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DOE OSTI2026

Efficient CP Rounding Using Alternating Least Squares with QR Decomposition

The CANDECOMP/PARAFAC (CP) decomposition is widely used for analyzing multidimensional data, and the alternating least squares (CP-ALS) algorithm is a common method for its computation. CP rounding is the problem of computing a lower-rank CP decomposition of an input already in a higher-rank CP format. While the normal equations (NE) approach in CP-ALS is efficient for the CP rounding problem and frequently used, it becomes unstable in the presence of ill-conditioned subproblems. This paper presents a new QR-based CP-ALS method for CP rounding that preserves both numerical stability and computational efficiency. Here, our experiments show that the proposed method offers significant speedup over a previous QR-based approach and the Tensor Toolbox's NE-based implementation, particularly for higher-order tensors. Furthermore, our approach demonstrates a marked reduction in error for ill-conditioned problems, with error reductions several orders of magnitude smaller compared to the NE-based method, while achieving faster convergence and more accurate solutions. By using a more numerically stable approach, we can solve more problems in reduced working precision, which enables further reduction in time to solution.

CANDECOMP/PARAFAC↗

NASA NTRS1985

Numerical solution of the vertical structure equation in the normal mode method

In the present model of multilayered stability stratification, aimed at obtaining the analytic eigensolutions of the vertical structure equation, each layer is characterized by its own static stability value. By requiring continuity of pressure and vertical velocity across each interface level, and by imposing suitable upper and lower boundary conditions, matching eigensolutions are obtained in terms of the Bessel functions. Attention is given to an explicit example of a double-layered stratified atmosphere which demonstrates the mathematical manipulations involved; the resultant vertical structure functions are used to check the accuracy of the numerical solutions by the finite difference and finite element methods.

Sasaki, Y. K.↗

NASA NTRS1983

Multiple-gridding of the Euler equations with an implicit scheme

The multiple-grid scheme of Ni (1981) for the solution of the unsteady Euler equations for quasi-one-dimensional transonic flow problems is analyzed according to its ability to accelerate convergence to a steady state solution, its applicability to an implicit scheme, its accuracy, and its stability limits. This scheme is applied successfully to McCormack's (1981) implicit method of solving quasi-one-dimensional transonic flow problems for CFL numbers significantly greater than unity. It is determined that the second order accuracy of this implicit method is preserved by employing the multiple gridding. However, stability limitations that are flow dependent are introduced into the implicit method by the use of the multiple-grid scheme which will curtail its use under certain flow conditions. A scaling modification for the multiple grid scheme is developed which further improves its performance when used with explicit and artificially-damped implicit methods without any increase in computational work.

Stubbs, R. M.↗

NASA NTRS1976

An analytical method for ride quality of flexible airplanes

A new and easily used state variable method of aircraft ride quality analysis is developed and its use is illustrated by a numerical example using DC-8 airplane equations of motion. The method readily allows any type of stability augmentation system to be included for good handling qualities. As part of the ride quality analysis, a particularly powerful method of specifying and achieving all roots of a desired closed-loop characteristic equation by use of full state variable feedback is described and applied to the DC-8 example.

Swaim, R. L.↗

DOE OSTI2026

Cold compressor performance and energy consumption improvements at Jefferson Lab’s Central Helium Liquefiers

Abstract Jefferson Lab operates two central helium liquefiers (CHLs) which both utilize full cold compression from the saturation pressure at operating temperature (approximately 2.1 K) to just over atmospheric pressure. The original plant, CHL1, was recently outfitted with a replacement subatmospheric cold box (SC1R) containing state-of-the-art cold compressor technology, while the newer plant, CHL2, uses an older cold compressor system. In both cases, the heat of compression is absorbed at low temperature at the expense of electrical power consumed by the warm compressors. Due to the superior efficiency and turndown capabilities of SC1R, a new operating mode has been identified for CHL1 in which the required number of operating warm compressors is reduced by one. A cost-based method for optimizing cold compressor stability and efficiency has been developed and applied to CHL2, improving its turndown and lowering the warm compressor discharge pressure. As a result of these efforts, power consumption of the combined CHLs during normal operations has been reduced by nearly 10%, or a total of 650 kW. The observed performance of CHL1 with SC1R, as well as the cold compressor optimization method, leading to this improved energy consumption rate will be discussed in detail.

