VTechWorks Repository :: Browsing by Author "Walters, Robert W."

Browsing by Author "Walters, Robert W."

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An actively cooled floating element skin friction balance for direct measurement in high enthalpy supersonic flows
Chadwick, Kenneth Michael (Virginia Tech, 1992-12-14)
An investigation was conducted to design instruments to directly measure skin friction along the chamber walls of supersonic combustor models. Measurements were made in a combustor at the General Applied Science Laboratory (GASL) and in the Direct Connect Arcjet Facility (DCAF) supersonic combustor at the NASA AMES Research Center. Flow conditions in the high enthalpy combustor models ranged from total pressures of 275-800 psia (1900-5550 kPa) and total temperatures from 5800-8400 R (3222-4667 K). This gives enthalpies in the range of 1700-3300 BTU/Ib_m (3950-7660 KJ/kg) and simulated flight Mach number from 9 to 13. A direct force measurement device was used to measure the small tangential shear force resulting from the flow passing over a non-intrusive floating element. The floating head is mounted to a stiff cantilever beam arrangement with deflection due to the shear force on the order of 0.0005 in (0.0125 mm). This small deflection allows the balance to be a non-nulling type. Several measurements were conducted in cold supersonic flows to verify the concept and establish accuracy and repeatability. This balance design includes actively controlled cooling of the floating sensor head temperature through an internal cooling system to eliminate nonuniform temperature effects between the head and the surrounding chamber wall. This enabled the device to be suitable for shear force measurement in very hot flows. The key to this device is the use of a quartz tube cantilever with strain gages bonded at orthogonal positions directly on the surface at the base. A symmetric fluid flow was developed inside the quartz tube to provide cooling to the backside of the floating head. Bench tests showed that this did not influence the force measurement. Numerical heat transfer calculations were conducted for design feasibility and analysis, and to determine the effectiveness of the active cooling of the floating head. Analysis of the measurement uncertainty in cold supersonic flow tests show that uncertainty under 8% is achievable, but variations in the balance cooling during a particular test raised uncertainty up to 20% in these very hot flows during the early tests. Improvements to the strain gages and balance cooling reduced uncertainty for the later tests to under 15%.
Advances In Computational Fluid Dynamics: Turbulent Separated Flows And Transonic Potential Flows
Neel, Reece E. (Virginia Tech, 1997-06-06)
Computational solutions are presented for flows ranging from incompressible viscous flows to inviscid transonic flows. The viscous flow problems are solved using the incompressible Navier-Stokes equations while the inviscid solutions are attained using the full potential equation. Results for the viscous flow problems focus on turbulence modeling when separation is present. The main focus for the inviscid results is the development of an unstructured solution algorithm. The subject dealing with turbulence modeling for separated flows is discussed first. Two different test cases are presented. The first flow is a low-speed converging-diverging duct with a rapid expansion, creating a large separated flow region. The second case is the flow around a stationary hydrofoil subject to small, oscillating hydrofoils. Both cases are computed first in a steady state environment, and then with unsteady flow conditions imposed. A special characteristic of the two problems being studied is the presence of strong adverse pressure gradients leading to flow detachment and separation. For the flows with separation, numerical solutions are obtained by solving the incompressible Navier-Stokes equations. These equations are solved in a time accurate manner using the method of artificial compressibility. The algorithm used is a finite volume, upwind differencing scheme based on flux-difference splitting of the convective terms. The Johnson and King turbulence model is employed for modeling the turbulent flow. Modifications to the Johnson and King turbulence model are also suggested. These changes to the model focus mainly on the normal stress production of energy and the strong adverse pressure gradient associated with separating flows. The performance of the Johnson and King model and its modifications, along with the Baldwin-Lomax model, are presented in the results. The modifications had an impact on moving the flow detachment location further downstream, and increased the sensitivity of the boundary layer profile to unsteady flow conditions. Following this discussion is the numerical solution of the full potential equation. The full potential equation assumes inviscid, irrotational flow and can be applied to problems where viscous effects are small compared to the inviscid flow field and weak normal shocks. The development of a code is presented which solves the full potential equation in a finite volume, cell centered formulation. The unique feature about this code is that solutions are attained on unstructured grids. Solutions are computed in either two or three dimensions. The grid has the flexibility of being made up of tetrahedra, hexahedra, or prisms. The flow regime spans from low subsonic speeds up to transonic flows. For transonic problems, the density is upwinded using a density biasing technique. If lift is being produced, the Kutta-Joukowski condition is enforced for circulation. An implicit algorithm is employed based upon the Generalized Minimum Residual method. To accelerate convergence, the Generalized Minimum Residual method is preconditioned. These and other problems associated with solving the full potential equation on an unstructured mesh are discussed. Results are presented for subsonic and transonic flows over bumps, airfoils, and wings to demonstrate the unstructured algorithm presented here.
