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NASA NTRS1994

Interaction of the sonic boom with atmospheric turbulence

Theoretical research was carried out to study the effect of free-stream turbulence on sonic boom pressure fields. A new transonic small-disturbance model to analyze the interactions of random disturbances with a weak shock was developed. The model equation has an extended form of the classic small-disturbance equation for unsteady transonic aerodynamics. An alternative approach shows that the pressure field may be described by an equation that has an extended form of the classic nonlinear acoustics equation that describes the propagation of sound beams with narrow angular spectrum. The model shows that diffraction effects, nonlinear steepening effects, focusing and caustic effects and random induced vorticity fluctuations interact simultaneously to determine the development of the shock wave in space and time and the pressure field behind it. A finite-difference algorithm to solve the mixed type elliptic-hyperbolic flows around the shock wave was also developed. Numerical calculations of shock wave interactions with various deterministic and random fluctuations will be presented in a future report.

Rusak, Zvi↗
NASA NTRS1994

Sonic boom interaction with turbulence

A recently developed transonic small-disturbance model is used to analyze the interactions of random disturbances with a weak shock. The model equation has an extended form of the classic small-disturbance equation for unsteady transonic aerodynamics. It shows that diffraction effects, nonlinear steepening effects, focusing and caustic effects and random induced vorticity fluctuations interact simultaneously to determine the development of the shock wave in space and time and the pressure field behind it. A finite-difference algorithm to solve the mixed-type elliptic hyperbolic flows around the shock wave is presented. Numerical calculations of shock wave interactions with various deterministic vorticity and temperature disturbances result in complicate shock wave structures and describe peaked as well as rounded pressure signatures behind the shock front, as were recorded in experiments of sonic booms running through atmospheric turbulence.

Zvi Rusak↗
NASA NTRS1994

Magnetometer-only attitude and rate determination for a gyro-less spacecraft

Attitude determination algorithms that requires only the earth's magnetic field will be useful for contingency conditions. One way to determine attitude is to use the time derivative of the magnetic field as the second vector in the attitude determination process. When no gyros are available, however, attitude determination becomes difficult because the rates must be propagated via integration of Euler's equation, which in turn requires knowledge of the initial rates. The spacecraft state to be determined must then include not only the attitude but also rates. This paper describes a magnetometer-only attitude determination scheme with no a priori knowledge of the spacecraft state, which uses a deterministic algorithm to initialize an extended Kalman filter. The deterministic algorithm uses Euler's equation to relate the time derivatives of the magnetic field in the reference and body frames and solves the resultant transcendental equations for the coarse attitude and rates. An important feature of the filter is that its state vector also includes corrections to the propagated rates, thus enabling it to generate highly accurate solutions. The method was tested using in-flight data from the Solar, Anomalous, and Magnetospheric Particles Explorer (SAMPEX), a Small Explorer spacecraft. SAMPEX data using several eclipse periods were used to simulate conditions that may exist during the failure of the on-board digital sun sensor. The combined algorithm has been found effective, yielding accuracies of 1.5 deg in attitude (within even nominal mission requirements) and 0.01 degree per second (deg/sec) in the rates.

Natanson, G. A.↗
NASA NTRS1995

On the breakup of viscous liquid threads

A one-dimensional model evolution equation is used to describe the nonlinear dynamics that can lead to the breakup of a cylindrical thread of Newtonian fluid when capillary forces drive the motion. The model is derived from the Stokes equations by use of rational asymptotic expansions and under a slender jet approximation. The equations are solved numerically and the jet radius is found to vanish after a finite time yielding breakup. The slender jet approximation is valid throughout the evolution leading to pinching. The model admits self-similar pinching solutions which yield symmetric shapes at breakup. These solutions are shown to be the ones selected by the initial boundary value problem, for general initial conditions. Further more, the terminal state of the model equation is shown to be identical to that predicted by a theory which looks for singular pinching solutions directly from the Stokes equations without invoking the slender jet approximation throughout the evolution. It is shown quantitatively, therefore, that the one-dimensional model gives a consistent terminal state with the jet shape being locally symmetric at breakup. The asymptotic expansion scheme is also extended to include unsteady and inerticial forces in the momentum equations to derive an evolution system modelling the breakup of Navier-Stokes jets. The model is employed in extensive simulations to compute breakup times for different initial conditions; satellite drop formation is also supported by the model and the dependence of satellite drop volumes on initial conditions is studied.

