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NASA NTRS2006

Adjoint Method and Predictive Control for 1-D Flow in NASA Ames 11-Foot Transonic Wind Tunnel

This paper describes a modeling method and a new optimal control approach to investigate a Mach number control problem for the NASA Ames 11-Foot Transonic Wind Tunnel. The flow in the wind tunnel is modeled by the 1-D unsteady Euler equations whose boundary conditions prescribe a controlling action by a compressor. The boundary control inputs to the compressor are in turn controlled by a drive motor system and an inlet guide vane system whose dynamics are modeled by ordinary differential equations. The resulting Euler equations are thus coupled to the ordinary differential equations via the boundary conditions. Optimality conditions are established by an adjoint method and are used to develop a model predictive linear-quadratic optimal control for regulating the Mach number due to a test model disturbance during a continuous pitch

Nguyen, Nhan↗

DOE OSTI2020

An Improved Model For Determining Salinity Recharge Time for Deep Borehole Disposal - 20405

In a previous publication (K. P. Travis, D. Burley and F. G. F. Gibb, WM2017 Conference, Phoenix Arizona paper no. 17480) we introduced a numerical model to estimate the time it would take for a pressure perturbation to subside following its creation from the construction of a deep geological borehole in water-saturated rock. The model was based on the notion of a point source of momentum - a solution of the time-dependent pressure-diffusion equation. Using the model, we estimated that it would take on the order of 10 k years for physical equilibrium to become re-established following the sinking of a 5 km borehole in granite. The significance of such a model is that it places an upper bound on the lifetime required of a borehole sealing system - a necessary input to a borehole post-closure safety case assessment. No engineered sealing system has ever been devised which is capable of retaining its sealing properties for 10 half-lives of long-lived radioisotopes in spent fuel or high-level waste. One of the key advantages of disposing of nuclear waste via Deep Borehole Disposal (DBD) is the natural sealing provided by density stratified groundwater. Upon sinking of a borehole, and subsequent filling with fresh water, brine or drilling mud, this natural barrier may be temporarily damaged. Over time, fresh brine from the far-field will flow towards or away from the hole (driven by a pressure gradient) and will eventually re-establish the original salinity gradient. It follows that the engineered seals need last only as long as the time required for this salinity gradient to reset itself. One of the limitations of our previous model was the use of a static boundary condition on the borehole wall. The model used a boundary pressure which varied quadratically with depth (arising from differences between the pressure of a column of fresh water in the borehole and that of a column of brine in the host rock). However as brine replaces fresh water in the borehole (driven by a pressure gradient), the boundary function must change with time. We now introduce an improved model which takes this time dependent boundary condition into account. The model also takes into account the time taken for a mixture of brine and fresh water to re-establish chemical equilibrium through the process of diffusion. The paper contains the mathematical details of our new iterative model as well as results showing the time taken to reach steady state, and concentration profiles for the components of the brine-filled borehole as a function of time together with a discussion on the implications of the results for developing a post-closure safety assessment for DBD. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2024

Detonation structure in the presence of mixture stratification using reaction-resolved simulations

Many investigations of detonation-based combustors have identified reactant mixture inhomogeneity as having a leading-order impact on wave dynamics and combustion efficiency. To examine this phenomenon in a simplified context, an array of two- and three-dimensional channel detonation simulations are conducted in the present work. The reactant mixture consists of stratified fuel and air, wherein the randomly distributed equivalence ratio field features a characteristic stratification length scale. Detailed chemical kinetics are implemented in an adaptive mesh refinement solution framework where the region near the shock front is resolved with Ο (100) cells per representative ZND induction length. The results show that in comparison to baseline cases with uniform reactant mixtures, reactant stratification has a marked impact on the detonation structure. Increasing the stratification length scale increases the size and irregularity of the detonation cells, yielding larger variations in wave speed. Triple point collisions in fuel-rich regions lead to local wave speeds above the notional mean CJ speed, but wave passage through inert regions causes the local wave speed and strength to diminish. Further, conditional statistics show that increasing the stratification length scale increases the variance in pressure and temperature in the primary reaction zone, as well as the variance in heat release over a range of mixture conditions. In addition to the reactant mixture, the impact of the boundary condition behind the detonation is also investigated. The results show that an inflow boundary condition acts to over-drive the wave, leading to higher peak pressures, smaller detonation cells, and increased reactant consumption. On the other hand, cases with a wall behind the wave exhibit weaker waves with lower peak pressures and heat release rates, as well as greater variance in conditional quantities. Comparisons between complementary two- and three-dimensional simulations show reasonable qualitative agreement in wave structure, speed, and conditional statistics.

