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NASA NTRSDate not supplied

Implicit Preconditioning for Explicit Multigrid Solvers on Cut-Cell Cartesian Meshes

This work assesses the effectiveness of linearized implicit Euler preconditioning for multigrid solvers using an unpreconditioned, Jacobian-free Newton Krylov method to converge the linear system of equations. Multigrid convergence rates improve to approximately 0.75 across the cases tested including a Mach 2 supersonic wedge, transonic NACA 0012 airfoil, and ONERA M6 wing. While larger Krylov subspaces increase the convergence rate, they also increase the computational cost, such that 4-8 Krylov vectors often offers the fastest turnaround. Further reductions in computational cost are achieved with a sequential hybrid preconditioner that begins with the explicit multigrid solver before transitioning to the preconditioned algorithm later on. In addition, a novel implementation of dual time stepping is extended to include both common BDF methods as well as high-order implicit Runge-Kutta schemes. This particular formulation, which uses A −1 preconditioning, is amenable to matrix-free solvers, and the L-stable methods are especially suited for meshes with arbitrarily small cut-cells. Asymptotic order of convergence is demonstrated for BDF1, BDF2, SDIRK2, and 3rd-order Radau IIA time integration with unsteady 2D vortex simulations.

ARMD↗

NASA NTRS1986

Upwind Navier-Stokes solutions for separated periodic flows

The application of an upwind implicit approximate factorization Navier-Stokes algorithm to highly separated flow is described. Using both the thin-layer and complete forms of the Navier-Stokes equations, the low Reynolds number laminar flow around a circular cylinder with periodic shedding is solved. The effect of grid density, grid extent, and time step on the Strouhal number is shown. Results from both sets of equations agree within the experimental data band. Unsteady, laminar flow computations around inclined plates and separated airfoils are also described. Strouhal numbers agree to within 5 percent of experiments for inclined plates. Differences between the complete equations and the thin-layer approximation for separated periodic flows are discussed. Computations of an impulsively started circular cylinder and airfoil yield time-accurate flowfield shapes in good agreement with experimental flow visualizations. The turbulent computation of an airfoil at a high angle-of-attack is massively separated, but shows no evidence of periodicity.

Rumsey, C. L.↗

NASA NTRS2024

Extending the Utility of Space-Borne Snow Water Equivalent Observations Over Vegetated Areas With Data Assimilation

Snow is a vital component of the earth system, yet no snow-focused satellite remote sensing platform currently exists. In this study, we investigate how synthetic observations of snow water equivalent (SWE) representative of a synthetic aperture radar remote sensing platform could improve spatiotemporal estimates of snowpack. We use a fraternal twin observing system simulation experiment, specifically investigating how much snow simulated using widely used models and forcing data could be improved by assimilating synthetic observations of SWE. We focus this study across a 24° x 37° domain in the western USA and Canada, simulating snow at 250 m resolution and hourly time steps in water year 2019. We perform two data assimilation experiments, including (1) a simulation excluding synthetic observations in forests where canopies obstruct remote sensing retrievals and (2) a simulation inferring snow distribution in forested grid cells using synthetic observations from nearby canopy-free grid cells. Results found that, relative to a nature run, or assumed true simulation of snow evolution, assimilating synthetic SWE observations improved average SWE biases at maximum snowpack timing in shrub, grass, crop, bare-ground, and wetland land cover types from 14 %, to within 1 %. However, forested grid cells contained a disproportionate amount of SWE volume. In forests, SWE mean absolute errors at the time of maximum snow volume were 111 mm and average SWE biases were on the order of 150 %. Here the data assimilation approach that estimated forest SWE using observations from the nearest canopy-free grid cells substantially improved these SWE biases (18 %) and the SWE mean absolute error (27 mm). Simulations employing data assimilation also improved estimates of the temporal evolution of both SWE and runoff, even in spring snowmelt periods when melting snow and high snow liquid water content prevented synthetic SWE retrievals. In fact, in the Upper Colorado River region, melt-season SWE biases were improved from 63 % to within 1 %, and the Nash–Sutcliffe efficiency of runoff improved from −2.59 to 0.22. These results demonstrate the value of data assimilation and a snow-focused globally relevant remote sensing platform for improving the characterization of SWE and associated water availability.

