Boundary-layer flow of Reiner–Philippoff fluids past a stretching wedge

This paper presents a numerical analysis of the steady boundary-layer flow of a Reiner–Philippoff fluid induced by a 90° stretching wedge in a variable free stream. The governing partial differential equations are converted into a set of two ordinary differential equations by the use of a similarity transformation. The flow is therefore governed by a stretching velocity parameter λ and two non-Newtonian fluid parameters γ and μ₀. The variation of the skin friction, as well as other flow characteristics, as a function of the governing parameters is presented graphically and tabulated. A stability analysis has also been performed for this self-similar flow based on linear disturbances to the steady similarity solutions. The results presented in this paper reveal that there are no multiple (dual) solutions for the present problem and the unique solution is stable.     

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.     

A mesoscopic modelling approach for direct numerical simulations of transition to turbulence in hypersonic flow with transpiration cooling

A rescaling methodology is developed for high-fidelity, cost-efficient direct numerical simulations (DNS) of flow through porous media, modelled at mesoscopic scale, in a hypersonic freestream. The simulations consider a Mach 5 hypersonic flow over a flat plate with coolant injection from a porous layer with 42 % porosity. The porous layer is designed using a configuration studied in the literature, consisting of a staggered arrangement of cylinder/sphere elements. A characteristic Reynolds number ${\mathit{Re}}_c$ of the flow in a pore cell unit is first used to impose aerodynamic similarity between different porous layers with the same porosity, $∊$, but different pore size. A relation between the pressure drop and the Reynolds number is derived to allow a controlled rescaling of the pore size from the realistic micrometre scales to higher and more affordable scales. Results of simulations carried out for higher cylinder diameters, namely 24 μm, 48 μm and 96 μm, demonstrate that an equivalent Darcy-Forchheimer behaviour to the reference experimental microstructure is obtained at the different pore sizes. The approach of a porous layer with staggered spheres is applied to a 3D domain case of porous injection in the Darcy limit over a flat plate, to study the transition mechanism and the associated cooling performance, in comparison with a reference case of slot injection. Results of the direct numerical simulations show that porous injection in an unstable boundary layer leads to a more rapid transition process, compared to slot injection. On the other hand, the mixing of coolant within the boundary layer is enhanced in the porous injection case, both in the immediate outer region of the porous layer and in the turbulent region. This has the beneficial effect of increasing the cooling performance by reducing the temperature near the wall, which provides a higher cooling effectiveness, compared to the slot injection case, even with an earlier transition to turbulence.     

An improved implicit finite-difference scheme for boundary-layer flows

The paper presents a modification to two well-known non-iterative implicit finite-difference schemes for confined and unconfined boundary-layer-type flows. The modification aims at improving the accuracy of these schemes by reducing the adverse effect of linearization, which is inherent in both of them. Using the present improved scheme, the same level of accuracy of the results could be obtained with large mesh sizes in the flow direction (coarse grid). The modification is done by adding a local iterative procedure at each computational step in the flow (marching) direction. As an example, to demonstrate the proposed modification, the simple case of developing forced convection in the entry region of concentric annuli has been considered. The results are presented, which prove the applicability of the proposed modification and show its effect on the obtained accuracy and on the required computer time.     

Convective inertia effects in wall-bounded thin film flows

We apply the boundary layer equations to inertial flow in wall bounded films that might be characterized as ‘thin’, say ɛ ≤ 0.1 where ɛ is the ratio of the characteristic lengths, yet to which the lubrication approximation of Reynolds no longer applies. Two particular flow geometries are investigated, nominally parallel plates and nominally inclined plates, both with and without spatially periodic perturbation of the stationary plate. A Galerkin-B spline formulation of the governing equations is employed, and we rely on parametric continuation to obtain solutions at higher values of the Reynolds number. In particular, we are able to demonstrate that the boundary layer equations yield accurate results for a wide range of Reynolds numbers when the aspect ratio is less than 1/10. We also find that in both nominally parallel and nominally inclined geometries the sign of the inertial force correction is determined by the film contour in the neighborhood of the exit, this result might have implications in the design of MEMS devices.     

MHD boundary layer equations for power-law fluids with variable electric conductivity

The boundary layer in a power-law fluid flowing in the presence of a transverse variable magnetic field is investigated. Assuming the electric conductivity of the fluid is dependent on its velocity, Meksyn's method is used to get an analytical solution for the velocity field and the coefficient of friction. The effect of the magnetic field is then discussed.

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Sommario Lo scopo di questo lavoro è di studiare lo strato limite laminare con relazione costitutiva a legge di potenza bidimensionale di un fluido non-newttoniano incompressibile elettroconduttore che scorre lungo una parete piana in presenza di un campo magnetico trasversale e di una pressione esterna. La conducibilità elettrica del fluido viene assunta come funzione della velocità nella forma =₀ u, dove ₀ è costante eu è la velocità del flusso parallela alla parete. L'equazione base è stata risolta applicando il metodo di Meksyn per ottenere una soluzione analitica per la velocità ed il coefficiente di attrito. Viene inoltre discusso l'effetto del campo magnetico e la variazione della conducibilità elettrica.

     

Experiments on localized disturbances in a flat plate boundary layer. Part 1. The receptivity and evolution of a localized free stream disturbance

The receptivity of a laminar boundary layer to free stream disturbances has been experimentally investigated through the introduction of deterministic localized disturbances upstream of a flat plate mounted in a wind tunnel. Hot-wire measurements indicate that the spanwise gradient of the normal velocity component (and hence the streamwise vorticity) plays an essential role in the transfer of disturbance energy into the boundary layer. Inside the laminar boundary layer the disturbances were found to give rise to the formation of longitudinal structures of alternating high and low streamwise velocity. Similar streaky structures exist in laminar boundary layers exposed to free stream turbulence, in which the disturbance amplitude increases in linear proportion to the displacement thickness. In the present study the perturbation amplitude of the streaks was always decaying for the initial amplitudes used, in contrast to the growing fluctuations that are observed in the presence of free stream turbulence. This points out the importance of the continuous influence from the free stream turbulence along the boundary layer edge.     

Comment on “Analysing flow and heat transfer of a viscoelastic fluid over a semi-infinite horizontal moving flat plate, IJNLM, 43 (2008) 772”

In this report we make corrections to a paper by Rafael Cortell (IJNLM, 43 (2008) 772). In this paper (IJNLM, 43 (2008) 772) the author considered an incorrect equation (by including a wrong term instead of correct term) for his considered flow and heat transfer problem and reported unrealistic results as a consequence. In this communication we have considered the correct equation (replacing the incorrect term by correct one) and solved it analytically. Our analysis shows that the unrealistic behavior as observed by Cortell (IJNLM, 43 (2008) 772) persists no more if one considers the correct term.     

Moving wedge and flat plate in a power-law fluid

The steady boundary-layer flow of a non-Newtonian fluid, represented by a power-law model, over a moving wedge in a moving fluid is studied in this paper. The transformed boundary-layer equation is solved numerically for some values of the involved parameters. The effects of these parameters on the skin friction coefficient are analyzed and discussed. It is found that multiple solutions exist when the wedge and the fluid move in the opposite directions, near the region of separation. It is also found that the drag force is reduced for dilatant fluids compared to pseudo-plastic fluids.