In this study, the sources of uncertainty of hot-wire anemometry (HWA) and oil-film interferometry (OFI) measurements are assessed. Both statistical and classical methods are used for the forward and inverse problems, so that the contributions to the overall uncertainty of the measured quantities can be evaluated. The correlations between the parameters are taken into account through the Bayesian inference with error-in-variable (EiV) model. In the forward problem, very small differences were found when using Monte Carlo (MC), Polynomial Chaos Expansion (PCE) and linear perturbation methods. In flow velocity measurements with HWA, the results indicate that the estimated uncertainty is lower when the correlations among parameters are considered, than when they are not taken into account. Moreover, global sensitivity analyses with Sobol indices showed that the HWA measurements are most sensitive to the wire voltage, and in the case of OFI the most sensitive factor is the calculation of fringe velocity. The relative errors in wall-shear stress, friction velocity and viscous length are , and , respectively. Note that these values are lower than the ones reported in other wall-bounded turbulence studies. Note that in most studies of wall-bounded turbulence the correlations among parameters are not considered, and the uncertainties from the various parameters are directly added when determining the overall uncertainty of the measured quantity. In the present analysis we account for these correlations, which may lead to a lower overall uncertainty estimate due to error cancellation Furthermore, our results also indicate that the crucial aspect when obtaining accurate inner-scaled velocity measurements is the wind-tunnel flow quality, which is more critical than the accuracy in wall-shear stress measurements.
In the current letter we present a numerical study to review the impacts of homogeneous–heterogeneous reactions on the stagnation point flow of Carreau fluid. In addition, an investigation is considered for the flow impelled by a shrinking sheet along with uniform suction on the wall. We explored the prototype model of homogeneous–heterogeneous reactions in which the diffusion coefficients of reactant and catalyst are identical. With the aid of non-dimensional variables, we get a non-linear system of differential equations which is integrated numerically using MATLAB builtin routine bvp4c. The flow and concentration are exceptionally impacted by the pertinent parameters, like, the Weissenberg number, shrinking parameter, mass transfer parameter, homogeneous/heterogeneous reactions parameter and Schmidt number. Likewise, we inspected that dual solutions for the velocity and concentration fields exist in the case of a shrinking sheet and for a fixed range of other parameters. Our review indicates that the momentum boundary layer thickness rises significantly with an increase in the shrinking parameter for the second solution. Besides, the strength of homogeneous reaction is extremely useful to reduce the concentration of reaction. Under some special assumptions, the consequences of the present study demonstrate a splendid relationship with prior works.
The classical Neumann–Kelvin (NK) linear potential flow theory of ship waves in calm water and the related Neumann–Michell (NM) theory are considered. Five alternative boundary integral representations are given: (1) the classical NK integro-differential representation, called “classical NK formulation”, which corresponds to an inconsistent linear flow model, (2) a modification of the classical NK flow formulation that corresponds to a consistent linear flow model and is called “consistent NK formulation”, (3) a flow representation, called “NM potential and velocity formulation”, that involves the flow potential and the velocity components and along two unit vectors and tangent to the ship hull surface, and yields an integro-differential equation for determining (4) a flow representation, called “NM velocity formulation”, that only involves and and yields a pair of coupled integral equations for determining and (5) a flow representation called “NM potential formulation” that only involves the flow potential and yields an integral equation for determining The two NK formulations involve both a surface integral over the ship hull surface and a line integral around the ship waterline, whereas the three NM formulations do not involve a waterline integral. All flow representations other than the classical NK representation are based on a consistent linear flow model.
