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NASA NTRS1992

An analytical approach to grid sensitivity analysis

Sensitivity analysis in Computational Fluid Dynamics with emphasis on grids and surface parameterization is described. An interactive algebraic grid-generation technique is employed to generate C-type grids around NACA four-digit wing sections. An analytical procedure is developed for calculating grid sensitivity with respect to design parameters of a wing section. A comparison of the sensitivity with that obtained using a finite-difference approach is made. Grid sensitivity with respect to grid parameters, such as grid-stretching coefficients, are also investigated. Using the resultant grid sensitivity, aerodynamic sensitivity is obtained using the compressible two-dimensional thin-layer Navier-Stokes equations.

Sadrehaghighi, Ideen↗

NASA NTRS1992

A numerical study of the effects of geometry on the performance of a supersonic combustor

A numerical study is conducted to investigate the effects of two combustor scale parameters, the expansion angle and the length of the constant area combustor section, on the mixing and combustion within a supersonic combustor. This study uses the SPARK 3D Navier-Stokes code. Turbulence is modeled utilizing an algebraic eddy viscosity model and the chemical mechanism is modeled with a 7-reaction, 7-species finite-rate chemistry model. The calculations show that, even at the relatively low flight Mach numbers (5-7) associated with the conditions examined, the chemical constituents are far from equilibrium, and therefore that kinetics effects are important.

Eklund, Dean R.↗

NASA NTRS1996

High Reynolds number analysis of flat plate and separated afterbody flow using non-linear turbulence models

The ability of the three-dimensional Navier-Stokes method, PAB3D, to simulate the effect of Reynolds number variation using non-linear explicit algebraic Reynolds stress turbulence modeling was assessed. Subsonic flat plate boundary-layer flow parameters such as normalized velocity distributions, local and average skin friction, and shape factor were compared with DNS calculations and classical theory at various local Reynolds numbers up to 180 million. Additionally, surface pressure coefficient distributions and integrated drag predictions on an axisymmetric nozzle afterbody were compared with experimental data from 10 to 130 million Reynolds number. The high Reynolds data was obtained from the NASA Langley 0.3m Transonic Cryogenic Tunnel. There was generally good agreement of surface static pressure coefficients between the CFD and measurement. The change in pressure coefficient distributions with varying Reynolds number was similar to the experimental data trends, though slightly over-predicting the effect. The computational sensitivity of viscous modeling and turbulence modeling are shown. Integrated afterbody pressure drag was typically slightly lower than the experimental data. The change in afterbody pressure drag with Reynolds number was small both experimentally and computationally, even though the shape of the distribution was somewhat modified with Reynolds number.

Carlson, John R.↗

NASA NTRS1978

Prediction of unsteady separated flows on oscillating airfoils

Techniques for calculating high Reynolds number flow around an airfoil undergoing dynamic stall are reviewed. Emphasis is placed on predicting the values of lift, drag, and pitching moments. Methods discussed include: the discrete potential vortex method; thin boundary layer method; strong interaction between inviscid and viscous flows; and solutions to the Navier-Stokes equations. Empirical methods for estimating unsteady airloads on oscillating airfoils are also described. These methods correlate force and moment data from wind tunnel tests to indicate the effects of various parameters, such as airfoil shape, Mach number, amplitude and frequency of sinosoidal oscillations, mean angle, and type of motion.

Mccroskey, W. J.↗

NASA NTRS1993

Prediction of engine and near-field plume reacting flows in low-thrust chemical rockets

A computational model is employed to study the reacting flow within the engine and near-field plumes of several small gaseous hydrogen-oxygen thrusters. The model solves the full Navier-Stokes equations coupled with species diffusion equations for a hydrogen-oxygen reaction kinetics system and includes a two-equation q-omega model for turbulence. Predictions of global performance parameters and localized flowfield variables are compared with experimental data in order to assess the accuracy with which these flowfields are modeled and to identify aspects of the model which require improvement. Predicted axial and radial velocities 3 mm downstream of the exit plane show reasonable agreement with the measurements. The predicted peak in axial velocity in the hydrogen film coolant along the nozzle wall shows the best agreement; however, predictions within the core region are roughly 15 percent below measured values, indicating an underprediction of the extent to which the hydrogen diffuses and mixes with the core flow. There is evidence that this is due to three-dimensional mixing processes which are not included in the axisymmetric model.

