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NASA NTRS2001

GRCop-84 Developed for Rocket Engines

GRCop-84 (Cu-8 at.% Cr-4 at.% Nb) was developed at the NASA Glenn Research Center for use in regeneratively cooled rocket engines. This alloy possesses an excellent combination of conductivity, thermal expansion, strength, creep resistance, ductility, and low-cycle fatigue (LCF) life. In comparison to the currently used alloy, NARloy-Z (Cu-3 wt % Ag-0.5 wt % Zr), GRCop-84's significantly better properties give it the potential for significant gains in engine performance and reliability. For GRCop-84 to be safely used in a rocket engine, it is critical to develop a detailed data base of the important thermophysical and mechanical properties. Work has focused on five major properties: thermal conductivity, thermal expansion, tensile strength, creep resistance, and LCF life. The analysis went beyond simply measuring the data and reporting averages. A detailed statistical analysis was conducted that allowed regression of the data over the entire temperature range tested and establishment of design minimums. The design values were expressed as simple mathematical formulas that are highly amenable to use in computer codes such as in finite element analysis and related computer modeling work.

Ellis, David L.↗

NASA NTRS1961

THEORETICAL STUDY OF ATOMIC AND MOLECULAR GASES AND THEIR REACTIONS IN THE UPPER ATMOSPHERE. SUMMARY OF WORK DONE IN THE PERIOD NOV. 1, 1960 TO APR. 30, 1961

In the previous report it was stated that the major mathematical problems of computations were nearly solved and an attempt is being made to start application of "Tables of Integrals" to the computation of the different states of atoms and molecules. In this respect I like to report that the computation of a number of states of atoms and molecules has been carried out. The results are so far confined only to the equilibrium distance of molecules. We are extending the calculation to other distances so as to compute potential energy curves of different states of molecules. We are also developing Thomas Fermi Statistical model of the atom to verify our results of more accurate calculation. The results so far have been very encouraging and I hope to report some of these results in the next paper.

Gas↗

NASA NTRS1985

Theoretical Studies of the Surface Tension of Liquid Metal System

A major goal of this project is to understand the surface tension and other thermophysical properties of liquid metals and alloys from a fundamental viewpoint. The approach is to calculate these quantities by a first principles technique which combines the statistical-mechanical theory of the liquid state with an electronic pseudopotential theory of electrons in metals. The inhomogeneity of the surface is treated using an ionic-density-functional formalism developed with the support of NASA. Of particular interest are the variation of surface tension with temperature and impurity concentration: such variations strongly influence the types of convection which make take place in a low-gravity environment. Some progress has already been achieved in computing the reduction of surface tension due to the presence of low-surface-tension impurities, and the corresponding surface segregation of such impurities. In the coming year, it is planned to concentrate on the surface properties of materials of particular interest to the MSA program: Si, Ga and GaSn alloys. An additional goal is to gain some theoretical understanding of the high temperature thermophysical properties of liquid metals, particularly high melting point materials which have not been studied extensively from a theoretical viewpoint.

Stroud, D. G.↗

NASA NTRSDate not supplied

Correlations Between Porosity, Spatter, and Process Metrics for Powder Bed Fusion Laser Beam Metallic Additive Manufacturing

Components fabricated using the powder bed fusion laser beam metallic (PBF-LB/M)additive manufacturing process are the result of a multitude of weld passes conducted sequentially. Qualifying components for aerospace applications requires a thorough understanding of the process-structure-properties relationships. Porosity defects are known to have a strong adverse effect on the mechanical properties of a component. In particular, porosity defects created by lack of fusion have high aspect ratio morphologies leading to stress concentrations that become crack initiation sites. In the present work, the occurrence of spatter induced lack of fusion porosity was studied using synchronized in-situ process monitoring, additive manufacturing model-based process metrics, and high-resolution X-ray computed tomography. The results show that lack of fusion porosity is statistically correlated with unremoved welding spatter ejecta of the PBF-LB/M process and process metrics related to the hatching strategy.

Qualification↗

NASA NTRS1988

Polarimetric microwave scattering from known randomly rough surfaces

Scattering from rough surfaces is reviewed, and artificial randomly rough surfaces are described. Measurements were made from 4 to 18 GHz for the 4 linear polarization states. The target consists of a metalized randomly rough surface constructed from known surface statistical information. The surface was generated using surface generation routines on the computer, and then the data was converted for the machining of the surface on a computer controlled mill. Bistatic and monostatic measurements were acquired at incident angles from 25 to 60 deg. At the 13.5 to 18 GHz frequencies, the effects of backscatter enhancement and depolarization effects can be studied in a regime which does not satisfy Kirchoff or small perturbation assumptions. This allows scattering mechanisms to be introduced into models, which may show missing elements in the more standard formulations. At lower frequency bands such as 4 to 8.5 GHz the scattering behavior was also examined to see the behavior as assumptions of other formulations are satisfied.

