Doctoral Dissertations

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Acceleration techniques for the radiative analysis of general computational fluid dynamics solutions using reverse Monte-Carlo ray tracing
Turk, Jeffrey A. (Virginia Tech, 1994)
A reverse Monte-Carlo ray trace capable of performing a radiative analysis on arbitrary multiple overlapping structured computational fluid dynamics solution sets is developed. In order to make effective use of time, a method based on a set of simplifying assumptions but using the same calculation procedures is developed for comparison and study purposes. Three acceleration techniques are tried. One acceleration technique reduces the grid dimensions to reduce the number of volumes intersected. The second acceleration technique develops a version of the code for execution in a parallel processing environment. The third acceleration technique mixes an orthogonal, evenly spaced grid with the computational fluid dynamics grids to obtain fast ray traversal of low variance areas while retaining the higher resolution of the computational fluid dynamics grids in the high variance areas. Two experimental data sets are used for comparison and as test cases during these studies: an exhaust plume from an auxiliary power unit, and a Boeing 747 in flight. Timing for the baseline and accelerated analyses is provided as well as numerical comparisons for a selected subset.
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%.
Analysis of the injection of a heated, turbulent jet into a moving mainstream, with emphasis on a thermal discharge in a waterway
Campbell, James F. (Virginia Polytechnic Institute and State University, 1972)
An experimental and theoretical investigation has been undertaken to study the trajectory and growth of thermal effluents having a range of discharge velocities and temperatures. The discharge of a turbulent effluent into a waterway was mathematically modeled as a submerged jet injection process by using an integral method which accounts for natural fluid mechanisms such as turbulence, entrainment, buoyancy, and heat transfer. The analytical results are supported by experimental data and demonstrate the usefulness of the theory for estimating the location and size of the effluent with respect to the discharge point. The capability of predicting jet flow properties, as well as two- and three-dimensional jet paths, was enhanced by obtaining the jet cross sectional area during the solution of the conservation equations (a number of previous studies assume a specific growth for the area). Realistic estimates of temperature in the effluent were acquired by accounting for heat losses in the jet flow due to forced convection and to entrainment of free-stream fluid into the jet.
Analysis of the vortical flow around a 60 degree delta wing with vortex flap
Sung, Bongzoo (Virginia Polytechnic Institute and State University, 1985)
Subsonic wind tunnel investigations were conducted on a 60° swept, flat plate, delta wing with a leading edge vortex flap. The pressure distributions were measured over a range of angles of attack starting from zero to 40° in 5° interval and flap deflection angles from zero to 45° with 5° increments at a Reynolds number of about 2.14 x 10‘ based on the root chord. The flow visualization experiments were performed from zero degree to the stall angle, with ten different flap deflection angles at the same Reynolds number. The mean flow field was measured at angles of attack l0° and 15° with the flap deflection angles of l0° and 30° at a Reynolds number of about 1.50 x 10°. The experimental results shows that the leading edge vortex flap is an effective means to control the vortex flow over a delta wing. The optimum flap deflection angles were found where the primary vortex was confined to the leading edge vortex flap, thus producing a thrust on the flap. It was found that flap deflection could be used to restore a vortex flow from burst vortex condition.
Analysis of the wake behind a propeller using the finite element method with a two-equation turbulence model
Kim, Seung J. (Virginia Polytechnic Institute and State University, 1988)
The finite element method in the form of the weak Galerkin formulation with the penalty function method was applied to several problems of axisymmetric turbulent flows including flow through a sudden pipe expansion, the stern region flow of a slender body, and flows past ducted and nonducted propellers in action. The coupled set of the Reynolds time-averaged Navier-Stokes equations and two turbulence transport equations for the turbulent kinetic energy and its rate of dissipation was solved by L/U decomposition and successive substitution with relaxation. An existing finite element code was modified with a low Reynolds number form for an appropriate treatment of wall influences on turbulence transport, which produces a better solution and provides an easier imposition of boundary conditions by solving up to wall with no slip boundary conditions. The two-equation turbulence model with the wall modification was first successfully tested by solving the turbulent flow through a sudden pipe expansion. The numerical simulation of the stern region flow of a streamlined body resulted in an excellent agreement with the measured data in terms of the mean-flow and turbulence quantities. Turbulent shear flows past a propeller at the rear end of the same slender body, modeled by an actuator disk, were successfully solved at two rotational speeds, self-propelled and 100% over-thrusted, using the same two-equation model. And finally, comparisons of the wake behind a propeller were made for the self-propelled conditions of a ducted and nonducted propeller on the same streamlined body.