Weiss, Jonathan M.↗

NASA NTRS1999

Acoustic Pyrometry Applied to Gas Turbines and Jet Engines

Internal gas temperature is one of the most fundamental parameters related to engine efficiency and emissions production. The most common methods for measuring gas temperature are physical probes, such as thermocouples and thermistors, and optical methods, such as Coherent Anti Stokes Raman Spectroscopy (CARS) or Rayleigh scattering. Probes are relatively easy to use, but they are intrusive, their output must be corrected for errors due to radiation and conduction, and their upper use temperature is limited. Optical methods are nonintrusive, and they measure some intrinsic property of the gas that is directly related to its temperature (e.g., lifetime or the ratio of line strengths). However, optical methods are usually difficult to use, and optical access is not always available. Lately, acoustic techniques have been receiving some interest as a way to overcome these limitations.

Fralick, Gustave C.↗

NASA NTRSDate not supplied

Adjoint-based Sensitivities of Flutter Predictions based on the Linearized Frequency-domain Approach

Flutter is a critical factor in designing and certifying aircraft. The linearized frequency-domain method offers a lower cost alternative to time-marching computational fluid dynamics for high-fidelity flutter analysis. In this work, adjoint-based sensitivities are added to a flutter analysis based on the linearized frequency-domain method to efficiently compute derivatives of flutter cost functions with respect to design variables or uncertain parameters. The derivation of the adjoint equations, which involve complications such as derivatives of a nonlinear generalized eigenvalue problem with complex-valued inputs and derivatives of the linearized Navier-Stokes equations, is provided. The implemented adjoint terms and derivatives are verified before demonstrating the approach for derivatives of flutter dynamic pressure with respect to Mach number for the AGARD 445.6 wing.

Aeroelasticity↗

NASA NTRS2005

The Apollo Capsule Optimization for Improved Stability and Computational/Experimental Data Comparisons

Numerical optimization was employed on the Apollo Command Module to modify its external shape. The Apollo Command Module (CM) that was used on all NASA human space flights during the Apollo Space Program is stable and trimmed in an apex forward (alpha of approximately 40 to 80 degrees) position. This poses a safety risk if the CM separates from the launch tower during abort. Optimization was employed on the Apollo CM to remedy the undesirable stability characteristics of the configuration. Geometric shape changes were limited to axisymmetric modifications that altered the radius of the apex (R(sub A)), base radius (R(sub O)), corner radius (R(sub C)), and the cone half angle (theta), while the maximum diameter of the CM was held constant. The results of multipoint optimization on the CM indicated that the cross-range performance can be improved while maintaining robust apex-aft stability with a single trim point. Navier-Stokes computations were performed on the baseline and optimized configurations and confirmed the Euler-based optimization results. Euler Analysis of ten alternative CM vehicles with different values of the above four parameters are compared with the published experimental results of numerous wind tunnel tests during the late 1960's. These comparisons cover a wide Mach number range and a full 180-degree pitch range and show that the Euler methods are capable of fairly accurate force and moment computations and can separate the vehicle characteristics of these ten alternative configurations.

