Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Analytic gradients”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 307 records · Page 17
All sourcesNASA NTRSDOE OSTI
NASA NTRSDate not supplied

On Generalizably Improving RANS Predictions of Flow Separation and Reattachment

This work presents progress in an ongoing data-driven turbulence modeling effort at NASA Langley Research Center to improve predictions for separated flows. Two augmentation strategies are presented – one to improve predictions for the point of reattachment after smooth-body separation, and another to improve predictions for flow separation due to prolonged adverse pressure gradients. The reattachment augmentation was inspired from lessons learned during attempts at using field inversion and machine learning (FIML); however, it is prescribed as a conventional analytic closed-form expression. Results show that, when introduced into the SST k-w model, it shortens the otherwise overpredicted separation bubble length for three cases characterized by different Reynolds numbers and flow geometries. The second augmentation, which addresses flow separation under prolonged adverse pressure gradients, is inferred via FIML and applied as a neural network within the Spalart-Allmaras model. It uses features that are chosen such that the presented results show an improved predictive accuracy for the training case without affecting other cases where the augmentation is not needed. Further testing is required to establish the generalizability of this augmentation. The rationale behind the chosen features that serve as inputs to both these augmentations is also presented for the benefit of the reader.

machine learning↗
NASA NTRS1980

Orbit-averaged behavior of magnetic control laws for momentum unloading

Analytical formulas are derived for orbit-averaged behavior of magnetic control laws for unloading the excess angular momentum of a spacecraft reaction wheel control system in the presence of secular environmental torques. The specific example of an axially symmetric spacecraft with an inertially fixed attitude for which the dominant environmental torque is the gravity-gradient torque is treated in detail, but extensions of the general approach to other inertially fixed and earth-pointing spacecraft are discussed. The analytical formulas are compared to detailed simulations performed for the Solar Maximum Mission spacecraft, and agreement to within 10% is found. The analytical formulas can be used in place of detailed simulations for preliminary studies, and can be used to find selected cases giving the most stringent tests of momentum unloading capability for which detailed simulations may be performed.

Camillo, P. J.↗
NASA NTRS1959

On Fully Developed Channel Flows: Some Solutions and Limitations, and Effects of Compressibility, Variable Properties, and Body Forces

An examination of the effects of compressibility, variable properties, and body forces on fully developed laminar flow has indicated several limitations on such streams. In the absence of a pressure gradient, but presence of a body force (e.g., gravity), an exact fully developed gas flow results. For a liquid this follows also for the case of a constant streamwise pressure gradient. These motions are exact in the sense of a Couette flow. In the liquid case two solutions (not a new result) can occur for the same boundary conditions. An approximate analytic solution was found which agrees closely with machine calculations.In the case of approximately exact flows, it turns out that for large temperature variations across the channel the effects of convection (due to, say, a wall temperature gradient) and frictional heating must be negligible. In such a case the energy and momentum equations are separated, and the solutions are readily obtained. If the temperature variations are small, then both convection effects and frictional heating can consistently be considered. This case becomes the constant-property incompressible case (or quasi-incompressible case for free-convection flows) considered by many authors. Finally there is a brief discussion of cases wherein streamwise variations of all quantities are allowed but only a such form that independent variables are separable. For the case where the streamwise velocity varies inversely as the square root distance along the channel a solution is given.

Maslen, Stephen H.↗
DOE OSTI2020

Interactions Between Microturbulence and Magnetohydrodynamic Instabilities in Magnetized Plasmas (Final Technical Report)

This document details the work accomplished during the period 04/15/2012-01/31/2020 for the collaborative project “Interactions Between Microturbulence and Magnetohydrodynamic Instabilities in Magnetized Plasmas,” and serves as the final report on the University of California, San Diego part of this collaborative project for Department of Energy Office of Science - Fusion Energy Sciences Grant No. DE- SC0007783. This project focused on the development of analytic and computational tools, seeking to better understand the mutual interactions between small-scale temperature-gradient driven microturbulence and macroscopic magnetohydrodynamic (MHD) instabilities, particularly tearing modes, in magnetically confined plasmas relevant for the generation of fusion energy. This project advanced understanding through numerical simulations of different sets of model equations, corresponding to different microturbulence instabilities. Questions addressed included how the magnitudes, spatial structures, and scaling's of turbulent forcing's and drags impact magnetic island dynamics, as well as quantifying the “region of influence” of an island on the microturbulence dynamics. A key finding of the project is that the microturbulence fluctuations and associated cross-field particle and energy fluxes exhibit spatial asymmetries for sufficiently large islands. The results have improved our fundamental understanding of plasma dynamics, motivated new experimental investigations, and will help inform future fusion predictive modeling efforts.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1972

