https://hdl.handle.net/1721.1/50867 2026-04-08T23:42:43Z 2026-04-08T23:42:43Z Vermeersch, Sabine https://hdl.handle.net/1721.1/70578 2019-04-10T19:15:36Z 1992-10-01T00:00:00Z

Investigation of the F117A Vortical Flow Characteristics Preliminary Results Vermeersch, Sabine The investigation of the vortical flow around the F117A Stealth Fighter is presented in order to demonstrate the capability to resolve leading edge vortices with an adaptive finite element solver for the Euler equations. The major goal is to capture vortex breakdown at high angles of attack. This work presents the five main steps involved in a typical study of the flow characteristics of a complete aircraft : the definition of the model geometry, the realization of a suitable grid around the discretized model, the implementation of a flow solver, the subsequent analysis of the flow field and the comparison to experimental data sets. The computational data are compared to the lift curves of the aircraft obtained in a subsonic 5' x 7' wind tunnel. The occurance and location of vortex breakdown is determined by performing flow visualization in the tunnel. Five cases are computed for this work. Each case is studied at Mach 0.3 and angles of attack range between 7 and 30 degrees.

1992-10-01T00:00:00Z Modiano, David https://hdl.handle.net/1721.1/70577 2019-04-12T20:59:34Z 1993-01-01T00:00:00Z

Adaptive Mesh Euler Equation Computations of Vortex Breakdown in Delta Wing Flow Modiano, David A solution method for the three-dimensional Euler equations is formulated and implemented. The solver uses an unstructured mesh of tetrahedral cells and performs adaptive refinement by mesh-point embedding to increase mesh resolution in regions of interesting flow features. The fourth-difference artificial dissipation is increased to a higher order of accuracy using the method of Holmes and Connell. A new method of temporal integration is developed to accelerate the explicit computation of unsteady flows. The solver is applied to the solution of the flow around a sharp edged delta wing, with emphasis on the behavior of the leading edge vortex above the leeside of the wing at high angle of attack, under which conditions the vortex suffers from vortex breakdown. Large deviations in entropy, which indicate vortical regions of the flow, specify the region in which adaptation is performed. Adaptive flow calculations are performed at ten different angles of attack, at seven of which vortex breakdown occurs. The aerodynamic normal force coefficients show excellent agreement with wind tunnel data measured by Jarrah, which demonstrates the importance of adaptation in obtaining an accurate solution. The pitching moment coefficient and the location of vortex breakdown are compared with experimental data measured by Hummel and Srinivasan, with which fairly good agreement is seen in cases in which the location of breakdown is over the wing. A series of unsteady calculations involving a pitching delta wing were performed. The use of the acceleration technique is validated. A hysteresis in the normal force is observed, as in experiments, and a lag in the breakdown position is demonstrated.

1993-01-01T00:00:00Z Rathnasingham, Ruben https://hdl.handle.net/1721.1/70576 2019-04-09T15:55:16Z 1997-06-01T00:00:00Z

System Identification and Active Control of a Turbulent Boundary Layer Rathnasingham, Ruben An experimental investigation is made into the active control of the near-wall region of a turbulent boundary layer using a linear control scheme. System identification in the boundary layer provides optimal transfer functions that predict the downstream of characteristics of the streamwise velocity and wall pressure fluctuation using an array of upstream flush-mounted sensors that are sensitive to spanwise shear. Enhanced direction techniques isolated the large scale turbulent motion and improved the downstream correlations resulting in greater controllability. The techniques were based on the conditioned spectral analysis between adjacent sensors to extract the most correlated flow structures that span the distance between them. The control is applied using a spanwise array of resonant actuators that introduce a pair of streamwise vortices into the flow. Control experiments were carried out for a single and multiple input/output configurations. The single output results show that a maximum reduction of 34% is achieved in the streamwise velocity fluctuation. This reduction is greatest at the point of optimization but spans over a few hundred viscous lengths downstream of the actuator and about 50 viscous lengths in the spanwise and wall-normal directions. The wall pressure fluctuation and the mean wall shear stress (measured approximately using mean velocity profiles near the wall) was reduced by 17% and 7% respectively. The multiple-input/single-output configuration resulted in a wider spatial influence of the control while maintaining the maximum reductions in the fluctuations. The multiple-input/multiple-output configuration showed a marked increase in the spatial extent of the control (primarily in the spanwise direction), at the expense of a lower reduction in the fluctuations (maximum of 30% and 15% for the streamwise velocity and wall pressure respectively). The bursting frequency was computed from a VITA algorithm applied to the streamwise velocity fluctuation. The bursting frequency was reduced at all threshold levels examined but the maximum reduction of 23% occurred at a threshold level of 3. The spanwise spatial correlation was measured at different streamwise locations downstream of the actuator array. This result suggests that the reduction in turbulent fluctuations obtained using the current control scheme was achieved by reducing the strength of the most coherent flow structures and to inhibit their ability to interact with each other by increasing their average spanwise separation by more than 25% (from ~ 90l* to 120l*).

1997-06-01T00:00:00Z Lindquist, Dana Rae https://hdl.handle.net/1721.1/70569 2019-04-12T20:59:33Z 1988-05-01T00:00:00Z

A Comparison of Numerical Schemes on Triangular and Quadrilateral Models Lindquist, Dana Rae

1988-05-01T00:00:00Z Lee, Kuok Ming https://hdl.handle.net/1721.1/70568 2019-04-09T16:14:16Z 1989-10-01T00:00:00Z

Numerical Simulation of Hypersonic Flow Over a Blunt Leading Edge Delta Wing Lee, Kuok Ming Euler and Navier-Stokes results are presented for a blunt delta wing at Mach 7.15 and 300 angle of attack. The viscous calculations were done at a Reynolds number based on chord of 5.85 x 106 with freestream and wall temperatures set to 74K and 288K respectively. The inviscid simulations were carried out using a finite volume, central difference code written by Roberts [21] and Goodsell [7]. The Navier-Stokes results were obtained on the semi-implicit extension of the inviscid code, developed by Loyd [17]. The inviscid results showed a strong shock on the windward side of the wing at a stand-off angle of about -5' from the body. As the flow traverses around the leading edge it accelerates strongly through an expansion fan. On the upper surface of the wing, separation occurs at about 60% span resulting in a region of reverse cross stream flow. The viscous calculations display a similar shock structure. Furthermore the boundary layer on the windward side is thin and variations in the circumferential direction are small. The flow on the leeward side of the wing separates in 2 places. The primary separation occurs just inside of the leading edge, and the secondary separation region is located further inboard. The inviscid CL and CD are 0.547 and 0.383 respectively, whereas the viscous values are 0.547 and 0.386. The viscous component contributes only an insignificant 2.32 x 10- S to the CD of the Navier-Stokes calculations.

