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All sourcesNASA NTRSDOE OSTI
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 NTRS1972

Comparison of the radiation flux profiles and spectral detail from three detailed nongray radiation models at conditions representative of hypervelocity earth entry

The radiation models were compared on the basis of the approaches used for the transport calculations and absorption coefficients and of results obtained for the radiation flux profiles and spectral distributions. The calculated results were for shock layer conditions representative of manned earth reentry from an interplanetary mission. The three models are RATRAP, RADICAL, and MDAC. The results show that significant differences exist in the radiation flux computed by the three models. The RADICAL model was found to depend on fewer approximations, to include more detail, and to require less computer time than the other models.

Suttles, J. T.↗
NASA NTRS1992

A solar radiation model for use in climate studies

A solar radiation routine is developed for use in climate studies that includes absorption and scattering due to ozone, water vapor, oxygen, carbon dioxide, clouds, and aerosols. Rayleigh scattering is also included. Broadband parameterization is used to compute the absorption by water vapor in a clear atmosphere, and the k-distribution method is applied to compute fluxes in a scattering atmosphere. The reflectivity and transmissivity of a scattering layer are computed analytically using the delta-four-stream discrete-ordinate approximation. The two-stream adding method is then applied to compute fluxes for a composite of clear and scattering layers. Compared to the results of high spectral resolution and detailed multiple-scattering calculations, fluxes and heating rate are accurately computed to within a few percent. The high accuracy of the flux and heating-rate calculations is achieved with a reasonable amount of computing time. With the UV and visible region grouped into four bands, this solar radiation routine is useful not only for climate studies but also for studies on photolysis in the upper atmosphere and photosynthesis in the biosphere.

Chou, Ming-Dah↗
NASA NTRS1984

Chandrasekhar equations and computational algorithms for distributed parameter systems

The Chandrasekhar equations arising in optimal control problems for linear distributed parameter systems are considered. The equations are derived via approximation theory. This approach is used to obtain existence, uniqueness, and strong differentiability of the solutions and provides the basis for a convergent computation scheme for approximating feedback gain operators. A numerical example is presented to illustrate these ideas.

Burns, J. A.↗
NASA NTRS1980

Collisional redistribution of radiation. II - The effects of degeneracy on the equations of motion for the density matrix. III - The equation of motion for the correlation function and the scattered spectrum

The effect of correlations between an absorber atom and perturbers in the binary-collision approximation are applied to degenerate atomic systems. A generalized absorption profile which specifies the final state of the atom after an absorption event is related to the total intensities of Rayleigh scattering and fluorescence from the atom. It is suggested that additional dynamical information to that obtainable from ordinary absorption experiments is required in order to describe redistributed atomic radiation. The scattering of monochromatic radiation by a degenerate atom is computed in a binary-collision approximation; an equation of motion is derived for the correlation function which is valid outside the quantum-regression regime. Solutions are given for the weak-field conditions in terms of generalized absorption and emission profiles that depend on the indices of the atomic multipoles.

Burnett, K.↗
NASA NTRS1994

Effect of grid aspect ratio on convergence

The effects of high-aspect-ratio grids on algorithm convergence are considered by means of vector stability theory and computational experiments. The results indicate that approximately factored implicit schemes experience convergence deterioration because of nonoptimum local time-stepping procedures and increased need for viscous preconditioning. Based on this insight, an enhanced algorithm is devised using improved selection of the local time step, appropriate definition of the viscous preconditioning matrix, and proper implementation of the boundary conditions. The new algorithm provides uniformly efficient convergence at all aspect ratios for both Euler and Navier-Stokes computations for a variety of test problems.

Buelow, P. E. O.↗
NASA NTRS1982

Solution of 3-dimensional time-dependent viscous flows. Part 3: Application to turbulent and unsteady flows

A numerical scheme is developed for solving the time dependent, three dimensional compressible viscous flow equations to be used as an aid in the design of helicopter rotors. In order to further investigate the numerical procedure, the computer code developed to solve an approximate form of the three dimensional unsteady Navier-Stokes equations employing a linearized block implicit technique in conjunction with a QR operator scheme is tested. Results of calculations are presented for several two dimensional boundary layer flows including steady turbulent and unsteady laminar cases. A comparison of fourth order and second order solutions indicate that increased accuracy can be obtained without any significant increases in cost (run time). The results of the computations also indicate that the computer code can be applied to more complex flows such as those encountered on rotating airfoils. The geometry of a symmetric NACA four digit airfoil is considered and the appropriate geometrical properties are computed.