Cliff, Susan E.↗

NASA NTRS2021

Assessment and Improvement of RANS-based Transition Models based on Experimental Data of the Common Research Model with Natural Laminar Flow

Transition models based on auxiliary transport equations augmenting the Reynolds-averaged Navier-Stokes (RANS) framework often rely upon the correlations that were derived from a limited number of low-speed experiments and do not account for all of the transition mechanisms and/or their variation with the significant flow parameters. Available data from a recent experiment in the National Transonic Facility at the NASA Langley Research Center are used to assess the current transition modeling capability in NASA's OVERFLOW 2.2o code for a swept wing configuration at transonic cruise conditions. Specifically, the OVERFLOW solutions are used together with detailed stability analysis of the boundary layer flow over the new Common Research Model with Natural Laminar Flow (CRM-NLF) to evaluate the accuracy and the robustness of the transport-equation-based transition models, with the goal of proposing improvements that would help to strengthen the physical basis of these models for the important class of flows involving the combined effects of crossflow and flow compressibility. Results highlight the significant underprediction of the laminar flow extent within the inboard region of the wing, wherein the onset of transition may be attributed to a gradual amplification of Tollmien-Schlichting instabilities.

Boundary layer transition↗

NASA NTRS1985

Higher-order derivative correlations and the alignment of small-scale structures in isotropic numerical turbulence

The classical approach to the investigation of small-scale intermittency in turbulence is based on the higher-order derivative correlations such as skewness and flatness factors. In the study of the small scales, numerial simulations can provide more detail than experiments. In the present paper, a variety of velocity- and scalar-derivative correlations are calculated over a range of Reynolds numbers. Particular attention is given to third- and fourth-order correlations, taking into account also some fifth- and sixth-order correlations to allow comparisons with the phenomenological models. The governing equations are the incompresssible Navier-Stokes equation for the velocity and transport equation for a passive scalar. Two numerical codes are used for the simulations presented. Attention is given to details regarding the numerical method used, forcing, simulation parameters, spectra and skewnesses, and graphics.

Kerr, R. M.↗

NASA NTRS1993

Improved Algorithm Computes Incompressible Flow

Algorithm numerically integrates Navier-Stokes equations of time-dependent or steady flow of incompressible, viscous fluid. Simulates realistic three-dimensional flows bounded by stationary or moving surface(s) of complicated shape(s). Only two arbitrary parameters specified by user. Algorithm described in "Numerical Simulation Of Flow Through An Artificial Heart" (ARC-12478). Algorithm tested by application to number of steady and unsteady flows, including flow in artificial heart discussed in noted prior article.

Rogers, Stuart E.↗

NASA NTRS1980

Analytical and design techniques for drag reduction studies on wavy surfaces

Numerical models for two dimensional turbulent boundary layers over wavy surfaces were investigated. Computations for wavy wall boundary layers indicate possibilities of overall drag reduction in a parameter range of the geometry of the wall. The correction technique using integral methods for analyzing arbitrary surfaces was found to be unsuitable for some cases of interest in drag reduction; a Navier-Stokes solver for wavy walls was built to test these problems. Test results of the Navier-Stokes solver indicate that the solution techniques are accurate enough to handle complex geometries and steep variations in fluid properties.

Balasubramanian, R.↗

NASA NTRS1989

A least-squares finite element method for incompressible Navier-Stokes problems

A least-squares finite element method, based on the velocity-pressure-vorticity formulation, is developed for solving steady incompressible Navier-Stokes problems. This method leads to a minimization problem rather than to a saddle-point problem by the classic mixed method, and can thus accommodate equal-order interpolations. This method has no parameter to tune. The associated algebraic system is symmetric, and positive definite. Numerical results for the cavity flow at Reynolds number up to 10,000 and the backward-facing step flow at Reynolds number up to 900 are presented.

Jiang, Bo-Nan↗

NASA NTRS1992

A least-squares finite element method for incompressible Navier-Stokes problems

A least-squares finite element method, based on the velocity-pressure-vorticity formulation, is developed for solving steady incompressible Navier-Stokes problems. This method leads to a minimization problem rather than to a saddle-point problem by the classic mixed method and can thus accommodate equal-order interpolations. This method has no parameter to tune. The associated algebraic system is symmetric, and positive definite. Numerical results for the cavity flow at Reynolds number up to 10,000 and the backward-facing step flow at Reynolds number up to 900 are presented.

