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NASA NTRS1979

A statistical model of turbulence in two-dimensional mixing layers

A statistical model of turbulence in fully developed two-dimensional incompressible turbulent mixing layers is proposed. The development of this model is largely motivated by the recent experimental observations of Brown and Roshko (1974). The model is based on the proposition that the turbulence of a fully developed two-dimensional incompressible mixing layer is in a state of quasi-equilibrium. The model is used to predict the second-order turbulence statistics of the flow including single-point turbulent Reynolds stress distribution, intensity of turbulent velocity components, rms turbulent pressure fluctuations, power spectra and two-point space-time correlation functions. It is shown that numerical results compare favorably with available experimental measurements.

Tam, C. K. W.↗

NASA NTRS1979

Sulfate and nitrate mixing ratios in the vicinity of the tropopause

Measurements of sulfate and nitrate in filter samples made during the Global Atmospheric Sampling Program (GASP) from aircraft flying near the tropopause over a period of 28 months beginning in early 1976 are presented. Sulfate and nitrate mixing ratios show a peak near or just above the tropopause during the winter-spring seasons. No peak is evident for sulfate during the summer-fall seasons. The sulfate mixing ratios show a constant average level in 1977-78 of 0.12 + or 0.04 ppbm above the tropopause and 0.05 + or - 0.04 ppbm below the tropopause with higher levels in the spring. Nitrate levels are similar but exhibit greater variability. Correlations between sulfate and nitrate (r = 0.78) and between sulfate and nitrate, on ozone (r = 0.80, 0.78) suggest a predominately stratospheric source for these species.

Lezberg, E. A.↗

NASA NTRS1980

Flow field in supersonic mixed-compression inlets

Program uses method of characteristics for steady three-dimensional flow to calculate flow field in supersonic portion of mixed-compression aircraft inlet at non-zero angle of attack. Results agree well with experimental data except in regions of high viscous interaction. Flow field for variety of mixed-compression inlets can be calculated. Input includes geometry and attack of inlet. Output consists of list of parameters, solution planes, and description of shock waves. Program is written in FORTRAN IV for batch execution on CDC 6000-series.

Bishop, A. R.↗

NASA NTRS1979

Large-scale turbulent structures in jets and in flows over cavities and their relationship to entrainment and mixing

Large scale structures in jets and in flows over cavities were investigated experimentally to determine their role in entrainment, mixing, and noise production. The presence of these structures resulted in growth of the shear layer and entrainment. Merging of adjacent large scale structures caused the near field pressure signal in excited flows. It is believed that both the entrained fluid as well as its eventual mixing with the jet flow can be controlled by introducing pulsation in the jet flow at a frequency for which the flow is most unstable.

Sarohia, V.↗

NASA NTRS1980

Stability of nonuniform rotor blades in hover using a mixed formulation

A mixed formulation for calculating static equilibrium and stability eigenvalues of nonuniform rotor blades in hover is presented. The static equilibrium equations are nonlinear and are solved by an accurate and efficient collocation method. The linearized perturbation equations are solved by a one step, second order integration scheme. The numerical results correlate very well with published results from a nearly identical stability analysis based on a displacement formulation. Slight differences in the results are traced to terms in the equations that relate moments to derivatives of rotations. With the present ordering scheme, in which terms of the order of squares of rotations are neglected with respect to unity, it is not possible to achieve completely equivalent models based on mixed and displacement formulations. The one step methods reveal that a second order Taylor expansion is necessary to achieve good convergence for nonuniform rotating blades. Numerical results for a hypothetical nonuniform blade, including the nonlinear static equilibrium solution, were obtained with no more effort or computer time than that required for a uniform blade.

