Unsteady flow separation represents a highly complex and important area of study within fluid mechanics. The extent of separation and specific time scales over which it occurs are not fully understood and has significant consequences in numerous industrial applications such as helicopters, jet engines, hydroelectric turbines and wind turbines. A direct consequence of unsteady separation is the erratic movement of the separation point which causes highly dynamic and unpredictable loads on an airfoil. Current computational models underestimate the aerodynamic loads due to the inaccurate prediction of the emergence and severity of unsteady flow separation especially in response to a sudden change in the effective angle of attack. To capture the complex flow phenomena over wind turbine blades during stall development, a scaled three-dimensional non-rotating blade model is designed to be dynamically similar to a rotating full-scale NREL 5MW wind turbine blade. A time-resolved particle image velocimetry (PIV) investigation of flow behavior during the stall cycle examines the processes of stall development and flow reattachment. The flow fields are examined through the application of Eulerian techniques such as proper orthogonal decomposition and empirical mode decomposition to capture unsteady separation characteristics within the flow field. Then, for a higher order description, coherent structures such as vortices and material lines are resolved to fully characterize the flow during a full pitching cycle in a Lagrangian framework. The Eulerian and Lagrangian methods described in the present analysis is extended to investigate the spanwise characteristics within the root section of a three dimensional airfoil. Furthermore, statistical information of the separation point is pursued along four spanwise positions during two cases of unsteady separation. The results of the study describe a critical role of surface vorticity accumulation in unsteady separation and reattachment. Evaluation of the unsteady characteristics of the shear layer reveal evidence that the build-up and shedding of surface vorticity directly influence the dynamic changes in separation point. The quantitative characterization of surface vorticity and shear layer stability enables improved aerodynamic design, but also has broader implications on the larger discipline of unsteady fluid dynamics.

After nearly 50 years of development, Computational Fluid Dynamics (CFD) has become an indispensable component of research, forecasting, design, prototyping and testing for a very broad spectrum of fields including geophysics, and most engineering fields (mechanical, aerospace, biomedical, chemical and civil engineering). The fastest and most affordable CFD approach, called Reynolds-Average-Navier-Stokes (RANS) can predict the drag around a car in just a few minutes of simulation. This feat is possible thanks to simplifying assumptions, semi-empirical models and empirical models that render the flow governing equations solvable at low computational costs. The fidelity of RANS model is good to excellent for the prediction of flow rate in pipes or ducts, drag, and lift of solid objects in Newtonian flows (e.g. air, water). RANS solutions for the prediction of scalar (e.g. temperature, pollutants, combustable chemical species) transport do not generally achieve the same level of fidelity. The main culprit is an assumption, called Reynolds analogy, which assumes analogy between the transport of momentum and scalar. This assumption is found to be somewhat valid in simple flows but fails for flows in complex geometries and/or in complex fluids. This research explores optimization methods to improve upon existing RANS models for scalar transport. Using high fidelity direct numerical simulations (numerical solutions in time and space of the exact transport equations), the most common RANS model is a-priori tested and investigated for the transport of temperature (as a passive scalar) in a turbulent channel flow. This one constant model is then modified to improve the prediction of the temperature distribution profile and the wall heat flux. The resulting modifications provide insights in the model’s missing physics and opens new areas of investigation for the improvement of the modeling of turbulent scalar transport.

A volume-filtered Large-Eddy Simulation (LES) of oscillatory flow over a rippled mobile bed is conducted using an Euler-Lagrange approach. As in unsteady marine flows over sedimentary beds, the experimental data, referenced in this work for validation, shows quasi-steady state ripples in the sand bed under oscillatory flow. This work approximately reproduces this configuration with a sinusoidal pressure gradient driven flow and a sinusoidally rippled bed of particles. The LES equations, which are volume-filtered to account for the effect of the particles, are solved on an Eulerian grid, and the particles are tracked in a Lagrangian framework. In the Discrete Particle Method (DPM) used in this work, the particle collisions are handled by a soft-sphere model, and the liquid and solid phases are coupled through volume fraction and momentum exchange terms. Comparison of the numerical results to the experimental data show that the LES-DPM is capable of capturing the mesoscale features of the flow. The large scale shedding of vortices from the ripple peaks are observed in both datasets, which is reflected in the good quantitative agreement between the wall-normal flow statistics, and good qualitative agreement in ripple shape evolution. Additionally, the numerical data provides three insights into the complex interaction between the three-dimensional flow dynamics and bed morphology: (1) there is no observable distinction between reptating and saltating particle velocities, angular velocities or observed Shields parameters; (2) the potential motion of the mobile bed may create issues in the estimation of the bed shear stress used in classical models; and, (3) a helical pairing of vortices is observed, heretofore not known to have to have been identified in this type of flow configuration.

