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NASA NTRS1977

The artificial compression method for computation of shocks and contact discontinuities. I - Single conservation laws

The paper discusses the use of the artificial compression method for the computation of discontinuous solutions of a single conservation law by finite difference methods. The single conservation law has either a shock or a contact discontinuity. Any monotone finite difference scheme applied to the original equation smears the discontinuity, while the same scheme applied to the equation modified by an artificial compression flux produces steady progressing profiles. If L is any finite difference scheme in conservation form and C is an artificial compressor, the split flux artificial compression method CL is a corrective scheme: L smears the discontinuity while propagating it; C compresses the smeared transition toward a sharp discontinuity. Numerical implementation of artificial compression is described.

Harten, A.↗

NASA NTRS1977

A few ways of calculating the similarity parameter kappa* for real gases

In connection with the question on the applicability of test results obtained from cryogenic wind tunnels to the large-scale model the similarity parameter is referred to. A simple method is given for calculating the similarity parameter. From the numerical values obtained it can be deduced that nitrogen behaves practically like an ideal gas when it is close to the saturation point and in a pressure range up to 4 bar. The influence of this parameter on the pressure distribution of a supercritical profile confirms this finding.

Lorenz-Meyer, W.↗

NASA NTRS1980

The near field interaction between a sound pulse and a jet shear layer

The in-flow and near field of a jet which is excited by an axial mass source located in the potential core is simulated numerically, taking due account of the jet spreading, and experimentally, using a shock-tube driver. Comparison is made for both excited and unexcited jets. It is shown that many of the features observed experimentally are consequences of the instability of the mean flow profile and not of turbulence. This instability is shown to be a significant amplifier of low frequency sound. The terms responsible for this amplification are those describing action between the fluctuating velocities and the gradient of the mean flow, which were identified by Ribner as the shear noise terms. The results demonstrate that a primary component of the observed shear noise in jets is generated by the mean profile instability.

Bayliss, A.↗

NASA NTRS1984

Chemoviscosity modeling for thermosetting resins - I

A new analytical model for chemoviscosity variation during cure of thermosetting resins was developed. This model is derived by modifying the widely used WLF (Williams-Landel-Ferry) Theory in polymer rheology. Major assumptions involved are that the rate of reaction is diffusion controlled and is linearly inversely proportional to the viscosity of the medium over the entire cure cycle. The resultant first order nonlinear differential equation is solved numerically, and the model predictions compare favorably with experimental data of EPON 828/Agent U obtained on a Rheometrics System 4 Rheometer. The model describes chemoviscosity up to a range of six orders of magnitude under isothermal curing conditions. The extremely non-linear chemoviscosity profile for a dynamic heating cure cycle is predicted as well. The model is also shown to predict changes of glass transition temperature for the thermosetting resin during cure. The physical significance of this prediction is unclear at the present time, however, and further research is required. From the chemoviscosity simulation point of view, the technique of establishing an analytical model as described here is easily applied to any thermosetting resin. The model thus obtained is used in real-time process controls for fabricating composite materials.

Hou, T. H.↗

NASA NTRS1989

Solutions of differential equations with regular coefficients by the methods of Richmond and Runge-Kutta

Numerical solutions of the differential equation which describe the electric field within an inhomogeneous layer of permittivity, upon which a perpendicularly-polarized plane wave is incident, are considered. Richmond's method and the Runge-Kutta method are compared for linear and exponential profiles of permittivities. These two approximate solutions are also compared with the exact solutions.

Cockrell, C. R.↗

NASA NTRS1991

Rapid near-optimal aerospace plane trajectory generation and guidance

Problems associated with onboard trajectory optimization, propulsion system cycle selection, and the synthesis of guidance laws are addressed for ascent to low earth orbit of an airbreathing, single-stage-to-orbit vehicle. A multicycle propulsion system is assumed that incorporates turbojet, ramjet, scramjet, and rocket engines. An energy state approximation is applied to a singularly perturbed, four-state dynamic model for flight of a point mass over a spherical nonrotating earth. An algorithm is then derived for generating both the fuel-optimal climb profile and the guidance commands required to follow that profile. In particular, analytic switching conditions are derived that, under appropriate assumptions, efficiently govern optimal transition from one propulsion cycle to another. The algorithm proves to be computationally efficient and suitable for real-time implementation. The paper concludes with the presentation of representative numerical results that illustrate the nature of the fuel-optimal climb paths and the tracking performance of the guidance algorithm.