1989-10-01T00:00:00Z Loyd, Bernard https://hdl.handle.net/1721.1/70567 2019-04-12T20:59:32Z 1989-02-01T00:00:00Z

A Semi-Implicit Navier-Stokes Solver and Its Application to a Study of Separated Flow about Blunt Delta Wings Loyd, Bernard A novel semi-implicit scheme for the Navier-Stokes equations is presented and evaluated. The semi-implicit scheme combines an implicit temporal integration in the bodynormal directions with explicit temporal integrations in the streamwise and cross stream directions. Thus, advantages of both explicit and implicit schemes are retained in the semi-implicit scheme. Numerical stiffness due to disparate physical scales in the normal direction is eliminated, since stability of the algorithm depends only on relatively coarse streamwise and cross stream grid spacing, not on the typically fine normal spacing. Approximate factorization is unnecessary and only one matrix inversion per multi-stage time step is required. Computations show that while a explicit scheme employing multigrid and residual smoothing and a fully implicit scheme are competitive for inviscid calculations, the semi-implicit scheme is superior for viscous flow calculations. Efficiency of the semi-implicit scheme is exploited in a study of flow separation around delta wings with blunt leading edges. Three-dimensional laminar vortical flows over two 65* swept semi-infinite elliptical wings of thickness to chord ratio 1 : 11.55 and 1 : 20 at Moo = 1.6, ReL = 106, and angles of attack of 40, and 8*, and a 60* swept elliptical wing with t/c = 1 : 11.55 at Moo = 1.4, ReL = 2 x 106 and a = 14* are considered. In these flow cases, separation line locations are fixed not by a particular geometric factor (eg. sharp leading edge), but by interaction of physical and geometric factors. Solutions with the semi-implicit scheme are shown to be significantly more efficient than solutions with a corresponding explicit scheme. Two distinct leading edge separation processes are identified: separation due to shock-less flow recompression leeward of the leading edge expansion in the t/c = 11.55, a = 40 case and separation involving a leading edge shock in the remaining cases.

1989-02-01T00:00:00Z https://hdl.handle.net/1721.1/70467 2019-04-10T13:24:33Z 1989-05-01T00:00:00Z

Visualization of Three Dimensional CFD Results We have developed an interactive graphics system for the display of three dimensional CFD solutions on unstructured hexahedral grids. This system is implemented on a high-performance graphics supercomputer. Visualization methods employed are shaded color surface plots, integration of particle trajectories, interpolation of volumetric data onto a plane, interpolation of planar data onto a line segment, and extraction of numerical quantities from a plane. We have used this graphics system to examine the inviscid flow about the NTF delta wing, as solved by Becker, and found that it allows us to locate flow features quickly. We were unable to find a satisfactory method to visualize the three dimensional mesh structure. With the exception of particle path integration, the algorithms we have implemented can be used to visualize any volumetric data.

1989-05-01T00:00:00Z Yano, Masayuki Darmofal, David L. https://hdl.handle.net/1721.1/66941 2019-04-12T15:00:29Z 2011-09-21T00:00:00Z

On Dual-Weighted Residual Error Estimates for p-Dependent Discretizations Yano, Masayuki; Darmofal, David L. This report analyzes the behavior of three variants of the dual-weighted residual (DWR) error estimates applied to the p-dependent discretization that results from the BR2 discretization of a second-order PDE. Three error estimates are assessed using two metrics: local effectivities and global effectivity. A priori error analysis is carried out to study the convergence behavior of the local and global effectivities of the three estimates. Numerical results verify the a priori error analysis.

2011-09-21T00:00:00Z Willcox, Karen Peraire, Jaime White, Jacob https://hdl.handle.net/1721.1/57612 2019-04-13T00:05:20Z 1999-01-01T00:00:00Z

An Arnoldi Approach for Generation of Reduced Order Models for Turbomachinery Willcox, Karen; Peraire, Jaime; White, Jacob A linear reduced-order aerodynamic model is developed for aeroelastic analysis of turbo-machines. The basis vectors are constructed using a block Arnoldi method. Although the model is cast in the time domain in state-space form, the spatial periodicity of the problem is exploited in the frequency domain to obtain these vectors efficiently. The frequency domain proper orthogonal decomposition is identified as a special case of the Arnoldi method. The aerodynamic model is coupled with a simple structural model that has two degrees of freedom for each blade. The technique is applicable to viscous and three-dimensional problems as well as multi-stage problems with inlet and exit disturbance flows, although here results are presented for two-dimensional, inviscid flow through a twenty-blade single-stage rotor. In this case, the number of states of the model is on the order of ten per blade passage, making it appropriate for control applications.

1999-01-01T00:00:00Z Arkilic, Errol B. https://hdl.handle.net/1721.1/57611 2019-04-10T10:25:06Z 1997-01-01T00:00:00Z

Measurement of the Mass Flow and Tangential Momentum Accommodation Coefficient in Silicon Micromachined Channels Arkilic, Errol B. An analytic and experimental investigation into gaseous flow with slight rarefaction through long microchannels is undertaken in an attempt to obtain values of the Tangential Momentum Accommodation Coefficient (TMAC) for a common MicroElectroMechanical Systems (MEMS) surface. A set of analytic expressions is developed from the slip- flow solutions of the Navier Stokes equations which can be used to interpret the results of flow in micromachined channels and to extract TMAC values from these results. In addition to the theoretical framework, a robust microchannel fabrication procedure and a dedicated high-resolution mass flow measurement technique is developed. These are used in conjunction to obtain TMAC values for single-crystal silicon upon which a native oxide resides for gas flows of argon, nitrogen and carbon dioxide. It is shown that the TMAC for this common MEMS surface can possess a value less than unity (0.75-0.85) for the conditions which are expected to be encountered with state-of-the-art MEMS.

