DIRECT NUMERICAL SIMULATION OF INCOMPRESSIBLE MULTIPHASE FLOW WITH PHASE CHANGE

Phase change problems arise in many practical applications such as air-conditioning and refrigeration, thermal energy storage systems and thermal management of electronic devices. The physical phenomenon in such applications are complex and are often difficult to be studied in detail with the help of only experimental techniques. The efforts to improve computational techniques for analyzing two-phase flow problems with phase change are therefore gaining momentum. The development of numerical methods for multiphase flow has been motivated generally by the need to account more accurately for (a) large topological changes such as phase breakup and merging, (b) sharp representation of the interface and its discontinuous properties and (c) accurate and mass conserving motion of the interface. In addition to these considerations, numerical simulation of multiphase flow with phase change introduces additional challenges related to discontinuities in the velocity and the temperature fields. Moreover, the velocity field is no longer divergence free. For phase change problems, the focus of developmental efforts has thus been on numerically attaining a proper conservation of energy across the interface in addition to the accurate treatment of fluxes of mass and momentum conservation as well as the associated interface advection. Among the initial efforts related to the simulation of bubble growth in film boiling applications the work in \cite{Welch1995} was based on the interface tracking method using a moving unstructured mesh. That study considered moderate interfacial deformations. A similar problem was subsequently studied using moving, boundary fitted grids \cite{Son1997}, again for regimes of relatively small topological changes. A hybrid interface tracking method with a moving interface grid overlapping a static Eulerian grid was developed \cite{Juric1998} for the computation of a range of phase change problems including, three-dimensional film boiling \cite{esmaeeli2004computations}, multimode two-dimensional pool boiling \cite{Esmaeeli2004} and film boiling on horizontal cylinders \cite{Esmaeeli2004a}. The handling of interface merging and pinch off however remains a challenge with methods that explicitly track the interface. As large topological changes are crucial for phase change problems, attention has turned in recent years to front capturing methods utilizing implicit interfaces that are more effective in treating complex interface deformations. The VOF (Volume of Fluid) method was adopted in \cite{Welch2000} to simulate the one-dimensional Stefan problem and the two-dimensional film boiling problem. The approach employed a specific model for mass transfer across the interface involving a mass source term within cells containing the interface. This VOF based approach was further coupled with the level set method in \cite{Son1998}, employing a smeared-out Heaviside function to avoid the numerical instability related to the source term. The coupled level set, volume of fluid method and the diffused interface approach was used for film boiling with water and R134a at the near critical pressure condition \cite{Tomar2005}. The effect of superheat and saturation pressure on the frequency of bubble formation were analyzed with this approach. The work in \cite{Gibou2007} used the ghost fluid and the level set methods for phase change simulations. A similar approach was adopted in \cite{Son2008} to study various boiling problems including three-dimensional film boiling on a horizontal cylinder, nucleate boiling in microcavity \cite{lee2010numerical} and flow boiling in a finned microchannel \cite{lee2012direct}. The work in \cite{tanguy2007level} also used the ghost fluid method and proposed an improved algorithm based on enforcing continuity and divergence-free condition for the extended velocity field. The work in \cite{sato2013sharp} employed a multiphase model based on volume fraction with interface sharpening scheme and derived a phase change model based on local interface area and mass flux. Among the front capturing methods, sharp interface methods have been found to be particularly effective both for implementing sharp jumps and for resolving the interfacial velocity field. However, sharp velocity jumps render the solution susceptible to erroneous oscillations in pressure and also lead to spurious interface velocities. To implement phase change, the work in \cite{Hardt2008} employed point mass source terms derived from a physical basis for the evaporating mass flux. To avoid numerical instability, the authors smeared the mass source by solving a pseudo time-step diffusion equation. This measure however led to mass conservation issues due to non-symmetric integration over the distributed mass source region. The problem of spurious pressure oscillations related to point mass sources was also investigated by \cite{Schlottke2008}. Although their method is based on the VOF, the large pressure peaks associated with sharp mass source was observed to be similar to that for the interface tracking method. Such spurious fluctuation in pressure are essentially undesirable because the effect is globally transmitted in incompressible flow. Hence, the pressure field formation due to phase change need to be implemented with greater accuracy than is reported in current literature. The accuracy of interface advection in the presence of interfacial mass flux (mass flux conservation) has been discussed in \cite{tanguy2007level,tanguy2014benchmarks}. The authors found that the method of extending one phase velocity to entire domain suggested by Nguyen et al. in \cite{nguyen2001boundary} suffers from a lack of mass flux conservation when the density difference is high. To improve the solution, the authors impose a divergence-free condition for the extended velocity field by solving a constant coefficient Poisson equation. The approach has shown good results with enclosed bubble or droplet but is not general for more complex flow and requires additional solution of the linear system of equations. In current thesis, an improved approach that addresses both the numerical oscillation of pressure and the spurious interface velocity field is presented by featuring (i) continuous velocity and density fields within a thin interfacial region and (ii) temporal velocity correction steps to avoid unphysical pressure source term. Also I propose a general (iii) mass flux projection correction for improved mass flux conservation. The pressure and the temperature gradient jump condition are treated sharply. A series of one-dimensional and two-dimensional problems are solved to verify the performance of the new algorithm. Two-dimensional and cylindrical film boiling problems are also demonstrated and show good qualitative agreement with the experimental observations and heat transfer correlations. Finally, a study on Taylor bubble flow with heat transfer and phase change in a small vertical tube in axisymmetric coordinates is carried out using the new multiphase, phase change method.

