Flow separation is a common fluid dynamics phenomenon that occurs within supersonic nozzles while operating at off-design pressures. Typically, off-design pressures result in a shock formation that leads to a non-uniformity of the exiting flow and creates flow separation and flow recirculation. So far, no effective solution has been presented to eliminate flow separation and increase the total performance of the nozzle. The purpose of this work is to investigate whether a Gurney flap may beneficially affect the exiting flow pattern. For a better understanding of the Gurney flap effect, this investigation used a supersonic nozzle geometry based on a previous study by Lechevalier [33]. Results from the tested cases showed a poor effect of the flap at high free-stream Mach number and lower pressure ratio. Simulations of different flap heights along with different parameters showed a slight increase of thrust.

Previous experimental and numerical studies showed that two-dimensional roughness elements can stabilize disturbances inside a hypersonic boundary layer, and eventually delay the transition onset. The objective of the thesis is to evaluate the response of disturbances propagating inside a hypersonic boundary layer to various two-dimensional surface deformations of different shapes. The proposed deformations consist of a backward step, forward step, a combination of backward and forward steps, two types of wavy surfaces, surface dips or surface humps. Disturbances inside of a Mach 5.92 flat-plate boundary layer are excited by pulsed or periodic wall blowing and suction at an upstream location. The numerical tools consist of the Navier-Stokes equations in curvilinear coordinates and a linear stability analysis tool. Results show that all types of surface deformations are able to reduce the amplitude of boundary layer disturbances to a certain degree. The amount of reduction in the disturbance energy is related to the type of pressure gradient created by the deformation, adverse or favorable.

Condensing ejectors utilize the beneficial thermodynamics of condensation to produce an exiting static pressure that can be in excess of either entering static pressure. The phase change process is driven by both turbulent mixing and interphase heat transfer. Semi-empirical models can be used in conjunction with computational fluid dynamics (CFD) to gain some understanding of how condensing ejectors should be designed and operated. The current work describes the construction of a multidimensional simulation capability built around an Eulerian pseudo-fluid approach. The transport equations for mass and momentum treat the two phases as a continuous mixture. The fluid is treated as being in a non-thermodynamic equilibrium state, and a modified form of the homogenous relaxation model (HRM) is employed. This model was originally intended for representing flash-boiling, but with suitable modification, the same ideas could be used for condensing flow. The computational fluid dynamics code is constructed using the open-source OpenFOAM library. Fluid properties are evaluated using the REFPROP database from NIST, which includes many common fluids and refrigerants. The working fluids used are water and carbon dioxide. For ejector flow, simulations using carbon dioxide are more stable than with water. Using carbon dioxide as the working fluid, the results of the validation simulations show a pressure rise that is comparable to experimental data. It is also observed that the flow is near thermodynamic equilibrium in the diffuser for these cases, suggesting that turbulence effects present the greatest challenge in modeling these ejectors.