1997-01-01T00:00:00Z Yano, Masayuki https://hdl.handle.net/1721.1/57610 2019-04-10T10:25:23Z 2009-06-01T00:00:00Z

Massively Parallel Solver for the High-Order Galerkin Least-Squares Method Yano, Masayuki A high-order Galerkin Least-Squares (GLS) finite element discretization is combined with massively parallel implicit solvers. The stabilization parameter of the GLS discretization is modified to improve the resolution characteristics and the condition number for the high-order interpolation. The Balancing Domain Decomposition by Constraints (BDDC) algorithm is applied to the linear systems arising from the two-dimensional, high-order discretization of the Poisson equation, the advectiondiffusion equation, and the Euler equation. The Robin-Robin interface condition is extended to the Euler equation using the entropy-symmetrized variables. The BDDC method maintains scalability for the high-order discretization for the diffusiondominated flows. The Robin-Robin interface condition improves the performance of the method significantly for the advection-diffusion equation and the Euler equation. The BDDC method based on the inexact local solvers with incomplete factorization maintains the scalability of the exact counterpart with a proper reordering.

2009-06-01T00:00:00Z Mohnot, Anshul https://hdl.handle.net/1721.1/57609 2019-04-13T00:05:31Z 2008-05-01T00:00:00Z

Solution of Fluid-Structure Interaction Problems using a Discontinuous Galerkin Technique Mohnot, Anshul The present work aims to address the problem of fluid-structure interaction using a discontinuous Galerkin approach. Starting from the Navier-Stokes equations on a fixed domain, an arbitrary Lagrangian Eulerian (ALE) approach is used to derive the equations for the deforming domain. A geometric conservation law (GCL) is then introduced, which guarantees freestream preservation of the numerical scheme. The space discretization is performed using a discontinuous Galerkin method and time integration is performed using either an explicit four stage Runge-Kutta scheme or an implicit BDF2 scheme. The mapping parameters for the ALE formulation are then obtained using algorithms based on radial basis functions (RBF) or linear elasticity. These strategies are robust and can be applied to bodies with arbitrary shapes and undergoing arbitrary motions. The robustnesss and accuracy of the ALE scheme coupled with these mapping strategies is then demonstrated by solving some model problems. The ability of the scheme to handle complex flow problems is demonstrated by analyzing the low Reynolds number flow over an oscillating circular cylinder.

2008-05-01T00:00:00Z Stirling, Leia Abigail https://hdl.handle.net/1721.1/57608 2019-04-13T00:05:32Z 2008-06-01T00:00:00Z

Development of Astronaut Reorientation Methods: A Computational and Experimental Study Stirling, Leia Abigail Past spaceflight missions have shown that astronauts adapt their motor-control strategies to the microgravity environment. Even though astronauts undergo hundreds of training hours, the strategies for locomotion and orientation are not specifically prescribed. The majority of an astronaut’s motion-control strategies are developed underwater. While underwater training can be beneficial in certain aspects, such as learning which orientations an astronaut will encounter and becoming familiar with task timelines, it is not effective for self-learned motor-control strategies. Further, the development of unfamiliar tasks, such as reorienting without external forces, will most likely not occur naturally. Self-rotations—human-body rotations without external torques—are not only helpful for reducing adaptation time, but can be a crucial safety countermeasure during extravehicular activity. In this thesis, computational and experimental methods are developed to create and analyze astronaut reorientation methods. The computational development of control methods for human motion planning offers a novel way to provide astronauts with maneuvers that are difficult to obtain experimentally in Earth gravity (1-G). Control of human-body dynamics can be posed as a motion-planning problem for which many different solution methods exist. This research considers two different frameworks—quantized control and optimal control. The quantized control method permits the development of complete maneuvers that are appropriate for humans to perform in high-stress situations by defining a set of specific finite-time trajectories called motion primitives. The implementation of an optimal control method allows for the refinement and further understanding of maneuver characteristics with an emphasis on how the central nervous system controls motion. Human rotation experiments provide further insight into the complexity of self-rotation techniques and a way to study the effects of training in a rigorous and realistic manner.

2008-06-01T00:00:00Z Oliver, Todd A. Darmofal, David L. https://hdl.handle.net/1721.1/57607 2019-04-10T10:25:23Z 2006-09-01T00:00:00Z

Analysis of Dual Consistency for Discontinuous Galerkin Discretizations of Source Terms Oliver, Todd A.; Darmofal, David L. The effects of dual consistency on discontinuous Galerkin (DG) discretizations of solution and solution gradient dependent source terms are examined. Two common discretizations are analyzed: the standard weighting technique for source terms and the mixed formulation. It is shown that if the source term depends on the first derivative of the solution, the standard weighting technique leads to a dual inconsistent scheme. A straightforward procedure for correcting this dual inconsistency and arriving at a dual consistent discretization is demonstrated. The mixed formulation, where the solution gradient in the source term is replaced by an additional variable that is solved for simultaneously with the state, leads to an asymptotically dual consistent discretization. A priori error estimates are derived to reveal the effect of dual inconsistent discretization on computed functional outputs. Combined with bounds on the dual consistency error, these estimates show that for a dual consistent discretization or the asymptotically dual consistent discretization resulting from the mixed formulation, O(h2p) convergence can be shown for linear problems and linear outputs. For similar but dual inconsistent schemes, only O(hp) can be shown. Numerical results for a one-dimensional test problem confirm that the dual consistent and asymptotically dual consistent schemes achieve higher asymptotic convergence rates with grid refinement than a similar dual inconsistent scheme for both the primal and adjoint solutions as well as a simple functional output.

