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All sources NASA NTRS DOE OSTI

DOE OSTI2024

Challenging Common Assumptions of Thick-Wall Chamber Dynamics in Inertial Fusion Systems using MOOSE

As an increasing number of companies look toward commercial Inertial Fusion Energy (IFE) designs, there is a pressing need to understand the physics of thick-wall chamber gas dynamics. The thick liquid wall approach implements a renewable wall to mitigate the fusion target emissions, thereby reducing the radiation damage rate and significantly extending the lifetime of chamber structures, leading to increased plant availability and reduced waste streams in comparison to dry wall chamber designs. It is necessary, however, to assess the critical performance and safety aspects of these systems. For example, it is crucial to predict (1) where the mass ablated from the liquid walls will vent, which determines the placement of condensing surfaces; (2) debris propagation up the beam lines, which provides essential information for design and protection requirements; (3) peak pressures and impulse on chamber walls, which affect chamber structural design; and (4) momentum transfer to the liquid jets, which constrains the shape and positioning of the jets. In turn, the chamber design and its liquid walls affect shielding requirements, material activation, and tritium fuel cycle. Currently available simulation tools, however, are unable to accurately capture key thick-wall chamber dynamics. Significant assumptions are often made to simplify the system and reduce computational cost and modeling capability needs, but the impact of these assumptions on simulation predictions has not been evaluated. For example, no three-dimensional simulations can be found in the open literature to evaluate gas venting and momentum transfer to the jets with simulations using two-dimensional domains to represent complex three-dimensional geometries. Moreover, limited studies have been dedicated to jet breakup due to both turbulence and neutron heating, and no studies have been found that evaluate how jet breakup can impact shock-jet interaction. Furthermore, effects of radiative heat transfer have rarely been included for the hydrodynamic phase of shock propagation, and integration of proper equations of state in shock dynamics codes has been mostly exploratory. In this study, we use the flexible, high-fidelity Multiphysics Object-Oriented Simulation Environment (MOOSE) to model these complex phenomena and inform design and safety studies. Capabilities to model thick-wall chamber gas dynamics are being developed, and the impact of the assumptions listed above (i.e., two-dimensional vs three-dimensional, absence of jet breakout, no radiative heat transfer, and ideal gas behavior) are being quantified.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Challenging Common Assumptions of Thick-Wall Chamber Dynamics in Inertial Fusion Systems Using MOOSE-based Multiphysics Simulations

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

Giant Domain Wall Conductivity in Self‐Assembled BiFeO 3 Nanocrystals

Abstract Ever‐increasing demand on electronic devices with ultrahigh‐density non‐volatile data storage has attracted great interest in novel ferroelectric memories based on conductive ferroelectric domain walls. Embedded in an insulating material, ferroelectric domain walls have the capability of being (re)created, displaced, erased, and altered in their spatial configurations and electronic characteristics. However, the domain wall conductivities are in most cases not yet sufficiently high to ensure the current density required to drive read‐out circuits operating at high speeds. In this work, a giant domain wall current (>10 µA) of a single charged domain wall is obtained through conductive atomic force microscopy with a bias field of 4 V. This is achieved in self‐assembled BiFeO 3 nanocrystals grown by sol‐gel method on Nb‐doped SrTiO 3 substrates. Local configurations of domains and domain wall types are studied using vector piezoresponse force microscopy and high‐resolution transmission electronic microscopy. The enhancement of the wall current is shown to be due to the formation of conducting pathways of charged defects accumulated along domain walls and traversing the nanocrystals. The diverse domain walls can be manipulated by electric field in a perpendicular architecture. The perpendicular array structure of BiFeO 3 nanocrystals should have great potentials for developing perpendicular nanoelectronic prototypes.