Corban, J. E.↗

NASA NTRS1954

Theoretical study of the transonic lift of a double-wedge profile with detached bow wave

A theoretical study is described of the aerodynamic characteristics at small angle of attack of a thin, double-wedge profile in the range of supersonic flight speed in which the bow wave is detached. The analysis is carried out within the framework of the transonic (nonlinear) small-disturbance theory, and the effects of angle of attack are regarded as a small perturbation on the flow previously calculated at zero angle. The mixed flow about the front half of the profile is calculated by relaxation solution of a suitably defined boundary-value problem for transonic small-disturbance equation in the hodograph plane (i.e., the Tricomi equation). The purely supersonic flow about the rear half is found by an extension of the usual numerical method of characteristics. Analytical results are also obtained, within the framework of the same theory, for the range of speed in which the bow wave is attached and the flow is completely supersonic.

Vincenti, Walter G↗

NASA NTRS1999

Abundances and Distributions of Volatile Elements (Na, S, Cl, K) Within Lunar Volcanic Glass Spheres

This research developed and applied high-precision analytical methods (electron microprobe) to determine the major- and minor-element abundances (Si, Ti, A], Cr, Fe, Mn, Mg, Ca, Na, K) in three suites of Apollo 14 volcanic green glasses. Since the precision of these data was a factor of 5-10 better than previously published results, the data provided the strongest constraints yet achieved on the geochemical processes that operated at depths less than 400 kilometers inside the Moon. The results of this work were submitted to the 29th Lunar and Planetary Science Conference, formed the basis for a Master's Thesis, and were published in the top-tier geochemical journal. Additional high-precision data on the trace abundances of sodium (Na), sulfur (S), and potassium (K) in the Apollo 17 volcanic orange glasses (74220) were also acquired during this grant-period. These data show diffusion profiles within individual 200-micron diameter, glass spherules that were apparently generated during the fire-fountain eruption of this magma in the presence of a transient vapor phase. Although these results have not yet been published, publication is planned in 2001 after additional numerical modeling has been completed. This work has also catalyzed on-going collaborative work with Professor Timothy Grove (MIT) to analyze and understand the origin of the Apollo 15 volcanic green glasses. That work will be completed for publication in 2001.

Delano, John W.↗

NASA NTRS2021

Numerical Simulation of Pressure-induced Separation of Turbulent Flat-plate Boundary Layers: Definition and Overview of New Cases with Suction-only Transpiration and a Step in Reynolds Number

Results from two new direct numerical simulations (DNSs) are added to the database described in Coleman, Rumsey & Spalart (2018) (henceforth CRS18), and available at the NASA TMR website (https://turbmodels.larc.nasa.gov). The new flows, Cases D and E, are similar to the earlier ones (Cases A–C) in that a transpiration profile above a flat plate creates a prolonged adverse pressure gradient (APG) that drives a canonical turbulent zero-pressure-gradient (ZPG), flat-plate boundary layer towards separation; they differ in that for the new cases (1) the APG is not followed by a favorable gradient (FPG), since only suction transpiration is employed, and (2) the mean shear stress does not cross zero, so that the width of the mean bubble, strictly defined, is essentially zero. However, the probability of reversed skin friction exceeds 49%. The motivation was to produce a flow that is more akin to technological flows, including shock-boundary-layer interaction, with a gradual turbulence-controlled recovery. One of the new simulations is also at a significantly higher Reynolds number than the earlier flows.

Turbulence↗

NASA NTRS1972

Errors incurred in profile reconstruction and methods for increasing inversion accuracies for occultation type measurements

A method for augmenting the occultation experiment is described for slightly refractive media. This method which permits separation of the components of the gradient of refractivity, appears applicable to most of the planets for a major portion of their atmospheres and ionospheres. The analytic theory is given, and the results of numerical tests with a radially and angularly varying model of an ionosphere are discussed.