Aerodynamic Design Sensitivities on an Unstructured Mesh Using the Navier-Stokes Equations and a Discrete Adjoint Formulation
Nielsen, Eric John (Virginia Tech, 1998-11-16)
A discrete adjoint method is developed and demonstrated for aerodynamic design optimization on unstructured grids. The governing equations are the three-dimensional Reynolds-averaged Navier-Stokes equations coupled with a one-equation turbulence model. A discussion of the numerical implementation of the flow and adjoint equations is presented. Both compressible and incompressible solvers are differentiated, and the accuracy of the sensitivity derivatives is verified by comparing with gradients obtained using finite differences and a complex-variable approach. Several simplifying approximations to the complete linearization of the residual are also presented. A first-order approximation to the dependent variables is implemented in the adjoint and design equations, and the effect of a "frozen" eddy viscosity and neglecting mesh sensitivity terms is also examined. The resulting derivatives from these approximations are all shown to be inaccurate and often of incorrect sign. However, a partially-converged adjoint solution is shown to be sufficient for computing accurate sensitivity derivatives, yielding a potentially large cost savings in the design process. The convergence rate of the adjoint solver is compared to that of the flow solver. For inviscid adjoint solutions, the cost is roughly one to four times that of a flow solution, whereas for turbulent computations, this ratio can reach as high as ten. Sample optimizations are performed for inviscid and turbulent transonic flows over an ONERA M6 wing, and drag reductions are demonstrated.
Aerodynamic Heating of a Hypersonic Naval Projectile Launched At Sea Level
Mabbett, Arthur Andrew (Virginia Tech, 2007-04-10)
Hypersonic flight at sea-level conditions induces severe thermal loads not seen by any other type of current hypersonic system. Appropriate design of the hypersonic round requires a solid understanding of the thermal environment. Numerous codes were obtained and assessed for their applicability to the problem under study, and outside of the GASP Conjugate Heat Transfer module, Navier-Stokes code from Aerosoft, Inc., no efficient codes are available that can model the aerodynamic heating response for a fully detailed projectile, including all subassemblies, over an entire trajectory. Although the codes obtained were not applicable to a fully detailed thermal soak analyses they were useful in providing insight into ablation effects. These initial trade studies indicated that ablation of up to 1.25 inches could be expected for a Carbon-Carbon nosetip in this flight environment. In order to capture the thermal soak effects a new methodology (BMA) was required. This methodology couples the Sandia aerodynamic heating codes with a full thermal finite element model of the desired projectile, using the finite element code ANSYS from ANSYS, Inc. Since ablation can be treated elsewhere it was not included in the BMA methodology. Various trajectories of quadrant elevations of 0.5, 10, 30, 50, and 80 degrees were analyzed to determine thermal time histories and maximum operating temperatures. All of the trajectories have the same launch condition, Mach 8 sea-level, and therefore will undergo the same initial thermal spike in temperature at the nose-tip of approximately 3,100 K (5600R). Of the five trajectories analyzed the maximum internal temperatures experienced occurred for the 50 degree quadrant elevation trajectory. This trajectory experienced temperatures in excess of 1,000 K (1800R) for more than 80% of its flight time. The BMA methodology was validated by comparisons with experiment and computational fluid solutions with an uncertainty of 10% at a cost savings of over three orders of magnitude.