Liu, Lisha↗

DOE OSTI2022

Interaction of cosmological domain walls with large classical objects, like planets and satellites, and the flyby anomaly

Cosmological domain walls can be formed as a result of symmetry breaking at any epoch during the evolution of our universe. We study their interaction with a classical macroscopic object, like Earth or a satellite in Earth’s orbit. We set up an action that includes the interaction term between the massive classical object and the scalar field that the domain wall is made of. We use numerical calculations to solve the coupled equations of motion which describe the crossing between the domain wall and the classical object. Depending on the strength of the interaction, relative velocity and size, the object can be either stopped by the wall, or it can pass through it inducing deformations in the wall that cost energy. At the same time, the coupling to the scalar filed might change the object’s mass during the crossover. The fact that satellites in Earth’s orbit (or planets in Sun’s orbit) can change their mass and/or lose energy interacting with walls can be used as a new domain wall detection probe. For example, a typical velocity precision of a satellite is about 0.5 mm/s, which directly puts an upper limit on its mass change to ΔM/M ≲ 5 × 10 –17 . Alternatively, a known satellite flyby anomaly can easily be explained as an interaction with a closed domain wall. We also show that the presence of matter modifies the scalar filed potential and can locally create a bubble of the true vacuum, and thus trigger the decay of the false vacuum. For a critical bubble which is able to expand, such an interaction with the domain wall must be strong enough.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Matrix polysaccharides affect preferred orientation of cellulose crystals in primary cell walls

The spatial organization and interactions of constituent components influence cell growth and determine physical and chemical properties of the cell wall, including its rigidity, flexibility, and degradability. Elucidating the interactions between cell wall polysaccharides is crucial for advancing our knowledge of how cell walls are assembled and for designing approaches to efficiently break down cell walls to produce renewable energy and biomaterials. Here, we investigated the effect of defects in the biosynthesis of cell wall components on the nanoscale organization of cellulose in primary cell walls through grazing incidence wide angle X-ray scattering (GIWAXS) measurements of hypocotyls of wild type Arabidopsis thaliana and of cellulose, pectin, and xyloglucan (hemicellulose) deficient mutants. GIWAXS reveals changes in lattice spacings, coherence lengths, and relative crystalline content for cellulose between wild type and mutant plants. In addition, X-ray pole figures constructed using GIWAXS and X-ray diffraction (XRD) rocking scans quantify an emerging measure of cellulose organization, the degree of preferred orientation (texture) of cellulose crystals with respect to the cell wall plane. Comparing X-ray pole figures from pectin-deficient and xyloglucan-deficient mutants to that of wild type plants reveals that cellulose texture is disrupted in pectin-deficient mutants, but not in xyloglucan mutants. Furthermore, our results indicate that a deficiency of pectin during cell wall biosynthesis alters cellulose organization in plant cell walls.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2022

Structural stability of thin overhanging walls during material extrusion additive manufacturing of thermoset-based ink

Recent developments have enabled material extrusion additive manufacturing of thermoset-based composite inks on the large scale. In addition, printing out-of-plane components is of broad interest to the polymer material extrusion community. Here, we address some of the challenges associated with both large-scale and out-of-plane thermoset material extrusion additive manufacturing by studying the height at which thin overhanging walls collapse. Walls at a range of overhang angles were printed until they collapsed. An optical camera captured the profile of each wall throughout the print, allowing the collapse height to be identified and the geometric fidelity to the programmed angle to be evaluated. Using previously measured rheological properties, predictive models were generated to approximate the collapse height and profile of the deflected walls. First, an analytical model was created to predict the height at which the walls would yield. The analytical model assumes the walls exhibit a perfectly linear profile; however, experiments proved this assumption to be false. Therefore, a finite element simulation was developed to account for the elastic deflection that occurs during printing. The finite element simulation predicts both the yield height and the deflected profile after the deposition of each layer. For the properties of the thermoset ink used here, the yield height predicted by the analytical model and finite element simulation are virtually identical. These predictions match experimental data reasonably well, but minor errors are observed. Accounting for the fully plastic moment appears to explain the small mismatch between experimental data and predictions. Additionally, the finite element simulation provides an excellent prediction of the deflected profile before the wall begins to collapse. Finally, by demonstrating that the collapse height and deflected profile of thin overhanging walls can be predicted, this work illustrates how the soft viscoelastic properties of thermoset-based composite inks limit the scale of a key feature required to print some nonplanar components. It also provides a basis to tailor in-process curing systems to suppress deflection and collapse of thin overhanging walls.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Domain-wall magnetoelectric coupling in multiferroic hexagonal YbFeO 3 films

