Heat transfer at a wedge in a hypersonic low-density gas stream

Results are presented of an approximate analysis of steady heat transfer on a sharp thin (sin < 1) strongly cooled (t_w 1) wedge, washed by a hypersonic (M 1) gas stream at zero angle of attack under almost free-molecule conditions. Dimensionless parameters on which the heat transfer depends have been established; approximate formulas for estimation purposes are given.The present analysis is not a rigorous quantitative theory and its results should be regarded only as estimates; its conclusions may be useful for experimental planning and for generalization of test data. The method used here is analogous to that applied in [1] in analyzing flow over a flat plate.     

Bases for predicting gas-particle flows with particular reference to turbomachinery

Advances in the understanding of particle dynamics and their trajectories and the resultant erosion of solid surfaces are reviewed. Particular attention is given to the calculation procedures used in the analysis of gas-particle flows, always with the intention of application to turbo-machines. One, two and three-dimensional analyses are considered and the limitations of each are discussed. As in the analysis of a real fluid flows, resort is made to empirical correlations of many phenomena and, even then, the predictions of particle trajectories are restricted. The correlation and restrictions are discussed where appropriate.     

Rheological characteristics of human joints with particular reference to the knee

Summary Stiffness is an important subjective phenomenon diagnostically and therapeutically in rheumatic diseases such as rheumatoid arthritis and osteoarthrosis. A quantitative and qualitative assessment of these phenomena have been made by arthrographs which impose a sinusoidal motion on the metacarpo-phalangeal and knee joints respectively and record the torque in relation to the displacement. The reproducibility with the joint in situ and moved is satisfactory. A hysteresis torque/ displacement plot is obtained with both joints. Reflex muscle activity may be measured at the joint, as in myotonia congenita and Parkinsonism. In patients without neuromuscular disorders electromyographic studies have shown that the muscles are electrically silent during sinusoidal motion and that active contraction distorts the tracing. The latter fact may be useful in the evaluation of patients with psychological factors producing muscle tension, which may be decreased with diazepam. Using the cat's wrist joint it has been shown that the passive stretching of muscles accounts for 41 per cent of the stiffness recorded at the joint and the capsule 47 per cent, a finding in keeping with work on the distal interphalangeal joint of the human finger.Stiffness increases with advancing age and decreased temperature. Conversely, warming the joint reduces its stiffness. Articular gelling in patients with osteoarthrosis may be demonstrated after periods of rest and the results suggest that such changes are due to alterations in the periarticular and muscle tissues. The rapid diminution in torque after rest in one position was not detected in normal joints even after longer periods of immobilisation.

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Zusammenfassung Steifheit ist ein Problem, das dem Kliniker bekannt ist. Steifheit am Morgen ist ein Hauptgesichtspunkt für die Diagnose von rheumatischer Arthritis und ist ein äußerst wichtiges Merkmal für die Diagnose von Wirbelsäulenversteifungs (pocker back). Diese ist ein wichtiges Merkmal in Fällen von Patienten mit Osteoarthrosis, die unter Gelenkschwellung leiden, und die Gelenke daher nach einer Ruheperiode viel steifer sind. Therapeutisch hat sie Bedeutung für das Symptomenbild des Patienten und sie ist ein Maßstab für die Wirksamkeit der Behandlung von rheumatischer Arthritis.Arthrographen wurden angefertigt, um die Steifheit des Metacarpophalangealgelenks des Fingers und des Kniegelenkes zu messen. Tierexperimente haben gezeigt, daß 50% der Gelenksteifheit von passiver Muskelstrek-kung und 50% von Geweben im Gelenk selbst und außerhalb herrühren. Reflexbedingte Muskelaktivität spielt keine Rolle, mit Ausnahme von Fällen mit neuro-muskulären Erkrankungen wieParkinsonismus und Myotonia Congenita. Um ein charakteristisches Spannungs-Dehnungsdiagramm zu erhalten, wird das Gelenk in eine sinusartige Bewegung gebracht. Untersuchungen der Spannungsrelaxation haben einige Hinweise auf die Komponenten der physischen Steifheit gegeben.Zunehmende Steifheit ist physiologisch altersbedingt. Eine Temperaturerhöhung auf 45 °C vermindert die Steifheit um etwa 25%, und eine Temperaturerniedrigung erhöht, im Gegensatz dazu, die Steifheit um etwa denselben Betrag. Erhöhte Steifheit ist pathologisch in Fällen mit rheumatischer Arthritis, Systemsklerose und Osteoarthrose. Das Auftreten von Gelenkschwellungen bei Osteoarthrose ist, wie die Analyse von Überlagerungsdiagrammen andeutet, mehr eine Erscheinung, die von Veränderungen der umhüllenden Gewebe herrührt, als von Veränderungen zwischen den Gelenkflächen. Mit diesem Gerät wurden einige künstliche Schmiermittel geprüft.

