Results for “nonlinear dynamics in fluids” — Page 15

NASA NTRS1987

A new hydrodynamic analysis of double layers

A genuine two-fluid model of plasmas with collisions permits the calculation of dynamic (not necessarily static) electric fields and double layers inside of plasmas including oscillations and damping. For the first time a macroscopic model for coupling of electromagnetic and Langmuir waves was achieved with realistic damping. Starting points were laser-produced plasmas showing very high dynamic electric fields in nonlinear force-produced cavitous and inverted double layers in agreement with experiments. Applications for any inhomogeneous plasma as in laboratory or in astrophysical plasmas can then be followed up by a transparent hydrodynamic description. Results are the rotation of plasmas in magnetic fields and a new second harmonic resonance, explanation of the measured inverted double layers, explanation of the observed density-independent, second harmonics emission from laser-produced plasmas, and a laser acceleration scheme by the very high fields of the double layers.

Hora, Heinrich↗

NASA NTRS2019

Generation of a Reduced-Order Model of an Unmanned Combat Air Vehicle Using Indicial Response Functions

Within the NATO STO AVT-251 Task Group, a generic Unmanned Combat Air Vehicle (UCAV) planform was redesigned based on requirements derived from parts of the flight envelope of the defined mission. Because of the lambda-shape planform and associated flow phenomena including shocks and vortices, the aerodynamic design process relies heavily on high-fidelity predictions from computational fluid dynamics (CFD). These simulations enable accurate flight dynamics predictions, allowing for the identification of any potential performance issues early in the design process. Potentially, a complete flight dynamics model can be derived from CFD calculations provided that the underlying reduced order model (ROM) captures the underlying physics contained within the CFD results. This work investigates the creation of a nonlinear ROM using indicial response functions. The response functions are obtained using a grid motion approach that separates the effects of angle of attack and pitch rate. This approach is demonstrated using three different CFD codes from various organizations: ENSOLV at Royal Netherlands Aerospace Centre, USM3D at NASA Langley Research Center, and Kestrel at the United States Air Force Academy. ROM predictions were generated for a manoeuver resembling a low-speed pull-up. The predictions are found to be sensitive to the quality of the steady-state solutions from which step-response calculations were started, as well as the convergence of the step responses themselves. Nevertheless, the indicial response method is shown to provide aerodynamic predictions with acceptable accuracy including transient effects, and as such is a promising method for computationally efficient flight dynamics predictions.

Michel P.C. van Rooij↗

NASA NTRS2004

Linearized Aeroelastic Solver Applied to the Flutter Prediction of Real Configurations

A fast-running unsteady aerodynamics code, LINFLUX, was previously developed for predicting turbomachinery flutter. This linearized code, based on a frequency domain method, models the effects of steady blade loading through a nonlinear steady flow field. The LINFLUX code, which is 6 to 7 times faster than the corresponding nonlinear time domain code, is suitable for use in the initial design phase. Earlier, this code was verified through application to a research fan, and it was shown that the predictions of work per cycle and flutter compared well with those from a nonlinear time-marching aeroelastic code, TURBO-AE. Now, the LINFLUX code has been applied to real configurations: fans developed under the Energy Efficient Engine (E-cubed) Program and the Quiet Aircraft Technology (QAT) project. The LINFLUX code starts with a steady nonlinear aerodynamic flow field and solves the unsteady linearized Euler equations to calculate the unsteady aerodynamic forces on the turbomachinery blades. First, a steady aerodynamic solution is computed for given operating conditions using the nonlinear unsteady aerodynamic code TURBO-AE. A blade vibration analysis is done to determine the frequencies and mode shapes of the vibrating blades, and an interface code is used to convert the steady aerodynamic solution to a form required by LINFLUX. A preprocessor is used to interpolate the mode shapes from the structural dynamics mesh onto the computational fluid dynamics mesh. Then, LINFLUX is used to calculate the unsteady aerodynamic pressure distribution for a given vibration mode, frequency, and interblade phase angle. Finally, a post-processor uses the unsteady pressures to calculate the generalized aerodynamic forces, eigenvalues, an esponse amplitudes. The eigenvalues determine the flutter frequency and damping. Results of flutter calculations from the LINFLUX code are presented for (1) the E-cubed fan developed under the E-cubed program and (2) the Quiet High Speed Fan (QHSF) developed under the Quiet Aircraft Technology project. The results are compared with those obtained from the TURBO-AE code. A graph of the work done per vibration cycle for the first vibration mode of the E-cubed fan is shown. It can be seen that the LINFLUX results show a very good comparison with TURBO-AE results over the entire range of interblade phase angle. The work done per vibration cycle for the first vibration mode of the QHSF fan is shown. Once again, the LINFLUX results compare very well with the results from the TURBOAE code.

