The linear stability of plane Poiseuille flow through a finite-length channel is studied. A weakly divergence-free basis finite element method with streamline upwind Petrov–Galerkin (SUPG) stabilization is used to formulate the weak form of the problem. The linear stability characteristics are studied under three possible inlet–outlet boundary conditions, and the corresponding perturbation kinetic energy transfer mechanisms are investigated. Active transfer of perturbation kinetic energy at the channel inlet and outlet, energy production due to convection and dissipation at the flow bulk provide a new perspective in understanding the distinct stability characteristics of plane Poiseuille flow under various boundary conditions.

A CFD study is carried out to model the effects of distributed roughness at the airfoil leading-edge using the equivalent sand grain approach and Reynolds-Averaged Navier Stokes (RANS) equations. The turbulence model κ – ω – SST is selected to emulate a fully-turbulent flow. Three κ and ω boundary conditions are studied to model roughness effects. One refers to Wilcox's boundary condition and the other two refer to Aupoix's boundary conditions. Besides, Hellsten's correction is used to ensure Wilcox's boundary condition compatibility with the SST limiter. After validating the implementation of these boundary conditions, they are applied to three different airfoils. One of them is a thick airfoil with industrial relevance. For this airfoil, Wilcox's boundary condition significantly underestimates the roughness impact on aerodynamic coefficients. The pressure gradient simplification in Wilcox's boundary condition formulation is the driving factor behind this effect. The pressure gradient effect on Aupoix's boundary condition is minimal.

This study investigates the fluid dynamics and performance characteristics in micronozzle flows with changes in various geometric parameters using Navier–Stokes simulation based on slip wall boundary conditions. The various geometric parameters considered for the study are (1) area ratio with fixed throat dimension and (2) the semidivergence angle variation with no change in area ratio. The simulation results show that the flow choking for micronozzle happens not at the geometric throat; rather pushed downstream to the divergent channel of the nozzle. This is due to the thick boundary layer growth, which reduces the effective flow area and shifts the minimum allowable flow area downstream to the throat. The distance to which the choking point shifts downstream to the throat reduces with Maxwell's slip wall conditions compared to the conventional no-slip wall condition. The downstream movement of the choking point from the throat reduces with an increase in area ratio and with increase in divergence angle with fixed area ratio. This is due to the fact that the increase in area ratio and divergence angle increases the nozzle height at any particular section in the divergent portion of the nozzle. As a result of this, the boundary layer profile also moves upward and the restriction of potential core by the thick boundary layer reduces, which in turn leads to an increase in the effective minimum flow area downstream to the throat.

Pump-turbines cope very well with modern electricity-market demand, having high operational flexibility and storage capabilities. Nevertheless, dynamic operation of these machines can lead to very challenging transient conditions, depending on the shape of the characteristic. Mechanical integrity can be correspondingly affected. Therefore, assessment of the characteristic during the design phase is of crucial importance. In the past years, different attempts to accurately compute the characteristic under steady and transient conditions have been undertaken using Reynolds-averaged Navier–Stokes (RANS) computational fluid dynamics. While the k– ω shear stress transport (SST) turbulence model has become the reference for machine design, it often fails for conditions close to or around instabilities. Under unstable conditions, which are characterized by continuous unsteady vortex formation, turbulence isotropy as assumed by linear two equation models is no longer the right choice. Accordingly, a turbulence model able to capture anisotropy, explicit algebraic Reynolds stress model (EARSM), has been implemented in an in-house code and used for the computation of the characteristic of various machines, stable and unstable, to assess the model performance. In this paper, computations of three different dynamic pump-turbine operating conditions are presented. Results using steady boundary conditions (BC) in the unstable region as well as transient BC like load-rejection and runaway are computed with EARSM, showing its superiority compared to linear two equation models. The model's capability to capture anisotropic effects—such as the influence of corners—produces more physical flow structures in the vaneless space, which lead to an overall improvement of the predicted stability characteristics.

Couette flow with nonhomogeneous partial-slip stripes on one plate is studied. Drag and flowrate are found by an efficient eigenfunction expansion and point match method. Longitudinal motion (parallel to the stripes) experiences lower drag than transverse motion. As the gap width between the two plates approaches zero, the drag increases to a finite value if the stripes have partial slip, as comparison to the infinite value for no slip. Analysis of the region near the junction of a perfect stick-slip boundary shows a weak stress singularity while there is no singularity for partial slip junctions.

