A trajectory piecewise-linear (TPWL) approach is developed for a computational fluid dynamics (CFD) model of the two-dimensional Euler equations. The approach uses a weighted combination of linearized models to represent the nonlinear CFD system. The proper orthogonal decomposition (POD) is then used to create a reduced-space basis, onto which the TPWL model is projected. This projection yields an efficient reduced-order model of the nonlinear system, which does not require the evaluation of any full-order system residuals. The method is applied to the case of flow through an actively controlled supersonic diffuser. With an appropriate choice of linearization points and POD basis vectors, the method is found to yield accurate results, including cases with significant shock motion. / Singapore-MIT Alliance (SMA)

The airflow field and particle trajectories inside hard disk drive (HDD) are investigated in this study using commercial software Fluent and Gambit. Three-dimensional grids inside the HDD configuration are built using Gambit taking into account all the components and their geometric details. The airflow field inside HDD is simulated using three incompressible Navier-Stokes equations for various disk rotational speeds. The effects of using the various turbulence models inside the Fluent software such as the standard k - ε , RNG k - ε and Reynolds Stress Method on the computed airflow characteristics are also assessed. Steady flow fields and the effects of rotational speeds are assessed. Based on the computed steady airflow patterns, particle trajectories are computed using routines available in Fluent as well as special particle trajectory functions defined by the user via the user-defined functions. Particles of different sizes and materials are injected at various locations in the computed flow field and the corresponding particle trajectories are studied. Based on the investigation, the trajectory tends to be different according to sizes and materials. The present work forms a basis for further investigation of heat transfer processes inside the HDD to address thermal management issues and also the computation of unsteady flow fields in the HDD due to the movement of the actuator arm during data storage and retrieval / Singapore-MIT Alliance (SMA)

This work is focused on a state-of-the-art tubular micro-solid oxide fuel cell (TSOFC), ~3 millimeters in diameter and ~300 microns thick, with Ni/YSZ and LSM/YSZ composite electrodes and a YSZ electrolyte. A 2D axi-symmetric, multi-scale CFD model is developed which includes the fluid flow, mass transfer, and heat transfer within the gas channels and the porous electrodes. The electrochemical reactions are modeled within the volume of the electrodes, enabling the model to account for the extent of the reaction zone. Thermodynamic expressions are developed to estimate the single-electrode reversible heat generation and the single-electrode electromotive force of a non-isothermal electrochemical cell. The isothermal, non-isothermal, and transient models are each validated against the experimental results, and consistent with the physical reality of the TSOFC. A novel approach is used to estimate the kinetic parameters, enabling the simulations to be used as a diagnostic tool. The model is used to gain a thorough insight about the TSOFC. The cathode electrochemical activity and the anode support ohmic loss are identified as the two major performance bottlenecks for this cell. Including radiation is found to be essential for a physically meaningful heat transfer model. The thermoelectric effects on the cell overall electromotive force is found to be negligible. It is found that the anode reaction is always endothermic, while the cathode reaction is always exothermic, and that the temperature gradients across the cell layers are less than 0.05C The cell transient response is found to be fast, and dominated by the thermal transients. Several physical properties used in the model are measured experimentally, indicating that that the correlations used in the literature are not always suitable, especially when new fabrication techniques are used. The conductivity of the anode support was measured to be several orders of magnitude lower than expected and very sensitive to temperature, which explains the lower than expected and occasionally degrading cell performance. A hypothesis is proposed to explain this phenomenon based on the thermal expansion effects which result in the formation and disruption of particle to particle contacts within the composite electrode. / Chemical Engineering

We present methods for incorporating bubbles into a photorealistc fluid simulation. Previous methods of fluid simulation in computer graphics do not include bubbles. Our system automatically creates bubbles, which are simulated on top of the fluid simulation. These bubbles are approximated by spheres and are rendered with the fluid to appear as one continuous surface. This enhances the overall realism of the appearance of a splashing fluid for computer graphics. Our methods leverage the particle level set representation of the fluid surface. We create bubbles from escaped marker particles from the outside to the inside. These marker particles might represent air that has been trapped within the fluid surface. Further, we detect when air is trapped in the fluid and create bubbles within this space. This gives the impression that the air pocket has become bubbles and is an inexpensive way to simulate the air trapped in air pockets. The results of the simulation are rendered with a raytracer that includes caustics. This allows the creation of photorealistic images. These images support our position that the simple addition of bubbles included in a fluid simulation creates results that are much more true to life.

