Rotationally symmetric flow of Reiner-Rivlin fluid over a heated porous wall using numerical approach

This research features one parameter family of solutions representing rotationally symmetric flow of non-Newtonian fluid obeying Reiner-Rivlin model. Such flows take place over a revolving plane permeable surface through origin such that fluid at infinity also undergoes uniform rotation about the vertical axis. Heat transfer accompanied with viscous heating effect is also analyzed. A similarity solution is proposed that results into a coupled non-linear system with four unknowns. Boundary layer structure is characterized by a parameter [Formula: see text] that compares angular velocity of external flow with that of the rotating surface. Solutions are developed by a well-known package bvp4c of MATLAB for full range of [Formula: see text]. Flow pattern for different choices of [Formula: see text] is scrutinized by computing both 2 D and 3 D streamlines. It is further noted that value of suction velocity is important with regards to the sign of axial velocity component. Boundary layer suppresses considerably whenever the surface is permeable. For sufficiently high suction velocity with [Formula: see text], entire fluid undergoes rigid body rotation. In no suction case, axially upward flow accelerates for increasing values of parameter [Formula: see text] in the range [Formula: see text], whereas opposite trend is apparent in the case [Formula: see text]. Results for normalized wall shear and Nusselt number are scrutinized for various choices of embedded parameters.

Numerical Investigation of MHD Pulsatile Flow of Micropolar Fluid in a Channel with Symmetrically Constricted Walls

This article presented an analysis of the pulsatile flow of non-Newtonian micropolar (MP) fluid under Lorentz force’s effect in a channel with symmetrical constrictions on the walls. The governing equations were first converted into the vorticity–stream function form, and a finite difference-based solver was used to solve it numerically on a Cartesian grid. The impacts of different flow controlling parameters, including the Hartman number, Strouhal number, Reynolds number, and MP parameter on the flow profiles, were studied. The wall shear stress (WSS), axial, and micro-rotation velocity profiles were depicted visually. The streamlines and vorticity patterns of the flow were also sketched. It is evident from the numerical results that the flow separation region near constriction as well as flattening of the axial velocity component is effectively controlled by the Hartmann number. At the maximum flow rate, the WSS attained its peak. The WSS increased in both the Hartmann number and Reynolds number, whereas it declined with the higher values of the MP parameter. The micro-rotation velocity increased in the Reynolds number, and it declined with increment in the MP parameter.

Large Eddy Simulations for Film Cooling Assessment of Cylindrical and Laidback Fan-Shaped Holes With Reverse Injection

The large eddy simulations (LES) are performed to access the film cooling performance of cylindrical and reverse shaped hole for forward and reverse injection configurations. In the case of reverse/backward injection, the secondary flow is injected in such a way that its axial velocity component is in the direction opposite to mainstream flow. The study is carried out for a blowing ratio (M = 1), density ratio (DR = 2.42), and injection angle (α = 35 deg). Formation of counter-rotating vortex pair (CRVP) is one of the major issues in the film cooling. This study revealed that the CRVP found in the case of forward cylindrical hole which promotes coolant jet “liftoff” is completely mitigated in the case of the reverse shaped hole. The coolant coverage for reverse cylindrical and reverse shaped holes is uniform and higher. The reverse shaped hole shows promising results among investigated configurations. The lateral averaged film cooling effectiveness of reverse shaped hole is 1.16–1.42 times higher as compared to the forward shaped holes. The improvement in the lateral averaged film cooling effectiveness of reverse cylindrical hole (RCH) injection over forward cylindrical hole (FCH) injection is 1.33–2 times.

Experimental validation of a ducted wind turbine design strategy

A synergistic design strategy for ducted horizontal axis wind turbines (DWTs), utilizing the numerical solution of a ducted actuator disk system as the input condition for a modified blade element momentum method, is presented. Computational results of the ducted disk have shown that the incoming flow field for a DWT differs substantially from that of a conventional open rotor. The rotor plane velocity is increased in the ducted flow field, and, more importantly, the axial velocity component varies radially. An experimental full-scale 2.5 m rotor and duct were designed, using this numerical strategy, and tested at the University of Waterloo's wind turbine test facility. Experimental results indicated a very good correlation of the data with the numerical predictions, namely a doubling of the power output at a given velocity, suggesting that the numerical strategy can provide a means for a scalable design methodology.

