Time resolved investigations on flow field and quasi wall shear stress of an impingement configuration with pulsating jets by means of high speed PIV and a surface hot wire array

The effects of jet pulsation on flow field and quasi wall shear stress of an impingement configuration were investigated experimentally. The excitation Strouhal number and amplitude were varied as the most influential parameters. A line-array with three submerged air jets, and a confining plate were used. The flow field analysis by means of time resolved particle image velocimetry shows that the controlled excitation can considerably affect the near-field flow of an impinging jet array. These effects are visualized as organization of the coherent flow structures. Augmentation of the Kelvin–Helmholtz vortices in the jet shear layer depends on the Strouhal number and pulsation magnitude and can be associated with pairing of small scale vortices in the jet. A total maximum of vortex strength was observed when exciting with Sr = 0.82 and coincident high amplitudes.Time resolved interaction between impinging vortices and impingement plate boundary layer due to jet excitation was verified by using an array of 5 μm surface hot wires. Corresponding to the global flow field modification due to periodic jet pulsation, the impact of the vortex rings on the wall boundary layer is highly influenced by the above mentioned excitation parameters and reaches a maximum at Sr = 0.82.     

Hydromagnetic free convection flow with induced magnetic field effects

An exact solution is presented for the hydromagnetic natural convection boundary layer flow past an infinite vertical flat plate under the influence of a transverse magnetic field with magnetic induction effects included. The transformed ordinary differential equations are solved exactly, under physically appropriate boundary conditions. Closed-form expressions are obtained for the non-dimensional velocity (u), non-dimensional induced magnetic field component (B _x ) and wall frictional shearing stress i.e. skin friction function (τ _x ) as functions of dimensionless transverse coordinate (η), Grashof free convection number (G _r ) and the Hartmann number (M). The bulk temperature in the boundary layer (Θ) is also evaluated and shown to be purely a function of M. The Rayleigh flow distribution (R) is derived and found to be a function of both Hartmann number (M) and the buoyant diffusivity parameter (ϑ ^*). The influence of Grashof number on velocity, induced magnetic field and wall shear stress profiles is computed. The response of Rayleigh flow distribution to Grashof numbers ranging from 2 to 200 is also discussed as is the influence of Hartmann number on the bulk temperature. Rayleigh flow is demonstrated to become stable with respect to the width of the boundary layer region and intensifies with greater magnetic field i.e. larger Hartman number M, for constant buoyant diffusivity parameter ϑ ^*. The induced magnetic field (B _x ), is elevated in the vicinity of the plate surface with a rise in free convection (buoyancy) parameter G _r , but is reduced over the central zone of the boundary layer regime. Applications of the study include laminar magneto-aerodynamics, materials processing and MHD propulsion thermo-fluid dynamics.     

An investigation of the scales in transitional boundary layers under high free-stream turbulence conditions

The scales in a transitional boundary layer subject to high (initially 8%) free-stream turbulence and strong acceleration (K as high as 9×10^–6) were investigated using wavelet spectral analysis and conditional sampling of experimental data. The boundary layer shows considerable evolution through transition, with a general shift from the lower frequencies induced by the free-stream unsteadiness to higher frequencies associated with near-wall-generated turbulence. Within the non-turbulent zone of the intermittent flow, there is considerable self-similarity in the spectra from the beginning of transition to the end, with the dominant frequencies in the boundary layer remaining constant at about the dominant frequency of the free-stream. The frequencies of the energy-containing scales in the turbulent zone change with streamwise location and are significantly higher than in the non-turbulent zone. When normalized on the local viscous length scale and velocity, however, the turbulent zone spectra also show good self-similarity throughout transition. Turbulence dissipation occurs almost exclusively in the turbulent zone. The velocity fluctuations associated with dissipation are isotropic, and their normalized spectra at upstream and downstream stations are nearly identical. The distinct differences between the turbulent and non-turbulent zones suggest the potential utility of intermittency based transition models in which these zones are treated separately. The self-similarity noted in both energy containing and dissipation scales in both zones suggests possibilities for simplifying the modeling for each zone.

