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Modeling the two-way coupling of stress, diffusion, and oxidation in heterogeneous CMC microstructures
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Effect of driven-wall motion on a turbulent boundary layer
An acoustically driven wall model with amplitudes greater than 0.01 cm was used to study the effect of unsteady wall boundary conditions on the structure of a zero-pressure-gradient turbulent boundary layer. Hot-wire measurements showed large variations in fluctuation quantities (including Reynolds stress) along each model wave. These longitudinal variations decreased rapidly with increasing distance from the driven wall, but the average level of these fluctuations decreased only slightly even outside the boundary layer. When the acoustical fluctuations were subtracted, the remaining fluctuations were essentially the same as for the undriven model. It is concluded that there is no significant interaction between the acoustic and turbulent fluctuations.
Reynolds stress closure in jet flows using wave models
Numerical methods were developed that will form the computational part of the turbulence closure scheme. A wave model was developed for the two-dimensional shear layer. This configuration is being used as a test case for the closure schemes. Various numerical schemes were examined to give efficient solutions of the Rayleigh equation for this geometry. These include both spectral and finite difference methods. Secondly, numerical methods are under development to solve the non-separable Rayleigh equation. This solution is required for the closure scheme in more complex geometries. A model problem was used to assist in the algorithm development. Two-dimensional spectral methods and a hybrid spectral/finite difference technique were developed. An analytic solution of the Rayleigh equation for a basic elliptic flow was obtained. This will be used to verify the stability codes developed for arbitrary geometries. Other numerical methods for solving the Rayleigh equation based on the boundary element technique were also examined. These solutions are forming the basis of a model for the shock structure in jets of arbitrary geometry.
Reynolds stress closure in jet flows using wave models
A wave model was developed for the two dimensional shear layer. This configuration is being used as a test case for the closure schemes. Numerical methods are under development to solve the nonseparable Rayleigh equation. A model problem is being used to assist in the algorithm development. An analytic solution of the Rayleigh equation for a basic elliptic flow was obtained. This will be used to verify the stability codes developed for arbitrary geometries. Other numerical methods for solving the Rayleigh equation based on the boundary element technique are being examined.
Reynold stress closure in jet flows using wave models
Research program efforts have continued to concentrate on the development of the numerical methods that will form the computational part of the turbulence closure scheme. Studies have continued on the wave model for the two dimensional shear layer. This configuration is being used as a test case for the closure schemes. Several numerical schemes for the solution of the non-separable Rayleigh equation were developed. This solution is required for the closure scheme in more complex geometries. The most efficient method found is a Hybrid scheme that combines both pseudospectral and finite difference techniques. In addition, conformal transformation techniques were developed to transform the arbitrary geometry of the jet to a simple computational domain. The study of the shock structure in arbitrary geometry jets and multiple jets. These developments are described briefly.
Reynolds stress closure in jet flows using wave models
Ways of implementing the turbulence closure scheme based on modeling the large scale coherent structures as instability waves were sought. The computational tools necessary to apply this scheme to jets of arbitrary geometry were developed. The model, developed earlier, was extended to the shock structure of supersonic jets of arbitrary geometry and multiple jets. It was found that though the qualititate features of the unsteady flow field could be predicted there were always difficulties with some of the quantitative features. This led to the new formation of the closure scheme. The schemes for computations tools which were developed are efficient and represent the application of the very powerful mathematical tools to the problems of practical significance.
Space Shuttle Main Engine structural analysis and data reduction/evaluation. Volume 3A: High pressure oxidizer turbo-pump preburner pump housing stress analysis report
The model generation and structural analysis performed for the High Pressure Oxidizer Turbopump (HPOTP) preburner pump volute housing located on the main pump end of the HPOTP in the space shuttle main engine are summarized. An ANSYS finite element model of the volute housing was built and executed. A static structural analysis was performed on the Engineering Analysis and Data System (EADS) Cray-XMP supercomputer
Reynolds stress closure in jet flows using wave models
A collection of papers is presented. The outline of this report is as follows. Chapter three contains a description of a weakly nonlinear turbulence model that was developed. An essential part of the application of such a closure scheme to general geometry jets is the solution of the local hydrodynamic stability equation for a given jet cross-section. Chapter four describes the conformal mapping schemes used to map such geometries onto a simple computational domain. Chapter five describes a solution of a stability problem for circular, elliptic, and rectangular geometries. In chapter six linear models for the shock shell structure in non-circular jets is given. The appendices contain reprints of papers also published during this study including the following topics: (1) instability of elliptic jets; (2) a technique for predicting the shock cell structure in non-circular jets using a vortex sheet model; and (3) the resonant interaction between twin supersonic jets.
