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NASA NTRSDate not supplied

Linear Parameter-Varying Control Compatible with Excitation for Real-Time Modeling

The Modeling and Control for Agile Aircraft Development project (MCAAD) seeks to reduce the time spent on wind tunnel testing and computational fluid dynamic modeling when developing control laws for new commercial and military aircraft. MCAAD uses advanced dynamic modeling procedures coupled with real-time control design which can reduce the time and cost spent on traditional aircraft development methods. This is done in-flight by using a real-time modeling procedure where programmed test inputs (PTI) deflect the aircraft control surfaces, and the responses are measured in order to create a dynamic model. This paper presents an 𝐻∞-based linear parameter-varying (LPV) control law designed on a nonlinear rigid-body dynamic model which commands control surface deflections at frequencies above the PTI frequency band. Thus the controller will not suppress the response due to the PTI. The LPV controller is compared with a previously designed Nonlinear Dynamic Inversion (NDI) controller and the coherence between the commanded control surface deflections and the PTI is plotted for both controllers. The LPV controller is shown to distort the PTI less than the NDI controller.

Luke J. Miller↗
NASA NTRS1992

Numerical simulation of aerothermal loads in hypersonic engine inlets due to shock impingement

The effect of shock impingement on an axial corner simulating the inlet of a hypersonic vehicle engine is modeled using a finite-difference procedure. A three-dimensional dynamic grid adaptation procedure is utilized to move the grids to regions with strong flow gradients. The adaptation procedure uses a grid relocation stencil that is valid at both the interior and boundary points of the finite-difference grid. A linear combination of spatial derivatives of specific flow variables, calculated with finite-element interpolation functions, are used as adaptation measures. This computational procedure is used to study laminar and turbulent Mach 6 flows in the axial corner. The description of flow physics and qualitative measures of heat transfer distributions on cowl and strut surfaces obtained from the analysis are compared with experimental observations. Conclusions are drawn regarding the capability of the numerical scheme for enhanced modeling of high-speed compressible flows.

Ramakrishnan, R.↗
DOE OSTI2022

LaSDI: Parametric Latent Space Dynamics Identification

Enabling fast and accurate physical simulations with data has become an important area of computational physics to aid in inverse problems, design-optimization, uncertainty quantification, and other various decision-making applications. This paper presents a data-driven framework for parametric latent space dynamics identification procedure that enables fast and accurate simulations. The parametric model is achieved by building a set of local latent space model and designing an interaction among them. An individual local latent space dynamics model achieves accurate solution in a trust region. By letting the set of trust region to cover the whole parameter space, our model shows an increase in accuracy with an increase in training data. Herein we introduce two different types of interaction mechanisms, i.e., point-wise and region-based approach. Both linear and nonlinear data compression techniques are used. We illustrate the framework of Latent Space Dynamics Identification (LaSDI) enable a fast and accurate solution process on various partial differential equations, i.e., Burgers’ equations, radial advection problem, and nonlinear heat conduction problem, achieving 0 (100)x speed-up and 0 (1)% relative error with respect to the corresponding full order models.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Reduced basis approximations of parameterized dynamical partial differential equations via neural networks

Projection-based reduced order models are effective at approximating parameter-dependent differential equations that are parametrically separable. When parametric separability is not satisfied, which occurs in both linear and nonlinear problems, projection-based methods fail to adequately reduce the computational complexity. Devising alternative reduced order models is crucial for obtaining efficient and accurate approximations to expensive high-fidelity models. In this work, we develop a timestepping procedure for dynamical parameter-dependent problems, in which a neural-network is trained to propagate the coefficients of a reduced basis expansion. This results in an online stage with a computational cost independent of the size of the underlying problem. Here, we demonstrate our method on several parabolic partial differential equations, including a problem that is not parametrically separable.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1993

Diabatic dynamic initialization

A version of the dynamical adjustment procedure is generalized in order to make the procedure applicable to a diabatic model. In this new initialization procedure, backward adiabatic model integration is followed by forward diabatic model integration, with a high-frequency (low-pass) time filter in the form of the Euler backward time-differencing scheme applied throughout the integration. The new procedure was applied to the Goddard Laboratory for Atmospheres 4D data-assimilation system. It was found that, right from the beginning of the forecast integration, the forecast tendencies (and fields) were free of any noise due to imbalance in initial conditions, and the shocks related to an initial imbalance between model physics and dynamics, or the initial spinup effect, were practically removed.