Approximate heat-transfer and wall-temperature calculations for aeroassisted orbital transfer vehicles
Deshpande, Samir M. (Virginia Tech, 1988-02-05)
The present work addresses the development of a method for the calculation of Convective heat-transfer and surface temperatures on heat-shields of Aeroassisted Orbital Transfer Vehicles (AOTVs) in hypersonic flow regimes. Inviscid flowfield solutions are obtained about the aerobraking shield on the AOTVs using axisymmetric Euler's equations. The flowfield solutions are coupled with laminar and turbulent boundary-layer equations and the heat-shield material properties to obtain convective heating rates and heat-shield wall temperatures. A method for obtaining non-dimensionalized solution of convective heat-transfer rates is obtained. This non-dimensionalized solution can be used for calculating convective heat-transfer rates and wall temperatures for various freestream conditions encountered during the aerobraking maneuvers. Calculations are carried out for perfect gas and equilibrium air cases, and the effect of wall catalysis on convective heat-transfer is also incorporated. The results are in good agreement with available experimental and numerical results for AOTVs.
A Brief History of Aerospace Engineering at the Virginia Polytechnic Institute and State University
Walters, Robert W.; Johnston, Jane Echols (American Institute of Aeronautics and Astronautics, 2004)
This book chapter provides an historical of Aerospace Engineering at Virginia Tech, covering 1913-2004.
A Cartesian finite-volume method for the Euler equations
Choi, Sang Keun (Virginia Polytechnic Institute and State University, 1987)
A numerical procedure has been developed for the computation of inviscid flows over arbitrary, complex two-dimensional geometries. The Euler equations are solved using a finite-volume method with a non-body-fitted Cartesian grid. A new numerical formulation for complicated body geometries is developed in conjunction with implicit flux-splitting schemes. A variety of numerical computations have been performed to validate the numerical methodologies developed. Computations for supersonic flow over a flat plate with an impinging shock wave are used to verify the numerical algorithm, without geometric considerations. The supersonic flow over a blunt body is utilized to show the accuracy of the non-body-fitted Cartesian grid, along with the shock resolution of flux-vector splitting scheme. Geometric complexities are illustrated with the flow through a two-dimensional supersonic inlet with and without an open bleed door. The ability of the method to deal with subsonic and transonic flows is illustrated by computations over a non-lifting NACA 0012 airfoil. The method is shown to be accurate, efficient and robust and should prove to be particularly useful in a preliminary design mode, where flows past a wide variety of complex geometries can be computed without complicated grid generation procedures.
A comparison of flux-splitting algorithms for the Euler equations with equilibrium air chemistry
Garrett, Joseph Lee (Virginia Tech, 1989-01-05)
The use of flux-splitting techniques on the Euler equations is considered for high Mach number, high temperature flows in which the fluid is assumed to be inviscid air in equilibrium. Three different versions of real gas extensions to the Steger-Warming and Van Leer flux-vector splitting, and four different versions of real gas extensions to the Roe flux-difference splitting, are compared with regard to general applicability and ease of implementation in existing perfect gas g algorithms. Test computations are performed for the M = 5, high temperature flow over a 10-degree wedge and the M = 24.5 flow over a blunt body. Although there were minor differences between the computed results for the three types of flux-splitting algorithms considered, little variation is observed between different versions of the same algorithm.
