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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 613 records · Page 34
All sourcesNASA NTRSDOE OSTI
NASA NTRS1981

Computer program for aerodynamic and blading design of multistage axial-flow compressors

A code for computing the aerodynamic design of a multistage axial-flow compressor and, if desired, the associated blading geometry input for internal flow analysis codes is presented. Compressible flow, which is assumed to be steady and axisymmetric, is the basis for a two-dimensional solution in the meridional plane with viscous effects modeled by pressure loss coefficients and boundary layer blockage. The radial equation of motion and the continuity equation are solved with the streamline curvature method on calculation stations outside the blade rows. The annulus profile, mass flow, pressure ratio, and rotative speed are input. A number of other input parameters specify and control the blade row aerodynamics and geometry. In particular, blade element centerlines and thicknesses can be specified with fourth degree polynomials for two segments. The output includes a detailed aerodynamic solution and, if desired, blading coordinates that can be used for internal flow analysis codes.

Crouse, J. E.↗
NASA NTRS1985

Minimal norm constrained interpolation

In computational fluid dynamics and in CAD/CAM, a physical boundary is usually known only discreetly and most often must be approximated. An acceptable approximation preserves the salient features of the data such as convexity and concavity. In this dissertation, a smooth interpolant which is locally concave where the data are concave and is locally convex where the data are convex is described. The interpolant is found by posing and solving a minimization problem whose solution is a piecewise cubic polynomial. The problem is solved indirectly by using the Peano Kernal theorem to recast it into an equivalent minimization problem having the second derivative of the interpolant as the solution. This approach leads to the solution of a nonlinear system of equations. It is shown that Newton's method is an exceptionally attractive and efficient method for solving the nonlinear system of equations. Examples of shape-preserving interpolants, as well as convergence results obtained by using Newton's method are also shown. A FORTRAN program to compute these interpolants is listed. The problem of computing the interpolant of minimal norm from a convex cone in a normal dual space is also discussed. An extension of de Boor's work on minimal norm unconstrained interpolation is presented.

Irvine, L. D.↗
NASA NTRS1961

A Method for Obtaining the Nonlinear Aerodynamic Stability Characteristics of Bodies of Revolution from Free-Flight Tests

A method is presented for obtaining the nonlinear aerodynamic stability characteristics of bodies of revolution from free-flight test.s The necessary conditions for the application of this method are: (1) that the roll rate and damping encountered in a single cycle of oscillation be small, and (2) that the resulting motion be reasonably planar. Four approximations to the nonlinear restoring moment are considered and solutions are obtained in closed form: 1. A single-term polynomial in an arbitrary power of the angle of attack. 2. A two-term polynomial having linear and cubic terms. 3. A three-term polynomial having linear, quadratic, and cubic terms. 4. A three-term polynomial having linear, quadratic, and cubic terms. An iteration procedure is formulated to allow the use of each of these approximations for obtaining the aerodynamic coefficients of bodies of revolution from free-flight test data. It is found that although the equations that are solved pertain strictly to planar motion, the solutions are applicable to motions that deviate to a fairly large degree from planar motion.

Kirk, Donn B.↗
DOE OSTI2026

Bayesian Adaptive Polynomial Chaos Expansions

Polynomial chaos expansions (PCEs) are widely used for uncertainty quantification (UQ) tasks, particularly in the applied mathematics community. However, PCE has received comparatively less attention in the statistics literature, and fully Bayesian formulations remain rare—especially with implementations in R. Motivated by the success of adaptive Bayesian machine learning models such as BART, BASS and BPPR, we develop a new fully Bayesian adaptive PCE method with an efficient and accessible R implementation: khaos. Our approach includes a novel proposal distribution that enables data-driven interaction selection and supports a modified g-prior tailored to PCE structure. Through simulation studies and real-world UQ applications, we demonstrate that the Bayesian adaptive PCE provides competitive performance for surrogate modeling, global sensitivity analysis and ordinal regression tasks.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1977

