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NASA NTRS2007

Summary of the Third AIAA CFD Drag Prediction Workshop

The workshop focused on the prediction of both absolute and differential drag levels for wing-body and wing-al;one configurations of that are representative of transonic transport aircraft. The baseline DLR-F6 wing-body geometry, previously utilized in DPW-II, is also augmented with a side-body fairing to help reduce the complexity of the flow physics in the wing-body juncture region. In addition, two new wing-alone geometries have been developed for the DPW-II. Numerical calculations are performed using industry-relevant test cases that include lift-specific and fixed-alpha flight conditions, as well as full drag polars. Drag, lift, and pitching moment predictions from previous Reynolds-Averaged Navier-Stokes computational fluid Dynamics Methods are presented, focused on fully-turbulent flows. Solutions are performed on structured, unstructured, and hybrid grid systems. The structured grid sets include point-matched multi-block meshes and over-set grid systems. The unstructured and hybrid grid sets are comprised of tetrahedral, pyramid, and prismatic elements. Effort was made to provide a high-quality and parametrically consistent family of grids for each grid type about each configuration under study. The wing-body families are comprised of a coarse, medium, and fine grid, while the wing-alone families also include an extra-fine mesh. These mesh sequences are utilized to help determine how the provided flow solutions fair with respect to asymptotic grid convergence, and are used to estimate an absolute drag of each configuration.

Vassberg, John C.↗

NASA NTRS2008

Supersonic Combusting Jet Experiments for Code Development and Validation

Computational fluid dynamics (CFD) methods based on the Reynolds averaged Navier-Stokes (RANS) equations are extensively employed in the design of hypersonic airbreathing engines. A fundamental weakness in these methods is the accurate mathematical modeling of turbulence and turbulence-combustion interactions. This paper is one of a companion pair of papers which describe the use of the combined dual pump CARS and newly developed interferometric Rayleigh scattering optical system to acquire time-accurate turbulence and mixing data with which to aid calibration and verification of the current turbulence models. This test program consisted of a pilot laboratory-scale experiment used to develop the optical system and data acquisition techniques, and a significantly larger experiment to acquire the necessary turbulence data. The flow is an axially-symmetric, supersonic, combusting, free jet that provides good optical access, consisting of a central jet of hot "vitiated air" and a coflow jet of hydrogen or ethylene fuel. In this paper the development of both experiments is described. Facility and flow visualization data are presented for various types of flames, including the flames selected for detailed study with the CARS/Rayleigh optical techniques.

Cutler, Andrew D.↗

NASA NTRS2013

Computational Fluid Dynamics Uncertainty Analysis for Payload Fairing Spacecraft Environmental Control Systems

Spacecraft thermal protection systems are at risk of being damaged due to airflow produced from Environmental Control Systems. There are inherent uncertainties and errors associated with using Computational Fluid Dynamics to predict the airflow field around a spacecraft from the Environmental Control System. This proposal describes an approach to validate the uncertainty in using Computational Fluid Dynamics to predict airflow speeds around an encapsulated spacecraft. The research described here is absolutely cutting edge. Quantifying the uncertainty in analytical predictions is imperative to the success of any simulation-based product. The method could provide an alternative to traditional"validation by test only'' mentality. This method could be extended to other disciplines and has potential to provide uncertainty for any numerical simulation, thus lowering the cost of performing these verifications while increasing the confidence in those predictions. Spacecraft requirements can include a maximum airflow speed to protect delicate instruments during ground processing. Computationaf Fluid Dynamics can be used to veritY these requirements; however, the model must be validated by test data. The proposed research project includes the following three objectives and methods. Objective one is develop, model, and perform a Computational Fluid Dynamics analysis of three (3) generic, non-proprietary, environmental control systems and spacecraft configurations. Several commercially available solvers have the capability to model the turbulent, highly three-dimensional, incompressible flow regime. The proposed method uses FLUENT and OPEN FOAM. Objective two is to perform an uncertainty analysis of the Computational Fluid . . . Dynamics model using the methodology found in "Comprehensive Approach to Verification and Validation of Computational Fluid Dynamics Simulations". This method requires three separate grids and solutions, which quantify the error bars around Computational Fluid Dynamics predictions. The method accounts for all uncertainty terms from both numerical and input variables. Objective three is to compile a table of uncertainty parameters that could be used to estimate the error in a Computational Fluid Dynamics model of the Environmental Control System /spacecraft system. Previous studies have looked at the uncertainty in a Computational Fluid Dynamics model for a single output variable at a single point, for example the re-attachment length of a backward facing step. To date, the author is the only person to look at the uncertainty in the entire computational domain. For the flow regime being analyzed (turbulent, threedimensional, incompressible), the error at a single point can propagate into the solution both via flow physics and numerical methods. Calculating the uncertainty in using Computational Fluid Dynamics to accurately predict airflow speeds around encapsulated spacecraft in is imperative to the success of future missions.

