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DOE OSTI2024

Quantification of modeling uncertainty in the Rayleigh damping model

Understanding and accurately characterizing energy dissipation mechanisms in civil structures during earthquakes is an important element of seismic assessment and design. The most commonly used model is attributed to Rayleigh. This paper proposes a systematic approach to quantify the uncertainty associated with Rayleigh's damping model. Bayesian calibration with embedded model error is employed to treat the coefficients of the Rayleigh model as random variables using modal damping ratios. Through a numerical example, we illustrate how this approach works and how the calibrated model can address modeling uncertainty associated with the Rayleigh damping model.

42 ENGINEERING↗

NASA NTRS1990

A comparison of different models for beam vibrations from the standpoint of control design

Different models for beam vibrations are analyzed from the standpoint of designing finite-dimensional controllers to stabilize the beam vibrations. A distributed system described by an undamped Euler-Bernoulli equation cannot be stabilized by any finite-dimensional controller, i.e., any controller which can be described an ordinary differential equation with constant coefficients. If viscous damping is included, a similar problem occurs in that all the poles can not be moved to the left of a given vertical line. These negative results should be interpreted as a commentary on the limitations of these models, rather than on the control of real beams. If a Rayleigh damping model is used, a finite-dimensional controller may be designed to move the closed loop system poles essentially as far to the left in the complex plane as desired. This result will also hold for certain hysteresis damping models. This has implications for the settling time of the vibrations.

Morris, K. A.↗

NASA NTRS1990

Overshooting thunderstorm cloud top dynamics as approximated by a linear Lagrangian parcel model with analytic exact solutions

Results are presented from a linear Lagrangian entraining parcel model of an overshooting thunderstorm cloud top. The model, which is similar to that of Adler and Mack (1986), gives analytic exact solutions for vertical velocity and temperature by representing mixing with Rayleigh damping instead of nonlinearly. Model results are presented for various combinations of stratospheric lapse rate, drag intensity, and mixing strength. The results are compared to those of Adler and Mack.

Schlesinger, Robert E.↗

NASA NTRS1989

Orthogonal canonical forms for second-order systems

The authors prove that a linear second-order system with arbitrary damping cannot be reduced to Hessenberg-triangular form by means of orthogonal transformations, while this reduction is always possible for the modal damping commonly assumed for models of flexible structures. The type of canonical form obtainable by means of orthogonal transformations acting on a second-order system is heavily dependent on the type of damping considered. If the damping matrix is merely positive semi-definite symmetric, it is generally not possible to obtain a reduction to Hessenberg-triangular form, while this reduction is trivial for zero or Rayleigh damping. If damping is modal, however, as is commonly assumed in structural models, the reduction exists and is nontrivial. Furthermore, reduction to triangular second-order Schur form is always possible for such damping: this canonical form appears likely to have applications to second-order system theory.

Williams, Trevor↗

NASA NTRS1985

Effects of Rayleigh and Newtonian damping on wave-mean flow interaction

A theoretical study is made of the effects of mean damping on wave-mean flow interactions. A condition is derived for the Eliassen-Palm flux divergence to balance the steady-state residual circulations induced by eddies in the presence of mean damping. It is shown by a simple analytical model that this balance holds for stratospheric planetary waves when the Rayleigh friction coefficient is one order smaller than the Newtonian cooling coefficient, although the tall mean flow condition is not violated. In this case, the Eliassen-Palm flux divergence can be interpreted as approximating the steady residual circulation (approximately equal to Lagrangian-mean circulations) induced by eddies as well as the net mean acceleration in the absence of mean damping. This balance is consistent with the stratospheric circulations of a dynamical model.

Hayashi, Y.↗

NASA NTRS1993

A nonreflecting upper boundary condition for anelastic nonhydrostatic mesoscale gravity-wave models

A sponge layer is formulated to prevent spurious reflection of vertically propagating quasi-stationary gravity waves at the upper boundary of a two-dimensional numerical anelastic nonhydrostatic model. The sponge layer includes damping of both Newtonian-cooling type and Rayleigh-friction type, whose coefficients are determined in such a way that the reflectivity of wave energy at the bottom of the layer is zero. Unlike the formulations in earlier studies, our formulation includes the effects of vertical discretization, vertical mean density variation, and nonhydrostaticity. This sponge formulation is found effective in suppressing false downward reflection of waves for various types of quasi-stationary forcing.