Compressible turbulence in a high-speed high Reynolds number mixing layer
Bowersox, Rodney (Virginia Tech, 1992-09-07)
Compressible turbulence in a high-speed, high Reynolds number, supersonic free shear layer was studied. A two-dimensional free mixing layer was chosen to study turbulence rather than a wall bounded flow due to the experimental fact that the effects of compressibility become significant at lower Mach numbers. The mixing layer was generated by supersonic injection of air (M_s = 1.8, P_ts = 0.5 atm. T_ts= 295K. and Re/m = 7x10⁶) through a rearward facing tangential slot, into a supersonic free stream (M_∞ = 4.0, P_t∞ = 12.5 atm, T_t∞ = 290K, and Re/m = 70x10⁶). Flow visualization was accomplished by nanosecond Shadowgraph photography. The overall flow structure was documented with the Shadowgraph and conventional mean flow probes (Pitot pressure, cone-static pressure, and thermocouple probes). The turbulent structure of the flow field was also clearly depicted in the Shadowgraphs. Image processing techniques were developed in order to determine root-mean-square index of refraction (density) fluctuation levels from the Shadowgraph plates. Multiple overheat normal and cross-wire techniques were developed and/or improved for this study. The present research concentrated on the Reynolds averaged form of the Navier-Stokes equations. where the effects of compressibility are manifested through "apparent mass" terms (i.e. p′u′_i). These terms appear in all of the Reynolds averaged Navier-Stokes equations (continuity, momentum, and energy). A new turbulence transformation, coupled with innovative experimental methods. allowed the full compressible Reynolds shear stress (the typical incompressible term, pu′_iu′_j as well as the apparent mass terms) to be directly measured. The full compressible heat flux and apparent mass terms were also estimated from the cross-wire results. Profiles were obtained at four downstream stations which were strategically located to map different levels of development of the shear flow. The first station was very close to the injector, about one free stream boundary layer thickness downstream (x/δ_∞ ≈ 1), hence, it is in the initial region. The second station was located at x/δ_∞ ≈ 28, which was near the beginning of the fully developed zone. The third station, x/δ_∞ = 83, was just prior the shear layer and floor boundary layer merging. The last station was positioned just aft of the layer merging, x/δ_∞ = 106. Reynolds averaging of the compressible Navier-Stokes equations implies that the compressible turbulence affects all of the governing equations. It was found, experimentally, that the effects of compressibility on turbulence were more than significant accounting for about 75% of the total level of the Reynolds shear stress formulation for the present study (i.e. the apparent mass term multiplied by the axial velocity was about 3-4 times the typical incompressible shear term). For the present mean adiabatic flow, the compressible turbulence accounted for 100% of the turbulent heat flux. The apparent mass in the continuity equation was, by definition, only due to compressibility. These results led to the development of anew Compressible Apparent Mass Mixing Length Extension (CAMMLE) model that accounts for compressible turbulence in all of the governing equations (i.e. the turbulence terms in the continuity, momentum, and energy were all consistently formulated). The CAMMLE formulation is a generalization of the Situ-Schetz compressible mixing length formulation, which was developed to account for the apparent mass terms in the momentum equation. A total of seven turbulence models were experimentally evaluated, the CAMMLE model, the Prandtl incompressible and the Situ-Schetz compressible mixing length models, the Prandtl and Bradshaw turbulent kinetic energy (TKE) formulations, and two compressible TKE extensions that are based upon a newly defined compressible TKE formulation. The measured turbulence data was used to assess the various models, where the measured mean flow profiles were used in the model formulations. The incompressible formulations were generally successful in representing the measured incompressible part of the Reynolds shear stress. However, this term only accounted for about 25% of the total shear stress level. All of the compressible extensions provided accurate estimates of the full compressible Reynolds shear stress. In addition, the newly developed CAMMLE model was also successful in representing the apparent mass terms in the continuity equation. The CAMMLE model was also the only formulation to accurately predict the measured compressible turbulent heat flux in the energy equation. The CAMMLE, Situ-Schetz, and Prandtl incompressible mixing length models were all incorporated in to a 3-D finite volume Navier-Stokes code (GASP 2.0). The numerical simulations indicated that the new compressible apparent mass mixing length extension performed very well. The CFD results also enlightened a misuse with all of the current compressible turbulence models. With the exception of the new apparent mass formulation, all existing turbulence models neglect the compressible turbulence effects on the continuity equation and treat the energy equation in an ad hoc effective eddy viscosity and thermal conductivity fashion. The numerical and theoretical studies indicated that this led to poor prediction of the mixing layer width for cases where the free stream Mach number was significantly higher than the injection Mach number.