Fox-Rabinovitz, Michael S.↗
NASA NTRS1996

Dynamic Calibration of the NASA Ames Rotor Test Apparatus Steady/Dynamic Rotor Balance

The NASA Ames Rotor Test Apparatus was modified to include a Steady/Dynamic Rotor Balance. The dynamic calibration procedures and configurations are discussed. Random excitation was applied at the rotor hub, and vibratory force and moment responses were measured on the steady/dynamic rotor balance. Transfer functions were computed using the load cell data and the vibratory force and moment responses from the rotor balance. Calibration results showing the influence of frequency bandwidth, hub mass, rotor RPM, thrust preload, and dynamic loads through the stationary push rods are presented and discussed.

Peterson, Randall L.↗
NASA NTRS1994

A dynamic localization model with stochastic backscatter

The modeling of subgrid scales in large-eddy simulation (LES) has been rationalized by the introduction of the dynamic localization procedure. This method allows one to compute rather than prescribe the unknown coefficients in the subgrid-scale model. Formally, the LES equations are supposed to be obtained by applying to the Navier-Stokes equations a 'grid filter' operation. Though the subgrid stress itself is unknown, an identity between subgrid stresses generated by different filters has been derived. Although preliminary tests of the Dynamic Localization Model (DLM) with k-equation have been satisfactory, the use of a negative eddy viscosity to describe backscatter is probably a crude representation of the physics of reverse transfer of energy. Indeed, the model is fully deterministic. Knowing the filtered velocity field and the subgrid-scale energy, the subgrid stress is automatically determined. We know that the LES equations cannot be fully deterministic since the small scales are not resolved. This stems from an important distinction between equilibrium hydrodynamics and turbulence. In equilibrium hydrodynamics, the molecular motions are also not resolved. However, there is a clear separation of scale between these unresolved motions and the relevant hydrodynamic scales. The result of molecular motions can then be separated into an average effect (the molecular viscosity) and some fluctuations. Due to the large number of molecules present in a box with size of the order of the hydrodynamic scale, the ratio between fluctuations and the average effect should be very small (as a result of the 'law of large numbers'). For that reason, the hydrodynamic balance equations are usually purely deterministic. In turbulence, however, there is no clear separation of scale between small and large eddies. In that case, the fluctuations around a deterministic eddy viscosity term could be significant. An eddy noise would then appear through a stochastic term in the subgrid-scale model and could be the source of backscatter.

Carati, Daniele↗
NASA NTRS1988

A NASTRAN DMAP alter for linear buckling analysis under dynamic loading

A unique modification to the NASTRAN solution sequence for transient analysis with direct time integration (COSMIC NASTRAN rigid format 9) was developed and incorporated into a DMAP alter. This DMAP alter calculates the buckling stability of a dynamically loaded structure, and is used to predict the onset of structural buckling under stress wave loading conditions. The modified solution sequence incorporates the linear buckling analysis capability (rigid format 5) of NASTRAN into the existing Transient solution rigid format in such a way as to provide a time dependent eigensolution which is used to assess the buckling stability of the structure as it responds to the impulsive load. As a demonstration of the validity of this modified solution procedure, the dynamic buckling of a prismatic bar subjected to an impulsive longitudinal compression is analyzed and compared to the known theoretical solution. In addition, a dynamic buckling analysis is performed for the analytically less tractable problem of the localized dynamic buckling of an initially flawed composite laminate under transverse impact loading. The addition of this DMAP alter to the transient solution sequence in NASTRAN facilitates the prediction of both time and mode of buckling.