Nance, C. E.↗

NASA NTRS1987

Advanced probabilistic method of development

Advanced structural reliability methods are utilized on the Probabilistic Structural Analysis Methods (PSAM) project to provide a tool for analysis and design of space propulsion system hardware. The role of the effort at the University of Arizona is to provide reliability technology support to this project. PSAM computer programs will provide a design tool for analyzing uncertainty associated with thermal and mechanical loading, material behavior, geometry, and the analysis methods used. Specifically, reliability methods are employed to perform sensitivity analyses, to establish the distribution of a critical response variable (e.g., stress, deflection), to perform reliability assessment, and ultimately to produce a design which will minimize cost and/or weight. Uncertainties in the design factors of space propulsion hardware are described by probability models constructed using statistical analysis of data. Statistical methods are employed to produce a probability model, i.e., a statistical synthesis or summary of each design variable in a format suitable for reliability analysis and ultimately, design decisions.

Wirsching, P. H.↗

NASA NTRS2009

A Biomechanical Approach to Assessing Hip Fracture Risk

Bone loss in microgravity is well documented, but it is difficult to quantify how declines in bone mineral density (BMD) contribute to an astronaut's overall risk of fracture upon return. This study uses a biomechanical approach to assessing hip fracture risk, or Factor of Risk (Phi), which is defined as the ratio of applied load to bone strength. All long-duration NASA astronauts from Expeditions 1-18 were included in this study (n=25), while crewmembers who flew twice (n=2) were treated as separate subjects. Bone strength was estimated based on an empirical relationship between areal BMD at the hip, as measured by DXA, and failure load, as determined by mechanical testing of cadaver femora. Fall load during a sideways fall was calculated from a previously developed biomechanical model, which takes into account body weight, height, gender, and soft tissue thickness overlying the lateral aspect of the hip that serves to attenuate the impact force. While no statistical analyses have been performed yet, preliminary results show that males in this population have a higher FOR than females, with a post- flight Phi of 0.87 and 0.36, respectively. FOR increases 5.1% from preflight to postflight, while only one subject crossed the fracture "threshold" of Phi = 1, for a total of 2 subjects with a postflight Phi > 1. These results suggest that men may be at greater risk for hip fracture due largely in part to their relatively thin soft tissue padding as compared to women, since soft tissue thickness has the highest correlation (R(exp 2)= .53) with FOR of all subject-specific parameters. Future work will investigate changes in FOR during recovery to see if baseline risk levels are restored upon return to 1-g activity. While dual x-ray absorptiometry (DXA) is the most commonly used clinical measure of bone health, it fails to provide compartment-specific information that is useful in assessing changes to bone quality as a result of microgravity exposure. Peripheral quantitative computed tomography (pQCT) accomplishes this by imaging transverse "slices" of the long bones. This project was a re-analysis of a 90 day bed rest study to determine if changes to cortical and trabecular compartments could be detected in the distal tibia with statistical significance using a new pQCT image analysis method. Nearly all changes in bone mineral density (BMD) and cross sectional area (CSA) measures were seen with statistical significance, with the exception of a change in cortical BMD. Total bone CSA increased by 1.1 % (p =0.01), cortical CSA decreased by - 5.6% (p<0.001) and trabecular CSA increased by 1.76% (p=0.007); the combination of which suggests bone resorption occurred at the endocortical surface in response to mechanical unloading by bed rest. Furthermore, total BMD and trabecular BMD decreased (-3.8%, p=0.001 and -2.8%, p =0.007, respectively), while decreases in cortical BMD failed to reach significance (-1.2%, p=0.07). Given that compartment-specific changes are seen with significance and are likely to influence bone strength, it is recommended that pQCT remain a standard measure used in bed rest because it provides a unique measure by which to better evaluate the efficacy of countermeasures to microgravity-induced bone loss.