Stephens, W. B.↗

NASA NTRS1980

A mixed-mode crack analysis of isotropic solids using conservation laws of elasticity

A simple and convenient method of analysis for studying two-dimensional mixed-mode crack problems is presented. The analysis is formulated on the basis of conservation laws of elasticity and of fundamental relationships in fracture mechanics. The problem is reduced to the determination of mixed-mode stress-intensity factor solutions in terms of conservation integrals involving known auxiliary solutions. One of the salient features of the present analysis is that the stress-intensity solutions can be determined directly by using information extracted in the far field. Several examples with solutions available in the literature are solved to examine the accuracy and other characteristics of the current approach. This method is demonstrated to be superior in its numerical simplicity and computational efficiency to other approaches. Solutions of more complicated and practical engineering fracture problems dealing with the crack emanating from a circular hole are presented also to illustrate the capacity of this method

Yau, J. F.↗

NASA NTRS1980

Alternating direction implicit methods for parabolic equations with a mixed derivative

Alternating direction implicit (ADI) schemes for two-dimensional parabolic equations with a mixed derivative are constructed by using the class of all A(0)-stable linear two-step methods in conjunction with the method of approximate factorization. The mixed derivative is treated with an explicit two-step method which is compatible with an implicit A(0)-stable method. The parameter space for which the resulting ADI schemes are second-order accurate and unconditionally stable is determined. Some numerical examples are given.

Beam, R. M.↗

NASA NTRS1982

Model Verification of Mixed Dynamic Systems

MOVER uses experimental data to verify mathematical models of "mixed" dynamic systems. The term "mixed" refers to interactive mechanical, hydraulic, electrical, and other components. Program compares analytical transfer functions with experiment.

Evensen, D. A.↗

NASA NTRS1981

JSC systems using solid ceramic oxygen electrolyte cells to measure oxygen fugacites in gas-mixing systems

Details are given for the construction and operation of a 101.3 KN/sq meter (1 atmosphere) redox control system. A solid ceramic oxygen electrolyte cell is used to monitor the oxygen fugacity in the furnace. The system consists of a vertical quench gas mixing furnace with heads designed for mounting the electrolyte cell and with facilities for inserting and removing the samples, a simplified version of a gas mixing apparatus, and devices for experiments under controlled rates of change of temperature. A thermogravimetric analysis system employing these techniques of redox control and measurement is also described. The calibration and maintenance of the system are discussed.

Williams, R. J.↗

NASA NTRS1981

Time and frequency domain analysis of sampled data controllers via mixed operation equations

Specification of the mathematical equations required to define the dynamic response of a linear continuous plant, subject to sampled data control, is complicated by the fact that the digital components of the control system cannot be modeled via linear ordinary differential equations. This complication can be overcome by introducing two new mathematical operations; namely, the operation of zero order hold and digial delay. It is shown that by direct utilization of these operations, a set of linear mixed operation equations can be written and used to define the dynamic response characteristics of the controlled system. It also is shown how these linear mixed operation equations lead, in an automatable manner, directly to a set of finite difference equations which are in a format compatible with follow on time and frequency domain analysis methods.

Frisch, H. P.↗

NASA NTRS1981

Mixing layer simulation by an improved three-dimensional vortex-in-cell algorithm

An extension is presented of the three-dimensional vortex-in-cell (VIC) method that allows for the simulation of incompressible turbulent flows such as plane mixing layers and wakes with exact boundary conditions in the normal direction. The vorticity is assumed to be confined between two parallel planes and the turbulence is assumed to be homogeneous in the two directions parallel to the planes. As an application, an analysis is presented of the evolution of the plane mixing layer subjected to random two- and three-dimensional initial disturbances.

Couet, B.↗

NASA NTRS1982

The Apollo 15 regolith - Chemical modeling and mare/highland mixing

The chemical compositions of thirty-one A-15 soils from nine sampling stations were studied. Mixing models were calculated using five components: 'representative A-15 mare basalt', anorthosite, low-K Fra Mauro basalt, green glass, and medium-K KREEP (Laul and Papike, 1980). A linear-least-squares mixing model (Boynton et al., 1975) was used with sum check and chi-square tests of the fit of components to soil composition. The soils show significant compositional variability, in some instances over relatively small distances within a sampling station. The models indicate that green-glass abundance does not vary systematically with location and that a significant KREEP component is found in all Apennine Front soils. The models also show the soils from the rim of Hadley Rille to be the most mare-enriched, and soils from Station 2 to be the most highland-enriched. The regolith from Station 8-LM is anomalously high in KREEP component relative to the other mare soils, possibly because of ray material.

