Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Reduce order modeling”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 811 records · Page 45
All sourcesNASA NTRSDOE OSTI
NASA NTRS1992

Combustion noise and combustion instabilities in propulsion systems

This paper is concerned with some aspects of non-linear behavior of unsteady motions in combustion chambers. The emphasis is on conditions under which organized oscillations having discrete frequencies may exist in the presence of random motions. In order to treat the two types of motions together, and particularly to investigate coupling between noise and combustion instabilities, the unsteady field is represented as a synthesis of acoustic modes having time-varying amplitudes. Each of the amplitudes are written as the sum of two parts, one associated with the random field and the remainder representing the organized oscillations. After spatial averaging, the general problem is reduced to solution of a set of second-order ordinary differential equations whose structure depends on the sorts of nonlinear processes accounted for. This formulation accommodates any physical process; in particular, terms are included to represent noise sources, although only limited modeling is discussed. Our results suggest that random sources of noise have only small effects on combustion instabilities and seem not to be a cause of unstable motions. However, the coupling between the two sorts of unsteady motions may be important as an essential process in a proposed scheme for noise control. It is now a familiar observation that many nonlinear deterministic systems are capable of exhibiting apparently random motions called 'chaos.' This is a particularly interesting possibility for systems which also executed non-deterministic random motions. In combustion chambers, a nonlinear deterministic system (acoustical motions) exists in the presence of noise produced by flow separation, turbulent motions, and energy released by combustion processes. The last part of the paper is directed to the matter of discovering whether or not chaotic motions exist in combustion systems. Analysis has not progressed sufficiently far to answer the question. We report here recent results of processing data taken in one combustor to determine the dimensions of any attractors in the motions. No evidence has been found for chaos in the strict sense, but the method seems to be an important means of investigating the nonlinear behavior of combustion systems.

F. E. C. Culick↗
NASA NTRS2011

USM3D Analysis of Low Boom Configuration

In the past few years considerable improvement was made in NASA's in house boom prediction capability. As part of this improved capability, the USM3D Navier-Stokes flow solver, when combined with a suitable unstructured grid, went from accurately predicting boom signatures at 1 body length to 10 body lengths. Since that time, the research emphasis has shifted from analysis to the design of supersonic configurations with boom signature mitigation In order to design an aircraft, the techniques for accurately predicting boom and drag need to be determined. This paper compares CFD results with the wind tunnel experimental results conducted on a Gulfstream reduced boom and drag configuration. Two different wind-tunnel models were designed and tested for drag and boom data. The goal of this study was to assess USM3D capability for predicting both boom and drag characteristics. Overall, USM3D coupled with a grid that was sheared and stretched was able to reasonably predict boom signature. The computational drag polar matched the experimental results for a lift coefficient above 0.1 despite some mismatch in the predicted lift-curve slope.

Carter, Melissa B.↗
NASA NTRS2014

A Regional CO2 Observing System Simulation Experiment for the ASCENDS Satellite Mission

Top-down estimates of the spatiotemporal variations in emissions and uptake of CO2 will benefit from the increasing measurement density brought by recent and future additions to the suite of in situ and remote CO2 measurement platforms. In particular, the planned NASA Active Sensing of CO2 Emissions over Nights, Days, and Seasons (ASCENDS) satellite mission will provide greater coverage in cloudy regions, at high latitudes, and at night than passive satellite systems, as well as high precision and accuracy. In a novel approach to quantifying the ability of satellite column measurements to constrain CO2 fluxes, we use a portable library of footprints (surface influence functions) generated by the WRF-STILT Lagrangian transport model in a regional Bayesian synthesis inversion. The regional Lagrangian framework is well suited to make use of ASCENDS observations to constrain fluxes at high resolution, in this case at 1 degree latitude x 1 degree longitude and weekly for North America. We consider random measurement errors only, modeled as a function of mission and instrument design specifications along with realistic atmospheric and surface conditions. We find that the ASCENDS observations could potentially reduce flux uncertainties substantially at biome and finer scales. At the 1 degree x 1 degree, weekly scale, the largest uncertainty reductions, on the order of 50 percent, occur where and when there is good coverage by observations with low measurement errors and the a priori uncertainties are large. Uncertainty reductions are smaller for a 1.57 micron candidate wavelength than for a 2.05 micron wavelength, and are smaller for the higher of the two measurement error levels that we consider (1.0 ppm vs. 0.5 ppm clear-sky error at Railroad Valley, Nevada). Uncertainty reductions at the annual, biome scale range from 40 percent to 75 percent across our four instrument design cases, and from 65 percent to 85 percent for the continent as a whole. Our uncertainty reductions at various scales are substantially smaller than those from a global ASCENDS inversion on a coarser grid, demonstrating how quantitative results can depend on inversion methodology. The a posteriori flux uncertainties we obtain, ranging from 0.01 to 0.06 Pg C yr-1 across the biomes, would meet requirements for improved understanding of long-term carbon sinks suggested by a previous study.

