Vortex-speed selection within the boundary-layer flow over a rotating sphere placed in an enforced axial flow

This paper furthers existing work into the instability mechanisms within the boundary-layer flow over a rotating sphere through the study of amplification rates within the convectively-unstable region. The onset of convective instability is associated with the experimentally observed onset of spiral vortices reported in the literature. Axial flow is found to stabilize the boundary layer by both delaying the onset of convective instability at all latitudes and also by significantly reducing the spatial amplification rates. We find that the type II (streamline curvature) mode becomes increasingly amplified with respect to the type I (crossflow) mode and is therefore likely to be selected in practice for sufficiently high axial flow rates. Furthermore, in experiments where special care is taken to remove all surface roughness, we predict that vortices will rotate at around 75% of the local surface speed. This is consistent with the experimental observations of Kobayashi & Arai who note a speed of around 76% under particular experimental conditions. These predictions are entirely consistent with related work on the rotating-disk and cone boundary layers.     

Experimental study on radial temperature gradient effect of a Taylor-Couette flow with axial wall slits

The flow between two concentric cylinders with the inner cylinder rotating and an imposed radial temperature gradient was studied using a digital particle image velocimetry method. The flow transition process under both a positive and negative temperature gradient with four different models of a stationary outer cylinder without and with differing numbers of slits (6, 9 and 18) was studied. The results showed that the buoyant force due to the temperature gradient clearly generated a helical flow when the rotating Reynolds number was small. For the plain and 6-slit models, the transition to a turbulent Taylor vortex flow was not affected by the temperature gradient considered in this study. In addition, the transition process of a larger number of slits (9-, 18-slit models) was accelerated due to the slit wall. As the temperature gradient became larger, the critical Reynolds number of the transition process decreased.     

Thermal-field structure of a non-premixed turbulent flame formed in a strong pressure-gradient flow

Statistical characteristics of a non-premixed turbulent flame formed in a curved-rectangular duct and spatio-temporal structures of the thermal field were investigated experimentally. The flame was much affected by a strong pressure gradient in the radial direction of the duct curvature, which caused strong gradient diffusion in turbulent heat transfer on the inner-wall side of the flame and, in contrast, counter-gradient heat transfer on the outer-wall side. Two-point correlation measurement of temperature fields revealed that, in the strong gradient diffusion region, a spatial thermal pattern generated by turbulent mixing of high- and low-temperature fluid parcels was advected downstream with little diffusion. In contrast, the pattern was attenuated and diffused rapidly in the counter-gradient diffusion region. These results accurately correspond to the generation mechanism of the counter-gradient heat transport so far observed in stably stratified turbulent flows.     

Study into thermal stresses due to turbulent flow in pipes

Flow through pipes with heat transfer finds wide applications in industry. The thermal stresses, which develop in the pipe limit the heat transfer rate in pipe flow. In the present study, a turbulent flow in thick pipe with external heating is considered. The flow and temperature fields in a pipe and in the fluid are predicted using a numerical scheme; which employs a control volume approach. A k- model is introduced to account for the turbulence. The thermal stresses developed in the pipe due to heat transfer are predicted. The simulations are repeated for different pipe materials and fluids. It is found that the temperature gradient in the pipe changes rapidly in the vicinity of the solid-fluid interface. This change is not affected considerably by the Reynolds number. The effective stress developed at mid-plane of the pipe is independent of the Reynolds number; however, the pipe material affects the effective stress considerably.     

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.     

Applicability of the boundary-layer approximation to the calculation of a plane turbulent mixing layer

Calculation of a mixing layer-a classical problem in the theory of jet flows-is usually performed with a boundary-layer approximation. If the velocity of one of the flows is small, then even in the case of an incompressible fluid the angle of expansion of the mixing layer reaches 20?, and in the case of flows with different densities this angle is even larger. Therefore, there is some doubt about the smallness of the neglected terms which refer to differentiation in the flow direction. In the present paper the problem of the mixing of two semiinfinite flows is solved both with a boundary-layer approximation and by using a complete system of Reynolds equations (the molecular viscosity is assumed small compared to the turbulent viscosity; Re→∞).     