2006-09-01T00:00:00Z Barter, Garrett Ehud https://hdl.handle.net/1721.1/57606 2019-04-13T00:05:32Z 2008-06-01T00:00:00Z

Shock Capturing with PDE-Based Artificial Viscosity for an Adaptive, Higher-Order Discontinuous Galerkin Finite Element Method Barter, Garrett Ehud The accurate simulation of supersonic and hypersonic flows is well suited to higher-order (p > 1), adaptive computational fluid dynamics (CFD). Since these cases involve flow velocities greater than the speed of sound, an appropriate shock capturing for higher-order, adaptive methods is necessary. Artificial viscosity can be combined with a higher-order discontinuous Galerkin finite element discretization to resolve a shock layer within a single cell. However, when a non-smooth artificial viscosity model is employed with an otherwise higher-order approximation, element-to-element variations induce oscillations in state gradients and pollute the downstream flow. To alleviate these difficulties, this work proposes a new, higher-order, state-based artificial viscosity with an associated governing partial differential equation (PDE).In the governing PDE, the shock sensor acts as a forcing term, driving the artificial viscosity to a non-zero value where it is necessary. The decay rate of the higher-order solution modes and edge-based jumps are both shown to be reliable shock indicators. This new approach leads to a smooth, higher-order representation of the artificial viscosity that evolves in time with the solution. For applications involving the Navier-Stokes equations, an artificial dissipation operator that preserves total enthalpy is introduced. The combination of higher-order, PDE-based artificial viscosity and enthalpy-preserving dissipation operator is shown to overcome the disadvantages of the non-smooth artificial viscosity. The PDE-based artificial viscosity can be used in conjunction with an automated grid adaptation framework that minimizes the error of an output functional. Higher-order solutions are shown to reach strict engineering tolerances with fewer degrees of freedom. The benefit in computational efficiency for higher-order solutions is less dramatic in the vicinity of the shock where errors scale with O(h/p). This includes the near-field pressure signals necessary for sonic boom prediction. When applied to heat transfer prediction on unstructured meshes in hypersonic flows, the PDE-based artificial viscosity is less susceptible to errors introduced by poor shock-grid alignment. Surface heating can also drive the output-based grid adaptation framework to arrive at the same heat transfer distribution as a well-designed structured mesh.

2008-06-01T00:00:00Z Lorkowski, Thomas https://hdl.handle.net/1721.1/57605 2019-04-10T10:25:05Z 1997-01-01T00:00:00Z

Small-Scale Forcing of a Turbulent Boundary Layer Lorkowski, Thomas In order to understand the effect of small scale forcing on turbulent flows and its implications on control, an experimental investigation is made into the forcing of the inertial scales in the wall region of a turbulent boundary layer. A wall-mounted resonant actuator is used to produce a local vortical structure in the streamwise direction which is convected downstream by the boundary layer flow. The frequency associated with this structure is governed by the resonant frequency of the device and falls in the range of the inertial scales at the Reynolds number of the experiment (Re[theta] [is approximately equal to] 1200). Single and multiple point measurements have been made to determine mean and fluctuating statistics as well as dual-point correlations. These data can be used to infer changes in the structure of the near wall region of the boundary layer that are due to the actuator forcing and subsequently, to construct transfer functions between the actuator and the fluid necessary for active control.

1997-01-01T00:00:00Z Ahn, Jon https://hdl.handle.net/1721.1/57604 2019-04-10T10:25:05Z 1997-02-01T00:00:00Z

Analysis and design of axisymmetric transonic flow with linearized three-dimensional flow prediction Ahn, Jon The primary goal of this thesis is the application of the proven stream-surface based Newton method to analysis/design of an axisymmetric nacelle with the actuator disk modeling of a fan. And to further utilize the benefits of the Newton method, full attention is given to the linearized prediction of three-dimensional flow from a base axisymmetric solution, with an aim at replacing costly three-dimensional flow computations during initial nacelle design stages. The resulting code is to be called AMIS (Axisymmetric Multiple-passage Interacting Stream_surface Euler solver) to denote the lineage of Newton solver family pioneered by Drela and Giles, although AMIS has been built from scratch and share a few code lines.

1997-02-01T00:00:00Z Rathnasingham, Ruben https://hdl.handle.net/1721.1/57603 2019-04-13T00:05:22Z 1997-06-01T00:00:00Z

System Identification and Active Control of a Turbulent Boundary Layer Rathnasingham, Ruben An experimental investigation is made into the active control of the near-wall region of a turbulent boundary layer using a linear control scheme. System identification in the boundary layer provides optimal transfer functions that predict the downstream characteristics of the streamwise velocity and wall pressure fluctuation using an array of upstream flush-mounted sensors that are sensitive to spanwise shear. Enhanced detection techniques isolated the large scale turbulent motion and improved the downstream correlations resulting in greater controllability. The techniques were based on the conditioned spectral analysis between adjacent sensors to extract the most correlated flow structures that span the distance between them. The control is applied using a spanwise array of resonant actuators that introduce a pair of streamwise vortices into the flow. Control experiments were carried out for single and multiple input/output configurations. The single output results show that a maximum reduction of 34% is achieved in the streamwise velocity fluctuation. This reduction is greatest at the point of optimization but spans over a few hundred viscous lengths downstream of the actuator and about 50 viscous lengths in the spanwise and wall-normal directions. The wall pressure fluctuation and the mean wall shear stress (measured approximately using mean velocity profiles near the wall) was reduced by 17% and7% respectively. The multiple-input/single-output configuration resulted in a wider spatial influence of the control while maintaining the maximum reductions in the fluctuations. The multiple-input/multiple-output configuration showed a marked increase in the spatial extent of the control (primarily in the spanwise direction), at the expense of a lower reduction in the fluctuations (maximum of 30% and 15% for the streamwise velocity and wall pressure respectively). The bursting frequency was computed from a VITA algorithm applied to the streamwise velocity fluctuation. The bursting frequency was reduced at all threshold levels examined but the maximum reduction of 23% occurred at a threshold level of 3. The span-wise spatial correlation was measured at different streamwise locations downstream of the actuator array. This result suggests that the reduction in turbulent fluctuations obtained using the current control scheme was achieved by reducing the strength of the most coherent flow structures and to inhibit their ability to interact with each other by increasing their average spanwise separation by more than 25% (from ≈ 90l* to 120l*).

