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All sourcesNASA NTRSDOE OSTI
NASA NTRS1996

Navier-Stokes Simulation of the Canard-Wing-Body Longitudinal Dynamic Stability Characteristics

Many modern aircraft are canard-configured for aircraft control and improved aerodynamic performance. Canards can often enhance aircraft cruise performance, maneuverability and agility. For close-coupled canard configurations, the aerodynamic interaction between the canard and wing significantly changes the flow characteristics of the wing. In unsteady flow, such changes in the flow structure and performance of wings can be quite pronounced. Accurate modeling of the unsteady aerodynamics is essential for potential CFD design and analysis of such configurations. A time-accurate numerical simulation is performed to study the unsteady aerodynamic interaction between a canard and wing with emphasis on the effects of the canard on the configuration's dynamic response characteristics. The thin-layer Reynolds-averaged Navier-Stokes Equations with various turbulence models are used in this study. Computations are made on a generic, analytically-defined, close-coupled canard-wing-body configuration which has been the subject of numerous previously published experimental studies during the 1970's to mid-80's. More recently, a series of steady-flow simulations has been performed and published by the author. In the current study, the configuration is given prescribed ramp and oscillatory motions in order to predict characteristics such as the damping-in-pitch and oscillatory longitudinal stability parameters. The current computations are made at high-subsonic and transonic Mach numbers, moderate angles-of- attack from -4 to 20 degrees, and at various pitch rates and reduced frequencies. Comparisons of pressures and integrated force quantities (e.g. lift, drag, pitching moment and selected dynamic parameters) are made with other published computational results and available experimental data. Results showing the unsteady effects of the canard on surface pressures, integrated forces, canard-wing vortex interaction and vortex breakdown will be presented.

Tu, Eugene L.↗
NASA NTRS1993

Numerical and experimental investigation of the bending response of thin-walled composite cylinders

A numerical and experimental investigation of the bending behavior of six eight-ply graphite-epoxy circular cylinders is presented. Bending is induced by applying a known end-rotation to each end of the cylinders, analogous to a beam in bending. The cylinders have a nominal radius of 6 inches, a length-to-radius ratio of 2 and 5, and a radius-to-thickness ratio of approximately 160. A (+/- 45/0/90)S quasi-isotropic layup and two orthotropic layups, (+/- 45/0 sub 2)S and (+/- 45/90 sub 2)S, are studied. A geometrically nonlinear special-purpose analysis, based on Donnell's nonlinear shell equations, is developed to study the prebuckling responses and gain insight into the effects of non-ideal boundary conditions and initial geometric imperfections. A geometrically nonlinear finite element analysis is utilized to compare with the prebuckling solutions of the special-purpose analysis and to study the buckling and post buckling responses of both geometrically perfect and imperfect cylinders. The imperfect cylinder geometries are represented by an analytical approximation of the measured shape imperfections. Extensive experimental data are obtained from quasi-static tests of the cylinders using a test fixture specifically designed for the present investigation. A description of the test fixture is included. The experimental data are compared to predictions for both perfect and imperfect cylinder geometries. Prebuckling results are presented in the form of displacement and strain profiles. Buckling end-rotations, moments, and strains are reported, and predicted mode shapes are presented. Observed and predicted moment vs. end-rotation relations, deflection patterns, and strain profiles are illustrated for the post buckling responses. It is found that a geometrically nonlinear boundary layer behavior characterizes the prebuckling responses. The boundary layer behavior is sensitive to laminate orthotropy, cylinder geometry, initial geometric imperfections, applied end-rotation, and non-ideal boundary conditions. Buckling end-rotations, strains, and moments are influenced by laminate orthotropy and initial geometric imperfections. Measured buckling results correlate well with predictions for the geometrically imperfect specimens. The postbuckling analyses predict equilibrium paths with a number of scallop-shaped branches that correspond to unique deflection patterns. The observed postbuckling deflection patterns and measured strain profiles show striking similarities to the predictions in some cases. Ultimate failure of the cylinders is attributed to an interlaminar shear failure mode along the nodal lines of the postbuckling deflection patterns.