Weinberg, B. C.↗
NASA NTRSDate not supplied

An Overview of the Patch Integral Method (PIM), a New Heat Transfer Analysis Tool for Hypersonic Wind Tunnel Facilities at NASA Langley

NASA Langley’s hypersonic wind tunnels are heavily leveraged for planetary missions. The data collection method in these tunnels is thermography, and surface temperature measurements of the model surface are collected and reduced to produce surface heating data, as seen in Fig 1. However, during model injection, no temperature data are collected, and thus conventional, integral heat transfer methods cannot be used to solve for surface heating. A method was developed in the 1990’s to reduce this data despite the data gap, known as the step approximation method. The method assumes that the film coefficient behaves as a step function, the model is semi-infinite, and thermal properties are constant. With these simplifying assumptions, a Laplace transform can be performed to result in an equation that takes the initial temperature of the model and a temperature at some point in time to back out the film coefficient at that time. This is the method that is used in the current thermographic data reduction software, IHEAT. While computationally light-weight, the step approximation has several issues associated with it. The time-history of temperature is not accounted for, which is vital as heat transfer is an integral process. Additionally, the required semi-infinite assumption is unnecessary and might be violated during runtime. Thermal variation of material properties can have a sizeable impact on heating results and are not modeled by the method. This method also takes multiple seconds to “collapse” to a steady state, which is undesirable from both a facility and data reduction standpoint. The method is also very sensitive to the “effective time” approximation, an approximation of when heating instantaneously starts (which is a nonphysical simplification), and a small variation in this value can result in an error in heating results.

J. S. Cheatwood↗
NASA NTRSDate not supplied

Eigenvalue Sensitivity Computations for Linear Stability Theory

To realize the drag reduction benefit of boundary-layer transition control strategies, it is crucial to integrate transition prediction into the vehicle design through an optimization process. The integration of transition prediction based on linear stability analysis into adjoint d design optimization requires coupling an adjoint enabled computational fluid dynamics (CFD) solver with an adjoint enabled linear stability code. In particular, the boundary-layer transition location is often predicted using the N-factor method based on linear stability theory (LST). Thus, sensitivity of the linear-stability eigenvalues constitute an essential building block for optimizing the laminar flow performance. The present paper describes an implementation of LST eigenvalue sensitivity analysis that can be easily coupled with a CFD solver. Specifically, we describe a discrete adjoint formulation for the transition location prediction based on the N-factor method. The verification of this formulation is carried out by comparing the adjoint-based sensitivity of the local growth rate of a given instability mode with respect to the disturbance frequency, and the adjoint-based sensitivity of the transition location with respect to spanwise wavenumber with those sensitivities computed using a finite-difference approximation. Finally, the adjoint LST formulation is applied to flat-plate boundary-layer flows at transonic, supersonic, and hypersonic conditions, to determine the behavior and sensitivities of the transition location with respect to a range of disturbance spanwise wavenumbers.

Boundary Layer Transition↗
NASA NTRS1981

Ellipsoidal corrections for geoid undulation computations

The computation of accurate geoid undulations is usually done combining potential coefficient information and terrestrial gravity data in a cap surrounding the computation point. In doing this a spherical approximation is made that can cause the errors that were investigated. The equations dealing with ellipsoidal corrections developed by Lelgemann and by Moritz were used to develop a computational procedure considering the ellipsoid as a reference surface. Terms in the resulting expression for the geoid undulation are identified as ellipsoidal correction terms. These equations were developed for the case where the Stokes function is used, and for the case where the modified Stokes function is used. For a cap of 20 deg the correction can reach -33 cm.

Rapp, R. H.↗
NASA NTRS1990

High order filtering methods for approximating hyberbolic systems of conservation laws

In the computation of discontinuous solutions of hyperbolic systems of conservation laws, the recently developed essentially non-oscillatory (ENO) schemes appear to be very useful. However, they are computationally costly compared to simple central difference methods. A filtering method which is developed uses simple central differencing of arbitrarily high order accuracy, except when a novel local test indicates the development of spurious oscillations. At these points, the full ENO apparatus is used, maintaining the high order of accuracy, but removing spurious oscillations. Numerical results indicate the success of the method. High order of accuracy was obtained in regions of smooth flow without spurious oscillations for a wide range of problems and a significant speed up of generally a factor of almost three over the full ENO method.

