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NASA NTRS1995

Euler/Navier-Stokes flow computations on flexible configurations for stability analysis

Longitudinal dynamic stability derivatives required for design of aircraft are computed by using the state-of-the-art numerical methods for wing-body configurations. The flow is modeled using the Euler/Navier-Stokes equations with turbulence models and solved using an efficient finite-difference scheme suitable for patched structured grids. Computations are made at a flow regime that is beyond the limits of the current linear methods mostly used for computing stability derivatives. Flow conditions include shockwaves and viscous dominated vortical flows. Effect of Mach number and angle-of-attack on stability derivatives are demonstrated for a typical wing-body configuration. For the same configuration the effects of wing flexibility on the magnitude and phase angles of stability derivatives are also demonstrated.

Guruswamy, G.↗

NASA NTRS1995

Euler/Navier-Stokes Flow Computations on Flexible Configurations for Stability Analysis

Abstract Longitudinal dynamic stability derivatives required for design of aircraft are computed by using the state-of-the-art numerical methods for wing-body configurations. The flow is modeled using the Euler/Navier-Stokes equations with turbulence models and solved using an efficient finite-difference scheme suitable for patched structured grids. Computations are made at a flow regime that is beyond the limits of the current linear methods mostly used for computing stability derivatives. Flow conditions include shock-waves and viscous dominated vortical flows. Effect of Mach number and angle-of-attack on stability derivatives are demonstrated for a typical wing-body configuration. For the same configuration the effects of wing flexibility on the magnitude and phase angles of stability derivatives are also demonstrated.

Guruswamy, Guru P.↗

NASA NTRSDate not supplied

An Improved Approach to the Predictability & Reliability of the Onset of Turbulence With Shocks

The construction of numerical schemes for (a) stable and accurate simulation of turbulence with strong shocks, and for (b) obtaining correct propagation speed of discontinuities in the presence of stiff source terms share one important ingredient – minimization of numerical dissipation while maintaining numerical stability. The dual requirements to achieve both numerical stability and minimal numerical dissipation are often conflicting since existing shock capturing schemes were designed mainly to be robust for rapidly developed turbulence-free flows and for shock waves without stiff source term. For the past two decades, Yee and collaborators have focused on an improved understanding of the nonlinear behavior of different high order shock-capturing methods. It was found that even very high order methods without proper nonlinear stability and numerical dissipation control can either numerically smear the onset of turbulence due to excess numerical dissipation, or induce (onset) numerical turbulence that is not physical turbulence due to lack of proper numerical dissipation to improve nonlinear stability for long time integration. Our approach is to combine (I) and (II) below for obtaining the physically correct onset of turbulence with shocks, including problems with stiff source terms: (I) Nonlinear dynamics is utilized to complement the traditional linearized stability theory (Yee & Sweby, Yee et al., Griffiths et al., Lafon & Yee, Yee, Wang et al., Kotov et al. 1990- 2015) in order to (i) Minimize numerically induced false transition to turbulence, (ii) Minimize numerical instability due to long time integration of turbulent flows, (iii) Minimize numerically induced standing wave solutions, and (iv) Minimize wrong propagation of speed of discontinuities due to the presence of stiff source terms. (II) Our recently developed physical preserving (structural preserving) high order methods with improved nonlinear stability & accuracy that are essential in minimizing spurious numerics are used.

HECC↗

NASA NTRS1987

Study of pickup of cometary ions in turbulent solar winds

The influence of moderately strong magnetic disturbances on the ion pickup process near a comet is studied by a test-particle method. The research is motivated by recent observations with ICE and Giotto at Giacobini-Zinner and Halley. In this numerical study, the intrinsic hydromagnetic turbulence is modelled based on the Giotto and ICE data. The time evolution of the distribution function of the newborn ions is investigated. It is found that, when the level of the intrinsic turbulence is sufficiently high, the pickup ions can form a shell distribution function rapidly. The typical time scale for such a process is of the order of a couple of ion gyroperiods. On the other hand, if the turbulence is not strong, the pickup ions usually form an incomplete shell in the initial stage. The results seem to be consistent with available observations.