Reddy, Tondapu S.↗

NASA NTRS2006

Stochastic Representation of Chaos Using Terminal Attractors

A nonlinear version of the Liouville equation based on terminal attractors is part of a mathematical formalism for describing postinstability motions of dynamical systems characterized by exponential divergences of trajectories leading to chaos (including turbulence as a form of chaos). The formalism can be applied to both conservative systems (e.g., multibody systems in celestial mechanics) and dissipative systems (e.g., viscous fluids). The development of the present formalism was undertaken in an effort to remove positive Lyapunov exponents. The means chosen to accomplish this is coupling of the governing dynamical equations with the corresponding Liouville equation that describes the evolution of the flow of error probability. The underlying idea is to suppress the divergences of different trajectories that correspond to different initial conditions, without affecting a target trajectory, which is one that starts with prescribed initial conditions.

Zak, Michail↗

NASA NTRS2006

Rapid Aeroelastic Analysis of Blade Flutter in Turbomachines

The LINFLUX-AE computer code predicts flutter and forced responses of blades and vanes in turbomachines under subsonic, transonic, and supersonic flow conditions. The code solves the Euler equations of unsteady flow in a blade passage under the assumption that the blades vibrate harmonically at small amplitudes. The steady-state nonlinear Euler equations are solved by a separate program, then equations for unsteady flow components are obtained through linearization around the steady-state solution. A structural-dynamics analysis (see figure) is performed to determine the frequencies and mode shapes of blade vibrations, a preprocessor interpolates mode shapes from the structural-dynamics mesh onto the LINFLUX computational-fluid-dynamics mesh, and an interface code is used to convert the steady-state flow solution to a form required by LINFLUX. Then LINFLUX solves the linearized equations in the frequency domain to calculate the unsteady aerodynamic pressure distribution for a given vibration mode, frequency, and interblade phase angle. A post-processor uses the unsteady pressures to calculate generalized aerodynamic forces, response amplitudes, and eigenvalues (which determine the flutter frequency and damping). In comparison with the TURBO-AE aeroelastic-analysis code, which solves the equations in the time domain, LINFLUX-AE is 6 to 7 times faster.

Trudell, J. J.↗

NASA NTRS1998

Numerical Experiment with Time and Spatial Accuracy of Navier-Stokes Computation For Helicopter Problems

Helicopter flowfields are highly unsteady, nonlinear and three-dimensional. In forward flight and in hover, the rotor blades interact with the tip vortex and wake sheet developed by either itself or the other blades. This interaction, known as blade-vortex interactions (BVI), results in unsteady loading of the blades and can cause a distinctive acoustic signature. Accurate and cost-effective computational fluid dynamic solutions that capture blade-vortex interactions can help rotor designers and engineers to predict rotor performance and to develop designs for low acoustic signature. Such a predictive method must preserve a blade's shed vortex for several blade revolutions before being dissipated. A number of researchers have explored the requirements for this task. This paper will outline some new capabilities that have been added to the NASA Ames' OVERFLOW code to improve its overall accuracy for both vortex capturing and unsteady flows. To highlight these improvements, a number of case studies will be presented. These case studies consist of free convection of a 2-dimensional vortex, dynamically pitching 2-D airfoil including light-stall, and a full 3-D unsteady viscous solution of a helicopter rotor in forward flight In this study both central and upwind difference schemes are modified to be more accurate. Central difference scheme is chosen for this simulation because the flowfield is not dominated by strong shocks. The feature of shock-vortex interaction in such a flow is less important than the dominant blade-vortex interaction. The scheme is second-order accurate in time and solves the thin-layer Navier-Stokes equations in fully-implicit manner at each time-step. The spatial accuracy is either second and fourth-order central difference or third-order upwind difference using Roe-flux and MUSCLE scheme. This paper will highlight and demonstrate the methods for several sample cases and for a helicopter rotor. Preliminary computations on a rotor were performed by using this method and are in the process of documentation.