Supersonic flow calculation using a Reynolds-stress and an eddy thermal diffusivity turbulence model
A second-order model for the velocity field and a two-equation model for the temperature field are used to calculate supersonic boundary layers assuming negligible real gas effects. The modeled equations are formulated on the basis of an incompressible assumption and then extended to supersonic flows by invoking Morkovin's hypothesis, which proposes that compressibility effects are completely accounted for by mean density variations alone. In order to calculate the near-wall flow accurately, correction functions are proposed to render the modeled equations asymptotically consistent with the behavior of the exact equations near a wall and, at the same time, display the proper dependence on the molecular Prandtl number. Thus formulated, the near-wall second order turbulence model for heat transfer is applicable to supersonic flows with different Prandtl numbers. The model is validated against flows with different Prandtl numbers and supersonic flows with free-stream Mach numbers as high as 10 and wall temperature ratios as low as 0.3. Among the flow cases considered, the momentum thickness Reynolds number varies from approximately 4,000 to approximately 21,000. Good correlation with measurements of mean velocity, temperature, and its variance is obtained. Discernible improvements in the law-of-the-wall are observed, especially in the range where the big-law applies.
Modeling the two-way coupling of stress, diffusion, and oxidation in heterogeneous CMC microstructures
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Constitutive response of Rene 80 under thermal mechanical loads
The applicability of a classical constitutive model for stress-strain analysis of a nickel base superalloy, Rene' 80, in the gas turbine thermomechanical fatigue (TMF) environment is examined. A variety of tests were conducted to generate basic material data and to investigate the material response under cyclic thermomechanical loading. Isothermal stress-strain data were acquired at a variety of strain rates over the TMF temperature range. Creep curves were examined at 2 temperature ranges, 871 to 982 C and 760 to 871 C. The results provide optimism on the ability of the classical constitutive model for high temperature applications.
Comparison between observed and calculated distributions of trace species in the middle atmosphere
The purpose is to identify major discrepancies between empirical models and theoretical models and to stress the need for additional observations in the atmosphere and for further laboratory work, since these differences suggest either problems associated with observation techniques or errors in chemical kinetics data (or the existence of unknown processes which appear to play an important role). The model used for this investigation extends from the earth's surface to the lower thermosphere. It includes the important chemical and photochemical processes related to the oxygen, hydrogen, carbon, nitrogen and chlorine families. The chemical code is coupled with a radiative scheme which provides the heating rate due to absorption of solar radiation by ozone and the cooling rate due to the emission and absorption of terrestrial radiation by CO2, H2O and O3. The vertical transport of the species is expressed by an eddy diffusion parameterization.
Deformation behavior of CP-titanium under strain path changes: Experiment and crystal plasticity modeling
The deformation behavior of commercially pure rolled titanium subjected to strain path changes is studied using experiments and a crystal plasticity model. Four different loading combinations are performed at room temperature to study the activation of slip, twinning, de-twinning and double-twinning in hexagonal closed packed titanium. The strain paths considered are: rolling direction compression (RDC) followed by normal direction compression (NDC), RDC followed by transverse direction compression (TDC), NDC followed by RDC, and NDC followed by TDC. An EBSD-based analysis of the distribution of boundary misorientation angles before and after reload was developed to analyze the evolution of {$10\bar{1}2$} tensile and {$11\bar{2}2$} compression twins. This analysis supports the model results concerning the treatment of twin reorientation. A de-twinning and double-twinning model accounting for back stress effects, an important feature of strain path changes, is implemented within the framework of the visco-plastic self-consistent (VPSC) model along with a dislocation density (DD) based hardening scheme. In the model, plasticity is accommodated by prismatic $\langle$a$\rangle$, basal $\langle$a$\rangle$ and pyramidal $\langle$c+a$\rangle$ slip modes, and {$10\bar{1}2$} tensile and {$11\bar{2}2$} compression twinning modes. The VPSC model predicts the evolution of twinning, de-twinning and double-twinning processes for both tensile and compression twinning modes under strain path change. The model predicts macroscopic stress-strain response, texture evolution, and twin volume fraction that are in agreement with experimental observations. The evolution of texture is investigated in detail by separately analyzing the twinned domains, rather than the evolution of the global texture.
