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NASA NTRS2022

Transition Analysis for the CRM-NLF Wind Tunnel Configuration using Transport Equation Models and Linear Stability Correlations

Transition models based on auxiliary transport equations augmenting the Reynolds-averaged Navier-Stokes (RANS) framework rely upon transition correlations that were derived from a limited number of low-speed experiments. Furthermore, these models often account for only a subset of the relevant transition mechanisms and/or cannot accurately predict the sensitivity of those mechanisms to the changes in significant flow parameters. A preceding investigation had targeted the assessment of the transport-equation-based transition models in NASA's OVERFLOW 2.3b solver, namely, the amplification factor transport (AFT-2017b) equation model coupled with the Spalart-Allmaras RANS model and the Langtry-Menter transition models (LM2009 without crossflow effects and LM2015 including the modeling of crossflow transition) implemented with Menter’s shear-stress transport equation (SST2003) RANS model. Comparisons with recent measurements at transonic freestream conditions on the Common Research Model with Natural Laminar Flow (CRM-NLF) reinforced our earlier finding that all three of the above models significantly underpredict the reported extent of the laminar flow region over the entire span of the wing, regardless of the dominant instability mechanism(s) underlying the onset of the transition process. The underprediction of the laminar flow extent was attributed to the failure of the above models in accounting for the stabilizing effect of compressibility on the amplification of Tollmien-Schlichting instabilities. Based on previous linear stability studies related to compressibility effects, the present work proposes modifications to the two classes of transition models that reduce to the original form of each model at low subsonic speeds and do not require any nonlocal flow information or additional transport equation(s). The modifications are shown to significantly improve the predicted laminar extent of the flow and compare well against the data from the CRM-NLF experiment. Additionally, a previous assessment of transition prediction based on the dual, nonparallel N -factor method in conjunction with linear parabolized stability equations (PSE) is extended to additional angles of attack to provide the first comprehensive assessment of transition models based on nonparallel disturbance amplification over the CRM-NLF. In general, the transition criterion based on the dual, nonparallel N-factor method with N TS = N CF = 6 is reasonably successful at correlating with the measured transition fronts at R eMAC = 15 million for all angles of attack investigated herein and provides additional validation of the improved predictions from the compressibility-corrected transition models.

CFD modeling↗

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 NTRS1985

Factorization and reduction methods for optimal control of distributed parameter systems

A Chandrasekhar-type factorization method is applied to the linear-quadratic optimal control problem for distributed parameter systems. An aeroelastic control problem is used as a model example to demonstrate that if computationally efficient algorithms, such as those of Chandrasekhar-type, are combined with the special structure often available to a particular problem, then an abstract approximation theory developed for distributed parameter control theory becomes a viable method of solution. A numerical scheme based on averaging approximations is applied to hereditary control problems. Numerical examples are given.

Burns, J. A.↗

NASA NTRS1988

Radiative transfer in rectangular enclosures - A discretized exchange factor solution

The discretized exchange factor method is used to analyze radiative exchange in a rectangular enclosure. The results compare excellently with those of other methods, especially the zonal method. Since the direct exchange factors are between nodal points no integration is necessary for evaluation of these factors. It is found that the present approach provides accurate results even when a small number of nodes is used.

Naraghi, M. H. N.↗

NASA NTRS1988

Explicit and implicit solution of the Navier-Stokes equations on a massively parallel computer

The design, implementation, and performance of a two-dimensional time-accurate Navier-Stokes solver for the CM2 supercomputer are described. The program uses a single processor for each grid point. Two different time-stepping methods have so far been implemented: an explicit third-order Runge-Kutta method and an implicit approximation-factorization method. The CM2 results are checked against those of a mature well-vectorized Cray 2 program, both for correctness and performance. The code is found to be correct, and the performance in some cases is up to several times that of the Cray 2.

Levit, Creon↗

NASA NTRS1986

Multigrid acceleration of the flux split Euler equations

Multigrid acceleration is applied to a flux-split algorithm for solving the Euler equations in two and three dimensions. The basic algorithm is an implicit spatially-split approximate factorization method. The stability of the scheme in comparison to other factorization is examined. Results are presented for two-dimensional airfoil flows and three-dimensional wing flows which demonstrate substantially improved convergence with the multigrid algorithm. An asymptotic spectral radius of 0.89 and 0.93 is attained for a 97 x 17 x 17 wing solution at subcritical and supercritical conditions, respectively.