Contractions and expansions are common features in various types of pipeline systems. The purpose of this study is to investigate the influence of a sudden cross section change on transient pressure waves. The paper presents laboratory data and numerical calculations of pressure oscillations during the valve-induced water hammer in serially connected steel pipes. Five different variants of experiments were conducted which included recording pressure changes at the downstream end of the pipeline system. The more sections with different diameters there are connected in series, the more complex the transient wave recorded is. Laboratory data indicate a significant influence of individual pipeline sections on the final course of pressure oscillations. Transient equations were solved using the explicit MacCormack scheme. In order to numerically simulate water hammers in pipe series, the improved junction boundary condition was established. It involves assigning two sets of values, which describe flow parameters, to the connection node thus causing it to act as two separate nodes. The numerical model was calibrated with the unsteady friction factor. The derivation of equations that take into account a sudden change in diameter in the connected pipes allowed the reproduction of the wave nature of the water hammer phenomenon, results were satisfactory as compared to experimental data. The numerical model correctly reproduced pressure wave interactions and pressure amplitudes.

The aim of the present study is to investigate fluid dynamics and pressure drop across sudden contractions in a two-dimensional, axisymmetric pipe carrying a two-phase mixture of air (secondary phase) and water (primary phase), using the Eulerian–Eulerian model of the multiphase flow physics to solve the mass, momentum, volume fraction and turbulent quantities with relevant boundary conditions in a finite volume framework. The realizable per-phase k-ε and Reynolds stress models have been used as the closure for turbulent quantities along with enhanced wall function for the near-wall treatment. The effects of various parameters such as mass flux, mass flow quality, area ratio (0.056–0.619), flow directions (horizontal/vertical), and system pressure on the two-phase pressure drops due to a contraction in the pipe have been quantified. For both the single and two-phase flows, it has been observed that the pressure drop decreases with area ratio, and increases with mass flux and mass flow quality of two-phase flow. The vena contracta for a single-phase flow was found. But for two-phase flow, neither the vena contracta nor the recirculation zone has been observed, as the mass quality exceeds above 50%. A higher pressure drop has been observed for vertical pipes as compared to horizontal pipes. The present numerical results have also been validated with published experimental results, believed to be one of the alternatives to the costly experimental methods for predicting the flow dynamics and pressure drop.

The motion of a spherical particle straddling the flat interface of a semi-infinite Brinkman flow is considered under the conditions of low Reynolds number and zero capillary number regime. The analysis is applied in the case of 90 deg contact angle and when the viscosity of the constituent fluid in the Brinkman region is much more than that of the adjacent fluid. Analytical expressions for the hydrodynamic scalar resistance coefficients are obtained and represented graphically as a function of the slip parameter at the surface of the particle and the permeability parameter of the porous region. The hydrodynamic mobilities are also obtained and represented in tables. The limiting cases of Stokes clear fluid and Darcy's flow are recovered.

In this work, forced convection in the laminar outflow between two disks is predicted. The disks can be corotating or contrarotating with equal or with different angular velocities. A published closed form solution is used to model the forced convection. The simplified energy equation is discretized using a finite difference method. The discretized equation is solved using the tridiagnal matrix algorithm (TDMA). Results are obtained for a heat flux as well as a specified temperature boundary condition and are presented for various flow parameters such as throughflow Reynolds number, rotational Reynolds number, gap ratio and speed ratio. The parameters except the speed ratio affect the temperature field strongly. The computed Nusselt number is in good agreement with the published experimental data. The coupling of closed form solution and energy equation predicts temperature field accurately. Additionally, the solution procedure is simplified considerably and the solution is obtained with lesser computational resources.

The ground proximity is known to induce an outboard movement and suppression of the wingtip vortices, leading to a reduced lift-induced drag. Depending on the ground boundary condition, a large scatter exists in the published lift-induced drag and vortex trajectory. In this experiment, the ground boundary condition-produced disparity in the vortex strength and induced drag were evaluated. No significant discrepancy appeared for a ground distance or clearance larger than 30% chord. As the stationary ground was further approached, there was the appearance of a corotating ground vortex (GV), originated from the downstream progression of a spanwise ground vortex filament, which added vorticity to the tip vortex, leading to a stronger tip vortex and a larger lift-induced drag compared to the moving ground. For the moving ground, the ground vortex was absent. In close ground proximity, the rollup of the high-pressure fluid flow escaped from the wing's tip always caused the formation of a counter-rotating secondary vortex, which dramatically weakened the tip vortex strength and produced a large induced-drag reduction. The moving ground effect, however, induced a stronger secondary vortex, leading to a smaller lift-induced drag and a larger outboard movement of the tip vortex as compared to the stationary ground effect.