1997-06-01T00:00:00Z Elliott, Jonathan Kindred https://hdl.handle.net/1721.1/57602 2019-04-10T10:25:23Z 1998-06-01T00:00:00Z

Aerodynamic Optimization Based on the Euler and Navier-Stokes Equations using Unstructured Grids Elliott, Jonathan Kindred The overall problem area addressed is that of efficient aerodynamic shape design through the use of computational fluid dynamics (CFD). A method is presented for performing optimization including modal inverse design and lift-constrained drag minimization -- based on the 2D and 3D Euler equations and the 2D and 3D laminar Navier-Stokes equations. The discrete adjoint approach was taken and the adjoint solvers developed were based on flow solvers developed for use with unstructured grids. Optimization exercises are presented which demonstrate the effectiveness and practicality of the optimization system in finding credible optimal geometries.

1998-06-01T00:00:00Z Bayt, Robert L. https://hdl.handle.net/1721.1/57601 2019-04-09T18:37:12Z 1999-06-01T00:00:00Z

Analysis, Fabrication and Testing of a MEMS-based Micropropulsion System Bayt, Robert L. Various trends in the spacecraft industry are driving the development of low-thrust propulsion systems. These may be needed for fine attitude control, or to reduce the mass of the propulsion system through the use of small lightweight components. The nozzle converts the stored energy in a pressurized gas into kinetic energy through an expansion. The nozzle efficiency is characterized by the amount of kinetic energy leaving the nozzle, and is governed by the exit velocity. Because of the increase in viscous losses as scale is reduced, it was feared that high Mach number supersonic flows could not be generated in micro devices. However, a scaling analysis indicates that the reduction in throat area can be offset by an increase in operating pressure to maintain a constant Reynolds number. Therefore, thrust can be decreased by reducing the nozzle scale, and viscous losses mitigated by running at higher chamber pressures. In order to operate a supersonic nozzle efficiently, the geometry must be contoured to guard against flow separation and reduce the boundary layer thickness at the throat. Deep Reactive Ion Etching enables extruded flow channels of arbitrary in-plane geometry to be created at scales an order of magnitude smaller than conventional machining. These channels are encapsulated by anodically bonding glass to the upper and lower surfaces. Testing indicates that 11.3 milliNewtons of thrust is generated for a nozzle with a 37micron throat width, 308 microns deep, and a 16.9:1 expansion ratio. The exit velocity was 650 m/s, which corresponds to an exit Mach number of 4.2, and an Isp of 66 seconds. This is 100 m/s higher than previously achieved in a micromachined device and demonstrates that supersonic flows can be generated at this scale. The performance of the system is increased by electrothermal augmentation. By resistively heating fins present in the chamber, a thruster temperature of 700◦C has been achieved. This will increase the theoretical Isp to 145 seconds. However, the reduction in Reynolds number with increased chamber temperature causes viscous dissipation to increase and thruster efficiencies to decline. The efficiencies vary with Reynolds number in the same fashion as their unheated counterparts, which confirms that Reynolds number is the governing similarity parameter. The thruster was operated at a temperature of 420◦C, and demonstrated an Isp of 83seconds. This represents an Isp efficiency of 79% for an 8.25:1 area ratio nozzle. These results suggest that MEMS-based micropropulsion systems offer higher performance at lower mass, when operated at Reynolds numbers above 2500 for both heated and unheated thrusters.

1999-06-01T00:00:00Z Padmanabhan, Aravind https://hdl.handle.net/1721.1/57600 2019-04-13T00:05:31Z 1997-02-01T00:00:00Z

Silicon micromachined sensors and sensor arrays for shear-stress measurements in aerodynamic flows Padmanabhan, Aravind In this thesis we report on a new micromachined floating-element shear-stress sensor for turbulent boundary layer research. Applications in low shear-stress environments such as turbulent boundary layers require extremely high sensitivity to detect the small forces (O(nN)) and correspondingly small displacements (O(A)) of the floating-element. In addition, unsteady measurements in turbulent flows require sensors with high operating bandwidth (~20 kHz). These requirements render most of the existing shear-stress measurement techniques inadequate for this application. In response to the limitations of the existing devices, we have developed a sensor based on a new transduction scheme (optical position sensing by integrated photodiodes). The sensors developed in this thesis have a measured resolution of 0.003 Pa, with a measured range of 133 Pa and the dynamic response of the sensor has been measured to 10 kHz. The new sensor comprises of a floating-element which is suspended by four support tethers. The element displaces in the plane of the sensor chip under the action of the wall shear stress. The displacement of the element causes a ‘shuttering’ of the photodiodes which are placed symmetrically underneath the element on the leading and trailing edge. Under uniform illumination from above, the differential photocurrent (normalized by the average current) from the photodiodes is directly proportional to the magnitude and sign of the shear stress. A set of analytical expressions were developed to predict the static and dynamic response characteristics of the sensor. Based on these estimates, sensors of two different floating-element sizes - 120 [mu]m x 120 [mu]m x 7 [mu]m and 500 [mu]m x500 [mu]m x 7 [mu]m - were fabricated. The devices were statically-calibrated in a laminar flow. The static calibration was performed in a custom-designed laminar-calibration flow cell. The sensors have been calibrated over a range of four orders of wall shear stress (0.003 Pa - 10 Pa) and have demonstrated a linear response over the entire regime (the measured non-linearity was 1% (or better) over the four orders of wall shear stress). In addition, the sensors have shown excellent repeatability, long-term stability and minimal drift. The lowest measured shear stress of 0.003 Pa is three orders of magnitude lower than that has been measured before using micromachined floating-element sensors. The dynamic response of the sensors has also been experimentally verified to 10 kHz. This measurement was performed in a custom-designed plane wave tube (PWT) which was capable of generating oscillating shear stresses of known magnitudes and frequencies, via acoustic plane wave excitation. The measured shear stress showed a square-root of frequency dependence, as predicted by the theoretical relationship. This is the first time that the dynamic response of a floating-element sensor has been experimentally verified using a direct scheme. The sensors have been tested in both laminar and turbulent boundary layers in the low-speed, low-turbulence wind tunnel at MIT. The response in the laminar boundary layer was found to be linear with the same sensitivity as measured in the laminar-calibration flow cell. The sensor was able to transduce shear stresses of 0.01 Pa and lower, in the laminar boundary layer. The same device also demonstrated a linear response during measurements in a turbulent boundary layer. We have made design improvements in the second-generation of floating-element sensors. The first-generation sensors employed a two-photodiode differential sensing scheme. This design was sensitive to non-uniformities in the incident illumination. In order to minimize this we have developed a new three-photodiode scheme. The new scheme was designed to null out any linear gradients in the intensity and has demonstrated 94% reduction in sensitivity to intensity variations when compared to the earlier design. The new photodiode design was implemented in the fabrication of one-dimensional arrays of sensors. The sensor arrays have been calibrated in a laminar flow environment. They exhibited a linear response with a measured sensitivity which was in good agreement with the theoretically predicted value.

