Rotating-disk-type flow over loose boundaries

Rotating-disk-type flow of a liquid over a loose boundary, such as a layer of sand, is investigated. For this flow the formation of a new large-scale spiral pattern has been discovered. The new pattern is reminiscent of the Type-I spiral-vortex structures which characterize the laminar–turbulent transition region of boundary layers over rigid rotating disks. Flow visualizations reveal that the new pattern and the Type-I spiral vortices co-exist in the loose-boundary flow. The research investigating the origin of the new large-scale pattern is reviewed. Then photographs from flow visualizations are analysed to obtain estimates for the critical Reynolds number for which Type-I spiral vortices first appear for the loose-boundary flow and for the critical Reynolds numbers for the laminar–turbulent transition of the boundary layer. The results suggest that Type-I vortices appear at much lower Reynolds numbers over loose boundaries in comparison with flow over rigid rotating disks and that transition also appears to be advanced to much lower Reynolds numbers. The discussion of the results suggests that advanced transition arises from disturbances introduced into the flow after the loose boundary has been mobilized and not from disturbances associated with the roughness that the surfaces of the granular layer represents to the flow while grains are at rest.     

Study on boundary layer transition of a rotating disk

Summary Behaviour of spiral vortices being generated in transition regime of a disk rotating in otherwise undisturbed fluid is experimentally studied in detail. Through visualizations of the transition regime by using close-up camera, new striped flow patterns originating along the axis of spital vortices are found to be ring-like vortices which occur on the surfaces of each spiral vortices. Mechanism of the spiral vortex is clarified by cutting the vortices by strobo slit light. It is also found out experimentally that the phase velocity of the vortices is zero.     

Stability of the boundary layer on a sphere rotating in still fluid

Summary A theoretical study of the transition of a three-dimensional boundary layer on a sphere rotating in still fluid is carried out by a linear stability analysis. A set of perturbation equations governing the instability of the flow field is derived assuming the perturbations to be consisting of spiral vortices. It is shown that the critical Reynolds numbers obtained in the present analytical study are close to those observed in experiments. It has been found that the streamline-curvature instability appears in the rotating sphere flow. It is also shown that the cross-flow instability is dominant near the poles of a sphere while the streamline-curvature instability overtakes near the equator.     

Transition of boundary layer flow past a stretching sheet due to a step change in applied constant mass flux

The problem of transition of boundary layer flow from the initial unsteady flow to the final steady flow past a permeable stretching sheet is considered in this paper. Two cases are considered: (1) Case-I deals with the transition of the unsteady flow due to a sudden application of constant suction/injection at the surface of the stretching sheet, from the initially prevailing steady flow; (2) Case-II deals with unsteady flow transition due to a sudden removal of constant suction/injection at the surface of the stretching sheet, from the initially prevailing steady flow. Numerical results are obtained using the implicit finite difference method of Crank-Nicholson type. The velocity and local skin friction for different values of injection/suction parameter are graphically presented and discussed. It is found that for the same magnitude of applied mass flux in Case-I and mass flux removal in Case-II, the time to reach steady-state flow is different.     

Vortex motion in the early stages of unsteady flow around a circular cylinder

In this paper, processes in the early stages of vortex motion and the development of flow structure behind an impulsively-started circular cylinder at high Reynolds number are investigated by combining the discrete vortex model with boundary layer theory, considering the separation of incoming flow boundary layer and rear shear layer in the recirculating flow region. The development of flow structure and vortex motion, particularly the formation and development of secondary vortex and a pair of secondary vortices and their effect on the flow field are calculated. The results clearly show that the flow structure and vortices motion went through a series of complicated processes before the symmetric main vortices change into asymmetric: development of main vortices induces secondary vortices; growth of the secondary vortices causes the main vortex sheets to break off and causes the symmetric main vortices to become “free” vortices, while a pair of secondary vortices is formed; then the vortex sheets, after breaking off, gradually extend downstream and the structure of a pair of secondary vortices becomes relaxed. These features of vortex motion look very much like the observed features in some available flow field visualizations. The action of the secondary vortices causes the main vortex sheets to break off and converts the main vortices into free vortices. This should be the immediate cause leading to the instability of the motion of the symmetric main vortices. The flow field structure such as the separation position of boundary layer and rear shear layer, the unsteady pressure distributions and the drag coefficient are calculated. Comparison with other results or experiments is also made. This work was presented at the First Asian Congress of Fluid Mechanics, Bangalore in December 1980.     