Sloshing control is key in the offshore storage and transportation of petroleum and other liquid phased products such as liquid natural gas (LNG). It is of interest in the enhancement of the structural stability of offshore platforms and floating production storage and offloading units. This work presents a numerical approach in the study and analysis of the effect of storage tank configurations on the hydrodynamic response of a multiphase-layered fluid undergoing sloshing. The study showed that tank configurations had an effect on the internal and free surface wave heights of the multiphase fluid sloshing in the tank, as well as on the dynamic pressure intensity being exerted on the tank walls, with some configurations exhibiting comparatively greater sloshing wave and pressure damping.

The discrepancy in the aerodynamic property and flowfield of a symmetric airfoil produced by the stationary and moving ground effect was quantified through surface pressure and particle-image-velocimetry measurements. The results show that the stationary ground effect produced a higher lift than the moving ground due to the flow passage restriction caused by the longitudinal boundary layer developed on its ground surface. In close ground proximity, the formation of a ground vortex beneath the airfoil's leading-edge region speeded up the flow, leading to a lower lift than its moving-ground counterpart. For the moving ground, the ground vortex was absent. In close ground proximity, the moving ground effect generated a larger wake and drag than the stationary ground effect.

An analytical Bessel-sine series solution is presented for inviscid, incompressible, axisymmetric, annular impinging jets. The inflow velocity profile is relatable to an aircraft engine thrust reverser, and has a velocity deficit as well as nonzero vorticity function at the inner radius. As a consequence, inviscid recirculation appears at the impingement corner, the strength of which is made determinate by assuming a local patch of constant vorticity function. Results are first compared against prior round jet solutions, with rigorous convergence and accuracy assessment, before extension to annular impinging jets. Finally, while the Bessel-sine series are consistent with the governing equations and boundary conditions, computational issues arise with steep near wall gradients of a composite parameter that is inherent to the methodology, necessitating extremely fine mesh resolution. A hybrid of finite differences and Bessel series is proposed to address these numerical issues.

Flow over a sphere is a frequently occurring phenomenon in a range of industries. The sphere is confined in a channel in most of these applications. Therefore, it is important to understand the effect of confinement on the hydrodynamics of the flow around a sphere placed in a channel. These spheres can be bubbles, solid particles or droplets resulting in different boundary conditions (stick or slip) on the surface of the sphere. In recent years, Janus spheres having slip and stick boundary conditions on parts of the sphere have gained importance because of their potential applications. In this article, drag coefficient for a spherical particle fixed at the centerline of a channel of square cross-section is obtained computationally for stick, slip, and stick-slip surfaces of the sphere for a range of particle Reynolds numbers (1–80) and particle to channel size ratios (0.05–0.80). Further, the position of stick particle in the channel is varied to understand the effect of particle location on the drag coefficient. Correlations are proposed to calculate the drag coefficient for no-slip and Janus particles when the particle is at the channel center.

Consider steady flows in a channel, cross section Ω , with the Navier slip boundary condition, and let the volume flowrate be denoted by Q. We present a new simple approximation, a rigorous lower bound on Q, requiring, along with the channel's area and perimeter, the calculation of just the torsional rigidity and two other domain functionals. This avoids the need for solving the partial differential equation repeatedly for differing values of the slip parameter. It also provides the opportunity to give tables for different shapes, requiring, for each shape, just its area and perimeter and the three domain functionals previously mentioned. We expect that for shapes used in practice, the approximation will be good for the entire range of slip parameter. This is illustrated with the case of Ω being rectangular.