remote sensing↗
NASA NTRS2020

Air Traffic Management TestBed Data Exchange Model

The Air Traffic Management (ATM) TestBed is a Platform as a Service that is being developed by the National Aeronautics and Space Administration (NASA) to help design, configure, integrate, run, and monitor air traffic simulations. The platform is designed to provide cloud services including back-end, big-data analytics tools, on-demand computing resource management, data storage, and communication middleware. The ATM TestBed reduces the time to test concepts and technologies, supports interactions among various methods such as human-in-the-loop and automation-in-the-loop simulations, and enables collaborative simulations by sharing technologies and tools in the ATM community. In order to allow easier access to simulation components, TestBed provides a messaging support layer for connectivity using a consistent set of input/output interfaces. In addition, a standard data format is introduced to facilitate communication between the components. The data exchange model, supported in the messaging support layer, standardizes the format of the information to be exchanged among the components. This document describes the messaging data model currently developed in TestBed and provides data dictionaries for references to component developers as well as simulation engineers.

air traffic simulation↗
NASA NTRS2000

Geoscience Laser Altimeter System (GLAS) Final Test Report of DM LHP TV Testing

Two loop heat pipes (LHPs) are to be used for thermal control of the Geoscience Laser Altimeter System (GLAS), planned for flight in 2001. One LHP will be used to transport 100 W from a laser to the radiator, the other will transport 210 W from electronic boxes to the radiator. In order to verify the LHP design for the GLAS application, an LHP Development Model has been fabricated, and ambient and thermal vacuum tested. Two aluminum blocks of 15 kg and 30 kg, respectively, were attached to the LHP to simulate the thermal masses connected to the heat sources. A 20 W starter heater was installed on the evaporator to aid the loop startup. A new concept to thermally couple the vapor and liquid line was also incorporated in the LHP design. Such a thermal coupling would reduce the power requirement on the compensation chamber in order to maintain the loop set point temperature. To avoid freezing of the liquid in the condenser during cold cases, propylene was selected as the working fluid. The LHP was tested under reflux mode and with adverse elevation. Tests conducted included start-up, power cycle, steady state and transient operation during hot and cold cases, and heater power requirements for the set point temperature control of the LHP. Test results showed very successful operation of the LHP under all conditions. The 20 W starter heater proved necessary in order to start the loop when a large thermal mass was attached to the evaporator. The thermal coupling between the liquid line and the vapor line significantly reduced the heater power required for loop temperature control, which was less than 5 watts in all cases, including a cold radiator. The test also demonstrated successful operation with a propylene working fluid, with successful startups with condenser temperatures as low as 100 C. Furthermore, the test demonstrated accurate control of the loop operating temperature within +/- 0.2 C, and a successful shutdown of the loop during the survival mode of operation.

Baker, Charles↗
NASA NTRS1997

Algorithms for Performance, Dependability, and Performability Evaluation using Stochastic Activity Networks

Modeling tools and technologies are important for aerospace development. At the University of Illinois, we have worked on advancing the state of the art in modeling by Markov reward models in two important areas: reducing the memory necessary to numerically solve systems represented as stochastic activity networks and other stochastic Petri net extensions while still obtaining solutions in a reasonable amount of time, and finding numerically stable and memory-efficient methods to solve for the reward accumulated during a finite mission time. A long standing problem when modeling with high level formalisms such as stochastic activity networks is the so-called state space explosion, where the number of states increases exponentially with size of the high level model. Thus, the corresponding Markov model becomes prohibitively large and solution is constrained by the the size of primary memory. To reduce the memory necessary to numerically solve complex systems, we propose new methods that can tolerate such large state spaces that do not require any special structure in the model (as many other techniques do). First, we develop methods that generate row and columns of the state transition-rate-matrix on-the-fly, eliminating the need to explicitly store the matrix at all. Next, we introduce a new iterative solution method, called modified adaptive Gauss-Seidel, that exhibits locality in its use of data from the state transition-rate-matrix, permitting us to cache portions of the matrix and hence reduce the solution time. Finally, we develop a new memory and computationally efficient technique for Gauss-Seidel based solvers that avoids the need for generating rows of A in order to solve Ax = b. This is a significant performance improvement for on-the-fly methods as well as other recent solution techniques based on Kronecker operators. Taken together, these new results show that one can solve very large models without any special structure.