Electrical modulation of magnetic states in single-phase multiferroic materials, using domain-wall magnetoelectric (ME) coupling, can be enhanced substantially by controlling the population density of the ferroelectric (FE) domain walls during polarization switching. In this work, we investigate the domain-wall ME coupling in multiferroic h-YbFeO 3 thin films, in which the FE domain walls induce clamped antiferromagnetic (AFM) domain walls with reduced magnetization magnitude. Simulation according to the phenomenological theory indicates that the domain-wall ME effect is dramatically enhanced when the separation between the FE domain walls shrinks below the characteristic width of the clamped AFM domain walls during the ferroelectric switching. Experimentally, we show that while the magnetization magnitude remains same for both the positive and the negative saturation polarization states, there is evidence of magnetization reduction at the coercive voltages. These results suggest that the domain-wall ME effect is viable for electrical control of magnetization.

42 ENGINEERING↗

DOE OSTI2024

An extended variational method for the resistive wall mode in toroidal plasma confinement devices

The external-kink stability of a toroidal plasma surrounded by a rigid resistive wall is investigated. The well-known analysis of Haney and Freidberg is rigorously extended to allow for a wall that is sufficiently thick that the thin-shell approximation does not necessarily hold. A generalized Haney–Freidberg formula for the growth-rate of the resistive wall mode is obtained. Thick-wall effects do not change the marginal stability point of the mode but introduce an interesting asymmetry between growing and decaying modes. Growing modes have growth-rates that exceed those predicted by the original Haney–Freidberg formula. On the other hand, decaying modes have decay-rates that are less than those predicted by the original formula. The well-known Hu–Betti formula for the rotational stabilization of the resistive wall mode is also generalized to take thick-wall effects into account. Increasing wall thickness facilitates the rotational stabilization of the mode, because it decreases the critical toroidal electromagnetic torque that the wall must exert on the plasma. On the other hand, the real frequency of the mode at the marginal stability point increases with increasing wall thickness.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Degenerate domain walls in supersymmetric theories

In supersymmetric Yang–Mills theories tension-degenerate domain walls are typical. Adding matter fields in fundamental representation, we arrive at supersymmetric quantum chromodynamics (SQCD) supporting similar walls. We demonstrate that the degenerate domain walls can belong to one of two classes: i) locally distinguishable, i.e. those which differ from each other locally (which could be detected in local measurements); and ii) those which have identical local structure and are differentiated only topologically, through a judicially chosen compactification of R 4 . Depending on the number of flavors F and the pattern of Higgsing, both classes can coexist among SQCD k walls interpolating between the vacua n and n + k . We prove that the overall multiplicity of the domain walls obtained after accounting for both classes is ν N , k walls = N ! / [ ( N − k ) ! k ! ] , as was discovered previously in limiting cases. (Here, N is the number of colors.) Thus, ν N , k walls is a peculiar index. For the locally distinguishable degenerate domain walls, we observe two-wall junctions, a phenomenon specific for supersymmetry with central extensions. This phenomenon does not exist for topological replicas.

Chen, Shi↗

DOE OSTI2023

Ferrorotational domain walls revealed by electric quadrupole second harmonic generation microscopy

Domain walls are ubiquitous in materials that undergo phase transitions driven by spontaneous symmetry breaking. Domain walls in ferroics and multiferroics have received tremendous attention recently due to their emergent properties distinct from their domain counterparts—for example, their high mobility and controllability, as well as their potential applications in nanoelectronics. However, it is extremely challenging to detect, visualize, and study the ferrorotational (FR) domain walls because the FR order, in contrast to ferromagnetism and ferroelectricity, is invariant under both the spatial-inversion and the time-reversal operations and, thus, hardly couple with conventional experimental probes. Here, a FR candidate NiTi⁢O 3 is investigated by ultrasensitive electric quadrupole (EQ) second-harmonic generation rotational anisotropy (SHG RA) to probe the point symmetries of the two degenerate FR domain states, showing their relation by the vertical mirror operations that are broken below the FR critical temperature. We then visualize the real-space FR domains by scanning EQ SHG microscopy, and further, resolve the FR domain walls by revealing a suppressed SHG intensity at the domain walls. By taking local EQ SHG RA measurements, we show the restoration of the mirror symmetry at FR domain walls and prove their unconventional nonpolar nature. In conclusion, our findings not only provide a comprehensive insight into FR domain walls, but also demonstrate a unique and powerful tool for future studies on domain walls of unconventional ferroics both of which pave the way towards future manipulations and applications of FR domain walls.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2024

