On the origin and part played by pulsations of a detonation front

Arguments are given which show that the occurrence of pulsations is independent of the part they play in self-sustained detonation. It is shown that the perturbations which generate kinks in the detonation front are not formed in the region of shock compression but in the burning gas. It is suggested that the primary cause of the perturbations could be strong fluctuations associated with intense chemical transformations.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 190–194, September–October, 1979.I am grateful to V. A. Levin and G. G. Chernii for discussions and valuable comments and to Ya. K. Troshin for support.     

Bubbly flow undergoing a steep pressure gradient

The effects of a steep pressure gradient on bubbly flow were studied to determine the cause of noise emanating from components of a piping system. We used an orifice to generate a local pressure difference. The behavior of bubbles passing through the orifice was observed by using a video camera, and the noise was measured by a condenser microphone outside the pipe. It was found that the sound pressure level of noise generated by a bubbly flow was proportional to the pressure difference. An empirical formula for estimating noise level is proposed. The changes in size and number of bubbles passing through an orifice were found related to the breakup, which is affected by pressure difference rather than airflow rate. The breakup of a single bubble undergoing a steep pressure difference was observed to determine the mechanism of sound generation. It was found that a bubble was broken by impingement of an inward protrusion in the bubble. The growth rate of the protrusion depended on the pressure difference.     

Heat transfer in a corner flow

The paper describes a method of evaluating heat transfer in corner flow of an incompressible fluid with suction

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Wärmeübertragung in einer Eckenströmung

Zusammenfassung Der Aufsatz beschreibt eine Methode zur Berechnung des Wärmeübergangs bei Strömung eines inkompressiblen Fluids in eine Ecke mit Absaugung.

     

Upper and lower bounds for the pressure error in the rectilinear flow along a slot with a pressure gradient

Summary The rectilinear flow of a second-order fluid is considered between two infinitely wide and long parallel plates. The bottom plate is at rest and has a longitudinal slot in the direction of the flow, while the top plate moves in the flow direction with a constant speed. Upper and lower bounds for the pressure error are obtained by the use of the maximum principle applied to harmonic functions.

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Zusammenfassung Es wird die geradlinige Strömung einer Flüssigkeit zweiter Ordnung zwischen zwei unendlich ausgedehnten parallelen Platten untersucht. Die mit einer rechteckigen, in Strömungsrichtung orientierten Nute versehene Grundplatte befindet sich in Ruhe, wohingegen die glatte Deckplatte sich mit konstanter Geschwindigkeit in Strömungsrichtung bewegt. Untere und obere Schranken für die Abweichung des Druckes infolge der Nute (pressure error) werden durch Anwendung des Maximumprinzips auf harmonische Funktionen berechnet.

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With 6 figures     

Nonisothermal Couette flow of a non-Newtonian fluid under the action of a pressure gradient

Nonisothermal Couette flow has been studied in a number of papers [1–11] for various laws of the temperature dependence of viscosity. In [1] the viscosity of the medium was assumed constant; in [2–5] a hyperbolic law of variation of viscosity with temperature was used; in [6–8] the Reynolds relation was assumed; in [9] the investigation was performed for an arbitrary temperature dependence of viscosity. Flows of media with an exponential temperature dependence of viscosity are characterized by large temperature gradients in the flow. This permits the treatment of the temperature variation in the flow of the fluid as a hydrodynamic thermal explosion [8, 10, 11]. The conditions of the formulation of the problem of the articles mentioned were limited by the possibility of obtaining an analytic solution. In the present article we consider nonisothermal Couette flows of a non-Newtonian fluid under the action of a pressure gradient along the plates. The equations for this case do not have an analytic solution. Methods developed in [12–14] for the qualitative study of differential equations in three-dimensional phase spaces were used in the analysis. The calculations were performed by computer.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 26–30, May–June, 1981.     

Magnetohydrodynamic flow through a rectangular duct due to a periodic pressure gradient

Summary The flow of an incompressible, viscous, electrically conducting fluid in a long channel of rectangular cross section due to a periodic pressure gradient, in the presence of a uniform transverse magnetic field is investigated. Exact solutions are obtained and asymptotic forms valid for large Hartmann numbers are discussed.     

A robust numerical method for flow through a pipe driven by an oscillating pressure gradient

The problem of periodic flow of an incompressible fluid through a pipe, which is driven by an oscillating pressure gradient (e.g. a reciprocating piston), is investigated in the case of a large Reynolds number. This process is described by a singularly perturbed parabolic equation with a periodic right‐hand side, where the singular perturbation parameter is the viscosity ν. The periodic solution of this problem is a solution of the Navier–Stokes equations with cylindrical symmetry. We are interested in constructing a parameter‐robust numerical method for this problem, i.e. a numerical method generating numerical approximations that converge uniformly with respect to the parameter ν and require a bounded time, independent of the value of ν, for their computation. Our method comprises a standard monotone discretization of the problem on non‐standard piecewise uniform meshes condensing in a neighbourhood of the boundary layer. The transition point between segments of the mesh with different step sizes is chosen in accordance with the behaviour of the analytic solution in the boundary layer region. In this paper we construct the numerical method and discuss the results of extensive numerical experiments, which show experimentally that the method is parameter‐robust. Copyright © 2006 John Wiley & Sons, Ltd.     