Anderson, W. K.↗

NASA NTRS1985

Implicit flux-split schemes for the Euler equations

Recent progress in the development of implicit algorithms for the Euler equations using the flux-vector splitting method is described. Comparisons of the relative efficiency of relaxation and spatially-split approximately factored methods on a vector processor for two-dimensional flows are made. For transonic flows, the higher convergence rate per iteration of the Gauss-Seidel relaxation algorithms, which are only partially vectorizable, is amply compensated for by the faster computational rate per iteration of the approximately factored algorithm. For supersonic flows, the fully-upwind line-relaxation method is more efficient since the numerical domain of dependence is more closely matched to the physical domain of dependence. A hybrid three-dimensional algorithm using relaxation in one coordinate direction and approximate factorization in the cross-flow plane is developed and applied to a forebody shape at supersonic speeds and a swept, tapered wing at transonic speeds.

Thomas, J. L.↗

NASA NTRS1978

Verification of redundancy management design

Statistical method checks designs by simulating system operating conditions and adding error factors. Method has potential applicability to commercial and industrial situations where redundancy management system is used to detect and isolate failed components.

Gelderloos, H. C.↗

NASA NTRS1989

Projection methods for the numerical solution of Markov chain models

Projection methods for computing stationary probability distributions for Markov chain models are presented. A general projection method is a method which seeks an approximation from a subspace of small dimension to the original problem. Thus, the original matrix problem of size N is approximated by one of dimension m, typically much smaller than N. A particularly successful class of methods based on this principle is that of Krylov subspace methods which utilize subspaces of the form span(v,av,...,A(exp m-1)v). These methods are effective in solving linear systems and eigenvalue problems (Lanczos, Arnoldi,...) as well as nonlinear equations. They can be combined with more traditional iterative methods such as successive overrelaxation, symmetric successive overrelaxation, or with incomplete factorization methods to enhance convergence.

Saad, Youcef↗

NASA NTRS1992

Aerostructural safety factor criteria

The present modification of the conventional safety factor method for aircraft structures evaluation involves the expression of deterministic safety factors in probabilistic tolerance limit ratios; these are found to involve a total of three factors that control the interference of applied and resistive stress distributions. The deterministic expression is extended so that it may furnish a 'relative ultimate safety' index that encompasses all three distribution factors. Operational reliability is developed on the basis of the applied and the yield stress distribution interferences. Industry standards are suggested to be derivable from factor selections that are based on the consequences of failure.

Verderaime, V.↗

NASA NTRS1993

Temperature and pressure effects on capacitance probe cryogenic liquid level measurement accuracy

The inaccuracies of liquid nitrogen and liquid hydrogen level measurements by use of a coaxial capacitance probe were investigated as a function of fluid temperatures and pressures. Significant liquid level measurement errors were found to occur due to the changes in the fluids dielectric constants which develop over the operating temperature and pressure ranges of the cryogenic storage tanks. The level measurement inaccuracies can be reduced by using fluid dielectric correction factors based on measured fluid temperatures and pressures. The errors in the corrected liquid level measurements were estimated based on the reported calibration errors of the temperature and pressure measurement systems. Experimental liquid nitrogen (LN2) and liquid hydrogen (LH2) level measurements were obtained using the calibrated capacitance probe equations and also by the dielectric constant correction factor method. The liquid levels obtained by the capacitance probe for the two methods were compared with the liquid level estimated from the fluid temperature profiles. Results show that the dielectric constant corrected liquid levels agreed within 0.5 percent of the temperature profile estimated liquid level. The uncorrected dielectric constant capacitance liquid level measurements deviated from the temperature profile level by more than 5 percent. This paper identifies the magnitude of liquid level measurement error that can occur for LN2 and LH2 fluids due to temperature and pressure effects on the dielectric constants over the tank storage conditions from 5 to 40 psia. A method of reducing the level measurement errors by using dielectric constant correction factors based on fluid temperature and pressure measurements is derived. The improved accuracy by use of the correction factors is experimentally verified by comparing liquid levels derived from fluid temperature profiles.

Edwards, Lawrence G.↗

NASA NTRS1993

Stability theory and transition prediction applied to a general aviation fuselage

The linear stability of a fully three-dimensional boundary layer formed over a general aviation fuselage was investigated. The location of the onset of transition was estimated using the N-factor method. The results were compared with existing experimental data and indicate N-factors of approximately 8.5 on the side of the fuselage and 3.0 near the top. Considerable crossflow existed along the side of the body, which significantly affected the unstable modes present in the boundary layer. Fair agreement was found between the predicted frequency range of linear instability modes and available experimental data concerning the spectral content of the boundary layer.