Fuchs, J. P.↗
NASA NTRSDate not supplied

Correlated Electromagnetic Levitation Actuator: A Reaction Sphere-Based Attitude Control System

To address problems experienced by current reaction wheels and control moment gyroscopebased attitude control systems (ACS), researchers at National Aeronautics and Space Administration’s (NASA’s) Marshall Space Flight Center (MSFC) have begun developing a reaction sphere actuator based on correlated electromagnetic levitation that will be immune to destructive bearing friction, momentum saturation, and gimbal lock. The Correlated Electromagnetic Levitation Actuator (CELA) advances the state of the art of reaction sphere ACSs by employing the concept of correlated magnetics. It is a frictionless, direct-drive reaction sphere that harnesses a unique technology with an array of applications across multiple disciplines. Correlated electromagnets function in a manner that is analogous to a matched filter; the convolution of two signals is peaked at the index representing the greatest match. For CELA, the signals are the patterns of magnetic flux density as a function of position. The magnitude of the convolution equates to an attractive or repulsive force, and these forces can be azimuthal or radial. The development of CELA is based in four distinct disciplines: Advanced Manufacturing, Prototype Development, Electromagnetic Modeling, and Controls. We are developing novel manufacturing techniques required to build arrays of permanent and electromagnet dipoles on curved surfaces. To print the permanent magnetic array, we have developed a probe with pyramidal magnets that will reside on a robotic arm to induce localized magnetic fields on a surface. We have also used high temperature ovens to erase dipole patterns from a permanent magnet by heating the surface to its Curie temperature. A number of test articles and prototypes have been developed using additive manufacturing methods. These prototypes have included hemispherical motors to test the drive algorithm, and a levitation test bed that demonstrates a magnetic bearing method based on attractive magnetic forces and ratiometric Hall effect sensors. We developed an array of electromagnetic dipoles on a printed circuit board (PCB) with individual H-bridges controlling each coil. This device created various flux density patterns and we measured their magnetic fields using a custom Hall effect 3-D probe and a LabVIEW virtual instrument. These data will serve as a benchmark for characterizing the accuracy of future models. Current work is focused on modeling the magnetic fields of our prototype arrays using COMSOL finite element analysis (FEA) and verifying the model against our test data. Accurate modeling will allow us to quickly test new patterns of electromagnets and their macro behavior. Eventually, the magnetic field models will be implemented in our controls simulations to facilitate precise control of the reaction sphere. Initial model results agree with field measurements to within 1 G (5% of measured flux density). Currently, we are testing different material properties of the electromagnets and their magnetic fields and thermal effects. These results will be used to refine the design of the electromagnetic dipoles. Our control efforts have centered on developing commutation, levitation, and field pattern shaping hardware in the form of breadboards and PCBs with software running on a local microcontroller. In addition, our partners developed MATLAB Simulink models to demonstrate a PID controller that mitigates disturbance forces resulting from the interaction of drive and levitation magnetics. Finally, we have designed a three-axis test stand that will be used in future work to demonstrate CELA’s orientation control capability.

reaction sphere↗
NASA NTRS1997

Experiments in Aircraft Roll-Yaw Control using Forebody Tangential Blowing

Advantages of flight at high angles of attack include increased maneuverability and lift capabilities. These are beneficial not only for fighter aircraft, but also for future supersonic and hypersonic transport aircraft during take-off and landing. At high angles of attack the aerodynamics of the vehicle are dominated by separation, vortex shedding and possibly vortex breakdown. These phenomena severely compromise the effectiveness of conventional control surfaces. As a result, controlled flight at high angles of attack is not feasible for current aircraft configurations. Alternate means to augment the control of the vehicle at these flight regimes are therefore necessary. The present work investigates the augmentation of an aircraft flight control system by the injection of a thin sheet of air tangentially to the forebody of the vehicle. This method, known as Forebody Tangential Blowing (FTB), has been proposed as an effective means of increasing the controllability of aircraft at high angles of attack. The idea is based on the fact that a small amount of air is sufficient to change the separation lines on the forebody. As a consequence, the strength and position of the vortices are altered causing a change on the aerodynamic loads. Although a very effective actuator, forebody tangential blowing is also highly non-linear which makes its use for aircraft control very difficult. In this work, the feasibility of using FTB to control the roll-yaw motion of a wind tunnel model was demonstrated both through simulations and experimentally. The wind tunnel model used in the experiments consists of a wing-body configuration incorporating a delta wing with 70-degree sweep angle and a cone-cylinder fuselage. The model is equipped with forebody slots through which blowing is applied. There are no movable control surfaces, therefore blowing is the only form of actuation. Experiments were conducted at a nominal angle of attack of 45 degrees. A unique apparatus that constrains the model to two degrees-of-freedom, roll and yaw, was designed and built. The apparatus was used to conduct dynamic experiments which showed that the system was unstable, its natural motion divergent. A model for the unsteady aerodynamic loads was developed based on the basic physics of the flow and results from flow visualization experiments. Parameters of the aerodynamic model were identified from experimental data. The model was validated using data from dynamic experiments. The aerodynamic model completes the equations of motion of the system which were used in the design of control laws using blowing as the only actuator. The unsteady aerodynamic model was implemented as part of the real-time vehicle control system. A control strategy using asymmetric blowing was demonstrated experimentally. A discrete vortex method was developed to help understand the main physics of the flow. The method correctly captures the interactions between forebody and wing vortices. Moreover, the trends in static loads and flow structure are correctly represented. Flow visualization results revealed the vortical structure of the flow to be asymmetric even for symmetric flight conditions. The effects of blowing, and roll and yaw angles on the flow structure were determined. It is shown that superimposing symmetric and asymmetric blowing has a linearizing effect on the actuator characteristics. Transient responses of roll and yaw moments to step input blowing were characterized, and their differences were explained based on the physical mechanisms through which these loads are generated.