Justin Pflug↗

NASA NTRS1990

Large scale nonlinear numerical optimal control for finite element models of flexible structures

This paper discusses the development of large scale numerical optimal control algorithms for nonlinear systems and their application to finite element models of structures. This work is based on our expansion of the optimal control algorithm (DDP) in the following steps: improvement of convergence for initial policies in non-convex regions, development of a numerically accurate penalty function method approach for constrained DDP problems, and parallel processing on supercomputers. The expanded constrained DDP algorithm was applied to the control of a four-bay, two dimensional truss with 12 soft members, which generates geometric nonlinearities. Using an explicit finite element model to describe the structural system requires 32 state variables and 10,000 time steps. Our numerical results indicate that for constrained or unconstrained structural problems with nonlinear dynamics, the results obtained by our expanded constrained DDP are significantly better than those obtained using linear-quadratic feedback control.

Shoemaker, Christine A.↗

NASA NTRS1986

Inelastic high-temperature thermomechanical response of ceramic coated gas turbine seals

Through the use of a constrained Newton-Raphson time stepping finite element scheme, the inelastic thermomechanical response of ceramic coated gas turbine parts is considered. Due to the generality of the solution procedure developed, the combined thermoelastic-plastic-creep properties associated with ceramics is treated. This includes the handling of temperature-dependent elastic-plastic creep and thermal material properties. To illustrate the procedure, the thermomechanical response of ceramic coated outer gas path seals is considered. This includes the evaluation of time-dependent thermal ratcheting and its concomitant residual stress and strain fields.

Padovan, J.↗

NASA NTRS1987

Concurrent algorithms for transient nonlinear FE analysis

A two-parameter class of time-stepping algorithms for nonlinear structural dynamics is investigated. What sets the present method apart from other concurrent algorithms is the fact that it can be used to some advantage in sequential machines as well. Thus, substantial speed-ups are obtained on a single processor as the number of subdomains is increased. An additional O(p) speed-up is obtained when p processors are utilized. The test case discussed is being repeated for a mesh comprising four times as many elements, in an effort to understand how the large scale asymptotic speed-ups are attained. A three dimensional example involving finite deformations and free body motions is also being pursued. A code optimized for concurrency in the Alliant FX8 computer is being finalized. This will provide the means for testing the performance of the algorithm in a multiprocessor environment.

Ortiz, M.↗

NASA NTRS2014

LightForce Photon-Pressure Collision Avoidance: Updated Efficiency Analysis Utilizing a Highly Parallel Simulation Approach

This paper provides an updated efficiency analysis of the LightForce space debris collision avoidance scheme. LightForce aims to prevent collisions on warning by utilizing photon pressure from ground based, commercial off the shelf lasers. Past research has shown that a few ground-based systems consisting of 10 kilowatt class lasers directed by 1.5 meter telescopes with adaptive optics could lower the expected number of collisions in Low Earth Orbit (LEO) by an order of magnitude. Our simulation approach utilizes the entire Two Line Element (TLE) catalogue in LEO for a given day as initial input. Least-squares fitting of a TLE time series is used for an improved orbit estimate. We then calculate the probability of collision for all LEO objects in the catalogue for a time step of the simulation. The conjunctions that exceed a threshold probability of collision are then engaged by a simulated network of laser ground stations. After those engagements, the perturbed orbits are used to re-assess the probability of collision and evaluate the efficiency of the system. This paper describes new simulations with three updated aspects: 1) By utilizing a highly parallel simulation approach employing hundreds of processors, we have extended our analysis to a much broader dataset. The simulation time is extended to one year. 2) We analyze not only the efficiency of LightForce on conjunctions that naturally occur, but also take into account conjunctions caused by orbit perturbations due to LightForce engagements. 3) We use a new simulation approach that is regularly updating the LightForce engagement strategy, as it would be during actual operations. In this paper we present our simulation approach to parallelize the efficiency analysis, its computational performance and the resulting expected efficiency of the LightForce collision avoidance system. Results indicate that utilizing a network of four LightForce stations with 20 kilowatt lasers, 85% of all conjunctions with a probability of collision Pc > 10 (sup -6) can be mitigated.

conjunction analysis↗

NASA NTRS1991

Transonic adaptive flutter suppression using approximate unsteady time domain aerodynamics

A digital adaptive controller is applied to the active flutter suppression problem of a wing under time varying flight conditions in subsonic and transonic flow. Linear quadratic controller gain at each time step is obtained using an iterative Riccati solver. The digital adaptive optimal controller is robust with respect to the unknown external loads. Flutter and divergence instabilities are simultaneously suppressed using a trailing-edge control surface and displacement sensing. A new transonic unsteady aerodynamic approximation methodology is developed which enables one to carry out the rapid calculation required for transonic aeroservoelastic applications. This approximation is based on a combination of unsteady subsonic aerodynamics combined with a transonic correction procedure. Aeroservoelastic transient time response is obtained using Roger's approximation, state transition matrices and an iterative time marching algorithm. The aeroservoelastic system in the time domain is modeled using a deterministic ARMA model together with a parameter estimator. Transonic flutter boundaries of a wing structure are computed, in the time domain, using an estimated aeroelastic system matrix and are in good agreement with experimental data for the low transonic Mach number range.

