Numerical Simulation of Vortex-Dominated Flows Using the Penalized VIC Method

Vorticity plays a key role in determining fluid flow dynamics, especially in vortex-dominated flows. Vortex methods, which are based on the vorticity-based formulation of the Navier-Stokes equations, have provided deeper insight into physical reality in a variety of flows using vorticity as a primary variable. The penalized vortex-in-cell (VIC) method is a state-of-the-art variant of vortex methods. In the penalized VIC method, Lagrangian fluid particles are traced by continuously updating their position and strength from solutions at an Eulerian grid. This hybrid method retains beneficial features of pure Lagrangian and Eulerian methods. It offers an efficient and effective way to simulate unsteady viscous flows, thereby enabling application to a wider range of problems in flows. This article presents the fundamentals of the penalized VIC method and its implementations

A lattice Boltzmann model for natural convection in cavities

We study a multiple relaxation time lattice Boltzmann model for natural convection with moment–based boundary conditions. The unknown primary variables of the algorithm at a boundary are found by imposing conditions directly upon hydrodynamic moments, which are then translated into conditions for the discrete velocity distribution functions. The method is formulated so that it is consistent with the second–order implementation of the discrete velocity Boltzmann equations for fluid flow and temperature. Natural convection in square cavities is studied for Rayleigh numbers ranging from 103 to 106. An excellent agreement with benchmark data is observed and the flow fields are shown to converge with second order accuracy

Numerical Simulation of Slow Drying in Porous Media Using Pore Network Model

In our first model, an internal and external coupled solver is presented to simulate the slow drying of a porous medium placed adjacent to a laminar flow of air in a slit. The porous medium is represented by a 20×20 pore-network model: the invasion-percolation algorithm is employed to simulate moisture redistribution; water-vapor migration in empty network is estimated using the purely diffusive approach. The external flow-field, unchanged during the drying simulation, is computed in the beginning using the Navier-Stokes equations. Subsequent water-vapor transport is modeled using a convection-diffusion type transport equation. A unique pore-to-cell meshing method and a novel unified (implicit) computational framework coupling the outer and the inner processes are proposed. Multi-scale problems in both space and time appear when solving the internal and external field simultaneously. To accurately simulate this kind of problem by aiming to minimize computation effort, the following aspects of the simulation are studied: space discretization schemes, numerical algorithms, mesh microstructure, and time-step refinement. The space discretization schemes tested in this paper include the Hybrid and the Hayase QUICK schemes. The numerical algorithms tested to solve the drying process include the operator-splitting and a non-operator-splitting algorithm. Different mesh densities are tested along the directions parallel to and normal to the outer flow- porous-medium interface. Different time-steps are tested to find a suitable time-step for both the internal and the external computations. The external air velocity has some impact on the drying in the initial stages. Significantly, the microstructure of the pore-network is found to have a strong influence on drying. In our second pore network model (which is based on our first model), the film effect is included and a novel logistic equation is used to relate the pore network variables with the external field variables. For migration of water vapors, the model accounts for both advective and diffusive transport in the external flow field while including diffusion in the dry part of the pore network. By conducting a parametric study on the drying of a 40×40 square network placed next to a slit flow, it is discovered that (a) higher hydraulic diameter of the throats leads to higher drying rates and longer constant drying-rate periods; (b) the drying time increases and the drying rate decreases as the throat cross section changes from a triangle to a square to a hexagon to a circle, which can be correlated to the weakening of the film effect; (c) increasing the external flow velocity (that leads to changing the Peclet number from 1 to 1000) has little effect on the drying rates and times; (d) increasing the external air humidity from 30% to 70 % leads to a large decrease in the drying rates and the consequent increase in the overall drying times. The developed model is then used to simulate the drying of several thin porous media (40×40, 80×20, and 160×10) with different aspect ratios placed either aligned-with or perpendicular-to a uniform 2-D flow. Plots of drying rates and drying times against the network saturation are studied. The presence of film during most of the drying period ensures that the surface pores are at saturated vapor pressure. As a result, the sharpest concentration gradients, which also control the drying rates, lie adjacent to the exposed surfaces. Consequently, the concentration gradients in the outer flow fields are very mild and play insignificant role in the drying of porous media. Hence, we reach a surprising conclusion—the orientation of thin porous media in the outer flow field is found to be irrelevant for drying. But expectedly, the higher exposed-area versus total volume ratio leads to faster drying. However, these conclusions should be examined further by future 3D simulations since a 2D simulation may underestimate the influence of external flow field on the drying of porous media. Finally, the model is applied to the dual-porosity porous media. The drying simulation of a square-shaped and dual-porosity pore network is compared with a previously published experimental study. Two cases of small-pores side open and large-pore side open are considered. It is observed that though the simulation results of the 12×12 network fail to match the experimental drying curves completely, important features of the drying process (such as complete emptying of large pores before the onset of drying in the small pore region of the large-pores side open case) are achieved. Next the drying of the same square-shaped, dual-porosity domain using a much refined 100×100 network is carried out in a uniform air flow after keeping either the large-pores or the small-pores side open. The former leads to faster drying and complete emptying of the large pores before the small pores. The latter witnesses the phenomenon of capillary pumping. Using the same refined network, the case of all side open is also studied. Changing the throat cross-section from circle to square leads to much faster drying. Introduction of microstructural irregularity in the network by randomly changing throat diameter and changing the coordination number of pores does not affect the drying rate and drying time significantly