Ionospheric Turbulence Near the Upper Hybrid Layer: Theory and Experiment

The thesis presents experimental results, simulations, and theory on turbulence excited in magnetized plasmas near the ionosphere’s upper hybrid layer. The results include: The first experimental observations of super small striations (SSS) excited by the High-Frequency Auroral Research Project (HAARP) The first detection of high-frequency (HF) waves from the HAARP transmitter over a distance of 16x10^3 km The first simulations indicating that upper hybrid (UH) turbulence excites electron Bernstein waves associated with all nearby gyroharmonics Simulation results that indicate that the resulting bulk electron heating near the upper hybrid (UH) resonance is caused primarily by electron Bernstein waves parametrically excited near the first gyroharmonic. On the experimental side we present two sets of experiments performed at the HAARP heating facility in Alaska. In the first set of experiments, we present the first detection of super-small (cm scale) striations (SSS) at the HAARP facility. We detected density structures smaller than 30 cm for the first time through a combination of satellite and ground based measurements. In the second set of experiments, we present the results of a novel diagnostic implemented by the Ukrainian Antarctic Station (UAS) in Verdansky. The technique allowed the detection of the HAARP signal at a distance of nearly 16 Mm, and established that the HAARP signal was injected into the ionospheric waveguide by direct scattering off of dekameter-scale density structures induced by the heater. On the theoretical side, we present results of Vlasov simulations near the upper hybrid layer. These results are consistent with the bulk heating required by previous work on the theory of the formation of descending artificial ionospheric layers (DIALs), and with the new observations of DIALs at HAARP’s upgraded effective radiated power (ERP). The simulations that frequency sweeps, and demonstrate that the heating changes from a bulk heating between gyroharmonics, to a tail acceleration as the pump frequency is swept through the fourth gyroharmonic. These simulations are in good agreement with experiments. We also incorporate test particle simulations that isolate the effects of specific wave modes on heating, and we find important contributions from both electron Bernstein waves and upper hybrid waves, the former of which have not yet been detected by experiments, and have not been previously explored as a driver of heating. In presenting these results, we analyzed data from HAARP diagnostics and assisted in planning the second round of experiments. We integrated the data into a picture of experiments that demonstrated the detection of SSS, hysteresis effects in simulated electromagnetic emission (SEE) features, and the direct scattering of the HF pump into the ionospheric waveguide. We performed simulations and analyzed simulation data to build the understanding of collisionless heating near the upper hybrid layer, and we used these simulations to show that bulk electron heating at the upper hybrid layer is possible, which is required by current theories of DAIL formation. We wrote a test particle simulation to isolate the effects of electron Bernstein waves and upper hybrid layers on collisionless heating, and integrated this code to work with both the output of Vlasov simulations and the input for simulations of DAIL formation.

Slot Film Cooling: A Comprehensive Experimental Characterization

When components of a propulsion system are exposed to elevated flow temperatures there is a risk for catastrophic failure if the components are not properly protected from the thermal loads. Among several strategies, slot film cooling is one of the most commonly used, yet poorly understood active cooling techniques. Tangential injection of a relatively cool fluid layer protects the surface(s) in question, but the turbulent mixing between the hot mainstream and cooler film along with the presence of the wall presents an inherently complex problem where kinematics, thermal transport and multimodal heat transfer are coupled. Furthermore, new propulsion designs rely heavily on CFD analysis to verify their viability. These CFD models require validation of their results, and the current literature does not provide a comprehensive data set for film cooling that meets all the demands for proper validation, namely a comprehensive (kinematic, thermal and boundary condition data) data set obtained over a wide range of conditions. This body of work aims at solving the fundamental issue of validation by providing high quality comprehensive film cooling data (kinematics, thermal mixing, heat transfer). 3 distinct velocity ratios (VR=uc/u∞) are examined corresponding to wall-wake (VR~0.5), min-shear (VR ~ 1.0), and wall-jet (VR~2.0) type flows at injection, while the temperature ratio TR= T∞/Tc is approximately 1.5 for all cases. Turbulence intensities at injection are 2-4% for the mainstream (urms/u∞, vrms/u∞,), and on the order of 8-10% for the coolant (urms/uc, vrms/uc,). A special emphasis is placed on inlet characterization, since inlet data in the literature is often incomplete or is of relatively low quality for CFD development. The data reveals that min-shear injection provides the best performance, followed by the wall-jet. The wall-wake case is comparably poor in performance. The comprehensive data suggests that this relative performance is due to the mixing strength of each case, as well as the location of regions of strong mixing with respect to the wall. Kinematic and thermal data show that strong mixing occurs in the wall-jet away from the wall (y/s>1), while strong mixing in the wall-wake occurs much closer to the wall (y/s<1). Min-shear cases exhibit noticeably weaker mixing confined to about y/s=1. Additionally to these general observations, the experimental data obtained in this work is analyzed to reveal scaling laws for the inlets, near-wall scaling, detecting and characterizing coherent structures in the flow as well as to provide data reduction strategies for comparison to CFD models (RANS and LES).