Wu, C. S.↗

NASA NTRS1995

Analytical and phenomenological studies of rotating turbulence

A framework, which combines mathematical analysis, closure theory, and phenomenological treatment, is developed to study the spectral transfer process and reduction of dimensionality in turbulent flows that are subject to rotation. First, we outline a mathematical procedure that is particularly appropriate for problems with two disparate time scales. The approach which is based on the Green's method leads to the Poincare velocity variables and the Poincare transformation when applied to rotating turbulence. The effects of the rotation are now reflected in the modifications to the convolution of a nonlinear term. The Poincare transformed equations are used to obtain a time-dependent analog of the Taylor-Proudman theorem valid in the asymptotic limit when the non-dimensional parameter mu is identical to Omega(t) approaches infinity (Omega is the rotation rate and t is the time). The 'split' of the energy transfer in both direct and inverse directions is established. Secondly, we apply the Eddy-Damped-Quasinormal-Markovian (EDQNM) closure to the Poincare transformed Euler/Navier-Stokes equations. This closure leads to expressions for the spectral energy transfer. In particular, an unique triple velocity decorrelation time is derived with an explicit dependence on the rotation rate. This provides an important input for applying the phenomenological treatment of Zhou. In order to characterize the relative strength of rotation, another non-dimensional number, a spectral Rossby number, which is defined as the ratio of rotation and turbulence time scales, is introduced. Finally, the energy spectrum and the spectral eddy viscosity are deduced.

Mahalov, Alex↗

NASA NTRS1972

Analytical and experimental investigation of circulation control by means of a turbulent Coanda jet

An analytical and experimental investigation of circulation control on a circular cylinder by means of tangential blowing (Coanda effect) is presented. The analytical method developed has also been used to estimate the blowing coefficients required for achieving potential flow on airfoils with flaps. The analysis is presented for conditions for which the flow in the boundary layer ahead of the jet exit is turbulent. The turbulent boundary layer and the jet layer on the upper surface, and the turbulent boundary layer on the lower surface are computed by a multi-strip integral method. The region of integration is between the correponding transition and separation points on each surface. Longitudinal curvature effects, which give rise to a radial pressure gradient across the jet layer and to an additional adverse tangential pressure gradient just upstream of the separation point, are included in the jet layer analysis in an approximate manner. The longitudinal curvature effect is found to have a pronounced influence on the separation of the jet layer.

Levinsky, E. S.↗

NASA NTRS2010

Analysis of Instabilities in Non-Axisymmetric Hypersonic Boundary Layers Over Cones

Hypersonic flows over circular cones constitute one of the most important generic configurations for fundamental aerodynamic and aerothermodynamic studies. In this paper, numerical computations are carried out for Mach 6 flows over a 7-degree half-angle cone with two different flow incidence angles and a compression cone with a large concave curvature. Instability wave and transition-related flow physics are investigated using a series of advanced stability methods ranging from conventional linear stability theory (LST) and a higher-fidelity linear and nonlinear parabolized stability equations (PSE), to the 2D eigenvalue analysis based on partial differential equations. Computed N factor distribution pertinent to various instability mechanisms over the cone surface provides initial assessments of possible transition fronts and a guide to corresponding disturbance characteristics such as frequency and azimuthal wave numbers. It is also shown that strong secondary instability that eventually leads to transition to turbulence can be simulated very efficiently using a combination of advanced stability methods described above.

Li, Fei↗

NASA NTRS1987

Modeling and calculation of turbulent transport in free-shear flows

In this work the applicability of the combined bulk convection and gradient transport hypotheses for modeling turbulent diffusion is investigated. The resulting model equation, namely the one-equation model, is solved for free-shear flows by an implicit finite-difference method. Results indicate that significant improvements over previous models can be achieved with this new formulation of turbulent diffusion for both heat and momentum transport.

Biringen, S.↗

NASA NTRS2009

MHD Modeling of the Solar Wind with Turbulence Transport and Heating

We have developed a magnetohydrodynamic model that describes the global axisymmetric steady-state structure of the solar wind near solar minimum with account for transport of small-scale turbulence associated heating. The Reynolds-averaged mass, momentum, induction, and energy equations for the large-scale solar wind flow are solved simultaneously with the turbulence transport equations in the region from 0.3 to 100 AU. The large-scale equations include subgrid-scale terms due to turbulence and the turbulence (small-scale) equations describe the effects of transport and (phenomenologically) dissipation of the MHD turbulence based on a few statistical parameters (turbulence energy, normalized cross-helicity, and correlation scale). The coupled set of equations is integrated numerically for a source dipole field on the Sun by a time-relaxation method in the corotating frame of reference. We present results on the plasma, magnetic field, and turbulence distributions throughout the heliosphere and on the role of the turbulence in the large-scale structure and temperature distribution in the solar wind.