Pak, Chan-Gi↗

NASA NTRS1999

Real-Time Simulation of the X-33 Aerospace Engine

This paper discusses the development and performance of the X-33 Aerospike Engine RealTime Model. This model was developed for the purposes of control law development, six degree-of-freedom trajectory analysis, vehicle system integration testing, and hardware-in-the loop controller verification. The Real-Time Model uses time-step marching solution of non-linear differential equations representing the physical processes involved in the operation of a liquid propellant rocket engine, albeit in a simplified form. These processes include heat transfer, fluid dynamics, combustion, and turbomachine performance. Two engine models are typically employed in order to accurately model maneuvering and the powerpack-out condition where the power section of one engine is used to supply propellants to both engines if one engine malfunctions. The X-33 Real-Time Model is compared to actual hot fire test data and is been found to be in good agreement.

Aguilar, Robert↗

NASA NTRS1993

Current capabilities for simulating the extreme distortion of thin structures subjected to severe impacts

The explicit transient dynamics technology in use today for simulating the impact and subsequent transient dynamic response of a structure has its origins in the 'hydrocodes' dating back to the late 1940's. The growth in capability in explicit transient dynamics technology parallels the growth in speed and size of digital computers. Computer software for simulating the explicit transient dynamic response of a structure is characterized by algorithms that use a large number of small steps. In explicit transient dynamics software there is a significant emphasis on speed and simplicity. The finite element technology used to generate the spatial discretization of a structure is based on a compromise between completeness of the representation for the physical processes modelled and speed in execution. That is, since it is expected in every calculation that the deformation will be finite and the material will be strained beyond the elastic range, the geometry and the associated gradient operators must be reconstructed, as well as complex stress-strain models evaluated at every time step. As a result, finite elements derived for explicit transient dynamics software use the simplest and barest constructions possible for computational efficiency while retaining an essential representation of the physical behavior. The best example of this technology is the four-node bending quadrilateral derived by Belytschko, Lin and Tsay. Today, the speed, memory capacity and availability of computer hardware allows a number of the previously used algorithms to be 'improved.' That is, it is possible with today's computing hardware to modify many of the standard algorithms to improve their representation of the physical process at the expense of added complexity and computational effort. The purpose is to review a number of these algorithms and identify the improvements possible. In many instances, both the older, faster version of the algorithm and the improved and somewhat slower version of the algorithm are found implemented together in software. Specifically, the following seven algorithmic items are examined: the invariant time derivatives of stress used in material models expressed in rate form; incremental objectivity and strain used in the numerical integration of the material models; the use of one-point element integration versus mean quadrature; shell elements used to represent the behavior of thin structural components; beam elements based on stress-resultant plasticity versus cross-section integration; the fidelity of elastic-plastic material models in their representation of ductile metals; and the use of Courant subcycling to reduce computational effort.

Key, Samuel W.↗

NASA NTRSDate not supplied

RDE Nozzle Computational Design Methodology Development and Application

The Open National Combustion Code (OpenNCC) is used to simulate the aerospike exhaust nozzle region of a rotating detonation engine (RDE).The main objectives of the current study are twofold. The first goal is to validate the proposed computational methodology using the experimental data. The second goal is to demonstrate how the validated prediction tool can be used to optimize the nozzle geometry. To achieve a significant speed-up of computational time, the computational domain in divided into two parts: a combustion region and a throat-nozzle section. In the combustion region, a validated quasi-two-dimensional in-house code is utilized to generate an unsteady RDE flow field solution just upstream of the combustor throat. Subsequently, the unsteady flow data is fed into the three-dimensional throat-nozzle section as the inflow boundary condition. This facilitates the design optimization process since the unsteady inflow can be reused, and a relatively coarse mesh (i.e., larger time-step) can be used to analyze the flow fields around the nozzle. Five nozzle designs were studied and the predicted performance (i.e., thrust)compared. The optimized nozzle was found to produce 3.2% more overall thrust than a baseline nozzle design. Without the nozzle, there is a large low-pressure region at the throat exit, which significantly reduces the overall performance. This methodology is shown to be a promising approach to explore a wide variety of nozzle geometries in a relatively short amount of time.