Gross, S. H.↗

NASA NTRS2004

Note on the Effect of Horizontal Gradients for Nadir-Viewing Microwave and Infrared Sounders

Passive microwave and infrared nadir sounders such as the Advanced Microwave Sounding Unit A (AMSU-A) and the Atmospheric InfraRed Sounder (AIRS), both flying on NASA s EOS Aqua satellite, provide information about vertical temperature and humidity structure that is used in data assimilation systems for numerical weather prediction and climate applications. These instruments scan cross track so that at the satellite swath edges, the satellite zenith angles can reach approx. 60 deg. The emission path through the atmosphere as observed by the satellite is therefore slanted with respect to the satellite footprint s zenith. Although radiative transfer codes currently in use at operational centers use the appropriate satellite zenith angle to compute brightness temperature, the input atmospheric fields are those from the vertical profile above the center of the satellite footprint. If horizontal gradients are present in the atmospheric fields, the use of a vertical atmospheric profile may produce an error. This note attempts to quantify the effects of horizontal gradients on AIRS and AMSU-A channels by computing brightness temperatures with accurate slanted atmospheric profiles. We use slanted temperature, water vapor, and ozone fields from data assimilation systems. We compare the calculated slanted and vertical brightness temperatures with AIRS and AMSU-A observations. We show that the effects of horizontal gradients on these sounders are generally small and below instrument noise. However, there are cases where the effects are greater than the instrument noise and may produce erroneous increments in an assimilation system. The majority of the affected channels have weighting functions that peak in the upper troposphere (water vapor sensitive channels) and above (temperature sensitive channels) and are unlikely t o significantly impact tropospheric numerical weather prediction. However, the errors could be significant for other applications such as stratospheric analysis. Gradients in ozone and tropospheric temperature appear to be well captured by the analyses. In contrast, gradients in upper stratospheric and mesospheric temperature as well as upper tropospheric humidity are less well captured. This is likely due in part to a lack of data to specify these fields accurately in the analyses. Advanced new sounders, like AIRS, may help to better specify these fields in the future.

Joiner, J.↗

NASA NTRS1985

Numerical experiments on the stability of controlled shear flows

Three-dimensional, nonlinear simulations are presented for the parallel water boundary layer subjected to pressure gradient, suction, or heating control. The focus is on the secondary instability responsible for the K-type transition. Heating control is found to be the least effective in delaying the secondary instability. Flow-field details (including temperature profiles) are presented for both the uncontrolled boundary layer and the heated boundary layer.

Zang, T. A.↗

NASA NTRSDate not supplied

Numerical Study of Combustor-Turbine Interactions Considering a Two-Stage High-Pressure Turbine

In this study, preliminary results are presented from the Open National Combustion Code (OpenNCC) applied to the two-stage high-pressure turbine (HTP) from the energy efficient engine (E3) program. Although the combustor is designed for efficient fuel–air mixing and a relatively uniform exit temperature profile, temporal and spatial variation in combustor exit conditions inevitably lead to hot-streaks in the HPT. These hot streaks can cause local hot spots on the HPT blade surfaces that reduce blade life. To improve understanding of these effects and the overall design of combustor and HPT, we are developing a fully-coupled combustor-turbine computational fluid dynamics (CFD) capability. Previous work has simulated the E^3 combustor at the simulated Sea-Level Take-off (SLTO) condition (P(41) = 2.4 [atm]) with and without the first-stage HPT stator included. This work addresses HPT simulations using inflow conditions based on previous simulation results of the E^3 combustor, as well as investigating the effects of spatial and temporal temperature non-uniformity of the combustor-exit flow on the HPT performance for a more realistic SLTO (P(41) = 27.4 [atm])). First, we analyze existing results from the combustor and the HPT 1st-stage stator simulation, where the unsteady hot gas coming out of the combustor exit travels between the stationary stators and then directly exits the computational domain (i.e., no effect from the rotors). Second, we simulate the HPT including the 1st and 2nd stage stators and rotors with the time-averaged, spatially-nonuniform inflow to the HPT taken from the combustor (with HPT 1st-stage stators) solution. Differences in simulations results for the flow field in the 1st-stage stator region are presented. The results of these two simulations (combustor and HPT simulated in a sequential manner) will be compared to a fully-coupled EEE combustor/HPT simulation to understand the impacts of fully-coupled simulations on combustor and HPT performance for two different operating conditions.