Goldstein, M. L.↗

NASA NTRS2000

A Method for Calculating Transient Surface Temperatures and Surface Heating Rates for High-Speed Aircraft

This report describes a method that can calculate transient aerodynamic heating and transient surface temperatures at supersonic and hypersonic speeds. This method can rapidly calculate temperature and heating rate time-histories for complete flight trajectories. Semi-empirical theories are used to calculate laminar and turbulent heat transfer coefficients and a procedure for estimating boundary-layer transition is included. Results from this method are compared with flight data from the X-15 research vehicle, YF-12 airplane, and the Space Shuttle Orbiter. These comparisons show that the calculated values are in good agreement with the measured flight data.

Quinn, Robert D.↗

NASA NTRS2020

Recommendations for Using Noise Monitors to Estimate Noise Exposure During X-59 Community Tests

A low fidelity simulation approach is used to explore how to place and use noise monitors during X-59 QueSST community tests, where people’s annoyance to the noise produced by the X-59 aircraft will be gathered. Several recommendations are provided including: 1) the desired number of sparsely spaced noise monitor sites within the survey area, 2) whether to group and average measurements across multiple noise monitors located at a site, 3) what spacing should be used if grouped noise monitors are used, 4) an approach to mitigate ambient noise contamination at the measurement sites, 5) a method to combine empirical and predicted dose estimates to provide a single dose estimate for respondents, and 6) assessing how changes in turbulence intensity and array configuration affect dose uncertainty. To make these recommendations, the error that is expected when fitting contrived, smoothly varying sonic boom “reference exposure surfaces” is studied when a spatially sparse and scattered set of samples is used as responses for the fit. The reference exposure surfaces mimic the sonic boom exposure at ground level that might be expected in the X-59 survey area in the absence of atmospheric turbulence, ambient noise, and other localized effects. The spatial extent of these surfaces varies and is representative of the different survey area sizes that might be expected during future X-59 community overflight tests. These contrived reference surfaces are sampled, and those reference samples are then perturbed to mimic atmospheric turbulence, ambient noise and other localized effects that might affect noise monitor measurements within overflown communities. Two different surface fitting methods are investigated when fitting these perturbed samples to approximate the reference surface. The first method uses interpolation between the perturbed data at the scattered sites to compute the fit. The second method fits a polynomial surface model to the perturbed data using ordinary least squares regression analysis. For both fitting methods, the root mean square fit error is computed from the pointwise difference between the fit surface and the reference surface as the count and configuration of the sites is varied while also averaging the error across many different realizations of both the smooth variation of the reference exposure surface and the random, localized perturbations at the sample sites. Different site configurations are compared using this error statistic to make the recommendations noted above. Additionally, the two fitting approaches (interpolation vs linear regression) are compared based on the fit error observed in these simulations. These analyses, comparisons, and recommendations should inform future decisions on the noise monitor placement and the methods used to analyze the noise monitor data that is collected during X-59 community overflights.

sonic boom↗

NASA NTRS2025

PSE-Based Aerodynamic Flow Transition Prediction Using Automated Unstructured CFD Integration

Accurate, robust, and efficient prediction of transition in viscous flows is a significant challenge in computational fluid dynamics. We present a coupled, high-fidelity, iterative approach that leverages the FUN3D flow solver and the LASTRAC stability code to predict transition in low-disturbance environments, initiated by the linear growth of boundary-layer instability modes. Our method integrates the ability of FUN3D to compute mixed laminar-transitional-turbulent mean flows via transition-sensitized Reynolds-Averaged Navier-Stokes equations with the ability of LASTRAC to perform linear stability analysis, all within an automated framework that requires no intermediate user involvement. Unlike conventional frameworks that rely on classical stability theory or reduced-order metamodels, our approach employs the parabolized stability equations to provide more accurate and reliable estimates of disturbance growth for multiple instability mechanisms, including Tollmien-Schlichting, Kelvin-Helmholtz, and crossflow modes. By accounting for the effects of mean-flow nonparallelism as well as the surface curvature, this approach lays the foundation for improved N-factor correlations for transition onset prediction in a broad class of flows. We apply this method to three distinct flow configurations: 1) flow over a zero-pressure-gradient flat plate, 2) the NLF-0416 airfoil with both natural and separation-induced transitions, and 3) a 6:1 prolate spheroid, where transition is primarily driven by crossflow instability. For the two-dimensional cases, a formulated intermittency distribution is used to model the transition zone in between the laminar and fully turbulent flows. The results include comparisons with experimental measurements, similar numerical approaches, and transport-equations-based models, demonstrating good agreement in surface pressure coefficients, transition onset locations, and skin-friction coefficients for all three configurations. Besides contributing a couple of new insights into boundary-layer transition in these canonical cases, this study provides a powerful tool for transition modeling in both research and design applications in aerodynamics.