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Paper presented to the British Society of Rheology Conference on Rheology in Medicine and Pharmacy, London, April 14–15, 1970.     

Receptivity of a flat plate boundary layer to a free stream axial vortex

A single free stream axial vortex of controlled strength and position was used to investigate a vortical receptivity of Blasius boundary layer. Excited boundary-layer disturbances were dominated by streamwise velocity perturbations, that grew downstream essentially linearly with the streamwise coordinate. It was shown that the disturbance characteristics are in agreement with data of previous experiments performed under natural and control conditions concerning the ‘by-pass’ transition initiated at high free stream disturbance levels. It was proved that the role of the leading edge in the receptivity process and disturbance growth under consideration is not dominant.     

Interaction of a two-dimensional nonstationary gas stream with a free cylindrical body in a channel

The stability of a circular cylinder in an unsteady gas stream is investigated in the case when shock waves are formed and interact in the flow region. The problem is of interest for simulating processes in light-gas mortars [2, 3] in which free bodies are launched by a gas stream [4] and the launching tube will be destroyed if the launched object strikes it at a high velocity.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 180–184, March–April, 1981.     

Oscillations of the fluid flow and the free surface in a cavity with a submerged bifurcated nozzle

The free surface dynamics and sub-surface flow behavior in a thin (height and width much larger than thickness), liquid filled, rectangular cavity with a submerged bifurcated nozzle were investigated using free surface visualization and particle image velocimetry (PIV). Three regimes in the free surface behavior were identified, depending on nozzle depth and inlet velocity. For small nozzle depths, an irregular free surface is observed without clear periodicities. For intermediate nozzle depths and sufficiently high inlet velocities, natural mode oscillations consistent with gravity waves are present, while at large nozzle depths long term self-sustained asymmetric oscillations occur.For the latter case, time-resolved PIV measurements of the flow below the free surface indicated a strong oscillation of the direction with which each of the two jets issue from the nozzle. The frequency of the jet oscillation is identical to the free surface oscillation frequency. The two jets oscillate in anti-phase, causing the asymmetric free surface oscillation. The jets interact through a cross-flow in the gaps between the inlet channel and the front and back walls of the cavity.     

Boundary layer development on a continuous moving surface with a parallel free stream due to impulsive motion

The development of the momentum and thermal boundary layers over a semi-infinite flat plate has been studied when the external stream as well as the plate are impulsively moved with constant velocities. At the same time the temperature of the wall is suddenly raised from T_∞, the temperature of the surrounding fluid, toT _w and maintained at this temperature. The problem has been formulated in a new system of scaled coordinates such that fort?=0 it reduces to Rayleigh type of equation and fort? → ∞ it reduces to Blasius or Sakiadis type of equation. A new scale of time has been used which reduces the region of integration from an infinite region to a finite region which reduces the computational time considerably. The governing singular parabolic partial differential equations have been solved numerically using an implicit finite difference scheme. For some particular cases, analytical solutions have been obtained. The results show that there is a smooth transition from Rayleigh solution to Blasius or Sakiadis solution as the dimensionless timeξ increases from zero to one. The shear stress at the wall is negative for the friction parameterλ<0.5, positive forλ>0.5 and zero forλ=0.5. The zero shear stress at the wall does not imply separation but corresponds to the parallel flow. The surface heat transfer is strongly dependent on the Prandtl numberPr and increases with it. Also forPr<Pr ₀, the surface heat transfer is enhanced as the friction parameterλ increases, but forPr>Pr ₀ it get reduced.     