LES↗

NASA NTRSDate not supplied

Numerical Study of Combustor-Turbine Interactions Considering a Two-Stage High-Pressure Turbine

In this study, preliminary results are presented from the Open National Combustion Code (OpenNCC) applied to the two-stage high-pressure turbine (HTP) from the energy efficient engine (E3) program. Although the combustor is designed for efficient fuel–air mixing and a relatively uniform exit temperature profile, temporal and spatial variation in combustor exit conditions inevitably lead to hot-streaks in the HPT. These hot streaks can cause local hot spots on the HPT blade surfaces that reduce blade life. To improve understanding of these effects and the overall design of combustor and HPT, we are developing a fully-coupled combustor-turbine computational fluid dynamics (CFD) capability. Previous work has simulated the E3 combustor at the simulated Sea-Level Take-off (SLTO) condition (P41 = 2.4 [atm]) with and without the first-stage HPT stator included. This work addresses HPT simulations using inflow conditions based on previous simulation results of the E3 combustor, as well as investigating the effects of spatial and temporal temperature non-uniformity of the combustor-exit flow on the HPT performance for a more realistic SLTO (P41 = 27.4 [atm])). First, we analyze existing results from the combustor and the HPT 1st-stage stator simulation, where the unsteady hot gas coming out of the combustor exit travels between the stationary stators and then directly exits the computational domain (i.e., no effect from the rotors). Second, we simulate the HPT including the 1st and 2nd stage stators and rotors with the time-averaged, spatially-nonuniform inflow to the HPT taken from the combustor (with HPT 1st-stage stators) solution. Differences in simulations results for the flow field in the 1st-stage stator region are presented. The results of these two simulations (combustor and HPT simulated in a sequential manner) will be compared to a fully-coupled EEE combustor/HPT simulation to understand the impacts of fully-coupled simulations on combustor and HPT performance for two different operating conditions.

LES↗

NASA NTRS1975

Remote sensing of atmospheric temperature profiles with the Nimbus 5 microwave spectrometer

The paper discusses the accuracy of atmospheric vertical temperature profile measurements performed by the Nimbus 5 microwave spectrometer and compares results obtained during the first 6 months of its operation with independent ground-truth measurements (coincident radiosonde measurements). The microwave spectrometer can measure temperature profiles averaged over the instrument weighting function (about 10 km) layers with a root-mean-square accuracy of a few tenths of a degree K for measurement integration times of 16 s. Lower tropospheric temperature data from the spectrometer measurements is used in the numerical weather prediction model of the National Meteorological Center.

Waters, J. W.↗

NASA NTRS1981

Unsteady boundary-layer injection

The boundary-layer equations for two-dimensional incompressible flow are integrated numerically for the flow over a flat plate and a Howarth body. Injection is introduced either impulsively or periodically along a narrow strip. Results indicate that injection perpendicular to the wall is transmitted instantly across the boundary layer and has little effect on the velocity profile parallel to the wall. The effect is a little more noticeable for flows with adverse pressure gradients. Injection parallel to the wall results in fuller velocity profiles. Parallel and oscillatory injection appears to influence the mean. The amplitude of oscillation decreases with distance from the injection strip but further downstream it increases again in a manner reminiscent of an unstable process.

Telionis, D. P.↗

NASA NTRS1991

User's manual for the Langley boundary layer noise propagation program (MRS-BLP)

A computer program, McAninch-Rawls-Spence Boundary Layer Propagation (MRS-BLP), is described. This program models the refractive and scattering effects on acoustic pressure waves propagating through a boundary layer encompassing an aircraft's fuselage. The noise source is assumed known and generated by a propeller. The fuselage is represented by an infinitely long cylinder embedded in a longitudinal flow. By matching a numerical solution inside the boundary layer with an analytical solution outside the boundary layer, the program calculates the acoustic pressure at the surface of the cylinder given the incident field at the top of the boundary layer. The boundary layer flow velocity and sound speed profiles, as well as the boundary layer thickness may be specified by the user. A detailed description of the input parameters and how to execute the program is given. Example executions of MRS-BLP showing results are also included.

Spence, Peter L.↗

NASA NTRS1995

Supersonic coaxial jet noise predictions

Predictions are made for the noise radiation from supersonic, coaxial jets. These predictions are based on the assumption that the noise radiation in the downstream direction of supersonic jets is dominated by sound generated by instability waves with supersonic phase velocities relative to ambient. Since the analysis requires a known mean flow and the coaxial jet mean flow is not described easily in terms of analytical functions, a numerical prediction is made for its development. The compressible, Reynolds averaged, boundary layer equations are solved with a modified mixing length turbulence model. The model has been calibrated to account for compressibility and temperature effects on the rate of mixing. Both normal and inverted velocity profile jets are considered. Predictions are made for the differences between the noise radiated by coaxial jets with difference operating conditions and a single reference jet with the same thrust, mass flow, and exit area. The effects of area ratio changes and simulated enhanced mixing on noise radiation are also considered.

Dahl, Milo D.↗