1997-02-01T00:00:00Z Duffner, John D. https://hdl.handle.net/1721.1/57599 2019-04-10T10:25:22Z 2008-06-01T00:00:00Z

The effects of manufacturing variability on turbine vane performance Duffner, John D. Gas turbine vanes have airfoil shapes optimized to deliver specific flow conditions to turbine rotors. The limitations of the manufacturing process with regards to accuracy and precision mean that no vane will exactly match the design intent. This research effort is an investigation of the effects of manufacturing-induced geometry variability on the performance of a transonic turbine vane. Variability is characterized by performing Principal Components Analysis (PCA) on a set of measured vanes and then applied to a different vane design. The performance scatter of that design is estimated through Monte Carlo analysis. The effect of a single PCA mode on performance is estimated and it is found that some modes with lower geometric variability can have greater impact on performance metrics. Linear sensitivity analysis, both viscous and inviscid, is carried out to survey performance sensitivity to localized surface perturbations, and tolerances are evaluated using these results. The flow field is seen to be practically insensitive to shape changes upstream of the throat. Especially sensitive locations like the throat and trailing edge are investigated further through nonlinear sensitivity analysis.

2008-06-01T00:00:00Z Venditti, David A. Darmofal, David L. https://hdl.handle.net/1721.1/57598 2019-04-10T10:25:06Z 2007-08-01T00:00:00Z

Anisotropic Grid Adaptation for Multiple Aerodynamic Outputs Venditti, David A.; Darmofal, David L. Anisotropic grid–adaptive strategies are presented for viscous flow simulations in which the accurate prediction of multiple aerodynamic outputs (such as the lift, drag, and moment coefficients) is required from a single adaptive solution. The underlying adaptive procedure is based on a merging of adjoint error estimation and Hessian-based anisotropic grid adaptation. Airfoil test cases are presented to demonstrate the various adaptive strategies including a single element airfoil at cruise conditions and a multi-element airfoil in high-lift configuration with flow separation. Numerical results indicate that the lift, drag and moment coefficients are accurately predicted by all of the output–based strategies considered, although slightly better accuracy is obtained in the output(s) for which a particular strategy is specifically designed. Furthermore, the output-based strategies are all shown to be significantly more efficient than pure Hessian-based adaptation in terms of output accuracy for a given grid size.

2007-08-01T00:00:00Z Wong, J. S. Darmofal, D. L. Peraire, J. https://hdl.handle.net/1721.1/57597 2019-04-13T00:05:31Z 2001-04-01T00:00:00Z

High Order Finite Element Discretization of the Compressible Euler and Navier-Stokes Equations Wong, J. S.; Darmofal, D. L.; Peraire, J. We present a high order accurate streamline-upwind/Petrov-Galerkin (SUPG) algorithm for the solution of the compressible Euler and Navier-Stokes equations. The flow equations are written in terms of entropy variables which result in symmetric flux Jacobian matrices and a dimensionally consistent Finite Element discretization. We show that solutions derived from quadratic element approximation are of superior quality next to their linear element counterparts. We demonstrate this through numerical solutions of both classical test cases as well as examples more practical in nature.

2001-04-01T00:00:00Z Sauer-Budge, A. M. Bonet, J. Huerta, A. Peraire, J. https://hdl.handle.net/1721.1/57596 2019-04-13T00:05:22Z 2003-01-01T00:00:00Z

Computing Bounds for Linear Functionals of Exact Weak Solutions to Poisson’s Equation Sauer-Budge, A. M.; Bonet, J.; Huerta, A.; Peraire, J. We present a method for Poisson’s equation that computes guaranteed upper and lower bounds for the values of linear functional outputs of the exact weak solution of the infinite dimensional continuum problem using traditional finite element approximations. The guarantee holds uniformly for any level of refinement, not just in the asymptotic limit of refinement. Given a finite element solution and its output adjoint solution, the method can be used to provide a certificate of precision for the output with an asymptotic complexity which is linear in the number of elements in the finite element discretization.

2003-01-01T00:00:00Z Fidkowski, Krzysztof J. Darmofal, David L. https://hdl.handle.net/1721.1/57595 2019-04-10T10:25:07Z 2006-10-01T00:00:00Z

Output-based Adaptive Meshing Using Triangular Cut Cells Fidkowski, Krzysztof J.; Darmofal, David L. This report presents a mesh adaptation method for higher-order (p > 1) discontinuous Galerkin (DG) discretizations of the two-dimensional, compressible Navier-Stokes equations. The method uses a mesh of triangular elements that are not required to conform to the boundary. This triangular, cut-cell approach permits anisotropic adaptation without the difficulty of constructing meshes that conform to potentially complex geometries. A quadrature technique is presented for accurately integrating on general cut cells. In addition, an output-based error estimator and adaptive method are presented, with emphasis on appropriately accounting for high-order solution spaces in optimizing local mesh anisotropy. Accuracy on cut-cell meshes is demonstrated by comparing solutions to those on standard boundary-conforming meshes. Adaptation results show that, for all test cases considered, p = 2 and p = 3 discretizations meet desired error tolerances using fewer degrees of freedom than p = 1. Furthermore, an initial-mesh dependence study demonstrates that, for sufficiently low error tolerances, the final adapted mesh is relatively insensitive to the starting mesh.