Analytical and experimental comparison of deterministic and probabilistic optimization
Ponslet, Eric (Virginia Tech, 1994)
The probabilistic approach to design optimization has received increased attention in the last two decades. It is widely recognized that such an approach should lead to designs that make better use of the resources than designs obtained with the classical deterministic approach by distributing safety onto the different components and/or failure modes of a system in an optimal manner. However, probabilistic models rely on a number of assumptions regarding the magnitude of the uncertainties, their distributions, correlations, etc. In addition, modelling errors and approximate reliability calculations (first order methods for example) introduce uncertainty in the predicted system reliability. Because of these inaccuracies, it is not clear if a design obtained from probabilistic optimization will really be more reliable than a design based on deterministic optimization. The objective of this work is to provide a partial answer to this question through laboratory experiments — such experimental validation is not currently available in the literature. A cantilevered truss structure is used as a test case. First, the uncertainties in stiffness and mass properties of the truss elements are evaluated from a large number of measurements. The transmitted scatter in the natural frequencies of the truss is computed and compared to experimental estimates obtained from measurements on 6 realizations of the structure. The experimental results are in reasonable agreement with the predictions, although the magnitude of the transmitted scatter is extremely small. The truss is then equipped with passive viscoelastic tuned dampers for vibration control. The controlled structure is optimized by selecting locations for the dampers and for tuning masses added to the truss. The objective is to satisfy upper limits on the acceleration at given points on the truss for a specified excitation. The properties of the dampers are the primary sources of uncertainties. Two optimal designs are obtained from deterministic and probabilistic optimizations; the deterministic approach maximizes safety margins while the probability of failure (i.e. exceeding the acceleration limit) is minimized in the probabilistic approach. The optimizations are performed with genetic algorithms. The predicted probability of failure of the optimum probabilistic design is less than half that of the deterministic optimum. Finally, optimal deterministic and probabilistic designs are compared in the laboratory. Because small differences in failure rates between two designs are not measurable with a reasonable number of tests, we use anti-optimization to identify a design problem that maximizes the contrast in probability of failure between the two approaches. The anti-optimization is also performed with a genetic algorithm. For the problem identified by the anti-optimization, the probability of failure of the optimum probabilistic design is 25 times smaller than that of the deterministic design. The rates of failure are then measured by testing 29 realizations of each optimum design. The results agree well with the predictions and confirm the larger reliability of the probabilistic design. However, the probabilistic optimum is shown to be very sensitive to modelling errors. This sensitivity can be reduced by including the modelling errors as additional uncertainties in the probabilistic formulation.
Analytical and experimental study of control effort associated with model reference adaptive control
Messer, Richard Scott (Virginia Tech, 1992)
During the past decade, researchers have shown much interest in control and identification of Large Space Structures (LSS). Our inability to model these LSS accurately has generated extensive research into robust controllers capable of maintaining stability in the presence of large structural uncertainties as well as changing structural characteristics. In this work the performance of Model Reference Adaptive Control - (MRAC) is studied in numerical simulations and verified experimentally, to understand how differences between the plant and the reference model affect the control effort. MRAC is applied analytically and experimentally to a single-degree-of-freedom system and analytically to a multi-degree-of-freedom system with multi-inputs and multi-outputs. Good experimental and analytical agreement is demonstrated in control experiments and it is shown that MRAC does an excellent job of controlling the structures and achieving the desired performance even when large differences between the plant and ideal reference model exist. However, it is shown that reasonable differences between the reference model and the plant significantly increase the required control effort. The effects of increased damping in the reference model are considered, and it is shown that requiring the controller to provide increased damping actually decreases the required control effort when differences between the plant and reference model exist. This result is very useful because one of the first attempts to counteract the increased control effort due to differences between the plant and reference model might be to require less damping, however, this would actually increase the control effort. The use of optimization to successfully improve performance and reduce control effort is shown to be limited, because the actual control-structure system can not realize all the performance improvements of the analytical optimal system. Finally, it is shown that very large sampling rates may be required to accurately implement MRAC.