This thesis describes a method for using physically based techniques to model an explosion and the resulting side effects. Explosions are some of the most visually exciting phenomena known to humankind and have become nearly ubiquitous in action films. A realistic computer simulation of this powerful event would be cheaper, quicker, and much less complicated than safely creating the real thing. The immense energy released by a detonation creates a discontinuous localized increase in pressure and temperature. Physicists and engineers have shown that the dissipation of this concentration of energy, which creates all the visible effects, adheres closely to the compressible Navier-Stokes equation. This program models the most noticeable of these results. In order to simulate the pressure and temperature changes in the environment, a three dimensional grid is placed throughout the area around the detonation and a discretized version of the Navier-Stokes equation is applied to the resulting voxels. Objects in the scene are represented as rigid bodies that are animated by the forces created by varying pressure on their hulls. Fireballs, perhaps the most awe-inspiring side effects of an explosion, are simulated using massless particles that flow out from the center of the blast and follow the currents created by the dissipating pressure. The results can then be brought into Maya for evaluation and tweaking.

Conventional one-point turbulence closures have beenextended with an additional transported scalar for modeling ofmagnetohydrodynamic (MHD) turbulence. The new scalar, α ,captures the length scale anisotropy and tendency towardstwo-dimensionality, which is characteristic feature of MHDturbulence, and allows accurate modeling of the Jouledissipation of turbulence. The concept has been used for both afull Reynolds stress closure, and a three-equationK-ε -αmodel. An exact transport equation forαwas derived from the governing equations. All terms inthe equation require modeling, however. The proposed modeltransport equation for α includes terms for magneticdissipation, nonlinear energy transfer, and effects of meanshear and strain. Modeling of the magnetic and strain-relatedterms was based on rapid distortion analysis of the linearizedequations, while modeling of nonlinear effects isphenomenological in nature. For homogeneous turbulence, themodel was compared with linear theory, direct numericalsimulations and experiments. For turbulence subjected to astrong magnetic field, the model reproduces the energy andlength scale evolution predicted by linear theory. Whennonlinear effects are of importance, it predicts energy decayand length scale evolution in agreement with experiments. Theeddy viscosity and Reynolds stress versions of the modelcoincide with the respective conventional models in the absenceof a magnetic field. The objective of this project has been todevelop efficient MHD turbulence models for engineeringapplications, especially for modeling of continuous steelcasting. The novel MHD turbulence models appear to benumerically robust, and they have been implemented in acommercial flow solver, together with electromagnetic equationsfor the Lorentz forces in the mean momentum equations. <b>Keywords:</b>Turbulence model, magnetohydrodynamics, MHD,magnetohydrodynamic turbulence, computational fluid dynamics,continuous casting, dimensionality, Reynolds stresses, eddyviscosity

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In this thesis a set of boundary conditions for multiphase flow is suggested. Characteristic-based boundary conditions are reviewed for single-phase flow. The problem of open-boundary conditions is investigated, and to avoid drifting values, the use of control functions is proposed. The use of control functions is also verified with a new test which assesses the quality of the boundary conditions. Particularly, P- and PI-control functions are examined. PI-controllers have the ability to specify a given variable exactly at the outlet as well as at the inlet, without causing spurious reflections which are amplified. Averaged multiphase flow equations are reviewed, and a simplified model is established. This model is used for the boundary analysis and the computations. Due to the averaging procedure, signal speeds are reduced to the order of the flow speed. This leads to numerical challenges. For a horizontal channel flow, a splitting of the interface pressure model is suggested. This bypasses the numerical problems associated with separation by gravity, and a physical realistic model is used. In this case, the inviscid model is shown to possess complex eigenvalues, and still the characteristic boundary conditions give reasonable results. The governing equations are solved with a Runge-Kutta scheme for the time integration. For the spatial discretisation, a finite-volume and a finite-difference method are used. Both implementations give equivalent results. In single-phase flow, the results improve significantly when a numerical filter is applied. For two-dimensional two-phase flow, the computations are unstable without a numerical filter.