Pedreiro, Nelson↗
DOE OSTI2025

Uncertainty estimation of bifurcated solutions in the Rayleigh–Bénard problem for advanced nuclear reactors applications

Multiphysics models of nuclear reactors frequently comprise nonlinear systems of equations. The nonlinear nature of these models could lead to solution bifurcations, where a small change in a certain parameter, e.g., the thermophysical properties of the coolant, can lead to a sudden change in the system’s behavior. At the point in parameter space where this happens, called a critical point, the Jacobian matrix of the model’s nonlinear operator becomes singular potentially permitting multiple solutions to coexist. In this paper, we perform uncertainty estimation (UE) in a parameter range that includes bifurcated solutions within the context of Rayleigh–Bénard problem. We perform this analysis assuming uncertain temperature difference, and tilt angle for the iterative solution algorithm with a unit Prandtl number (Pr = 1). Also, we perform this analysis under uncertain thermophysical properties for both FLiBe molten salt and liquid sodium as working fluid. We deploy two approaches to compute statistical moments for the resulting distributions of selected flow-field variables. The first approach is the blind computation of the mean and the standard deviation without any consideration of solution bifurcation, while the second approach utilizes k-means clustering to cluster each branch’s solutions together and compute separate statistical moments for each branch. The statistical distributions are obtained by perturbing the selected parameters about nominal values that correspond to a solution on one of the valid branches, and that solution is used as initial guess for the iterative solution algorithm. We found that perturbation of any parameter when its nominal value is close to its critical point always leads to branch jumping, i.e., the iterations converge to a solution on a branch different from the branch of the initial guess. This produces a statistical ensemble comprised of fundamentally different solutions leading to wrong mean values and uncertainty estimates, whereas clustering provides an efficient way to deal with this type of computation. This work is important for developing Gen IV nuclear systems because many of these systems rely on natural convection for cooling especially in accident conditions.

97 - MATHEMATICS AND COMPUTING↗
DOE OSTI2025

OpenSn: A massively parallel, open-source simulation environment for discrete ordinates radiation transport

OpenSn is an open-source, massively parallel deterministic radiation transport code for solving the discrete-ordinates ( S N ) form of the Boltzmann transport equation on unstructured, arbitrary polyhedral meshes. It supports high-fidelity simulations involving steady-state, eigenvalue, and adjoint problems for neutral particles (e.g., neutrons, photons, multi-particles), using the multigroup approximation in energy. OpenSn combines angular discretization via discrete ordinates with a discontinuous Galerkin finite element method (DGFEM) in space, enabling accurate resolution of transport physics on arbitrary polyhedral cells, included locally refined spatial grids. It includes multiple angular quadrature types, including locally refined angular quadratures. Written in modern C++ with a Python API, OpenSn runs efficiently on platforms ranging from laptops to supercomputers. The transport sweep algorithm is implemented using a task-based, directed-acyclic-graph (DAG) approach for each angle and supports asynchronous parallelism across thousands of MPI ranks. Group-set aggregation improves compute intensity, and synthetic acceleration techniques (e.g., diffusion synthetic acceleration, second-moment method) enhance solver convergence. OpenSn has been verified on reactor physics problems and demonstrated excellent weak and strong scaling performance on more than 32,768 processes, making it a versatile and robust platform for large-scale transport simulations in complex geometries.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1996

