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The topics of discussion addressed were material behavior, design analysis, deformation kinetics, metallurgical characterization, mechanical subelement models, stress analysis, fracture mechanics, viscoplasticity, and thermal loading.
Families of lineaments in the Gilomesh and Ninki basins of Ganymede imply post impact tectonic activity. The grooves, previously considered the youngest tectonic features, are estimated to have formed between 3.8 and 3.1 Gyr ago. One rayed crater however, is probably less than 1 Gyr old, implying tectonic activity on Ganymede has extended nearly to the present. Like the grooves, the lineaments appear to be extensional. The parallel trends and nearly contiguous associations of the lineaments with the grooves imply that both are products of the same stress systems. The young inferred age of the lineaments implies that they (and presumably also the grooves) are not associated with stresses in the cooling of fresh deposits of bright terrain, but are probably associated with underlying convective stress patterns, the long implied duration of an extensional stress regime in Ganymede's lithosphere is consistent with the stress models of derived assuming a differentiated interior.
Morphological analyses of landforms on Rhea are used to define three physiographic provinces: cratered terrain 1 undifferentiated; cratered terrain 1 lineated; and cratered terrain 2. The important statigraphic relationships between the different provinces are examined with respect to major impact basins and tectonic features. It is shown that the formation of multiringed basins may have caused, or at least controlled the locations of major resurfacing and mantling events. The diameters of the central peaks relative to the impact crater diameters are found to be significantly larger than those within the craters of the moon or Mercury. Both cratered and noncrater lineaments have regional orientations which do not fit current global or regional stress models. On the basis of the morphological analysis, a chronological order is established for the origin of the three provinces: the cratered terrain 1 province was formed first; and cratered terrain 1 lineated and cratered terrain 2 were formed second, and last, respectively. It is shown that the chronological order is generally consistent with current theoretical models of the evolution of Rhea.
The mechanics of continua, which is based on the general stress model of Cauchy, up to the present has almost exclusively been applied to liquid and solid elastic bodies. Saint-Venant has developed a theory for the plastic or remaining form changes of solids, but it does not give the required number of equations for determining motion. A complete set of equations of motion for plastic deformable bodies is derived. This is done within the framework of Cauch mechanics. And it is supported by certain experimental facts which characterize the range of applications.
Analytical and experimental work were combined to develop a stress model to determine the temperature profile which will yield a satisfactory web. A thermal model of the web will be used to determine the thermal configuration which will yield the desired temperature profile. Thermal analysis of growth interface and the susceptor melt will be developed to determine a thermal configuration which will improve stability of growth process. The thermal configurations will be designed, fabricated, and tested and the results fed back into the models.
The specific activities summarized include: verification experiments (base program); thermomechanical cycling model; multiaxial stress state model; cumulative loading model; screening of potential environmental and protective coating models; and environmental attack model.
A data base program to generate statistically significant material-property data for carbon-carbon and carbon phenolic materials to be used in designs of Space Shuttle is described. The program, which will provide data necessary for thermal and stress modeling of Shuttle nozzle and exit cone structures, includes evaluation of tension, compression, shear strength, shear modulus, thermal expansion, thermal conductivity, permeability, and emittance for both materials; the testing of carbon phenolic materials also includes CTE, off-gassing, pyrolysis, and RTG. Materials to be tested will be excised from Space Shuttle inlet, throat, and exit cone billets and modified involute carbon-carbon exit cones; coprocessed blocks, panels, and cylinders will also be tested.
A theoretical expression for the slow part (the nonlinear fluctuation part) of the pressure-strain rate is compared with simulations of anisotropic homogeneous flows. The objective is to determine the quantitative accuracy of the theory and to test its prediction that the generalized Rotta coefficient, a non-dimensionalized ratio of slow term to the Reynolds stress anisotropy, varies with direction and can be negative. Comparisons are made between theoretical and simulation values of the slow term itself and of the generalized Rotta coefficients. The implications of the comparison for two-point closure theories and for Reynolds stress modeling are pointed out.
The structure of the subgrid scale fields in plane channel flow has been studied at various stages of the transition process to turbulence. The residual stress and subgrid scale dissipation calculated using velocity fields generated by direct numerical simulations of the Navier-Stokes equations are significantly different from their counterparts in turbulent flows. The subgrid scale dissipation changes sign over extended areas of the channel, indicating energy flow from the small scales to the large scales. This reversed energy cascade becomes less pronounced at the later stages of transition. Standard residual stress models of the Smagorinsky type are excessively dissipative. Rescaling the model constant improves the prediction of the total (integrated) subgrid scale dissipation, but not that of the local one. Despite the somewhat excessive dissipation of the rescaled Smagorinsky model, the results of a large eddy simulation of transition on a flat-plate boundary layer compare quite well with those of a direct simulation, and require only a small fraction of the computational effort. The inclusion of non-dissipative models, which could lead to further improvements, is proposed.
A method is developed for predicting three-dimensional turbulent boundary layers occurring in internal flows, including rotor blades of turbomachinery. These boundary layers are complex, turbulent, and are subject to Coriolis and centrifugal forces. The algebraic Reynolds stress model (ARSM) developed in this paper satisfies the realizability conditions exactly and captures the changes in turbulenet structure arising from curvature and rotation. The prediction of pressure driven secondary flow agrees well with the data and all the three turbulent models (k-e, algebraic eddy viscosity, and ARSM) show the same level of agreement. The prediction of boundary layer on rotor blades shows much better agreement with the ARSM. It is essential to employ the higher order models to capture the effects of rotation and curvature and three-dimensional boundary layers in turbomachinery.