In this thesis, the effects of split canard on the aerodynamic characteristics of missiles at high angles of attack are numerically investigated. Moreover, an enhanced semi-empirical engineering-level method is developed for prediction of normal force and pitching moment of split canard mounted missiles. In order to analyze the effects of split canard, a generic test case model is created by mounting a split canard to a generic test case model, NASA Dual Control Missile (NDCM), which was previously modeled and analyzed for the validation of CFD modeling. After obtaining a generic missile model with split canard, the effects of split canard on the aerodynamic characteristics of this missile in case of no control, pitch control, yaw control, and roll control deflections are numerically investigated. It is seen that the split canard decreases the local angle of attack of existing canard, increases the normal force and the maneuverability of the missile, and reduces the induced rolling moment at high angles of attack. Five different aerodynamic design parameters are determined for split canard and the effects of each parameter on missile aerodynamics are numerically investigated. It is seen that the roll orientation, deflection angle, size of the split canards have strong effects on missile&rsquo / s aerodynamic performance whereas longitudinal position of the split canards only affects the pitching moment of the missile. Finally, an enhanced semi-empirical engineering-level method, CFD-CBU, is developed for split canard mounted missiles in order to predict the normal force and the pitching moment coefficients. The developed method is validated with NDCM test case model. After this validation, the method is applied to the split canard mounted generic missile in case of no control deflection and pitch control deflection. The results of this method are compared with CFD results and it is seen that the results are in good agreement with each other.

This work presents a number of the practical aspects of developing reduced- order models (ROMs) based on proper orthogonal decomposition (POD). ROMS are derived and implemented for multiphase flow, quasi-2D nozzle flow and 2D inviscid channel flow. Results are presented verifying the ROMs against existing full-order models (FOM). POD is a method for separating snapshots of a flow field that varies in both time and space into spatial basis functions and time coefficients. The partial differential equations that govern fluid flow can then be pro jected onto these basis functions, generating a system of ordinary differential equations where the unknowns are the time coefficients. This results in the reduction of the number of equations to be solved from hundreds of thousands or more to hundreds or less. A ROM is implemented for three-dimensional and non-isothermal multiphase flows. The derivation of the ROM is presented. Results are compared against the FOM and show that the ROM agrees with the FOM. While implementing the ROM for multiphase flow, moving discontinuities were found to be a ma jor challenge when they appeared in the void fraction around gas bubbles. A point-mode POD approach is proposed and shown to have promise. A simple test case for moving discontinuities, the first order wave equation, is used to test an augmentation method for capturing the discontinuity exactly. This approach is shown to remove the unphysical oscillations that appear around the discontinuityin traditional approaches. A ROM for quasi-2D inviscid nozzle flow is constructed and the results are com- pared to a FOM. This ROM is used to test two approaches, POD-Analytical and POD-Discretized. The stability of each approach is assessed and the results are used in the implementation of a ROM for the Navier-Stokes equations. A ROM for a Navier-Stokes solver is derived and implemented using the results of the nozzle flow case. Results are compared to the FOM for channel flow with a bump. The computational speed-up of the ROM is discussed. Two studies are presented with practical aspects of the implementation of POD- based ROMs. The first shows the effect of the snapshot sampling on the accuracy of the POD basis functions. The second shows that for multiphase flow, the cross- coupling between field variables should not be included when computing the POD basis functions.