Transition Prediction↗

NASA NTRSDate not supplied

Effect of Flight on the Noise from Turbulent Jets in the Generalized Acoustic Analogy

This presents an extension of a noise prediction method for static jets based on the Generalized Acoustic Analogy to include a non-zero ambient stream to simulate the effects of flight. Extended formulae for the propagator functions, source terms and the far-field acoustic spectrum are derived. The formulations of the equation and the boundary conditions for numerical solution of the scalar adjoint Green’s function in the presence of a non-zero ambient stream are also given. Wherever possible, the corresponding equations in the original papers for the static case and their extensions to include a flight stream are identified. The extended formulation is implemented into an existing code and used to make predictions of the effect of the flight stream on the observed far-field noise for a series of subsonic, unheated, axisymmetric jets over a range of jet-exit and free-stream velocities using Reynolds-averaged Navier-Stokes flow solutions as input. The predictions are compared with data from experiments conducted at NASA Glenn Research Center which extend a fundamental jet noise database to include a flight stream of various speeds. Descriptions of the experimental setup, data acquisition, post-processing and corrections applied to account for the external shear-layer are given. It is shown that the acoustic analogy-based method can provide reasonably good predictions of the impact of an external flight stream on the spectral characteristics of noise from unheated round jets.

Jet noise↗

NASA NTRS1993

A time-accurate finite volume method valid at all flow velocities

A finite volume method to solve the Navier-Stokes equations at all flow velocities (e.g., incompressible, subsonic, transonic, supersonic and hypersonic flows) is presented. The numerical method is based on a finite volume method that incorporates a pressure-staggered mesh and an incremental pressure equation for the conservation of mass. Comparison of three generally accepted time-advancing schemes, i.e., Simplified Marker-and-Cell (SMAC), Pressure-Implicit-Splitting of Operators (PISO), and Iterative-Time-Advancing (ITA) scheme, are made by solving a lid-driven polar cavity flow and self-sustained oscillatory flows over circular and square cylinders. Calculated results show that the ITA is the most stable numerically and yields the most accurate results. The SMAC is the most efficient computationally and is as stable as the ITA. It is shown that the PISO is the most weakly convergent and it exhibits an undesirable strong dependence on the time-step size. The degenerated numerical results obtained using the PISO are attributed to its second corrector step that cause the numerical results to deviate further from a divergence free velocity field. The accurate numerical results obtained using the ITA is attributed to its capability to resolve the nonlinearity of the Navier-Stokes equations. The present numerical method that incorporates the ITA is used to solve an unsteady transitional flow over an oscillating airfoil and a chemically reacting flow of hydrogen in a vitiated supersonic airstream. The turbulence fields in these flow cases are described using multiple-time-scale turbulence equations. For the unsteady transitional over an oscillating airfoil, the fluid flow is described using ensemble-averaged Navier-Stokes equations defined on the Lagrangian-Eulerian coordinates. It is shown that the numerical method successfully predicts the large dynamic stall vortex (DSV) and the trailing edge vortex (TEV) that are periodically generated by the oscillating airfoil. The calculated streaklines are in very good comparison with the experimentally obtained smoke picture. The calculated turbulent viscosity contours show that the transition from laminar to turbulent state and the relaminarization occur widely in space as well as in time. The ensemble-averaged velocity profiles are also in good agreement with the measured data and the good comparison indicates that the numerical method as well as the multipletime-scale turbulence equations successfully predict the unsteady transitional turbulence field. The chemical reactions for the hydrogen in the vitiated supersonic airstream are described using 9 chemical species and 48 reaction-steps. Consider that a fast chemistry can not be used to describe the fine details (such as the instability) of chemically reacting flows while a reduced chemical kinetics can not be used confidently due to the uncertainty contained in the reaction mechanisms. However, the use of a detailed finite rate chemistry may make it difficult to obtain a fully converged solution due to the coupling between the large number of flow, turbulence, and chemical equations. The numerical results obtained in the present study are in good agreement with the measured data. The good comparison is attributed to the numerical method that can yield strongly converged results for the reacting flow and to the use of the multiple-time-scale turbulence equations that can accurately describe the mixing of the fuel and the oxidant.

