Agitation of Complex Fluids in Cylindrical Vessels by Newly Designed Anchor Impellers

The fluid flows and power consumption in a vessel stirred by anchor impellers are investigated in this paper. The case of rheologically complex fluids modeled by the Bingham-Papanastasiou model is considered. New modifications in the design of the classical anchor impeller are introduced. A horizontal blade is added to the standard geometry of the anchor, and the effect of its inclination angle (α) is explored. Four geometrical configurations are realized, namely: α = 0°, 20°, 40°, and 60°. The effects of the number of added horizontal blades, Reynolds number, and Bingham number are also examined. The obtained findings reveal that the most efficient impeller design is that with (case 4) arm blades inclined by 60°.This case allowed the most expansive cavern size with enhanced shearing in the whole vessel volume. The effect of adding second horizontal arm blades (with 60°) gave better hydrodynamic performance only with a slight increase in power consumption. A significant impact of Bingham number (Bn) was observed, where Bn = 5 allowed obtaining the lowest power input and most expansive well-stirred region.

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.

A minimum transmitted load control method for shock isolation mounts with magnetorheological energy absorbers

This paper proposed a minimum transmitted load (MTL) control method for drop-induced shock isolation mounts (SIM) with magnetorheological energy absorbers (MREAs). MTL control method consists of two parts of maximum damping force (MDF) control and one part of constant acceleration (CA) control, which can make the payload stop after fully utilize MREA stroke (soft landing) with minimum transmitted load. The control algorithm of MTL control method is derived in a single-degree-of-freedom (SDOF) system. The relationship between the controllable velocity range of MTL control method and parameters of shock isolation mounts is also derived. An optimal control method selection criterion between Bingham number (BN) control method and MTL control method is developed. The performance of MTL control method and selection criterion are shown by applying to the SIM system with variable drop velocities and system parameters. Results shows that MTL control method has the minimum transmitted load and the selection criterion is feasible.

An adaptive shock mitigation control method for helicopter seat system with magnetorheological energy absorbers

This research presents a minimal maximum deceleration (MMD) control method which can be used in the shock mitigation system with magnetorheological energy absorbers (MREAs). The proposed control method can make the payload stop at the end of the available MREA stroke with the lowest maximum deceleration, which does not exceed the deceleration threshold value and lead to the lowest occupant injury probability. The shock mitigation system controlled by MMD will experience constant deceleration control stage and maximum damping force control stage while making full use of the available MREA stroke. The comparative performance of the MMD control method with Bingham number (BN) control, constant deceleration (CD) control and minimum duration deceleration exposure (MDDE) control is shown. Then, the controllable drop velocity range and the required maximum MREA controllable damping force range of MMD control method is calculated. Subsequently, the optimal control method selection criterion among BN control method, CD control method and MMD control method is developed. Finally, the optimal selection criterion is applied to the drop induced shock mitigation system with varying payload velocity, payload mass (occupant type) and the maximum controllable damping force of MREA.

Numerical Simulation of Natural Convection and Calculation of Heat Transfer Coefficient in Wellbore Annulus during Deep-Water Gas Well Testing

Most of the current prediction model of wellbore temperature for deep-water gas well does not consider the influence of natural convection in annulus on the heat dissipation of the system, resulting in a lower prediction accuracy of temperature. In this study, three-dimensional simulation on the heat transfer by natural convective of testing fluid in annulus was performed. The mechanism of heat transfer are studied for different values of Rayleigh number (Ra) and Bingham number (Bn). The results show that the occurrence of natural convection in the annulus can significantly increase the heat loss of the fluid in the tubing. With the increases in Ra or decreases in Bn, the convective transport in annulus gradually strengthens, and the heat transfer coefficient gradually increases. However, when the Bingham number increases to about 100, the heat transfer mode in annulus becomes a single heat conduction. Based on the simulation results, a new correlation of heat transfer coefficients in annulus was proposed. The introduction of this correlation can significantly improve the prediction accuracy of wellbore temperature during deep water gas well testing, and lay a foundation for the prevention and control of hydrate and wax formation in wellbore.

Laminar Free Convection From a Heated Square Cylinder in Bingham Plastic Fluids

The free convection phenomenon from a heated square cylinder submerged in Bingham Plastic fluids is numerically investigated. The governing equations are solved for a wide range of physical dimensionless parameters, such as Rayleigh number (10^2 ≤ Ra ≤ 10^5), Prandtl number (10 ≤ Pr ≤ 100) and Bingham number (0 ≤ Bn ≤ 10^7). The heat transfer characteristics are investigated in terms of local Nusselt number distribution over the surface of the cylinder surface average Nusselt number. Streamlines, isothermal contours, yielded and unyielded regions are visualized in detail.