Computational aspects of sensitivity calculations in linear transient structural analysis
Greene, William H. (Virginia Polytechnic Institute and State University, 1989)
A study has been performed focusing on the calculation of sensitivities of displacements, velocities, accelerations, and stresses in linear, structural, transient response problems. One significant goal of the study was to develop and evaluate sensitivity calculation techniques suitable for large-order finite element analyses. Accordingly, approximation vectors such as vibration mode shapes are used to reduce the dimensionality of the finite element model. Much of the research focused on the accuracy of both response quantities and sensitivities as a function of number of vectors used. Two types of sensitivity calculation techniques were developed and evaluated. The first type of technique is an overall finite difference method where the analysis is repeated for perturbed designs. The second type of technique is termed semianalytical because it involves direct, analytical differentiation of the equations of motion with finite difference approximation of the coefficient matrices. To be computationally practical in large-order problems, the overall finite difference methods must use the approximation vectors from the original design in the analyses of the perturbed models. In several cases this fixed mode approach resulted in very poor approximations of the stress sensitivities. Almost all of the original modes were required for an accurate sensitivity and for small numbers of modes, the accuracy was extremely poor. To overcome this poor accuracy, two semi-analytical techniques were developed. The first technique accounts for the change in eigenvectors through approximate eigenvector derivatives. The second technique applies the mode acceleration method of transient analysis to the sensitivity calculations. Both result in accurate values of the stress sensitivities with a small number of modes. In both techniques the computational cost is much less than would result if the vibration modes were recalculated and then used in an overall finite difference method.
Computational Studies of Penetration and Mixing for Complex Jet Injectors to Aid in Design of Hypersonic Systems
Campioli, Theresa Lynn (Virginia Tech, 2007-06-21)
A computational study of sonic light-gas jet injection into a supersonic cross flow was conducted. The scope of the numerical analysis encompassed many studies that affect how the flow-field is numerically modeled and the behavior, specifically mixing, of the flow-field itself. A single, round injector was used for the Baseline design. Simulated conditions involved sonic injection of helium heated to 313 K into a Mach 4 air cross-stream with average Reynolds number 5.77 e+7 per meter and a freestream momentum flux ratio of 2.1. Experiments at these conditions were available for comparison. The primary numerical flow solver employed was GASP v. 4.2. The Menter Shear Stress Transport (SST) turbulence model was used, since the algorithm has good capability of solving both wall-bounded and free-shear flows. The SST model was able to capture the mixing behavior of the complex flow-field. Important numerical parameters that affect the capabilities of the numerical solver were studied for the Baseline injector. These sensitivity studies varied the choice of turbulent Prandtl number, Schmidt number, freestream turbulence intensity, boundary layer size, steady and unsteady approaches and computational software packages. A decrease in the turbulent Prandtl number resulted in better mixing behavior of the prediction and better agreement with the experiment. An increase in the turbulent Schmidt number had a small adverse effect on the predictions. The mixing characteristics remained constant with an increase in freestream turbulence intensity. The best Baseline prediction was then compared to three different injector configurations: an aerodynamic ramp consisting of four injectors in an array, a diamond injector both aligned and yawed 15° to the oncoming flow. The Computational Fluid Dynamics (CFD) tools were more accurate compared to experiment in the prediction of the aeroramp injector than the diamond-shaped injectors. The aeroramp injector slightly improved mixing efficiency over the Baseline injector at these conditions. Both of the diamond-shaped injectors had similar mixing as the Baseline injector but did not predict significant improvement in penetration for the analyzed conditions. Additional studies involving the interaction of transverse injection with impinging oblique shock waves were performed. The impingement of a shock upon light gas jet injection increased mixing. The closer the shock is to the injection point, the larger the effect on mixing and vorticity. The last analyses involved a numerical comparison of a non-reacting model to a reacting hydrogen-air model. The reacting analysis prediction had an improved spreading rate and larger counter-rotating vortex pair with downstream distance over the non-reacting analysis. The mixing was not significantly altered by the addition of hydrogen-air reactions to the numerical equations. The numerical tools used are capable of reasonable accuracy in predicting the complex flow-field of jet injection into a supersonic freestream with proper choice of models and parameters. Numerical modeling offers a way to study the entire flow-field thoroughly in a cost and time efficient manner.
