Session ER: CFD: Discrete Methods

Simulation Approach for Microscale Noncontinuum Gas-Phase Heat Transfer

In microscale thermal actuators, gas-phase heat transfer from the heated beams to the adjacent unheated substrate is often the main energy-loss mechanism. Since the beam-substrate gap is comparable to the molecular mean free path, noncontinuum gas effects are important. A simulation approach is presented in which gas-phase heat transfer is described by Fourier's law in the bulk gas and by a wall boundary condition that equates the normal heat flux to the product of the gas-solid temperature difference and a heat transfer coefficient. The dimensionless parameters in this heat transfer coefficient are determined by comparison to Direct Simulation Monte Carlo (DSMC) results for heat transfer from beams of rectangular cross section to the substrate at free-molecular to near-continuum gas pressures. This simulation approach produces reasonably accurate gas-phase heat-transfer results for wide ranges of beam geometries and gas pressures. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.   

Stochastic Particle Advection in Hybrid Large Eddy Simulation/Filtered Density Function Methods

We describe an efficient combination of interpolation and stochastic time integration schemes for the advection of computational particles in Large Eddy Simulation/Filtered Density Function (LES/FDF) methods. In this setting, particle positions evolve by a standard diffusion process whose drift and diffusion coefficients are determined from flow properties which are known in the form of face- and cell-average values. We demonstrate that a stochastic time integration scheme, developed by Cao and Pope in 2003, yields second-order accurate values of the particle position density function, provided that the interpolation schemes used reconstruct the diffusion and drift terms with second-order accuracy, and their first derivatives with first-order accuracy. Here, we present a velocity interpolation scheme, called the Polar Parabolic Edge Reconstruction Method (PPERM), and a scalar interpolation scheme, called the Multilinear Gradients Method (MLG), which satisfy these requirements, and we compare the performance of the Cao {\&} Pope SDE integration scheme with that of a weak second-order accurate derivative-free scheme proposed by Tocino and Vigo-Aguiar in 2002.   

Simulation of the Dynamics of Bubble Rising in viscous fluid using Lattice Boltzmann Equation Method

A stable Lattice Boltzmann Equation (LBE) Model based on the Cahn-Hilliard diffuse interface approach is presented for simulation of incompressible two-phase flows having large density and viscosity ratios. This model utilizes two particle distribution functions which recover the evolution of composition, pressure and momentum. This model is validated by analyzing the dynamics of a single rising gas bubble in viscous fluid. Terminal shape and Reynolds number (Re) are interactive quantities that depend on size of bubble, surface tension, viscosity and density of surrounding fluid. Accurate simulation of terminal shape and Re are obtained for different regimes. The regimes achieved were spherical, ellipsoidal, skirted and spherical cap. These were successfully achieved by systematically changing the values of Morton number (Mo) and Bond number (Bo) within the following ranges (10$^{-12} \quad <$ Mo $<$ 10$^{6})$ and (1 $<$ Bo $<$ 10$^{3})$. Re and final bubble shape for each regime could be satisfactorily predicted and simulated since they are also function of Morton and Bond number. Re results are compared with previous simulation and experimental results.   

3D Phase-Field Simulations of Interfacial Dynamics in Viscoelastic Fluids with Adaptive Meshing

We have developed a diffuse-interface algorithm for computing two-component interfacial flows of Newtonian and non-Newtonian fluids in 3D. An adaptive meshing scheme produces fine grid near the interface and coarse mesh in the bulk, and leads to accurate resolution of the interface at moderate computational cost. Another advantage of the method is that there is no need for manual intervention during topological changes of the interface such as rupture and coalescence. However, the fully implicit time-stepping results in a large matrix system for complex 3D flows, with high demands for memory and CPU speed. As validating examples, we discuss a drop spreading on a partially wetting substrate and drop deformation in Newtonian and viscoelastic fluids. The results show very good agreement with those from the literature and our own 2D axisymmetric simulations.   