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Influence of the Prandtl Number on the Unsteady Thermo-Fluid Dynamic Field Around a Thick Plate

The problem of a semi-infinite “thick” plate impulsively accelerated to a constant speed is discussed, considering a compressible laminar boundary layer when the thermo-fluid dynamic field in the flow is coupled with the thermal field in the solid (conjugated heat transfer). Different cases are defined by the boundary condition for the thermal field on the unwetted plate side, A first-order analytical approximation of a more general method of solution is here proposed, with emphasis to the analysis of the effects of the Prandtl number (Pr), when the temperature on the unwetted side of the plate is assumed constant. The comparison with some reference solution available for the limiting conditions of steady flow and plate of infinite length shows a very satisfactory accuracy of the present results in spite of the first order approximation.     

Effect of local forcing on a turbulent boundary layer

An experimental study is performed to analyze flow structures behind local suction and blowing in a flat-plate turbulent boundary layer. The local forcing is given to the boundary layer flow by means of a sinusoidally oscillating jet issuing from a thin spanwise slot at the wall. The Reynolds number based on the momentum thickness is about Re _θ =1700. The effects of local forcing are scrutinized by altering the forcing frequency (0.011 ≤ f ⁺≤ 0.044). The forcing amplitude is fixed at A ₀=0.4. It is found that a small local forcing reduces the skin friction and the skin friction reduction increases with the forcing frequency. A phase-averaging technique is employed to capture the large-scale vortex evolution. An organized spanwise vortical structure is generated by the local forcing. The cross-sectional area of vortex and the time fraction of vortex are examined by changing the forcing frequency. An investigation of the random fluctuation components reveals that turbulent energy is concentrated near the center of vortical structures. Received: 17 March 2000/Accepted: 3 April 2001     

Disturbance evolution in the leading-edge region of a blunt flat plate in supersonic flow

The spatio-temporal dynamics of small disturbances in viscous supersonic flow over a blunt flat plate at freestream Mach number M_∞=2.5 is numerically simulated using a spectral approximation to the Navier–Stokes equations. The unsteady solutions are computed by imposing weak acoustic waves onto the steady base flow. In addition, the unsteady response of the flow to velocity perturbations introduced by local suction and blowing through a slot in the body surface is investigated. The results indicate distinct disturbance/shock-wave interactions in the subsonic region around the leading edge for both types of forcing. While the disturbance amplitudes on the wall retain a constant level for the acoustic perturbation, those generated by local suction and blowing experience a strong decay downstream of the slot. Furthermore, the results prove the importance of the shock in the distribution of perturbations, which have their origin in the leading-edge region. These disturbance waves may enter the boundary layer further downstream to excite instability modes.     

Flow of power-law fluids over a moving wedge surface with wall mass injection

The boundary layer problem of a power-law fluid flow with fluid injection on a wedge whose surface is moving with a constant velocity in the opposite direction to that of the uniform mainstream is analyzed. The free stream velocity, the injection velocity at the surface, moving velocity of the wedge surface, the wedge angle and the power law index of non-Newtonian fluid are assumed variables. The fourth order Runge–Kutta method modified by Gill is used to solve the non-dimensional boundary layer equations for non-Newtonian flow field. Without fluid injection, for every angle of wedge β, a limiting value for velocity ratio λ _cr (velocity of the wedge surface/velocity of the uniform flow) is found for each power-law index n. The value of λ _cr increases with the increasing wedge angle β. The value of wedge angle also restricts the physical characteristics of the fluid to be used. The effects of the different parameters on velocity profile and on skin friction are studied and the drag reduction is discussed. In case of C = 2.5 and velocity ratio λ = 0.2 for wedge angle β = 0.5 with the fluid with power law-index n = 0.5, 48.8% drag reduction is obtained.     

Effects of sub-millimeter-bubble injection on transition to turbulence in natural convection boundary layer along a vertical plate in water

Temperature and velocity measurements are performed to clarify the effects of sub-millimeter-bubble injection on the transition to turbulence in the natural convection boundary layer along a vertical plate in water. In particular, we focus on the relationship between the bubble injection position L and the transition to turbulence in the natural convection boundary layer. The bubble injection positions used in our experiments are L = 1.6 and 3.6 mm. Bubble injection at L = 1.6 mm delays the transition to turbulence in the natural convection boundary layer, while that at L = 3.6 mm accelerates the transition to turbulence in the boundary layer. In the case of L = 1.6 mm, the appearance region of the liquid velocity fluctuation in the bubble-induced upward flow in the upstream unheated section is restricted to near the wall, although the peak of the liquid velocity fluctuation is high. In contrast, in the case of L = 3.6 mm, the relatively large liquid velocity fluctuation is distributed widely over the laminar boundary layer width. These results suggest that the effect of the liquid velocity fluctuation on the laminar boundary layer is quite different between L = 1.6 and 3.6 mm. It is therefore expected that the transition to turbulence in the natural convection boundary layer for the case with bubble injection is dependent on the magnitude and appearance region of the liquid velocity fluctuation in the bubble-induced upward flow in the upstream unheated section.     