Jiang, Bo-Nan↗

NASA NTRS2003

Transient Interfacial Phenomena in Miscible Polymer Systems (TIPMPS)

Almost one hundred years ago Korteweg published a theory of how stresses could be induced in miscible fluids by concentration gradients, causing phenomena that would appear to be the same as with immiscible fluids. Miscible fluids could manifest a transient or effective interfacial tension (EIT). To this day, there has been no definitive experiment to confirm Korteweg's model but numerous fascinating and suggestive experiments have been reported. The goal of TIPMPS is to answer the question: Can concentration and temperature gradients in miscible materials induce stresses that cause convection? Many polymer processes involving miscible monomer and polymer systems could be affected by fluid flow and so this work could help understand miscible polymer processing, not only in microgravity, but also on earth. Demonstrating the existence of this phenomenon in miscible fluids will open up a new area of study for materials science. The science objectives of TIPMPS are: (1) Determine if convection can be induced by variation of the width of a miscible interface; (2) Determine if convection can be induced by variation of temperature along a miscible interface; (3) Determine if convection can be induced by variation of conversion along a miscible interface An interface between two miscible fluids can best be created via a spatially-selective photopolymerization of dodecyl acrylate with a photoinitiator, which allows the creation of precise and accurate concentration gradients between polymer and monomer. Optical techniques will be used to measure the refractive index variation caused by the resultant temperature and concentration fields. The viscosity of the polymer will be measured from the increase in the fluorescence of pyrene. Because the large concentration and temperature gradients cause buoyancy-driven convection that prevents the observation of the predicted flows, the experiment must be done in microgravity. In this report, we will consider our efforts to estimate the square gradient parameter, k, and our use of the estimates in modeling of the planned TIPMPS experiments. We developed a model consisting of the heat and diffusion equations with convective terms and of the Navier-Stokes equations with an additional volume force written in the form of the Korteweg stresses arising from nonlocal interaction in the fluid. The fluid's viscosity dependence on polymer conversion and temperature was taken from measurements of poly(dodecyl acrylate). Numerical modeling demonstrated that significant flows would arise for conditions corresponding to the planned experiments.

Pojman, John A.↗

NASA NTRS1985

Application of a viscous-inviscid interaction method to predict transonic separated flows

A viscous-inviscid interaction numerical procedure is used to predict turbulent transonic separated flows over axisymmetric bodies. The viscous flow solutions are obtained by solving the boundary-layer equations inversely in a coupled manner by a finite-difference scheme; the inviscid flow is determined by a finite-difference solution to the full-potential equation in conservative form. Parameters affecting the convergence rate of the interaction procedure are discussed. The predictions of a new turbulence model proposed by Johnson and King are compared with experimental data and numerical solutions to the Navier-Stokes equations for flows with large regions of separation.

Lee, D. S.↗

NASA NTRS1989

Solution of the incompressible Navier-Stokes equations using artificial compressibility methods

A modified artificial compressibility formulation is derived from a preconditioned low Mach number compressible formulation, and these two methods are compared on a two-dimensional laminar leading edge flow using a LBI/ADI solution algorithm. The two methods are essentially equivalent with appropriate preconditioning parameters and have the same convergence rates and efficiency, giving 4 orders of residual reduction in about 75 iterations with a vectorized CRAY-XMP run time of 20 seconds for 3000 grid points.

Briley, W. R.↗

NASA NTRS1991

Transonic swirling nozzle flow

A numerical model of viscous transonic swirling flow in axisymmetric nozzles is developed. MacCormack's implicit Gauss-Seidel method is applied to the thin-layer Navier-Stokes equations in transformed coordinates. Numerical results are compared with experimental data to validate the method. The effect of swirl and viscosity on nozzle performance are demonstrated by examining wall pressures, Mach contours, and integral parameters.

Keith, Theo G., Jr.↗