Ellman, Rachel↗

NASA NTRS1988

Monolithic ceramic analysis using the SCARE program

The Structural Ceramics Analysis and Reliability Evaluation (SCARE) computer program calculates the fast fracture reliability of monolithic ceramic components. The code is a post-processor to the MSC/NASTRAN general purpose finite element program. The SCARE program automatically accepts the MSC/NASTRAN output necessary to compute reliability. This includes element stresses, temperatures, volumes, and areas. The SCARE program computes two-parameter Weibull strength distributions from input fracture data for both volume and surface flaws. The distributions can then be used to calculate the reliability of geometrically complex components subjected to multiaxial stress states. Several fracture criteria and flaw types are available for selection by the user, including out-of-plane crack extension theories. The theoretical basis for the reliability calculations was proposed by Batdorf. These models combine linear elastic fracture mechanics (LEFM) with Weibull statistics to provide a mechanistic failure criterion. Other fracture theories included in SCARE are the normal stress averaging technique and the principle of independent action. The objective of this presentation is to summarize these theories, including their limitations and advantages, and to provide a general description of the SCARE program, along with example problems.

Manderscheid, Jane M.↗

NASA NTRS2000

The Turbulent/Non-Turbulent Interface Bounding a Far-Wake

The velocity fields of a turbulent wake behind a flat plate obtained from the direct numerical simulations of Moser et al. are used to study the structure of the flow in the intermittent zone where there are, alternately, regions of fully turbulent flow and non-turbulent velocity fluctuations either side of a thin randomly moving interface. Comparisons are made with a wake that is 'forced' by amplifying initial velocity fluctuations. There is also a random temperature field T in the flow; T varies between constant values of 0.0 and 1.0 on the sides of the wake. The value of the Reynolds number based on the centreplane mean velocity defect and halfwidth b of the wake is Re approx. = 2000. It is found that the thickness of the continuous interface is about equal to 0.07b, whereas the amplitude of fluctuations of the instantaneous interface displacement y(sub I)(t) is an order of magnitude larger, being about 0.5b. This explains why the mean statistics of vorticity in the intermittent zone can be calculated in terms of the probability distribution of y(sub I) and the instantaneous discontinuity in vorticity across the interface. When plotted as functions of y - y(sub I), the conditional mean velocity (U) and temperature (T) profiles show sharp jumps Delta(U) and Delta(T) at the interface adjacent to a thick zone where (U) and (T) vary much more slowly. Statistics for the vorticity and velocity variances, available in such detail only from DNS data, show how streamwise and spanwise components of vorticity are generated by vortex stretching in the bulges of the interface. Flow fields around the interface, analyzed in terms of the local streamline pattern, confirm previous results that the advancement of the vortical interface into the irrotational flow is driven by large-scale eddy motion. It is argued that because this is an inviscid mechanism the entrainment process is not sensitive to the value of Re, and that small-scale nibbling only plays a subsidiary role. While mean Reynolds stresses decrease gradually in the intermittent zone, conditional stresses are found to decrease sharply towards zero at the interface. Using one-point turbulence models applied to either unconditional or conditional statistics for the turbulent region and then averaged, the entrainment rate E(sub b) would, if calculated exactly, be zero. But if computed with standard computational methods, E(sub b) would be non-zero because of numerical diffusion. It is concluded that the current practice in statistical models of approximating entrainment by a diffusion process is computationally arbitrary and physically incorrect. An analysis shows how E(sub b) is related to Delta(U) and the jump in shear stress at the interface, and correspondingly to Delta(T) and the heat flux.

Bisset, David K.↗

NASA NTRS2007

Robust Fuzzy Controllers Using FPGAs

Electro-mechanical device controllers typically come in one of three forms, proportional (P), Proportional Derivative (PD), and Proportional Integral Derivative (PID). Two methods of control are discussed in this paper; they are (1) the classical technique that requires an in-depth mathematical use of poles and zeros, and (2) the fuzzy logic (FL) technique that is similar to the way humans think and make decisions. FL controllers are used in multiple industries; examples include control engineering, computer vision, pattern recognition, statistics, and data analysis. Presented is a study on the development of a PD motor controller written in very high speed hardware description language (VHDL), and implemented in FL. Four distinct abstractions compose the FL controller, they are the fuzzifier, the rule-base, the fuzzy inference system (FIS), and the defuzzifier. FL is similar to, but different from, Boolean logic; where the output value may be equal to 0 or 1, but it could also be equal to any decimal value between them. This controller is unique because of its VHDL implementation, which uses integer mathematics. To compensate for VHDL's inability to synthesis floating point numbers, a scale factor equal to 10(sup (N/4) is utilized; where N is equal to data word size. The scaling factor shifts the decimal digits to the left of the decimal point for increased precision. PD controllers are ideal for use with servo motors, where position control is effective. This paper discusses control methods for motion-base platforms where a constant velocity equivalent to a spectral resolution of 0.25 cm(exp -1) is required; however, the control capability of this controller extends to various other platforms.