Electrokinetic peristaltic multi-layered transport is considered in a micro-channel under the action of an axial electrical field. Three different layers i.e. the are simulated with three different viscosities for each fluid layer. The unsteady two-dimensional conservation equations for mass and momentum with electrokinetic body forces, are transformed from the wave frame to the laboratory frame and the electrical field terms are rendered into electrical potential terms via the Poisson–Boltzmann equation, Debye length approximation and ionic Nernst–Planck equation. The dimensionless emerging linearized electrokinetic boundary value problem is solved using integral methods. Closed-form expressions are derived for stream functions in the core, intermediate and peripheral layers. Expressions are also derived for the core–intermediate interface shape and the intermediate–peripheral interface shape. Maximum pressures are also computed. To study bolus migration, the range of the trapping limit is also determined in the peripheral layer. It is found that in the core layer larger boluses are computed in the case of lower intermediate layer viscosity relative to peripheral layer viscosity although the number of boluses is greater when the intermediate layer viscosity exceeds the peripheral layer viscosity. Furthermore, in the intermediate layer, stronger concentration of streamlines is computed in the lower half space with positive Helmholtz–Smoluchowski velocity. Also negative Helmholtz–Smoluchowski velocity reduces the core layer (H ) interface shape whereas it enhances the peripheral layer (H) and intermediate layer (H ) shapes. At lower values of volume flow rate ratio, hydromechanical efficiency is positive Helmholtz–Smoluchowski velocity whether intermediate layer viscosity is less or greater than peripheral layer viscosity. Finally, greater with greater peristaltic wave amplitude and also for positive Helmholtz–Smoluchowski velocity there is an increase in time-averaged flow rate, whether intermediate layer viscosity is less or greater than peripheral layer viscosity. The analysis is relevant to electro-kinetic hemodynamics and bio-micro-fluidics.
In this paper, double-diffusive natural convection, studying Soret and Dufour effects and viscous dissipation in an open cavity filled with Bingham fluid has been simulated by Finite Difference Lattice Boltzmann Method (FDLBM). In addition, entropy generations through fluid friction, heat transfer, and mass transfer has been studied. The problem has been solved by applying the regularized Papanastasiou model. However, the Bingham model without regularizations for some cases have been studied to demonstrate the accuracy of the applied regularization. This study has been conducted for certain pertinent parameters of Rayleigh number ( , and ), Bingham number ( ), Lewis number ( , 5 and 10), Dufour parameter ( =0, 1, and 5), Soret parameter ( =0, 1, and 5), Eckert number ( , 0.001, and 0.01), and the Buoyancy ratio ( , 0.1, 1). Results indicate that the increase in Rayleigh number enhances heat and mass transfer for various Bingham numbers. The rise of Bingham number reduces heat and mass transfer. In addition, the increase in Bingham number enlarges the unyielded zones. The increase in the Lewis number augments mass transfer in different Rayleigh and Bingham numbers, although the enhancement of Lewis number causes heat transfer to drop marginally. The rise of Dufour parameter increases heat transfer gradually. The increase in Soret parameter enhances mass transfer for different Bingham and Rayleigh numbers. The addition of Soret parameter, Dufour parameter and Lewis number do not affect the unyielded zone considerably. The augmentation of the buoyancy ratio number enhances heat and mass transfer at and . The rise of buoyancy ratio number alters the unyielded section significantly. The increase in Eckert number influences heat and mass transfer marginally. The augmentation of Rayleigh number enhances different entropy generations and reduces the average Bejan number. The increase in the Bingham number provokes various irreversibilities to drop significantly. The rise of Soret and Dufour parameters enhances the entropy generations due to heat transfer and fluid friction. The rise of Eckert number alters various entropy generations, but the alteration does not follow a specific manner in different studied parameters.
In this paper, asymptotic analysis of the chemical reaction and the Newtonian heating parameters is carried out. A mathematical model of a convective micropolar fluid flow over a permeable stretching/shrinking sheet is taken into account in the presence of the slip flow regime. A nonlinear system of transformed equations is solved by a semi-analytical technique called Homotopy Analysis Method (HAM). The current investigation is in a good agreement with the already published analytical and the numerical results with the help of tabular and graphical representations. In comparison with the stretching sheet, it is observed that the shrinking sheet produces a wider concentration boundary layer thickness by a small change in the chemical reaction parameter. In contrast to the stretching sheet, the Newtonian heating parameter raises the thermal boundary layer thickness by for the shrinking sheet. The chemical reaction with the Newtonian heating effect is an important consideration in the solidification process of the liquid crystals and the polymeric suspensions.