Kim, Young-Joon↗

DOE OSTI2024

Recommendations on setup in simulating atmospheric gravity waves under conventionally neutral boundary layer conditions

Wind farm-induced atmospheric gravity waves have been the subject of recent research as they can impact wind farm performance. Pressure variations associated with gravity waves can contribute to the global blockage effect and wind farm wake recovery. Therefore, accurate numerical simulation of flow fields, where wind-farm-induced gravity waves may be produced, is important. Three main considerations in such simulations are the overall domain size, the use of Rayleigh damping near domain boundaries to dampen gravity waves, and advection damping at the inlet to prevent spurious oscillations. Often these considerations are treated ad hoc rather than systematically. This work aims to test and extend the systematic modelling of internal gravity waves proposed in a preliminary investigation to modelling of both internal and trapped gravity waves. The preliminary study identifies the length scales to set the domain and damping layer sizes and the time scale to configure the Rayleigh damping coefficient but under linearly stratified conditions. Large eddy simulations of flow through a wind farm canopy are performed under conventionally neutral boundary layer (CNBL) conditions to test the validity of proposed setups for CNBL conditions. Background atmospheric parameters, such as Froude number (Fr), inversion height (H i ), and inversion layer Froude number (Fr i ) control most of the atmospheric gravity wave characteristics. We validated for CBNL conditions that the effective wavelengths of the internal gravity waves are the correct length scale to configure the domain size and damping layer thickness. Likewise, the optimum damping coefficient to dampen the internal gravity waves relates to the free atmosphere's buoyancy frequency or buoyant perturbations' time scale. We infer that the damping coefficient in the inversion layer may relate to the inversion buoyancy frequency to effectively dampen the trapped gravity waves. Moreover, the advection damping length is linked to the horizontal wavelength of the trapped gravity waves in the inversion layer to prevent spurious waves at the inlet by retaining wave energy accumulation.

17 WIND ENERGY↗

NASA NTRS1994

A thermosphere-ionosphere-mesosphere-electrodynamic general circulation model (time-GCM): Equinox solar cycle minimum simulations (30-500 km)

A new simulation model of the mesosphere, thermosphere, and ionosphere with coupled electrodynamics has been developed and used to calculate the global circulation, temperature and compositional structure between 30-500 km for equinox, solar cycle minimum, geomagnetic quiet conditions. The model incorporates all of the features of the National Center for Atmospheric Research (NCAR) thermosphere-ionosphere- electrodynamics general circulation model (TIE-GCM) but the lower boundary has been extended downward from 97 to 30 km (10 mb) and it includes the physical and chemical processes appropriate for the mesosphere and upper stratosphere. The first simulation used Rayleigh friction to represent gravity wave drag in the middle atmosphere and although it was able to close the mesospheric jets it severely damped the diurnal tide. Reduced Rayleigh friction allowed the tide to penetrate to thermospheric heights but did not close the jets. A gravity wave parameterization developed by Fritts and Lu (1993) allows both features to exist simultaneously with the structure of tides and mean flow dependent upon the strength of the gravity wave source. The model calculates a changing dynamic structure with the mean flow and diurnal tide dominant in the mesosphere, the in-situ generated semi-diurnal tide dominating the lower thermosphere and an in-situ generated diurnal tide in the upper thermosphere. The results also show considerable interaction between dynamics and composition, especially atomic oxygen between 85 and 120 km.

Roble, R. G.↗

NASA NTRS2014

In-Flight Aeroelastic Stability of the Thermal Protection System on the NASA HIAD, Part I: Linear Theory

Conical shell theory and piston theory aerodynamics are used to study the aeroelastic stability of the thermal protection system (TPS) on the NASA Hypersonic Inflatable Aerodynamic Decelerator (HIAD). Structural models of the TPS consist of single or multiple orthotropic conical shell systems resting on several circumferential linear elastic supports. The shells in each model may have pinned (simply-supported) or elastically-supported edges. The Lagrangian is formulated in terms of the generalized coordinates for all displacements and the Rayleigh-Ritz method is used to derive the equations of motion. The natural modes of vibration and aeroelastic stability boundaries are found by calculating the eigenvalues and eigenvectors of a large coefficient matrix. When the in-flight configuration of the TPS is approximated as a single shell without elastic supports, asymmetric flutter in many circumferential waves is observed. When the elastic supports are included, the shell flutters symmetrically in zero circumferential waves. Structural damping is found to be important in this case. Aeroelastic models that consider the individual TPS layers as separate shells tend to flutter asymmetrically at high dynamic pressures relative to the single shell models. Several parameter studies also examine the effects of tension, orthotropicity, and elastic support stiffness.