Aiello, Robert A.↗
NASA NTRS1989

A NASTRAN DMAP alter for linear buckling analysis under dynamic loading

A modification to the NASTRAN solution sequence for transient analysis with direct time integration (COSMIC NASTRAN rigid format 9) was developed and incorporated into a DMAP alter. This DMAP alter calculates the buckling stability of a dynamically loaded structure, and is used to predict the onset of structural buckling under stress-wave loading conditions. The modified solution sequence incorporates the linear buckling analysis capability (rigid format 5) of NASTRAN into the existing Transient solution rigid format in such a way as to provide a time dependent eigensolution which is used to assess the buckling stability of the structure as it responds to the impulsive load. As a demonstration of the validity of this modified solution procedure, the dynamic buckling of a prismatic bar subjected to an impulsive longitudinal compression is analyzed and compared to the known theoretical solution. In addition, a dynamic buckling analysis is performed for the analytically less tractable problem of the localized dynamic buckling of an initially flawed composite laminate under transverse impact loading. The addition of this DMAP alter to the transient solution sequence in NASTRAN facilitates the computational prediction of both the time at which the onset of dynamic buckling occurs in an impulsively loaded structure, and the dynamic buckling mode shapes of that structure.

Aiello, Robert A.↗
NASA NTRS1984

Identification of dynamic coefficients of annular turbulent seals

An identification procedure to determine dynamic coefficients of annular turbulent seals in turbopumps is presented. Measurements were carried out at a built test rig with two symmetrical arranged seals. A rigid rotating shaft is surrounded by an elastically supported housing, which is excited by impact forces. The relative radial motion between the rotating parts and the housing, respectively between the seal surfaces, is measured by displacement pick-ups and from the time signals complex frequency response functions can be calculated. Finally an analytical model, depending on the seal parameters, is fitted to the measured data, to find the dynamic coefficients.

Nordmann, R.↗
NASA NTRS1973

Rapid iterative reanalysis for automated design

A method for iterative reanalysis in automated structural design is presented for a finite-element analysis using the direct stiffness approach. A basic feature of the method is that the generalized stiffness and inertia matrices are expressed as functions of structural design parameters, and these generalized matrices are expanded in Taylor series about the initial design. Only the linear terms are retained in the expansions. The method is approximate because it uses static condensation, modal reduction, and the linear Taylor series expansions. The exact linear representation of the expansions of the generalized matrices is also described and a basis for the present method is established. Results of applications of the present method to the recalculation of the natural frequencies of two simple platelike structural models are presented and compared with results obtained by using a commonly applied analysis procedure used as a reference. In general, the results are in good agreement. A comparison of the computer times required for the use of the present method and the reference method indicated that the present method required substantially less time for reanalysis. Although the results presented are for relatively small-order problems, the present method will become more efficient relative to the reference method as the problem size increases. An extension of the present method to static reanalysis is described, ana a basis for unifying the static and dynamic reanalysis procedures is presented.

Bhatia, K. G.↗
NASA NTRS1993

Large eddy simulation of a boundary layer with concave streamwise curvature

One of the most exciting recent developments in the field of large eddy simulation (LES) is the dynamic subgrid-scale model. The dynamic model concept is a general procedure for evaluating model constants by sampling a band of the smallest scales actually resolved in the simulation. To date, the procedure has been used primarily in conjunction with the Smagorinsky model. The dynamic procedure has the advantage that the value of the model constant need not be specified a priori, but rather is calculated as a function of space and time as the simulation progresses. This feature makes the dynamic model especially attractive for flows in complex geometries where it is difficult or impossible to calibrate model constants. The dynamic model was highly successful in benchmark tests involving homogeneous and channel flows. Having demonstrated the potential of the dynamic model in these simple flows, the overall direction of the LES effort at CTR shifted toward an evaluation of the model in more complex situations. The current test cases are basic engineering-type flows for which Reynolds averaged approaches were unable to model the turbulence to within engineering accuracy. Flows currently under investigation include a backward-facing step, wake behind a circular cylinder, airfoil at high angles of attack, separated flow in a diffuser, and boundary layer over a concave surface. Preliminary results from the backward-facing step and cylinder wake simulations are encouraging. Progress on the LES of a boundary layer on a concave surface is discussed. Although the geometry of a concave wall is not very complex, the boundary layer that develops on its surface is difficult to model due to the presence of streamwise Taylor-Gortler vortices. These vortices arise as a result of a centrifugal instability associated with the convex curvature.