Modal characteristics of a flexible cylinder in turbulent axial flow from numerical simulations

In this paper the vibration behavior of a flexible cylinder subjected to an axial flow is investigated numerically. Therefore a methodology is constructed, which relies entirely on fluid–structure interaction calculations. Consequently, no force coefficients are necessary for the numerical simulations. Two different cases are studied. The first case is a brass cylinder vibrating in an axial water flow. This calculation is compared to experiments in literature and the results agree well. The second case is a hollow steel tube, subjected to liquid lead–bismuth flow. Different flow boundary conditions are tested on this case. Each type of boundary conditions leads to a different confinement and results in different eigenfrequencies and modal damping ratios. Wherever appropriate, a comparison has been made with an existing theory. Generally, this linear theory and the simulations in this paper agree well on the frequency of a mode. With respect to damping, the agreement is highly dependent on the correlation used for the normal friction coefficients in the linear theory.     

Particle deposition on a channel wall in a turbulent disperse flow with gradient

Kinetic ideas about the motion of a set of particles (droplets) in a turbulent gas flow with gradient are used to derive a Fokker-Planck equation for the case of sufficiently large particles (more than few microns). This equation describes the process in which they are deposited on the wall of a channel. Satisfactory agreement has been obtained between the numerical solution to this equation for the deposition rate and the experimental data published in the literature. Under the assumption that the parameters of the carrier gaseous flow vary fairly slowly, a generalized equation is derived for particle diffusion in turbulent flow. This takes into account the intensity gradient of transverse pulsations in the velocity of the carrier gaseous flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 57–63, July–August, 1985.     

An invariant solution of the turbulent boundary-layer equations

The problem of the group stratification of the system of equations describing motion in the laminar sublayer and the turbulent core is considered. The fundamental group admissible by the initial system is constructed; invariant solutions constructed on one of the subgroups lead to a system of ordinary differential equations. Joining of the solutions and interchange of the equations occur at the boundary of the laminar sublayer. A class of power-law flows of a turbulent boundary layer is investigated. In the region of decelerated motion a double-valued solution is found corresponding to attached or separated flow. The commonly used integral characteristics are calculated and presented in the form of an interpolation polynomial.Translated from Zhurnal Prikladnoi Mekhaniki i Teknicheskoi Fiziki, No. 4, pp. 126–132, July–August, 1975.     

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.     

Numerical investigation of the effect of convex transverse curvature and concave grooves on the turbulent boundary layer along a cylinder in axial flow

Axisymmetric turbulent boundary layers that develop around streamwise oriented long cylinder-like objects can be found in many applications, such as towed array sonars or marine seismic streamers. In many of these applications, turbulent fluctuations within the boundary layer flow can have a negative impact compared with laminar flow conditions. The aim of the present work is to design a surface modification that influences the turbulent boundary layer around a cylinder in axial flow in order to reduce turbulent fluctuations. To design the surface we consider recent findings regarding the turbulence damping effects of groove-like surface structures and combine these insights with the effect of convex transverse curvature on turbulence. We use large-eddy simulations to investigate the flow around a cylinder of modified design and around a reference circular cylinder. Both flows have a radius-based Reynolds number of ${\text{Re}}_a\approx 1.23\cdot 10^4$. The modified design leads to a 20 % decrease in the average wall shear stress and results in local reductions in the turbulent intensities, Reynolds stress, the temporal velocity spectrum, and the turbulent dissipation rate. The analysis within the anisotropy-invariant space reveals a tendency towards flow relaminarization. However, the new design has no effect on turbulent pressure fluctuations. We provide suggestions on how to further improve the surface design to achieve even greater flow stabilization.     

Model study of noise field in the human chest due to turbulent flow in a larger blood vessel

An acoustic generation of noise by a larger human blood vessel and noise transmission in the thorax is modelled and studied. In making this, the random statistical nature of the noise sources, the basic vessel properties and the main features of the human chest structure are taken into account. Also the effects of changes in the basic vessel parameters are considered as a first approach to study acoustic effects of a vascular stenosis. The analysis of the resultant acoustic field reveals its similarity to the acoustic fields recorded in the appropriate experiments. The variations in the basic vessel parameters are found to cause the corresponding changes in the sound level and the production of new frequency components in the acoustic power spectrum. The acoustic power from a slightly thickened vessel is shown to be approximately proportional to the fourth power of the flow Reynolds number in the originally normal vessel and the eighth power of the ratio of the vessel diameters.     