Mixed convection combined with entropy generation of an alumina–water nanofluid in a lid-driven cavity with a bottom solid wall of finite thickness and conductivity has been examined numerically. Governing equations formulated in dimensionless stream function and vorticity variables on the basis of a single-phase nanofluid model under the effect of Brownian diffusion have been solved by finite difference method of the second-order accuracy. The effects of Richardson number ( 0.01–10.0), thermal conductivity ratio (1.0 20.0), solid wall thickness (0.1 0.3) and nanoparticles volume fraction (0 0.05) on streamlines, isotherms and isentropic lines as well as average Nusselt number at solid–fluid interface and rate of fluid flow have been analyzed. It has been found that an increase in nanoparticles volume fraction leads to the heat transfer enhancement and reduction of the average Bejan number.
In this article the Homann stagnation-point flow of a micropolar fluid over a spiraling disk is considered. A spiraling motion is produced due to uniform rotation and linear radial stretching of the disk. The coupled ordinary differential equations are obtained through the similarity reduction of the governing flow equations of micropolar fluid. A numerical technique known as the shooting method is implemented for obtaining the numerical results. Important features of the flow are investigated for various values of the spiral angle, spiraling parameter and material parameters.
The present paper considers the flow of micropolar fluid through a membrane modeled as a swarm of solid cylindrical particles with porous layer using the cell model technique. Traditional boundary conditions on hypothetical cell surface were added with an additional condition: the no spin condition / no couple stress condition. Expressions for velocity and microrotation vector components have been obtained analytically. Effect of various parameters such as particle volume fraction, permeability parameter, micropolarity number etc. on hydrodynamic permeability of membrane has been discussed.
Vortex shedding by a swimming sphere in a viscous incompressible fluid is studied for surface modulation characterized by a superposition of dipolar and quadrupolar, as well as for quadrupolar and octupolar displacements, varying harmonically in time. The time-dependent swimming velocity and the flow velocity are calculated to second order in the amplitude of surface modulation for both models. The models are also useful for the discussion of bird flight.
This paper is aimed at assessing the ability of the Lattice-Boltzmann Method (LBM) in reproducing the fundamental features of lock-exchange gravity currents. Both two- and three-dimensional numerical simulations are presented at different Reynolds numbers ( ). Turbulence has been accounted for by implementing an equivalent Large Eddy Simulation (LES) model in the LBM framework. The advancement of the front position and the front velocity obtained by LBM numerical simulations are compared with laboratory experiments appositely performed with similar initial and boundary conditions and with previous results from literature, revealing that the dynamics of the gravity current as a whole is correctly reproduced. Lobes and clefts instabilities arising in three-dimensional simulations and the entrainment parameter are also analysed and comparisons with previous studies are presented.
Similarity solutions are found for radiative heat transfer in Bödewadt slip flow past rough disk subjected to wall suction. The idea of non-linear thermal radiation for the Bödewadt boundary layer is just introduced here. An early study determined that a physically plausible solution of the energy equation fails to exist as long as the surface is impermeable. By using von-Kármán transformations, the relevant equations are changed into locally similar forms and then numerical solutions are constructed for broad range of embedded parameters. Our calculations show remarkable effects of fluid suction and slip coefficients on the solution profiles. Stability of the solutions is checked by computing lowest eigenvalues of the governing boundary value problem. Fluid temperature is highly sensitive to a parameter measuring the importance of wall temperature relative to ambient temperature. Interesting implications of this parameter on the underlying flow physics are clarified. Analysis of entropy generation for the Bödewadt’s boundary layer is carried out in the existence of new physical mechanism, namely non-linear radiation in this research. The paper also aims to deduce the behaviors of slip coefficients and temperature ratio parameter on the heat transfer rate, which has definite role in many heat transfer applications.
