Experimental study of turbulent axisymmetric cavity flow

An experimental study is made of turbulent axisymmetric cavity flow. The flow configuration consists of a sudden expansion and contraction pipe joint. In using the LDV system, in an effort to minimize refraction of laser beams at the curved interface, a refraction correction formula for the Reynolds shear stress is devised. Three values of the cavity length (L = 300, 600 and 900 mm) are chosen, and the cavity height (H) is fixed at 55 mm. Both open and closed cavities are considered. Special attention is given to the critical case L = 600 mm, where the cavity length L is nearly equal to the reattachment length of the flow. The Reynolds number, based on the inlet diameter (D = 110 mm) is 73,000. Measurement data are presented for the static wall pressure, mean velocity profiles, vorticity thickness distributions, and turbulence quantities.List of symbols C _f velocity correction factor - C _p static wall pressure coefficient - D diameter of inlet pipe = 110 mm - H step height or difference in radii of two pipes = 55 mm - L cavity length = 300, 600 and 900 mm - n _a , n _w , n _f refraction indices of the medium between the transmitting lens and window, the window itself, and the working fluid - signal validation rate in LDV, Hz - P wall static pressure, Pa - P _ref wall static pressure at x = -70 mm, Pa - r radial distance from centreline, m - r _a radial position of the virtual intersection, m - r _d radial location of the dividing streamline, m - r _f radial position of the real beam intersection, m - Re Reynolds number based on the inlet diameter - R _i inner radius of the cylindrical cavity=110 mm - t thickness of the window, m - T ₁ integral time scale, s - U streamwise mean velocity, m/s - U _c centreline mean velocity, m/s - U _ref maximum upstream velocity at x= -70 mm, m/s - r.m.s. intensity of streamwise, radial and circumferential velocity fluctuations respectively, m/s - Reynolds shear stress, m²/s² - x distance in the streamwise direction, m - x _a streamwise position of virtual intersection, m - x _f streamwise position of real beam intersection, m - x _r mean reattachment length, m - x nondimensional streamwise distance - y distance normal to the wall=R–r, m Greek symbols vorticity thickness - stream function of dividing streamline      

Numerical simulation of a pulsating flow arising over an axisymmetric spiked blunt body at Mach 2.21 and Mach 6.00

The present paper reports a numerical simulation of the supersonic/hypersonic unsteady flow over a spiked blunt body. Axisymmetric compressible Navier-Stokes equations are solved using a high-resolution unfactored implicit upwind Roe's scheme and a time-accurate pseudo-time method is employed for advancing in time. Unsteady flows arising at Mach 2.21 and Mach 6.00 around a spiked cylinder are simulated and the computational results are compared with measurements. The simulated results are used to increase understanding of the mechanisms of the flow. Received 28 September 1999 / Accepted 26 July 2000     

Numerical study of vortex-breakdown over a slender wing in transonic flow at high incidence

The transonic flowfields and vortex-breakdown over a slender wing with the angle of attack from 10° to 28° are studied numerically, and the emphasis is on the secondary separation and the charateristics of vortex-breakdown. The results indicated that: (a) TVD schemes have strong capability for capturing vortices in three-dimensional transonic separated flow at large angle of attack. (b) The development of secondary vortices is more complex than that of leading-edge ones, and is affected by wing's configuration, angle of attack and compressibility simultaneously, and the effect of compressibility is more severe at low angle of attack. (c) The starting angle of attack for vortex-breakdown (when vortex bursting point crosses trailing-edge) is about 18° forM∞=0.85, then the bursting point moves upstream quickly with increasing angle of attack. (d) At α=24°, breakdown occurs over most part of upper side, and the wing begins to stall. Therefore, there is a large lag of angle of attack between the beginning of vortex-breakdown and the stall of the wing. (e) This lag increase with the decreasing of Mach number.     