Mastracci, B [Thomas Jefferson National Accelerato↗

DOE OSTI2023

IPL-Annealed Mixed-Cation Perovskites with Robust Coating Window toward Scalable Manufacturing of Commercial Perovskite Solar Cells

Perovskite solar cells (PSCs) are a promising alternative solar technology, but the technical challenges of (1) stability/durability, (2) efficiency at scale, and (3) manufacturability must be overcome to achieve widespread PSC commercialization. The challenge of balancing solution ink formulation and scalable manufacturing is often overlooked in the literature, where focus is on adopting inks from processes that will not scale. In this study, we apply a classical roll-to-roll manufacturing perspective, utilizing both compositional engineering and intense pulsed light (IPL) annealing, to develop a mixed-cation perovskite ink with a robust coating window that simultaneously solve issues of stability and manufacturability for PSCs. Our method resulted in blade-coated, flexible, mixed-cation PSCs on ITO-PET substrates with a champion power conversion efficiency (PCE) efficiency of 16.7% using IPL annealing of the absorber layer and, to our knowledge, is one of the fastest processing methods for the perovskite layer. This overall reduction in processing time with a stable ink represents an advance toward the scaled production of perovskite solar cells on flexible substrates.

flexible perovskite solar cells↗

NASA NTRS1975

Estimation and Analysis of Nonlinear Stochastic Systems

The algebraic and geometric structures of certain classes of nonlinear stochastic systems were exploited in order to obtain useful stability and estimation results. The class of bilinear stochastic systems (or linear systems with multiplicative noise) was discussed. The stochastic stability of bilinear systems driven by colored noise was considered. Approximate methods for obtaining sufficient conditions for the stochastic stability of bilinear systems evolving on general Lie groups were discussed. Two classes of estimation problems involving bilinear systems were considered. It was proved that, for systems described by certain types of Volterra series expansions or by certain bilinear equations evolving on nilpotent or solvable Lie groups, the optimal conditional mean estimator consists of a finite dimensional nonlinear set of equations. The theory of harmonic analysis was used to derive suboptimal estimators for bilinear systems driven by white noise which evolve on compact Lie groups or homogeneous spaces.

Marcus, S. I.↗

NASA NTRS1975

Reduction of trimmed drag

Methods are reported for reducing the aircraft drag coefficient for a given aircraft lift coefficient, or speed. The emphasis is placed in determining the load distribution between the wing-body combination and the tail which reduces overall drag coefficient. Furthermore, a technique is presented which allows the determination of various aerodynamic and geometric parameters to permit the best location to satisfy inherent stability requirements. Included in the method is the calculation of sensitivity coefficients which indicate the importance of various parameters in achieving specified goals. Preliminary results indicate that such an approach is feasible.

Lutze, F. H., Jr.↗

NASA NTRS1992

Design optimization of natural laminar flow bodies in compressible flow

An optimization method has been developed to design axisymmetric body shapes such as fuselages, nacelles, and external fuel tanks with increased transition Reynolds numbers in subsonic compressible flow. The new design method involves a constraint minimization procedure coupled with analysis of the inviscid and viscous flow regions and linear stability analysis of the compressible boundary-layer. In order to reduce the computer time, Granville's transition criterion is used to predict boundary-layer transition and to calculate the gradients of the objective function, and linear stability theory coupled with the e(exp n)-method is used to calculate the objective function at the end of each design iteration. Use of a method to design an axisymmetric body with extensive natural laminar flow is illustrated through the design of a tiptank of a business jet. For the original tiptank, boundary layer transition is predicted to occur at a transition Reynolds number of 6.04 x 10(exp 6). For the designed body shape, a transition Reynolds number of 7.22 x 10(exp 6) is predicted using compressible linear stability theory coupled with the e(exp n)-method.

Dodbele, Simha S.↗

NASA NTRS2022

The Harmonic Linearized Navier-Stokes Equations for Transition Prediction in Three-Dimensional Flows

The conventional method to predict the onset of laminar-turbulent transition in convectively unstable boundary-layer flows is based on the logarithmic amplification ratio, the so-called N-factor, of the linear instability waves. To calculate the N-factor, the flow variables are decomposed into a laminar basic state solution and the linear disturbances, which are assumed to be harmonic in time. The most commonly used linear stability analysis approaches include the locally parallel linear stability theory (LST) and the non-local, weakly nonparallel parabolized stability equations (PSE). However, these methods do not account for strong streamwise gradients that are encountered in several configurations of interest, as roughness elements, steps, gaps, or corners. To solve the linear evolution of disturbances along such strongly nonparallel regions, the harmonic linearized Navier-Stokes equations (HLNSE) need to be solved. The discretization of the HLNSE for spanwise/azimuthally inhomogeneous laminar basic states yields a linear system of complex arithmetic with a leading dimension of the order of 107 to 108. A combined multithread and multiprocessor algorithm is implemented for the direct solution of such linear system. Results for a supersonic boundary layer over a three-dimensional roughness patch show good agreement with experimental measurements when the evolution of the instability waves over the roughness patch is included via the HLNSE.

