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The Plane Wave Approximation (PWA) is widely used in finite element analysis to implement the loading generated by an underwater shock wave. The method required to implement the PWA in NASTRAN is presented along with example problems. A theoretical background is provided and the limitations of the PWA are discussed.
Probabilistic CFD design is needed because we are asked to do more with less. To cost effectively accomplish the design task, we need to formally quantify the effect of uncertainties (variables) in the design. Probabilistic design is one effective method to formally quantify the effect of uncertainties. Our objective is to establish a revolutionary new early design process, by developing non-deterministic physics-based probabilistic design tools, which will include all the life cycle processes. Breakthroughs will be sought in speed, accuracy, intelligence, and usability of the system. This paper is concerned with the usefulness of parametric optimization method coupled with a Navier-Stokes analysis code for the aero-thermodynamic design of turbomachinery combustor liner. The interconnection between the CFD code and NESSUS codes facilitated the coupling between the thermal profiles and structural design. We have developed new concepts for reducing the computational cost of unsteady, three-dimensional, compressible aerodynamic analyses for multistage turbomachinery flows. The flow was modeled by the three-dimensional Favre-Reynolds-averaged Navier-Stokes equations using the k-epsilon turbulence closure, which was integrated using an implicit third-order upwind solver. The methodology developed in this paper is expected to lead to the design optimization of turbomachinery blades.
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The fluid-thermal-structural interactions of a compliant panel embedded in a compression ramp are explored experimentally at Mach 6. The panel structural response is investigated for turbulent and transitional shock-wave/boundary-layer interactions at five distinct interaction strengths and up to four different pressure differentials. Upstream of the compression corner, fast-response piezoresistive pressure transducers show the feedback of the panel vibrations and static deflection on the upstream pressure fluctuations. The magnitude of the pressure fluctuation rms shows a reduction in the upstream disturbances when a pressure differential is applied across the compliant panel. Photogrammetry and IR thermography are used simultaneously to measure the panel deformations and surface temperature. Panel deformation, frequency shifting, and frequency bifurcation are consistent with post-thermal-buckling behavior.
An experimental study is conducted of the fluid-thermal-structural interaction of a clamped compliant panel exposed to a three dimensional shock-wave/boundary-layer interaction (SWBLI) induced by a Mach-6 compression ramp with a spanwise nonuniform incoming boundary layer. The nonuniform boundary layer was produced by placing trips on one side of the upstream flat plate, resulting in largely turbulent flow on the tripped side and transitional flow on the untripped side. Measurements of the flowfield confirmed that the tripped boundary layer contained elevated levels of unsteadiness, and the SWBLI was observed to vary from attached to fully separated as the ramp angle was increased from 10◦ to 38◦; the separation region on the tripped side of the panel was noticeably smaller, showing the elevated turbulence levels of the tripped-side flow to remain relatively localized rather than diffusing across the whole model. Full-field, time-resolved panel deformations were measured using high-speed photogrammetry and the vibrational response at each compression angle was characterized. Although the measured modes conformed largely to those from classical clamped-plate theory, some skewing of the mode shapes was observed. IR thermography highlighted regions of the compliant region where elevated temperatures were likely to promote thermal softening effects to the transient panel response. The quasi-static deformation and stress field was used to characterize the internal stress factor of each mode and showed a meaningful relationship between transient panel response and stress contained within each mode: modes with antinodes lying in high-stress areas of the plate tended to exhibit increases in vibrational frequency and decreases in vibrational power, whereas the opposite was true for modes with antinodes in low-stress areas.
Aerothermodynamics and hypersonic flows involve complex multi-disciplinary physics, including finite-rate gas-phase kinetics, finite-rate internal energy relaxation, gas-surface interactions with finite-rate oxidation and sublimation, transition to turbulence, large-scale unsteadiness, shock-boundary layer interactions, fluid-structure interactions, and thermal protection system ablation and thermal response. Many of the flows have a large range of length and time scales, requiring large computational grids, implicit time integration, and large solution run times. The University of Minnesota NASA US3D code was designed for the simulation of these complex, highly-coupled flows. It has many of the features of the well-established DPLR code, but uses unstructured grids and has many advanced numerical capabilities and physical models for multi-physics problems. The main capabilities of the code are described, the physical modeling approaches are discussed, the different types of numerical flux functions and time integration approaches are outlined, and the parallelization strategy is overviewed. Comparisons between US3D and the NASA DPLR code are presented, and several advanced simulations are presented to illustrate some of novel features of the code.