Groves, Curtis E.↗

NASA NTRS1993

Flow of Supercritical Hydrogen in a Uniformly Heated Circular Tube

Turbulent flow of supercritical hydrogen through a uniformly heated circular tube has been investigated using numerical methods, for the range of 4 x 10(exp 5) less than Re less than 3 x 10(exp 6), 5 less than or equal to q(sub W) less than or equal to 10 MW/sq m, 30 less than or equal to T(sub in) less than or equal to 90 K, and 5 less than or equal to P(sub in) less than or equal to 15 MPa. The purpose is to validate a turbulence model and calculation method for the design of active cooling systems of hydrogen-fueled hypersonic aircraft, where the hydrogen fuel a used as coolant. The PHOENICS software package was used for the computations, which required special provision for evaluation of the thermophysical properties of the supercritical hydrogen, and a low Reynolds number form of the k-epsilon turbulence model. Pressure drop and heat transfer data were compared with experiment and existing correlations and good agreement was demonstrated. For the pressure range considered here a "thermal spike" was observed and shown to be due to the secondary peak in specific heat, rather than the primary peak.

Youn, B.↗

NASA NTRS1986

The structure of separated flow regions occurring near the leading edge of airfoils including transition

A semi-empirical method for predicting separation bubble characteristics was evaluated using low Reynolds number test data. On the basis of this data, several observations were made. First, a sizable growth in the momentum thickness can occur in the laminar portion of a separation bubble. This is in direct contrast to the theory and is apparently due to low Reynolds number effects. Secondly, the transition Reynolds number (R sub l sub 1) which governs the extent of a bubble's laminar region, was found to be much lower than that used in the method. At present, there does not seem to be any evidence supporting a single value for R sub l sub 1. Apparently, R sub l sub 1 is affected by the freestream disturbance environment, and airfoil's pressure distribution, and possibly the chord Reynolds number as well. Thirdly, the growth in momentum thickness over a bubble's turbulent region was predicted reasonably well by the method, provided that Roberts' suggested value for the mean dissipation coefficient was used. Finally, the present data does not substantiate the universality of the velocity profile at reattachment. However, measurement error may be responsible for this result.

Mueller, T. J.↗

NASA NTRS1991

The study of PDF turbulence models in combustion

In combustion computations, it is known that the predictions of chemical reaction rates are poor if conventional turbulence models are used. The probability density function (pdf) method seems to be the only alternative that uses local instantaneous values of the temperature, density, etc., in predicting chemical reaction rates, and thus is the only viable approach for more accurate turbulent combustion calculations. The fact that the pdf equation has a very large dimensionality renders finite difference schemes extremely demanding on computer memories and thus impractical. A logical alternative is the Monte Carlo scheme. Since CFD has a certain maturity as well as acceptance, it seems that the use of a combined CFD and Monte Carlo scheme is more beneficial. Therefore, a scheme is chosen that uses a conventional CFD flow solver in calculating the flow field properties such as velocity, pressure, etc., while the chemical reaction part is solved using a Monte Carlo scheme. The discharge of a heated turbulent plane jet into quiescent air was studied. Experimental data for this problem shows that when the temperature difference between the jet and the surrounding air is small, buoyancy effect can be neglected and the temperature can be treated as a passive scalar. The fact that jet flows have a self-similar solution lends convenience in the modeling study. Futhermore, the existence of experimental data for turbulent shear stress and temperature variance make the case ideal for the testing of pdf models wherein these values can be directly evaluated.