Lafon, F.↗
NASA NTRS1990

User manual for VICONOPT: An exact analysis and optimum design program covering the buckling and vibration of prismatic assemblies of flat in-plane loaded, anisotropic plates, with approximations for discrete supports, and transverse stiffeners

A computer program which is designed for efficient, accurate buckling and vibration analysis and optimum design of composite panels is described. The capabilities of the program are given along with detailed user instructions. It is written in FORTRAN 77 and is operational on VAX, IBM, and CDC computers and should be readily adapted to others. Several illustrations of the various aspects of the input are given along the example problems illustrating the use and application of the program.

Williams, F. W.↗
NASA NTRS1993

A rational interpolation method to compute frequency response

A rational interpolation method for approximating a frequency response is presented. The method is based on a product formulation of finite differences, thereby avoiding the numerical problems incurred by near-equal-valued subtraction. Also, resonant pole and zero cancellation schemes are developed that increase the accuracy and efficiency of the interpolation method. Selection techniques of interpolation points are also discussed.

Kenney, Charles↗
NASA NTRS2011

Linear Approximation to Optimal Control Allocation for Rocket Nozzles with Elliptical Constraints

In this paper we present a straightforward technique for assessing and realizing the maximum control moment effectiveness for a launch vehicle with multiple constrained rocket nozzles, where elliptical deflection limits in gimbal axes are expressed as an ensemble of independent quadratic constraints. A direct method of determining an approximating ellipsoid that inscribes the set of attainable angular accelerations is derived. In the case of a parameterized linear generalized inverse, the geometry of the attainable set is computationally expensive to obtain but can be approximated to a high degree of accuracy with the proposed method. A linear inverse can then be optimized to maximize the volume of the true attainable set by maximizing the volume of the approximating ellipsoid. The use of a linear inverse does not preclude the use of linear methods for stability analysis and control design, preferred in practice for assessing the stability characteristics of the inertial and servoelastic coupling appearing in large boosters. The present techniques are demonstrated via application to the control allocation scheme for a concept heavy-lift launch vehicle.

Orr, Jeb S.↗
NASA NTRS2018

Multi-Scale Modeling of Low-Density Carbon-Phenolic Ablators

Protecting a spacecraft during atmospheric entry is one of highest risk factors that needs to be mitigated during design of a space exploration mission. At entry speeds from space, air turns into high-temperature plasma, and spacecraft Thermal Protection Systems (TPS) are needed to protect the vehicle payload. Modern successful material architectures of spacecraft shields use a porous carbon fiber substrate impregnated with phenolic as an ablator material. In the lecture, efforts to build a Predictive Material Modeling framework for porous ablators from micro-scale to macro-scale will be presented. Several numerical methods and techniques will be summarized that use voxelized images to compute geometrical properties of the porous substrate. These computed properties include porosity, specific surface area and tortuosity that are otherwise indirectly measured through experimental techniques. Direct simulation Monte Carlo (DSMC), a particle-based method for approximating the Boltzmann equation, is used to compute the permeability coefficient of the porous substrate based on its digitized representation. The method computes the flow within the microstructure, where the size of the pores may approach the mean-free-path of the flow. Finally, a high-fidelity model implemented in PATO (Porous-material Analysis Toolbox) is discussed, and some examples of ablative material response are presented, including for the first time 3D simulations of the full tiled heat shield for the Mars Science Laboratory (MSL) capsule.

Ablators↗
NASA NTRS1972

Constrained Chebyshev approximations to some elementary functions suitable for evaluation with floating point arithmetic

Approximations which can be evaluated with precision using floating-point arithmetic are presented. The particular set of approximations thus far developed are for the function TAN and the functions of USASI FORTRAN excepting SQRT and EXPONENTIATION. These approximations are, furthermore, specialized to particular forms which are especially suited to a computer with a small memory, in that all of the approximations can share one general purpose subroutine for the evaluation of a polynomial in the square of the working argument.

Manos, P.↗
NASA NTRS1975

Shuttle orbiter S-band quad antenna switching evaluation

Automatic switching of the shuttle orbiter S-band quad antennas by the orbiter on-board computers was evaluated. The development and use of an extensive computer program to determine antenna switch position states as a function of time for various orbital activities is described. The selection of the optimum quad antenna element at any given time is based on the look angle to the appropriate Tracking Data Relay Satellite (TDRS). It is shown that a 2.4 second period is required for updating the S-band quad antenna switch state based on a maximum roll rate of 2 deg per second. The possibility of a variable update period is suggested since the 2 deg per second attitude rate is seldom encountered and would, for example, dictate approximately 248,000 on-board computer calculations during Reference Mission 2. The average number of antenna switch state changes was found to be in the range of 1,300 for Reference Mission 2.

Lindsey, J. F.↗