Computational and experimental study of supersonic flow over axisymmetric cavities

Laminar and turbulent computations are presented for annular rectangular-section cavities, on a body of revolution, in a Mach 2.2 flow. Unsteady ‘open cavity flows’ result for all laminar computations for all cavity length-to-depth ratios, L/D (1.33, 10.33, 11.33 and 12.33). The turbulent computations produce ‘closed cavity flows’ for L/D of 11.33 and 12.33. Surface pressure fluctuations at the front corner of the L/D = 1.33 cavity are periodic in some cases depending on the cavity length and depth, the boundary layer at the cavity front lip and the cavity scale. The turbulent computations are supported by experimental schlieren images, obtained using a spark light source, and time-averaged surface pressure data.     

Vorticity shedding from a lentil-shaped body at large incidence in uniform flow

The 2D flow about a lentil-shaped body at high incidence in uniform stream is numerically simulated for high Reynolds numbers. The separation points are fixed on the body edges and the vorticity released through a Kutta-like condition is spatially discretized by point vortices. Their Lagrangianinviscid dynamics is described by using both aconformal mapping and aboundary elements method. The present results are in good agreement with previous calculations but still not satisfactory when compared with the experiments.The aim of the present work is to investigate the effect of different Kutta conditions and the effect of different amalgamation procedures in the far wake on global quantities such as theStrouhal number or the total shed circulation. Other remarkable effects induced either by the action of viscosity or by the rising of secondary 3D motion, may not be analyzed by the present simplified model.

---

Sommario Si studia il flusso attorno ad una lente ad elevata incidenza nelle ipotesi di elevato numero di Reynolds e flusso bidimensionale. I punti di separazione sono fissati sulle estremità della lente e la produzione di vorticità da questi è realizzata con opportune condizioni di Kutta. La dinamica dei vortici è descritta con un modello Lagrangiano non viscoso. I risultati, ottenuti sia con l'uso di una trasformazione conforme che con un metodo agli elementi di contorno, sono in ottimo accordo con i risultati di precedenti simulazioni numeriche, ma non sono ancora soddisfacenti se confrontati con gli esperimenti.Si analizza in termini di grandezze globali del flusso, quali il numero di Strouhal e la circolazione totale rilasciata, l'effetto di due diverse condizioni di Kutta e dell'uso di procedure di compattazione della scia lontana. Si conclude che l'uso di diverse condizioni di Kutta produce risultati pressoché identici mentre l'utilizzo di procedure di compattazione della scia può alterare in modo significativo il numero di Strouhal del flusso. Rimangono da analizzare altre possibili cause del disaccordo con le sperimentazioni quali la diffusione viscosa e la probabile presenza di moti tridimensionali.

     

Measurements in the flow around a marine propeller at the stern of an axisymmetric body

An experimental study of the flow around and behind an axisymmetric body driven by a marine propeller is reported. Experiments were performed in a wind tunnel to document this complex, unsteady, three-dimensional, turbulent shear flow. Measurements were made in the boundary layer and wake of the bare body with a fixed dummy hub for the propeller, with the dummy hub rotating, and finally, with the propeller in operation. A five-hole yaw probe was employed for the mean-flow measurements, and two- and threesensor hotwires were used to obtained the mean and turbulent velocity fields. Part 1 of this two-part paper describes the experimental arrangement and circumferentially-averaged results which clarify certain overall aspects of the flow when it is viewed as a rotationally-symmetric flow. These are of special interest in marine hydrodynamics. In Part 2, the triple-sensor hotwire data are analyzed using phase-averaging techniques to reconstruct the instantaneous velocity and Reynolds-stress fields downstream of the propeller to show the evolution of the wakes of individual blades, blade-tip vortices, and the complex flow associated with vortices generated at hub-blade junctions.     