Wall modes and the transition to bulk convection in rotating Rayleigh-Bénard convection

We investigate states of rapidly rotating Rayleigh-Bénard convection in a cylindrical cell over a range of Rayleigh numbers 3 × 10 5 ≤ Ra ≤ 5 × 10 9 and Ekman numbers 10 − 6 ≤ Ek ≤ 10 − 4 for Prandtl number Pr = 0.8 and aspect ratios 1 / 5 ≤ Γ ≤ 5 using direct numerical simulations. We characterize, for perfectly insulating sidewall boundary conditions, the first transition to convection via wall mode instability and the nonlinear growth and instability of the resulting wall mode states, including a secondary transition to time dependence. We show how the radial structure of the vertical velocity u z and the temperature T is captured well by the linear eigenfunctions of the wall mode instability where the radial width of u z is δ u z ∼ Ek 1 / 3 r / H whereas δ T ∼ e − k r ( k is the wave number of a laterally infinite wall mode state). The disparity in spatial scales for Ek = 10 − 6 means that the heat transport is dominated by the radial structure of u z since T varies slowly over the radial scale δ u z . We further describe how the transition to a state of bulk convection is influenced by the presence of the wall mode states. We use temporal and spatial scales as measures of the local state of convection and the Nusselt number Nu as representative of global transport. Our results elucidate the evolution of the wall state of rotating convection and confirm that wall modes are strongly linked with the boundary zonal flow being the robust remnant of nonlinear wall mode states. We also show how the heat transport ( Nu ) contributions of wall modes and bulk modes are related and discuss approaches to disentangling their relative contributions. Published by the American Physical Society 2024

58 GEOSCIENCES↗

DOE OSTI2023

Burst Pressure Solutions of Thin and Thick-Walled Cylindrical Vessels

Pressure vessels (PVs) are widely used in the energy industry. Accurate burst pressure is critical to structural design and safe operation for both thin and thick-walled PVs. The traditional strength theories utilized a single-parameter material property, such as the yield stress or the ultimate tensile stress (UTS) to develop failure models for determining the yield or ultimate pressure carrying capacity in the PV design. The UTS-based Barlow formula is a typical burst pressure model developed from the Tresca strength theory that provides the basis for developing regulation rules and failure models for different industry design codes, such as ASME BPVC, ASME B31.3, and ASME B31G, among others. In order to reduce the conservatism of the Tresca strength model, ASME BPVC recently adapted failure models developed from the von Mises strength theory for the PV design and analysis. It has been commonly accepted that the burst pressure of pipelines depends on the UTS and strain hardening exponent, n, of the pipeline steel. An average shear stress yield theory was thus developed, and the Zhu-Leis solution of burst pressure was obtained as a function of UTS and n for thin-walled line pipes. Experiments showed that the Zhu-Leis solution provides an accurate, reliable prediction of burst pressure for defect-free thin-walled pipes. In order to extend the Zhu–Leis solution to thick-walled cylindrical PVs, this paper defined three new flow stresses, modified the traditional strength theories, and obtained three new burst pressure solutions that are valid for both thin and thick-walled cylindrical vessels. The proposed flow stresses are able to describe the tensile strength and the plastic flow response of PVs for a strain hardening steel. The associated strength theories were then developed in terms of the Tresca, von Mises, and Zhu-Leis yield criteria. From these new strength theories, three burst pressure solutions were obtained for thick-walled cylinders, where the von Mises solution is an upper bound prediction, the Tresca solution is a lower bound prediction, and the Zhu-Leis solution is an intermediate prediction of burst pressure for thick-walled cylinders. Lastly, the proposed burst pressure solutions were evaluated and validated by two large datasets of full-scale burst tests for thick-walled tubes and for thin-walled pipes.