Topological Characteristics of Obstacles and Nonlinear Rheological Fluid Flow in Presence of Insulated Fins: A Fluid Force Reduction Study

In this work, a comprehensive study of fluid forces and thermal analysis of two-dimensional, laminar, and incompressible complex (power law, Bingham, and Herschel–Bulkley) fluid flow over a topological cross-sectional cylinder (square, hexagon, and circle) in channel have been computationally done by using finite element technique. The characteristics of nonlinear flow for varying ranges of power law index 0.4 ≤ n ≤ 1.6 , Bingham number 0 ≤ Bn ≤ 50 , Prandtl number 0.7 ≤ Pr ≤ 10 , Reynolds number 10 ≤ Re ≤ 50 , and Grashof number 1 ≤ Gr ≤ 10 have been examined. Considerable evaluation for thermal flow field in the form of dimensionless velocity profile, isotherms, drag and lift coefficients, and average Nusselt number Nu avg is done. Also, for a range of Bn , the drag forces reduction is observed for circular and hexagonal obstacles in comparison with the square cylinder. At Bn = 0 corresponding to Newtonian fluid, maximum reduction in drag force is reported.

Flow of the Bingham-Papanastasiou Regularized Material in a Channel in the Presence of Obstacles: Correlation between Hydrodynamic Forces and Spacing of Obstacles

The numerical modeling and simulation for the stationary Bingham fluid flow around two confined circular cylinders with various gap ratios are studied. The singularity in the model’s apparent viscosity is dealt by Papanastasiou’s regularization. The model equations are discretized by adopting the methodology based on finite element method (FEM) by choosing a mixed higher order LBB-stable P 2 − P 1 finite element pair. The direct solver PARADISO has been utilized to solve the linearized system of equations. Hydrodynamic forces represented by drag and lift coefficients are computed, and a correlation coefficient is calculated for the gap ratios 0.1 ≤ G p ≤ 0.3 and for several values of the Bingham number 0 ≤ B n ≤ 50 . Line graphs for horizontal and vertical velocities are drawn. Moreover, velocity and pressure profiles are plotted for pertinent values of the parameters. Plug and shear zones are revealed via velocity snapshots in the domain. Pressure is nonlinear in the vicinity of the obstacles and becomes linear downstream in the cylinders as expected in channel flows.

Magnetohydrodynamic Flow of a Bingham Fluid in a Vertical Channel: Mixed Convection

In this paper, we describe our study of the mixed convection of a Boussinesquian Bingham fluid in a vertical channel in the absence and presence of an external uniform magnetic field normal to the walls. The velocity, the induced magnetic field, and the temperature are analytically obtained. A detailed analysis is conducted to determine the plug regions in relation to the values of the Bingham number, the buoyancy parameter, and the Hartmann number. In particular, the velocity decreases as the Bingham number increases. Detailed considerations are drawn for the occurrence of the reverse flow phenomenon. Moreover, a selected set of diagrams illustrating the influence of various parameters involved in the problem is presented and discussed.

Effect of Sinusoidally Varying Flow of Yield Stress Fluid On Heat Transfer From a Cylinder

The effect of pulsating laminar flow of a Bingham plastic fluid on heat transfer from a constant temperaturre cylinder is studied numerically over wide ranges of conditions as: Reynolds number (0.1 = Re = 40) and Bingham number (0.01 = Bn = 50) based the on mean velocity, Prandtl number (10 = Pr = 100), pulsation frequency (0 = w* = Pi) and amplitude (0 = A = 0.8). Results are visualized in terms of instantaneous streamlines, isotherms, apparent yield surfaces at different instants of time during a pulsation cycle. The overall behavior is discussed in terms of the instantaneous and time averaged values of the drag coefficient and Nusselt number. The size of the yielded zone is nearly in phase with the pulsating velocity whereas the phase shift has been observed in both drag coefficient and Nusselt number. The maximum augmentation ( ~30 %) in Nusselt number occurs at Bn = 1, Re = 40, Pr = 100, w* = Pi and A = 0.8 with respect to that for uniform flow. However, the increasing yield stress tends to suppress the potential for heat transfer enhancement. Conversely, this technique of process intensification is best suited for Newtonian fluids in the limit of Bn ~ 0. Finally, a simple expression consolidates the numerical values of the time-average of the Nusselt number as a function of the pertinent dimensionless parameters which is consistent with the widely accepted scaling of the Nusselt number with ~Pe1/3 under these conditions.