Combustion instability (CI) has been persistent in all forms of propulsion since their inception. CI is characterized by pressure oscillations within the propulsion system. If even a small fraction of the dense energy within the system is converted to acoustic oscillations the system vibrations can be devastating. The coupling of combustion and fluid dynamic phenomena in a nonlinear system poses CI as a significant engineering challenge. Drawing from previous analysis, second order acoustic energy models are taken to third order. Second order analysis predicts exponential growth. The addition of the third order terms capture the nonlinear acoustic phenomena (such as wave steepening) observed in experiments. The analytical framework is derived such that the energy sources and sinks are properly accounted for. The resulting third order solution is compared against a newly performed simplified acoustic closed tube experiment. This experiment provides the interesting result that in a forced system, as the 2nd harmonic is driven, no energy is transferred back into the 1st mode. The subsequent steepened waveform is a summation of 2nd mode harmonics (2, 4, 6, 8...) where all odd modes are nonexistent. The current third order acoustic model recreates the physics as seen in the experiment. Numerical experiments show the sensitivity of the pressure wave limit cycle amplitude to the second order growth rate, highlighting the importance of correctly calculating the growth rates. The sensitivity of the solution to the third order parameter is shown as well. Exponential growth is found if the third order parameter is removed, and increased nonlinear behavior is found if it retained and as it is increased. The solutions sensitivity to this term highlights its importance and shows the need for continued analysis via increasing the models generality by including neglected effects. In addition, the affect of a time varying second order growth rate is shown. This effect shows the importance of modeling the system in time because of the time lag between changes in the growth rate to a change in the limit cycle amplitude.

Combustion instability is a problem that has plagued the development of rocket-propelled devices since their conception. It is characterized by the occurrence of high-frequency nonlinear gas oscillations inside the combustion chamber. This phenomenon degrades system performance and can result in damage to both structure and instrumentation. The goal of this dissertation is to clarify the role of unsteady combustion in the combustor instability problem by providing the first quantified estimates of its effect upon the stability of liquid rocket engines. The combination of this research with a new system energy balance method, accounting for all dynamic interactions within a system, allows for the isolation of combustion effects for this study. These effects are quantified through use of classical linear stability analysis to calculate the unsteady combustion heat release growth rate. Since combustion modeling can become very involved, including the mixing process and multiple reactions concerned, for this initial evaluation the model is limited to a one-dimensional flame analysis for a one-step premixed chemical reaction. Using classical analysis of oscillatory burning, the governing combustion equations are expanded into sets of steady and unsteady equations adapted for premixed liquid rockets. From this expansion process, the first real treatment of the effects of unsteady combustion in a rocket system is presented, and the first quantified values of the unsteady heat release in a rocket system are computed. Finally, the corresponding linear heat release growth rate for the system is then calculated for the first quantified effects of unsteady combustion on the overall system stability. The mechanism of unsteady combustion is shown to behave as a driving mechanism, serving as one of the more important stability mechanisms comparable to the magnitude of the nozzle damping mechanism. This analysis confirms that unsteady combustion is an important stability mechanism that warrants further investigation. This study also creates a firm foundation upon which to extend the analysis of this important mechanism to fully understand all of its effects within a rocket system.

State of the art research in hydrodynamic stability analysis has moved from classic one-dimensional methods such as the local nonparallel approach and the parabolized stability equations to two-dimensional, biglobal, methods. The paradigm shift toward two dimensional techniques with the ability to accommodate fully three-dimensional base flows is a necessary step toward modeling complex, multidimensional flowfields in modern propulsive applications. Here, we employ a two-dimensional spatial waveform with sinusoidal temporal dependence to reduce the three-dimensional linearized Navier-Stokes equations to their biglobal form. Addressing hydrodynamic stability in this way circumvents the restrictive parallel-flow assumption and admits boundary conditions in the streamwise direction. Furthermore, the following work employs a full momentum formulation, rather than the reduced streamfunction form, accounting for a nonzero tangential mean flow velocity. This approach adds significant complexity in both formulation and implementation but renders a more general methodology applicable to a broader spectrum of mean flows. Specifically, we consider the stability of three models for bidirectional vortex flow. While a complete parametric study ensues, the stabilizing effect of the swirl velocity is evident as the injection parameter, kappa, is closely examined.