42 ENGINEERING↗

NASA NTRS2007

New Observations of the Heliospheric Magnetic Field from the Voyager Spacecraft

We review recent observations of variations of the heliospheric magnetic field B(t) made by Voyager 1 and 2 (V1 and V2), and we discuss the boundary conditions needed for models to explain the observations. Usually, observations from a spacecraft close to the Sun, such as ACE, WIND or Ulysses are used as input to a time-dependent model. Generally, the predicted profile B(t) can be compared directly with the observed profile only when either V1 or V2 is approximately radially aligned with a near-Sun spacecraft; this happens rarely and only for a brief time interval. The Bastille Day events illustrate this situation. In the absence of radial alignment of the spacecraft it is possible to predict the development of a global structure (a GMIR) with data from ACE or WIND, if they obtain a representative sample the flows that merge to form a GMIR. When latitudinal gradients are small and when there is statistical homogeneity in the azimuthal direction, it is possible to predict the statistical properties of the large-scale fluctuations of B(t) observed by V1 or V2 during a year or so. We illustrate this situation with observations from the recent solar maximum and the declining phase of the solar cycle. Predictions of detailed observations made by V1 and V2 under general conditions (e.g., when there is a large latitudinal gradient) require boundary conditions as a function of time on a surface, such as a Sun-centered sphere with a radius of 1 AU. These conditions can only be provided by global solar observations. We suggest the feasibility of such an approach, using V2 observations for 2005 and 2006. The prediction of observations in the heliosheath requires the solution of the 3-D boundary problem for the supersonic solar wind and propagation of solar wind through the termination shock into the heliosphere. The properties of B(t) observed in the heliosheath have not yet been predicted.

Burlaga, Leonard F.↗

NASA NTRS1999

Numerical Investigation of the ARMSEF Arc-Jet

The NASA/JSC 10 MW Atmospheric Reentry Materials and Structures Evaluation Facility (ARMSEF) is used for the development and evaluation of thermal protection systems for manned reentry vehicles. In an effort at better understanding the flow characteristics of an arc-jet wind tunnel and hence the correlation between simulation and actual flight conditions, preliminary numerical analyses have been made. Difficulties in defining inlet boundary conditions to the plenum chamber, where there is very little usable experimental data, are discussed. Two different boundary conditions for the plenum, a straight profile and parabolic profile, are employed to describe the conditions in this very important flow defining region. Comparisons are made to experimental data with the results showing that some type of parabolic or step profile is needed to adequately resolve the strong core flow that is present in the nozzle and plume region. Recommendations are made regarding future efforts in analyzing this challenging flow field.

Cox, Carey F.↗

DOE OSTI2022

Uncertainties in Local Intense Precipitation Flood Modeling

In the Task 1 report for the U.S. Nuclear Regulatory Commission (NRC) funded Local Intense Precipitation (LIP) Probabilistic Flood Hazard Assessment (PFHA) Pilot Study, the Pacific Northwest National Laboratory (PNNL) reviewed hydrologic and hydraulic modeling approaches for estimation of LIP flooding and their implementation in readily available simulation software packages (Prasad and Yuan 2020). NRC’s interest is in developing guidance for performing LIP PFHA at nuclear power plant (NPP) sites. This report describes the work done under Task 2 of the study that focused on describing uncertainties associated with LIP flood modeling. Two main types of uncertainties exist in LIP flood modeling: (1) aleatory uncertainties that arise from the inherent natural variability of the hydrometeorological system and (2) epistemic uncertainties that arise from the analysts’ incomplete knowledge of the hydrometeorological and site configuration. Principal sources for aleatory variability in LIP flood simulations at NPP sites include precipitation (i.e., magnitude, duration, and temporal distribution of LIP events), initial conditions (e.g., soil moisture content, stormwater drainage discharge, surface storage), boundary conditions (e.g., upstream discharge, downstream water surface elevations), and long-term temporal trends (e.g., climate change). This report describes approaches used for estimating the aleatory variability in precipitation including precipitation-frequency analysis, numerical weather prediction, and stochastic weather generation. Data sources that can be used to estimate aleatory variability in initial and boundary conditions are also described. Approaches to include effects of long-term trends like those from climate change into estimation of aleatory variability are summarized. Sources of epistemic uncertainty in LIP flood simulations at NPP sites include process representation (e.g., multiple approaches to represent runoff generation, stormwater drainage, and hydraulic routing), site configurations (e.g., site layout, flow features, status of temporary flood protection, blockage of drains), model resolution, and long-term temporal trends (e.g., known/planned site alterations, land-use changes at and in the vicinity of the site). The report describes alternative process representations (methods and models), particularly those implemented in the LIP flood simulation software packages reviewed in Task 1 report, and lists the associated model parameters. Approaches for estimating model parameters when surface and subsurface water exchanges occur are also described.