Deavours, Daniel D.↗
NASA NTRS1999

A Quantitative Study of Oxygen as a Metabolic Regulator

An acute reduction in oxygen (O2) delivery to a tissue is generally associated with a decrease in phosphocreatine, increases in ADP, NADH/NAD, and inorganic phosphate, increased rates of glycolysis and lactate production, and reduced rates of pyruvate and fatty acid oxidation. However, given the complexity of the human bioenergetic system and its components, it is difficult to determine quantitatively how cellular metabolic processes interact to maintain ATP homeostasis during stress (e.g., hypoxia, ischemia, and exercise). Of special interest is the determination of mechanisms relating tissue oxygenation to observed metabolic responses at the tissue, organ, and whole body levels and the quantification of how changes in tissue O2 availability affect the pathways of ATP synthesis and the metabolites that control these pathways. In this study, we extend a previously developed mathematical model of human bioenergetics to provide a physicochemical framework that permits quantitative understanding of O2 as a metabolic regulator. Specifically, the enhancement permits studying the effects of variations in tissue oxygenation and in parameters controlling the rate of cellular respiration on glycolysis, lactate production, and pyruvate oxidation. The whole body is described as a bioenergetic system consisting of metabolically distinct tissue/organ subsystems that exchange materials with the blood. In order to study the dynamic response of each subsystem to stimuli, we solve the ordinary differential equations describing the temporal evolution of metabolite levels, given the initial concentrations. The solver used in the present study is the packaged code LSODE, as implemented in the NASA Lewis kinetics and sensitivity analysis code, LSENS. A major advantage of LSENS is the efficient procedures supporting systematic sensitivity analysis, which provides the basic methods for studying parameter sensitivities (i.e., changes in model behavior due to parameter variation). Sensitivity analysis establishes relationships between model predictions and problem parameters (i.e., initial concentrations, rate coefficients, etc). It helps determine the effects of uncertainties or changes in these input parameters on the predictions, which ultimately are compared with experimental observations in order to validate the model. Sensitivity analysis can identify parameters that must be determined accurately because of their large effect on the model predictions and parameters that need not be known with great precision because they have little or no effect on the solution. This capability may prove to be important in optimizing the design of experiments, thereby reducing the use of animals. This approach can be applied to study the metabolic effects of reduced oxygen delivery to cardiac muscle due to local myocardial ischemia and the effects of acute hypoxia on brain metabolism. Other important applications of sensitivity analysis include identification of quantitatively relevant pathways and biochemical species within an overall mechanism, when examining the effects of a genetic anomaly or pathological state on energetic system components and whole system behavior.

Radhakrishnan, Krishnan↗
NASA NTRS1994

Preliminary estimates of Gulf Stream characteristics from TOPEX data and a precise gravimetric geoid

TOPEX sea surface height data has been used, with a gravimetric geoid, to calculate sea surface topography across the Gulf Stream. This topography was initially computed for nine tracks on cycles 21 to 29. Due to inaccurate geoid undulations on one track, results for eight tracks are reported. The sea surface topography estimates were used to calculate parameters that describe Gulf Stream characteristics from two models of the Gulf Stream. One model was based on a Gaussian representation of the velocity while the other was a hyperbolic representation of velocity or the sea surface topography. The parameters of the Gaussian velocity model fit were a width parameter, a maximum velocity value, and the location of the maximum velocity. The parameters of the hyperbolic sea surface topography model were the width, the height jump, position, and sea surface topography at the center of the stream. Both models were used for the eight tracks and nine cycles studied. Comparisons were made between the width parameters, the maximum velocities, and the height jumps. Some of the parameter estimates were found to be highly (0.9) correlated when the hyperbolic sea surface topography fit was carried out, but such correlations were reduced for either the Gaussian velocity fits or the hyperbolic velocity model fit. A comparison of the parameters derived from 1-year TOPEX data showed good agreement with values derived by Kelly (1991) using 2.5 years of Geosat data near 38 deg N, 66 deg W longitude. Accuracy of the geoid undulations used in the calculations was of order of +/- 16 cm with the accuracy of a geoid undulation difference equal to +/- 15 cm over a 100-km line in areas with good terrestrial data coverage. This paper demonstrates that our knowledge or geoid undulations and undulation differences, in a portion of the Gulf Stream region, is sufficiently accurate to determine characteristics of the jet when used with TOPEX altimeter data. The method used here has not been shown to be more accurate than methods that average altimeter data to form a reference surface used in analysis to obtain the Gulf Stream characteristics. However, the results show the geoid approach may be used in areas where lack of current meandering reduces the accuracy of the average surface procedure.