Monroe, Author Gene S., Jr.↗

NASA NTRS2019

Challenges in Qualification of Thermal Protection Systems in Extreme Entry Environments

Planetary entry vehicles employ ablative TPS materials to shield the aeroshell from entry aeroheating environments. To ensure mission success, it must be demonstrated that the heat shield system, including local features such as seams, does not fail at conditions that are suitably margined beyond those expected in flight. Furthermore, its thermal response must be predictable, with acceptable fidelity, by computational tools used in heat shield design. Mission assurance is accomplished through a combination of ground testing and material response modelling. A material's robustness to failure is verified through arcjet testing while its thermal response is predicted by analytical tools that are verified against experimental data. Due to limitations in flight-like ground testing capability and lack of validated high-fidelity computational models, qualification of heat shield materials is often achieved by piecing together evidence from multiple ground tests and analytical simulations, none of which fully bound the flight conditions and vehicle configuration. Extreme heating environments (>2000 W/sq. cm heat flux and >2 atm pressure), experienced during entries at Venus, Saturn and Ice Giants, further stretch the current testing and modelling capabilities for applicable TPS materials. Fully-dense Carbon Phenolic was the material of choice for these applications; however, since heritage raw materials are no longer available, future uses of re-created Carbon Phenolic will require re-qualification. To address this sustainability challenge, NASA is developing a new dual-layer material based on 3D weaving technology called Heat shield for Extreme Entry Environments (HEEET). Regardless of TPS material, extreme environments pose additional certification challenges beyond what has been typical in recent NASA missions. Scope of this presentation: This presentation will give an overview of challenges faced in verifying TPS performance at extreme heating conditions. Examples include: (1) Bounding aeroheating parameters (heat flux, pressure, shear and enthalpy) in ground facilities. How to certify TPS if environments can't be bounded or aeroheating parameters can't be simultaneously achieved. (2) Higher uncertainties in ground test environments (facility calibration and analytical predictions) at extreme conditions. (3) Testing in flows similar to planetary atmosphere composition (H2/He for Gas and Ice Giants). (4) Test sample size limitations for qualifying seam designs. (5) Lack of computational tools capable of simulating all significant aspects of TPS performance (including initiation and propagation of failures). This presentation will provide recommendations on how the EDL community can address these challenges and mitigate some of the risks involved in flying TPS materials at extreme conditions. Examples include: (1) Dedicated activity to understanding TPS failure modes. Develop computational tools capable of modelling fluid interaction with material's thermostructural response. Validate these tools through failure testing. A better understanding of failure mechanisms may eliminate the need to fully bound all aeroheating parameters in ground testing. (2) Enhancements to current testing facilities to simulate flight-like ablation mechanism (ex. testing in Nitrogen at Ames Interaction Heating Facility to limit oxidation in favor of more sublimation). (3) Improved characterization of test conditions with new diagnostic methods and determination of environment uncertainty through rigorous statistical analysis of available data. (4) Design margin policies that are directly tied to uncertainties in ground test environments and modelling fidelity