X-29A Lateral-Directional Stability and Control Derivatives Extracted From High-Angle-of-Attack Flight Data

The lateral-directional stability and control derivatives of the X-29A number 2 are extracted from flight data over an angle-of-attack range of 4 degrees to 53 degrees using a parameter identification algorithm. The algorithm uses the linearized aircraft equations of motion and a maximum likelihood estimator in the presence of state and measurement noise. State noise is used to model the uncommanded forcing function caused by unsteady aerodynamics over the aircraft at angles of attack above 15 degrees. The results supported the flight-envelope-expansion phase of the X-29A number 2 by helping to update the aerodynamic mathematical model, to improve the real-time simulator, and to revise flight control system laws. Effects of the aircraft high gain flight control system on maneuver quality and the estimated derivatives are also discussed. The derivatives are plotted as functions of angle of attack and compared with the predicted aerodynamic database. Agreement between predicted and flight values is quite good for some derivatives such as the lateral force due to sideslip, the lateral force due to rudder deflection, and the rolling moment due to roll rate. The results also show significant differences in several important derivatives such as the rolling moment due to sideslip, the yawing moment due to sideslip, the yawing moment due to aileron deflection, and the yawing moment due to rudder deflection.

Iliff, Kenneth W.↗
DOE OSTI2021

Filtering, averaging, and scale dependency in homogeneous variable density turbulence

We investigate relationships between statistics obtained from filtering and from ensemble or Reynolds-averaging turbulence flow fields as a function of length scale. Generalized central moments in the filtering approach are expressed as inner products of generalized fluctuating quantities, q ' ( ξ , x ) = q ( ξ ) - q ¯ ( x ) , representing fluctuations of a field q ( ξ ) , at any point ξ, with respect to its filtered value at x. For positive-definite filter kernels, these expressions provide a scale-resolving framework, with statistics and realizability conditions at any length scale. In the small-scale limit, scale-resolving statistics become zero. In the large-scale limit, scale-resolving statistics and realizability conditions are the same as in the Reynolds-averaged description. Using direct numerical simulations (DNS) of homogeneous variable density turbulence, we diagnose Reynolds stresses, T i j , resolved kinetic energy, kr, turbulent mass-flux velocity, a i , and density-specific volume covariance, b, defined in the scale-resolving framework. These variables, and terms in their governing equations, vary smoothly between zero and their Reynolds-averaged definitions at the small and large scale limits, respectively. At intermediate scales, the governing equations exhibit interactions between terms that are not active in the Reynolds-averaged limit. For example, in the Reynolds-averaged limit, b follows a decaying process driven by a destruction term; at intermediate length scales, it is a balance between production, redistribution, destruction, and transport, where b grows as the density spectrum develops and then decays when mixing becomes strong enough. This work supports the notion of a generalized, length-scale adaptive model that converges to DNS at high resolutions and to Reynolds-averaged statistics at coarse resolutions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1995

Development of Fast Algorithms Using Recursion, Nesting and Iterations for Computational Electromagnetics

In the first phase of our work, we have concentrated on laying the foundation to develop fast algorithms, including the use of recursive structure like the recursive aggregate interaction matrix algorithm (RAIMA), the nested equivalence principle algorithm (NEPAL), the ray-propagation fast multipole algorithm (RPFMA), and the multi-level fast multipole algorithm (MLFMA). We have also investigated the use of curvilinear patches to build a basic method of moments code where these acceleration techniques can be used later. In the second phase, which is mainly reported on here, we have concentrated on implementing three-dimensional NEPAL on a massively parallel machine, the Connection Machine CM-5, and have been able to obtain some 3D scattering results. In order to understand the parallelization of codes on the Connection Machine, we have also studied the parallelization of 3D finite-difference time-domain (FDTD) code with PML material absorbing boundary condition (ABC). We found that simple algorithms like the FDTD with material ABC can be parallelized very well allowing us to solve within a minute a problem of over a million nodes. In addition, we have studied the use of the fast multipole method and the ray-propagation fast multipole algorithm to expedite matrix-vector multiplication in a conjugate-gradient solution to integral equations of scattering. We find that these methods are faster than LU decomposition for one incident angle, but are slower than LU decomposition when many incident angles are needed as in the monostatic RCS calculations.