Analysis of transient flow of MHD nanofluid past a non-linear stretching sheet considering Navier’s slip boundary condition

Induced boundary layer flow in the nanofluid caused by impulsively started nonlinear stretching sheet is analyzed in the presence of thermal radiation and magnetic field considering Navier’s velocity sip boundary condition. The similarity solution is achieved numerically using Galerkin finite element technique. The variation of flow characteristics viz. nanofluid velocity, temperature and nanoparticle concentration is examined corresponding to different flow parameters considered in the problem. The findings of the investigation reveal that nonlinearity in the stretching sheet leads to a deceleration in the nanofluid velocity, temperature and nanoparticle concentration while the unsteadiness in the stretching tends to decelerate the velocity whereas temperature and nanoparticle concentration are found to be increasing with increase in unsteadiness. The problem investigated in this article is basically an extension for unsteady case of the previously done works on nanofluid flow over a sheet stretching with a power-law velocity.     

Three-dimensional waves beneath an ice sheet due to a steadily moving pressure

Solutions of the nonlinear water wave equations under an ice sheet are computed using a boundary integral equation method. The ice sheet is modelled as a thin elastic plate and the fluid equations are nonlinear. Depending on the velocity of the moving disturbance generating the flow, different types of responses of the floating ice sheet are discussed.     

Primary crossflow vortices,secondary absolute instabilities and their control in the rotating-disk boundary layer

The three-dimensional boundary layer produced by a disk rotating in otherwise still fluid is analytically investigated and its stability properties are systematically established. Using a local parallel flow approximation, finite-amplitude primary travelling vortices governed by a nonlinear dispersion relation are obtained. A secondary stability analysis yields the secondary linear dispersion relation and the secondary absolute growth rate, which determines the long-term stability of the primary nonlinear vortex-trains. By using these local characteristics, spatially developing global patterns of crossflow vortices are derived by employing asymptotic techniques. This approach accounts for both the self-sustained behaviour, exhibiting a sharp transition from laminar to turbulent flow, and the spatial response to external harmonic forcing, for which onset of nonlinearity and transition both depend on the forcing parameters. Based on these results, an open-loop control method is described in detail. Its aim is not to suppress the primary fluctuations but rather to enhance them and to tune them to externally imposed frequency and modenumber, and thereby to delay onset of secondary absolute instability and transition. It is shown that transition can be delayed by more than 100 boundary-layer units.     

The flow structure of a puff

From time-resolved stereoscopic particle image velocimetry measurements over the entire circular cross section of a pipe, a first-of-its-kind quasi-instantaneous three-dimensional velocity field of a turbulent puff at a low Reynolds number is reconstructed. At the trailing edge of the puff, where the laminar flow undergoes transition to turbulence, pairs of counterrotating streamwise vortices are observed that form the legs of large hairpin vortices. At the upstream end of the puff, a quasi-periodic regeneration of streamwise vortices takes place. Initially, the vortex structure resembles a travelling wave solution, but as the vortices propagate into the turbulent region of the puff, they continue to develop into strong hairpin vortices. These hairpin vortices extract so much energy from the mean flow that they cannot be sustained. This structure provides a possible explanation for the intermittent character of the puffs in pipe flow at low Reynolds numbers.     

A New Interpretation of Oscillating Flow Experiments in Superfluid Helium II

We consider some classic experimental data from oscillating superfluid helium II flows and reinterpret them in terms of our recent results on superfluid vortices in helium II boundary layer flows. We find evidence that the lowest critical velocity in these experiments is due to a boundary layer effect. We show that the critical velocities measured in the oscillating disk experiments agree well with the critical velocities for the existence of stable stationary superfluid vortices in the boundary layer flow.     