Spall, R. E.↗

NASA NTRS1987

An implicit flux-split algorithm for the compressible Navier-Stokes equations

An implicit upwind scheme for the compressible Navier-Stokes equations is described and applied to the internal flow in a dual-throat nozzle. The method is second-order accurate spatially and naturally dissipative. A spatially-split approximate factorization method is used to obtain efficient steady-state solutions on the NASA Langley VPS-32 (CYBER 205) supercomputer.

Thomas, James L.↗

NASA NTRS1978

A reformulation of the Linear-Quadratic-Gaussian stochastic control problem for application to low thrust navigation analysis

The formulation of the classical Linear-Quadratic-Gaussian stochastic control problem as employed in low thrust navigation analysis is reviewed. A reformulation is then presented which eliminates a potentially unreliable matrix subtraction in the control calculations, improves the computational efficiency, and provides for a cleaner computational interface between the estimation and control processes. Lastly, the application of the U-D factorization method to the reformulated equations is examined with the objective of achieving a complete set of factored equations for the joint estimation and control problem.

Jacobson, R. A.↗

NASA NTRSDate not supplied

Aerodynamic Design Optimization for Natural Laminar Flow Airfoils

Natural laminar flow technology is a passive laminar flow control (LFC) strategy that seeks to delay the onset of boundary-layer transition (BLT) through shape optimization to reduce the drag of the aerodynamic vehicle. Adjoint-based design optimization for LFC is proposed in an integrated multidisciplinary framework, which includes the computational fluid dynamics (CFD), geometry and grid deformation, and linear stability analysis (LSA) for transition prediction. In particular, the BLT location is predicted using the dual N-factor method that is based on a linear stability theory (LST) eigenvalue problem. The dual N-factor criterion accounts for the amplification of planar Tollmien-Schlichting (TS) and stationary crossflow (CF) boundary-layer instabilities to predict the transition location in three-dimensional boundary-layer flows. The adjoint-based shape optimization procedure is based on an iteratively coupled CFD and LSA methodology to converge the transition location and flow solutions, as well as to calculate the sensitivities of the aerodynamic metrics of interest with respect to the flow and shape design parameters. The RAE 2822 airfoil at 0 and 30 degrees yaw angles, an angle of attack of 0.72 degrees, and subsonic conditions (M∞ = 0.19, Rec = 5.6 × 106 ) are used as baseline configurations for design optimization. The angle of attack and the vertical displacement of free-form-deformation control points are used as design variables to reduce the drag coefficient while reaching a specified lift coefficient. The optimized unswept airfoil designs achieve a 30% drag reduction accompanied by a downstream shift of the transition locations over both suction and pressure sides of the airfoil. The initial design iterations for the swept case also show a favorable trend in the drag reduction with transition delay over both sides.

Transition↗

NASA NTRS2010

Methods and compositions for regulating gene expression in plant cells

Novel chimeric plant promoter sequences are provided, together with plant gene expression cassettes comprising such sequences. In certain preferred embodiments, the chimeric plant promoters comprise the BoxII cis element and/or derivatives thereof. In addition, novel transcription factors are provided, together with nucleic acid sequences encoding such transcription factors and plant gene expression cassettes comprising such nucleic acid sequences. In certain preferred embodiments, the novel transcription factors comprise the acidic domain, or fragments thereof, of the RF2a transcription factor. Methods for using the chimeric plant promoter sequences and novel transcription factors in regulating the expression of at least one gene of interest are provided, together with transgenic plants comprising such chimeric plant promoter sequences and novel transcription factors.

Beachy, Roger N.↗

NASA NTRS1994

Computing Misalignments From Measured Contact Resistances

Misalignments of contacts in integrated circuits computed, and measured contact resistances corrected for effects of misalignments by use of method based on relatively simple mathematical model of measured contact resistance. Flange resistance of aligned contact multiplied by semiempirical factor. Method particularly useful in estimating effects of misalignments on four- and six-terminal (Kelvin-tap) contact-resistance measurements taken with L-shaped test structures.

Lieneweg, Udo↗

NASA NTRS1981

Forebody and base region real gas flow in severe planetary entry by a factored implicit numerical method. II - Equilibrium reactive gas

The factored-implicit, gas-dynamic algorithm has been adapted to the numerical simulation of equilibrium reactive flows. Changes required in the perfect gas version of the algorithm are developed, and the method of coupling gas-dynamic and chemistry variables is discussed. A flow-field solution that approximates a Jovian entry case was obtained by this method and compared with the same solution obtained by HYVIS, a computer program much used for the study of planetary entry. Comparison of surface pressure distribution and stagnation line shock-layer profiles indicates that the two solutions agree well.

Davy, W. C.↗