A consistent direct-iterative inverse design method for the Euler equations
Brock, Jerry S. (Virginia Tech, 1993-04-05)
A new, consistent direct-iterative method is proposed for the solution of the aerodynamic inverse design problem. Direct-iterative methods couple analysis and shape modification methods to iteratively determine the geometry required to support a target surface pressure. The proposed method includes a consistent shape modification method wherein the identical governing equations are used in both portions of the design procedure. The new shape modification method is simple, having been developed from a truncated, quasi-analytical Taylor's series expansion of the global governing equations. This method includes a unique solution algorithm and a design tangency boundary condition which directly relates the target pressure to shape modification. The new design method was evaluated with an upwind, cell-centered finite-volume formulation of the two-dimensional Euler equations. Controlled inverse design tests were conducted with a symmetric channel where the initial and target geometries were known. The geometric design variable was a channel-wall ramp angle, 0, which is nominally five degrees. Target geometries were defined with ramp angle perturbations of J10 = 2 %, 10%, and 20 %. The new design method was demonstrated to accurately predict the target geometries for subsonic, transonic, and supersonic test cases; M=0.30, 0.85, and 2.00. The supersonic test case efficiently solved the design tests and required very few iterations. A stable and convergent solution process was also demonstrated for the lower speed test cases using an under-relaxed geometry update procedure. The development and demonstration of the consistent direct-iterative method herein represent the important first steps required for a new research area for the advancement of aerodynamic inverse design methods.
The Development and Applications of a Numerical Method for Compressible Vorticity Confinement in Vortex-Dominant Flows
Hu, Guangchu (Virginia Tech, 2001-06-08)
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.
Development and Use of a Spatially Accurate Polynomial Chaos Method for Aerospace Applications
Schaefer, John Anthony (Virginia Tech, 2023-01-24)
Uncertainty is prevalent throughout the design, analysis, and optimization of aerospace products. When scientific computing is used to support these tasks, sources of uncertainty may include the freestream flight conditions of a vehicle, physical modeling parameters, geometric fidelity, numerical error, and model-form uncertainty, among others. Moreover, while some uncertainties may be treated as probabilistic, aleatory sources, other uncertainties are non-probabilistic and epistemic due to a lack of knowledge, and cannot be rigorously treated using classical statistics or Bayesian approaches. An additional complication for propagating uncertainty is that many aerospace scientific computing tools may be computationally expensive; for example, a single high-fidelity computational fluid dynamics solution may require several days or even weeks to complete. It is therefore necessary to employ uncertainty propagation strategies that require as few solutions as possible. The Non-Intrusive Polynomial Chaos (NIPC) method has grown in popularity in recent decades due to its ability to propagate both aleatory and epistemic parametric sources of uncertainty in a computationally efficient manner. While traditional Monte Carlo methods might require thousands to millions of function evaluations to achieve statistical convergence, NIPC typically requires tens to hundreds for problems with similar numbers of uncertain dimensions. Despite this efficiency, NIPC is limited in one important aspect: it can only propagate uncertainty at a particular point in a design space or flight envelope. For optimization or aerodynamic database problems that require uncertainty estimates at many more than one point, the use of NIPC quickly becomes computationally intractable. This dissertation introduces a new method entitled Spatially Accurate Polynomial Chaos (SAPC) that extends the original NIPC approach for the spatial regression of aleatory and epistemic parametric sources of uncertainty. Throughout the dissertation, the SAPC method is applied to various aerospace problems of interest. These include the regression of aerodynamic force and moment uncertainties throughout the flight envelope of a commercial aircraft, the design under uncertainty of a two-stream propulsive mixer device, and the robust design of a low-boom supersonic demonstrator aircraft. Collectively the results suggest that SAPC may be useful for a large variety of engineering applications.