Automated design of composite plates for improved damage tolerance
Gürdal, Zafer (Virginia Polytechnic Institute and State University, 1985)
An automated procedure for designing minimum-weight composite plates subject to a local damage constraint under tensile and compressive loadings has been developed. A strain based criterion was used to obtain fracture toughness of cracked plates under tension. Results of an experimental investigation of the effects of simulated through-the-thickness cracks on the buckling, postbuckling, and failure characteristics of composite flat plates are presented. A model for kinking failure of fibers at the crack tip was developed - for compression loadings. A finite element program based on linear elastic fracture mechanics for calculating stress intensity factor (SIF) was incorporated in the design cycle. A general purpose mathematical optimization algorithm was used for the weight minimization. Analytical sensitivity derivatives of the SIF, obtained by employing the adjoint variable technique, were used to enhance the computational efficiency of the procedure. Design results for both unstiffened and stiffened plates are presented.
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.
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 and experimental study of trailing vortices
Lee, Heehwan (Virginia Polytechnic Institute and State University, 1983)
A coordinated computational undertaken to investigate the and experimental study was behavior of the vortices trailing from low aspect ratio lifting surfaces. Vortex formation in the near-wake was measured in a wind tunnel with yaw-head and hot-wire probes at three different Reynolds numbers, the highest of which was greater than most previous studies. These near-wake measurements provided initial conditions for the far-field computation with the parabolized Navier-Stokes equations written in terms of vorticity and stream function. Turbulent transport was modeled through the turbulent kinetic energy and the Prandtl-Kolmogorov hypothesis to give an eddy viscosity. The experimental results showed that the effects of Reynolds number are significant for vortex formation in the nearwake, and the computation adequately effects. However, the decay trend in the far-field is essentially unaffected by the Reynolds number, and the predicted decay for maximum tangential velocity agreed very well with Iversen's correlation.
Constrained control allocation for systems with redundant control effectors
Bordignon, Kenneth A. (Virginia Tech, 1996-12-19)
Control allocation is examined for linear time-invariant problems that have more controls than degrees of freedom. The controls are part of a physical system and are subject to limits on their maximum positions. A control allocation scheme commands control deflections in response to some desired output. The ability of a control allocation scheme to produce the desired output without violating the physical position constraints is used to compare allocation schemes. Methods are developed for computing the range of output for which a given scheme will allocate admissible controls. This range of output is expressed as a volume in the n-dimensional output space. The allocation schemes which are detailed include traditional allocation methods such as Generalized Inverse solutions as well as more recently developed methods such as Daisy Chaining, Cascading Generalized Inverses, Null-Space Intersection methods, and Direct Allocation. Non-linear time-varying problems are analyzed and a method of control allocation is developed that uses Direct Allocation applied to locally linear problems to allocate the controls. This method allocates controls that do not violate the position limits or the rate limits for all the desired outputs that the controls are capable of producing. The errors produced by the non-linearities are examined and compared with the errors produced by globally linear methods. The ability to use the redundancy of the controls to optimize some function of the controls is explored and detailed. Additionally, a method to reconfigure the controls in the event of a control failure is described and examined. Detailed examples are included throughout, primarily applying the control allocation methods to an F-18 fighter with seven independent moment generators controlling three independent moments and the F-18 High Angle of Attack Research Vehicle (HARV) with ten independent moment generators.