Flow of a sonic free gas stream around a profile

The stream function far from a profile in a two-dimensional sonic free gas jet is constructed. The stream function satisfies the Tricomi equation and is constructed on the , plane by the method of singular integral equations. With unlimited increase of the jet width and by satisfying a certain condition, the stream function transforms to the self-similar solution of Frank [1, 2] and Guderley, which describes an unbounded sonic stream far from the profile. In conclusion, flow of a sonic jet issuing from a duct about a profile is considered.The author wishes to thank S. V. Fal'kovich for valuable suggestions in discussing this article.     

Flow properties of a dusty-gas point source in a supersonic free stream

By using Lagrangian method, the flow properties of a dusty-gas point source in a supersonic free stream were studied and the particle parameters in the near-symmetry-axis region were obtained . It is demonstrated that fairly inertial particles travel along oscillating and intersecting trajectories between the bow and termination shock waves . In this region, formation of " mufti- layer structure" in panicle distribution with alternating low- and high density layers is revealed. Moreover, sharp accumulation of particles occurs near the envelopes of particle trajectories .     

Magnetohydrodynamic laminar boundary-layer flow over a porous wedge with thermophoresis particle deposition in the presence of variable stream conditions

An analysis is presented to investigate the effects of thermophoresis variable viscosity on MHD mixed convective heat and mass transfer of a viscous, incompressible and electrically conducting fluid past a porous wedge in the presence of chemical reaction. The wall of the wedge is embedded in a uniform porous medium in order to allow for possible fluid wall suction or injection. The governing boundary layer equations are written into a dimensionless form by local non-similarity transformations. The transformed coupled nonlinear ordinary differential equations are solved numerically by using the R.K. Gill and shooting methods. Favorable comparison with previously published work is performed. Numerical results for the dimensionless velocity, temperature and concentration profiles are obtained and displayed graphically for pertinent parameters to show interesting aspects of the solution.     

Experimental behaviour of the free surface in a uniform laminar stream

Summary It has been experimentally shown that in a uniform laminar free surface flow, the boundary conditions at the free surface cannot be represented by a simple non-shear condition.This statement is in particular supported by some experiments performed by the author on a high viscosity oil flow in a rectangular pipe. A surface shear viscosity may be introduced in order to characterize the behaviour of the free surface (Boussinesq).The velocity profile was measured along the axis of simmetry of the cross section. The results were in agreement with these of some numerical computations based on the above model. Similar agreement was not achieved on comparing the experimental and theoretical values obtained for the shape factor, a global parameter depending on the shape of the cross section.Such a disagreement cannot be due to experimental error and suggests that the above model is unable.

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Sommario E' fatto sperimentalmente accertato che in un moto laminare uniforme le condizioni al contorno sulla superficie libera non possono essere rappresentate dalla semplice assenza di tensioni tangenziali superficiali. Una chiara conferma viene dalla attuale serie di misure eseguite su una condotta rettangolare percorsa da olio.Per caratterizzare il comportamento della superficie libera si introduce un coefficiente di viscosità tangenziale superficiale, nell'ipotesi di comportamento newtoniano della superficie stessa (Boussinesq).I confronti fra i nostri risultati sperimentali ed i risultati numerici derivanti da tale ipotesi mostrano una possibile concordanza nella distribuzione di velocità sull'asse di simmetria della condotta ma mettono in evidenza andamenti decisamente discordanti per quanto riguarda il comportamento di un coefficiente globale, variabile con la forma della sezione.Tale discordanza non è attribuibile ad errori di misura ed indica l'inadeguatezza di un modello basato sull'ipotesi di comportamento newtoniano della superficie libera.

     

Translationally nonequilibrium free jet boundary layer in the wake behind a wedge

Macroscopic equations obtained as a thin-layer version of the 13-moment Grad equations derived from kinetic considerations are used for describing the translationally nonequilibrium monatomic gas flow in a hypersonic free jet boundary layer formed in the wake behind a wedge. This model makes it possible to investigate flows with strong violations of equilibrium with respect to the translational degrees of freedom. A method of constructing the solution of this kinetically justified problem based on the solution of an analogous problem in the Navier-Stokes interpretation is proposed. It is established that for the kinetic variant of the problem considered the gas flow velocity distribution along the separating streamline in a plane orthogonal to the wedge generator coincides with the distribution obtained in solving the Navier-Stokes variant. It is found that taking into account the nonequilibrium nature of the flow with respect to the translational degrees of freedom of the gas particles has no effect on the base pressure and the wake angle.     