42 ENGINEERING↗

DOE OSTI2024

Assessment of Machine Learning Wall Modeling Approaches for Large Eddy Simulation of Gas Turbine Film Cooling Flows: An a Priori Study

Here, in this work, a priori analysis of machine learning (ML) strategies is carried out with the goal of data-driven wall modeling for large eddy simulation (LES) of gas turbine film cooling flows. High-fidelity flow datasets are extracted from wall-resolved LES (WRLES) of flow over a flat plate interacting with the coolant flow supplied by a single row of 7-7-7 shaped cooling holes inclined at 30 degrees with the flat plate at different blowing ratios (BR). The WRLES are performed using the high-order Nek5000 spectral element computational fluid dynamics (CFD) solver. Light gradient boosting machine (LightGBM) is employed as the ML algorithm for the data-driven wall model. Parametric tests are conducted to systematically assess the influence of a wide range of input flow features (velocity components, velocity gradients, pressure gradients, and fluid properties) on the accuracy of ML wall model with respect to prediction of wall shear stress. In addition, the use of spatial stencil and time delay is also explored within the ML wall modeling framework. It is shown that features associated with gradients of the streamwise and spanwise velocity components have a major impact on the prediction fidelity of wall model, while the effect of gradients of wall-normal velocity component is found to be negligible. Moreover, adding flow feature information from an x-y-z spatial stencil significantly improves the ML model accuracy and generalizability compared to just using local flow features from the matching location. Overall, highest prediction accuracy is achieved when both spatial stencil and time delay features are incorporated within the data-driven wall modeling paradigm.

33 ADVANCED PROPULSION SYSTEMS↗

DOE OSTI2023

Performance of Windows in Walls With Continuous Insulation

Window openings in walls are a significant contributor to poor thermal performance because of thermal bridging through the framing members (e.g., studs, joists, plates, bracing) and because windows lack the thermal properties of insulation. Window installation guidance for walls with continuous insulation (CI) is critical for continued market growth of this energy efficiency technology. This research project offers window manufacturers a starting point and a potential path toward developing installation instructions for windows over CI. The objectives of the research include evaluating the common method for installing windows in walls with CI, as well as establishing acceptance criteria for evaluating the performance of windows installed in walls with and without CI. The research measures: 1. The performance characteristics (e.g., water management, structural integrity) of windows in walls without CI. 2. The performance of different thicknesses and types of CI used in walls. 3. The performance of different types of window assemblies (e.g., double-hung windows, mulled double-hung windows, mulled casement windows, and slider windows) installed over CI. 4. The performance of window flange types (e.g., rigid mounting and less robust flanges) installed over CI. 5. Installing windows over CI using baseline installation instructions versus window manufacturer installation instructions. The project’s sequential testing protocol consists of the following: • A water penetration resistance testing adapted from two ASTM standards: E331 (uniform static air pressure in four steps) and E547 (cyclic static air pressure) • A temperature cycling adapted from ASTM E2264 Method B (convective hot air) • A service condition wind loading test adapted from ASTM E330 • A six-month vertical displacement observation phase prior to the structural performance testing • A final water penetration resistance test after vertical displacement observation • A structural performance test adapted from ASTM E330. Key research findings include: • The criterion for passing a water penetration resistance test is that there is no water overflowing at the interior face of the studs. If there is any bubbling or slight pooling of water at the sill, then it must recede after the pressure is removed. Excessive leakage and/or water leaking to the interior face of the framing around the window constitutes a failure. • All single double-hung windows installed directly to lumber or over oriented strand board passed all test protocols. • For most wall specimens, the test results showed that the use of foam sheathing did not affect the performance of the window for water leakage. • All wall specimens underwent temperature cycling. The results indicated that temperature cycling had little to no effect on windows installed over foam sheathing. • For wall specimens that underwent six-month vertical displacement monitoring, the results showed that windows installed over foam sheathing do not sag over time. • The single-hung and double-hung windows installed using window manufacturer installation instructions passed the structural performance test, compared to failures observed in windows that were installed using generic installation instructions. The generic and manufacturer installation methods differed on the following construction details: type of fasteners, fastening patterns on the flanges, and window shimming details. • Additional testing is required to determine methods to improve structural pressure performance of slider windows. Potential solutions that would require additional testing may include fastener spacing, different types of fasteners, masonry window clips, construction adhesive, foam sealant, stronger window flange material, and/or straps.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

NASA NTRS1983

Effect of boundary layers on solid walls in three-dimensional subsonic wind tunnels