CFD↗

NASA NTRS2021

Seasonal Glacier and Snow Loading in Svalbard Recovered from Geodetic Observations

We processed time series from seven Global Navigation Satellite System (GNSS) stations and one Very Long Baseline Interferometry (VLBI) station in Svalbard. The goal was to capture the seasonal vertical displacements caused by elastic response of variable mass load due to ice and snow accumulation. We found that estimates of the annual signal in different GNSS solutions disagree by more than 3 mm which makes geophysical interpretation of raw GNSS time series problematic. To overcome this problem, we have used an enhanced Common Mode (CM) filtering technique. The time series are differentiated by the time series from remote station BJOS with known mass loading signals removed a priori. Using this technique, we have achieved a substantial reduction of the differences between the GNSS solutions. We have computed mass loading time series from a regional Climatic Mass Balance (CMB) and snow model that provides the amount of water equivalent at a 1 km resolution with a time step of 7 days. We found that the entire vertical loading signal is present in data of two totally independent techniques at a statistically significant level of 95%. This allowed us to conclude that the remaining errors in vertical signal derived from the CMB model are less than 0.2 mm at that significance level. Refining the land water storage loading model with a CMB model resulted in a reduction of the annual amplitude from 2:1 mm to 1:1 mm in the CM filtered time series, while it had only a marginal impact on raw time series. This provides a strong evidence that CM filtering is essential for revealing local periodic signals when a millimetre level of accuracy is required.

H P Kierulf↗

NASA NTRS2013

Photosynthesis-dependent Isoprene Emission from Leaf to Planet in a Global Carbon-chemistry-climate Model

We describe the implementation of a biochemical model of isoprene emission that depends on the electron requirement for isoprene synthesis into the FarquharBallBerry leaf model of photosynthesis and stomatal conductance that is embedded within a global chemistry-climate simulation framework. The isoprene production is calculated as a function of electron transport-limited photosynthesis, intercellular and atmospheric carbon dioxide concentration, and canopy temperature. The vegetation biophysics module computes the photosynthetic uptake of carbon dioxide coupled with the transpiration of water vapor and the isoprene emission rate at the 30 min physical integration time step of the global chemistry-climate model. In the model, the rate of carbon assimilation provides the dominant control on isoprene emission variability over canopy temperature. A control simulation representative of the present-day climatic state that uses 8 plant functional types (PFTs), prescribed phenology and generic PFT-specific isoprene emission potentials (fraction of electrons available for isoprene synthesis) reproduces 50 of the variability across different ecosystems and seasons in a global database of 28 measured campaign-average fluxes. Compared to time-varying isoprene flux measurements at 9 select sites, the model authentically captures the observed variability in the 30 min average diurnal cycle (R2 6496) and simulates the flux magnitude to within a factor of 2. The control run yields a global isoprene source strength of 451 TgC yr1 that increases by 30 in the artificial absence of plant water stress and by 55 for potential natural vegetation.

photosynthesis↗

NASA NTRS2015

A Numerical Solution Routine for Investigating Oxidation-Induced Strength Degradation Mechanisms in SiC/SiC Composites

The stress rupture strength of silicon carbide fiber-reinforced silicon carbide (SiCSiC) composites with a boron nitride (BN) fiber coating decreases with time within the intermediate temperature range of 700-950 C. Various theories have been proposed to explain the cause of the time dependent stress rupture strength. Some previous authors have suggested that the observed composite strength behavior is due to the inherent time dependent strength of the fibers, which is caused by the slow growth of flaws within the fibers. Flaw growth is supposedly enabled by oxidation of free carbon at the grain boundaries. The objective of this paper is to investigate the relative significance of the various theories for the time-dependent strength of SiCSiC composites. This is achieved through the development of a numerically-based progressive failure analysis routine and through the application of the routine to simulate the composite stress rupture tests. The progressive failure routine is a time marching routine with an iterative loop between a probability of fiber survival equation and a force equilibrium equation within each time step. Failure of the composite is assumed to initiate near a matrix crack and the progression of fiber failures occurs by global load sharing. The probability of survival equation is derived from consideration of the strength of ceramic fibers with randomly occurring and slow growing flaws as well as the mechanical interaction between the fibers and matrix near a matrix crack. The force equilibrium equation follows from the global load sharing presumption. The results of progressive failure analyses of the composite tests suggest that the relationship between time and stress-rupture strength is attributed almost entirely to the slow flaw growth within the fibers. Although other mechanisms may be present, they appear to have only a minor influence on the observed time dependent behavior.

degradation↗

NASA NTRS2016

Time-Dependent Stress Rupture Strength Degradation of Hi-Nicalon Fiber-Reinforced Silicon Carbide Composites at Intermediate Temperatures