Contributions to model following control theory
Durham, Wayne (Virginia Polytechnic Institute and State University, 1989)
A standard form for linear and nonlinear perfect model following control problems is introduced, and the associated control laws developed. The error dynamics of such systems are analyzed with respect to stability of the error. The effects on the error dynamics of measurement errors and parameter variations are also analyzed, and it is seen that the perfect model following control problem is reduced to that of an error regulator. The linear problem is analyzed to show that virtually all common problems are equivalent to standard form problems through similarity transformations. In the standard form, simple expressions for the control law and error dynamics are used to solve the problem. The linear problem is also analyzed with respect to problems of different order model and plant systems, resulting in augmented system equations. These augmented systems are chosen so that the original dynamics are retained, and so that the higher order problem is in the standard form. The standard form problem is then solved as before. Imperfect model following control problems are analyzed, with three associated results. First, a new t€St for perfect model following is developed. Pairs of models and plants that fail this or other tests are imperfect model following control problems. Second, the effect of using perfect model following control laws on such problems is determined to be equivalent to the addition of a forcing function on the error regulator problem. Third, a new approach to the solution of imperfect model following control problems is shown. This approach seeks to find models that simultaneously satisfy the criteria for perfect model following while retaining the desired characteristics of the intended model. The methods developed in this analysis are applied to problems that illustrate all the principles addressed. The final example is a detailed application to a nonlinear simulation of the F-18 airplane involving control of all degrees of freedom over a large range of angles of attack.
Curvature effects on the stability of three-dimensional laminar boundary layers
Collier, Fayette (Virginia Polytechnic Institute and State University, 1988)
The linear stability equations which govern the growth of small periodic disturbances for compressible, three-dimensional laminar boundary layer flow are derived in an orthogonal curvilinear coordinate system. The parallel flow assumption is utilized in the derivation. The system of equations is solved using a finite difference scheme similar to that in a current state-of-the-art stability analysis code, COSAL. The LR method and the inverse Rayleigh iteration procedure are used to calculate the eigenvalues. The stability of the three-dimensional compressible laminar boundary layer including the effects of streamline and surface curvature for flows past swept wings where crossflow type disturbances dominate is calculated. A parametric study is performed varying Reynolds number and sweep angle on an airfoil with a concave cutout in the leading edge region of the lower surface. It is known that convex curvature has a stabilizing effect on the laminar boundary layer. Conversely, concave curvature has a destabilizing effect. The magnitude of these effects for swept wing flows is determined. Non-stationary as well as stationary disturbances are calculated, and the most amplified frequencies are identified. N-factor correlations at the measured location of transition are made utilizing flight test data. Results indicate that amplification rates and hence, N-factors, for swept wing flows over convex surfaces are reduced by about 30 to 50 percent when curvature effects are included in the linear stability analysis. In addition, comparisons are made with some experimental results on a swept concave-convex surface. Calculated velocity vector plots show good agreement with observed disturbances in the laminar boundary layer over the concave surface. The results of the calculations show that concave curvature destabilizes "crossflow” type disturbances with a 30 percent increase in amplification rate.
Delamination initiation in postbuckled dropped-ply laminates
Dávila, Carlos G. (Virginia Tech, 1991-04-06)
The compression strength of dropped-ply, graphite-epoxy laminated plates for the delamination mode of failure is studied by analysis and corroborated with experiments. The nonlinear response of the test specimens is modeled by a geometrically nonlinear finite element analysis. The methodology for predicting delamination is based on a quadratic interlaminar stress criterion evaluated at a characteristic distance from the ply drop-off. The details of the complex state of stress in the region of the thickness discontinuity are studied using three-dimensional solid elements, while the uniform sections of the plate are modeled with quadrilateral shell elements. A geometrically nonlinear transition element was developed to couple the shell elements to the solid elements. The analysis was performed using the COmputational MEchanics Testbed (COMET), an advanced structural analysis software environment developed at the NASA Langley Research Center to provide a framework for research in structural analysis methods. Uniaxial compression testing of dropped-ply, graphite-epoxy laminated plates has confirmed that delamination along the interfaces above and/or below the dropped plies is a common mode of failure initiation. The compression strength of specimens exhibiting a linear response is greater than the compression strength of specimens with the same layup exhibiting geometrically nonlinear response. Experimental and analytical results also show a decrease in laminate strength with increasing number of dropped plies. For linear response there is a large decrease in compression strength with increasing number of dropped plies. For nonlinear response there is less of a reduction in compression strength with increasing number of dropped plies because the nonlinear response causes a redistribution and concentration of interlaminar stresses toward the unloaded edges of the laminate.