Oblique stagnation-point flow of a viscoelastic fluid with heat transfer

The two-dimensional forced convection stagnation-point flow and heat transfer of a viscoelastic second grade fluid obliquely impinging on an infinite plane wall is considered as an exact solution of the full partial differential equations. This oblique flow consists of an orthogonal stagnation-point flow to which a shear flow whose vorticity is fixed at infinity is added. The relative importance of these flows is measured by a parameter γ. The viscoelastic problem is reduced to two ordinary differential equations governed by the Weissenberg number W_e, two parameters α and β, the later being a free parameter β, introduced by Tooke and Blyth [A note on oblique stagnation-point flow, Physics of Fluids 20 (2008) 033101-1–3], and the Prandtl number Pr. The two cases when α=β and α≠β are, respectively, considered. Physically the free parameter may be viewed as altering the structure of the shear flow component by varying the magnitude of the pressure gradient. It is found that the location of the separation point x_s of the boundary layer moves continuously from the left to the right of the origin of the axes (x_s<0).     

Tailoring turbulence with an active grid

Using an active grid in a wind tunnel, we generate homogeneous shear turbulence and initiate turbulent boundary layers with adjustable properties. Homogeneous shear turbulence is characterized by a constant gradient of the mean velocity and a constant turbulence intensity. It is the simplest anisotropic turbulent flow thinkable, and it is generated traditionally by equipping a wind tunnel with screens which have a varying transparency and flow straighteners. This is not done easily, and the reachable turbulence levels are modest. We describe a new technique for generating homogeneous shear turbulence using an active grid only. Our active grid consists of a grid of rods with attached vanes which can be rotated by servo motors. We control the grid by prescribing the time-dependent angle of each axis. We tune the vertical transparency profile of the grid by setting appropriate angles of each rod such as to generate a uniform velocity gradient, and set the rods in flapping motion around these angles to tailor the turbulence intensity. The Taylor Reynolds number reached was R _λ = 870, the shear rate S = ∂U/∂y = 9.2 s⁻¹, the nondimensional shear parameter S ^*≡ Sq ²/ε = 12 and u = 1.4 ms⁻¹. As a further application of this idea we demonstrate the generation of a simulated atmospheric boundary layer in a wind tunnel which has tunable properties. This method offers a great advantage over the traditional one, in which vortex-generating structures need to be placed in the wind tunnel to initiate a fat boundary layer.     

MHD flow and heat transfer for the upper-convected Maxwell fluid over a stretching sheet

In the present work, the effect of MHD flow and heat transfer within a boundary layer flow on an upper-convected Maxwell (UCM) fluid over a stretching sheet is examined. The governing boundary layer equations of motion and heat transfer are non-dimensionalized using suitable similarity variables and the resulting transformed, ordinary differential equations are then solved numerically by shooting technique with fourth order Runge–Kutta method. For a UCM fluid, a thinning of the boundary layer and a drop in wall skin friction coefficient is predicted to occur for higher the elastic number. The objective of the present work is to investigate the effect of Maxwell parameter β, magnetic parameter Mn and Prandtl number Pr on the temperature field above the sheet.     

Fluid dynamics analysis of channel flow geometries for materials characterization in microfluidic devices

The fluid dynamics of geometries for liquid state materials characterization in microfluidic devices are investigated. Numerical simulation together with flow classification criteria are used to explore combinations of geometry and boundary conditions for which the flow type can be adjusted between simple shear and extension, while providing adequate flow strength and a stable environment for material observation. Two classes of flow geometries are identified. Both make use of opposing, laterally offset fluid streams that produce a stagnation point in the center of the geometry. In the first class, the flow type is manipulated by changing parameters inherent to the base geometry. This first case serves as a basis for identifying a second class in which the flow type is manipulated by changing the pressure boundary conditions, while keeping the geometry constant.Electronic Supplementary Material is available for this article if you access the article at .