Ahmad, Jasim↗

NASA NTRS1992

Homogeneous quantum electrodynamic turbulence

The electromagnetic field equations and Dirac equations for oppositely charged wave functions are numerically time-integrated using a spatial Fourier method. The numerical approach used, a spectral transform technique, is based on a continuum representation of physical space. The coupled classical field equations contain a dimensionless parameter which sets the strength of the nonlinear interaction (as the parameter increases, interaction volume decreases). For a parameter value of unity, highly nonlinear behavior in the time-evolution of an individual wave function, analogous to ideal fluid turbulence, is observed. In the truncated Fourier representation which is numerically implemented here, the quantum turbulence is homogeneous but anisotropic and manifests itself in the nonlinear evolution of equilibrium modal spatial spectra for the probability density of each particle and also for the electromagnetic energy density. The results show that nonlinearly interacting fermionic wave functions quickly approach a multi-mode, dynamic equilibrium state, and that this state can be determined by numerical means.

Shebalin, John V.↗

NASA NTRS1985

High-speed compressible flow and other advection-dominated problems of fluid dynamics

Finite element methods are described for modeling high speed compressible flows with strong advection, problems important to aerodynamics. The situations are characterized by high pressure and temperature gradients, transients and the appearance of discontinuities, factors which require mesh refinement during computations. Techniques are developed for temporal and spatial discretization of a model problem. Several observations are made regarding the explicit and implicit features of the calculations, the use of the Lax-Wendroff scheme to produce a mass-matrix for obtaining accurate results for transients, methods of performing stability analyses, and simplification techniques. Examples are provided of solving the nonlinear shallow-water equations and describing compressible flows, particularly transonic flows. Domain splitting is defined for improving the calculations at each time step and in different parts of the flow regime while simultaneously advancing the calculations towards a solution.

Zienkiewicz, O. C.↗

NASA NTRS1983

Implicit Total Variation Diminishing (TVD) schemes for steady-state calculations

The application of a new implicit unconditionally stable high resolution total variation diminishing (TVD) scheme to steady state calculations. It is a member of a one parameter family of explicit and implicit second order accurate schemes developed by Harten for the computation of weak solutions of hyperbolic conservation laws. This scheme is guaranteed not to generate spurious oscillations for a nonlinear scalar equation and a constant coefficient system. Numerical experiments show that this scheme not only has a rapid convergence rate, but also generates a highly resolved approximation to the steady state solution. A detailed implementation of the implicit scheme for the one and two dimensional compressible inviscid equations of gas dynamics is presented. Some numerical computations of one and two dimensional fluid flows containing shocks demonstrate the efficiency and accuracy of this new scheme.

Yee, H. C.↗

NASA NTRS1983

Implicit total variation diminishing (TVD) schemes for steady-state calculations

The application of a new implicit unconditionally stable high resolution total variation diminishing (TVD) scheme to steady state calculations. It is a member of a one parameter family of explicit and implicit second order accurate schemes developed by Harten for the computation of weak solutions of hyperbolic conservation laws. This scheme is guaranteed not to generate spurious oscillations for a nonlinear scalar equation and a constant coefficient system. Numerical experiments show that this scheme not only has a rapid convergence rate, but also generates a highly resolved approximation to the steady state solution. A detailed implementation of the implicit scheme for the one and two dimensional compressible inviscid equations of gas dynamics is presented. Some numerical computations of one and two dimensional fluid flows containing shocks demonstrate the efficiency and accuracy of this new scheme. Previously announced in STAR as N83-23085

Yee, H. C.↗

NASA NTRS1988

The onset of plume dynamics in the spectral space

Time-dependent convection for infinite Prandtl number fluids has been investigated hitherto in the physical domain. Dynamics of plumelike structures resulting from boundary-layer instabilities can be interpreted in the spectral domain as having both direct and inverse cascades of energy taking place. In the physical domain only a small part of the spectrum is discernible. But the rest of the spectrum is needed for properly describing the nonlinear process. Only a relatively few modes, fewer than ten, are actually required for describing the essential features associated with the onset of plume dynamics.