Lattice Boltzmann simulation of dynamics of plunge and pitch of 3D flexible wing

The method of lattice Boltzmann (LB) simulation has been used to simulate fluid structures and motion of a flexible insect wing in a 3D space. In the method, a beam has been discretized into a chain of rigid segments. Each segment is connected through ball and socket joints at its ends. One segment may be bent and twisted with its neighboring segment. A constraint force is applied to each joint to ensure the solid structure moving as a whole flexible elastic body.We have demonstrated that the LB method is suitable for modeling of aerodynamics of insects flight at low Reynolds numbers. First, a simulation of plunging and pitching of a rigid wing is performed at $Re=75$ in a 2D space and the results of lift forces and flow structures are in excellent agreement with the previous results. Second, plunging and pitching of a flexible wing in span-wise direction is simulated at $Re=136$ in a 3D space. We found that when twisting elasticity is large enough the twisting angle could be controlled at a level of smaller than 0.2 degree. It is shown that as bending and twisting elasticity is large enough, the motion of flexible wing approaches that of a rigid membrane wing. The simulation results show that the optimization of flexibility in span-wise direction will benefit thrust and an intermediate level is favorable. The results are consistent with experimental finding.   

Numerical Simulation of a Droplet Bouncing on a Soap Film

We present a numerical method to simulate the interaction of a droplet with a soap film. Our numerical method uses two level set functions to track respectively the droplet and the soap film. The Navier-Stokes equations are solved in 3D using finite differences and a projection method. The proper jump and boundary conditions are enforced in a sharp (sub-grid) manner to maintain accuracy in the zone where both interfaces are close. We validated our approach by reproducing experiments performed by Gilet and Bush at MIT. We will show the ability of the method to reproduce bouncing, break-through, and partial break-through and conclude with some future applications.   

Direct Numerical Simulations of Turbulent Flows over Superhydrophobic Surfaces

Direct numerical simulations are used to investigate the drag reducing performance of superhydrophobic surfaces in turbulent channel flow. Slip velocities, wall shear stresses, and Reynolds stresses are considered for a variety of superhydrophobic surface micro-feature geometry configurations at a friction Reynolds number of Re$_{\tau }$ = 180. For the largest micro-feature spacing of 90$\mu $m an average slip velocity over 75{\%} of the bulk velocity is obtained, and the wall shear stress reduction is nearly found to be nearly 40{\%}. The simulation results suggest that the mean velocity profile near the superhydrophobic wall continues to scale with the wall shear stress, but is offset by a slip velocity that increases with increasing micro-feature spacing.   

Eigenvalue Analysis for Error Dynamics of Measurement Integrated Simulation to Reproduce Real Flows

A measurement-integrated simulation (MI simulation) is a numerical simulation with a feedback loop to compensate the difference between the simulation and real phenomena in a condition of different boundary/initial condition. The origin of this methodology is the observer in the control theory. Although the validity of MI simulation has been proved in several applications, such as an ultrasonic measurement integrated simulation of blood flow or hybrid wind tunnel to reproduce Karman vortex street, a theory of MI simulation has not been established yet. As a fundamental consideration to construct a general theory of MI simulation, we formulated the linearized error dynamics equation to express time development of the error between the simulation and the real flow, and its eigenvalue analysis. The validity of the method was investigated for the problem of the low-order model problem of the turbulent flow in a square duct. The result of numerical experiment of MI simulation was well predicted by a result of eigenvalue analysis proving the validity of the eigenvalue analysis of liearaized error dynamics in evaluating the effectiveness of MI simulation.   

Adaptive Moment-of-Fluid Method for Multi-Material Flow

A novel adaptive mesh refinement (AMR) strategy based on Moment-of-fluid (MOF) method for volume-tracking evolving interface computation is presented. Moment-of-fluid method is a new interface reconstruction and volume advection method using volume fraction as well as material centroid. Using the AMR-MOF method, the accuracy of volume-tracking computation with evolving interfaces is improved significantly compared to other published results. The effectiveness and efficiency of AMR-MOF method is demonstrated with classical test problems, such as Zalesak's disk and reversible vortex problem. The comparison with previously published results for these problems shows the superior accuracy of the AMR-MOF method over other methods. In addition, two new test cases with severe deformation rates are introduced, namely droplet deformation and $\mathcal{S}$-shape deformation problems, for further demonstrating the capabilities of the AMR-MOF method. Extensions to multi-material ($n_{mat}>2$) and compressible flow cases will also be addressed.