2006-10-01T00:00:00Z Tan, Bui-Thanh https://hdl.handle.net/1721.1/57594 2019-04-13T00:05:22Z 2007-05-01T00:00:00Z

Model-Constrained Optimization Methods for Reduction of Parameterized Large-Scale Systems Tan, Bui-Thanh Most model reduction techniques employ a projection framework that utilizes a reduced-space basis. The basis is usually formed as the span of a set of solutions of the large-scale system, which are computed for selected values (samples) of input parameters and forcing inputs. In existing model reduction techniques, choosing where and how many samples to generate has been, in general, an ad-hoc process. A key challenge is therefore how to systematically sample the input space, which is of high dimension for many applications of interest. This thesis proposes and analyzes a model-constrained greedy-based adaptive sampling approach in which the parametric input sampling problem is formulated as an optimization problem that targets an error estimation of reduced model output prediction. The method solves the optimization problem to find a locally-optimal point in parameter space where the error estimator is largest, updates the reduced basis with information at this optimal sample location, forms a new reduced model, and repeats the process. Therefore, we use a systematic, adaptive error metric based on the ability of the reduced-order model to capture the outputs of interest in order to choose the snapshot locations that are locally the worst case scenarios. The state-of-the-art subspace trust-region interior-reflective inexact Newton conjugate-gradient optimization solver is employed to solve the resulting greedy partial differential equation constrained optimization problem, giving a reduction methodology that is efficient for large-scale systems and scales well to high-dimensional input spaces. The model-constrained adaptive sampling approach is applied to a steady thermal fin optimal design problem and to probabilistic analysis of geometric mistuning in turbomachinery. The method leads to reduced models that accurately represent the full large-scale systems over a wide range of parameter values in parametric spaces up to dimension 21.

2007-05-01T00:00:00Z Israeli, Emily Renee https://hdl.handle.net/1721.1/57593 2019-04-13T00:05:21Z 2008-08-01T00:00:00Z

Simulations of a passively actuated oscillating airfoil using a Discontinuous Galerkin method Israeli, Emily Renee Natural flappers, such as birds and bats, effectively maneuver in transitional, low Reynolds number flow, outperforming any current small engineered flapping vehicle. Thus, engineers are inspired to investigate the flapping dynamics present in nature to further understand the non-tradional flow aerodynamics in which they operate. Undeniably the success of biological flapping flight is the exploitation of fluid structure interaction response i.e. wing mechanics, deformation, and morphing. Even though all these features are encountered in nature, it is important to note that natural flappers have not just adapted to optimize their aerodynamic behavior, they also have evolved due to biological constraints. Therefore, in bio-inspired design one carefully uses the insight gained from understanding natural flappers. Here, a 2-D simulation of a pitching and heaving foil attempts to indicate flapping parameter specifics that generate an efficient, thrust producing flapper. The simulations are performed using a high-order Discontinuous Galerkin finite element solver for the compressible Navier Stokes equations. A brief investigation of a simple problem in which pitch and heave of a foil are prescribed highlights the necessity to use an inexpensive lower fidelity model to narrow down the large design space to a manageable region of interest. A torsional spring is placed at the foil's leading edge to passively modulate the pitch while the foil is harmonically heaved. This model gives the foil passive structural compliance that automatically determines the pitch. The two-way fluid structure interaction thus results from the simultaneous resolution of the fluid and moment equations. This thesis explores the pitch profile and force generation characteristics of the spring-driven, oscillating foil. The passive strategy is found to enhance the propulsive efficiency and thrust production of the flappers specifically in cases where separation is encountered. Furthermore, the passive spring system performs like an ideal actuator that enables the oscillating foil to extract energy from the fluid motion without additional power input. Thus, this is the optimal mechanism to drive the foil dynamics for efficient flight with kinematic flexibility.

2008-08-01T00:00:00Z Wogrin, Sonja https://hdl.handle.net/1721.1/57592 2019-04-09T19:18:36Z 2008-06-01T00:00:00Z

Model Reduction for Dynamic Sensor Steering: A Bayesian Approach to Inverse Problems Wogrin, Sonja In many settings, distributed sensors provide dynamic measurements over a specified time horizon that can be used to reconstruct information such as parameters, states or initial conditions. This estimation task can be posed formally as an inverse problem: given a model and a set of measurements, estimate the parameters of interest. We consider the specific problem of computing in real-time the prediction of a contamination event, based on measurements obtained by mobile sensors. The spread of the contamination is modeled by the convection diffusion equation. A Bayesian approach to the inverse problem yields an estimate of the probability density function of the initial contaminant concentration, which can then be propagated through the forward model to determine the predicted contaminant field at some future time and its associated uncertainty distribution. Sensor steering is effected by formulating and solving an optimization problem that seeks the sensor locations that minimize the uncertainty in this prediction. An important aspect of this Dynamic Sensor Steering Algorithm is the ability to execute in real-time. We achieve this through reduced-order modeling, which (for our two-dimensional examples) yields models that can be solved two orders of magnitude faster than the original system, but only incur average relative errors of magnitude O(10−3). The methodology is demonstrated on the contaminant transport problem, but is applicable to a broad class of problems where we wish to observe certain phenomena whose location or features are not known a priori.

2008-06-01T00:00:00Z Bui-Thanh, T. Willcox, K. Ghattas, O. https://hdl.handle.net/1721.1/57591 2019-04-10T10:25:07Z 2007-08-01T00:00:00Z

Model Reduction for Large-Scale Systems with High Dimensional Parametric Input Space Bui-Thanh, T.; Willcox, K.; Ghattas, O. A model-constrained adaptive sampling methodology is proposed for reduction of large-scale systems with high-dimensional parametric input spaces. Our model reduction method uses a reduced basis approach, which requires the computation of high-fidelity solutions at a number of sample points throughout the parametric input space. A key challenge that must be addressed in the optimization, control, and probabilistic settings is the need for the reduced models to capture variation over this parametric input space, which, for many applications, will be of high dimension. We pose the task of determining appropriate sample points as a PDE-constrained optimization problem, which is implemented using an efficient adaptive algorithm that scales well to systems with a large number of parameters. The methodology is demonstrated for examples with parametric input spaces of dimension 11 and 21, which describe thermal analysis and design of a heat conduction fin, and compared with statistically-based sampling methods. For this example, the model-constrained adaptive sampling leads to reduced models that, for a given basis size, have error several orders of magnitude smaller than that obtained using the other methods.

