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NASA NTRS1988

Mixing rates calculated from potential vorticity

Horizontal mixing coefficients K(yy) and K(yz) were computed using potential vorticity and gradients calculated from NMC data for geopotential heights and temperatures. It was found that the mid-latitude to polar mixing coefficients depend on the use of nongeostrophic winds, which yield K(yy) values which are mostly positive, whereas geostophic winds yield K(yy) values which were largely negative near the polar region. A comparison of the K(yy) values calculated from the potential vorticity fluxes and gradients with the K(yy) values calculated using the momentum balance between the flux of potential vorticity and the residual circulation has shown that the residual-circulation-balanced K(yy) values in the upper stratosphere were much larger than the values calculated by the present method. It is suggested that this difference is the result of breaking gravity waves in the upper stratosphere and lower mesosphere.

Newman, Paul A.↗

NASA NTRS1988

Saturation and the limit of jet mixing enhancement by single frequency plane wave excitation - Experiment and theory

The limitations of single frequency plane wave excitation in mixing enhancement are investigated for a circular jet. Measurements made in an 8.8 cm diameter jet are compared with a theoretical model. The measurements are made to quantify mixing at excitation amplitudes up to 2 percent of the jet exit velocity. The initial boundary layer state, the exit mean and fluctuating velocity profiles and spectra are documented for all cases considered. The amplitude of the fundamental wave is recorded along the jet axis for various levels of excitation. As the amplitude of excitation is increased the jet spreading rate is increased, but beyond a saturation amplitude further increases have no effect on the spreading. The experimental results are compared with theoretical estimates. In the theory the flow is split into the mean flow, large scale motions, and fine scale turbulence. Shape assumptions for the mean flow, and fine scale turbulence along with the shape for the large scale motions obtained from a linear stability theory provide the closure. The experimental results compare reasonably well with predictions.

Raman, Ganesh↗

NASA NTRS1988

Retrieval of constituent mixing ratios from limb thermal emission spectra

An onion-peeling iterative, least-squares relaxation method to retrieve mixing ratio profiles from limb thermal emission spectra is presented. The method has been tested on synthetic data, containing various amounts of added random noise for O3, HNO3, and N2O. The retrieval method is used to obtain O3 and HNO3 mixing ratio profiles from high-resolution thermal emission spectra. Results of the retrievals compare favorably with those obtained previously.

Shaffer, William A.↗

NASA NTRS1988

A mixed-mode bending apparatus for delamination testing

A mixed-mode delamination test procedure was developed combining double cantilever beam mode I loading and end notch flexure mode II loading on a split unidirectional laminate. By loading the specimen with a lever, a single applied load simultaneously produces mode I and II bending loads on the specimen. This mixed mode bending (MMB) test was analyzed using both finite element procedures and beam theory to calculate the mode I and II components of strain energy release rate, G sub I and G sub II, respectively. The analyses showed that a wide range of G sub I/G sub II ratios could be produced by varying the applied load position on the loading lever. As the delamination extended, the G sub I/G sub II ratios varied by less than 5 percent. The simple beam theory equations were modified to account for the elastic interaction between the two arms of the specimen and to account for shear deformations. The resulting equations agreed closely with the finite element results and provide a basis for selection of G sub I/G sub II test ratios and a basis for computing the mode I and II components of measured delamination toughness. The MMB specimen analysis and test procedures were demonstrated using unidirectional laminates.