Critical issues for predicting worker exposure to gaseous contaminants in a wind tunnel

In this study, three dimensional computational fluid dynamics (CFD) simulations are used to investigate the distribution and level of contaminant concentrations in the breathing zone of a worker when airborne contaminants are released within an arm\u27s-length in front of the worker who has his back to the airflow. The main goals were to numerically evaluate the effect of different factors on the worker exposure and to recommend a turbulence model preferable for this type of simulation. These factors include the body shape, the heat flux from the body, the ventilation intensity, the free stream turbulence, and the unsteadiness. The comparison between the numerical results and the experimental data has shown good agreement.;An extensive case study with FLUENT concluded with the following observations: (1) The heat flux from the body significantly affects the flow field and the subsequent contaminant concentration field at low Reynolds numbers; (2) The free stream turbulence plays an important role in the variation of exposure measurements at low Reynolds numbers; (3) Results calculated with the Large Eddy Simulation (LES) illustrate the turbulence structure in the wake of the manikin and indicate that the flow unsteadiness plays an important role in the variation of exposure measurements; (4) Calculations with various body shapes suggests that oversimplified body shapes may lead to inaccurate predictions in worker exposure assessment; (5) The concentrations measured at the lapel could be very different than the concentrations measured near the mouth.;To further improve the predictability of turbulence models for the present study, a non-linear (cubic) low-Re turbulence model has been selected, modified and implemented in the DREAM code which was developed at West Virginia University. Benchmark tests on turbulent channel flow, backward facing step flow and flow around a square cylinder have shown that this model is remarkably superior to linear eddy-viscosity models, and the results are even comparable to others\u27 predictions with LES, which is much more computationally expensive. So it could be a good alternative as a reliable and accurate turbulence model in simulating turbulent flow past a bluff body

Meshless Direct Numerical Simulation of Turbulent Incompressible Flows

A meshless direct pressure-velocity coupling procedure is presented to perform Direct Numerical Simulations (DNS) and Large Eddy Simulations (LES) of turbulent incompressible flows in regular and irregular geometries. The proposed method is a combination of several efficient techniques found in different Computational Fluid Dynamic (CFD) procedures and it is a major improvement of the algorithm published in 2007 by this author. This new procedure has very low numerical diffusion and some preliminary calculations with 2D steady state flows show that viscous effects become negligible faster that ever predicted numerically. The fundamental idea of this proposal lays on several important inconsistencies found in three of the most popular techniques used in CFD, segregated procedures, streamline-vorticity formulation for 2D viscous flows and the fractional-step method, very popular in DNS/LES. The inconsistencies found become important in elliptic flows and they might lead to some wrong solutions if coarse grids are used. In all methods studied, the mathematical basement was found to be correct in most cases, but inconsistencies were found when writing the boundary conditions. In all methods analyzed, it was found that it is basically impossible to satisfy the exact set of boundary conditions and all formulations use a reduced set, valid for parabolic flows only. For example, for segregated methods, boundary condition of normal derivative for pressure zero is valid only in parabolic flows. Additionally, the complete proposal for mass balance correction is right exclusively for parabolic flows. In the streamline-vorticity formulation, the boundary conditions normally used for the streamline function, violates the no-slip condition for viscous flow. Finally, in the fractional-step method, the boundary condition for pseudo-velocity implies a zero normal derivative for pressure in the wall (correct in parabolic flows only) and, when the flows reaches steady state, the procedure does not guarantee mass balance. The proposed procedure is validated in two cases of 2D flow in steady state, backward-facing step and lid-driven cavity. Comparisons are performed with experiments and excellent agreement was obtained in the solutions that were free from numerical instabilities. A study on grid usage is done. It was found that if the discretized equations are written in terms of a local Reynolds number, a strong criterion can be developed to determine, in advance, the grid requirements for any fluid flow calculation. The 2D-DNS on parallel plates is presented to study the basic features present in the simulation of any turbulent flow. Calculations were performed on a short geometry, using a uniform and very fine grid to avoid any numerical instability. Inflow conditions were white noise and high frequency oscillations. Results suggest that, if no numerical instability is present, inflow conditions alone are not enough to sustain permanently the turbulent regime. Finally, the 2D-DNS on a backward-facing step is studied. Expansion ratios of 1.14 and 1.40 are used and calculations are performed in the transitional regime. Inflow conditions were white noise and high frequency oscillations. In general, good agreement is found on most variables when comparing with experimental data