Papageorgiou, Demetrios T.↗
NASA NTRS1995

More About Pressure Probes For Turbulent Flows

Array of probes yields data on static and total pressures and cross-stream turbulence. Is combination of separate pressure-probe arrays described in "Measuring Streamwise Momentum and Cross-Stream Turbulence" (ARC-11934), and "Probe Rakes To Measure Static Pressure and Turbulence" (ARC-12973). Equations that express directional responses of various probes in array solved together to eliminate unknown quantities; makes it possible to process digitized time-averaged probe readings together to obtain time-averaged static, stagnation, and cross-stream-turbulence pressures.

Rossow, Vernon J.↗
NASA NTRS1999

Use of Boundary Layer Transition Detection to Validate Full-Scale Flight Performance Predictions

Full-scale flight performance predictions can be made using CFD or a combination of CFD and analytical skin-friction predictions. However, no matter what method is used to obtain full-scale flight performance predictions knowledge of the boundary layer state is critical. The implementation of CFD codes solving the Navier-Stokes equations to obtain these predictions is still a time consuming, expensive process. In addition, to ultimately obtain accurate performance predictions the transition location must be fixed in the CFD model. An example, using the M2.4-7A geometry, of the change in Navier-Stokes solution with changes in transition and in turbulence model will be shown. Oil flow visualization using the M2.4-7A 4.0% scale model in the 14'x22' wind tunnel shows that fixing transition at 10% x/c in the CFD model best captures the flow physics of the wing flow field. A less costly method of obtaining full-scale performance predictions is the use of non-linear Euler codes or linear CFD codes, such as panel methods, combined with analytical skin-friction predictions. Again, knowledge of the boundary layer state is critical to the accurate determination of full-scale flight performance. Boundary layer transition detection has been performed at 0.3 and 0.9 Mach numbers over an extensive Reynolds number range using the 2.2% scale Reference H model in the NTF. A temperature sensitive paint system was used to determine the boundary layer state for these conditions. Data was obtained for three configurations: the baseline, undeflected flaps configuration; the transonic cruise configuration; and, the high-lift configuration. It was determined that at low Reynolds number conditions, in the 8 to 10 million Reynolds number range, the baseline configuration has extensive regions of laminar flow, in fact significantly more than analytical skin-friction methods predict. This configuration is fully turbulent at about 30 million Reynolds number for both 0.3 and 0.9, Mach numbers. Both the transonic cruise and the high-lift configurations were fully turbulent aft of the leading-edge flap hingeline at all Reynolds numbers.

Hamner, Marvine↗
NASA NTRS2001

Computational Aeroacoustics by the Space-time CE/SE Method

In recent years, a new numerical methodology for conservation laws-the Space-Time Conservation Element and Solution Element Method (CE/SE), was developed by Dr. Chang of NASA Glenn Research Center and collaborators. In nature, the new method may be categorized as a finite volume method, where the conservation element (CE) is equivalent to a finite control volume (or cell) and the solution element (SE) can be understood as the cell interface. However, due to its rigorous treatment of the fluxes and geometry, it is different from the existing schemes. The CE/SE scheme features: (1) space and time treated on the same footing, the integral equations of conservation laws are solve( for with second order accuracy, (2) high resolution, low dispersion and low dissipation, (3) novel, truly multi-dimensional, simple but effective non-reflecting boundary condition, (4) effortless implementation of computation, no numerical fix or parameter choice is needed, an( (5) robust enough to cover a wide spectrum of compressible flow: from weak linear acoustic waves to strong, discontinuous waves (shocks) appropriate for linear and nonlinear aeroacoustics. Currently, the CE/SE scheme has been developed to such a stage that a 3-13 unstructured CE/SE Navier-Stokes solver is already available. However, in the present paper, as a general introduction to the CE/SE method, only the 2-D unstructured Euler CE/SE solver is chosen as a prototype and is sketched in Section 2. Then applications of the CE/SE scheme to linear, nonlinear aeroacoustics and airframe noise are depicted in Sections 3, 4, and 5 respectively to demonstrate its robustness and capability.