Vincent, Alain P.↗

NASA NTRS1991

Nonlinear modal resonances in low-gravity slosh-spacecraft systems

Nonlinear models of low gravity slosh, when coupled to spacecraft vibrations, predict intense nonlinear eigenfrequency shifts at zero gravity. These nonlinear frequency shifts are due to internal quadratic and cubic resonances between fluid slosh modes and spacecraft vibration modes. Their existence has been verified experimentally, and they cannot be correctly modeled by approximate, uncoupled nonlinear models, such as pendulum mechanical analogs. These predictions mean that linear slosh assumptions for spacecraft vibration models can be invalid, and may lead to degraded control system stability and performance. However, a complete nonlinear modal analysis will predict the correct dynamic behavior. This paper presents the analytical basis for these results, and discusses the effect of internal resonances on the nonlinear coupled response at zero gravity.

Peterson, Lee D.↗

NASA NTRSDate not supplied

Analysis of Ice Mass Growth Over Time on the CRM65 Midspan Hybrid Model

The Aeronautics Research Mission Directorate at NASA is developing and applying tools to enable future technologies towards sustainable flight. Aircraft icing has been identified as a potential barrier to entry into service for innovative designs necessitating improvements to computational ice accretion tools. NASA is developing the Glenn Icing Computational Environment (GlennICE) to address deficiencies in the computational modeling capabilities of previously developed ice accretion solvers. To benchmark and improve the ability to model highly three-dimensional ice accretion, high quality validation data against experimental data is required. The CRM65 Midspan Hybrid geometry was previously tested at the NASA Icing Research Tunnel to generate experimental data for swept wing geometries typical for commercial transport aircraft. As a part of a 2018 icing test campaign, experimental data characterizing the relationship between ice accretion time and ice mass growth was obtained and can be leveraged for use in validation of computational tools. The desire for computational ice accretion solvers to predict ice shapes profiles accreted experimentally has often overshadowed the comparison to the mass and bulk volume of ice accreted. To address this deficiency, an analysis is presented in which GlennICE is applied to simulations of the CRM65 Midspan Hybrid model tested in the NASA Icing Research Tunnel. Results from the computational fluid dynamics simulations compared favorably to the experimental pressure coefficient data, thus validating the modeling setup. The experimental data showed excellent repeatability for the 15.0 minute accretion time. The comparisons between the experimental and computational ice mass over time showed good agreement up to 10.0 minutes after which the ice mass was underpredicted. The experimental ice mass was largely linear with some nonlinear data. The bulk volume of ice accreted experimentally compared well to GlennICE for the scanned ice shapes and mean combined cross section ice shapes, but was underpredicted for the maximum combined cross section ice shapes at longer accretion times. The experimental minimum combined cross section, mean combined cross section, and maximum combined cross section profiles when compared to GlennICE show good agreement for the mean combined cross section up to 15.0 minutes. The analyses show that with a single-shot method, GlennICE currently underpredicts the ice mass for longer accretion times, is not able to match the bulk volume of the maximum combined cross section due to dominating scallop features, and future work is required to generate a more generalized ice bulk density model.

Icing↗

NASA NTRSDate not supplied

Analysis of Ice Mass Growth Over Time on the CRM65 Midspan Hybrid Model

The Aeronautics Research Mission Directorate at NASA is developing and applying tools to enable future technologies towards sustainable flight. Aircraft icing has been identified as a potential barrier to entry into service for innovative designs necessitating improvements to computational ice accretion tools. NASA is developing the Glenn Icing Computational Environment (GlennICE) to address deficiencies in the computational modeling capabilities of previously developed ice accretion solvers. To benchmark and improve the ability to model highly three-dimensional ice accretion, high quality validation data against experimental data is required. The CRM65 Midspan Hybrid geometry was previously tested at the NASA Icing Research Tunnel to generate experimental data for swept wing geometries typical for commercial transport aircraft. As a part of a 2018 icing test campaign, experimental data characterizing the relationship between ice accretion time and ice mass growth was obtained and can be leveraged for use in validation of computational tools. The desire for computational ice accretion solvers to predict ice shapes profiles accreted experimentally has often overshadowed the comparison to the mass and bulk volume of ice accreted. To address this deficiency, an analysis is presented in which GlennICE is applied to simulations of the CRM65 Midspan Hybrid model tested in the NASA Icing Research Tunnel. Results from the computational fluid dynamics simulations compared favorably to the experimental pressure coefficient data, thus validating the modeling setup. The experimental data showed excellent repeatability for the 15.0 minute accretion time. The comparisons between the experimental and computational ice mass over time showed good agreement up to 10.0 minutes after which the ice mass was underpredicted. The experimental ice mass was largely linear with some nonlinear data. The bulk volume of ice accreted experimentally compared well to GlennICE for the scanned ice shapes and mean combined cross section ice shapes, but was underpredicted for the maximum combined cross section ice shapes at longer accretion times. The experimental minimum combined cross section, mean combined cross section, and maximum combined cross section profiles when compared to GlennICE show good agreement for the mean combined cross section up to 15.0 minutes. The analyses show that with a single-shot method, GlennICE currently underpredicts the ice mass for longer accretion times, is not able to match the bulk volume of the maximum combined cross section due to dominating scallop features, and future work is required to generate a more generalized ice bulk density model.