Measurements in the flow around a marine propeller at the stern of an axisymmetric body

Experiments were performed in a wind tunnel to study the flow around an axisymmetric body driven by a marine propeller. Measurements were made in the boundary layer and wake of the bare body, on the body with only a dummy hub rotating, and finally, with the propeller in operation. Part 1 of this paper described the experimental arrangement and instrumentation. Also, circumferentially-averaged results were presented to clarify certain aspects of the overall flow. In the present part, measurements made with a triplesensor hotwire are analyzed using phase-averaging techniques to reconstruct the instantaneous velocity and Reynolds-stress fields downstream of the propeller and show the evolution of the wakes of individual blades, blade-tip vortices, and the complex flow associated with vortices generated at hub-blade junctions. It is found that the blade wakes and features of the tip and hub flow are evident up to about two propeller diameters, beyond which the wake of the body-propeller combination can be regarded as a rotationally-symmetric flow.     

Analytic solution for axisymmetric flow over a nonlinearly stretching sheet

An analysis is performed for the boundary-layer flow of a viscous fluid over a nonlinear axisymmetric stretching sheet. By introducing new nonlinear similarity transformations, the partial differential equations governing the flow are reduced to an ordinary differential equation. The resulting ordinary differential equation is solved using the homotopy analysis method (HAM). Analytic solution is given in the form of an infinite series. Convergence of the obtained series solution is explicitly established. The solution for an axisymmetric linear stretching sheet is obtained as a special case.     

Free convection through conducting non-Newtonian fluids over a thin axisymmetric body

An analysis of free convection heat transfer in electrically conducting power law non-Newtonian fluid over a thin axisymmetric body of constant temperature is carried out. The uniform external magnetic field acts normally to the surface through the induced boundary layer. In view of the fact that most of the non-Newtonian fluids have large Prandtl number, the momentum equation is simplified. The equations of conservation of mass, momentum and energy which govern and describe the flow and heat transfer are solved numerically. The effect of the magnetic field on the velocity, temperature, the coefficient of friction and the Nusselt number are investigated. Numerical results are tabulated, presented graphically and discussed.     

Experimental investigation of three-dimensional supersonic flow past an axisymmetric body with an annular cavity

The results of an experimental investigation of supersonic Mach 2.5 flow past an axisymmetric cylindrical model body with a rectangular annular cut-out on its lateral surface are presented. The evolution of the structure of the flow over the cavity with continuous variation in the angle of attack is studied on the basis of the data of flow visualization and balance measurements on the range of the relative cavity lengths L/h from 8 to 16. Hysteresis phenomena are revealed and analyzed.     

Asymptotics of steady axisymmetric flow of incompressible fluid past a bluff body at high Reynolds number

Steady axisymmetric separated flow at high Reynolds number is considered. It is shown that the body scale flow does not correspond to the Kirchhoff model because near the body there is a fairly strong reversed flow causing the secondary separation which is observed in numerical computations. Quantitative theoretical results are compared with the numerical results.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 37–44, January–February, 1995.     

Inviscid flow past a ducted axisymmetric body with annular elliptical region

The flow regime with an annular elliptical region between the shock wave and a ducted body is realized when the ratio of the duct diameter to the characteristic body thickness is sufficiently large and the backpressure is sufficiently low. In the present paper we consider the application of the method of integral relations in the first approximation to the calculation of such a flow. The examples were calculated on a computer.     

Distributed forcing of the flow past a blunt-based axisymmetric bluff body

In this paper, we address the influence of a blowing-/suction-type distributed forcing on the flow past a blunt-based axisymmetric bluff body by means of direct numerical simulations. The forcing is applied via consecutive blowing and suction slots azimuthally distributed along the trailing edge of the bluff body. We examine the impact of the forcing wavelength, amplitude and waveform on the drag experienced by the bluff body and on the occurrence of the reflectional symmetry preserving and reflectional symmetry breaking wake modes, for Reynolds numbers 800 and 1,000. We show that forcing the flow at wavelengths inherent to the unforced flow drastically damps drag oscillations associated with the vortex shedding and vorticity bursts, up to their complete suppression. The overall parameter analysis suggests that this damping results from the surplus of streamwise vorticity provided by the forcing that tends to stabilize the ternary vorticity lobes observed at the aft part of the bluff body. In addition, conversely to a blowing-type or suction-type forcing, the blowing-/suction-type forcing involves strong nonlinear interactions between locally decelerated and accelerated regions, severely affecting both the mean drag and the frequencies representative of the vortex shedding and vorticity bursts.     

