaks which are explained by the wall pressure fluctuations measurements.     

Modeling micro-inertia in heterogeneous materials under dynamic loading

A continuum model including micro-inertia for heterogeneous materials under dynamic loading is proposed using a micro-mechanics method. The macro strain and stress are defined as the volume averages of the strain and stress fields in the representative volume element (RVE). The macro equations of motion are derived by using Hamilton’s principle together with the strain energy density and kinetic energy density involving the micro-inertia terms. The new macro equations of motion are used to study harmonic and transient wave propagation in layered media. Using a simple linear displacement field for the RVE, the dispersion curves obtained from the present model agree with the exact solutions very well for a range of wavelengths. The present model is also applied to analyze the transient response of layered media subjected to a triangular pulse loading. Comparison is made between the results of the present model and a finite element analysis.     

Effect of high-frequency vibrations on the stability of advective flow

The stability of plane convective flow in a horizontal layer with a longitudinal temperature gradient under the action of longitudinal vibrations is considered. The behavior of small normal plane and spiral perturbations is investigated. It is shown that the vibrations enhance the stability with respect to almost all types of perturbations. The sole exception is plane thermal waves whose existence domain extends toward low Prandtl numbers. Perm’. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 16–22, January–February, 1998. The work was supported by the Russian Foundation for Fundamental Research (project No. 94-01-01730).     

Dislocation behaviours ahead of crack tip

In this paper, a unified mechanics model for dislocation nucleation, emission and dislocation free zone is proposed based on the Peierls framework. Three regions are identified ahead of the crack tip. The emitted dislocations within the plastic zone in the form of an inverse pile up are treated as discrete elastic edge dislocations. Between that zone and the cohesive zone immediately ahead of the crack tip, there is a dislocation free zone. With the stress field and the dislocation density field in the cohesive zone, respectively, expressed in the first and second Chebyshev polynomial series, and the opening and slip displacements in trigonometric series, a set of nonlinear governing equations are obtained which take into account for the interaction between the emitted dislocations and cohesive zone and the nonlinear interaction between sliding displacement and the opening displacement. After discretization, the governing equations are transformed into a set nonlinear algebraic equations which are solved with Newton-Raphson Method. The results of calculation for pure shearing and combined tension and shear loading after dislocation emission are given in detail. Finally, the process of dislocation nucleation and emission on a pair of symmetric slip planes of angle α with respect to the crack plane under pure mode I load is analysed. The equilibrium positions and the number of emitted dislocation are determined. Several possible competition behaviors of dislocation emission vs cleavage are revealed.     

The influence of peak-locking errors on turbulence statistics computed from PIV ensembles

The influence of peak-locking errors on turbulence statistics computed from ensembles of PIV data is considered. PIV measurements are made in the streamwise–wall-normal plane of turbulent channel flow. The PIV images are interrogated in three distinct ways, generating ensembles of velocity fields with absolute, moderate, and minimal peak locking. Turbulence statistics computed for all three ensembles of data indicate a general sensitivity to peak locking in the single-point statistics, except for the mean velocity profile. Peak-locking errors propagate into the fluctuations of velocity, rendering single-point statistics inaccurate when severe peak locking is present. Multi-point correlations of both streamwise and wall-normal velocity are also found to be influenced by severe levels of peak locking. The displacement range of the measurement, defined by the PIV time delay, appears to affect the influence of peak-locking errors on turbulence statistics. Smaller displacement ranges, particularly those that produce displacement fluctuations that are less than one pixel in magnitude, yield inaccurate turbulence statistics in the presence of peak locking.     

A new solution for the rotation-driven spreading of a thin fluid film

Lie groups are used to solve the equation governing the flow of a thin liquid film subject to centrifugal spreading and viscous resistance. A new implicit solution is found. It is shown how this relates to the previous known solutions for the spreading of an initially flat film, the steady state and a separable solution. New permissible forms for the film evolution are also studied, including solutions exhibiting finite time blow-up. Near the contact line, where the film height tends to zero, an approximate explicit solution is obtained which may be used to describe a film with any size contact angle.     

Stability of noisy nonlinear auto-parametric systems

The purpose of this work is to examine the stationary motion and stability properties of stationary motion of two degree-of-freedom noisy auto-parametric systems We shall use analytical techniques to extend the existing results to examine such multi-dimensional nonlinear systems with noise, and in particular additive white noise. We obtain an approximation for the top Lyapunov exponent, the exponential growth rate, of the response of the so-called single-mode stationary motion. We show analytically that the top Lyapunov exponent is positive, and for small values of noise intensity ɛ and dissipation ɛ² the exponent grows in proportion with ɛ^2/3.     

Heat transfer from non-isothermal surfaces in the stagnation-point flow of a micropolar fluid

Summary This paper contains a numerical study of the development of the thermal boundary layer on an impermeable flat surface, following a step change in surface temperature, for stagnation-point flow of a micropolar fluid. A study is made of the relative effects of the individual parameters in the equations, and a comparison of certain integral parameters, representative of the flow, is used to assess the accuracy of the results.

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Zusammenfassung Diese Arbeit enthält eine numerische Untersuchung der Entwicklung der thermischen Grenzschicht auf einer undurchlässigen ebenen Oberfläche nach stufenförmigem Sprung in der Oberflächentemperatur für die Staupunktsströmung einer mikropolaren Flüssigkeit. Die relativen Auswirkungen der einzelnen Parameter in den Gleichungen werden untersucht und ein Vergleich von gewissen, für die Strömung repräsentativen integralen Parametern wird durchgeführt, um die Genauigkeit der Ergebnisse abzuschätzen.

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With 4 figures and 1 table     

Multiple scale fourier transformation: An application to nonlinear dispersive waves

A Fourier transformation involving multiple scales is applied to describe the far-field asymptotic behaviour of nonlinear dispersive waves. It is shown that a nonlinear asymptotic perturbation can be carried out in terms of simple calculations with respect to Dirac delta functions involving a multiple scale wave number and frequency space. Fourier transformed versions of the nonlinear Schrödinger and Korteweg-de Vries equations are derived explicitly.     

Heat transfer in flow past a continuously moving semi-infinite flat plate in transverse magnetic field with heat flux

Thermal boundary layer on a continuously moving semi-infinite flat plate in the presence of transverse magnetic field with heat flux has been examined. Similarity solutions have been derived and the resulting equations are integrated numerically. This investigation has indicated a fall in the temperature of the thermal boundary layer with increase in magnetic field parameter.

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Wärmeübertragung in Strömungen an einer gleichmäßig bewegten, halbunendlichen ebenen Platte in einem quergerichteten Magnetfeld mit Wärmefluß

Zusammenfassung Es ist die thermische Grenzschicht auf einer gleichmäßig bewegten, halbunendlichen ebenen Platte in einem quergerichteten Magnetfeld mit Wärmefluß untersucht worden. Ähnlichkeitslösungen sind abgeleitet und die erhaltenen Gleichungen numerisch integriert worden. Diese Untersuchung hat einen Rückgang der Temperatur in der thermischen Grenzschicht mit steigendem Magnetfeldparameter nachgewiesen.