Goldman, Benjamin D.↗

DOE OSTI2024

A study of the Rayleigh-Taylor Instability during deceleration in inertial confinement fusion relevant conditions [Slides]

Large Planar targets with significant room for RTI evolution could have the potential to reach regimes where magnetic field damping of RTI is observable. Hot-electron generation at 1 PW/cm 2 and greater can introduced substantial preheat to experimental targets. Manufacturing defects can create further 3D complexity in targets designed and modeled in 2D. Computational models used in experimental designing do not always account for all the physics present and must be reevaluated based on experimental data. 3D modeling and provide high fidelity estimates on what the experimental data will look like, and can be utilized for high fidelity bench-marking or complex 3D experimental design work.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Investigating the relationship between simulation parameters and flow variables in simulating atmospheric gravity waves for wind energy applications

Wind farms, particularly offshore clusters, are becoming larger than ever before. Besides influencing the surface wind flow and the inflow for downstream wind farms, large wind farms can trigger atmospheric gravity waves in the inversion layer and the free atmosphere aloft. Wind-farm-induced gravity waves can cause adverse pressure gradients upstream of the wind farm, which contribute to the global blockage effect, and can induce favorable pressure gradients above and downstream of the wind farm that enhance wake recovery. Numerical modeling is a powerful means of studying these wind-farm-induced atmospheric gravity waves, but it comes with the challenge of handling spurious reflections of these waves from domain boundaries. Typically, approaches which employ radiation boundary conditions and forcing zones are used to avoid these reflections. However, the simulation setup of these approaches relies heavily on ad hoc processes. For instance, the widely used Rayleigh damping method requires ad hoc tuning to produce a setup that may only produce satisfactory results for a particular case. To provide more systematic guidance on setting up realistic simulations of atmospheric gravity waves, we conduct a large-eddy simulation (LES) study of flow over a 2D hill and through a wind farm canopy that explores the optimum domain size and damping layer setup depending on the fundamental parameters which determine the flow characteristics. In this work, we only consider linearly stratified conditions (i.e., no inversion layer), thereby focusing on internal gravity waves in the free atmosphere and their reflections from the domain boundaries. This type of flow is governed by a single Froude number, which dictates most of the internal wave properties, such as wavelength, amplitude, and direction. This, in turn, will dictate the optimum domain size and Rayleigh damping layer setup. We find the effective horizontal and vertical wavelengths (the representative wavelengths of the entire wave spectrum) to be the appropriate length scales to size the domain and damping layer thickness, and the optimal Rayleigh damping coefficient scales with the Brunt–Väisälä frequency. Considering Froude numbers seen in wind farm applications, we propose recommendations to limit the reflections to less than 10 % of the total upward-propagating wave energy. Typically, damping is done at the top boundary, but given the non-periodic lateral boundary conditions of practical wind farm simulation domains, we find that damping the inflow–outflow boundaries is of equal importance to damping the top boundary. The Brunt–Väisälä frequency-normalized damping coefficient should be between 1 and 10. The damping layer thickness should be at least one effective vertical wavelength; damping layers exceeding 1.5 times the vertical wavelength are found to be unnecessary. The domain length and height should accommodate at least one effective horizontal and vertical wavelength, respectively. Moreover, Rayleigh damping does not damp the waves completely, and the non-damped energy might accumulate over the simulation time.

17 WIND ENERGY↗

NASA NTRS2000

Magnetic Field Suppression of Flow in Semiconductor Melt

One of the most promising approaches for the reduction of convection during the crystal growth of conductive melts (semiconductor crystals) is the application of magnetic fields. Current technology allows the experimentation with very intense static fields (up to 80 KGauss) for which nearly convection free results are expected from simple scaling analysis in stabilized systems (vertical Bridgman method with axial magnetic field). However, controversial experimental results were obtained. The computational methods are, therefore, a fundamental tool in the understanding of the phenomena accounting during the solidification of semiconductor materials. Moreover, effects like the bending of the isomagnetic lines, different aspect ratios and misalignments between the direction of the gravity and magnetic field vectors can not be analyzed with analytical methods. The earliest numerical results showed controversial conclusions and are not able to explain the experimental results. Although the generated flows are extremely low, the computational task is a complicated because of the thin boundary layers. That is one of the reasons for the discrepancy in the results that numerical studies reported. Modeling of these magnetically damped crystal growth experiments requires advanced numerical methods. We used, for comparison, three different approaches to obtain the solution of the problem of thermal convection flows: (1) Spectral method in spectral superelement implementation, (2) Finite element method with regularization for boundary layers, (3) Multiquadric method, a novel method with global radial basis functions, that is proven to have exponential convergence. The results obtained by these three methods are presented for a wide region of Rayleigh and Hartman numbers. Comparison and discussion of accuracy, efficiency, reliability and agreement with experimental results will be presented as well.