I samband med det globala samhällets ökande populationsmängd och ekonomiska utveckling ökar färskvattenkonsumtionen och mängden avloppsvatten som produceras. Avloppsvatten behöver renas innan det släpps ut för att inte påverka miljön negativt. En av de vanligaste vattenreningsteknikerna är aerob biologisk rening, för vilken bottenluftningen – då luftbubblor trycks ut genom diffusörer i botten på reningsreaktorn för att syresätta avloppsvattnet – är den mest energikrävande processen. Syretransportshastigheten från luftbubblorna till avloppsvattnet påverkas negativt av närvaron av surfaktanter, vilket är en vanligt förekommande förorening både i kommunala och industriella avloppsvatten.  För att säkerställa en tillräcklig reningsgrad så energieffektivt som möjligt krävs förståelse för syretransporten i bottenluftningssystem, och vid dimensionering av nya system och kalibrering av existerande system behövs verktyg som kan underlätta för förutsägandet av syretransportshastigheten. Syftet med studien var att utveckla ett numeriskt verktyg för att uppskatta syretransportshastigheten vid bottenluftning i labbskalesystem och bidra till kunskapsbasen beträffande syresättningen i surfaktantlösningar. Det primära målet var at ta fram en CFD-modell kopplat med en masstransportsmodell som kan förutsäga syretransportshastigheten i bubbelkolumner med rent vatten, och det sekundära målet var att använda modellen för vatten innehållande surfaktanten laurinsyra (DDA) och identifiera alternativ för vidareutveckling av modellen så att den även kan hantera surfaktantlösningar. Modellen byggdes i COMSOL Multiphysics 5.5 och inkluderade en tvådimensionell axisymmetrisk geometri, URANS-ekvationer och standard k-ε för turbulenshantering och en Euler-Euler mixture-modell för tvåfasmodelleringen. Masstransportsteorierna två-filmsteorin, Higbies penetrationsteori samt advektions-diffusionsekvationen användes för att modellera syretransporten. Bubbeldiametern är en viktig parameter i flera ekvationer och för att uppskatta en representativ genomsnittlig diameter för bubbelstorleksfördelningen beräknades Sauter Mean Diameter baserat på experimentella data för olika kombinationer av luftflöden och DDA-koncentration. Resultaten från simuleringarna angående syretransportshastigheten i rent vatten visades stämma väl överens med experimentella data vid låga luftflöden, där skillnaden för den volymetriska masstransportskoefficienten var 0,7 % och 3,3 % för luftflödena 0,1 respektive 0,2 l/min. Vid luftflödet 0,3 l/min var skillnaden 14 %; eftersom strömningsregimen blir mer heterogen vid högre luftflöden tenderar modellen att överskatta syretransportshastigheten. I vatten innehållande surfaktanter överskattade modellen syretransportshastigheten eftersom adsorptionen av surfaktanter på bubbelytorna – och tillhörande minskning av masstransports-koefficienten – inte modellerades. Antingen behöver en korrektionsfaktor för masstransportskoefficienten – baserad på skillnaden mellan simulerade resultat och experimentella data – tas fram och tillämpas, eller så behöver den bakomliggande teorin för beräkning av syretransporten omprövas. Eventuellt skulle masstransporten av surfaktanter och adsorptionen på bubbelytorna kunna modelleras för att mer precist efterlikna verkligheten. / In connection with a global population increase and economic development, the consumption of freshwater and the production of wastewater is increasing. Wastewater needs to be treated to convert it into an effluent that can be safely released without negative environmental impacts. One of the most common wastewater treatment technologies is aerobic biological treatment, where bottom aeration – the procedure of pumping air through submerged diffusers which generate bubbles to oxygenate the wastewater – is the most energy demanding process. The oxygen transfer rate from air bubbles to wastewater is negatively affected by the presence of surfactants, a ubiquitous contaminant in both municipal and industrial wastewaters. To assure a sufficient treatment efficiency as energy efficiently as possible, an understanding of the oxygen transfer process in bottom aeration systems is necessary, and for designing of new systems and calibration of existing ones, tools facilitating prediction of the oxygen transfer rate are required. The purpose of this study was to develop a numerical tool to estimate the oxygen transfer rate for lab-scale bottom aeration systems and to contribute to the basis of knowledge regarding oxygenation of surfactant solutions. The primary goal of the study was to develop a CFD-model coupled with a mass transfer model to predict the oxygen transfer rate in bubble columns containing clean water, and the secondary goal was to apply the model to water-based solutions of the surfactant lauric acid (DDA) and identify options for further development of the model to make it applicable for surfactant solution systems. The model was developed with COMSOL Multiphysics 5.5 and included a two-dimensional axisymmetric geometry, URANS-equations and standard k-ε to for turbulence modelling, and an Euler-Euler mixture model for the two-phase flow. For oxygen transfer modelling the two-film theory, Higbies penetration theory and the advection-diffusion equation were used. Bubble diameter is an important parameter in several of the equations used and the Sauter Mean Diameter was calculated to represent the average bubble diameter, based on available experimental data for different combinations of air flow rate and DDA-concentration. Results of the simulations regarding the oxygen transfer rate in clean water fit well with experimental data at lower air flow rates, and the difference for the volumetric mass transfer coefficient was 0,7 % and 3,3 % for the air flow rates 0,1 l/min and 0,2 l/min, respectively. For the air flow rate 0,3 l/min the difference was 14 %; because of the flow regime being more heterogenous at higher air flow rates, the model tends to overestimate the oxygen transfer rate. In surfactant solutions the model overestimated the oxygen transfer rate due to surfactant adsorption on the bubble-water interface – and the consequent decrease of the mass transfer coefficient – not being modelled. Either a correction factor for the mass transfer coefficient – based on the difference between simulated results and experimental data – needs to be calculated and applied, or the underlying theories describing the oxygen transfer require revision. Potentially the mass transfer and interfacial adsorption of surfactants could be modelled to emulate reality more accurately.