Loh, Ching Y.↗
NASA NTRS2005

A First and Second Order Moment Approach to Probabilistic Control Synthesis

This paper presents a robust control design methodology based on the estimation of the first two order moments of the random variables and processes that describe the controlled response. Synthesis is performed by solving an multi-objective optimization problem where stability and performance requirements in time- and frequency domains are integrated. The use of the first two order moments allows for the efficient estimation of the cost function thus for a faster synthesis algorithm. While reliability requirements are taken into account by using bounds to failure probabilities, requirements related to undesirable variability are implemented by quantifying the concentration of the random outcome about a deterministic target. The Hammersley Sequence Sampling and the First- and Second-Moment- Second-Order approximations are used to estimate the moments, whose accuracy and associated computational complexity are compared numerically. Examples using output-feedback and full-state feedback with state estimation are used to demonstrate the ideas proposed.

Crespo, Luis G.↗
NASA NTRS2019

Series solution for motion in an arbitrary potential field

The equations of motion for a test particle in an arbitrary potential field is solved as a formal power series. This solution is in terms of the time derivatives of the motion of the test particle. These derivative may be used to construct a Taylor series for the motion of the particle in the vicinity of given initial conditions.

Strange, Nathan↗
NASA NTRSDate not supplied

Full Stall Simulations of a Redesigned Ventilation Fan for the ISS

The concept of a stall is studied rigorously in the aerospace industry. From a design standpoint, instabilities such as stall are undesirable– operation in the stall regime has a tremendous impact on aerodynamic performance as well as structural integrity. In extreme cases, operating in stall conditions can cause failure. Further, stall can cause a loss of lift on aircraft wings or a loss of thrust in aircraft engines. In any case, stall continues to be a topic of interest in the aerospace industry. The present work aims to analyze the stall characteristics of a ventilation fan that was recently designed for the International Space Station (ISS). Although the ventilation fan has a rotor-stator design, this paper considers a rotor-only configuration. The FUN3D Computational Fluid Dynamic (CFD) solver developed by NASA Langley Research Center was used to simulate the operational characteristics of the ventilation fan. FUN3D solves the Unsteady Reynolds-Averaged Naiver-Stokes (URANS) equations using implicit time marching and a dynamic overset grid. The FUN3D solver was originally written for exterior flow fields; however, this work represents an extension of the FUN3D solver to turbomachinery or interior flow fields. The FUN3D results for the rotor-only ventilation fan accurately captured the operational characteristics inherent to compressors– the results shared similar performance trends when compared to the experimental results for the rotor-stator case. A peak adiabatic efficiency of 96% occurred at a MFR of 105.2 CFM, the minimum aerodynamically stable point. A computationally stable stall occurred at a mass flow rate of 43.8 CFM where the adiabatic efficiency dropped to 69%.

CFD↗
NASA NTRS2023

Aviation 2072: Scenario Planning for Wicked Problems

The world is changing rapidly. And with it, so are the potential futures for humanity. Many of these potential futures pose hidden threats, while others offer new opportunities for aviation and the broader aerospace community. To mitigate these risks and capitalize on opportunities, organizations must work to deeply understand these potential future scenarios and uncover any underlying drivers. Organizations will be more equipped and informed when making strategic investment decisions by better understanding these threats, opportunities, and drivers . The future scenarios and their threats and opportunities described in this paper were identified through a series of extensive brainstorming workshops, collectively titled MADNESS (Mapping for Aviation Driven by Needs Emergence and Satiating Society). These workshops engaged NASA civil servants and contractors with diverse backgrounds through a facilitated process of future scenario development and critique. The participants were led through exercises focused on a time horizon spanning from 2022 to 2072 and on problems that aviation might solve and or create during this period. From the broad results, two patterns of critical uncertainty emerged: “availability” (scarcity versus abundance) and “transparency” (openness versus security and privacy). The successful iteration and ideation across the MADNESS workshops also suggests a repeatable mechanism for strategic risk exploration across a variety of NASA and industry stakeholders.