Fedoseyev, A. I.↗

DOE OSTI2024

The Effect of Spatially Varying Collision Frequency on the Development of the Rayleigh–Taylor Instability

Abstract The Rayleigh–Taylor (RT) instability is ubiquitously observed, yet has traditionally been studied using ideal fluid models. Collisionality can vary strongly across the fluid interface, and previous work demonstrates the necessity of kinetic models to completely capture dynamics in certain collisional regimes. Where previous kinetic simulations used spatially and temporally constant collision frequency, this work presents five-dimensional (two spatial, three velocity dimensions) continuum-kinetic simulations of the RT instability using a more realistic spatially varying collision frequency. Three cases of collisional variation are explored for two Atwood numbers: low to intermediate, intermediate to high, and low to high. The low-to-intermediate case exhibits no RT instability growth, while the intermediate-to-high case is similar to a fluid-limit kinetic case with interface widening biased toward the lower-collisionality region. A novel contribution of this work is the low-to-high collisionality case that shows significantly altered instability growth through an upward movement of the interface and damped spike growth due to increased free-streaming particle diffusion in the lower region. Contributions to the energy flux from the non-Maxwellian portions of the distribution function are not accessible to fluid models and are greatest in magnitude in the spike and regions of low collisionality. Increasing the Atwood number results in greater RT instability growth and reduced upward interface movement. Deviation of the distribution function from Maxwellian is inversely proportional to collision frequency and concentrated around the fluid interface. The linear phase of RT instability growth is well described by theoretical linear growth rates accounting for viscosity and diffusion.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1993

Moist wind relationships

Equations describing the temporal and spatial behavior of the kinematic moisture and heat flux are introduced. In these nonlinear equations, the contribution by diabatic processes to the large-scale flux is composed of two parts. One part is associated with a Rayleigh damping term, while the other arises from temporal and spatial changes in the pressure gradient term. The influence of diabatic processes on the large-scale moisture fluxes depends greatly on the degree of balance between forcing and damping terms in the governing equations. The existence of a near balance requires a reduction in the large-scale horizontal geostrophic wind speed. From a scale analysis of the moisture flux equations it is argued that reductions in the large-scale horizontal wind speed, observed within major cumulus cloud systems, help conserve large-scale moisture fluxes. The deviation of the wind from geostrophic conditions is easily estimated. This wind modification induces secondary vertical circulations that contribute to the convergence, creating or supporting long-lived mesoscale flows. In the tropics the wind modification has an antitriptic relationship. These diagnostic findings suggest possible modifications to the wind field in the application of cumulus parameterization, and may be important in diabatic initialization of numerical weather prediction models.

Raymond, William H.↗

NASA NTRS1990

Moist wind relationships

The equations describing the temporal and spatial behavior of the kinematic moisture and heat flux are described. In these nonlinear equations, the contribution by diabatic processes to the large-scale flux is composed of two parts. One part is associated with a Rayleigh damping term while the other arises from temporal and spatial changes in the pressure gradient term. It was found that the influence of diabatic processes on large-scale moisture fluxes depends greatly on the degree of balance between forcing and damping terms in the governing kinematic flux equations. The existence of a near balance requires a reduction in the large-scale horizontal geostrophic wind speed. Based on an examination of the moisture flux equations, it is argued that reductions in the large-scale horizontal wind speed observed within major cumulus cloud systems help conserve large-scale moisture fluxes. The deviation of the wind from geostrophic conditions is easily estimated for a near balanced state. This wind modification induces secondary vertical circulations that contribute to convergence, creating or supporting long-lived mesoscale flows. We believe this process to be a major supporter of the mesoscale circulations observed in severe storms and squall lines. In the tropics the wind modification has an antitriptic relationship. These diagnostic findings suggest possible modifications to the wind field in the application of a cumulus parameterization, and may be important in diabatic initialization of numerical weather prediction models.

Raymond, William H.↗