Symbolic computation of recurrence equations for the Chebyshev series solution of linear ODE's

If a linear ordinary differential equation with polynomial coefficients is converted into integrated form then the formal substitution of a Chebyshev series leads to recurrence equations defining the Chebyshev coefficients of the solution function. An explicit formula is presented for the polynomial coefficients of the integrated form in terms of the polynomial coefficients of the differential form. The symmetries arising from multiplication and integration of Chebyshev polynomials are exploited in deriving a general recurrence equation from which can be derived all of the linear equations defining the Chebyshev coefficients. Procedures for deriving the general recurrence equation are specified in a precise algorithmic notation suitable for translation into any of the languages for symbolic computation. The method is algebraic and it can therefore be applied to differential equations containing indeterminates.

Geddes, K. O.↗
NASA NTRS2001

A Global Optimization Methodology for Rocket Propulsion Applications

While the response surface method is an effective method in engineering optimization, its accuracy is often affected by the use of limited amount of data points for model construction. In this chapter, the issues related to the accuracy of the RS approximations and possible ways of improving the RS model using appropriate treatments, including the iteratively re-weighted least square (IRLS) technique and the radial-basis neural networks, are investigated. A main interest is to identify ways to offer added capabilities for the RS method to be able to at least selectively improve the accuracy in regions of importance. An example is to target the high efficiency region of a fluid machinery design space so that the predictive power of the RS can be maximized when it matters most. Analytical models based on polynomials, with controlled level of noise, are used to assess the performance of these techniques.

Source record↗
NASA NTRS1982

Numerical computation of exponential matrices using the Cayley-Hamilton theorem

A method for computing exponential matrices, which often arise naturally in the solution of systems of linear differential equations, is developed. An exponential matrix is generated as a linear combination of a finite number (equal to the matrix order) of matrices, the coefficients of which are scalar infinite sums. The method can be generalized to apply to any formal power series of matrices. Attention is focused upon the exponential function, and the matrix exponent is assumed tri-diagonal in form. In such cases, the terms in the coefficient infinite sums can be extracted, as recursion relations, from the characteristic polynomial of the matrix exponent. Two numerical examples are presented in some detail: (1) the three dimensional infinitesimal rotation rate matrix, which is skew symmetric, and (2) an N-dimensional tri-diagonal and symmetric finite difference matrix which arises in the numerical solution of the heat conduction partial differential equation. In the second example, the known eigenvalues and eigenvectors of the finite difference matrix permit an analytical solution for the exponential matrix, through the theory of diagonalization and similarity transformations, which is used for independent verification. The convergence properties of the scalar infinite summations are investigated for finite difference matrices of various orders up to ten, and it is found that the number of terms required for convergence increases slowly with the order of the matrix.

Walden, H.↗
NASA NTRS1986

A new VLSI complex integer multiplier which uses a quadratic-polynomial residue system with Fermat numbers

A quadratic-polynomial Fermat residue number system (QFNS) has been used to compute complex integer multiplications. The advantage of such a QFNS is that a complex integer multiplication requires only two integer multiplications. In this article, a new type Fermat number multiplier is developed which eliminates the initialization condition of the previous method. It is shown that the new complex multiplier can be implemented on a single VLSI chip. Such a chip is designed and fabricated in CMOS-pw technology.

Truong, T. K.↗
NASA NTRS1987

A new VLSI complex integer multiplier which uses a quadratic-polynomial residue system with Fermat numbers

A quadratic-polynomial Fermat residue number system (QFNS) has been used to compute complex integer multiplications. The advantage of such a QFNS is that a complex integer multiplication requires only two integer multiplications. In this article, a new type Fermat number multiplier is developed which eliminates the initialization condition of the previous method. It is shown that the new complex multiplier can be implemented on a single VLSI chip. Such a chip is designed and fabricated in CMOS-Pw technology.