Free-surface fluctuations in hydraulic jumps: Experimental observations

A hydraulic jump is the rapid and sudden transition from a high-velocity supercritical open channel flow to a subcritical flow. It is characterised by the dynamic interactions of the large-scale eddies with the free-surface. New series of experimental measurements were conducted in hydraulic jumps with Froude numbers between 3.1 and 8.5 to investigate these interactions. The dynamic free surface measurements were performed with a non-intrusive technique while the two-phase flow properties were recorded with a phase-detection probe. The shape of the mean free surface profile was well defined and the turbulent fluctuation profiles highlighted a distinct peak of turbulent intensity in the first part of the jump roller, with free-surface fluctuation levels increasing with increasing Froude number. The dominant free-surface fluctuation frequencies were typically between 1 and 4 Hz. A comparison between the acoustic sensor signals and conductivity probe data suggested that the air–water “free-surface” detected by the acoustic sensor corresponded to about the boundary between the turbulent shear layer and the upper free-surface layer. Simultaneous measurements of free surface and bubbly flow fluctuations for Fr = 5.1 indicated that the frequency ranges of both sensors were similar (F < 5 Hz) whatever the position downstream of the toe. The present results highlighted that the dynamic free-surface measurements can be conducted successfully using acoustic displacement meters, and the time-averaged depth measurements was a physical measure of the free-surface location in hydraulic jumps.     

Development of a turbulent boundary layer after a step from smooth to rough surface

The flow developing downstream of a step change from smooth to rough surface condition is studied in the light of Townsend’s wall similarity hypothesis. Previous studies seem to support the hypothesis for channel and pipe flows, but there are considerable controversies about its application to boundary layers and in particular to surface roughness formed by spanwise bars. It has been suggested that this controversy arises from insufficient separation of scales between the boundary layer thickness and the roughness length scale. An experimental investigation has therefore been undertaken where the flow evolves from a fully developed smooth wall boundary layer at high Reynolds numbers over a step in surface roughness (Re _θ = 13,400 at the step). The flow is mapped through the development of the internal layer until the flow is fully developed over the rough wall. The internal layer is found to grow as δ ∼ X ^0.73, and after about 15 boundary layer thicknesses at the step, the internal layer has reached the outer edge of the incoming layer. At the last rough wall measurement station, the Reynolds number has grown to Re _θ ≈ 32,600 and the ratio of boundary layer to roughness length scales is δ/k ≈ 140. The outer layer differences between the smooth and the rough wall data were found to be sufficiently small to conclude that for this setup the Townsend’s wall similarity hypothesis appears to hold.     

The onset of buoyancy-driven convection in a ferromagnetic fluid saturated porous medium

The onset of buoyancy-driven convection in an initially quiescent ferrofluid saturated horizontal porous layer in the presence of a uniform vertical magnetic field is investigated. The Brinkman-Lapwood extended Darcy equation with fluid viscosity different from effective viscosity is used to describe the flow in the porous medium. The lower boundary of the porous layer is assumed to be rigid-paramagnetic, while the upper paramagnetic boundary is considered to be either rigid or stress-free. The thermal conditions include fixed heat flux at the lower boundary, and a general convective–radiative exchange at the upper boundary, which encompasses fixed temperature and fixed heat flux as particular cases. The resulting eigenvalue problem is solved numerically using the Galerkin technique. It is found that increase in the Biot number Bi, porous parameter σ, viscosity ratio Λ, magnetic susceptibility χ, and decrease in the magnetic number M ₁ and non-linearity of magnetization M ₃ is to delay the onset of ferroconvection in a porous medium. Further, increase in M ₁, M ₃, and decrease in χ, Λ, σ and Bi is to decrease the size of convection cells.     

Non-isobaric Marangoni boundary layer flow for Cu,Al<Subscript>2</Subscript>O<Subscript>3</Subscript> and TiO<Subscript>2</Subscript> nanoparticles in a water based fluid

In this paper, a non-isobaric Marangoni boundary layer flow that can be formed along the interface of immiscible nanofluids in surface driven flows due to an imposed temperature gradient, is considered. The solution is determined using a similarity solution for both the momentum and energy equations and assuming developing boundary layer flow along the interface of the immiscible nanofluids. The resulting system of nonlinear ordinary differential equations is solved numerically using the shooting method along with the Runge-Kutta-Fehlberg method. Numerical results are obtained for the interface velocity, the surface temperature gradient as well as the velocity and temperature profiles for some values of the governing parameters, namely the nanoparticle volume fraction φ (0≤φ≤0.2) and the constant exponent β. Three different types of nanoparticles, namely Cu, Al₂O₃ and TiO₂ are considered by using water-based fluid with Prandtl number Pr =6.2. It was found that nanoparticles with low thermal conductivity, TiO₂, have better enhancement on heat transfer compared to Al₂O₃ and Cu. The results also indicate that dual solutions exist when β<0.5. The paper complements also the work by Golia and Viviani (Meccanica 21:200–204, 1986) concerning the dual solutions in the case of adverse pressure gradient.     