42 ENGINEERING↗

NASA NTRS1981

Turbulent solution of the Navier-Stokes equations for uniform shear flow

To study the nonlinear physics of uniform turbulent shear flow, the unaveraged Navier-Stokes equations are solved numerically. This extends our previous work in which mean gradients were absent. For initial conditions, modified three-dimensional-cosine velocity fluctuations are used. The boundary conditions are modified periodic conditions on a stationary three-dimensional numerical grid. A uniform mean shear is superimposed on the initial and boundary conditions. The three components of the mean-square velocity fluctuations are initially equal for the conditions chosen. As in the case of no shear the initially nonrandom flow develops into an apparently random turbulence at higher Reynolds number. Thus, randomness or turbulence can apparently arise as a consequence of the structure of the Navier-Stokes equations. Except for an initial period of adjustment, all fluctuating components grow with time. The initial equality of the three intensity components is destroyed by the shear, the transverse components becoming smaller than the longitudinal one, in agreement with experiment. Also, the shear creates a small-scale structure in the turbulence. The nonlinear solutions are compared with linearized ones.

Deissler, R. G.↗

DOE OSTI2020

Analysis of the SBP-SAT Stabilization for Finite Element Methods Part I: Linear Problems

In the hyperbolic community, discontinuous Galerkin (DG) approaches are mainly applied when finite element methods are considered. As the name suggested, the DG framework allows a discontinuity at the element interfaces, which seems for many researchers a favorable property in case of hyperbolic balance laws. On the contrary, continuous Galerkin methods appear to be unsuitable for hyperbolic problems and there exists still the perception that continuous Galerkin methods are notoriously unstable. To remedy this issue, stabilization terms are usually added and various formulations can be found in the literature. However, this perception is not true and the stabilization terms are unnecessary, in general. In this paper, we deal with this problem, but present a different approach. We use the boundary conditions to stabilize the scheme following a procedure that are frequently used in the finite difference community. Here, the main idea is to impose the boundary conditions weakly and specific boundary operators are constructed such that they guarantee stability. This approach has already been used in the discontinuous Galerkin framework, but here we apply it with a continuous Galerkin scheme. No internal dissipation is needed even if unstructured grids are used. Further, we point out that we do not need exact integration, it suffices if the quadrature rule and the norm in the differential operator are the same, such that the summation-by-parts property is fulfilled meaning that a discrete Gauss Theorem is valid. This contradicts the perception in the hyperbolic community that stability issues for pure Galerkin scheme exist. In numerical simulations, we verify our theoretical analysis.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1996

Effective Boundary Treatment for the Biharmonic Dirichlet Problem

The biharmonic equation can be rewritten as a system of two Poisson equations. Multigrid solution of this system is expected to converge with the same amount of work as solving two Poisson equations, requiring less than 70 floating point operations (scalar multiply or addition) per fine grid point to reach a solution using an FMG algorithm. For periodic boundary conditions, this goal is attained by simple, straightforward application of multigrid. For Dirichlet boundary conditions, however, convergence is impeded by poor interaction with the boundaries. Attempts to overcome the slowness without specifically addressing the boundaries have resulted in multigrid algorithms not attaining the Poisson convergence rate. We present three methods of boundary treatment with which full multigrid efficiency can be obtained. All implement an approach described by Brandt, concentrating some additional effort near the boundary. The first approach simply adds a number of relaxation sweeps over points close to the boundary. The second uses joint relaxation on near-boundary points. The third method takes something from each of the first two methods, resulting in a solver more suitable for highly parallel applications.