This paper investigates the effects of slip condition on an unsteady magnetohydrodynamic (MHD) flow of a viscous incompressible electrically conducting fluid past a periodically accelerated horizontal porous plate under the influence of transverse magnetic field and Hall current. A uniform magnetic field is applied transverse to the direction of the flow. The flow is generated due to the accelerated motion of the porous plate. A unified closed form analytical solution of governing equations has been obtained by employing the Laplace transform technique. The influences of the pertinent parameters on the velocity field and shear stress are displayed through graphs. The numerical results reveal that an increase in Hall parameter leads to an increase in momentum boundary layer thickness.
Short-wave approximations are obtained within the framework of the Neumann–Michell (NM) linear theory of potential flow around a ship that travels at a constant speed in calm water. Specifically, the integral over the ship hull surface – that determines ship waves within the Fourier–Kochin representation related to the NM theory – is approximated as a line integral around the ship waterline via Laplace’s method. This waterline-integral approximation is further approximated via Kelvin’s method of stationary phase. The short-wave asymptotic approximations obtained via successive applications of Laplace’s method and Kelvin’s method of stationary phase provide theoretical insight into short (transverse and divergent) waves created by ships that travel at low Froude numbers, and short divergent waves created by ships traveling at moderate or high Froude numbers. In particular, these analytical approximations show that short ship waves are related to the Froude number and the hull form in a fairly complicated manner.
Swimming of a sphere in a viscous incompressible fluid is studied on the basis of the Navier–Stokes equations for wave-type distortions of the spherical shape. At sizable values of the dimensionless scale number the mean swimming velocity is the result of a delicate balance between the net time-averaged flow generated directly by the surface distortions and the flow generated by the mean Reynolds force density. Depending on the stroke, this can lead to a surprising dependence of the mean swimming velocity on the kinematic viscosity of the fluid. The net flow pattern is calculated as a function of kinematic viscosity for axisymmetric strokes of the swimming sphere. The calculation covers the full range of scale number, from the friction-dominated Stokes regime in the limit of vanishing scale number to the inertia-dominated regime at large scale number. The model therefore provides paradigmatic insight into the fluid dynamics of swimming or flying of a wide range of organisms.
The Neumann–Michell (NM) theory – a practical linear potential flow theory – is applied to four freely-floating ship models (Wigley, S60, DTMB5415, KCS), assumed to advance at a constant speed in calm water of large depth, to investigate nonlinear effects on the wave drag, the sinkage, the trim, and the wave profile along the hull, and to approximately account for these effects via simple corrections of the linear theory. Nonlinear effects are found to be relatively small. However, an important exception to this general finding is that the wave drag of a bulbous ship (DTMB5415, KCS) is greatly reduced due to the nonlinear component of the pressure in the Bernoulli relation. This important nonlinear effect is readily included in the NM theory. The nonlinear component of the pressure in the Bernoulli relation also yields a small increase of the sinkage, likewise readily included in the NM theory. Moreover, free-surface nonlinearities can have appreciable, although not large, effects on the wave profile. These nonlinear effects can also be approximately taken into account via a simple transformation of the linear wave profile. Indeed, the flow computations for the four ship models considered here suggest that simple (post-processing) nonlinear corrections (that require no additional flow computations) of the NM theory yield numerical predictions of the wave drag, the sinkage, the trim and the wave profile that agree well with experimental measurements, and compare favorably with predictions given by more complex computational methods.