Lund, Thomas S.↗
NASA NTRS1996

Dynamic Inlet Distortion Prediction with a Combined Computational Fluid Dynamics and Distortion Synthesis Approach

A procedure has been developed for predicting peak dynamic inlet distortion. This procedure combines Computational Fluid Dynamics (CFD) and distortion synthesis analysis to obtain a prediction of peak dynamic distortion intensity and the associated instantaneous total pressure pattern. A prediction of the steady state total pressure pattern at the Aerodynamic Interface Plane is first obtained using an appropriate CFD flow solver. A corresponding inlet turbulence pattern is obtained from the CFD solution via a correlation linking root mean square (RMS) inlet turbulence to a formulation of several CFD parameters representative of flow turbulence intensity. This correlation was derived using flight data obtained from the NASA High Alpha Research Vehicle flight test program and several CFD solutions at conditions matching the flight test data. A distortion synthesis analysis is then performed on the predicted steady state total pressure and RMS turbulence patterns to yield a predicted value of dynamic distortion intensity and the associated instantaneous total pressure pattern.

Norby, W. P.↗
DOE OSTI2022

Latent Space Dynamics Identification

LaSDI is a data-driven physical simulation software that forms a latent space for a given high-fidelity model and discovers a set of ordinary differential equations for the latent space dynamics. It allows a fast and accurate solution process, which is useful for multi-query decision making applications, such as design optimization and uncertainty quantification. The performance of the LaSDI framework is demonstrated on four different problems, i.e., 1D and 2D Burgers equations, nonlinear heat conduction, and radial advection problems. Both linear and nonlinear compression techniques, such as neural network and proper orthogonal decomposition, are used to form a latent space. A concept of local dynamics identification procedure is introduced to enable a parametric model, which enhances the accuracy level over a given parameter space.

Fries, William↗
NASA NTRS1974

Short-range forecasts with the GISS model of the global atmosphere

Results of tests carried out during the period from December 1972 through January 1973 to determine the short-term forecasting accuracy of a multilevel numerical primitive-equation (PE) model of the global atmosphere developed at the Goddard Institute for Space Studies (GISS). Six 48-hr forecasts were carried out with the aid of this model, using nine vertical levels and a horizontal grid spacing of 4 deg in latitude and 5 deg in longitude for an effective grid point separation averaging slightly more than 400 km. Verification of forecast sea-level pressures, 1000-mb heights, and 500-mb heights, as well as 1000-mb and 500-mb vector geostrophic winds, shows that the model has forecast skill comparable to that of operational PE models. Based on the 36-hr evolution of 18 extratropical cyclones, the model forecasts exhibit a tendency toward underestimating their propagation speeds and overestimating their central pressures. Both deficiencies are attributed to inadequate horizontal grid resolution. Quantitative verification of forecast surface temperatures over the eastern United States shows a forecast skill equal to that achieved by combined dynamical-statistical procedures.

Druyan, L. M.↗
NASA NTRS1976

NASTRAN component-mode synthesis

Procedure for dynamic substructuring analysis technique is generally as follows: calculation of component modes; selection of component normal modes, calculation of component generalized matrices, assembly of system matrices, and computation of normal modes; and retrieval of component response.

Guyan, R. J.↗