Experimental Validation of a Ducted Wind Turbine Design Strategy

A synergistic design strategy for ducted horizontal axis wind turbines (DWTs), utilizing the numerical solution of a ducted actuator disk system as input conditions for a modified blade element momentum method, is presented. Computational results of the ducted disk have shown that the flow field for a DWT differs substantially from that of a conventional open rotor. The rotor plane velocity is higher in the ducted flow field, and more importantly, the axial velocity component varies radially. An experimental full scale 2.5 m rotor and duct were designed, using this strategy, and tested at the University of Waterloo’s wind turbine test facility. Experimental results indicated a very good correlation of the data with the numerical predictions, that being a doubling of the power output at a given velocity.

Nested First-Passages of Tracer Particles in Flows of Blood and Control Suspensions: Symmetry and Lorentzian Transformations

Theory of molecular Taylor-Aris dispersion (TAD) is an accepted framework describing tracer dispersion in suspension flows and determining effective diffusion coefficients. Our group reported a pseudo-Lagrangian method to study dispersion in suspension flows at FEDSM-2000. Tracer motions were studied in a steadily moving inertial reference frame (SMIRF) aligned with the flow direction; increments of change of axial position of individual tracers were collected to demonstrate how the tracer moved as they, individually, interacted with similar collections of other bodies brought to and from the region. First, individual tracers with no apparent axial velocity component (NAAVC) were identified; they exhibited fixed positions in video recordings of images collected in the SMIRF. Then, time increments were measured for tracers to pass at least 5, but usually 10 pre-selected, nested distances in the up- or downstream direction laid out with respect to the zero-site in the SMIRF. Such data were richer than measurements of tracer spread over time because stations along each path were serial first-passages (FP) with probabilistic meaning. Dispersion of various types of suspension and two transformation rules for combining velocity components are discussed herein. Traditional low-speed continuum theory and particle dynamics use Galilean transforms. Yet, to recognize the limited speed in laws for channel flows, Lorentzian transformations may be appropriate. In a four-space, deterministic paths would begin at NAAVC sites and continue in time-like conical regions of four-space. Distances in this space are measured using Minkowski’s metric; at the NAAVC site and on the boundary of the space-time cone, this metric has the format of the Fürth, Ornstein, and Taylor (FOT) equation when only terms to order t2 are used. Data shown at FEDSM-2000 can be reinterpreted as “prospective paths” in time-like regions that were consolidated in normalized cumulative probability distributions to provide retrospective descriptions. The ad hoc sign alteration of the FOT equation to fit the data of FEDSM-2000 is now taken as a part of measuring lengths using a Minkowski metric, which signifies a hyperbolic geometry, for which an inherent scaling constant is a negative curvature. The space also has an intrinsic distance of ℓ = Sτ, obtained from fitting parameters (S, τ) for the FOT equation. Integrals of the area under the FOT curve have units of volume, which are considered as describing an average volume of dispersion on S3, the 3-sphere. Path motion through this volume was kinematic dispersion, S2τ, which was the form for effective diffusivity in continuum theory used in FEDSM-2000. Weiner and Wilmer describe transformations in four-spaces in terms of commutating rotations on orthogonal planes, a concept readily linked to symmetries in the hyperbolic space typical of Lorentzian transformations; they also describe a second order ODE like the FOT equation.

ADOMIAN DECOMPOSITION METHOD FOR MAGNETOHYDRODYNAMIC FLOW OF BLOOD INDUCED BY PERISTALTIC WAVES

The present investigation deals with the application of Adomian decomposition method (ADM) to blood flow through an asymmetric non-uniform channel induced by peristaltic wave in the presence of magnetic field and the velocity slip at the wall. The ADM is applied with an aim to avoid any simplifications and restrictions, which changes non-linearity of the problem as well as to provide analytical solution. The blood flowing through the vessel is assumed to be Newtonian and incompressible with constant viscosity. The analytical expressions for the axial velocity component, streamlines and wall shear stress are presented. The numerical results of these physical quantities are obtained for different values of the Reynolds number, wave number and Hartmann number. The results obtained for different values of the parameters involved in the problem under consideration show that the flow is appreciably influenced by the presence of slip velocity as well as magnetic field. From this study, we conclude that the assumption of long wavelength and low Reynolds number overestimates the flow characteristics even for a small change in the parameters.