Rapp, Richard H.↗
NASA NTRS1980

Stresses in a three-dimensional unidirectional composite containing broken fibers

An approximate solution is developed for the determination of the interlaminar normal and shear stresses in the vicinity of a crack in a three dimensional composite containing unidirectional linearly elastic fibers in an infinite linearly elastic matrix. In order to reduce the complexity of the formulation, certain assumptions are made as to the physically significant stresses to be retained. These simplifications reduce the partial differential equations of elasticity to differential-difference equations which are tractable using Fourier transform techniques. This 'material modeling' approach is in contrast with solutions developed by considering each lamina as a homogeneous, orthotropic layer. The resulting solution does not contain the classical singular stress field for the fibers and the influence of broken fibers on unbroken fibers is felt by a change in stress concentration factors. The matrix stresses however, are unbounded as the fiber spacing vanishes and an equivalent fiber-matrix geometry is proposed which gives the correct singular behavior. The numerical solution is considered in detail and several specific examples are presented. The potential for damaged or debonded zones to be generated by an embedded crack is discussed, and stress concentration factors for fibers near the crack are given. Detailed comparisons are made between the present solution, the analogous two-dimensional problem, and corresponding shear-lag models.

Goree, J. G.↗
NASA NTRS1989

Turbofan engine control system design using the LQG/LTR methodology

Application of the Linear-Quadratic-Gaussian with Loop-Transfer-Recovery methodology to design of a control system for a simplified turbofan engine model is considered. The importance of properly scaling the plant to achieve the desired Target-Feedback-Loop is emphasized. The steps involved in the application of the methodology are discussed via an example, and evaluation results are presented for a reduced-order compensator. The effect of scaling the plant on the stability robustness evaluation of the closed-loop system is studied in detail.

Garg, Sanjay↗
NASA NTRS1989

A defect stream function, law of the wall/wake method for compressible turbulent boundary layers

The application of the defect stream function to the solution of the two-dimensional, compressible boundary layer is examined. A law of the wall/law of the wake formulation for the inner part of the boundary layer is presented which greatly simplifies the computational task near the wall and eliminates the need for an eddy viscosity model in this region. The eddy viscosity model in the outer region is arbitrary. The modified Crocco temperature-velocity relationship is used as a simplification of the differential energy equation. Formulations for both equilibrium and nonequilibrium boundary layers are presented including a constrained zero-order form which significantly reduces the computational workload while retaining the significant physics of the flow. A formulation for primitive variables is also presented. Results are given for the constrained zero-order and second-order equilibrium formulations and are compared with experimental data. A compressible wake function valid near the wall has been developed from the present results.

Barnwell, Richard W.↗
NASA NTRS2016

Uncertainty and Sensitivity Analysis of Afterbody Radiative Heating Predictions for Earth Entry

The objective of this work was to perform sensitivity analysis and uncertainty quantification for afterbody radiative heating predictions of Stardust capsule during Earth entry at peak afterbody radiation conditions. The radiation environment in the afterbody region poses significant challenges for accurate uncertainty quantification and sensitivity analysis due to the complexity of the flow physics, computational cost, and large number of un-certain variables. In this study, first a sparse collocation non-intrusive polynomial chaos approach along with global non-linear sensitivity analysis was used to identify the most significant uncertain variables and reduce the dimensions of the stochastic problem. Then, a total order stochastic expansion was constructed over only the important parameters for an efficient and accurate estimate of the uncertainty in radiation. Based on previous work, 388 uncertain parameters were considered in the radiation model, which came from the thermodynamics, flow field chemistry, and radiation modeling. The sensitivity analysis showed that only four of these variables contributed significantly to afterbody radiation uncertainty, accounting for almost 95% of the uncertainty. These included the electronic- impact excitation rate for N between level 2 and level 5 and rates of three chemical reactions in uencing N, N(+), O, and O(+) number densities in the flow field.