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.

The Goldschmied Propulsor is a concept that was introduced in mid 1950's by Fabio Goldschmied. The concept combines boundary layer suction and boundary layer ingestion technologies to reduce drag and increase propulsor efficiency. The most recent testing, done in 1982, left questions concerning the validity of the results. To answer these questions a 38.5in Goldschmied Propulsor was constructed and tested in Cal Poly's 3x4ft wind tunnel. The focus of their wind tunnel investigation was to replicate Goldschmied's original testing and increase the knowledge base on the subject. The goal of this research was to create a computational fluid dynamics (CFD) model to help visualize the flow phenomenon and see how well CFD was able to replicate Cal Poly’s wind tunnel results. CFD cases were run to get a comparison of the computational model and the wind tunnel results. For the straight tunnel geometry for the 0.385” slot and cusp A we found a body, pressure and friction drag, fan off CD of 0.0526 and a fan on at 500 Pascals with a CD of 0.0545. This is similar to the wind tunnel results but because of large errors in measuring overall drag we are not able to directly compare to the wind tunnel results. Overall we see that the trends match, mainly that the fan does not decrease the total pressure drag. This was a result of poor geometry and high fan speeds needed for attachment. The tested geometry is less than ideal and has a long way to go before it is of a shape that would have the potential to reduce the pressure drag as much as Goldschmied claimed. Future efforts should be put forth optimizing the aft body to reduce the low pressure in front of the slot and improving aft entrance of the slot to allow for a smoother flow.

The performance of a vapor compression system is known to be affected by the ingestion of liquid droplets in the compressor. In these multiphase flows, the liquid and the vapor phase are tightly coupled. Therefore the interphase heat, mass and momentum transfer as well as droplet dynamics including droplet breakup and droplet-wall interactions play a vital role in governing these flows. Only thermodynamic analyses or two-dimensional mean-line calculations are not sufficient to gain an in-depth understanding of the complex multiphase flow field within the compressor. The objective of this research was to extend the current understanding of the operation of a multistage centrifugal compressor under two-phase flow conditions, by performing three-dimensional computational analysis. In this work, two-phase flow of a single constituent (refrigerant R134a) through a two-stage, in-line centrifugal compressor was analyzed using CFD. The CFD model accounted for real gas behavior of the vapor phase. Novel user defined routines were implemented to ensure accurate calculations of interphase heat, mass and momentum transfer terms and to model droplet impact on the compressor surfaces. An erosion model was developed and implemented to locate the erosion "hot spots" and to estimate the amount of material eroded. To understand the effects of increasing liquid carryover, the mass flow rate of the liquid phase was increased from 1% to 5% of the vapor mass flow rate. The influence of droplet size on the compressor performance was assessed by varying the droplet diameter at the inlet from 100 microns to 400 microns. The results of the two-phase flow simulations were compared with the simulation involving only the vapor phase. Liquid carryover altered the flow field within the compressor, and as a result, both impellers were observed to operate at off-design conditions. This effect was more pronounced for the second impeller. The overall effects of liquid carryover were detrimental to the compressor performance. The erosion calculations showed maximum erosion potential on the blade and shroud of the first impeller. The results from this investigation provided new and useful information that can be used to support improved design solutions. / Ph. D.