Tethered body problems and relative motion orbit determination

Selected problems dealing with orbiting tethered body systems have been studied. In addition, a relative motion orbit determination program was developed. Results from these tasks are described and discussed. The expected tethered body motions were examined, analytically, to ascertain what influence would be played by the physical parameters of the tether, the gravity gradient and orbit eccentricity. After separating the motion modes these influences were determined; and, subsequently, the effects of oscillations and/or rotations, on tether force, were described. A study was undertaken, by examining tether motions, to see what type of control actions would be needed to accurately place a mass particle at a prescribed position relative to a main vehicle. Other applications for tethers were studied. Principally these were concerned with the producing of low-level gee forces by means of stabilized tether configurations; and, the initiation of free transfer trajectories from tether supported vehicle relative positions.

Eades, J. B., Jr.↗
NASA NTRS1983

Magnetic drifts at Io - Depletion of 10-MeV electrons at Voyager 1 encounter due to a forbidden zone

A model for magnetic field lines is used to track the Voyager spacecraft trajectory past Io back to the equatorial plane in order to determine the cause of an observed depletion of 10 MeV electrons in Io's orbit. The field lines are in the vicinity of an Alfven wing, a noncompressive field perturbation. It is suggested that the Jovian magnetospheric drift features influence the behavior of particles around Io, which also has a zone of reduced convection velocity. An analytical model is developed that demonstrates that a forbidden zone may exist around Io due to the gradient drifts and reduced convection velocity, and projections of particles convecting to the Io surface agree well with the Voyager data for particle concentrations. Discrepancies in the measured 9 MeV fluxes with respect to Pioneer data indicate that a possible change in the Io conductance in the interval between the passages of the two spacecraft.

Goldstein, B. E.↗
NASA NTRS1985

Resistive wave dissipation on magnetic inhomogeneities Normal modes and phase mixing

Numerical solutions of the linearized, resistive MHD equations indicate the presence of two characteristic forms of wave decay on magnetic inhomogeneities. Solutions for relatively long-wavelength disturbances and large values of the resistivity have the behavior of decaying normal modes. In the opposite limits, phase mixing becomes important, with the eventual build-up of large spatial gradients in which the resistive terms dominate. This composite behavior is shown to be conceptually consistent with analytic results, which predict that the complete solution consists of the sum of collective and noncollective contributions. The numerical simulations go beyond analytic theory by defining where each contribution prevails and computing wave decay when phase mixing is effective. The dispersion relation in the normal-mode regime is also determined analytically, with some approximations, and is in good agreement with the numerical solution. The decay time of the normal modes varies with Lundquist number at S1/6, while the phase-mixed decay time scales as S1/3.

Steinolfson, R. S.↗
NASA NTRS1993

Extension of state-vector splitting to the Navier-Stokes equations

A multi-dimensional upwind scheme for solving the Euler equations has been extended to solve the Navier-Stokes equations. These methods share the property of not requiring body-fitted computational grids. A time advance scheme which is second-order accurate in time and space has been developed for use in conjunction with state-vector splitting to accurately resolve regions with significant gradients in flow quantities. The scheme has been tested on several simple viscous flow problems for which analytic solutions are known; the agreement of computation with theory is excellent.

Gooch, Carl F.↗
NASA NTRS1997

Current Collection in a Magnetic Field

It is found that the upper-bound limit for current collection in the case of strong magnetic field from the current is close to that given by the Parker-Murphy formula. This conclusion is consistent with the results obtained in laboratory experiments. This limit weakly depends on the shape of the wire. The adiabatic limit in this case will be easily surpassed due to strong magnetic field gradients near the separatrix. The calculations can be done using the kinetic equation in the drift approximation. Analytical results are obtained for the region where the Earth's magnetic field is dominant. The current collection can be calculated (neglecting scattering) using a particle simulation code. Dr. Singh has agreed to collaborate, allowing the use of his particle code. The code can be adapted for the case when the current magnetic field is strong. The needed dm for these modifications is 3-4 months. The analytical description and essential part of the program is prepared for the calculation of the current in the region where the adiabatic description can be used. This was completed with the collaboration of Drs. Khazanov and Liemohn. A scheme of measuring the end body position is also proposed. The scheme was discussed in the laboratory (with Dr. Stone) and it was concluded that it can be proposed for engineering analysis.