West, Thomas K., IV↗
NASA NTRS1999

Modeling Studies of PVT Growth of ZnSe: Current Status and Future Course

Bulk growth of wide band gap II-VI semiconductors by physical vapor transport (PVT) has been developed and refined over the past several years at NASA Marshall Space Flight Center. Results from a modeling study of PVT crystal growth of ZnSe are reported in this paper. The PVT process is numerically investigated using a two-dimensional formulation of the governing equations and associated boundary conditions. Both the incompressible Boussinesq approximation and a compressible model are tested to determine the influence of gravity on the process and to discern the differences between the two approaches. The influence of a residual gas is included in the models. The results show that both the incompressible and compressible approximations provide comparable results and the presence of a residual gas tends to measurably reduce the mass flux in the system. Detailed flow, thermal and concentration profiles are provided. The simulations show that the Stefan flux dominates the system flow field and the subtle gravitational effects can be gauged by subtracting this flux from the calculated profiles. Shear flows, due to solutal buoyancy, of the order of 50 microns/s for the liorizont,-d growth orientation and 10 microns/s for the vertical orientation are predicted. Whether these flows can fully account for the observed gravity related growth morphological effects and inhomogeneous solute and dopant distributions is a matter of conjecture. A template for future modeling efforts in this area is suggested which incorporates a mathematical approach to the tracking of the growth front based on energy of formation concepts.

Ramachandran, N.↗
NASA NTRS1999

Bubble Generation in a Flowing Liquid Medium and Resulting Two-Phase Flow in Microgravity

The present investigation reports a study of bubble generation under reduced gravity conditions, using both a co-flow and a cross-flow configuration. This study may be used in the conceptual design of a space-based thermal management system. Ensuing two-phase flow void fraction can be accurately monitored using a single nozzle gas injection system within a continuous liquid flow conduit, as utilized in the present investigation. Accurate monitoring of void fraction leads to precise control of heat and mass transfer coefficients related to a thermal management system; hence providing an efficient and highly effective means of removing heat aboard spacecraft or space stations. Our experiments are performed in parabolic flight aboard the modified DC-9 Reduced Gravity Research Aircraft at NASA Lewis Research Center, using an air-water system. For the purpose of bubble dispersion in a flowing liquid, we use both a co-flow and a cross-flow configuration. In the co-flow geometry, air is introduced through a nozzle in the same direction with the liquid flow. On the other hand, in the cross-flow configuration, air is injected perpendicular to the direction of water flow, via a nozzle protruding inside the two-phase flow conduit. Three different flow conduit (pipe) diameters are used, namely, 1.27 cm, 1.9 cm and 2.54 cm. Two different ratios of nozzle to pipe diameter (D(sub N))sup * are considered, namely (D(sub N))sup * = 0.1 and 0.2, while superficial liquid velocities are varied from 8 to 70 cm/s depending on flow conduit diameter. It is experimentally observed that by holding all other flow conditions and geometry constant, generated bubbles decrease in size with increase in superficial liquid velocity. Detached bubble diameter is shown to increase with air injection nozzle diameter. Likewise, generated bubbles grow in size with increasing pipe diameter. Along the same lines, it is shown that bubble frequency of formation increases and hence the time to detachment of a forming bubble decreases, as the superficial liquid velocity is in-creased. Furthermore, it is shown that the void fraction of the resulting two-phase flow increases with volumetric gas flow rate Q(sub d), pipe diameter and gas injection nozzle diameter, while they decrease with surrounding liquid flow. The important role played by flowing liquid in detaching bubbles in a reduced gravity environment is thus emphasized. We observe that the void fraction can be accurately controlled by using single nozzle gas injection, rather than by employing multiple port injection, since the later system gives rise to unpredictable coalescence of adjacent bubbles. It is of interest to note that empirical bubble size and corresponding void fraction are somewhat smaller for the co-flow geometry than the cross-flow configuration at similar flow conditions with similar pipe and nozzle diameters. In order to supplement the empirical data, a theoretical model is employed to study single bubble generation in the dynamic (Q(sub d) = 1 - 1000 cu cm/s) and bubbly flow regime within the framework of the co-flow configuration. This theoretical model is based on an overall force balance acting on the bubble during the two stages of generation, namely the expansion and the detachment stage. Two sets of forces, one aiding and the other inhibiting bubble detachment are identified. Under conditions of reduced gravity, gas momentum flux enhances, while the surface tension force at the air injection nozzle tip inhibits bubble detachment. In parallel, liquid drag and inertia can act as both attaching and detaching forces, depending on the relative velocity of the bubble with respect to the surrounding liquid. Predictions of the theoretical model compare well with our experimental results. However, at higher superficial liquid velocities, as the bubble loses its spherical form, empirical bubble size no longer matches the theoretical predictions. In summary, we have developed a combined experimental and theoretical work, which describes the complex process of bubble generation and resulting two-phase flow in a microgravity environment. Results of the present study can be used in a wide range of space-based applications, such as thermal energy and power generation, propulsion, cryogenic storage and long duration life support systems, necessary for programs such as NASA's Human Exploration for the Development of Space (HEDS).