The structure of the subgrid scale fields in plane channel flow has been studied at various stages of the transition process to turbulence. The residual stress and subgrid scale dissipation calculated using velocity fields generated by direct numerical simulations of the Navier-Stokes equations are significantly different from their counterparts in turbulent flows. The subgrid scale dissipation changes sign over extended areas of the channel, indicating energy flow from the small scales to the large scales. This reversed energy cascade becomes less pronounced at the later stages of transition. Standard residual stress models of the Smagorinsky type are excessively dissipative. Rescaling the model constant improves the prediction of the total (integrated) subgrid scale dissipation, but not that of the local one. Despite the somewhat excessive dissipation of the rescaled Smagorinsky model, the results of a large eddy simulation of transition on a flat-plate boundary layer compare quite well with those of a direct simulation, and require only a small fraction of the computational effort. The inclusion of non-dissipative models, which could lead to further improvements, is proposed.
Large-eddy simulations of transition on a flat-plate boundary layer have been carried out. Standard residual stress models of the Smagorinsky type are excessively dissipative, but rescaling the model constant improves the prediction of the total (integrated) subgrid scale dissipation, leading to results that compare favorably with those of a direct simulation, at a small fraction of the computational effort.
The northern areas of Tharsis, south of Alba Patera, are remarkable in that they are dominated by extensive, generally north trending graben. Some graben are small isolated features whereas others are complex overlapping features in which individual fault pairs are impossible to separate. This pattern indicates an east-west extensional stress regime, consistent with stress models for Tharsis. To estimate the regional east-west extension and strain, graben along a profile at 35 N latitude, between longitudes 135 and 93 degs were studied. This profile was chosen because the graben have a northerly trend, the structures are relatively simple, the profile is anchored to ancient Noachian age crust, and high resolution images are available. The western end of the profile begins at Acheron Fossae and ends in the east at the southwestern part of Tempe Fossae. Plains units cut by the graben include Hesperian and Amazonian age members of the Alba Patera and Ceraunius Fossae Formations.
Turbulent channel flow and homogeneous shear flow have served as basic building block flows for the testing and calibration of Reynolds stress models. A direct theoretical connection is made between homogeneous shear flow in equilibrium and the log-layer of fully-developed turbulent channel flow. It is shown that if a second-order closure model is calibrated to yield good equilibrium values for homogeneous shear flow it will also yield good results for the log-layer of channel flow provided that the Rotta coefficient is not too far removed from one. Most of the commonly used second-order closure models introduce an ad hoc wall reflection term in order to mask deficient predictions for the log-layer of channel flow that arise either from an inaccurate calibration of homogeneous shear flow or from the use of a Rotta coefficient that is too large. Illustrative model calculations are presented to demonstrate this point which has important implications for turbulence modeling.
The critical strain for matrix cracking of ceramic matrix composites has been studied; emphasis is placed on the effects of the fiber/matrix debonding length and interfacial debonding energy. Based on a modified shear-lag model, stresses in the fiber and matrix have been found for both the bonded and debonded regions. An energy-balance approach, based upon the stress field, is then adopted to evaluate the critical strain for matrix cracking. From the general equation for the critical strain, close form solutions have been deduced for two limiting cases: complete debonding and perfect bonding. Numerical solutions are given for the cases of nonzero debonding energy and partial fiber debonding. The results show that the interfacial debonding energy, which has been ignored by most of the investigators, is an important factor in determining both the critical strain and the debonding length.
The prediction of turbulent secondary flows, with Reynolds stress models, in circular pipes and non-circular ducts is reviewed. Turbulence-driven secondary flows in straight non-circular ducts are considered along with turbulent secondary flows in pipes and ducts that arise from curvature or a system rotation. The physical mechanisms that generate these different kinds of secondary flows are outlined and the level of turbulence closure required to properly compute each type is discussed in detail. Illustrative computations of a variety of different secondary flows obtained from two-equation turbulence models and second-order closures are provided to amplify these points.
The work done during the progress report period from May-October 1992 is summarized. The effect of wall thermal boundary conditions on flows over a step or rib when repeated rib roughness is used for heating augmentation is examined. In numerical investigations of various such laminar and turbulent flows, the local heat transfer coefficients on a forward-facing step or on a rib were found to be very sensitive to the wall thermal boundary condition. For the computation of constant property laminar flow, the wall thermal boundary conditions were either a uniform heat flux or a uniform temperature. Results (Nusselt number and isotherms) of the studies are included. The second part of the work consisted of using PHOENICS to solve the conjugate heat transfer problem of flow over a rib in channel. Finally, the algebraic stress model in the TEAM (Turbulent Elliptic Algorithm-Manchester) code was tested for jet impingement flow, but there needs to be an addition of the energy equation to the code.
Turbulent channel flow and homogeneous shear flow have served as basic building block flows for the testing and calibration of Reynolds stress models. A direct theoretical connection is made between homogeneous shear flow in equilibrium and the log-layer of fully-developed turbulent channel flow. It is shown that if a second-order closure model is calibrated to yield good equilibrium values for homogeneous shear flow it will also yield good results for the log-layer of channel flow provided that the Rotta coefficient is not too far removed from one. Most of the commonly used second-order closure models introduce an ad hoc wall reflection term in order to mask deficient predictions for the log-layer of channel flow that arise either from an inaccurate calibration of homogeneous shear flow or from the use of a Rotta coefficient that is too large. Illustrative model calculations are presented to demonstrate this point which has important implications for turbulence modeling.