Correct Definition of Sound Speed and Its Consequences in the Tasks of Hydrodynamics

The paper considers the applied problems of hydrodynamics and based on the new results, published by the author in recent years, shows that main assumptions used in the course of their solution, namely, incompressibility of liquids and potentiality of their movement, are not applicable to liquids in the gravitational field of the Earth.

Plane Waves and Fundamental Solutions in Heat Conducting Micropolar Fluid

In the present investigation, we study the propagation of plane waves in heat conducting micropolar fluid. The phase velocity, attenuation coefficient, specific loss, and penetration depth are computed numerically and depicted graphically. In addition, the fundamental solutions of the system of differential equations in case of steady oscillations are constructed. Some basic properties of the fundamental solution and special cases are also discussed.

Effect of Yield Power Law Fluid Rheological Properties on Cuttings Transport in Eccentric Horizontal Narrow Annulus

Narrow annular drilling such as casing-while-drilling technique is gaining popularity due to its ability to mitigate nonproductive time during oil and gas drilling operations. However, very little is known about the flow dynamics in narrow annular drilling. In this study, the Eulerian-Eulerian two-fluid model was used to examine the influence of Yield Power Law fluid rheological properties on cuttings transport in eccentric horizontal narrow annulus. The flow was assumed as fully developed, laminar, and transient state. The present simulation model was validated against experimental data, where a mean percent error of −1.2% was recorded. Results revealed an increase in the radial distribution of cuttings transport velocity in the wide annular region as the consistency index, K, and the flow behavior index, n, increase. Nonetheless, increasing the yield stress, τo, had insignificant effect on the cuttings transport velocity. Three-dimensional profiles showed how cuttings preferred to travel in less resistant flow area, whereas cuttings concentration builds up in the narrow annular region. Furthermore, annular frictional pressure losses also increased as K, n, and τo increased. This study serves as a guide to properly optimize drilling fluid rheological properties for efficient cuttings transport and equivalent circulating density (ECD) management in narrow annular drilling.

Mathematical Analysis on Heat Transfer during Peristaltic Pumping of Fractional Second-Grade Fluid through a Nonuniform Permeable Tube

This mathematical study is related to heat transfer under peristaltic flow of fractional second-grade fluid through nonuniform cylindrical tube with permeable walls. The analysis is performed under low Reynolds number and long wavelength approximation. The analytical solution for pressure gradient, friction force, and temperature field is obtained. The effects of appropriate parameters such as Grashof number, nonuniformity of tube, permeability of tube wall, heat source/sink parameter, material constant, fractional time derivative parameter and amplitude ratio on pressure rise, friction force, and temperature distribution are discussed. It is found that an increase in amplitude ratio and material constant causes increase in pressure but increase in nonuniformity of the tube causes decrease in pressure. It is also observed that variation of friction force against flow rate shows opposite behavior to that of pressure. Increase in temperature is also observed due to increase in heat source/sink parameter at inlet as well as downstream.

Mathematical Modeling of Local Scour at Slender and Wide Bridge Piers

Most existing equations for predicting local scour at bridge piers suffer from overprediction of the scour depths which results in higher foundation costs. To tackle this problem, a mathematical model for predicting bridge pier scour is developed herein based on an energy balance theory. The present study equation was compared to commonly used bridge scour equations using scour field data in USA. The developed equation has several advantages among which we have the following: it adds to the understanding of the physics of bridge pier scour, is valid for slender and wide piers, does not suffer from overprediction of scour depths, addresses clear water and live bed scour, and includes the effects of various characteristics of the bed material such as specific gravity (or density), porosity, size, and angle of repose. In addition, the developed equation accounts for the debris effect and aids in the design of scour mitigation methods such as collars, side bars, slots, and pier protective piles.

A Volumetric Approach to Wake Reduction: Design, Optimization, and Experimental Verification

Wake reduction is a crucial link in the chain leading to undetectable watercraft. Here, we explore a volumetric approach to controlling the wake in a stationary flow past cylindrical and spherical objects. In this approach, these objects are coupled with rigid, fluid-permeable structures prescribed by a macroscopic design approach where all solid boundaries are parameterized and modeled explicitly. Local, gradient-based optimization is employed which permits topological changes in the manifold describing the composite solid component(s) while still allowing the use of adjoint optimization methods. This formalism works below small Reynolds number (Re) turbulent flow (Re≈100–10,000) when simulated using small Reynolds-averaged Navier-Stokes (RANS) models. The output of this topology optimization yields geometries that can be fabricated immediately using fused deposition modeling (FDM). Our prototypes have been verified in an experimental water tunnel facility, where the use of Particle Image Velocimetry (PIV) described the velocity profile. Comparisons with our computational models show excellent agreement for the spherical shapes and reasonable match for cylindrical shapes, with well-understood sources of error. Two important figures of merit are considered: domain-wide wake (DWW) and maximum local wake (MLW), metrics of the flow field disturbance whose definitions are described.