Mapping↗
NASA NTRS2003

Shared Activity Coordination

Interacting agents that interleave planning and execution must reach consensus on their commitments to each other. In domains where agents have varying degrees of interaction and different constraints on communication and computation, agents will require different coordination protocols in order to efficiently reach consensus in real time. We briefly describe a largely unexplored class of real-time, distributed planning problems (inspired by interacting spacecraft missions), new challenges they pose, and a general approach to solving the problems. These problems involve self-interested agents that have infrequent communication but collaborate on joint activities. We describe a Shared Activity Coordination (SHAC) framework that provides a decentralized algorithm for negotiating the scheduling of shared activities in a dynamic environment, a soft, real-time approach to reaching consensus during execution with limited communication, and a foundation for customizing protocols for negotiating planner interactions. We apply SHAC to a realistic simulation of interacting Mars missions and illustrate the simplicity of protocol development.

coordination↗
NASA NTRS1953

Transient temperature distributions in simple conducting bodies steadily heated through a laminar boundary layer

An analysis is made of the transient heat-conduction effects in three simple semi-infinite bodies: the flat insulated plate, the conical shell, and the slender solid cone. The bodies are assumed to have constant initial temperatures and, at zero time, to begin to move at a constant speed and zero angle of attack through a homogeneous atmosphere. The heat input is taken as that through a laminar boundary layer. Radiation heat transfer and transverse temperature gradients are assumed to be zero. The appropriate heat-conduction equations are solved by an iteration method, the zeroeth-order terms describing the situation in the limit of small time. The method is presented and the solutions are calculated to three orders which are sufficient to give reasonably accurate results when the forward edge has attained one-half the total temperature rise (nose half-rise time). Flight Mach number and air properties occur as parameters in the result. Approximate expressions for the extent of the conduction region and nose half-rise times as functions of the parameters of the problem are presented. (author)

Parker, Hermon M↗
NASA NTRS1998

Computational Modeling of Vertical-Cavity Surface-Emitting Lasers

Vertical-Cavity Surface-Emitting Lasers (VCSELs) have become increasingly important for many applications, such as optical interconnects and optical data storages. In many applications, critical requirements are very often high beam quality and/or high output powers. To help the design and optimization of VCSELs for such applications, it is essential to have a simulation model that includes the time evolution of the transverse space dependence of the hewn. Such models allow arbitrary transverse profiles of laser intensity or carrier density to develop in time without any a priori assumption about the number and types of transverse modes. In addition, extensive research in the past has shown that many-body effects are important in influencing the optical gain and the refractive index of semiconductor quantum wells. It is thus important to include the key many-body effects in simulation models for semiconductor lasers. A computational model, called the Maxwell-Effective Bloch Equations (MEBE) was developed recently that simulates the above features and effects. This model combines the space-time resolution with microscopic many-body effects in a way that is both accurate enough and computationally manageable. This model has been used to simulate edge-emitting high power lasers recently. A new finite-difference algorithm has been developed for solving these equations and will be shown in the presentation. That algorithm will be used to calculate the detailed time evolution of the transverse mode profiles of VCSELs. The VCSELs are based on InGaAs/GaAs quantum well structures. Effects of pumping current and refractive index profiles will be investigated in detail. The simulation results will be compared with other results the use the rate-equation model.

Goorjian, Peter M.↗
NASA NTRS1998

Computational Nonlinear of Vertical-Cavity Surface-Emitting Lasers

Vertical-Cavity Surface-Emitting Lasers (VCSELs) have become increasingly important for many applications, such as optical interconnects and optical data storages. In many applications, critical requirements are very often high beam quality and/or high output powers. To help the design and optimization of VCSELs for such applications, it is essential to have a simulation model that includes the time evolution of the transverse space dependence of the beam. Such models allow arbitrary transverse profiles of laser intensity or carrier density to develop in time without any a priori assumption about the number and types of transverse modes. In addition, extensive research in the past has shown that many-body effects are important in influencing the optical gain and the refractive index of semiconductor quantum wells. It is thus important to include the key many-body effects in simulation models for semiconductor lasers. A computational model, called the Maxwell-Effective Bloch Equations (MEBE) was developed recently that simulates the above features and effects. This model combines the space-time resolution with microscopic many-body effects in a way that is both accurate enough and computationally manageable. This model has been used to simulate edge-emitting high power lasers recently. A new finite-difference algorithm has been developed for solving these equations and will be shown in the presentation. That algorithm will be used to calculate the detailed time evolution of the transverse mode profiles of VCSELs. The VCSELs are based on InGaAs/GaAs quantum well structures. Effects of pumping current and refractive index profiles will be investigated in detail. The simulation results will be compared with other results the use the rate-equation model.