Pais, S. C.↗
NASA NTRS1999

Characteristics of Non-Premixed Turbulent Flames in Microgravity

The momentum of the fuel (and/or air) jet is important in classifying gas-jet diffusion flame behavior. Normal-gravity data on gas-jet flames show that the flame height (non-dimensionalized with respect to an effective diameter) can be correlated to a density weighted Froude number in the buoyancy-dominated limit. In the momentum-dominated limit this non-dimensional flame height asymptotes to a constant value. The momentum-dominated limit under normal gravity conditions is usually obtained for very high injection velocities which in turn results in high values of the injection Reynolds number. This results in a complicated flame structure because of the large number of turbulence scales involved. In order to gain better insight into the structure of these flames it would be useful to reduce the injection Reynolds number while still maintaining turbulent conditions. This can be done in microgravity where momentum-dominated turbulent flames are obtained at much smaller velocities than in normal gravity. In this paper, experimental results on the effects of nozzle diameter and fuel dilution on flame height are discussed. The experimental values are compared with predictions from a numerical procedure utilizing the standard k-epsilon turbulence model. Flame height scaling with nozzle size and dilution is established. Differences between model predictions and measurements are presented. In order to explain these differences, evolutions of turbulent spectra and Taylor microscale along the flame axis are considered.

Hegde, U.↗
NASA NTRS1988

Structure of a fluid interface near the critical point

The structure of the liquid-liquid interface of three very different mixtures (carbon disulfide + methanol, methanol + cyclohexane + deuterated cyclohexane, and nitrobenzene + n-decane) has been studied using ellipsometry in the reduced temperature range between 0.0009 and 0.042. Although the elliptical thickness varies by an order of magnitude between these mixtures, the data from all three mixtures can be scaled to the same universal constant by a combined mean-field plus capillary-wave model of the interface. The universal constant determined experimentally is significantly less than the theoretical value.

Schmidt, James W.↗
NASA NTRS1991

Guided waves in a multilayered composite and ultrasonic nondestructive evaluation

Analysis of wave propagation in a laminated composite plate with many layers is made difficult by the anisotropy of the laminae, different lay-ups, many layers and defects in the fabricated plate. A good understanding of the wave field in such a plate without defects is a prerequisite for use of ultrasonic techniques to evaluate the various defects that can substantially reduce the strength and service life of this structure. Results of modeling studies of wave propagation and scattering in a multilayered composite plate are presented. The analysis technique combines the finite element discretization through the thickness with wave form representation along the plate in order to calculate the dispersive modes of propagation in the plate. To study scattering of these waves by a matrix crack that grows into delaminations, a hybrid finite element representation of the field near the crack and the modal representation of the scattered exterior field are used. Results are presented showing the dependence of the reflection and transmission coefficients on the size of the crack with delamination which can be used to size the defect using ultrasonic techniques.

Datta, S. K.↗
NASA NTRS1996

Reduced Stress Tensor and Dissipation and the Transport of Lamb Vector

We develop a methodology to ensure that the stress tensor, regardless of its number of independent components, can be reduced to an exactly equivalent one which has the same number of independent components as the surface force. It is applicable to the momentum balance if the shear viscosity is constant. A direct application of this method to the energy balance also leads to a reduction of the dissipation rate of kinetic energy. Following this procedure, significant saving in analysis and computation may be achieved. For turbulent flows, this strategy immediately implies that a given Reynolds stress model can always be replaced by a reduced one before putting it into computation. Furthermore, we show how the modeling of Reynolds stress tensor can be reduced to that of the mean turbulent Lamb vector alone, which is much simpler. As a first step of this alternative modeling development, we derive the governing equations for the Lamb vector and its square. These equations form a basis of new second-order closure schemes and, we believe, should be favorably compared to that of traditional Reynolds stress transport equation.

Wu, Jie-Zhi↗