Various methods have been used, including airborne radars, LIDAR, observation of flying birds, towers, tethered balloons, and aircraft to gain both a qualitative and quantitative representation of how heat and moisture are transported to higher altitudes and grow the boundary or mixing layer by thermal updrafts. This paper builds upon that research using an instrumented glider to determine the structure and build a mathematical model of thermals in a desert environment. During these flights, it was discovered that the traditional view of a thermal as a singular rising plume of air did not sufficiently explain what was being observed, but rather another phenomenon was occurring. This paper puts forth the argument and a mathematical model to show that thermals actually take the form of a hexagonal convection cell at higher levels in the convective boundary layer when the thermal acts as if unrestrained by borders as in non-linear cases of free convection.

The purpose of this study is to investigate the execution and validity of various predictive methods used in the design of the aerodynamic pod housing NASA’s Marshall Airborne Polarimetric Imaging Radiometer (MAPIR) on the University of Tennessee Space Institute’s Piper Navajo research aircraft. Potential flow theory and wing theory are both used to analytically predict the lift the MAPIR Pod would generate during flight; skin friction theory, empirical data, and induced drag theory are utilized to analytically predict the pod’s drag. Furthermore, a simplified computational fluid dynamics (CFD) model was also created to approximate the aerodynamic forces acting on the pod. A limited flight test regime was executed to collect data on the actual aerodynamic effects of the MAPIR Pod. Comparison of the various aerodynamic predictions with the experimental results shows that the assumptions made for the analytic and CFD analyses are too simplistic; as a result, the predictions are not valid. These methods are not proven to be inherently flawed, however, and suggestions for future uses and improvements are thus offered.

A numerical analysis was conducted to study the effects of geometrically scaling scramjet inlet-combustor isolators. Three-dimensional fully viscous numerical simulation of the flow inside constant area rectangular ducts, with a downstream back pressure condition, was analyzed using the SolidWorks Flow Simulation software. The baseline, or 1X, isolator configuration has a 1” x 2.67” cross section and 20” length. This baseline configuration was scaled up based on the 1X configuration mass flow to 10X and 100X configurations, with ten and one hundred times the mass flow rate, respectively. The isolator aspect ratio of 2.67 was held constant for all configurations. To provide for code validation, the Flow Simulation program was first used to analyze a converging-diverging channel and a wind tunnel nozzle. The channel case was compared with analytical theory and showed good agreement. The nozzle case was compared with AFRL experimental data and showed good agreement with the entrance and exit conditions (Pi0= 40 psia, Ti0= 530ºR, Pe= 18.86 psia, Te= 456ºR, respectively). While the boundary layer thickness remained constant, the boundary layer thickness with respect to the isolator height decreased as the scale increased. For all the isolator simulations, a shock train was expected to form inside the duct. However, the flow simulation failed to generate this flow pattern, due to improper sizing of the isolator and combustor for a 3-D model or having a low pressure ratio of 2.38. Instead, a single normal shock wave was established at the same relative location within the length of each duct, approximately 80% of the duct length from the isolator entrance. The shape of the shock changed as the scale increased from a normal shock wave, to a bifurcated shock wave, and to a normal shock train, respectively for the 1X, 10X, and 100X models.

A computer model of a blow-down free-jet hypersonic propulsion test facility exists to validate facility control systems as well as predict problems with facility operation. One weakness in this computer model is the modeling of an air ejector diffuser system. Two examples of facilities that could use this ejector diffuser model are NASA Langley Research Center's 8-ft High Temp. Tunnel (HTT) and the Aero-Propulsion Test Unit (APTU) located at Arnold Engineering Development Center. Modeling an air ejector diffuser system for a hypersonic propulsion test facility includes modeling three coupled systems. These are the ejector system, the primary free-jet nozzle that entrains secondary airflow from the test cell, and the test article. Both of these facilities are capable of testing scramjets/ramjets at high Mach numbers. Compared with computer simulation data, experimental test cell pressure data do not agree due to the current modeling technique used. An improved computer model was derived that incorporates new techniques for modeling the ejector diffuser. This includes real gas effects at the ejector nozzles, flow constriction due to free-jet nozzle and ejector plumes, test article effects, and a correction factor of the normal shock pressure ratio in a supersonic diffuser. A method was developed to account for the drag and thrust terms of the test article by assuming a blockage factor and using a drag coefficient*Area term for both the test article and thrust stand derived from experimental data. An ideal ramjet model was also incorporated to account for the gross thrust of the test article on the system. The new ejector diffuser model developed improved the accuracy and fidelity of the facility model as compared with experimental test data while only negligibly affecting computational speed. Comparisons of the model data with experimental test data showed a close match for test cell pressure (within 1 percent for final test cell pressure). The model accurately simulated both the unstarted and started modes of ejector flow, in which test cell pressure increases with nozzle total pressure once in started mode.