Hsu, Andrew T.↗

NASA NTRS1991

High-order ENO methods for the unsteady compressible Navier-Stokes equations

The adaptive stencil concepts of ENO (Essentially Non-Oscillatory) methods are applied to the laminar Navier-Stokes equations to yield a high-order, time-accurate algorithm with a shock-capturing capability. The method targets problems in the areas of nonlinear acoustics, compressible transition, and turbulence which, due to the presence of shocks or complex geometries, are not easily solved by spectral methods. The present approach has been implemented and tested for the full three-dimensional Navier-Stokes equations in a transformed curvilinear coordinate system. Validation results are presented for a variety of problems which verify the method's accuracy properties and shock capturing capabilities, as well as demonstrate its use as a direct simulation tool.

Atkins, H. L.↗

NASA NTRS1992

PDF turbulence modeling and DNS

The problem of time discontinuity (or jump condition) in the coalescence/dispersion (C/D) mixing model is addressed in probability density function (pdf). A C/D mixing model continuous in time is introduced. With the continuous mixing model, the process of chemical reaction can be fully coupled with mixing. In the case of homogeneous turbulence decay, the new model predicts a pdf very close to a Gaussian distribution, with finite higher moments also close to that of a Gaussian distribution. Results from the continuous mixing model are compared with both experimental data and numerical results from conventional C/D models. The effect of Coriolis forces on compressible homogeneous turbulence is studied using direct numerical simulation (DNS). The numerical method used in this study is an eight order compact difference scheme. Contrary to the conclusions reached by previous DNS studies on incompressible isotropic turbulence, the present results show that the Coriolis force increases the dissipation rate of turbulent kinetic energy, and that anisotropy develops as the Coriolis force increases. The Taylor-Proudman theory does apply since the derivatives in the direction of the rotation axis vanishes rapidly. A closer analysis reveals that the dissipation rate of the incompressible component of the turbulent kinetic energy indeed decreases with a higher rotation rate, consistent with incompressible flow simulations (Bardina), while the dissipation rate of the compressible part increases; the net gain is positive. Inertial waves are observed in the simulation results.

Hsu, A. T.↗

NASA NTRS1990

Development of Renormalization Group Analysis of Turbulence

The renormalization group (RG) procedure for nonlinear, dissipative systems is now quite standard, and its applications to the problem of hydrodynamic turbulence are becoming well known. In summary, the RG method isolates self similar behavior and provides a systematic procedure to describe scale invariant dynamics in terms of large scale variables only. The parameterization of the small scales in a self consistent manner has important implications for sub-grid modeling. This paper develops the homogeneous, isotropic turbulence and addresses the meaning and consequence of epsilon-expansion. The theory is then extended to include a weak mean flow and application of the RG method to a sequence of models is shown to converge to the Navier-Stokes equations.

L M Smith↗

NASA NTRS1984

Accuracy and directional sensitivity of the single-wire technique

Multi-orientation of a single-hot-wire is a novel way to measure the three time-mean velocities, the three turbulent normal stresses, and the three turbulent shear stresses. The present study focuses on the accuracy and directional sensitivity of the technique with respect to mean flow velocity orientation to the probe. Results demonstrate relative insensitivity, indicating that the method is a useful cost-effective tool for turbulent flows of unknown dominant flow direction.