2007-08-01T00:00:00Z Willcox, Karen Elizabeth https://hdl.handle.net/1721.1/57590 2019-04-13T00:05:21Z 2000-02-01T00:00:00Z

Reduced-order aerodynamic models for aeroelastic control of turbomachines Willcox, Karen Elizabeth Aeroelasticity is a critical consideration in the design of gas turbine engines, both for stability and forced response. Current aeroelastic models cannot provide high-fidelity aerodynamics in a form suitable for design or control applications. In this thesis low-order, high-fidelity aerodynamic models are developed using systematic model order reduction from computational fluid dynamic (CFD) methods. Reduction techniques are presented which use the proper orthogonal decomposition, and also a new approach for turbomachinery which is based on computing Arnoldi vectors. This method matches the input-output characteristic of the CFD model and includes the proper orthogonal decomposition as a special case. Here, reduction is applied to the linearised two-dimensional Euler equations, although the methodology applies to any linearised CFD model. Both methods make efficient use of linearity to compute the reduced-order basis on a single blade passage. The reduced-order models themselves are developed in the time domain for the full blade row and cast in state-space form. This makes the model appropriate for control applications and also facilitates coupling to other engine components. Moreover, because the full blade row is considered, the models can be applied to problems which lack cyclic symmetry. Although most aeroelastic analyses assume each blade to be identical, in practice variations in blade shape and structural properties exist due to manufacturing limitations and engine wear. These blade to blade variations, known as mistuning, have been shown to have a significant effect on compressor aeroelastic properties. A reduced-order aerodynamic model is developed for a twenty-blade transonic rotor operating in unsteady plunging motion, and coupled to a simple typical section structural model. Stability and forced response of the rotor to an inlet flow disturbance are computed and compared to results obtained using a constant coefficient model similar to those currently used in practice. Mistuning of this rotor and its effect on aeroelastic response is also considered. The simple models are found to inaccurately predict important aeroelastic results, while the relevant dynamics can be accurately captured by the reduced-order models with less than two hundred aerodynamic states. Models are also developed for a low-speed compressor stage in a stator/rotor configuration. The stator is shown to have a significant destabilising effect on the aeroelastic system, and the results suggest that analysis of the rotor as an isolated blade row may provide inaccurate predictions.

2000-02-01T00:00:00Z Mughal, Bilal Hafeez https://hdl.handle.net/1721.1/57588 2019-04-10T10:25:06Z 1998-02-01T00:00:00Z

Integral methods for three-dimensional boundary layers Mughal, Bilal Hafeez Several distinct issues important in integral approximations of the three-dimensional boundary-layer equations are addressed. One of these is the requirement, justified on the basis of the nature of the full differential equations, for hyperbolicity of integral equation systems. It is generally not feasible to analytically determine the mathematical character of these systems, except in very simple cases, because of the empiricism necessary for closure. Furthermore, the use of general systems is inhibited because there is no guarantee that they are hyperbolic. A novel method accommodating the role of both equations and closure, so that systems are always hyperbolic with physically-consistent characteristic directions, is proposed. Another issue considered is the calculation of bidirectional crossflows for which a well-conditional system, for use in Newton solvers, is devised. The validity of this system is demonstrated by comparing results with a numerical solution of the full differential boundary-layer equations for the case of an infinite-swept wing. Finally, a fully-simultaneous scheme coupling inviscid flow, calculated using a simple Panel method, to general integral systems is devised with the facility to use empirical closure parameters as system parameters. The coupling scheme is demonstrated by computing the separated flow downstream of a smooth obstacle. For calculations, the equations are posed in conservation form in local Cartesian coordinates and discretized using the finite-element method. Unlike dissipation schemes used in previous methods, a Petrov-Galerkin streamline upwinding weight function, adapted heuristically for the coupled equation system, is used to control spurious oscillations.

1998-02-01T00:00:00Z Vailong, Hubert J. B. https://hdl.handle.net/1721.1/57586 2019-04-13T00:05:21Z 1997-02-01T00:00:00Z

A Posteriori Bounds for Linear Functional Outputs of Hyperbolic Partial Differential Equations Vailong, Hubert J. B. One of the major difficulties faced in the numerical resolution of the equations of physics is to decide on the right balance between computational cost and solutions accuracy, and to determine how solutions errors affect some given “outputs of interest.” This thesis presents a technique to generate upper and lower bounds for outputs of hyperbolic partial differential equations. The outputs of interest considered are linear functionals of the solutions of the equations. The method is based on the construction of an “augmented” Lagrangian, which includes a formulation of the output as a quadratic form to be minimized and the equilibrium equations as a constraint. The corresponding Lagrange multiplier, or adjoint , is determined by solving a problem involving the adjoint of the operator in the original equations. The bounds are then derived from the underlying unconstrained max-min problem. A predictor is also evaluated as the average value of the bounds. Because the resolution of the max-min problem implies the resolution of the original discrete equations, the adjoint on a fine grid is approximated by a hierarchical procedure that consists of the resolution of the problem on a coarser grid followed by an interpolation on the fine grid. The bounds derived from this approximation are then optimized by the choice of natural boundary conditions for the adjoint and by selecting the value of a stabilization parameter. The Hierarchical Bounds Method is illustrated on three cases. The first one is the convection-diffusion equation, where the bounds obtained are very sharp. The second one is a purely convective problem, discretized using a Taylor-Galerkin approach. The third case is based on the Euler equations for a nozzle flow, which can be reduced to a single nonlinear scalar continuous equation. The resulting discrete nonlinear system of equations is obtained by a Taylor-Galerkin method and is solved by the Newton-Raphson method. The problem is then linearized about the computed solution to obtain a linear system similar to the previous cases and produce the bounds. In a last chapter, the Domain Decomposition is introduced. The domain is decomposed into K subdomains and the problem is solved separately on each of them before continuity at the boundaries is imposed, allowing the computation of the bounds to be parallelized. Because the cost of sparse matrix inversion is of order O(N[third]), Domain Decomposition becomes very useful for two-dimensional problems,where the overall cost is divided by K[squared].

1997-02-01T00:00:00Z