Chew, W. C.↗
NASA NTRSDate not supplied

Dynamics of A Vibration Isolation System Including Inertia of the Human Body

Using an exercise device in a spacecraft is liable to transmit an unacceptable amount of vibration to that vehicle. This is commonly mitigated by a Vibration Isolation System (VIS), whose dynamics must be analyzed to confirm that the oscillatory forces on the spacecraft remain within allowed range, both from a structural and microgravity perspective (see, e.g., [1]). When modeling a VIS for countermeasures devices, one common approach is to record forces and moments applied on the floor while exercising, and then drive the VIS simulation by applying these recorded loads to the exercise platform part of the VIS mechanical model. This approach misses the fact that when exercising on a moving platform, the force and moment on it will differ from that on the stationary floor due to inertial effects involving the human body. For example, standing up on a platform as it gives under the subject’s feet reduces the foot force on it, and such inertial effects are especially complex for rotational motion. In principle, one could model both the motion of the human body and dynamics of the VIS mechanism in a single combined simulation, e.g., employing a tool such as the commonly used biomechanical simulation OpenSim. Here, the joints of the human body would be driven kinematically along prescribed exercise trajectories while the dynamics engine computed the response of the VIS degrees of freedom. However, mechanism designers and biomechanics experts have their own established tools, making it very desirable to have a way of decoupling the biomechanics from the VIS modeling, simulation, and analyses. We have derived a set of equations that rigorously accomplishes this goal, and have implemented them as an interface function that provides an alternative driving mechanism for an existing force-based VIS analysis simulation. When enabled, the simulated human/VIS system dynamics is now driven by this function, instead of the recorded force methodology described above. The function is designed to accept input from a data file containing the required time-stamped human motion and inertia terms corresponding to the specific exercise in question. This data file is generated by an OpenSim plugin written for that purpose. The existing VIS analytical simulation is developed using NASA’s Trick Simulation Environment [2], as well as its MBDyn multibody dynamics [3] package. The presentation will provide a detailed overview of the mathematical formulation, assumptions, plugin implementation, software interfaces, and results for a sample set of representative exercises. The results from this work aim to better inform VIS design efforts, as well as countermeasure device/protocol designs with respect to exercise type and frequency effects on vehicle structural and microgravity restrictions.

Countermeasures↗
NASA NTRS1972

The stability of motion of satellites with flexible appendages

The mathematical formulation associated with the problem of stability of motion of a satellite consisting of a main rigid body and three (or less) pairs of flexible rods is presented. The rods are capable of flexure in two orthogonal directions. Whereas the rotational motion of the body is described by generalized coordinates depending on time alone, the elastic displacements of the rods depend both on spatial position and time. Assuming no external torques, there exist motion integrals in the form of momentum integrals. These integrals can be regarded as constraint equations relating the system velocities, and used to reduce the number of variables describing the motion. The stability analysis has been carried out by means of an extension of the Liapunov direct method. Since the elastic vibrations result in energy dissipation, it is shown that the equilibrium position is asymptotically stable if the Hamiltonian is positive definite and unstable if it can take negative values in the neighborhood of the equilibrium. Determining the sign definiteness of the Hamiltonian is complicated by the fact that it contains spatial derivatives of the elastic displacements. Two methods are presented to cope with this problem. The first, the standard modal analysis in conjunction with series truncation, develops criteria in terms of infinite series associated with the natural modes and frequencies of the elastic rods. The second, the method of integral coordinates, yields closed-form stability criteria involving the system parameters, such as the body moments of inertia, the length and mass distribution of the rods, the lowest natural frequencies of the rods, and the satellite spin velocity.

Meirovitch, L.↗
DOE OSTI2020

Spatial and momentum imaging of the pion and kaon

We determine the leading Fock state light front wave functions (LFWFs) of the pion and kaon via light front projections of the covariant Bethe-Salpeter wave function. Using these LFWFs we study the multidimensional images of the valence quarks in the pion and kaon that are provided by their generalized parton distribution functions (GPDs) and transverse momentum dependent parton distribution functions (TMDs). Moments of the GPDs are taken to obtain the electromagnetic and gravitational form factors of the pion and kaon, and comparisons to available experimental and lattice data are made. Highlights from this study include predictions that the mean-squared impact parameter for the quarks in the pion and kaon are: ( b T 2 ) u π = 0.11 fm 2 , ( b T 2 ) s K = 0.08 fm 2 , and ( b T 2 ) u K = 0.13 fm 2 , and therefore the s quark in the kaon is much closer to the center of transverse momentum than the u quark. From the electromagnetic and gravitational form factors we find that the light-cone energy radii are about 60% smaller than the light-cone charge radii for each quark sector in the pion and kaon. A quantitative measure of the importance of the leading Fock state is obtained via comparison with a full Dyson-Schwinger equations calculation (containing an infinite tower of Fock states) for the pion form factor.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1976