Lilley, D. G.↗

NASA NTRS2010

Effect of Turbulence Modeling on an Excited Jet

The flow dynamics in a high-speed jet are dominated by unsteady turbulent flow structures in the plume. Jet excitation seeks to control these flow structures through the natural instabilities present in the initial shear layer of the jet. Understanding and optimizing the excitation input, for jet noise reduction or plume mixing enhancement, requires many trials that may be done experimentally or computationally at a significant cost savings. Numerical simulations, which model various parts of the unsteady dynamics to reduce the computational expense of the simulation, must adequately capture the unsteady flow dynamics in the excited jet for the results are to be used. Four CFD methods are considered for use in an excited jet problem, including two turbulence models with an Unsteady Reynolds Averaged Navier-Stokes (URANS) solver, one Large Eddy Simulation (LES) solver, and one URANS/LES hybrid method. Each method is used to simulate a simplified excited jet and the results are evaluated based on the flow data, computation time, and numerical stability. The knowledge gained about the effect of turbulence modeling and CFD methods from these basic simulations will guide and assist future three-dimensional (3-D) simulations that will be used to understand and optimize a realistic excited jet for a particular application.

Brown, Clifford A.↗

NASA NTRS1970

Optical probing of supersonic aerodynamic turbulence

Laser quasi-schlieren system and laser shadow-correlation system retrieve flow-related signals sufficient for computing accurate, reproducible correlation peaks. Statistical method for obtaining one-shot measurements of the decay history of turbulent structures in a stationary frame of reference is discussed.

Cikanek, H. A., Jr.↗

NASA NTRS1995

A pseudo-sound constitutive relationship for the dilatational covariances in compressible turbulence: An analytical theory

The mathematical consequences of a few simple scaling assumptions about the effects of compressibility are explored using a simple singular perturbation idea and the methods of statistical fluid mechanics. Representations for the pressure-dilation and dilatational dissipation covariances appearing in single-point moment closures for compressible turbulence are obtained. While the results are expressed in the context of a second-order statistical closure they provide some interesting and very clear physical metaphors for the effects of compressibility that have not been seen using more traditional linear stability methods. In the limit of homogeneous turbulence with quasi-normal large-scales the expressions derived are - in the low turbulent Mach number limit - asymptotically exact. The expressions obtained are functions of the rate of change of the turbulence energy, its correlation length scale, and the relative time scale of the cascade rate. The expressions for the dilatational covariances contain constants which have a precise and definite physical significance; they are related to various integrals of the longitudinal velocity correlation. The pressure-dilation covariance is found to be a nonequilibrium phenomena related to the time rate of change of the internal energy and the kinetic energy of the turbulence. Also of interest is the fact that the representation for the dilatational dissipation in turbulence, with or without shear, features a dependence on the Reynolds number. This article is a documentation of an analytical investigation of the implications of a pseudo-sound theory for the effects of compressibility.

Ristorcelli, J. R.↗

NASA NTRS2001

A Highly Accurate Technique for the Treatment of Flow Equations at the Polar Axis in Cylindrical Coordinates using Series Expansions

Numerical methods for solving the flow equations in cylindrical or spherical coordinates should be able to capture the behavior of the exact solution near the regions where the particular form of the governing equations is singular. In this work we focus on the treatment of these numerical singularities for finite-differences methods by reinterpreting the regularity conditions developed in the context of pseudo-spectral methods. A generally applicable numerical method for treating the singularities present at the polar axis, when nonaxisymmetric flows are solved in cylindrical, coordinates using highly accurate finite differences schemes (e.g., Pade schemes) on non-staggered grids, is presented. Governing equations for the flow at the polar axis are derived using series expansions near r=0. The only information needed to calculate the coefficients in these equations are the values of the flow variables and their radial derivatives at the previous iteration (or time) level. These derivatives, which are multi-valued at the polar axis, are calculated without dropping the accuracy of the numerical method using a mapping of the flow domain from (0,R)*(0,2pi) to (-R,R)*(0,pi), where R is the radius of the computational domain. This allows the radial derivatives to be evaluated using high-order differencing schemes (e.g., compact schemes) at points located on the polar axis. The proposed technique is illustrated by results from simulations of laminar-forced jets and turbulent compressible jets using large eddy simulation (LES) methods. In term of the general robustness of the numerical method and smoothness of the solution close to the polar axis, the present results compare very favorably to similar calculations in which the equations are solved in Cartesian coordinates at the polar axis, or in which the singularity is removed by employing a staggered mesh in the radial direction without a mesh point at r=0, following the method proposed recently by Mohseni and Colonius (1). Extension of the method described here for incompressible flows or for any other set of equations that are solved on a non-staggered mesh in cylindrical or spherical coordinates with finite-differences schemes of various level of accuracy is immediate.

