Computational Analysis of Fluid Forces on an Obstacle in a Channel Driven Cavity: Viscoplastic Material Based Characteristics

In the current work, an investigation has been carried out for the Bingham fluid flow in a channel-driven cavity with a square obstacle installed near the inlet. A square cavity is placed in a channel to accomplish the desired results. The flow has been induced using a fully developed parabolic velocity at the inlet and Neumann condition at the outlet, with zero no-slip conditions given to the other boundaries. Three computational grids, C1, C2, and C3, are created by altering the position of an obstacle of square shape in the channel. Fundamental conservation and rheological law for viscoplastic Bingham fluids are enforced in mathematical modeling. Due to the complexity of the representative equations, an effective computing strategy based on the finite element approach is used. At an extra-fine level, a hybrid computational grid is created; a very refined level is used to obtain results with higher accuracy. The solution has been approximated using P2 − P1 elements based on the shape functions of the second and first-order polynomial polynomials. The parametric variables are ornamented against graphical trends. In addition, velocity, pressure plots, and line graphs have been provided for a better physical understanding of the situation Furthermore, the hydrodynamic benchmark quantities such as pressure drop, drag, and lift coefficients are assessed in a tabular manner around the external surface of the obstacle. The research predicts the effects of Bingham number (Bn) on the drag and lift coefficients on all three grids C1, C2, and C3, showing that the drag has lower values on the obstacle in the C2 grid compared with C1 and C3 for all values of Bn. Plug zone dominates in the channel downstream of the obstacle with augmentation in Bn, limiting the shear zone in the vicinity of the obstacle.

Flow Characteristics of Gerotor Motors with Pin and Nonpin Designs

The geometric design of a gerotor motor has a significant impact on its function, performance, quality, reliability and cost. When designing a gerotor motor all these features must be considered. A gerotor motor can be classified into two types based on the geometric design; gerolor (pin design) and gerotor (nonpin design). In this article geometric parameters of the two design types are discussed briefly and the operation of the gerotor motor is described as well. A numerical analysis is carried out by using computational fluid dynamics (CFD) tool (PumpLinx) to analyze the fluid flow and predict the performance of both types of gerotor designs. Various characteristics of the two designs of the gerotor motor are investigated and compared which include the gerotor design, fluid flow rate, velocity, pressure and output torque. Comparison of the results found out that using pin design gerotor motor, the flow rate, flow velocity, pressure and torque will vary greatly. Nonpin design can significantly reduce variations in all the flow characteristics thereby enhancing the stability and reduction in the leakage risk.

A Monolithic Finite Element Formulation for Magnetohydrodynamics Involving a Compressible Fluid

This work develops a new monolithic finite-element-based strategy for magnetohydrodynamics (MHD) involving a compressible fluid based on a continuous velocity–pressure formulation. The entire formulation is within a nodal finite element framework, and is directly in terms of physical variables. The exact linearization of the variational formulation ensures a quadratic rate of convergence in the vicinity of the solution. Both steady-state and transient formulations are presented for two- and three-dimensional flows. Several benchmark problems are presented, and comparisons are carried out against analytical solutions, experimental data, or against other numerical schemes for MHD. We show a good coarse-mesh accuracy and robustness of the proposed strategy, even at high Hartmann numbers.

A mixed elasticity formulation for fluid-poroelastic structure interaction

We develop a mixed finite element method for the coupled problem arising in the interaction between a free fluid governed by the Stokes equations and flow in deformable porous medium modeled by the Biot system of poroelasticity. Mass conservation, balance of stress, and the Beavers-Joseph-Saffman condition are imposed on the interface. We consider a fully mixed Biot formulation based on a weakly symmetric stress-displacement-rotation elasticity system and Darcy velocity-pressure flow formulation. A velocity-pressure formulation is used for the Stokes equations. The interface conditions are incorporated through the introduction of the traces of the structure velocity and the Darcy pressure as Lagrange multipliers. Existence and uniqueness of a solution are established for the continuous weak formulation. Stability and error estimates are derived for the semi-discrete continuous-in-time mixed finite element approximation. Numerical experiments are presented to verify the theoretical results and illustrate the robustness of the method with respect to the physical parameters.