We study turbulent channel flows of monodisperse and polydisperse suspensions of finite-size spheres by means of Direct Numerical Simulations using an immersed boundary method to account for the dispersed phase. Suspensions with 3 different Gaussian distributions of particle radii are considered (i.e. 3 different standard deviations). The distributions are centered on the reference particle radius of the monodisperse suspension. In the most extreme case, the radius of the largest particles is 4 times that of the smaller particles. We consider two different solid volume fractions, and . We find that for all polydisperse cases, both fluid and particles statistics are not substantially altered with respect to those of the monodisperse case. Mean streamwise fluid and particle velocity profiles are almost perfectly overlapping. Slightly larger differences are found for particle velocity fluctuations. These increase close to the wall and decrease towards the centerline as the standard deviation of the distribution is increased. Hence, the behavior of the suspension is mostly governed by excluded volume effects regardless of particle size distribution (at least for the radii here studied). Due to turbulent mixing, particles are uniformly distributed across the channel. However, smaller particles can penetrate more into the viscous and buffer layer and velocity fluctuations are therein altered. Non trivial results are presented for particle-pair statistics.
An effective-medium approach, based on the Brinkman equation is used to study the axisymmetric quasi-steady motion of two spherical particles embedded in a porous medium. The particles are in general of different sizes and translating with different velocities along the line connecting their centers, and allowing for the hydrodynamic slip at their surfaces. Under the Stokes flow approximation, a general solution is constructed using superposition of the basic solutions in two moving spherical coordinate systems based on the centers of the particles. A collocation technique is used to satisfy the boundary conditions on the surfaces of the particles. Numerical results for the normalized drag force acting on each particle are obtained with rapid convergence for various values of slip coefficients, size ratio, separation parameter, velocity ratio of the particles, and permeability parameter. The normalized drag force on each particle reach the single particle limit as the distance between centers grows large enough and each particle then may be translated independent of each other. The accuracy of the numerical technique has been tested against known solutions for two spheres with no-slip surfaces and when the porous medium becomes a clear fluid.
Three-dimensional turbulent flow over a circular cylinder performing sinusoidal rotational motions around its axis is investigated using Large Eddy Simulation (LES). The simulation is carried out for Reynolds number equal to 3900 with rotation rate ( * , where is oscillation amplitude, cylinder radius, and flow velocity) varying from 0.5 to 2; and with non-dimensional forcing frequencies (ratio of the frequency of the cylinder oscillation and that of the vortex-shedding from a stationary cylinder) from 0 to 8. Time-averaged flow parameters as well as mean drag and lift coefficients, mean base pressure coefficient, and separation angle and mean length of the vortex formation region are obtained and thoroughly analyzed. It was found that under forcing control, 50% of drag reduction was achieved and the flow three-dimensionality was reduced in the lock-on range.
Heat transfer characteristics of the traditional wall jet flows subject to various thermal boundary conditions including isothermal surface, prescribed temperature, constant heat flux, prescribed heat flux, adiabatic surface and thermally convective surface are documented in analytic closed forms. Heat dissipation has been also included where the similarity energy equation could structurally adjust to this specific term (for the adiabatic case, this term has been necessarily included). In all the studied cases, both the transpiration velocity and moving wall conditions are allowed to exist (where applicable) in such a way, being consistent with the Glauert integral constraint and subject to the context of exponentially decaying wall jet flows. In particular, it is analytically proved (even without having the closed form solutions) that for the Glauert original case, a surface with a prescribed temperature in the form of serves zero contribution to heat transfer at the wall (the Induced Heat Shield). More precisely, the value as the prescribing parameter is the Surface Heat Transfer Stopping Point and below this point, heat transfer phenomenon falls from a usual physical interpretation, expressing spectrums of thermal instabilities through a hyper geometric function. Furthermore, it is argued that a normalized similarity temperature in the form of results in the appearance of an uninterruptable singularity within the heat transfer phenomenon for the Glauert case subject to a rigorous physical ground; and as an immediate practical consequence, there is no physically-valid similarity solution for an adiabatic surface or more precisely, for energy equation with heat dissipation consideration. It should be mentioned that the concept of Induced Heat Shield is discussed in here for the first time (to our knowledge) which may inspire a concealed fact regarding the restrictions of the thermal similarity solutions. Therefore, it is hopeful that heat transfer phenomenon in the Glauert type wall jet flows and the associated physical representations can be better understood by the present research.