Shyu, H. C.↗
NASA NTRS1990

Optimal aeroassisted orbital transfer with plane change using collocation and nonlinear programming

The fuel optimal control problem arising in the non-planar orbital transfer employing aeroassisted technology is addressed. The mission involves the transfer from high energy orbit (HEO) to low energy orbit (LEO) with orbital plane change. The basic strategy here is to employ a combination of propulsive maneuvers in space and aerodynamic maneuvers in the atmosphere. The basic sequence of events for the aeroassisted HEO to LEO transfer consists of three phases. In the first phase, the orbital transfer begins with a deorbit impulse at HEO which injects the vehicle into an elliptic transfer orbit with perigee inside the atmosphere. In the second phase, the vehicle is optimally controlled by lift and bank angle modulations to perform the desired orbital plane change and to satisfy heating constraints. Because of the energy loss during the turn, an impulse is required to initiate the third phase to boost the vehicle back to the desired LEO orbital altitude. The third impulse is then used to circularize the orbit at LEO. The problem is solved by a direct optimization technique which uses piecewise polynomial representation for the state and control variables and collocation to satisfy the differential equations. This technique converts the optimal control problem into a nonlinear programming problem which is solved numerically. Solutions were obtained for cases with and without heat constraints and for cases of different orbital inclination changes. The method appears to be more powerful and robust than other optimization methods. In addition, the method can handle complex dynamical constraints.

Shi, Yun. Y.↗
NASA NTRSDate not supplied

Shock Capturing via Limiting for High-Order Methods including Discontinuous Galerkin

High-order methods, such as discontinuous Galerkin (DG), spectral, and flux reconstruction (FR), are prone to generating unwanted oscillations near shocks and discontinuities. Conventional limiting techniques, while effective in suppressing oscillations near shocks, often compromise accuracy near extrema, where the solution is only first-order accurate. This paper introduces a novel limiting technique for these high-order schemes, aimed at effectively managing shocks while preserving accuracy. The key idea is to expand the standard monotonicity limits to provide “room” near smooth extrema, ensuring that limiting has no effect and thus preserving accuracy. Near a discontinuity, these expanded limits effectively reduce to the original monotonicity limits, suppressing oscillations. Additional motivation is drawn from a formula for the derivative of Radau polynomials, which depicts the behavior of oscillations resulting from discontinuities. This behavior leads to a simplification by applying the limits to the sum of magnitudes of all modes, linear and higher degree. Unlike typical approaches, which rely on successful detection to activate limiting, our limiter depends continuously on the data, there by avoiding potential issues if detection fails. To reduce computing time, efficient criteria for detecting smooth regions where limiting is unnecessary are presented. Combined with detection, the continuous dependence on the data is lost, but the method is more economical. A notable characteristic of the entire process is its simplicity in both concept and implementation. Numerical tests for advection and Euler equations are conducted to demonstrate the effectiveness of the proposed method.

numerical methods↗
NASA NTRSDate not supplied

Shock Capturing via Limiting for High-Order Methods including Discontinuous Galerkin

High-order methods, such as discontinuous Galerkin (DG), spectral, and flux reconstruction (FR), are prone to generating unwanted oscillations near shocks and discontinuities. Conventional limiting techniques, while effective in suppressing oscillations near shocks, often compromise accuracy near extrema, where the solution is only first-order accurate. This paper introduces a novel limiting technique for these high-order schemes, aimed at effectively managing shocks while preserving accuracy. The key idea is to expand the standard monotonicity limits to provide “room” near smooth extrema, ensuring that limiting has no effect and thus preserving accuracy. Near a discontinuity, these expanded limits effectively reduce to the original monotonicity limits, suppressing oscillations. Additional motivation is drawn from a formula for the derivative of Radau polynomials, which depicts the behavior of oscillations resulting from discontinuities. This behavior leads to a simplification by applying the limits to the sum of magnitudes of all modes, linear and higher degree. Unlike typical approaches, which rely on successful detection to activate limiting, our limiter depends continuously on the data, there by avoiding potential issues if detection fails. To reduce computing time, efficient criteria for detecting smooth regions where limiting is unnecessary are presented. Combined with detection, the continuous dependence on the data is lost, but the method is more economical. A notable characteristic of the entire process is its simplicity in both concept and implementation. Numerical tests for advection and Euler equations are conducted to demonstrate the effectiveness of the proposed method.