Mahzari, Milad↗

NASA NTRS2002

Risk-Based Probabilistic Approach to Aeropropulsion System Assessment

In an era of shrinking development budgets and resources, where there is also an emphasis on reducing the product development cycle, the role of system assessment, performed in the early stages of an engine development program, becomes very critical to the successful development of new aeropropulsion systems. A reliable system assessment not only helps to identify the best propulsion system concept among several candidates, it can also identify which technologies are worth pursuing. This is particularly important for advanced aeropropulsion technology development programs, which require an enormous amount of resources. In the current practice of deterministic, or point-design, approaches, the uncertainties of design variables are either unaccounted for or accounted for by safety factors. This could often result in an assessment with unknown and unquantifiable reliability. Consequently, it would fail to provide additional insight into the risks associated with the new technologies, which are often needed by decision makers to determine the feasibility and return-on-investment of a new aircraft engine. In this work, an alternative approach based on the probabilistic method was described for a comprehensive assessment of an aeropropulsion system. The statistical approach quantifies the design uncertainties inherent in a new aeropropulsion system and their influences on engine performance. Because of this, it enhances the reliability of a system assessment. A technical assessment of a wave-rotor-enhanced gas turbine engine was performed to demonstrate the methodology. The assessment used probability distributions to account for the uncertainties that occur in component efficiencies and flows and in mechanical design variables. The approach taken in this effort was to integrate the thermodynamic cycle analysis embedded in the computer code NEPP (NASA Engine Performance Program) and the engine weight analysis embedded in the computer code WATE (Weight Analysis of Turbine Engines) with the fast probability integration technique (FPI). FPI was developed by Southwest Research Institute under contract with the NASA Glenn Research Center. The results were plotted in the form of cumulative distribution functions and sensitivity analyses and were compared with results from the traditional deterministic approach. The comparison showed that the probabilistic approach provides a more realistic and systematic way to assess an aeropropulsion system. The current work addressed the application of the probabilistic approach to assess specific fuel consumption, engine thrust, and weight. Similarly, the approach can be used to assess other aspects of aeropropulsion system performance, such as cost, acoustic noise, and emissions. Additional information is included in the original extended abstract.

Tong, Michael T.↗

NASA NTRS1977

Flight inspection data and crack initiation times

Lockheed C-130 service-flight inspection data is reduced by means of fracture mechanics and statistical analysis into a form from which the probability of time to crack initiation and the distribution of initial flaw sizes for various locations on the aircraft can be determined. Crack sizes are normalized by extrapolating a growing crack backwards from its first recorded size to .03 inches (crack initiation size) yielding the time to crack initiation. In a similar fashion, the crack is grown backwards to a time equal to zero to yield an initial flaw size. In order to perform the discussed computations, crack growth constants were computed for each individual location and were analyzed statistically. Statistical distributions were fitted to times to crack initiation and to initial flaw sizes in order to describe their expected behavior. Weibull and Johnson distributions have been found to fit the data reasonably well but for a better fit convolution integrals of Poisson load distributions and Weibull strength distributions are needed.

Johnson, W. S.↗

NASA NTRS1990

Models of space averaged energetics of plates

The analysis of high frequency vibrations in plates is of particular interest in the study of structure borne noise in aircrafts. The current methods of analysis are either too expensive (finite element method) or may have a confidence band wider than desirable (Statistical Energy Analysis). An alternative technique to model the space and time averaged response of structural acoustics problems with enough detail to include all significant mechanisms of energy generation, transmission, and absorption is highly desirable. The focus of this paper is the development of a set of equations which govern the space and time averaged energy density in plates. To solve this equation, a new type of boundary value problem must be treated in terms of energy density variables using energy and intensity boundary conditions. A computer simulation verification study of the energy governing equation is performed. A finite element formulation of the new equations is also implemented and several test cases are analyzed and compared to analytical solutions.

Bouthier, O. M.↗

NASA NTRS1985

Statistical mechanics of light elements at high pressure. VII - A perturbative free energy for arbitrary mixtures of H and He

A model free energy is presented which accurately represents results from 45 high-precision Monte Carlo calculations of the thermodynamics of hydrogen-helium mixtures at pressures of astrophysical and planetophysical interest. The free energy is calculated using free-electron perturbation theory (dielectric function theory), and is an extension of the expression given in an earlier paper in this series. However, it fits the Monte Carlo results more accurately, and is valid for the full range of compositions from pure hydrogen to pure helium. Using the new free energy, the phase diagram of mixtures of liquid metallic hydrogen and helium is calculated and compared with earlier results. Sample results for mixing volumes are also presented, and the new free energy expression is used to compute a theoretical Jovian adiabat and compare the adiabat with results from three-dimensional Thomas-Fermi-Dirac theory. The present theory gives slightly higher densities at pressures of about 10 megabars.

Hubbard, W. B.↗

NASA NTRS1986

Dynamic remapping of parallel computations with varying resource demands

A large class of computational problems is characterized by frequent synchronization, and computational requirements which change as a function of time. When such a problem must be solved on a message passing multiprocessor machine, the combination of these characteristics lead to system performance which decreases in time. Performance can be improved with periodic redistribution of computational load; however, redistribution can exact a sometimes large delay cost. We study the issue of deciding when to invoke a global load remapping mechanism. Such a decision policy must effectively weigh the costs of remapping against the performance benefits. We treat this problem by constructing two analytic models which exhibit stochastically decreasing performance. One model is quite tractable; we are able to describe the optimal remapping algorithm, and the optimal decision policy governing when to invoke that algorithm. However, computational complexity prohibits the use of the optimal remapping decision policy. We then study the performance of a general remapping policy on both analytic models. This policy attempts to minimize a statistic W(n) which measures the system degradation (including the cost of remapping) per computation step over a period of n steps. We show that as a function of time, the expected value of W(n) has at most one minimum, and that when this minimum exists it defines the optimal fixed-interval remapping policy. Our decision policy appeals to this result by remapping when it estimates that W(n) is minimized. Our performance data suggests that this policy effectively finds the natural frequency of remapping. We also use the analytic models to express the relationship between performance and remapping cost, number of processors, and the computation's stochastic activity.