The development of solution algorithms for compressible flows
Slack, David Christopher (Virginia Tech, 1991)
This work investigates three main topics. The first of these is the development and comparison of time integration schemes on two-dimensional unstructured meshes. Both explicit and implicit solution algorithms for the two-dimensional Euler equations on unstructured grids are presented. Cell-centered and cell-vertex finite volume upwind schemes utilizing Roe’s approximate Riemann solver are developed. For the cell-vertex scheme, a four stage Runge-Kutta time integration with and without implicit residual averaging, a point Jacobi method, a symmetric point Gauss-Seidel method, and two methods utilizing preconditioned sparse matrix solvers are investigated. For the cell-centered scheme, a Runge-Kutta scheme, an implicit tridiagonal relaxation scheme modeled after line Gauss-Seidel, a fully implicit LU decomposition, and a hybrid scheme utilizing both Runge-Kutta and LU methods are presented. A reverse Cuthill-McKee renumbering scheme is employed for the direct solver in order to decrease CPU time by reducing the fill of the Jacobian matrix. Comparisons are made for both first-order and higher-order accurate solutions using several different time integration algorithms. Higher-order accuracy is achieved by using multi-dimensional monotone linear reconstruction procedures. Results for flow over a transonic circular arc are compared for the various time integration methods. The second topic involves an interactive adaptive remeshing algorithm. The interactive adaptive remeshing algorithm utilizing a frontal grid generator is compared to a single grid calculation. Several device dependent interactive graphics interfaces have been developed along with a device independent DI-3000 interface which can be employed on any computer that has the supporting software including the Cray-2 supercomputers Voyager and Navier. Solutions for two-dimensional, inviscid flow over a transonic circular arc and a Mach 3.0 internal flow with an area change are examined. The final topic examined in this work is the capabilities developed for a structured three-dimensional code called GASP. The capabilities include: generalized chemistry and thermodynamic modeling, space marching, memory management through the use of binary C Input/Output, and algebraic and two-equation eddy viscosity turbulence modeling. Results are given for a Mach 1.7 three-dimensional analytic forebody, a Mach 1.38 axisymmetric nozzle with hydrogen-air combustion, a Mach 14.1 15° ramp, and Mach 0.3 viscous flow over a flat plate. The incorporation of these capabilities and the two-dimensional unstructured time integration schemes into a three-dimensional unstructured solver is also discussed.
Direct measurement of skin friction in complex supersonic flows
Novean, Michael George Bernard (Virginia Tech, 1996)
An instrument for the direct measurement of skin friction in complex supersonic and hypersonic flows was developed. The flows were complex because they were of very short duration, with high temperature and shocks and often injection, mixing, and combustion. A wall-mounted, miniature cantilevered beam device measured the small tangential shear force on the non-intrusive floating element. Semiconductor strain gages mounted at the beam’s base measure the small strains that are generated. By modifying the geometry of the sensing unit, this design can be adapted for a variety of test flows. The use of engineering plastics and short beam length provide high frequency response and make the beam stiff so that the floating head’s deflection due to the shear is negligible, allowing for a non-nulling design. Measurements were made in scramjet models at the NASA Ames 16-inch Shock Tunnel and the General Applied Science Laboratory HYPULSE facility. Test flow conditions were harsh with the facilities simulating Mach 14 enthalpy conditions (320 atm and 10000 R total temperatures) for 0.3-2 milliseconds. The use of engineering plastics reduces heat transfer, so that measurements can be made in these very hot impulsive flows without thermal contamination of the data. Skin friction data in agreement with other correlations and measurements were obtained at both facilities. Mach 2.4 cold flow tests were also performed in the Virginia Tech Supersonic Tunnel. These helped verify the concept and to establish pressure gradient sensitivity in the case of a shock wave impacting directly on the sensing head. Analysis of the measurement uncertainty in the cold supersonic flow tests showed that an uncertainty of approximately 10 percent is achievable. An uncertainty of 15-20% is estimated for the most severe hot cases. An assortment of variations were applied to the gage to extend gage life. The most significant was the replacement of the oil in the sensing gap with a silicon rubber, eliminating service requirements. Tests at all of the facilities confirmed that the rubber-filled gages provided approximately the same level of accuracy as was achieved with the original oil-filled gage design, except when shocks impacted the gage head.
Distributed Vibration Sensing using Rayleigh Backscatter in Optical Fibers
Sang, Alexander Kipkosgei (Virginia Tech, 2011-12-05)
Sensing has been essential for the investigation, understanding, exploitation, and utilization of physical phenomena. Traditional single-point sensing methods are being challenged by the multi-point or distributed sensing capabilities afforded by optical fiber sensors. A powerful technique available for distributed sensing involves the use of the Optical Frequency Domain Reflectometry (OFDR). This work focuses on using OFDR as a means of obtaining distributed vibration measurements using the Rayleigh scatter along a single-mode optical fiber. The effort begins by discussing various distributed measurement techniques currently in use before discussing the OFDR technique. Next, a thorough discussion on how high spatially resolved Rayleigh measurements are acquired and how such measurements can be used to make static strain measurements is presented. A new algorithm to resolve strain at regions of high spatial gradient is developed. This results in enhanced measurement performance of systems using the Rayleigh scatter to determine static strain or temperature measurements by improving measurement fidelity at the high gradient locations. Next, discussions on how dynamic strain (vibration) couples to optical fiber in a single point and in a distributed setting are presented. Lessons learned are then used to develop a new and unique distributed vibration measurement algorithm. Various consequential benefits are then reviewed before concluding remarks are stated. A simulation model was developed and used to supplement this investigation in every step of the discussion. The model was used to gain insight on how various physical phenomena interact with the optical fiber. The simulation was also used to develop and optimize the high gradient and vibration algorithms developed herein. Simple experiments were then used to validate the theory and the simulation models.