Development of advanced modal methods for calculating transient thermal and structural response
Camarda, Charles J. (Virginia Tech, 1990-09-06)
This dissertation evaluates higher-order modal methods for predicting thermal and structural response. More accurate methods or ones which can significantly reduce the size of complex, transient thermal and structural problems are desirable for analysis and are required for synthesis of real structures subjected to thermal and mechanical loading. A unified method is presented for deriving successively higher-order modal solutions related to previously developed, lower-order methods such as the mode-displacement and mode-acceleration methods. A new method, called the force derivative method, is used to obtain higher-order modal solutions for both uncoupled (proportionally-damped) structural problems as well as thermal problems and coupled (non-proportionally damped) structural problems. The new method is called the force-derivative method because, analogous to the mode-acceleration method, it produces a term that depends on the forcing function and additional terms that depend on the time derivatives of the forcing function. The accuracy and convergence history of various modal methods are compared for several example problems, both structural and thermal. The example problems include the case of proportional damping for: a cantilevered beam subjected to a quintic time varying tip load and a unit step tip load and a muItispan beam subjected to both uniform and discrete quintic time-varying loads. Examples of non-proportional damping include a simple two-degree-of-freedom spring-mass system with discrete viscous dampers subjected to a sinusoidally varying load and a multispan beam with discrete viscous dampers subjected to a uniform, quintic time varying load. The last example studied is a transient thermal problem of a rod subjected to a linearly-varying, tip heat load.
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.
The effect of departure from ideality of a multiply ionized monatomic gas on the performance of rocket engines
Perkins, John Noble (Virginia Tech, 1963)
Using the Debye-Huckle approximation, the effects of Coulomb interactions on the equilibrium, frozen, and nonequilibrium flow of an ionized gas have been investigated. The gas is assumed to be monatomic, electrically neutral, and thermal equilibrium (i.e., a one temperature fluid); but the composition of the gas is arbitrary, that is, multiple ionization of any degree is allowed. The thermodynamic variables are derived starting from the appropriate expression for the Helmholtz free energy. Using Boltzmann statistics and assuming that the velocity distribution functions are given by their Maxwellian values, the rate of ionization is derived for atom-atom, atom-ion, and atom-electron collisions. The resulting expressions are then employed in solving the quasi-one-dimensional flow in a converging-diverging nozzle for the equilibrium, frozen, and nonequilibrium cases. Numerical examples, using argon as the working substance, are discussed and the results presented graphically. The results of these calculations indicate that, for single ionization, the effect of Coulomb interactions on the performance of rocket engines is negligible; but that data obtained from hypersonic arc jet wind-tunnels can be significantly influenced by the presence of the interactions.
The effect of free stream disturbances and control surface deflections on the performance of the Wortmann airfoil at low Reynolds numbers
Sumantran, V. (Virginia Polytechnic Institute and State University, 1985)
A wing with a Wortmann FX-63-137-ESM airfoil section has been used to study some unique problems encountered in wing aerodynamics in the range of Reynolds numbers between 50,000 and 500,000. The wind-tunnel testing conducted in the 6'x 6' Stability tunnel included strain-gauge data, pressure data, and flow-visualization studies. The laminar separation bubble which frequently occurs on the upper surface of the wing is found to dominate its performance and gives rise to a hysteresis loop for lift and drag. Changes in airfoil performance due to positive flap or control surface deflections resemble changes witnessed at higher Reynolds numbers. Negative deflections are seen to considerably change the stall behavior and the flow over the airfoil. This is due to the considerably greater effect on the separation bubble for negative flap deflections. The structure and mechanism of the laminar separation bubble can also be altered by the introduction of selected acoustic disturbance and increased free-stream turbulence. The wind-tunnel test-section environment is, therefore, capable of considerably altering wing performance in this regime.

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