numerical methods↗
NASA NTRS1972

A fast numerical method for determining the optimum SNR of an array subject to a Q factor constraint.

The problem of finding the optimum current excitations for a point-detector array which extracts a signal from background noise using the criterion of maximizing the SNR subject to a constraint on the supergain ratio (or Q factor) has recently been solved. The formulation reduced the problem to one of solving for the roots of a polynomial whose coefficients are, in general, complex. We demonstrate that by making a certain transformation, it becomes possible to employ a state variable technique which changes the problem into one of finding the eigenvalues of a real matrix which is considerably faster to do.

Winkler, L. P.↗
DOE OSTI2025

Analytical expression of a finite, long, conical canted-cosine-theta coil for particle collider interaction regions

Magnets in the accelerator interaction region (IR) present significant challenges because of high field requirements and limited available space. Conical-shaped magnets offer advantages in these environments by allowing closer placement to the interaction point while maintaining clearance from synchrotron radiation. Interestingly, numerical studies have shown that conical canted-cosine-theta (CCT) designs produce a constant field distribution along the axial direction in the IR quadrupoles for the Electron-Ion Collider (EIC) at Brookhaven National Laboratory. However, the field harmonics generated by conical CCT windings are not yet fully understood. This paper presents an analytical approach to describe the magnetic field produced by a conical surface current and proposes a method for designing conical CCT magnets for accelerator applications. First, we begin with a surface current sheet having a general cosine-theta distribution in spherical coordinates and solve the vector potential using the Green’s function. The magnetic fields generated by the conical current sheet are expressed using associated Legendre polynomials. These results are then related to circular field harmonics and integral field harmonics for designing a coil that produces a pure multipole field. Next, a single layer of the conical CCT winding path is produced based on the cosine-theta current distribution. Finally, the magnetic field quality of dipole and quadrupole conical CCT coils with multiple layers is verified using the Biot-Savart law.

Yang, Ye↗
NASA NTRS1991

Minimum fuel coplanar aeroassisted orbital transfer using collocation and nonlinear programming

The fuel optimal control problem arising in coplanar orbital transfer employing aeroassisted technology is addressed. The mission involves the transfer from high energy orbit (HEO) to low energy orbit (LEO) without plane change. The basic approach here is to employ a combination of propulsive maneuvers in space and aerodynamic maneuvers in the atmosphere. The basic sequence of events for the coplanar aeroassisted HEO to LEO orbit transfer consists of three phases. In the first phase, the transfer begins with a deorbit impulse at HEO which injects the vehicle into a elliptic transfer orbit with perigee inside the atmosphere. In the second phase, the vehicle is optimally controlled by lift and drag modulation to satisfy heating constraints and to exit the atmosphere with the desired flight path angle and velocity so that the apogee of the exit orbit is the altitude of the desired LEO. Finally, the second impulse is required to circularize the orbit at LEO. The performance index is maximum final mass. Simulation results show that the coplanar aerocapture is quite different from the case where orbital plane changes are made inside the atmosphere. In the latter case, the vehicle has to penetrate deeper into the atmosphere to perform the desired orbital plane change. For the coplanar case, the vehicle needs only to penetrate the atmosphere deep enough to reduce the exit velocity so the vehicle can be captured at the desired LEO. The peak heating rates are lower and the entry corridor is wider. From the thermal protection point of view, the coplanar transfer may be desirable. Parametric studies also show the maximum peak heating rates and the entry corridor width are functions of maximum lift coefficient. The problem is solved using a direct optimization technique which uses piecewise polynomial representation for the states and controls and collocation to represent the differential equations. This converts the optimal control problem into a nonlinear programming problem which is solved numerically by using a modified version of NPSOL. Solutions were obtained for the described problem for cases with and without heating constraints. The method appears to be more robust than other optimization methods. In addition, the method can handle complex dynamical constraints.