This study presents a 3-D Fluid-Structure Interaction (FSI) simulation of breastfeeding mechanism to provide a better understanding of the milk flow behavior in the ductal system of the human breast as the breast interacts with the infant's oral cavity. The breast geometry consists of one lobe with three-bifurcation levels. The boundary conditions include: (1) The intraoral vacuum pressure, obtained from the clinical measurements, (2) Dynamic motion of the tongue, nipple, and jaw (maxilla and mandible) motion captured by ultrasound images. Simulation is conducted from the instance of latching and continues for two cycles of periodic tongue motion and in various boundary conditions and mouthing positions. The results from the simulation show that milk removal is not only due to the negative pressure applied by the infant sucking, but also the tongue movement and mouthing and squeezing of nipple and breast, i.e. a positive force deforming the nipple is responsible for the expression of milk. The developed model can contribute to a better understanding of breastfeeding complications due to physical infant and/or breast abnormalities and the design of medical devices such as artificial teats and breast pumps.

A comparison of several Reynolds-averaged Navier–Stokes (RANS) based transition models is presented. Four of the most widespread models are selected: the γ − Re θ , γ , amplification factor transport (AFT), and k T − k L − ω models, representative of different modeling approaches. The calculations are performed on several geometries: a flat plate, the Eppler 387 and NACA 0012 two-dimensional (2D) airfoils at two angles of attack, and the SD7003 wing. Distinct features such as the influence of the inlet boundary conditions, discretization error, and modeling error are discussed. It is found that all models present a strong sensitivity to the turbulence quantities inlet boundary conditions, and with the exception of the AFT model, are severely influenced by the decay of turbulence predicted by the underlying turbulence model. This makes the estimation of modeling errors troublesome because these quantities are rarely reported in experiments. Despite not having specific terms in their formulation to deal with separation-induced transition, both the AFT and k T − k L − ω models manage to predict it for the Eppler 387 foil, although presenting higher numerical uncertainty than the remaining models. However, both models show difficulties in the simulation of flows at Reynolds numbers under 10 5 . The γ − Re θ and γ models are the most robust alternatives in terms of iterative and discretization error. The use of RANS compatible transition models allows for laminar flow and features such as laminar separation bubbles to be reproduced and can lead to greatly improved numerical solutions when compared to simulations performed with standard turbulence models.

The impacts of a plate on an asymmetric water wedge with constant and varying speeds are studied in this paper by considering the fluid to be incompressible, inviscid, and weightless; the effect of surface tension to be negligible; and the flow to be irrotational. A similarity solution for an impact with a constant speed is derived with the help of Wagner's function and the Schwarz–Christophel mapping technique and then numerically solved by employing an iterative method. An approximate solution is derived for the impact with a varying speed satisfying a power law in time based on the computational fluid dynamics (CFD) results with the volume of fluid (VOF) method. The approximate solution can provide an explicit expression for the pressure acting on the plate. The CFD validation shows that the pressure expression can also be applicable to other cases in which the speed of the plate is not a power law in time.

The parasitic drag losses incurred by wet clutches, used in transmission systems, can significantly affect vehicular powertrain efficiency. This paper presents a novel implicit solution for hydrodynamic parasitic drag losses of disengaged clutches. These are generated by conjunctional friction, taking into account lubricant film separation during codirectional and counter-directional disk pair rotations. Lubricant film rupture is considered through application of incipient reverse flow boundary condition, which is representative of lubricant film separation. The results point to the operating conditions at which significant power losses occur. In particular, the time efficient model is able to represent the small losses incurred during codirectional rotation of disk pairs.

We study drag reduction of a uniform flow over a flat surface due to a series of rectangular microgrooves created on the surface. The results reveal that making grooves on the surface usually leads to the generation of secondary vortices inside the grooves that, in turn, decreases the friction drag force and increases the pressure drag force. By increasing the thickness of the grooves to the thickness of the obstacle, the pressure drag increases due to the enhancement of the generated vortices and the occurrence of separation phenomenon and the friction drag reduces due to a decrease of the velocity gradient on the surface. In addition, by increasing the grooves depth ratio, the pressure drag coefficient decreases and the friction drag coefficient increases. However, the impact of the pressure drag coefficient is higher than that of the friction drag coefficient. From a specific point, increasing the groove depth ratio does not effect on decreasing the total pressure drag of the plate. Therefore, creating the grooves in flat surfaces would reduce the total drag coefficient of the plate if the thickness of the grooves does not exceed a specific size and the depth of the grooves is chosen to be sufficiently large. The lattice-Boltzmann method (LBM) is used and the optimal reduction of the drag coefficient is calculated. It is found that for the width ratio equal to 0.19 and the groove depth ratio equal to 0.2548, about 7% decrease is achieved for the average total drag.