Krivorutsky, E. N.↗
NASA NTRS2010

Asymptotic Linearity of Optimal Control Modification Adaptive Law with Analytical Stability Margins

Optimal control modification has been developed to improve robustness to model-reference adaptive control. For systems with linear matched uncertainty, optimal control modification adaptive law can be shown by a singular perturbation argument to possess an outer solution that exhibits a linear asymptotic property. Analytical expressions of phase and time delay margins for the outer solution can be obtained. Using the gradient projection operator, a free design parameter of the adaptive law can be selected to satisfy stability margins.

Nguyen, Nhan T.↗
NASA NTRS2019

Using Graph Coloring to Compute Total Derivatives More Efficiently in OpenMDAO

When they are applicable, gradient based optimization algorithms are the most efficient way to solve design optimization problems. Although gradient based methods are generally efficient, they can be made significantly more so through the usage of analytic techniques to compute the necessary total derivatives. The traditional forward (direct) and reverse (adjoint) analytic techniques have computational costs that scale linearly with the number of design variables and the number of constraints, respectively. In this work, we present an application of a graph coloring algorithm to the analytic techniques for computing total derivative Jacobians in order to achieve much better computational scaling than the pure analytic methods can provide alone. A detailed theoretical explanation of how coloring algorithms interact with analytic derivative methods is presented that illustrates specific types of sparsity patterns that must be present in total derivative Jacobians in order for this coloring technique to be effective. The new technique has been implemented as a feature in the OpenMDAO framework and the implementation is demonstrated on two example problems. The performance on the example problems up to 50% reduction in compute cost for optimizations with bi-directional coloring compared to traditional constraint aggregation. Additionally, the results show how coloring technique alleviates some of the numerical difficulties that constraint aggregation can cause, leading to the ability to solve larger problems. It is expected that the new method will have wide applicability to multidisciplinary optimization problems, and that its availability in OpenMDAO will offer significant computational savings for users without the need for them to implement the coloring algorithm themselves.

Trajectory↗
DOE OSTI2024

Transport coefficient sensitivities in a semi-analytic model for magnetized liner inertial fusion

Performance of magnetized liner inertial fusion (MagLIF) experiments is highly dependent on transport processes including magnetized heat flows and magnetic flux losses. Magnetohydrodynamic simulations used to model these experiments require a choice of model for the transport coefficients, which are the constants of proportionality relating driving terms, such as temperature gradients and currents, to the associated heat and magnetic field transport. The coefficients have been the subject of repeated recalculation using various methods throughout the years. Using a semi-analytic MagLIF model, we compare models for the transport coefficients. The choice of model modifies magnetic-flux losses caused by the Nernst thermoelectric effect and thermal conduction losses. We present simulated results from parameter scans conducted in order to compare the effects of the different models on parameters of interest in MagLIF. In some regions of parameter space, discrepancies of up to 38% are found in integrated quantities like the fusion yield. These results may serve as a guide for experimental validation of the various models, particularly as laser preheat energies and initial axial field strengths are increased on MagLIF experiments.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1994

An Approximate Solution for the Circumsolar Flow Field of a Sun Moving Through the Local Interstellar Medium (LISM)

The solar system is in relative motion with respect to the ambient interstellar medium. The supersonic solar wind is expected to pass through the termination shock, thus the solar wind plasma eventually has to enter into an asymptotic outflow geometry appropriately adopted to this counterflow situation. Many attempts have been done to simulate the interaction between the solar wind and the LISM numerically. In this paper we generalize a Parker type analytical solution of the counterflow. The idea is to introduce a special kind of compressibility of the solar wind flow. With the assumption that only a transversal component of the density gradient normal to the flow lines exists we are able to calculate a full set of hydrodynamical quantities describing the circumsolar flow field of a Sun moving through the LISM. The equations governing the velocity and density fields lead to analytical solutions which can be taken as good approximations to the more general case of compressible plasma flows.

Ratkiewicz, Romana E.↗
DOE OSTI2024

FLOWERS AEP: An Analytical Model for Wind Farm Layout Optimization

Annual energy production (AEP) is commonly used in objective functions for wind farm layout optimization. AEP is proportional to wind farm power production integrated over an annual distribution of free-stream wind conditions. Physics-based estimates of wind farm power production typically rely on low-fidelity engineering wake models that approximate the steady-state wind farm flow field. AEP estimates are then obtained by performing independent simulations for discrete wind conditions and using rectangular quadrature to account for each condition's expected frequency of occurrence. Depending on the number of simulated discrete wind conditions, this numerical integral could be hampered by poor accuracy or high computational costs. The FLOWERS AEP model instead poses an analytical integral of the engineering wake model over the variable wind conditions, yielding a closed-form, analytical function for wind farm AEP. This paper derives the analytical functions for FLOWERS AEP and its derivatives with respect to turbine position, which are useful for gradient-based wind farm layout optimization, in nondimensional form. We then analyze the benefits of the FLOWERS AEP model over conventional reference models, focusing on its low cost, adequate wake loss predictions, and smooth design space. Although the FLOWERS approach is found to predict the exact value of AEP with some error relative to the reference model (within 14% on average), it dramatically reduces computation time by an order of magnitude, produces a qualitatively similar design space at relatively low resolution, and yields comparable optimal layouts. This significant speed improvement is critical in layout optimization applications, where determining an optimal layout in an efficient manner is more important than precise AEP prediction.