Constantinescu, George S.↗

NASA NTRS2014

Dissertation Defense: Computational Fluid Dynamics Uncertainty Analysis for Payload Fairing Spacecraft Environmental Control Systems

Spacecraft thermal protection systems are at risk of being damaged due to airflow produced from Environmental Control Systems. There are inherent uncertainties and errors associated with using Computational Fluid Dynamics to predict the airflow field around a spacecraft from the Environmental Control System. This paper describes an approach to quantify the uncertainty in using Computational Fluid Dynamics to predict airflow speeds around an encapsulated spacecraft without the use of test data. Quantifying the uncertainty in analytical predictions is imperative to the success of any simulation-based product. The method could provide an alternative to traditional validation by test only mentality. This method could be extended to other disciplines and has potential to provide uncertainty for any numerical simulation, thus lowering the cost of performing these verifications while increasing the confidence in those predictions.Spacecraft requirements can include a maximum airflow speed to protect delicate instruments during ground processing. Computational Fluid Dynamics can be used to verify these requirements; however, the model must be validated by test data. This research includes the following three objectives and methods. Objective one is develop, model, and perform a Computational Fluid Dynamics analysis of three (3) generic, non-proprietary, environmental control systems and spacecraft configurations. Several commercially available and open source solvers have the capability to model the turbulent, highly three-dimensional, incompressible flow regime. The proposed method uses FLUENT, STARCCM+, and OPENFOAM. Objective two is to perform an uncertainty analysis of the Computational Fluid Dynamics model using the methodology found in Comprehensive Approach to Verification and Validation of Computational Fluid Dynamics Simulations. This method requires three separate grids and solutions, which quantify the error bars around Computational Fluid Dynamics predictions. The method accounts for all uncertainty terms from both numerical and input variables. Objective three is to compile a table of uncertainty parameters that could be used to estimate the error in a Computational Fluid Dynamics model of the Environmental Control System spacecraft system.Previous studies have looked at the uncertainty in a Computational Fluid Dynamics model for a single output variable at a single point, for example the re-attachment length of a backward facing step. For the flow regime being analyzed (turbulent, three-dimensional, incompressible), the error at a single point can propagate into the solution both via flow physics and numerical methods. Calculating the uncertainty in using Computational Fluid Dynamics to accurately predict airflow speeds around encapsulated spacecraft in is imperative to the success of future missions.

Fluid Dynamics↗

NASA NTRS2014

Dissertation Defense Computational Fluid Dynamics Uncertainty Analysis for Payload Fairing Spacecraft Environmental Control Systems