Elliptical instability of the Moore–Saffman model for a trailing wingtip vortex

In this paper, we investigate the elliptical instability exhibited by two counter-rotating trailing vortices. This type of instability can be viewed as a resonance between two normal modes of a vortex and an external strain field. Recent numerical investigations have extended earlier results that ignored axial flow to include models with a simple wake-like axial flow such as the similarity solution found by Batchelor (J. Fluid Mech., vol. 20, 1964, pp. 645–658). We present herein growth rates of elliptical instability for a family of velocity profiles found by Moore & Saffman (Proc. R. Soc. Lond. A, vol. 333, 1973, pp. 491–508). These profiles have a parameter $n$ that depends on the wing loading. As a result, unlike the Batchelor vortex, they are capable of modelling both the jet-like and the wake-like axial flow present in a trailing vortex at short and intermediate distances behind a wingtip. Direct numerical simulations of the linearized Navier–Stokes equations are performed using an efficient spectral method in cylindrical coordinates developed by Matsushima & Marcus (J. Comput. Phys., vol. 53, 1997, pp. 321–345). We compare our results with those for the Batchelor vortex, whose velocity profiles are closely approximated as the wing loading parameter $n$ approaches 1. An important conclusion of our investigation is that the stability characteristics vary considerably with $n$ and $W_{0}$, a parameter measuring the strength of the mean axial velocity component. In the case of an elliptically loaded wing ($n=0.50$), we find that the instability growth rates are up to 50 % greater than those for the Batchelor vortex. Our results demonstrate the significant effect of the distribution and intensity of the axial flow on the elliptical instability of a trailing vortex.

The Effects of Entrainment on Pore Shape in Keyhole Mode Welding

This study theoretically investigates the effects of the entrainment accompanying mass, momentum, and energy transport on pore size during high power density laser and electron beam welding processes. The physics of macroporosity formation is not well understood, even though macroporosity often occurs and limits the widespread industrial application of keyhole mode welding. This work is an extension of a previous work dealing with collapses of keyholes induced by high intensity beam drilling. In order to determine the pore shape, this study, however, introduces the equations of state at the times when the keyhole is about to be enclosed and when the temperature drops to melting temperature. The gas pressure required at the time when keyhole collapses is determined by calculating the compressible flow of the two-phase, vapor–liquid dispersion in a vertical keyhole with varying cross sections, paying particular attention to the transition between annular and slug flows. It is found that the pore size increases as entrainment fluxes decrease in the lower and upper regions of the keyhole containing a supersonic mixture. The pore size also increases with decreasing total energy of entrainment and an increasing axial velocity component ratio between entrainment and mixture through the core region. With a subsonic mixture in the keyhole, the final pore size increases with entrainment fluxes in the lower and upper regions. This work provides an exploratory and systematical investigation of pore size induced by entrainment accompanied by mass, momentum, and energy transport during keyhole mode welding.

PIV Investigation of Couette-Taylor Flows With Axial Flows

The Couette Taylor flows CTF strongly depend on geometrical characteristics of CT systems radio and aspect ratios. The superposition of axial flow may accentuate this dependence. Previous studies carried with relatively small radial and/or aspect ratios [1–3] or relatively low Taylor numbers (or rotational Reynolds number ReΩ) and/or low axial flux rates (exp. [4]: ReΩ < 50 and Reax < 400; [1] : Reax < 4), or limited to analytical approaches or numerical simulations adopting simplified hypothesis and assumptions. In order to complete information obtained for vortices characterization for relatively “high” Taylor numbers (303 ≤Ta≤ 1212) and relatively “high” axial Reynolds numbers (Reax ≤107), for relatively “big” CTS with a radial ratio η = Rint/Rout = 0.855 and an aspect ratio Γ= H/d = 31.03 (where H is the CTS height and d = (Rout – Rint) is the gap thickness), we realized a quantitative experimental study using standard and speed Velocimetry per Image of Particles (PIV) technique. The vortex structures for CTF with and without an “ascending” axial flow, according to the “direct protocol” i.e. The axial flow is superposed to an initial fully developed rotational flow were studied [5]. The vortex direction strongly depends on protocol history. The cartographies of velocity components are illustrated. The results mainly concern axial and radial velocity components. The cartographies of the vorticity ω, and the detection criteria Q and Γ2 are presented and discussed. The alternating between positive and negative values of axial velocity component characterizes the presence of contrarotating vortices. This allows determining the axial wavelengths (λ) for WTVF and MWTVF with and without axial flows. A same axial flow can have a stabilizing effect for a regime flow and a destabilizing effect for another. It enhanced the overlapping, the stretching, the folding or the breaking of vortices. From WTVF to MWTVF to TN, we illustrated that the vortices mixing is enhanced when the Taylor number increases due to vortices stretching and folding.