The passage of a distorted velocity field through a cascade of airfoils

An analysis has been developed to predict the unsteady force and moment generated by the passage of a timewise periodic total pressure distortion through an arbitrary cascade of airfoils. The mathematical formulation of this analysis is based on the assumption that the magnitudes of the timewise fluctuations of the variables which describe the flow field are small compared to their time average values. This assumption permits the development of a linear unsteady perturbation analysis about a steady flow field. In addition to this linearization assumption the fluid medium is assumed to be incompressible and inviscid. The mathematical development begins by decomposing the velocity field surrounding an infinite cascade of airfoils into its irrotational and rotational components. The rotational component is associated with an upstream unsteady total pressure distortion and is defined in terms of the vorticity field associated with the distortion pattern. The irrotational component is further decomposed into a steady and unsteady part. A combined analytical and numerical procedure has been developed to solve the field equations which govern the rotational and irrotational velocity fields. Results of this analysis show a strong influence of mean loading on the unsteady force generated by the passage of a one dimensional gust through a cascade of compressor blades.

Adamczyk, J. J.↗
NASA NTRS1990

Implicit flux-split Euler schemes for unsteady aerodynamic analysis involving unstructured dynamic meshes

Improved algorithm for the solution of the time-dependent Euler equations are presented for unsteady aerodynamic analysis involving unstructured dynamic meshes. The improvements were developed recently to the spatial and temporal discretizations used by unstructured grid flow solvers. The spatial discretization involves a flux-split approach which is naturally dissipative and captures shock waves sharply with at most one grid point within the shock structure. The temporal discretization involves an implicit time-integration scheme using a Gauss-Seidel relaxation procedure which is computationally efficient for either steady or unsteady flow problems. For example, very large time steps may be used for rapid convergence to steady state, and the step size for unsteady cases may be selected for temporal accuracy rather than for numerical stability. Steady and unsteady flow results are presented for the NACA 0012 airfoil to demonstrate applications of the new Euler solvers. The unsteady results were obtained for the airfoil pitching harmonically about the quarter chord. The resulting instantaneous pressure distributions and lift and moment coefficients during a cycle of motion compare well with experimental data. A description of the Euler solvers is presented along with results and comparisons which assess the capability.

Batina, John T.↗
NASA NTRS1990

Implicit flux-split Euler schemes for unsteady aerodynamic analysis involving unstructured dynamic meshes

Improved algorithms for the solution of the time-dependent Euler equations are presented for unsteady aerodynamic analysis involving unstructured dynamic meshes. The improvements have been developed recently to the spatial and temporal discretizations used by unstructured grid flow solvers. The spatial discretization involves a flux-split approach which is naturally dissipative and captures shock waves sharply with at most one grid point within the shock structure. The temporal discretization involves an implicit time-integration shceme using a Gauss-Seidel relaxation procedure which is computationally efficient for either steady or unsteady flow problems. For example, very large time steps may be used for rapid convergence to steady state, and the step size for unsteady cases may be selected for temporal accuracy rather than for numerical stability. Steady and unsteady flow results are presented for the NACA 0012 airfoil to demonstrate applications of the new Euler solvers. The unsteady results were obtained for the airfoil pitching harmonically about the quarter chord. The resulting instantaneous pressure distributions and lift and moment coefficients during a cycle of motion compare well with experimental data. The paper presents a description of the Euler solvers along with results and comparisons which assess the capability.

Batina, John T.↗
DOE OSTI2025

The Stochastic Gause Predator-Prey model: Noise-induced extinctions and invariance

We consider the Gause predator-prey with general bounded or sub‑linear functional responses, – which includes those of Holling types Ⅰ–Ⅳ. – and multiplicative Gaussian noise. In contrast to previous studies, the prey in our model follows logistic dynamics while the predator's population is solely regulated by consumption of the prey. To ensure well-posedeness, we derive explicit Lyapunov‐type criteria ensuring global positivity and moment boundedness of solutions. We find conditions for noise‑induced extinctions, proving that stochasticity can drive either population to collapse even when the deterministic analogue predicts stable coexistence. In the case when the predator becomes extinct, we establish a limiting distribution for the predator's population. Last, for functional responses of Holling type Ⅰ, we provide sufficient conditions on the intensity of the noise for the existence and uniqueness of a stationary distribution.