Crews, John H., Jr.↗

NASA NTRS1989

Nitric acid oxide mixing ratio measurements using a rocket launched chemiluminescent instrument

A total of 18 rocket launched parachute borne nitric oxide instruments were launched from 1977 to 1985. A very precise instrument for the measurement of the nitric oxide mixing ratio was fabricated. No changes were made in the main body of the instruments, i.e., things associated with the reaction volume. Except for the last 4 launches, however, it did not yield the required absolute values that was hoped for. Two major problems were encountered. First, the wrong choice of the background calibration gas, nitrogen, caused the first 10 data sets to be too low in the absolute mixing ratio by nearly the order of 2 to 5 ppbv. The error was realized, and air was substituted for the bias gas measurement. Second, in the desire to extend the measurement to higher altitudes, the problem of contaminating the inlet flow tube with ozone from the reagent gas was encountered. The ozone valve was opened too early in the flight and this caused the pressure in the reaction volume to exceed the pressure at the flow tube entrance, permitting the ozone to migrate backwards. This problem was restricted to an altitude above 45 km.

Horvath, Jack J.↗

NASA NTRS1989

Mixed finite element models for free vibrations of thin-walled beams

Simple, mixed finite element models are developed for the free vibration analysis of curved thin-walled beams with arbitrary open cross section. The analytical formulation is based on a Vlasov's type thin-walled beam theory with the effects of flexural-torsional coupling, transverse shear deformation and rotary inertia included. The fundamental unknowns consist of seven internal forces and seven generalized displacements of the beam. The element characteristic arrays are obtained by using a perturbed Lagrangian-mixed variational principle. Only C(sup o) continuity is required for the generalized displacements. The internal forces and the Lagrange multiplier are allowed to be discontinuous at interelement boundaries. Numerical results are presented to demonstrate the high accuracy and effectiveness of the elements developed. The standard of comparison is taken to be the solutions obtained by using 2-D plate/shell models for the beams.

Noor, Ahmed K.↗

NASA NTRS1989

Mixed formulation for frictionless contact problems

Simple mixed finite element models and a computational precedure are presented for the solution of frictionless contact problems. The analytical formulation is based on a form of Reissner's large rotation theory of the structure with the effects of transverse shear deformation included. The contact conditions are incorporated into the formulation by using a perturbed Lagrangian approach with the fundamental unknowns consisting of the internal forces (stress resultants), the generalized displacements, and the Lagrange multipliers associated with the contact conditions. The element characteristic array are obtained by using a modified form of the two-field Hellinger-Reissner mixed variational principle. The internal forces and the Lagrange multipliers are allowed to be discontinuous at interelement boundaries. The Newton-Raphson iterative scheme is used for the solution of the nonlinear algebraic equations, and the determination of the contact area and the contact pressures.

Noor, Ahmed K.↗

NASA NTRS1989

Inviscid spatial stability of a compressible mixing layer. Part 2: The flame sheet model

The results of an inviscid spatial calculation for a compressible reacting mixing layer are reported. The limit of infinitive activation energy is taken and the diffusion flame is approximated by a flame sheet. Results are reported for the phase speeds of the neutral waves and maximum growth rates of the unstable waves as a function of the parameters of the problem: the ratio of the temperature of the stationary stream to that of the moving stream, the Mach number of the moving streams, the heat release per unit mass fraction of the reactant, the equivalence ratio of the reaction, and the frequency of the disturbance. These results are compared to the phase speeds and growth rates of the corresponding nonreacting mixing layer. We show that the addition of combustion has important, and complex effects on the flow stability.

Jackson, T. L.↗

NASA NTRS1989

Numerical studies of the effects of jet-induced mixing on liquid-vapor interface condensation

Numerical solutions of jet-induced mixing in a partially full cryogenic tank are presented. An axisymmetric laminar jet is discharged from the central part of the tank bottom toward the liquid-vapor interface. Liquid is withdrawn at the same volume flow rate from the outer part of the tank. The jet is at a temperature lower than the interface, which is maintained at a certain saturation temperature. The interface is assumed to be flat and shear-free and the condensation-induced velocity is assumed to be negligibly small compared with radial interface velocity. Finite-difference method is used to solve the nondimensional form of steady state continuity, momentum, and energy equations. Calculations are conducted for jet Reynolds numbers ranging from 150 to 600 and Prandtl numbers ranging from 0.85 to 2.65. The effects of above stated parameters on the condensation Nusselt and Stanton numbers which characterize the steady-state interface condensation process are investigated. Detailed analysis to gain a better understanding of the fundamentals of fluid mixing and interface condensation is performed.