The stress rupture strength of silicon carbide fiber-reinforced silicon carbide composites with a boron nitride fiber coating decreases with time within the intermediate temperature range of 700 to 950 degree Celsius. Various theories have been proposed to explain the cause of the time-dependent stress rupture strength. The objective of this paper is to investigate the relative significance of the various theories for the time-dependent strength of silicon carbide fiber-reinforced silicon carbide composites. This is achieved through the development of a numerically based progressive failure analysis routine and through the application of the routine to simulate the composite stress rupture tests. The progressive failure routine is a time-marching routine with an iterative loop between a probability of fiber survival equation and a force equilibrium equation within each time step. Failure of the composite is assumed to initiate near a matrix crack and the progression of fiber failures occurs by global load sharing. The probability of survival equation is derived from consideration of the strength of ceramic fibers with randomly occurring and slow growing flaws as well as the mechanical interaction between the fibers and matrix near a matrix crack. The force equilibrium equation follows from the global load sharing presumption. The results of progressive failure analyses of the composite tests suggest that the relationship between time and stress-rupture strength is attributed almost entirely to the slow flaw growth within the fibers. Although other mechanisms may be present, they appear to have only a minor influence on the observed time-dependent behavior.

Progressive Failure Analysis↗

NASA NTRS1988

A multi-element vortex lattice method for calculating the geometry and effects of a helicopter rotor wake in forward flight

A method is described for the analysis of the unsteady, incompressible potential flow associated with a helicopter rotor and it's wake in forward flight. This method is particularly useful in low advance ratio flight due to the major contribution, in the near field, of the deformed wake. The rotor geometry is prescribed and the unsteady wake geometry is computed from the local flow perturbation velocities. The wake is modeled as a full vortex lattice. The rotor geometry is arbitrary and several rotor blades can be represented. The unsteady airloads on the rotor blades are computed in the presence of the deformed rotor wake by a time-stepping technique. Solution for the load distribution on the blade surfaces is found by prescribing boundary conditions in a reference system which rotates with the blade tips. Transformation tensors are used to describe the contribution of the wake in the inertial system to the rotor in the rotating reference system. The effects of blade cyclic pitch variation are computed using a rotation tensor. The deformation of the wake is computed in the inertial frame. The wake is started impulsively from rest, allowing a natural convection of the wake with time.

Berry, John D.↗

NASA NTRS1989

Numerical Simulation of Flow Through an Artificial Heart

A solution procedure was developed that solves the unsteady, incompressible Navier-Stokes equations, and was used to numerically simulate viscous incompressible flow through a model of the Pennsylvania State artificial heart. The solution algorithm is based on the artificial compressibility method, and uses flux-difference splitting to upwind the convective terms; a line-relaxation scheme is used to solve the equations. The time-accuracy of the method is obtained by iteratively solving the equations at each physical time step. The artificial heart geometry involves a piston-type action with a moving solid wall. A single H-grid is fit inside the heart chamber. The grid is continuously compressed and expanded with a constant number of grid points to accommodate the moving piston. The computational domain ends at the valve openings where nonreflective boundary conditions based on the method of characteristics are applied. Although a number of simplifing assumptions were made regarding the geometry, the computational results agreed reasonably well with an experimental picture. The computer time requirements for this flow simulation, however, are quite extensive. Computational study of this type of geometry would benefit greatly from improvements in computer hardware speed and algorithm efficiency enhancements.

Rogers, Stuart E.↗

NASA NTRS1991

Combustion of liquid fuel droplets in supercritical conditions

A comprehensive analysis of liquid-fuel droplet combustion in both sub- and super-critical environments has been conducted. The formulation is based on the complete conservation equations for both gas and liquid phases, and accommodates finite-rate chemical kinetics and a full treatment of liquid-vapor phase equilibrium at the droplet surface. The governing equations and the associated interface boundary conditions are solved numerically using a fully coupled, implicit scheme with the dual time-stepping integration technique. The model is capable of treating the entire droplet history, including the transition from the subcritical to the supercritical state. As a specific example, the combustion of n-pentane fuel droplets in air is studied for pressures of 5-140 atm. Results indicate that the ambient gas pressure exerts significant control of droplet gasification and burning processes through its influences on the fluid transport, gas/liquid interface thermodynamics, and chemical reactions. The droplet gasification rate increases progressively with pressure. However, the data for the overall burnout time exhibits a significant variation near the critical burning pressure, mainly as a result of reduced mass-diffusion rate and latent heat of vaporization with increased pressure. The influence of droplet size on the burning characteristics is also noted.

Shuen, J. S.↗