Icing↗

NASA NTRS1979

An explicit algorithm for a fluid approach to nonlinear optics propagation using splitting and rezoning techniques

The paper presents a three-dimensional analysis of the nonlinear light matter interaction in a hydrodynamic context. It is reported that the resulting equations are a generalization of the Navier-Stokes equations subjected to an internal potential which depends solely upon the fluid density. In addition, three numerical approaches are presented to solve the governing equations using an extension of McCormack predict-corrector scheme. These are a uniform grid, a dynamic rezoned grid, and a splitting technique. It is concluded that the use of adaptive mapping and splitting techniques with McCormack two-level predictor-corrector scheme results in an efficient and reliable code whose storage requirements are modest compared with other second order methods of equal accuracy.

Mattar, F. P.↗

NASA NTRSDate not supplied

An Interactive MATLAB Program for Fitting Transfer Functions to Frequency Responses

A computer program called FRFit (Frequency Response Fitting) is described for fitting single-input single-output transfer function models to empirical frequency response data. The program is interactive in that the user specifies ``elementary factors'' (gain, delay, pure differentiators and integrators, and first- and second-order zeros and poles) by entering numerical values or moving sliders in a graphical user interface. A nonlinear optimization can then be performed to obtain maximum likelihood estimates of transfer function parameters and uncertainties to provide feedback on the modeling and refine estimates. Several examples are discussed, including the identification of aircraft pitch dynamics from simulation data and data reported in the literature, approximating Theodorsen's function of unsteady aerodynamics, and obtaining a reduced-order model of a computational fluid dynamics code describing the unsteady aerodynamics around an aeroelastic wing. The program has some usefulness as a teaching aid, and can be applied to model structure determination, reduced-order modeling, preliminary analysis, and simple system identification problems. The program was written in MATLAB and is planned for public release through the NASA Software Catalog.

System identification↗

NASA NTRS1976

Mantle plumes - A boundary layer approach for Newtonian and non-Newtonian temperature-dependent rheologies

Stress is placed on the temperature dependence of both a linear Newtonian rheology and a nonlinear olivine rheology in accounting for narrow mantle flow structures. The boundary-layer theory developed incorporates an arbitrary temperature-dependent power-law rheology for the medium, in order to facilitate the study of mantle plume dynamics under real conditions. Thermal, kinematic, and dynamic structures of mantle plumes are modelled by a two-dimensional natural-convection boundary layer rising in a fluid with a temperature-dependent power-law relationship between shear stress and strain rate. An analytic similarity solution is arrived at for upwelling adjacent to a vertical isothermal stress-free plane. Newtonian creep as a deformation mechanism, thermal anomalies resulting from chemical heterogeneity, the behavior of plumes in non-Newtonian (olivine) mantles, and differences in the dynamics of wet and dry olivine are discussed.

Yuen, D. A.↗

NASA NTRS1984

Alternative experiments using the geophysical fluid flow cell

This study addresses the possibility of doing large scale dynamics experiments using the Geophysical Fluid Flow Cell. In particular, cases where the forcing generates a statically stable stratification almost everywhere in the spherical shell are evaluated. This situation is typical of the Earth's atmosphere and oceans. By calculating the strongest meridional circulation expected in the spacelab experiments, and testing its stability using quasi-geostrophic stability theory, it is shown that strongly nonlinear baroclinic waves on a zonally symmetric modified thermal wind will not occur. The Geophysical Fluid Flow Cell does not have a deep enough fluid layer to permit useful studies of large scale planetary wave processes arising from instability. It is argued, however, that by introducing suitable meridional barriers, a significant contribution to the understanding of the oceanic thermocline problem could be made.

Hart, J. E.↗