Transients in flow and local heat transfer due to a pressure wave in pipe flow

The effect of a pressure wave on the turbulent flow and heat transfer in a rectangular air flow channel has been experimentally studied for fast transients, occurring due to a sudden increase of the main flow by an injection of air through the wall. A fast response measuring technique using a hot film sensor for the heat flux, a hot wire for the velocities and a pressure transducer have been developed. It was found that in the initial part of the transient the heat transfer change is independent of the Reynolds number. For the second part the change in heat transfer depends on thermal boundary layer thickness and thus on the Reynolds number. Results have been compared with a simple numerical turbulent flow and heat transfer model. The main effect on the flow could be well predicted. For the heat transfer a deviation in the initial part of the transient heat transfer has been found. From the turbulence measurements it has been found that a pressure wave does not influence the absolute value of the local turbulent velocity fluctuations. They could be considered to be frozen.Nomenclature A surface area (m²) - D diameter (m) - h heat transfer coefficient (Wm^–2 K^–1) - p pressure drop (Pa) - P pressure (Pa) - Q heat flow (W) - R tube radius (m) - T bulk temperature (K) - T _s surface temperature (K) - t time (s) - u velocity (m/s) - V voltage (V) - y distance from wall (m) - viscosity (N s m^–2) - kinematic viscosity (m^–2 s^–1) - density (kg m^–3) - _w wall shear stress (N m^–2) - Nu Nusselt number - Re Reynolds number     

Flow of elastico-viscous liquids in channels under the influence of a periodic pressure gradient,part 1

Summary The flow of a non-Newtonian incompressible liquid in a straight pipe of circular cross-section under the influence of a periodic pressure gradient is investigated; the viscous and elastic properties of the liquid are defined in terms of a spectrum of relaxation times. Such a flow is of interest to the experimentalist, because the flow could be readily attained and controlled in practice. A solution is obtained which determines the variation in the mean-square velocity over the section of the pipe. In the numerical illustrations given, it is shown that the general nature of the flow is similar to that of a purely viscous liquid of constant viscosity, a high peak of average velocity occurring near the wall of the pipe. However, it is shown that elasticity of the type considered could strongly affect the value and position of this peak of the average velocity.     

Compression shock in the transonic flow around a convex corner

The interaction between mixed sub-and supersonic flow near a convex breakpoint of a profile with a rectilinear wall downstream of this breakpoint is investigated. If we start from the fact that the initial flow has the character of a singularity in the domain ahead of the last characteristic of the rarefaction node [1], then the solution in the interaction domain, obtained in the hodograph plane under the assumption of its continuity in the physical plane, is not realizable because of the presence of limit lines. This governs the hypotheses of the formation of the compression shock emerging from the corner point and having zero intensity there.     

Separation zones in the flow near a small-angle convex corner

On the basis of an asymptotic analysis of the Navier-Stokes system of equations for large Reynolds numbers (Re → ∞), the plane incompressible fluid flow near a surface having a convex corner with a small angle 2θ* is investigated. It is shown that for θ* = O(Re^?1/4), in addition to the known solution that describes a separated flow completely localized in a thin “viscous” sublayer of the interaction region near the corner point, another solution corresponding to a flow with a developed separation zone is possible. For θ ₀ = Re^1/4 θ* = O(1), the longitudinal dimension of this zone varies from finite values up to values of the order of Re^?3/8. The nonuniqueness of the solution is established on a certain range of variation of the parameter θ ₀. The dependence of the drag coefficient on the angle θ* is found.     

On the flows produced by sudden application of a constant pressure gradient or by impulsive motion of a boundary

Some properties of the time-dependent Navier-Stokes equations are discussed for flows impulsively started from rest by sudden application of a constant pressure gradient or by the impulsive motion of a boundary. Five illustrative examples are given. They are: unsteady flow in a circular cylinder moving parallel to its length, starting flow in a circular pipe, unsteady flow in a rotating cylinder, starting flow in a rectangular channel moving parallel to its length and unsteady flow in a channel of rectangular cross-section. It is found that the expressions of the quantities such as velocity, flux and skin friction are in series forms which may be rapidly convergent for large values of the time but slowly convergent for small values of the time or vice versa. It is shown that if their expressions can be found for one of large values of the time or small values of the time, these expressions can be used for the other.     

Magnetoaerodynamic boundary layer flow with pressure gradient and separation

This study considers the large interaction parameter magnetoaerodynamic boundary layer associated with the free stream flow of a conducting fluid over an infinitely long circular insulator cylinder with the applied magnetic field normal to the distant free stream flow. The investigation is conducted in two parts; a theoretical solution of the associated boundary layer equations and a qualitative experimental investigation to allow visualization of flow separation caused by the magnetic field. The general integral formulation of Galerkin-Kantorovich-Dorodnitsyn is used to determine the boundary layer thickness, momentum thickness, displacement thickness, approximate separation point, and velocity profiles.     

Comparison of organized motions in a constant and an adverse pressure gradient turbulent flow

The distribution of the statistical properties of coherent motions across a fully developed feed pipe is observed to change drastically as adverse pressure gradient is applied in a conical diffuser. These changes are associated with distortion of the turbulence structure and becomes more pronounced as the flow approaches detachment. A conceptual model based on present measurements effectively accounts for major turbulence characteristics in the diffuser.