Goorjian, Peter M.↗
NASA NTRS2017

Model-Based Thermal System Design Optimization for the James Webb Space Telescope

Spacecraft thermal model validation is normally performed by comparing model predictions with thermal test data and reducing their discrepancies to meet the mission requirements. Based on thermal engineering expertise, the model input parameters are adjusted to tune the model output response to the test data. The end result is not guaranteed to be the best solution in terms of reduced discrepancy and the process requires months to complete. A model-based methodology was developed to perform the validation process in a fully automated fashion and provide mathematical bases to the search for the optimal parameter set that minimizes the discrepancies between model and data. The methodology was successfully applied to several thermal subsystems of the James Webb Space Telescope (JWST). Global or quasiglobal optimal solutions were found and the total execution time of the model validation process was reduced to about two weeks. The model sensitivities to the parameters, which are required to solve the optimization problem, can be calculated automatically before the test begins and provide a library for sensitivity studies. This methodology represents a crucial commodity when testing complex, large-scale systems under time and budget constraints. Here, results for the JWST Core thermal system will be presented in detail.

Cataldo, Giuseppe↗
NASA NTRS1995

A 3D High-Order Unstructured Finite-Volume Algorithm for Solving Maxwell's Equations

A three-dimensional finite-volume algorithm based on arbitrary basis functions for time-dependent problems on general unstructured grids is developed. The method is applied to the time-domain Maxwell equations. Discrete unknowns are volume integrals or cell averages of the electric and magnetic field variables. Spatial terms are converted to surface integrals using the Gauss curl theorem. Polynomial basis functions are introduced in constructing local representations of the fields and evaluating the volume and surface integrals. Electric and magnetic fields are approximated by linear combinations of these basis functions. Unlike other unstructured formulations used in Computational Fluid Dynamics, the new formulation actually does not reconstruct the field variables at each time step. Instead, the spatial terms are calculated in terms of unknowns by precomputing weights at the beginning of the computation as functions of cell geometry and basis functions to retain efficiency. Since no assumption is made for cell geometry, this new formulation is suitable for arbitrarily defined grids, either smooth or unsmooth. However, to facilitate the volume and surface integrations, arbitrary polyhedral cells with polygonal faces are used in constructing grids. Both centered and upwind schemes are formulated. It is shown that conventional schemes (second order in Cartesian grids) are equivalent to the new schemes using first degree polynomials as the basis functions and the midpoint quadrature for the integrations. In the new formulation, higher orders of accuracy are achieved by using higher degree polynomial basis functions. Furthermore, all the surface and volume integrations are carried out exactly. Several model electromagnetic scattering problems are calculated and compared with analytical solutions. Examples are given for cases based on 0th to 3rd degree polynomial basis functions. In all calculations, a centered scheme is applied in the interior, while an upwind matching scheme is employed at material interfaces and the Engquist-Majda non-reflecting boundary condition is implemented at the numerical outer boundaries. The staggered leapfrog scheme and the Runge-Kutta methods are utilized for the time integration. Excellent agreements are found between the numerical and analytical solutions.

Liu, Yen↗
NASA NTRS1986

A robust adaptive flightpath reconstruction technique

Computational schemes are presented that allow accurate reconstruction of an aircraft's flightpath in real-time. The reconstruction of the flightpath is formulated as a linear state reconstruction problem, which can be solved via Kalman filtering (KF) techniques. This imposes some conditions upon the flight-test equipment. A reliable square root covariance KF (SRCF) implementation is chosen and further developed into a fully adaptive flightpath reconstruction scheme. Therefore, the basic SRCF is modified in order to cope with several practical problems such as: the automatic control of the convergence of the recursive KF calculations, time varying zero-bias errors on the input signal of the system model used in the KF, and the changing aircraft dynamics owing to a change in reference flight condition. The developed solutions for these problems are all implemented in a numerically stable way, which guarantees the overall flightpath reconstruction scheme to be robust. Furthermore, some special features of the used system model are exploited to make the algorithmic implementation very efficient. An experimental simulation study using simulated flight test data demonstrated these different capabilities.

Verhaegen, M. H.↗