Walker, R. J.↗

NASA NTRS1982

Stability of mixed time integration schemes for transient thermal analysis

A current research topic in coupled-field problems is the development of effective transient algorithms that permit different time integration methods with different time steps to be used simultaneously in various regions of the problems. The implicit-explicit approach seems to be very successful in structural, fluid, and fluid-structure problems. This paper summarizes this research direction. A family of mixed time integration schemes, with the capabilities mentioned above, is also introduced for transient thermal analysis. A stability analysis and the computer implementation of this technique are also presented. In particular, it is shown that the mixed time implicit-explicit methods provide a natural framework for the further development of efficient, clean, modularized computer codes.

Liu, W. K.↗

NASA NTRS1982

Detection of aspen-conifer forest mixes from LANDSAT digital data

Aspen, conifer and mixed aspen/conifer forests were mapped for a 15-quadrangle study area in the Utah-Idaho Bear River Range using LANDSAT multispectral scanner data. Digital classification and statistical analysis of LANDSAT data allowed the identification of six groups of signatures which reflect different types of aspen/conifer forest mixing. Photo interpretations of the print symbols suggest that such classes are indicative of mid to late seral aspen forests. Digital print map overlays and acreage calculations were prepared for the study area quadrangles. Further field verification is needed to acquire additional information about the nature of the forests. Single date LANDSAT analysis should be a cost effective means to index aspen forests which are at least in the mid seral phase of conifer invasion. Since aspen canopies tend to obscure understory conifers for early seral forests, a second date analysis, using data taken when aspens are leafless, could provide information about early seral aspen forests.

Jaynes, R. A.↗

NASA NTRS1983

Modeling of space vehicle propellant mixing

An experimental program was conducted to examine the liquid flow patterns that result from the axial-jet mixing of ethanol in 10-cm-diameter spherical and cylindrical containers under zero-, reduced-, and normal-gravity conditions. Dimensionless parameters were developed that characterized the observed liquid flow patterns and the bulk-liquid mixing phenomena. The correlations developed, were used to analyze a typical liquid hydrogen tank and internal thermodynamic vent system for a shuttle-compatible space tug similar to current orbit transfer vehicle concepts.

Aydelott, J. C.↗

NASA NTRS1982

Mixed time integration methods for transient thermal analysis of structures, appendix 5

Mixed time integration methods for transient thermal analysis of structures are studied. An efficient solution procedure for predicting the thermal behavior of aerospace vehicle structures was developed. A 2D finite element computer program incorporating these methodologies is being implemented. The performance of these mixed time finite element algorithms can then be evaluated employing the proposed example problem.

Liu, W. K.↗

NASA NTRS1983

Single cell performance studies on the Fe/Cr Redox Energy Storage System using mixed reactant solutions at elevated temperature

Experimental studies in a 14.5 sq cm single cell system using mixed reactant solutions at 65 C are described. Systems were tested under isothermal conditions i.e., reactants and the cell were at the same temperature. Charging and discharging performance were evaluted by measuring watt-hour and coulombic efficiencies, voltage-current relationships, hydrogen evolution and membrane resistivity. Watt-hour efficiencies ranged from 86% at 43 ma/sq cm to 75% at 129 ma/sq cm with corresponding coulombic efficiencies of 92% and 97%, respectively. Hydrogen evolution was less than 1% of the charge coulombic capacity during charge-discharge cycling. Bismuth and bismuth-lead catalyzed chromium electrodes maintained reversible performance and low hydrogen evolution under normal and adverse cycling conditions. Reblending of the anode and cathode solutions was successfully demonstrated to compensate for osmotic volume changes. Improved performance was obtained with mixed reactant systems in comparison to the unmixed reactant systems.

Gahn, R. F.↗

NASA NTRS1983

Dilution Zone Mixing

Studies to characterize dilution zone mixing; experiments on the effects of free-stream turbulence on a jet in crossflow; and the development of an interactive computer code for the analysis of the mixing of jets with a confined crossflow are reviewed.

Holdeman, J. D.↗