Efficient and robust design optimization of transonic airfoils
Joh, Changyeol (Virginia Tech, 1991-05-05)
Numerical optimization procedures have been employed for the design of airfoils in transonic flow based on the transonic small-disturbance (TSD) and Euler equations. A sequential approximation optimization technique was implemented for solving the design problem of lift maximization with wave drag and area constraints. A simple linear approximation was utilized for the approximation of the lift. Accurate approximations for sensitivity derivatives of the wave drag were obtained through the utilization of Nixon's coordinate straining approach. A modification of the Euler surface boundary conditions was implemented in order to efficiently compute design sensitivities without recreating the grid. Our design procedures experienced convergence problems for some TSD solutions, where the wave drag was found not to vary smoothly with the design parameters and consequently create local optimum problems. A procedure interchanging the role of the objective function and constraint, initially minimizing drag with a constraint on the lift was found to be effective in producing converged designs, usually in approximately 10 global iterations. This procedure was also shown to be robust and efficient for cases where the drag varied smoothly, such as with the Euler solutions. The direct lift maximization with move limits which were fixed absolute values rather than fractions of the design variables, was also found to be a reliable and efficient procedure for designs based upon the Euler equations.
Efficient inverse methods for supersonic and hypersonic body design, with low wave drag analysis
Lee, Jaewoo (Virginia Tech, 1991-04-05)
With the renewed interest in the supersonic and hypersonic flight vehicles, new inverse Euler methods are developed in these flow regimes where a space marching numerical technique is valid. In order to get a general understanding for the specification of target pressure distributions, a study of minimum drag body shapes was conducted over a Mach number range from 3 to 12. Numerical results show that the power law bodies result in low drag shapes, where the n=.69 (l/d = 3) or n=.70 (l/d = 5) shapes have lower drag than the previous theoretical results (n=.75 or n=.66 depending on the particular form of the theory). To validate the results, a numerical analysis was made including viscous effects and the effect of gas model. From a detailed numerical examination for the nose regions of the minimum drag bodies, aerodynamic bluntness and sharpness are newly defined. Numerous surface pressure-body geometry rules are examined to obtain an inverse procedure which is robust, yet demonstrates fast convergence. Each rule is analyzed and examined numerically within the inverse calculation routine for supersonic (M_∞= 3) and hypersonic (M_∞ = 6.28) speeds. Based on this analysis, an inverse method for fully three dimensional supersonic and hypersonic bodies is developed using the Euler equations. The method is designed to be easily incorporated into existing analysis codes, and provides the aerodynamic designer with a powerful tool for design of aerodynamic shapes of arbitrary cross section. These shapes can correspond to either "wing like" pressure distributions or to "body like" pressure distributions. Examples are presented illustrating the method for a non-axisymmetric fuselage type pressure distribution and a cambered wing type application. The method performs equally well for both nonlifting and lifting cases. For the three dimensional inverse procedure, the inverse solution existence and uniqueness problem are discussed. Sample calculations demonstrating this problem are also presented.
The efficient use of vectorized direct solvers in computational fluid dynamics
Riggins, David W. (Virginia Polytechnic Institute and State University, 1988)
The feasibility of using a vectorized banded direct solver for the compressible Euler and Navier-Stokes equations is examined for both single-grid and multi-grid strategies. A procedure is developed for comparing the computational effort required for the direct method with that of the vertical line Gauss-Seidel iteration scheme in order to provide a criteria for choosing between the two techniques. The direct method is shown to have a relatively wide range of application on a vector processor with large memory. Indeed, the primary limitation of the direct method at this time is machine memory. Results for both inviscid and viscous test problems over a range of Mach numbers and Reynolds numbers are examined for two dimensions.

Browsing by Author "Walters, Robert W."

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