Boundary Layer Stability↗

DOE OSTI2024

Pressure-stabilized fixed-stress iterative solutions of compositional poromechanics

We consider the numerical behavior of the fixed-stress splitting method for coupled poromechanics as undrained regimes are approached. We explain that pressure stability is related to the splitting error of the scheme, not the fact that the discrete saddle point matrix never appears in the fixed-stress approach. This observation reconciles previous results regarding the pressure stability of the splitting method. Using examples of compositional poromechanics with application to geological CO sequestration, we see that solutions obtained using the fixed-stress scheme with a low order finite element-finite volume discretization which is not inherently inf-sup stable can exhibit the same pressure oscillations obtained with the corresponding fully implicit scheme. Moreover, pressure jump stabilization can effectively remove these spurious oscillations in the fixed-stress setting, while also improving the efficiency of the scheme in terms of the number of iterations required at every time step to reach convergence.

42 ENGINEERING↗

NASA NTRS2004

Alternative Attitude Commanding and Control for Precise Spacecraft Landing

A report proposes an alternative method of control for precision landing on a remote planet. In the traditional method, the attitude of a spacecraft is required to track a commanded translational acceleration vector, which is generated at each time step by solving a two-point boundary value problem. No requirement of continuity is imposed on the acceleration. The translational acceleration does not necessarily vary smoothly. Tracking of a non-smooth acceleration causes the vehicle attitude to exhibit undesirable transients and poor pointing stability behavior. In the alternative method, the two-point boundary value problem is not solved at each time step. A smooth reference position profile is computed. The profile is recomputed only when the control errors get sufficiently large. The nominal attitude is still required to track the smooth reference acceleration command. A steering logic is proposed that controls the position and velocity errors about the reference profile by perturbing the attitude slightly about the nominal attitude. The overall pointing behavior is therefore smooth, greatly reducing the degree of pointing instability.

Singh, Gurkirpal↗

NASA NTRS2022

The Harmonic Linearized Navier-Stokes Equations for Transition Prediction in Three-Dimensional Flows

The conventional method to predict the onset of laminar-turbulent transition in convectively unstable boundary-layer flows is based on the logarithmic amplification ratio, the so-called N-factor, of the linear instability waves. To calculate the N-factor, the flow variables are decomposed into a laminar basic state solution and the linear disturbances, which are assumed to be harmonic in time. The most commonly used linear stability analysis approaches include the locally parallel linear stability theory (LST) and the nonlocal, weakly nonparallel parabolized stability equations (PSE). However, these methods do not account for strong streamwise gradients that are encountered in several configurations of interest, such as those in the vicinity of roughness elements, steps, gaps, or corners. To compute the linear evolution of disturbances along such strongly nonparallel regions, the harmonic linearized Navier-Stokes equations (HLNSE) need to be solved. The discretization of the HLNSE for spanwise/azimuthally inhomogeneous laminar basic states yields a linear system of complex arithmetic with a leading dimension of the order of 10^(7) to 10^(8) even in relatively simple flows. A combined multithread and multiprocessor algorithm is implemented for the direct solution of such linear systems. Results for a supersonic boundary layer over a three-dimensional roughness patch show good agreement with experimental measurements when the evolution of the instability waves over the roughness patch is included via the HLNSE. Additionally, inflow-resolvent analysis based on the HLNSE for discrete-roughness-induced disturbances in the nose tip of a blunt cone at Mach 6 demonstrates the importance of including the disturbance amplification along the near vicinity of the roughness element and separation region.

Boundary Layer Stability↗

DOE OSTI2021

Stability-based optimization of ACRT for the growth of CZT by the traveling heater method

Numerical modeling is employed to study the effects of several accelerated crucible rotation technique (ACRT) rotation schedules on the growth of cadmium zinc telluride (CZT) by the traveling heater method (THM). In conjunction with these analyses, a measure is developed to estimate the amplitude of disturbances associated with cellular interface growth morphologies that develop over time and across the melt-solid interface. Furthermore, this disturbance amplitude measure is used to assess the ability of ACRT to stabilize the growth interface and thereby minimize inclusion formation processes. Notably, our analyses reveal that interfacial instability is not well correlated with melt undercooling, explaining why classical ACRT approaches to reduce undercooling by mixing may not stabilize growth. Computations show that interface stability is best achieved via rotation schedules that accentuate outward Ekman flows during spin-up and, during spin-down, eliminate Taylor-Görtler flows and minimize inward Ekman flows.