Combined heat and mass transfer along a vertical moving cylinder with a free stream

The mixed convection flow over a continuous moving vertical slender cylinder under the combined buoyancy effect of thermal and mass diffusion has been studied. Both uniform wall temperature (concentration) and uniform heat (mass) flux cases are included in the analysis. The problem is formulated in such a manner that when the ratio λ(= u _w/(u _w + u _∞), where u _w and u _∞ are the wall and free stream velocities, is zero, the problem reduces to the flow over a stationary cylinder, and when λ = 1 it reduces to the flow over a moving cylinder in an ambient fluid. The partial differential equations governing the flow have been solved numerically using an implicit finite-difference scheme. We have also obtained the solution using a perturbation technique with Shanks transformation. This transformation has been used to increase the range of the validity of the solution. For some particular cases closed form solutions are obtained. The surface skin friction, heat transfer and mass transfer increase with the buoyancy forces. The buoyancy forces cause considerable overshoot in the velocity profiles. The Prandtl number and the Schmidt number strongly affect the surface heat transfer and the mass transfer, respectively. The surface skin friction decreases as the relative velocity between the surface and free stream decreases. Received on 17 May 1999     

Apparent and effective drag for circular cylinders oscillating transverse to a free stream

This communication brings forward the concept of an effective drag for circular cylinders undergoing controlled or self-excited oscillation transverse to a free stream. A relationship between the effective drag and the apparent drag customarily measured by force transducers, is derived on the basis of the average rate of energy dissipation in the fluid. The effective drag is employed to gain insight into the fluid dynamics of vortex-induced vibrations using available data from the published literature. It is shown that the effective drag varies almost continuously as a function of the true reduced velocity except for a sudden decrease near conditions of maximum amplitude. The variation displays similarities but also important differences among independent experiments, which highlight the importance of various influencing parameters whose effect on the free response is currently not well understood. Some evidence is found that self-excited oscillations occur at points in the frequency–amplitude space where the effective drag is comparatively low avoiding the region where energy transfer from the fluid to the structure is most efficient. A total energy balance is employed to reveal the effect of mechanical damping on the free response which indicates that the amplitude scales with the inverse of the square root of damping in conformity with experimental data. The dimensionless damping parameters proposed by Vandiver are examined in light of the present analysis, and alternative empirical formulas are suggested for organizing the free vibration response.     

Injection of ideal fluid from a slot into a free stream

A cold gas is injected from a slot into a free stream of hot gas. In a simple model this leads to a two-fluid free boundary problem with the jump relation |u^-|²–|u⁺|² = ( constant) on the free boundary {u=0}, where u is the stream function. We prove that for any (–1, ) there exists a unique solution (Q, u) where Q is the flux of the injected fluid. Various properties of the solution u and of the free boundary are established.     

An improved method to determine free stream conditions in hypersonic facilities

For determing pressure coefficients and Stanton numbers from the measured surface pressures and heat fluxes at a model surface, the dynamic pressure, mass flux and the total enthalpy of the free stream have to be known. Usually these values are determined by computing the wind tunnel nozzle flow. But a lot of uncertainties enter the computation which may lead to unreliable results. Therefore, a simple method was developed which yields the desired free stream conditions with high accuracy. This could be achieved by using mainly values which are measured within the test section. The method requires the measurement of the Pilot pressure, the stagnation point heat flux on a sphere and the static pressure of the free stream. For the static pressure an estimated value can also be used, because it has no large influence on the result. Some simple considerations show that the derived method is also valid for nonequilibrium free stream conditions. With the procedure presented the accuracy of the pressure coefficients and Stanton numbers could be increased significantly. Further, it improved the repeatability of these test results. This is very important for fundamental research, for the design of hypersonic vehicles as well as for CFD-validation with experimental data. The application of the method presented is not limited to short duration facilities, it can also be used for continuously working wind tunnels.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.