Shi, Yun Yuan↗
NASA NTRSDate not supplied

Extending Explicit Guidance Methods to Higher Dimensions, Additional Conditions, and Higher Order Integration

Guidance functions play critical roles in autonomy to steer vehicles and aircraft to the intended target or destination. Explicit guidance (E Guidance) solves the two-point boundary value problem with initial and final conditions for position and velocity. The original formulation of E Guidance involves translational acceleration commands with a direct relationship to time, and it is possible to modify E Guidance for rotational acceleration. Other extensions for E Guidance include higher dimensions, additional conditions, and higher-order integration of the linearly independent E Guidance functions. The most promising extension involves higher-order integration of the E Guidance functions, but it may be physically impractical by initially moving away from the target. This paper provides a brief overview of some methods that extend E Guidance to higher dimensions, utilize additional conditions, or perform higher-order integration, and if they satisfy the two-point boundary value problem.

explicit guidance↗
NASA NTRSDate not supplied

Extending Explicit Guidance Methods to Higher Dimensions, Additional Conditions, and Higher Order Integration

Guidance functions play critical roles in autonomy to steer vehicles and aircraft to the intended target or destination. Explicit guidance (E Guidance) solves the two-point boundary value problem with initial and final conditions for position and velocity. The original formulation of explicit guidance involves translational acceleration commands with a direct relationship to time, and it is possible to modify E Guidance for rotational acceleration. Other extensions for E Guidance include higher dimensions, additional conditions, and higher-order integration of the linearly independent E Guidance functions. The most promising extension involves higher-order integration of the E Guidance functions, but it may be physically impractical by initially moving away from the target. This paper provides a brief overview of some methods that extend E Guidance to higher dimensions, utilize additional conditions, or perform higher-order integration, and if they satisfy the two-point boundary value problem.

explicit guidance↗
NASA NTRS2023

Tracking Nonradial Outflows in Extreme Ultraviolet and White Light Solar Images

Understanding the solar corona requires knowledge of its dynamics through its various layers and subsequent connectivity to the heliosphere. This requires understanding the nature of the outflows and the physical transitions through the middle corona (∼1.5–6.0 Rs). While this region is still inaccessible to in situ measurements, remote sensing observations are available, but their interpretation can be controversial due to line-of-sight effects and the nonradial motion of outflowing structures close to the Sun (≤3.0 Rs). In this work, we describe a method to mitigate these challenges by generating nonradial height–time profiles of outflows by using advanced image processing techniques. The northern and southern boundaries of a large equatorial streamer during the 2008 solar minimum were identified in STEREO/SECCHI solar images, using two different methodologies based on thresholds of brightness and piecewise polynomial function fitting. To address line-of-sight issues, we used tomographic reconstruction of the 3D distribution of the coronal electron density based on SECCHI/COR2 images. Spectral analysis of the time series of the position angle of the streamer boundary revealed its oscillatory nature at some heights at 36–48 and 10.5–14.6 hr. Dividing the distance between the northern and southern streamer boundaries in equal parts at each height, we obtained nonradial height–time paths from which we generated nonradial profiles of corona/solar wind plasma outflow. We tracked outflows as they moved uninterruptedly from the Sun in EUVI, through COR1 and into COR2. Finally, we discuss the preliminary results of nonradial plane-of-sky velocities for a coronal mass ejection and two small-scale features.

Nathalia Alzate↗