A linear method is developed which accounts for the effects of boundary layers on solid walls in subsonic three-dimensional wind tunnels. The streamwise gradient of the displacement thickness for a solid-wall boundary layer is expressed in terms of the von Karman momentum integral. The growth of the boundary layer due to the wall shearing stress is small compared to the variation caused by the model-induced pressure gradient. The viscous boundary condition can be expressed in terms of the edge velocity gradient and the gradient of the inviscid velocity potential function at the wall. Utilizing this analysis on the solid walls of several three-dimensional wind tunnel configurations shows that the most pronounced wall boundary-layer effect is on solid blockage for completely closed wind tunnels. For solid-wall tunnel configurations, the streamline curvature interference factor is reduced by a significant amount, while the lift interference factor at the model station does not depend on the boundary-layer parameter. For combination wall configurations, the slot effect of the horizontal walls dominates the viscous effect of the solid sidewalls.

Adcock, J. B.↗

NASA NTRS1984

Progress in wind tunnel wall interference assessment/correction procedures at the NAE

Wall corrections as a function of wall porosity in the transonic wall interference problem was assessed. Effective porosities primarily for the two dimensional case were established as follows: (1) comparison of experimental data for two geometrically similar models of different chord/height ratio, an overall value of wall porosity could be deduced; (2) theoretical development which allows for unequal porosity for the floor and ceiling and wall boundary pressure measurements, porosities for floor and ceiling could be deduced; (3) a scheme was developed which allowed unequal porosity of floor and ceiling and streamwise varying porosity. The boundary layer development along the perforated floor and ceiling under the influence of the model pressure field, variations in boundary layer thickness underlining the difficulties in deducing meaningful values of wall porosity were determined. Wall boundary pressure measurement, in combination with singularity modelling of the airfoil, was sufficient to yield required information on the wall interference flow without having to establish some value for wall porosity. The singularity modelling of the airfoil initially covered only lift and volume but was extended to include drag and pitching moment, and second order volume term. It is shown by asymptotic transonic small disturbance analysis, that the derived corrections to angle of attack and free stream Mach number are correct to the first order.

Ohman, L. H.↗

NASA NTRS1990

Near-wall modelling of compressible turbulent flows

Work was carried out to formulate near-wall models for the equations governing the transport of the temperature-variance and its dissipation rate. With these equations properly modeled, a foundation is laid for their extension together with the heat-flux equations to compressible flows. This extension is carried out in a manner similar to that used to extend the incompressible near-wall Reynolds-stress models to compressible flows. The methodology used to accomplish the extension of the near-wall Reynolds-stress models is examined and the actual extension of the models for the Reynolds-stress equations and the near-wall dissipation-rate equation to compressible flows is given. Then the formulation of the near-wall models for the equations governing the transport of the temperature variance and its dissipation rate is discussed. Finally, a sample calculation of a flat plate compressible turbulent boundary-layer flow with adiabatic wall boundary condition and a free-stream Mach number of 2.5 using a two-equation near-wall closure is presented. The results show that the near-wall two-equation closure formulated for compressible flows is quite valid and the calculated properties are in good agreement with measurements. Furthermore, the near-wall behavior of the turbulence statistics and structure parameters is consistent with that found in incompressible flows.

So, Ronald M. C.↗

NASA NTRS1991

The effect of compliant walls on secondary instabilities in boundary layer transition

The effect of compliant walls on the stage of transition where three-dimensional secondary instabilities (SIs) are excited is studied. A theory developed by Herbert (1983) to represent SIs for two-dimensional primary instabilities is extended to allow for oblique waves. The effects of the variations in primary amplitude, spanwise, wavenumber, and Reynolds number on the SIs are examined. As in the rigid-wall case, the subharmonic mode of SI dominates for low-amplitude disturbances over compliant walls. Both isotropic and nonisotropic compliant walls lead to reduced SI growth rates as compared to the rigid-wall results. Calculations show that, for high frequencies, the nonisotropic wall suppresses the amplification of the SIs, while for the isotropic wall SIs grow with an explosive rate similar to the rigid-wall results. For lower frequencies, both types of compliant wall suppress the amplification of SIs.

Joslin, Ronald D.↗