Modeling Thermal Turbulence Using Implicit Large Eddy Simulation

A general description of a thermally coupled fluid flow is given by the incompressible Navier-Stokes equations coupled with the heat equation using Boussinesq approximation, whose mathematical structure is much well understood. A variational multiscale finite element approximation has been considered for the formulation of incompressible Navier-Stokes equation and heat equation. The complexity of these problems makes their numerical solution very difficult as the standard finite element method is unstable. In the incompressible Navier Stokes equations, two well known sources of numerical instabilities are the incompressibility constraint and the presence of the convective term. Many stabilization techniques used nowadays are based on scale separation, splitting the unknown into a coarse part induced by the discretization of the domain and a fine subgrid part. The modeling of the subgrid scale and its influence leads to a modified coarse scale problem providing stability. In convection-diffusion problem once global instabilities have been overcome by a stabilization method, there are still local oscillations near layers due to the lack of monotonicity of the method. Shock capturing techniques are often employed to deal with them. Proper choice of stabilization and shock capturing techniques can eliminate the local instabilities near layers of convection-diffusion equation. A very important issue of the formulation presented in this thermally coupled incompressible flow is the possibility to model turbulent flows. Some terms involving the velocity subgrid scale arise from the convective term in the Navier-Stokes equations which can be understood as the contribution from the Reynolds tensor of a LES approach and the contribution from the cross stress tensor. This opens the door of modeling thermal turbulence using LES automatically inherited by the formulation used in this work. Different classical benchmark problems are numerically solved in this thesis work for the convection-diffusion equation to show the capabilities of different combination of stabilization and shock capturing methods. In the case of thermally coupled incompressible flows some numerical and industrial examples are exhibited to check the performance of the different combination of stabilization and shock capturing methods and to compare them. The objective is to conclude which method works better to approximate the exact solution and eliminate instabilities and local oscillations

Preliminary finite element modeling of a piezoelectric actuated marine propulsion fin

New technologies surrounding composite materials and autonomous underwater vehicle (AUV) design have led to numerous studies involving the marine propulsion for these AUVs. AUVs traditionally are classified as highly efficient, payload capable, and can be utilized as reconnaissance or surveillance vehicles. Undullatory and oscillatory propulsion devices have been conceived to replace the present propulsion technologies, of propellers, with highly maneuverable, efficient, and quiet propulsion systems. Undullatory and oscillatory propulsion has been around for centuries employed by aquatic life, but only recently have the mini-technologies been available to present such propulsion devices economically and with enough materials research as to mimic biologic life on the same scale. Piezoelectric properties coupled with a thin plate allow for actuation properties, similar to bimetallic metals. Applying two piezoelectrics to the fixed end of a cantilevered beam or plate, on opposite sides, and actuating them with an opposite phase shift in electrical voltage potential results in transverse motion of the beam from the orthogonal plane to the vertical axis of the piezoelectric device. Coupling this property to a particular fiber orientation, composite thin plate, significantly increases the actuation properties. In addition, placing more than two piezoelectrics along the length of the thin composite plate gives the potential to increase actuation properties and change the motion from oscillatory to undullatory. These motions can again be increased by utilizing the natural vibration modes of the thin composite plate with piezoelectrics near resonance actuation. The current research is involved with modeling a piezoelectric actuated marine propulsion fin using the Galerkin finite element technique. An experimental proof of concept was developed to compare results. Using fluid-structure interaction (FSI) methods, it is proposed that the fluid and structure programs are resolved within one program. This is in contrast to traditional attempts at FSI problems that utilize a computational fluid dynamics (CFD) solver transferring load data between a structural dynamics/finite element (FE) program

Development of unsteady aerodynamic analyses for turbomachinery aeroelastic and aeroacoustic applications

Theoretical analyses and computer codes are being developed for predicting compressible unsteady inviscid and viscous flows through blade rows. Such analyses are needed to determine the impact of unsteady flow phenomena on the structural durability and noise generation characteristics of turbomachinery blading. Emphasis is being placed on developing analyses based on asymptotic representations of unsteady flow phenomena. Thus, flow driven by small-amplitude unsteady excitations in which viscous effects are concentrated in thin layers are being considered. The resulting analyses should apply in many practical situations, lead to a better understanding of the relevent physics, and they will be efficient computationally, and therefore, appropriate for aeroelastic and aeroacoustic design applications. Under the present phase (Task 3), the effort was focused on providing inviscid and viscid prediction capabilities for subsonic unsteady cascade flows