Wave processes in an elastic half-plane impacted by a blunt-nosed rigid body

The problem of unsteady deformation of an elastic half-plane is considered whose surface is impacted, at an initial instant, by a blunt-nosed rigid body, which generates diverging unsteady elastic waves and deforms the medium. The corresponding initial-boundary-value problem is formulated whose solution is constructed for the early stage of the interaction. The integral Laplace transform in the time variable and the integral Fourier transform in the one of the spatial variables are used. The solution of the problem is obtained in terms of the transforms and a formal solution is constructed in terms of the original functions. For a body with a fixed contact region, an analytical expression of the normal stress at an arbitrary point of the half-plane as a function of time is obtained. For a body shaped as an obtuse-angled wedge, analytical expressions of the normal stress and displacement at an arbitrary point at the symmetry axis of the problem are obtained. Calculations are performed and used to analyze the characteristic features of the wave processes in the medium as functions of time, the surface distance, and the mechanical properties of the material.     

Thin triangular blunt-nosed plate in a viscous hypersonic flow

The effect of a small blunt nose on the hypersonic flow past a thin, high-sweep and high-aspect-ratio plate at small incidence is investigated. The analysis is made by means of numerical simulation within the framework of the parabolized Navier-Stokes equations and the Euler equations in combination with approximate methods for calculating the heat transfer. The results are compared with the data of experiments in which some nontrivial features of the heat flux distributions over the thin plate surface were revealed.     

Influence of injection on stabilization of flow over an axisymmetric body with a recess facing into a supersonic oncoming stream

Numerical modeling of supersonic flow over a body with an annular step formed by two coaxial cylinders is performed by the Godunov method within the framework of the model of an ideal gas. Regimes of nonsteady streamline flow and peculiarities of the flow associated with the presence of a cylindrical recess in the nose part of the body are analyzed. The influence of the intensity of injection of an annular wall jet from the bottom of the recess on flow stabilization and the body drag is investigated. The domain of the existence of steady streamline flow is established. Khar'kov Aviation Institute, Khar'kov 310070. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 4, pp. 84–90, July–August, 1998.     

On axisymmetric flow of Sisko fluid over a radially stretching sheet

This study presents an analysis of the axisymmetric flow of a non-Newtonian fluid over a radially stretching sheet. The momentum equations for two-dimensional flow are first modeled for Sisko fluid constitutive model, which is a combination of power-law and Newtonian fluids. The general momentum equations are then simplified by invoking the boundary layer analysis. Then a non-linear ordinary differential equation governing the axisymmetric boundary layer flow of Sisko fluid over a radially stretching sheet is obtained by introducing new suitable similarity transformations. The resulting non-linear ordinary differential equation is solved analytically via the homotopy analysis method (HAM). Closed form exact solution is then also obtained for the cases n=0 and 1. Analytical results are presented for the velocity profiles for some values of governing parameters such as power-law index, material parameter and stretching parameter. In addition, the local skin friction coefficient for several sets of the values of physical parameter is tabulated and analyzed. It is shown that the results presented in this study for the axisymmetric flow over a radially non-linear stretching sheet of Sisko fluid are quite general so that the corresponding results for the Newtonian fluid and the power-law fluid can be obtained as two limiting cases.     

Calculation of heat transfer accompanying hypersonic three-dimensional flow of air over slender blunt-nosed cones

The effective length method [1, 2] has been used to make systematic calculations of the heat transfer for laminar and turbulent boundary layers on slender blunt-nosed cones at small angles of attack ( + 5° in a separationless hypersonic air stream dissociating in equilibrium (half-angles of the cones 0 20°, angles of attack 0 15°, Mach numbers 5 M 25). The parameters of the gas at the outer edge of the boundary layer were taken equal to the inviscid parameters on the surface of the cones. Analysis of the results leads to simple approximate dependences for the heat transfer coefficients.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 173–177, September–October, 1981.