An accurate and efficient numerical method for Compressible Vorticity Confinement (CVC) was developed. The methodology follows from Steinhoff's vorticity confinement approach that was developed for incompressible flows. In this research, the extension of this approach to compressible flows has been developed by adding a vorticity confinement term as a "body force" into the governing compressible flow equations. This vorticity confinement term tends to cancel the numerical dissipative errors inherently related to the numerical discretization in regions of strong vorticity gradients. The accuracy, reliability, efficiency and robustness of this method were investigated using two methods. One approach is directly applying the CVC method to several real engineering problems involving complex vortex structures and assessing the accuracy by comparison with existing experimental data and with other computational techniques. Examples considered include supersonic conical flows over delta wings, shock-bubble and shock-vortex interactions, the turbulent flow around a square cylinder and the turbulent flow past a surface-mounted 3D cube in a channel floor. A second approach for evaluating the effectiveness of the CVC method is by solving simplified "model problems" and comparing with exact solutions. Problems that we have considered are a two-dimensional supersonic shear layer, flow over a flat plate and a two-dimensional vortex moving in a uniform stream. The effectiveness of the compressible confinement method for flows with shock waves and vortices was evaluated on several complex flow applications. The supersonic flow over a delta wing at high angle of attack produces a leeward vortex separated from the wing and cross flow, as well as bow shock waves. The vorticity confinement solutions compare very favorably with experimental data and with other calculations performed on dense, locally refined grids. Other cases evaluated include isolated shock-bubble and shock-vortex interactions. The resulting complex, unsteady flow structures compare very favorably with experimental data and computations using higher-order methods and highly adaptive meshes. Two cases involving massive flow separation were considered. First the two-dimensional flow over a square cylinder was considered. The CVC method was applied to this problem using the confinement term added to the inviscid formulation, but with the no-slip condition enforced. This produced an unsteady separated flow that agreed well with experimental data and existing LES and RANS calculations. The next case described is the flow over a cubic protuberance on the floor of a channel. This flow field has a very complex flow structure involving a horseshoe vortex, a primary separation vortex and secondary corner vortices. The computational flow structures and velocity profiles were in good agreement with time-averaged values of the experimental data and with LES simulations, even though the confinement approach utilized more than a factor of 50 fewer cells (about 20,000 compared to over 1 million). In order to better understand the applicability and limitations of the vorticity confinement, particularly the compressible formulation, we have considered several simple model problems. Classical accuracy has been evaluated using a supersonic shear layer problem computed on several grids and over a range of values of confinement parameter. The flow over a flat plate was utilized to study how vorticity confinement can serve as a crude turbulent boundary layer model. Then we utilized numerical experiments with a single vortex in order to evaluate a number of consistency issues related to the numerical implementation of compressible confinement. / Ph. D.

A CFD model to simulate two-phase flow in refrigerant ejectors is described. This work is part of an effort to develop the ejector expansion refrigeration cycle, a device which increases performance of a standard vapor compression cycle by replacing the throttling valve with a work-producing ejector. Experimental results have confirmed the performance benefit of the ejector cycle, but significant improvement can be obtained by optimally designing the ejector. The poorly understood two-phase, non-equilibrium flow occuring in the ejector complicates this task. The CFD code is based on a parabolic two-fluid model. The applicable two-phase flow conservation equations are presented. Also described are the interfacial interaction terms, important in modelling non-equilibrium effects. Other features of the code, such as a mixing length turbulence model and wall function approximation, are discussed. Discretization of the equations by the control volume method and organization of the computer program is described. Code results are shown and compared to experimental data. It is shown that experimental pressure rise through the mixing section matches well against code results. Variable parameters in the code, such as droplet diameter and turbulence constants, are shown to have a large influence on the results. Results are shown in which an unexpected problem, separation in the mixing section, occurs. Also described is the distribution of liquid across the mixing section, which matches qualitative experimental observations. From these results, conclusions regarding ejector design and two-phase CFD modelling are drawn. / Ph. D.