Lin, Chin-Shun↗

NASA NTRS1988

Dynamics of coherent structures in a plane mixing layer

An incompressible, time developing 3-D mixing layer with idealized initial conditions was simulated numerically. Consistent with the suggestions from experimental measurements, the braid region between the dominant spanwise vortices or rolls develops longitudinal vortices or ribs, which are aligned upstream and downstream of a roll and produce spanwise distortion of the rolls. The process by which this distortion occurs is explained by studying a variety of quantities of dynamic importance (e.g., production of enstrophy, vortex stretching). Other quantities of interest (dissipation, helicity density) are also computed and discussed. The currently available simulation only allows the study of the early evolution (before pairing) of the mixing layer. New simulations in progress will relieve this restriction.

Hussain, Fazle↗

NASA NTRS1989

A numerical study of a class of TVD schemes for compressible mixing layers

At high Mach numbers the two-dimensional time-developing mixing layer develops shock waves, positioned around large-scale vortical structures. A suitable numerical method has to be able to capture the inherent instability of the flow, leading to the roll-up of vortices, and also must be able to capture shock waves when they develop. Standard schemes for low speed turbulent flows, for example spectral methods, rely on resolution of all flow-features and cannot handle shock waves, which become too thin at any realistic Reynolds number. The performance of a class of second-order explicit total variation diminishing (TVD) schemes on a compressible mixing layer problem was studied. The basic idea is to capture the physics of the flow correctly, by resolving down to the smallest turbulent length scales, without resorting to turbulence or sub-grid scale modeling, and at the same time capture shock waves without spurious oscillations. The present study indicates that TVD schemes can capture the shocks accurately when they form, but (without resorting to a finer grid) have poor accuracy in computing the vortex growth. The solution accuracy depends on the choice of limiter. However a larger number of grid points are in general required to resolve the correct vortex growth. The low accuracy in computing time-dependent problems containing shock waves as well as vortical structures is partly due to the inherent shock-capturing property of all TVD schemes. In order to capture shock waves without spurious oscillations these schemes reduce to first-order near extrema and indirectly produce clipping phenomena, leading to inaccuracy in the computation of vortex growth. Accurate simulation of unsteady turbulent fluid flows with shock waves will require further development of efficient, uniformly higher than second-order accurate, shock-capturing methods.

Sandham, N. D.↗

NASA NTRS1987

Mixed-initiative control of intelligent systems

Mixed-initiative user interfaces provide a means by which a human operator and an intelligent system may collectively share the task of deciding what to do next. Such interfaces are important to the effective utilization of real-time expert systems as assistants in the execution of critical tasks. Presented here is the Incremental Inference algorithm, a symbolic reasoning mechanism based on propositional logic and suited to the construction of mixed-initiative interfaces. The algorithm is similar in some respects to the Truth Maintenance System, but replaces the notion of 'justifications' with a notion of recency, allowing newer values to override older values yet permitting various interested parties to refresh these values as they become older and thus more vulnerable to change. A simple example is given of the use of the Incremental Inference algorithm plus an overview of the integration of this mechanism within the SPECTRUM expert system for geological interpretation of imaging spectrometer data.