Spacecraft thermal protection systems are at risk of being damaged due to airflow produced from Environmental Control Systems. There are inherent uncertainties and errors associated with using Computational Fluid Dynamics to predict the airflow field around a spacecraft from the Environmental Control System. This paper describes an approach to quantify the uncertainty in using Computational Fluid Dynamics to predict airflow speeds around an encapsulated spacecraft without the use of test data. Quantifying the uncertainty in analytical predictions is imperative to the success of any simulation-based product. The method could provide an alternative to traditional "validation by test only" mentality. This method could be extended to other disciplines and has potential to provide uncertainty for any numerical simulation, thus lowering the cost of performing these verifications while increasing the confidence in those predictions. Spacecraft requirements can include a maximum airflow speed to protect delicate instruments during ground processing. Computational Fluid Dynamics can be used to verify these requirements; however, the model must be validated by test data. This research includes the following three objectives and methods. Objective one is develop, model, and perform a Computational Fluid Dynamics analysis of three (3) generic, non-proprietary, environmental control systems and spacecraft configurations. Several commercially available and open source solvers have the capability to model the turbulent, highly three-dimensional, incompressible flow regime. The proposed method uses FLUENT, STARCCM+, and OPENFOAM. Objective two is to perform an uncertainty analysis of the Computational Fluid Dynamics model using the methodology found in "Comprehensive Approach to Verification and Validation of Computational Fluid Dynamics Simulations". This method requires three separate grids and solutions, which quantify the error bars around Computational Fluid Dynamics predictions. The method accounts for all uncertainty terms from both numerical and input variables. Objective three is to compile a table of uncertainty parameters that could be used to estimate the error in a Computational Fluid Dynamics model of the Environmental Control System /spacecraft system. Previous studies have looked at the uncertainty in a Computational Fluid Dynamics model for a single output variable at a single point, for example the re-attachment length of a backward facing step. For the flow regime being analyzed (turbulent, three-dimensional, incompressible), the error at a single point can propagate into the solution both via flow physics and numerical methods. Calculating the uncertainty in using Computational Fluid Dynamics to accurately predict airflow speeds around encapsulated spacecraft in is imperative to the success of future missions.

CFD↗

NASA NTRS2004

Theory and Simulation of Real and Ideal Magnetohydrodynamic Turbulence

Incompressible, homogeneous magnetohydrodynamic (MHD) turbulence consists of fluctuating vorticity and magnetic fields, which are represented in terms of their Fourier coefficients. Here, a set of five Fourier spectral transform method numerical simulations of two-dimensional (2-D) MHD turbulence on a 512(sup 2) grid is described. Each simulation is a numerically realized dynamical system consisting of Fourier modes associated with wave vectors k, with integer components, such that k = |k| less than or equal to k(sub max). The simulation set consists of one ideal (non-dissipative) case and four real (dissipative) cases. All five runs had equivalent initial conditions. The dimensions of the dynamical systems associated with these cases are the numbers of independent real and imaginary parts of the Fourier modes. The ideal simulation has a dimension of 366104, while each real simulation has a dimension of 411712. The real runs vary in magnetic Prandtl number P(sub M), with P(sub M) is a member of {0.1, 0.25, 1, 4}. In the results presented here, all runs have been taken to a simulation time of t = 25. Although ideal and real Fourier spectra are quite different at high k, they are similar at low values of k. Their low k behavior indicates the existence of broken symmetry and coherent structure in real MHD turbulence, similar to what exists in ideal MHD turbulence. The value of PM strongly affects the ratio of kinetic to magnetic energy and energy dissipation (which is mostly ohmic). The relevance of these results to 3-D Navier-Stokes and MHD turbulence is discussed.

Shebalin, John V.↗

NASA NTRS1974

Acoustic scattering from a turbulent vortex

With the aid of the Born approximation, the time autocorrelation and power spectral density are calculated for the received acoustic signal scattered from velocity fluctuations in a turbulent aircraft trailing vortex. The turbulence is required to be globally stationary, but only locally homogeneous. The treatment includes the effects of spectral broadening due to convection of the scattering eddies by a spatially varying mean flow and by macroeddies. The 3 db bandwidth of the received signal is related to the scattering angle and the core Mach number of the vortex. A primary feature of the analysis is that it provides a method for inferring the radial intensity distribution of turbulence in a vortex. The analysis technique is also applicable to scattering from other turbulent flows where significant variations of turbulence level occur over distances on the order of the macroeddy size.

Ramsey, V. W.↗