36 MATERIALS SCIENCE↗

NASA NTRS1993

Effects of free-stream turbulence on boundary-layer transition

Traditional methods for the prediction of the transition location rest either on lump parameters like the momentum thickness or on N factors obtained from the approximate linear stability characteristics of the flow. These methods account for the effects of the disturbance environment by empirical correlation with observed transition locations. We have developed a highly efficient and accurate approach to stability analysis and transition simulation based on parabolized stability equations (PSE). Here we present a first application of this approach to realistic problems of practical interest. We study the effects of the turbulence level on transition and heat transfer in flows over flat plates, curved plates, and the stator blade of a gas-turbine model. We discuss the formulation of an input model for the PSE analysis in the light of the present knowledge of receptivity mechanisms. The input model is used to compute transition locations for various configurations and flow conditions. The results compare favorably with experimental data.

Herbert, TH.↗

DOE OSTI2023

Evaluation of Distributed Power Apportioning with Net Load Management Engine in Microgrids Using Power Hardware-in-the-Loop Simulation

This article presents the performance evaluation of ratio consensus-based distributed power apportioning engine along with centralized net load management (NLM) engine that ensures viable and stable operation of an islanded microgrid. Managing net load variability in a microgrid with high penetrations of uncertain renewable generation and ever-changing load demands is a crucial need in order to ensure viable and stable operation of the microgrid. Centralized “dispatch-rule”-based and/or multi-agent-based distributed control of distributed energy resources (DERs) in microgrid are well accepted for microgrid by adapting ANSI/ISA-95-based hierarchical control architecture. In the application where microgrid network has large geographical span with multiple DERs dispersed in the network, high penetration of uncertain renewable energy resources, and ever-changing load demands, a judicious selection of techniques/solutions for managing net-load resources for maintaining viability and stability is required. With this motivation, this article proposes a novel solution to mitigate the challenges by incorporating a mixed centralized NLM engine and distributed power apportioning control of DERs and loads. A power-hardware-in-the-loop (PHIL) -based experiment is conducted with the centralized NLM engine and the distributed power apportioning engine along with two commercial inverters. The experimental results validates the efficacy of the proposed method in ensuring viability and stability of a microgrid.

hardware-in-the-loop simulation↗

NASA NTRS2021

Coupling of the FUN3D Unstructured Flow Solver and the LASTRAC Stability Code to Model Transition

We develop an iterative automated method to predict transition locations in boundary-layer flows by using the FUN3D solver to perform flow simulations and the LASTRAC code for linear stability computations. The coupling of FUN3D and LASTRAC allows for a robust physics-based approach to model boundary-layer transition by analyzing the growth of different instability waves and then using that information to iteratively update the resulting transition location. There is no user involvement during the iterative computations. We apply this automated method to subsonic flow over a flat plate with a sharp leading edge. The final solution has regions of laminar and turbulent flow with a transition onset location that agrees with experiments and stability-based correlations. This iterative automated method is also applied to an NLF(1)-0416 airfoil for conditions with and without a separation bubble. Along with predicting transition locations, we compare the streamwise distributions of surface-pressure and skin-friction coefficients to a transport-equation-based model. We consider a 6:1 prolate spheroid at three angles of attack, namely, five, ten, and fifteen degrees, where mixed-mode transition occurs due to both Tollmien-Schlichting and crossflow instabilities. The skin-friction contours and transition fronts at every angle of attack from our iterative automated method show good agreement with past experimental and computational results in the literature for the 6:1 prolate spheroid.

Transition↗

NASA NTRS1987

Nonlinear stability of a flow with bound eddies

Kovasznay (1948) obtained an exact solution of the Navier-Stokes equations that describes a flow with periodic bound eddies. The stability of this nonparallel flow with respect to three-dimensional finite amplitude disturbances is analyzed by use of the energy method. A sufficient condition for global stability is obtained. It is shown that the additional nonhomogeneity in shear stress distribution in a nonparallel flow is a destabilizing factor.

Lin, S. P.↗