A two-dimensional finite element approach is presented for the integrated fluid-thermal-structural analysis of aerodynamically heated leading edges. The approach is combined with an adaptive unstructured remeshing technique to solve the Navier-Stokes equations for high speed compressible flow, the energy equation for the structure thermal response, and the quasi-static equilibrium equations for the structural response. Coupling and interaction between the three disciplines are demonstrated using two applications for high speed flow over a cylinder and a simulated engine leading edge verification test.
Shock-wave boundary-layer interactions (SWBLI) pose unique challenges for the slender airframes and sharp control surfaces characteristic of high-speed airbreathing aircraft. Spikes in pressure and thermal loading have been shown to occur in SWBLI regions; thus, predicting their location and behavior proves critical for assuring aircraft structural integrity and fatigue resilience. SWBLIs frequently lead to severe turbulent boundary-layer separation and corresponding unsteady motions characterized by a wide range of frequencies. Low-frequency motion has been shown to couple with the structure of a compliant panel, and turbulent boundary layers thus present a particular danger for thin control surfaces. Previous studies have shown that the thermal loading on a compliant panel in a ramp-induced SWBLI may have a signi cant impact on the panel vibrations. A multitude of studies has investigated the heating on rigid structures, but a charactrization of the heating effects on compliant structures is necessary to fully understand the fluid-thermal-structural interactions (FTSI) occurring in ramp-induced SWBLIs. This studuses infrared thermography and high-frequency Kulite pressure transducers to examine the heating loads on rigid and compliant ramps at various angles and flow conditions at Mach 6.
Shock-wave boundary-layer interactions (SWBLI) pose unique challenges for the slender airframes and sharp control surfaces characteristic of high-speed airbreathing aircraft. Spikes in pressure and thermal loading have been shown to occur in SWBLI regions; thus, predicting their location and behavior proves critical for assuring aircraft structural integrity and fatigue resilience. SWBLIs frequently lead to severe turbulent boundary-layer separation and corresponding unsteady motions characterized by a wide range of frequencies. Low-frequency motion has been shown to couple with the structure of a compliant panel, and turbulent boundary layers thus present a particular danger for thin control surfaces. Previous studies have shown that the thermal loading on a compliant panel in a ramp-induced SWBLI may have a signi cant impact on the panel vibrations. A multitude of studies has investigated the heating on rigid structures, but a charactrization of the heating effects on compliant structures is necessary to fully understand the fluid-thermal-structural interactions (FTSI) occurring in ramp-induced SWBLIs. This studuses infrared thermography and high-frequency Kulite pressure transducers to examine the heating loads on rigid and compliant ramps at various angles and flow conditions at Mach 6.
A fluid-structure interaction code, ENSAERO, has been used to compute the aerodynamic loads on a swept-tapered wing. The code has the capability of using Euler or Navier-Stokes equations. Both options have been used and compared in the present paper. In the calculation of the steady-state solution, we are interested in knowing how the flexibility of the wing influences the lift coefficients. If the results of a flexible wing are not affected by the flexibility of the wing significantly, one could consider the wing to be rigid and reduce the problem from fluid-structure interaction to a fluid problem.
Here, this paper presents a novel sharp front-tracking method designed to address limitations in classical front-tracking approaches, specifically their reliance on smooth interpolation kernels and extended stencils for coupling the front and fluid mesh. In contrast, the proposed method employs exclusively sharp, localized interpolation and spreading kernels, restricting the coupling to the interfacial fluid cells–those containing the interface/front. This localized coupling is achieved by integrating a divergence-preserving velocity interpolation method with a piecewise parabolic interface calculation (PPIC) and a polyhedron intersection algorithm to compute the indicator function and local interface curvature. Surface tension is computed using the Continuum Surface Force (CSF) method, maintaining consistency with the sharp representation. Additionally, we propose an efficient local roughness smoothing implementation to account for surface mesh undulations, which is easily applicable to any triangulated surface mesh. Building on our previous work, the primary innovation of this study lies in the localization of the coupling for both the indicator function and surface tension calculations. By reducing the interface thickness on the fluid mesh to a single cell, as opposed to the 4–5 cell spans typical in classical methods, the proposed sharp front-tracking method achieves a highly localized and accurate representation of the interface. This sharper representation mitigates parasitic currents and improves force balancing, making it particularly suitable for scenarios where the interface plays a critical role, such as microfluidics, fluid-fluid interactions, and fluid-structure interactions. The proposed method is comprehensively validated and tested on canonical interfacial flow problems, including stationary and translating Laplace equilibria, oscillating droplets, and rising bubbles. The presented results demonstrate that the sharp front-tracking method significantly outperforms the classical approach in terms of accuracy, stability, and computational efficiency. Notably, parasitic currents are reduced by approximately two orders of magnitude and stable results are obtained for parameter ranges where classical front tracking fails to converge.