Growth of boundary-layer streaks due to free-stream turbulence

The growth of laminar boundary-layer streaks caused by free-stream turbulence encountering a flat plate in zero-pressure-gradient conditions is investigated experimentally in a wind tunnel and numerically by solving the unsteady boundary-region equations. A comparative discussion amongst the most relevant theoretical frameworks, such as the Goldstein theory, the Taylor–Stewartson theory, the optimal-growth theory and the Orr-Sommerfeld theory, is first presented and parallels and complimentary aspects of the theories are pointed out to justify the use of the Goldstein theory in our study. The statistical properties of the positive and negative fluctuations of the laminar streaks are discussed, showing how the total time average of the boundary-layer fluctuations masks the true character of the disturbance flow and revealing that the maximum values and the root-mean-square of positive and negative fluctuations grow downstream at the same rate. The downstream growth rate of the low-frequency disturbances and the decay rate of the high-frequency disturbances are also computed for the first time. The numerical solutions of the unsteady boundary-region equations are compared successfully with the streak profiles measured in the wind tunnel and with direct numerical simulation results available in the literature.     

Elastico-viscous boundary-layer flow on the surface of a sphere

Summary The Prandtl boundary-layer theory is extended for an idealized elastico-viscous liquid. The boundary layer equations are solved approximately by Kármán-Pohlhausen technique for the case of a sphere. It is shown that the increase in the elasticity of the liquid causes a shift in the point of separation towards the forward stagnation point.

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Zusammenfassung Die Prandtlsche Grenzschicht-Theorie wird für eine idealisierte viskoelastische Flüssigkeit erweitert. Die Grenzschichtgleichungen werden für den Fall einer angeströmten Kugel näherungsweise mit Hilfe der Kármán-Pohlhausen-Methode gelöst. Es wird gezeigt, daß das Anwachsen der Flüssigkeitselastizität eine Verschiebung des Ablösepunktes auf den vorderen Staupunkt hin zur Folge hat.

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Nomenclature b ^ik arbitrary contravariant tensor - D non-dimensional boundary layer thickness - g _ik metric tensor of a fixed coordinate system - K curvature at any point on the generating curve - K ₀ elastico-viscous parameter - p arbitrary hydrostatic pressure - p _ik stress tensor - p ^ik part of stress tensor associated with the change of shape of material - R radius of the sphere - r radius of any transverse cross-section of the sphere - t time - U potential velocity around the body - U stream-velocity at a large distance from the body - u, w velocity components along (x, z) directions respectively - x distance measured along a generating line from the forward stagnation point - z distance measured along a normal to the surface - non-dimensional elastico-viscous parameter - density of the liquid - boundary layer thickness - convected time derivative - ₀ limiting viscosity for very small changes in deformation velocity - angle measured along the transverse direction - x/R - v kinematic coefficient of viscosity - T _s shearing stress on the surface of the sphere With 2 figures and 1 table     

Memory effects in a turbulent plane wake

Memory effects in turbulent plane wakes have been investigated for various wake generators (circular, triangular and square cylinders and a screen of 50% solidity) using orthogonal arrays of X-wires, eight in the (x,y) plane and eight in the (x, z) plane. In the far-wake region, discernible differences are observed for different generators, in the measured Reynolds stresses, spectra of v and approximations to the rms spanwise and lateral vorticities. These differences, which reflect variations in various aspects of the organised large-scale structures, are quantified through the contributions these structures make to the Reynolds stresses. The difference between the screen and the solid body wakes is especially pronounced.The support of the Australian Research Council is gratefully acknowledged     

The effect of the expansion ratio on a turbulent non-Newtonian recirculating flow

 Measurements of the mean and turbulent flow characteristics of shear-thinning moderately elastic 0.1% and 0.2% xanthan gum aqueous solutions were carried out in a sudden expansion having a diameter ratio of 2. The inlet flow was turbulent and fully developed, and the results were compared with data for water in the same geometry and with previous published Newtonian and non-Newtonian data in a smaller expansion of diameter ratio equal to 1.538. An increase in expansion ratio led to an increase in the recirculation length and in the axial normal Reynolds stress at identical normalised locations, but the difference between Newtonian and non-Newtonian characteristics was less intense than in the smaller expansion. An extensive comparison of mean and turbulent flow characteristics was carried out in order to understand the variation of flow features. Received: 31 July 2000 / Accepted: 27 August 2001     

Orthogonal wavelet analysis of counter gradient transport phenomena in turbulent asymmetric channel flow

In this paper four families of orthogonal wavelets are applied to analyze the turbulent counter gradient transport phenomena in fully developed asymmetric channel flows. The results show that: (1) In the instance of counter gradient transport, the principal scale of the coherent structure is responsible for the strong local counter gradient transport; (2) Counter gradient transport phenomena have a strong effect on the intermittency of turbulence; (3) Non-Gaussian part of the principal coherent structure is essential for counter gradient transport phenomena.The project supported by the National Natural Science Foundation of China (10272071, 10472063)