Computational Fluid Dynamics (CFD) has been widely used as a tool to analyze physical phenomena involving fluids. To perform a CFD simulation, the governing equations are discretized to formulate a set of nonlinear algebraic equations. Typical spatial discretization schemes include finite-difference methods, finite-volume methods, and finite-element methods. Error introduced in the discretization process is called discretization error and defined as the difference between the exact solution to the discrete equations and the exact solution to the partial differential or integral equations. For most CFD simulations, discretization error accounts for the largest portion of the numerical error in the simulation. Discretization error has a complicated nonlinear relationship with the computational grid and the discretization scheme, which makes it especially difficult to estimate. Thus, it is important to study the discretization error to characterize numerical errors in a CFD simulation. Discretization error estimation is performed using the Error Transport Equations (ETE) in this work. The original nonlinear form of the ETE can be linearized to formulate the linearized ETE. Results of the two types of the ETE are compared. This work implements the ETE for finite-volume methods and Discontinuous Galerkin (DG) finite-element methods. For finite volume methods, discretization error estimates are obtained for both steady state problems and unsteady problems. The work on steady-state problems focuses on turbulent flow modelled by the Spalart-Allmaras (SA) model and Menter's $k-omega$ SST model. Higher-order discretization error estimates are obtained for both the mean variables and the turbulence working variables. The type of pseudo temporal discretization used for the steady-state problems does not have too much influence on the final converged solution. However, the temporal discretization scheme makes a significant difference for unsteady problems. Different temporal discretizations also impact the ETE implementation. This work discusses the implementation of the ETE for the 2-step Backward Difference Formula (BDF2) and the Singly Diagonally Implicit Runge-Kutta (SDIRK) methods. Most existing work on the ETE focuses on finite-volume methods. This work also extends ETE to work with the DG methods and tests the implementation with steady state inviscid test cases. The discretization error estimates for smooth test cases achieve the expected order of accuracy. When the test case is non-smooth, the truncation error estimation scheme fails to generate an accurate truncation error estimate. This causes a reduction of the discretization error estimate to first-order accuracy. Discussions are made on how accurate truncation error estimates can be found for non-smooth test cases. / Doctor of Philosophy / For a general practical fluid flow problem, the governing equations can not be solved analytically. Computational Fluid Dynamics (CFD) approximates the governing equations by a set of algebraic equations that can be solved directly by the computer. Compared to experiments, CFD has certain advantages. The cost for running a CFD simulation is typically much lower than performing an experiment. Changing the conditions and geometry is usually easier for a CFD simulation than for an experiment. A CFD simulation can obtain information of the entire flow field for all field variables, which is nearly impossible for a single experiment setup. However, numerical errors are inherently persistent in CFD simulations due to the approximations made in CFD and finite precision arithmetic of the computer. Without proper characterization of errors, the accuracy of the CFD simulation can not be guaranteed. Numerical errors can even result in false flow features in the CFD solution. Thus, numerical errors need to be carefully studied so that the CFD simulation can provide useful information for the chosen application. The focus of this work is on numerical error estimation for the finite-volume method and the Discontinuous Galerkin (DG) finite-element method. In general, discretization error makes the most significant contribution to the numerical error of a CFD simulation. This work estimates discretization error by solving a set of auxiliary equations derived for the discretization error of a CFD solution. Accurate discretization error estimates are obtained for different test cases. The work on the finite-volume method focus on discretization error estimation for steady state turbulent test cases and unsteady test cases. To the best of the author's knowledge, the implementation of the current discretization error estimation scheme has only been applied as an intermediate step for the error estimation of functionals for the DG method in the literature. Results for steady-state inviscid test cases for the DG method are presented.