Kim, S.-W.↗

NASA NTRS1990

Analysis and prediction of tilt rotor hover noise

This paper presents new and improved tilt rotor hover noise prediction methods. Calculations include both discrete frequency harmonic noise and broadband noise mechanisms due to the ground plane/fountain recirculating flow. The noise mechanisms studied are thickness, loading, and inflow turbulence noise. In each case aeroacoustic models are developed and compared to noise measurements obtained experimentally for the XV-15 experimental tilt rotor aircraft. Both the effects of the mean and the turbulent fountain flows are found to be important noise sources and have strongly directional radiation patterns toward the rear of the aircraft (the direction of the rotor motion through the fountain flow). Calculations also show that the noise generated by the inflow of ambient atmospheric turbulence can also be an important noise source in hover in some directions. Further development of the methods and models, and precise information about the fountain flow, are needed to improve the predictions and to initiate noise minimization studies.

Coffen, Charles D.↗

NASA NTRS1993

Turbulence and transition modeling for high-speed flows

Research conducted during the past three and a half years aimed at developing and testing a turbulence/transition model applicable to high-speed turbulent flows is summarized. The first two years of the project focused on fully turbulent flows, while emphasis shifted to boundary-layer development in the transition region during the final year and a half. A brief summary of research accomplished during the first three years is included and publications that describe research results in greater detail are cited. Research conducted during the final six months of the period of performance is summarized. The primary results of the last six months of the project are elimination of the k-omega model's sensitivity to the freestream value of omega and development of a method for triggering transition at a specified location, independent of the freestream turbulence level.

Wilcox, David C.↗

NASA NTRS1994

The Effect of Two-Dimensional Forcing on Self-Similar Turbulent Plane Wakes

Three direct numerical simulations of time-evolving turbulent plane wakes with velocity deficit Reynolds numbers of about 2,000 have been simulated using a spectral numerical method with up to 600 x 260 x 160 modes. The initial conditions for the simulations are generated from direct numerical simulations of a turbulent boundary layer (momentum thickness Reynolds number of 670), and varying amounts of additional two- dimensional, forcing. In order to preserve the self-similar flow evolution, the forcing is implemented by multiplying all the two-dimensional modes in the initial condition by a constant factor. In the "natural" case no additional forcing is used; in the "forced" and "heavily forced" cases this factor is 5 and 20, respectively. The wake spreading rate Is increased by factors of 1.7 and 7.1 for the two forced cases. The Reynolds stresses are also increased by a similar or even larger factor. These results indicate that the plane wake is much more sensitive to initial forcing than the plane mixing layer. As in the plane mixing layer, two-dimensional forcing promotes more organized large-scale vortical flow structures and these structures axe sometimes separated by "braid regions" containing streamwise "rib" vortices, unlike in the unforced wake.

Rogers, M. M.↗

NASA NTRS1987

Analysis of non-premixed turbulent reacting flows

Studies of chemical reactions occurring in turbulent flows are important in the understanding of combustion and other applications. Current numerical methods are limited in their applications due to the numerical resolution required to completely capture all length scales, but, despite the fact that realistic combustion cannot be solved completely, numerical simulations can be used to give insight into the interaction between the processes of turbulence and chemical reaction. The objective was to investigate the effects of turbulent motion on the effects of chemical reaction to gain some insight on the interaction of turbulence, molecular diffusion, and chemical reaction to support modeling efforts. A direct turbulence simulation spectral code was modified to include the effects of chemical reaction and applied to an initial value problem of chemical reaction between non-premixed species. The influence of hydrodynamics on the instantaneous structure of the reaction was investigated. The local scalar dissipation rates and the local reaction rates were examined to determine the influence of vorticity or rate of strain on the reaction and the structure of the scalar field.

Leonard, Andy D.↗