An effect of sudden circumferential strain on the laminar boundary layer on a rotating cylinder in an axial flow

Summary The laminar boundary layer which develops on a rotating thin cylinder fitted with an aft-section rotating with an angular velocity different from that of a fore-section is examined numerically. This problem concerns a relaxation process of the boundary layer subjected to a sudden circumferential rate of strain. Two methods are adopted: one is to regard the flow on the aft-cylinder as perturbations of that on the fore-section, and the other is to approximate the discontinuous change in the angular velocity by the cumulative normal distribution function. It is shown that the flow fields are largely influenced by the degree of favorable pressure gradient produced in the boundary layer. Especially, in case of flow passing onto the aft-section with a smaller angular velocity, adverse pressure gradient is induced immediately after the junction between two cylinders, and when the degree of the discontinuity is increased, flow separation can be provoken.With 11 Figures     

Questions Related to the Oscillatory Flow of He II through a Grid at Low Temperatures

No Heading The flow of pure He II at low temperatures and a range of pressures is probed using an electrostatically-driven oscillating grid. With increasing oscillation amplitude, a (history dependent) first threshold is reached where the initially pure superflow abruptly changes: the resonant frequency decreases and the response becomes strongly nonlinear, attributable to quantized vortices responding to the motion of the grid so as to increase its effective mass without additional damping. On further increase of oscillation amplitude a second threshold is reached, probably marking the onset of superfluid turbulence. The increase in effective mass is believed to be due to a boundary layer of vortex loops that can evolve into turbulent flow at the second threshold. Open questions and problems for future research are formulated.     

Edge effects in flow around a plasma actuator

We have studied the structure of flow formed in the boundary layer at the lateral edge of the discharge zone of a dielectric barrier discharge plasma actuator. It is established that a region with nonzero component of tangential velocity exists near the plasma layer boundary. At some distance downstream of the actuator, a concentrated vortex is formed with the axis aligned with the flow direction. In the presence of two closely spaced boundaries of the plasma region, a pair of counter-rotating vortices is formed. Separate microdischarges in the plasma layer also appear to be a source of similar longitudinal vortices with smaller amplitude.

     

Comments and authors' reply on “On vibration and buckling of symmetric laminated plates according to shear deformation theories. Part I and II”, by A. Nosier and J. N. Reddy

Summary Viscous flow past a stretching sheet in the presence of a uniform magnetic field is considered. An exact similarity solution for velocity and pressure of the two-dimensional Navier-Stokes equations is presented, which is formally valid for all Reynolds numbers. The solution for the velocity field turns out to be the identical solution derived earlier by Pavlov [1] within the framework of high-Reynolds-number boundary layer theory, in which the pressure distribution cannot be determined.     

Liquid metal MHD flow in a duct whose cross section changes from a rectangle to a trapezoid

This paper treats the liquid-metal MHD flow in a semi-infinite rectangular duct and a semi-infinite trapezoidal duct, which are connected by a finite-length transition duct. There is a strong, transverse, uniform magnetic field. The walls parallel to the magnetic field (sides) remain parallel, while the walls intersecting the magnetic field are twisted in the transition duct to provide the change in cross-sectional shape. The left side has a constant height, while the height of the right side increases or decreases in the transition duct. This geometry gives a skewed velocity profile with a high velocity near the left side, provided that the right side is relatively thick. All walls are thin and electrically conducting, but the sides are considerably thicker than the other walls. Junctions of different ducts with walls parallel to the magnetic field are treated for the first time. In expansions, contractions and other geometric transition ducts, as well as in straight ducts with axially varying magnetic fields, the fluid flow and the electric currents are concentrated in boundary layers adjacent to the sides and in the sides. At a junction with a straight duct with a uniform magnetic field, the flow and current must transfer from the boundary layers and sides to the core regions. These transfers at junctions play a key role in any three-dimensional flow.     