Gause model↗
NASA NTRS1998

Effect of Apex Flap Deflection on Vertical Tail Buffeting

A computational study of the effect of vortex breakdown location on vertical tail buffeting is conducted. The position of the breakdown is modified by employing an apex flap deflected by an experimentally determined optimal angle. The delayed breakdown flow and buffeting response is then compared to the nominal undeflected case. This multidisciplinary problem is solved sequentially for the fluid flow, the elastic tail deformations and the grid displacements. The fluid flow is simulated by time accurately solving the unsteady, compressible, Reynolds-averaged Navier-Stokes equations using an implicit, upwind, flux-difference splitting finite volume scheme. The elastic vibrations of the tails are modeled by uncoupled bending and torsion beam equations. These equations are solved accurately in time using the Galerkin method and a five-stage Runge-Kutta-Verner scheme. The grid for the fluid dynamics calculations is continuously deformed using interpolation functions to disperse the displacements smoothly throughout the computational domain. An angle-of-attack of 35 deg.is chosen such that the wing primary-vortex cores experience vortex breakdown and the resulting turbulent wake flow impinges on tile vertical tails. The dimensions and material properties of the vertical tails are chosen such that the deflections are large enough to insure interaction with the flow, and the natural frequencies are high enough to facilitate a practical computational solution. Results are presented for a baseline uncontrolled buffeting case and a delayed breakdown case in which the apex flap has been deflected 15 deg. The flap was found to be very effective in delaying the breakdown, increasing the location from 50%c to 94%c, which resulted in a 6% increase in lift coefficient and pitching moment. However, the integrated buffet loads and tip responses were roughly equivalent for the two cases.

Massey, Steven J.↗
NASA NTRS2003

Development of Numerical Codes for Modeling Electromagnetic Behavior at High Frequencies Near Large Objects

A study into the problem of determining electromagnetic solutions at high frequencies for problems involving complex geometries, large sizes and multiple sources (e.g. antennas) has been initiated. Typical applications include the behavior of antennas (and radiators) installed on complex conducting structures (e.g. ships, aircrafts, etc..) with strong interactions between antennas, the radiation patterns, and electromagnetic signals is of great interest for electromagnetic compatibility control. This includes the overall performance evaluation and control of all on-board radiating systems, electromagnetic interference, and personnel radiation hazards. Electromagnetic computational capability exists at NASA LaRC, and many of the codes developed are based on the Moment Method (MM). However, the MM is computationally intensive, and this places a limit on the size of objects and structures that can be modeled. Here, two approaches are proposed: (i) a current-based hybrid scheme that combines the MM with Physical optics, and (ii) an Alternating Direction Implicit-Finite Difference Time Domain (ADI-FDTD) method. The essence of a hybrid technique is to split the overall scattering surface(s) into two regions: (a) a MM zone (MMZ) which can be used over any part of the given geometry, but is most essential over irregular and "non-smooth" geometries, and (b) a PO sub-region (POSR). Currents induced on the scattering and reflecting surfaces can then be computed in two ways depending on whether the region belonged to the MMZ or was part of the POSR. For the MMZ, the current calculations proceed in terms of basis functions with undetermined coefficients (as in the usual MM method), and the answer obtained by solving a system of linear equations. Over the POSR, conduction is obtained as a superposition of two contributions: (i) currents due to the incident magnetic field, and (ii) currents produced by the mutual induction from conduction within the MMZ. This effectively leads to a reduction in the size of linear equations from N to N - Npo with N being the total number of segments for the entire surface and Npo the number of segments over the POSR. The scheme would be appropriate for relatively large, flat surfaces, and at high frequencies. The ADI-FDTD scheme provides for both transient and steady state analyses. The restrictive Courant-Friedrich-Levy (CFL) condition on the time-step is removed, and so large time steps can be chosen even though the spatial grids are small. This report includes the problem definition, a detailed discussion of both the numerical techniques, and numerical implementations for simple surface geometries. Numerical solutions have been derived for a few simple situations.

Joshi, R. P.↗