The Impact of Rock Microstructure and Petrophysical Properties on the Velocity-Pressure Relationship of Carbonates

This study investigates the impact of petrophysical rock properties on the velocity-pressure relationship in carbonates. It presents an approach to predict the changes in compressional velocity (Vp) as function of pressure in carbonates. The approach honors the complexity of carbonates by incorporating various petrophysical rock properties including bulk density, porosity, mineralogy and pore stiffness. The data used in this study consists of rock properties (density, porosity, mineralogy) and elastic velocity measured as function of confining pressure for 220 carbonate core plug samples from published literature. Pearson correlation coefficient was calculated to evaluate the significance of each property in predicting velocity-pressure relationship. A simple regression was formulated incorporating all significant input rock properties to predict Vp as function of pressure based on initial measured velocity at a given pressure. The predictions were compared with the measured Vp. The results show that the sensitivity of Vp to changes in pressure increases as the porosity and pore compressiblity increases. On the other hand, samples with higher bulk density and Vp / Vs ratio (at initial lowest pressure) show little Vp variations as function of increasing pressure. High Vp / Vs values are observed in samples that are well cemented and have less clay or silisiclastic fraction. Such characteristics reduce the compressibility of pores leading to non-variable velocity-pressure relationship. Incorporating the rock properties in regression analysis could successfully predict Vp as function of pressure with a correlation coefficient of 0.99 and average absolute error of less than 3%. Since all input parameters (rock properties) can be estimated from well logs, the presented approach can potentially be used to predict in-situ changes in Vp due to pressure changes. This can assist the interpretation of time lapse seismic, and in geomechanics-related applications.

Enhanced algorithms for solving the spectral discretization of the vorticity–velocity–pressure formulation of the Navier–Stokes problem

The objective of the article is to improve the algorithms for the resolution of the spectral discretization of the vorticity–velocity–pressure formulation of the Navier–Stokes problem in two and three domains. Two algorithms are proposed. The first one is based on the Uzawa method. In the second one we consider a modified global resolution. The two algorithms are implemented and their results are compared.

Thermal Environment and Aeroheating Mechanism of Protuberances on Mars Entry Capsule

Mars has only thin atmosphere composed mainly of carbon dioxide that differs significantly from the atmosphere of Earth in terms of characteristics of reentry flows. To connect with the orbiter, the Mars entry capsule is provided with titanium pipes and other units installed on the heat-shield. These units will create significant local interaction flow on the surface of the capsule and cause additional heating on the surface of the shield during the entry of the capsule. With a view to interaction thermal environment issues for the surface of the shield, in this paper, the characteristics of protrusion interaction flow on different location of the shield were studied by means of numerical simulation. Heating mechanisms of protuberances on different location were derived by analyzing characteristic parameters such as local flow velocity, pressure, and Mach number. The results show that the interaction thermal environment of protuberances in the windward area is smaller than that of protuberances in the leeward area, mainly because subsonic flow dominates in the windward area, and the interaction is weak, while in the leeward area, the direction of flow intersects with protuberances to form a boundary layer shear flow, which results in a stronger interaction before the protuberances.

Experimental Research and Numerical Analysis of Pressure Fluctuation Characteristics of Rim Driven Propulsion Pump Outlet

The pressure fluctuation characteristics of a rim driven propulsion pump are studied by an experimental method firstly, and then its unsteady inner flow is studied by numerical simulation to reveal the generating mechanism of the pressure fluctuation. In the experiment, a monitoring point was set in a downstream region with a distance of 1D (D, Diameter of impeller) to the impeller. The monitoring point’s dominant frequencies within a low frequency band are 1APF (APF, Axial Passing Frequency) and 2APF. In the numerical simulation, the main fluctuation near the impeller region appears at 1BPF (BPF, Blade Passing Frequency) and as the monitoring point moves downstream, the amplitude becomes smaller. The 1BPF fluctuation nearly disappears when the distance exceeds 1D, and the main frequency moves to 1APF and 2APF, which is in good agreement with the experimental results in the low frequency band. The transient velocity, pressure and vorticity distribution were studied to reveal the causes of 1BPF, 1APF and 2APF fluctuation. The main cause of 1BPF is the jet from the tail of the blade and the main cause of 2APF is the movement of a large-scale double vortex structure on both sides of the low-pressure zone. The movement of the vortex group near the wall may be the main cause that induces the 1APF fluctuation.

Numerical Modeling of the Leak through Semipermeable Walls for 2D/3D Stokes Flow: Experimental Scalability of Dual Algorithms

The paper deals with the Stokes flow subject to the threshold leak boundary conditions in two and three space dimensions. The velocity–pressure formulation leads to the inequality type problem that is approximated by the P1-bubble/P1 mixed finite elements. The resulting algebraic system is nonsmooth. It is solved by the path-following variant of the interior point method, and by the active-set implementation of the semi-smooth Newton method. Inner linear systems are solved by the preconditioned conjugate gradient method. Numerical experiments illustrate scalability of the algorithms. The novelty of this work consists in applying dual strategies for solving the problem.