Magnetohydrodynamic stability of boundary layers along a flat plate with pressure gradient

Summary The purpose of the paper is to consider theoretically the characteristics of steady two-dimensional magnetohydrodynamic boundary layer flow past a flat plate with pressure gradient in the presence of transverse magnetic field and its stability problem. The boundary layer equation is transformed into a non-similar one and numerical solutions are obtained by the difference-differential method. The neutral stability curves for wavelike disturbances of Tollmien-Schlichting type are then presented for the velocity profiles obtained above. Numerical results for the magnetic parameter and pressure gradient parameter are given for the velocity profiles, coefficient of skin friction, displacement thickness and the critical Reynolds number.With 10 Figures     

Boundary layer transition experiments with embedded streamwise vortices

Experiments were conducted with a counter-rotating, streamwise vortex pair embedded in flat plate boundary layers, in a low-turbulence wind tunnel, to understand the role of local separation on transition. Steady, streamwise vortices were generated downstream of gaps in spanwise-uniform, smooth hills (of height h) affixed to the plate, 175 mm from its leading edge. The flow between is directed away from the plate. At the four tunnel speeds 1.8–3.5 m/s considered, the Reynolds numbers based on displacement thickness at this location varied from 248 to 346. Small, medium and large gaps of 2, 4 and 8 mm, respectively, were set up; they were about a third to twice the boundary layer thickness (\(2/3< b/h < 8/3\)). With the closest vortex pairs, transition was observed at all freestream speeds considered. With larger spacing, transition occurred at the highest speed only. The vortex pair caused the flow to separate in all but the largest-gap cases. Separation was steady and re-attachment unsteady in all cases. Velocity fluctuations grew slightly upstream of re-attachment in transitional cases. No evidence was found for separation or re-attachment as a direct cause for transition; transition occurred even without separation. Instead, whenever transition was observed, its origin could be traced to instability of a streak of sufficient amplitude that had been created by the vortex pair. Streak instability appeared as fluctuations growing along its sides and spreading. Anomalous behaviour was also observed with moderate spacing, where transition did not occur in spite of flow separation and streak amplitudes in excess of known thresholds for streak instability.     

The axisymmetric micropolar boundary layer on a long thin cylinder

The laminar micropolar boundary layer in axial flow along a long, thin cylinder is investigated using the theory of micropolar fluids due to Eringen. The governing equations are solved numerically by expanding the velocity and angular velocity functions in the form of power series. Wall values of the momentum and angular momentum functions are tabulated for a wide range of values of the material parameters and the transverse curvature parameter.     

Roll‐up of a viscous vortex sheet

Abstract

The vortex sheet roll‐up for a viscous fluid flow under an initially periodic perturbation is studied by using a core‐spreading vortex method [2]. The viscous term, usually neglected in prior studies, is considered in the present study. In order to avoid the singularity at the center of point vortices, a convolution decomposition procedure is applied to form the vortex blobs. When calculating the stream function and the velocity field, the computations for the vortex method are usually time‐consuming due to the involvement of a large number of vortex blobs. This is improved by employing an efficient algorithm based on multipole expansions [6] to perform far‐field calculations. With the help of the fast algorithm, the time complexity of the one‐step calculation is directly proportional to the number of vortex blobs.

Numerical results show that the roll‐up of a vortex sheet with the viscous effect is slower than that of an inviscid vortex sheet. During the roll‐up of the vortex sheet, the spread and the flatness of the vorticity distribution are also studied by calculating the second moments and the fourth moments, respectively. Both results indicate the roll‐up of an inviscid vortex sheet is stretched slightly longer than that of a viscous vortex sheet.     

驻波场中圆柱形换热管外声流特性的数值研究

基于非线性Navier-Stokes方程推导了一般性的声流控制方程,并利用有限元软件COMSOL对平面驻波声场中单根圆柱形换热管和双圆柱形换热管外包含二阶流场信息的Navier-Stokes方程进行全域求解,得到了一阶和二阶流场信息。研究了雷诺数Re和斯特劳哈尔数Sr对换热管外声流结构的影响规律。研究发现:随Re和Sr的增大,换热管边界层内的涡流区域变小,直至消失,而边界层外的涡流区域逐渐增大;且单换热管外涡流个数由8个减少到4个,双换热管外涡流个数从12个减少到8个。此外,边界层内和边界层外的涡流结构呈反向旋转;边界层外流场沿着振荡方向远离换热管,而在垂直方向流向换热管。