Brandt, A.↗

NASA NTRS1993

Approximating the stress field within the unit cell of a fabric reinforced composite using replacement elements

This report concerns the prediction of the elastic moduli and the internal stresses within the unit cell of a fabric reinforced composite. In the proposed analysis no restrictions or assumptions are necessary concerning yarn or tow cross-sectional shapes or paths through the unit cell but the unit cell itself must be a right hexagonal parallelepiped. All the unit cell dimensions are assumed to be small with respect to the thickness of the composite structure that it models. The finite element analysis of a unit cell is usually complicated by the mesh generation problems and the non-standard, adjacent-cell boundary conditions. This analysis avoids these problems through the use of preprogrammed boundary conditions and replacement materials (or elements). With replacement elements it is not necessary to match all the constitutional material interfaces with finite element boundaries. Simple brick-shaped elements can be used to model the unit cell structure. The analysis predicts the elastic constants and the average stresses within each constituent material of each brick element. The application and results of this analysis are demonstrated through several example problems which include a number of composite microstructures.

Foye, R. L.↗

DOE OSTI2020

A particle finite element-based model for droplet spreading analysis

Here, a particle finite element method-based model is proposed to analyze droplet dynamics problems, particularly droplet spreading on solid substrates (wetting). The model uses an updated Lagrangian framework to formulate the governing equations of the liquid. The curvature of the liquid surface is tracked accurately using a deforming boundary mesh. In order to predict the spreading rate of the droplet on the solid substrate and track the corresponding contact angle evolution, dissipative forces at the contact line are included in the formulation in addition to the Navier-slip boundary conditions at the solid–liquid interface. The inclusion of these boundary conditions makes it possible to account for the induced Young’s stress at the contact line and for the viscous dissipation along the solid–liquid interfacial region. These are found to be essential to obtain a mesh-independent physical solution. The temporal evolution of the contact angle and the contact line velocity of the proposed model are compared with spreading droplets and micro-sessile droplet injection experiments and are shown to be in good agreement.

42 ENGINEERING↗

NASA NTRS1977

Three-dimensional low Reynolds number flows with a free surface

The two-dimensional leveling problem (Degani, Gutfinger, 1976) is extended to three dimensions in the case where the flow Re number is very low and attention is paid to the free surface boundary condition with surface tension effects included. The no-slip boundary condition on the wall is observed. The numerical solution falls back on the Marker and Cell (MAC) method (Harlow and Welch, 1965) with the computation region divided into a finite number of stationary rectangular cells (or boxes in the 3-D case) and fluid flow traverses the cells (or boxes).

Degani, D.↗

NASA NTRS1991

Calculating Transient Vibrations Of Coupled Substructures

Finite-element, numerical-integration method for estimating transient vibrational response of structure composed of coupled substructures entails less computation. Responses of substructures to external forces and to forces of interaction between substructures computed. Equations of motion of each substructure solved independently. Applicable to any number and configuration of linearly responding substructures and to both determinate and indeterminate boundary conditions at interfaces between substructures. Also applicable to changing interface boundary conditions.

Admire, J. R.↗

NASA NTRS1990

Removing spurious reflections from CFD solutions by using the Complex Cepstrum

The Complex Cepstrum is shown to remove spurious reflections from artificial boundaries in computational fluid dynamic (CFD) solutions. First, the Complex Cepstrum theory is presented. A model time sequence consisting of a direct signal and reflections is analyzed theoretically with the Complex Cepstrum, and it is shown that the direct signal uncontaminated by reflections may be recovered in the time domain. Next, the Complex Cepstrum is applied to one- and three-dimensional CFD solutions, and spurious reflections from the boundary conditions are removed. By eliminating spurious reflections introduced by artificial boundary conditions, the applicability of CFD methods to aeroacoustic problems is greatly enhanced.