Borchardt, G. C.↗

NASA NTRS1989

Inviscid spatial stability of a compressible mixing layer. Part 3: Effect of thermodynamics

The results of a comprehensive comparative study of the inviscid spatial stability of a parallel compressible mixing layer using various models for the mean flow are reported. The models are: (1) the hyperbolic tangent profile for the mean speed and the Crocco relation for the mean temperature, with the Chapman viscosity-temperature relation and a Prandtl number of one; (2) the Lock profile for the mean speed and the Crocco relation for the mean temperature, with the Chapman viscosity-temperature relation and a Prandtl number of one; and (3) the similarity solution for the coupled velocity and temperature equations using the Sutherland viscosity temperature relation and arbitrary but constant Prandtl number. The purpose was to determine the sensitivity of the stability characteristics of the compressible mixing layer to the assumed thermodynamic properties of the fluid. It is shown that the quantative features of the stability characteristics are quite similiar for all models but that there are quantitative differences resulting from the difference in the thermodynamic models. In particular, it is shown that the stability characteristics are sensitive to the value of the Prandtl number.

Jackson, T. L.↗

NASA NTRS1988

The origin of pristine KREEP - Effects of mixing between UrKREEP and the magmas parental to the Mg-rich cumulates

The fact that pristine KREEP basalts generally have bulk-rock molar MgO/(MgO+FeO) ratios lower than average for the lunar crust despite their extraordinarily high incompatible element contents is discussed. Pristine KREEP basalts also have primitive Ni contents compared to mare basalts with comparable REE contents. It is suggested that these facts can be explained through mixing between ancient KREEP precursor materials and primitive Mg-rich melts. Finite-difference models of this mixing, followed by anorthosite assimilation and fractional crystallization provide satisfactory fits to the composition of these basalts. It is suggested that this is a further confirmation of the magmasphere hypothesis.

Warren, Paul H.↗

NASA NTRS1988

A new method for estimating the turbulent heat flux at the bottom of the daily mixed layer

Temperature data in the mixed layer and net solar irradiance data at the sea surface are used to estimate the vertical turbulent heat flux at the bottom of the daily mixed layer. The method is applied to data obtained in the eastern tropical Pacific, where the daily cycle in the temperature field is confined to the upper 10-25 m. Equatorial turbulence measurements indicate that the turbulent heat flux is much greater during nighttime than daytime.

Imawaki, Shiro↗

NASA NTRS1989

Adaptive computations of multispecies mixing between scramjet nozzle flows and hypersonic freestream

The objective of this paper is to compute the expansion of a supersonic flow through an internal-external nozzle and its viscous mixing with the hypersonic flow of air. The supersonic jet may be that of a multispecies gas other than air. Calculations are performed for one case where both flows are those of air, and another case where a mixture of freon-12 and argon is discharged supersonically to mix with the hypersonic airflow. Comparisons are made between these two cases with respect to gas compositions, and fixed versus flow-adaptive grids. All the computational results are compared successfully with the wind-tunnel tests results.

Baysa, Oktay↗

NASA NTRS1988

An approach to probabilistic finite element analysis using a mixed-iterative formulation

An efficient algorithm for computing the response sensitivity of finite element problems based on a mixed-iterative formulation is proposed. This method does not involve explicit differentiation of the tangent stiffness array and can be used with formulations for which a consistent tangent stiffness is not readily available. The method has been successfully applied to probabilistic finite element analysis of problems using the proposed mixed formulation, and this exercise has provided valuable insights regarding the extension of the method to a more general class of problems to include material and geometric nonlinearities.

Dias, J. B.↗

NASA NTRS1989

An equivalent domain integral for analysis of two-dimensional mixed mode problems

An equivalent domain integral (EDI) method for calculating J-integrals for two-dimensional cracked elastic bodies subjected to mixed mode loading is presented. The total and product integrals consist of the sum of an area or domain integral and line integrals on the crack faces. The EDI method gave accurate values of the J-integrals for two mode I and two mixed mode problems. Numerical studies showed that domains consisting of one layer of elements are sufficient to obtain accurate J-integral values. Two procedures for separating the individual modes from the domain integrals are presented. The procedure that uses the symmetric and antisymmetric components of the stress and displacement fields to calculate the individual modes gave accurate values of the integrals for all the problems analyzed.

Raju, I. S.↗