Nicol, D. M.↗

NASA NTRS1991

Center for Space Power, Texas A and M University

Johnson Controls is a 106 year old company employing 42,000 people worldwide with $4.7 billion annual sales. Though we are new to the aerospace industry we are a world leader in automobile battery manufacturing, automotive seating, plastic bottling, and facilities environment controls. The battery division produces over 24,000,000 batteries annually under private label for the new car manufacturers and the replacement market. We are entering the aerospace market with the nickel hydrogen battery with the help of NASA's Center for Space Power at Texas A&M. Unlike traditional nickel hydrogen battery manufacturers, we are reaching beyond the space applications to the higher volume markets of aircraft starting and utility load leveling. Though space applications alone will not provide sufficient volume to support the economies of scale and opportunities for statistical process control, these additional terrestrial applications will. For example, nickel hydrogen batteries do not have the environmental problems of nickel cadmium or lead acid and may someday start your car or power your electric vehicle. However you envision the future, keep in mind that no manufacturer moves into a large volume market without fine tuning their process. The Center for Space Power at Texas A&M is providing indepth technical analysis of all of the materials and fabricated parts of our battery as well as thermal and mechanical design computer modeling. Several examples of what we are doing with nickel hydrogen chemistry to lead to these production efficiencies are presented.

Jones, Ken↗

NASA NTRS2004

Interaction of a Boundary Layer with a Turbulent Wake

The objective of this grant was to study the transition mechanisms on a flat-plate boundary layer interacting with the wake of a bluff body. This is a simplified configuration presented and designed to exemplify the phenomena that occur in multi-element airfoils, in which the wake of an upstream element impinges on a downstream one. Some experimental data is available for this configuration at various Reynolds numbers. The first task carried out was the implementation and validation of the immersed-boundary method. This was achieved by performing calculations of the flow over a cylinder at low and moderate Reynolds numbers. The low-Reynolds number results are discussed, which is enclosed as Appendix A. The high-Reynolds number results are presented in a paper in preparation for the Journal of Fluid Mechanics. We performed calculations of the wake-boundary-layer interaction at two Reynolds numbers, Re approximately equal to 385 and 1155. The first case is discussed and a comparison of the two calculations is reported. The simulations indicate that at the lower Reynolds number the boundary layer is buffeted by the unsteady Karman vortex street shed by the cylinder. This is shown: long streaky structures appear in the boundary layer in correspondence of the three-dimensionalities in the rollers. The fluctuations, however, cannot be self-sustained due to the low Reynolds-number, and the flow does not reach a turbulent state within the computational domain. In contrast, in the higher Reynolds-number case, boundary-layer fluctuations persist after the wake has decayed (due, in part, to the higher values of the local Reynolds number Re achieved in this case); some evidence could be observed that a self-sustaining turbulence generation cycle was beginning to be established. A third simulation was subsequently carried out at a higher Reynolds number, Re=3900. This calculation gave results similar to those of the Re=l155 case. Turbulence was established at fairly low Reynolds number, as a consequence of the high level of the free-stream perturbation. An instantaneous flow visualization for that case is shown. A detailed examination of flow statistics in the transitional and turbulent regions, including the evolution of the turbulent kinetic energy (TKE) budget and frequency spectra showed the formation and evolution of turbulent spots characteristic of the bypass transition mechanism. It was also observed that the turbulent eddies achieved an equilibrium, fully developed turbulent states first, as evidenced by the early agreement achieved by the terms in the TKE budget with those observed in turbulent flows. Once a turbulent Reynolds stress profile had been established, the velocity profile began to resemble a turbulent one, first in the inner region and later in the outer region of the wall layer. An extensive comparison of the three cases, including budgets, mean velocity and Reynolds stress profiles and flow visualization, is included. The results obtained are also presented.

Piomelli, Ugo↗