Mathematical Model of ATM Activation and Chromatin Relaxation by Ionizing Radiation
We propose a comprehensive mathematical model to study the dynamics of ionizing radiation induced Ataxia-telangiectasia mutated (ATM) activation that consists of ATM activation through dual mechanisms: the initiative activation pathway triggered by the DNA damage-induced local chromatin relaxation and the primary activation pathway consisting of a self-activation loop by interplay with chromatin relaxation. The model is expressed as a series of biochemical reactions, governed by a system of differential equations and analyzed by dynamical systems techniques. Radiation induced double strand breaks (DSBs) cause rapid local chromatin relaxation, which is independent of ATM but initiates ATM activation at damage sites. Key to the model description is how chromatin relaxation follows when active ATM phosphorylates KAP-1, which subsequently spreads throughout the chromatin and induces global chromatin relaxation. Additionally, the model describes how oxidative stress activation of ATM triggers a self-activation loop in which PP2A and ATF2 are released so that ATM can undergo autophosphorylation and acetylation for full activation in relaxed chromatin. In contrast, oxidative stress alone can partially activate ATM because phosphorylated ATM remains as a dimer. The model leads to predictions on ATM mediated responses to DSBs, oxidative stress, or both that can be tested by experiments.
Bayes Analysis and Reliability Implications of Stress-Rupture Testing a Kevlar/Epoxy COPV Using Temperature and Pressure Acceleration
Composite Overwrapped Pressure Vessels (COPVs) that have survived a long service time under pressure generally must be recertified before service is extended. Flight certification is dependent on the reliability analysis to quantify the risk of stress rupture failure in existing flight vessels. Full certification of this reliability model would require a statistically significant number of lifetime tests to be performed and is impractical given the cost and limited flight hardware for certification testing purposes. One approach to confirm the reliability model is to perform a stress rupture test on a flight COPV. Currently, testing of such a Kevlar49 (Dupont)/epoxy COPV is nearing completion. The present paper focuses on a Bayesian statistical approach to analyze the possible failure time results of this test and to assess the implications in choosing between possible model parameter values that in the past have had significant uncertainty. The key uncertain parameters in this case are the actual fiber stress ratio at operating pressure, and the Weibull shape parameter for lifetime; the former has been uncertain due to ambiguities in interpreting the original and a duplicate burst test. The latter has been uncertain due to major differences between COPVs in the database and the actual COPVs in service. Any information obtained that clarifies and eliminates uncertainty in these parameters will have a major effect on the predicted reliability of the service COPVs going forward. The key result is that the longer the vessel survives, the more likely the more optimistic stress ratio model is correct. At the time of writing, the resulting effect on predicted future reliability is dramatic, increasing it by about one "nine," that is, reducing the predicted probability of failure by an order of magnitude. However, testing one vessel does not change the uncertainty on the Weibull shape parameter for lifetime since testing several vessels would be necessary.
Features of a reattaching turbulent shear layer subject to an adverse pressure gradient
Experimental data have been obtained in an incompressible turbulent flow over a rearward-facing step with superimposed adverse pressure gradient. Mean velocities, Reynolds stresses and triple-products measured by a laser Doppler velocimeter are presented for two cases of adverse pressure gradient. Mixing lengths, eddy viscosities, production, convection, turbulent diffusion, and dissipation terms are extracted from the data. These data are compared with various mixing length and eddy-viscosity turbulence models. Numerical calculations incorporating the k-epsilon and the algebraic-stress turbulence models are compared with the data. When determining quantities of engineering interest, the modified algebraic-stress model (ASM) is a significant improvement over the unmodified ASM and the unmodified k-epsilon model
Simple and Sophisticated Models of Taylor's Cylinder Impact
We present a study based on the simplest possible models for Taylor’s cylinder impact problem, in addition to examination of using convolutional neural networks (CNNs) to map cylinder profiles to strength calibrations. We find that the approximate treatments of Taylor and Hawkyard compare well with hydrodynamic simulations using an equivalent assumption of constant flow stress. The CNN models prove to be well suited to successfully infer parameterizations of the Preston-Tonks-Wallace model of plastic deformation based on the deformed profile of an impacted cylinder