Natural Convection Induced by a Centrifugal Force Field in a Horizontal Annular Porous Layer Saturated with a Binary Fluid

The Darcy Model with the Boussinesq approximation is used to study natural convection in a horizontal annular porous layer filled with a binary fluid, under the influence of a centrifugal force field. Neumann boundary conditions for temperature and concentration are applied on the inner and outer boundary of the enclosure. The governing parameters for the problem are the Rayleigh number, Ra, the Lewis number, Le, the buoyancy ratio, j{\varphi } , the radius ratio of the cavity, R, the normalized porosity, e{\varepsilon } , and parameter a defining double-diffusive convection (a = 0) or Soret induced convection (a = 1). For convection in a thin annular layer (R → 1), analytical solutions for the stream function, temperature and concentration fields are obtained using a concentric flow approximation and an integral form of the energy equation. The critical Rayleigh number for the onset of supercritical convection is predicted explicitly by the present model. Also, results are obtained from the analytical model for finite amplitude convection for which the flow and heat and mass transfer are presented in terms of the governing parameters of the problem. Numerical solutions of the full governing equations are obtained for a wide range of the governing parameters. A good agreement is observed between the analytical model and the numerical simulations.     

A simple model for the effect of peak-locking on the accuracy of boundary layer turbulence statistics in digital PIV

A simple model was constructed to study the effect of peak-locking on the accuracy of particle image velocimetry (PIV) turbulence statistics. A crucial parameter is the ratio between the root-mean-square (rms) velocity and the discretization velocity, which reflects the number of peaks distributed over the velocity probability density functions. When the ratio of the discretization velocity, which is set by the PIV setup parameters, to the rms, given by the flow, is larger than two, the maximum errors introduced in the mean and rms values become significant (larger than 1%). The errors introduced also depend on the amplitude, or severity, of the peak-locking, and whether the mean displacement corresponds to an integer or a fractional number of pixels. The peak-locking affects the statistical moments of different order in such a way that the errors are phase shifted. The proposed model can be used to predict errors in the turbulence statistics in a laboratory PIV experiment. According to our model predictions, the most significant influence of peak-locking in a boundary layer type of flow is an overall underestimation of the wall-normal rms. Our predictions are in good agreement with our experimental results from turbulent boundary layers and the recent experimental results from a turbulent channel flow by Christensen (Exp Fluids 36:484–497, 2004) for a case of moderate peak-locking.

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Mixed Convection Boundary Layer Flow from a Horizontal Circular Cylinder Embedded in a Porous Medium Filled with a Nanofluid

Steady mixed convection boundary layer flow from an isothermal horizontal circular cylinder embedded in a porous medium filled with a nanofluid has been studied for both cases of a heated and cooled cylinder. The resulting system of nonlinear partial differential equations is solved numerically using an implicit finite-difference scheme. The solutions for the flow and heat transfer characteristics are evaluated numerically for various values of the governing parameters, namely the nanoparticle volume fraction φ and the mixed convection parameter λ. Three different types of nanoparticles are considered, namely Cu, Al₂O₃ and TiO₂. It is found that for each particular nanoparticle, as the nanoparticle volume fraction φ increases, the magnitude of the skin friction coefficient decreases, and this leads to an increase in the value of the mixed convection parameter λ which first produces no separation. On the other hand, it is also found that of all the three types of nanoparticles considered, for any fixed values of φ and λ, the nanoparticle Cu gives the largest values of the skin friction coefficient followed by TiO₂ and Al₂O₃. Finally, it is worth mentioning that heating the cylinder (λ > 0) delays separation of the boundary layer and if the cylinder is hot enough (large values of λ > 0), then it is suppressed completely. On the other hand, cooling the cylinder (λ < 0) brings the boundary layer separation point nearer to the lower stagnation point and for a sufficiently cold cylinder (large values of λ < 0) there will not be a boundary layer on the cylinder.