Meadows, Kristine R.↗

NASA NTRS2001

Development of an Innovative Algorithm for Aerodynamics-Structure Interaction Using Lattice Boltzmann Method

The lattice Boltzmann equation (LBE) is a kinetic formulation which offers an alternative computational method capable of solving fluid dynamics for various systems. Major advantages of the method are owing to the fact that the solution for the particle distribution functions is explicit, easy to implement, and the algorithm is natural to parallelize. In this final report, we summarize the works accomplished in the past three years. Since most works have been published, the technical details can be found in the literature. Brief summary will be provided in this report. In this project, a second-order accurate treatment of boundary condition in the LBE method is developed for a curved boundary and tested successfully in various 2-D and 3-D configurations. To evaluate the aerodynamic force on a body in the context of LBE method, several force evaluation schemes have been investigated. A simple momentum exchange method is shown to give reliable and accurate values for the force on a body in both 2-D and 3-D cases. Various 3-D LBE models have been assessed in terms of efficiency, accuracy, and robustness. In general, accurate 3-D results can be obtained using LBE methods. The 3-D 19-bit model is found to be the best one among the 15-bit, 19-bit, and 27-bit LBE models. To achieve desired grid resolution and to accommodate the far field boundary conditions in aerodynamics computations, a multi-block LBE method is developed by dividing the flow field into various blocks each having constant lattice spacing. Substantial contribution to the LBE method is also made through the development of a new, generalized lattice Boltzmann equation constructed in the moment space in order to improve the computational stability, detailed theoretical analysis on the stability, dispersion, and dissipation characteristics of the LBE method, and computational studies of high Reynolds number flows with singular gradients. Finally, a finite difference-based lattice Boltzmann method is developed for inviscid compressible flows.

Mei, Ren-Wei↗

NASA NTRS2004

An Investigation of Wave Propagations in Discontinuous Galerkin Method

Analysis of the discontinuous Galerkin method has been carried out for one- and two-dimensional system of hyperbolic equations. Analytical, as well as numerical, properties of wave propagation in a DGM scheme are derived and verified with direct numerical simulations. In addition to a systematic examination of the dissipation and dispersion errors, behaviours of a DG scheme at an interface of two different grid topologies are also studied. Under the same framework, a quantitative discrete analysis of various artificial boundary conditions is also conducted. Progress has been made in numerical boundary condition treatment that is closely related to the application of DGM in aeroacoustics problems. Finally, Fourier analysis of DGM for the Convective diffusion equation has also be studied in connection with the application of DG schemes for the Navier-Stokes equations. This research has resulted in five(5) publications, plus one additional manuscript in preparation, four(4) conference presentations, and three(3) departmental seminars, as summarized in part II. Abstracts of papers are given in part 111 of this report.

Hu, Fang Q.↗

NASA NTRS2004

The Contribution of Dynamic Interannual Variability to Ozone Trends

At middle latitudes the total column ozone and the lower stratospheric ozone mixing ratio exhibit natural variability. Models and statistical analyses of observations such as SAGE ozone profiles and TOMS column measurements show that seasonal cycle, solar cycle, and interannual dynamical variability and dynamical phenomena such as the quasi- biennial oscillation all contribute to ozone variability. These must be accounted for when deriving ozone trends. Systematic or random changes in the atmospheric circulation may also contribute to ozone trends. It is presently unclear how much of the ozone trend derived from observations is due to changes in the chemical composition of the stratosphere and how much is due to changes in the atmospheric circulation. We are attempting to resolve this issue by comparing a twenty-five year simulation of ozone with fixed source gas boundary conditions with an identical simulation with time dependent source gas boundary conditions. Both simulations are driven with output from a general circulation model that produces realistic interannual variability in dynamical forcing. The model trend in ozone due to changes in composition is determined from the difference in these simulations. We compare these trends with trends determined from observations and model output using the same analysis techniques. Initial results emphasize the complications to attribution of observed ozone trends to dynamical and photochemical effects that are due to interrelationships between trends in transport, temperature, and photochemical effects. It may not be possible to describe the ozone trend as a superposition of dynamical and photochemical contributions.

Douglass, Anne↗

NASA NTRS1985

Dynamic ground effects on a two-dimensional flat plate

The effect of time-variant vortex shedding is simulated by a sequence of discrete vortices convecting downstream in the wake of a two-dimensional flat plate whose lifting condition is modeled by means of the quasi-vortex lattice method. The boundary condition of this problem is specified in such a way that the tangency condition on the surface of the flat plate is satisfied; the boundary condition also takes into account the effect of airfoil motion relative to the ground. Significant lift changes are shown to occur, due to the dynamic ground effect, that are crucial in aircraft takeoff and landing transitions.

Chen, Y.-S.↗