Rheological Behavior of Physiological Pulsatile Flow through a Model Arterial Stenosis with Moving Wall

The paper presents a numerical investigation of non-Newtonian modeling effects on unsteady periodic flows in a two-dimensional (2D) constricted channel with moving wall using finite volume method. The governing Navier-Stokes equations have been modified using the Cartesian curvilinear coordinates to handle complex geometries, such as, arterial stenosis. The physiological pulsatile flow has been used at the inlet position as an inlet velocity. The flow is characterized by the Reynolds numbers 300, 500, and 750 that are appropriate for large arteries. The investigations have been carried out to characterize four different non-Newtonian constitutive equations of blood, namely, the (i) Carreau, (ii) Cross, (iii) Modified-Casson, and (iv) Quemada. In these four models, blood viscosity is a nonlinear function of shear rates. The Newtonian model has been investigated to study the physics of fluid and the results are compared with the non-Newtonian viscosity models. The numerical results are presented in terms of streamwise velocity, wall shear stress, pressure distribution as well as the vorticity, streamlines, and vector plots indicating recirculation zones at the poststenotic region. Comparison has also been illustrated in terms of wall pressure and wall shear stress for the Cross model considering different amplitudes of wall oscillation.

Separation Criteria for Off-Axis Binary Drop Collisions

Off-axis collisions of two equal size droplets are investigated numerically. Various governing processes in such collisions are discussed. Several commonly used theoretical models that predict the onset of separation after collision are evaluated based on the processes observed numerically. A separation criterion based on droplet deformation is found. The numerical results are used to assess the validity of some commonly used phenomenological models for drop separation after collision. Also, a critical Weber number for the droplet separation after grazing collision is reported. The effect of Reynolds number is investigated and regions of permanent coalescence and separation are plotted in a Weber-Reynolds number plane for high impact parameter collisions.

Unsteady/Steady Hydromagnetic Convective Flow between Two Vertical Walls in the Presence of Variable Thermal Conductivity

Unsteady as well as steady natural convection flow in a vertical channel in the presence of uniform magnetic field applied normal to the flow region and temperature dependent variable thermal conductivity is studied. The nonlinear partial differential equations governing the flow have been solved numerically using unconditionally stable and convergent semi-implicit finite difference scheme. For steady case, approximate solutions have been derived for velocity, temperature, skin friction, and the rate of heat transfer using perturbation series method. Results of the computations for velocity, temperature, skin friction, and the rate of heat transfer are presented graphically and discussed quantitatively for various parameters embedded in the problem. An excellent agreement was found during the numerical computations between the steady-state approximate solutions and unsteady numerical solutions at steady-state time. In addition, comparison with previously published work is performed and the results agree well.

Effects of Heat and Mass Transfer on the Peristaltic Transport of MHD Couple Stress Fluid through Porous Medium in a Vertical Asymmetric Channel

The intrauterine fluid flow due to myometrial contractions is peristaltic type motion and the myometrial contractions may occur in both symmetric and asymmetric directions. The channel asymmetry is produced by choosing the peristaltic wave train on the walls to have different amplitude, and phase due to the variation of channel width, wave amplitudes and phase differences. In this paper, we study the effects of heat and mass transfer on the peristaltic transport of magnetohydrodynamic couple stress fluid through homogeneous porous medium in a vertical asymmetric channel. The flow is investigated in the wave frame of reference moving with constant velocity with the wave. The governing equations of couple stress fluid have been simplified under the long wave length approximation. The exact solutions of the resultant governing equations have been derived for the stream function, temperature, concentration, pressure gradient, and heat transfer coefficients. The pressure difference and frictional forces at both the walls are calculated using numerical integration. The influence of diverse flow parameters on the fluid velocity, pressure gradient, temperature, concentration, pressure difference, frictional forces, heat transfer coefficients, and trapping has been discussed. The graphical results are also discussed for four different wave shapes. It is noticed that increasing of couple stresses and heat generation parameter increases the size of the trapped bolus. The heat generation parameter increases the peristaltic pumping and temperature.