17 WIND ENERGY↗
DOE OSTI2022

A Theory for the Response of Tropical Moist Convection to Mechanical Orographic Forcing

Abstract Spatial patterns of tropical rainfall are strongly influenced by mountains. Although theories for precipitation induced by convectively stable upslope ascent exist for the midlatitudes, these do not represent the interaction of moist convection with orographic forcing. Here, we present a theory for convective precipitation produced by the mechanical interaction of a tropical ridge with a basic-state horizontal wind. Deviations from this basic state are represented as the sum of a “dry” perturbation, due to the stationary orographic gravity wave, and a “moist” perturbation that carries the convective response. The moist component dynamics are subject to the weak temperature gradient approximation; they are forced by the dry mode’s influence on lower-tropospheric moisture and temperature. Analytical solutions provide estimates of the precipitation distribution, including peak precipitation, upstream extent, and rain shadow extent. The theory can be used with several degrees of complexity depending on the technique used to compute the dry mode, which can be drawn from linear mountain wave theory or full numerical simulations. To evaluate the theory, we use a set of convection-permitting simulations with a flow-perpendicular ridge in a long channel. The theory makes a good prediction for the cross-slope precipitation profile, indicating that the organization of convective rain by orography can be quantitatively understood by considering the effect of stationary orographic gravity waves on a lower-tropospheric convective quasi-equilibrium state.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1977

Effect of gravity-gradient torques on the dynamics of a spinning spacecraft with telescoping appendages

The effects of gravity-gradient torques during boom deployment maneuvers of a spinning spacecraft are examined with a combination of numerical and analytical methods. It is assumed that the spacecraft consists of a rigid central hub and movable rigid telescoping booms where the booms extend only along the hub principal axes. For the special case of symmetric deployment the stability boundaries are determined and a stability chart is used to study the system behavior. Possible cases of instability during this type of maneuver are identified.

Rajan, M.↗
NASA NTRS1987

Digital robust active control law synthesis for large order systems using constrained optimization

This paper presents a direct digital control law synthesis procedure for a large order, sampled data, linear feedback system using constrained optimization techniques to meet multiple design requirements. A linear quadratic Gaussian type cost function is minimized while satisfying a set of constraints on the design loads and responses. General expressions for gradients of the cost function and constraints, with respect to the digital control law design variables are derived analytically and computed by solving a set of discrete Liapunov equations. The designer can choose the structure of the control law and the design variables, hence a stable classical control law as well as an estimator-based full or reduced order control law can be used as an initial starting point. Selected design responses can be treated as constraints instead of lumping them into the cost function. This feature can be used to modify a control law, to meet individual root mean square response limitations as well as minimum single value restrictions. Low order, robust digital control laws were synthesized for gust load alleviation of a flexible remotely piloted drone aircraft.

Mukhopadhyay, Vivek↗
NASA NTRS1991

Aerodynamic design optimization using sensitivity analysis and computational fluid dynamics

A new and efficient method is presented for aerodynamic design optimization, which is based on a computational fluid dynamics (CFD)-sensitivity analysis algorithm. The method is applied to design a scramjet-afterbody configuration for an optimized axial thrust. The Euler equations are solved for the inviscid analysis of the flow, which in turn provides the objective function and the constraints. The CFD analysis is then coupled with the optimization procedure that uses a constrained minimization method. The sensitivity coefficients, i.e. gradients of the objective function and the constraints, needed for the optimization are obtained using a quasi-analytical method rather than the traditional brute force method of finite difference approximations. During the one-dimensional search of the optimization procedure, an approximate flow analysis (predicted flow) based on a first-order Taylor series expansion is used to reduce the computational cost. Finally, the sensitivity of the optimum objective function to various design parameters, which are kept constant during the optimization, is computed to predict new optimum solutions. The flow analysis of the demonstrative example are compared with the experimental data. It is shown that the method is more efficient than the traditional methods.

Baysal, Oktay↗