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At least 397 records · Page 22
All sourcesNASA NTRSDOE OSTI
NASA NTRS2003

A Nonlinear Model for Fuel Atomization in Spray Combustion

Most gas turbine combustion codes rely on ad-hoc statistical assumptions regarding the outcome of fuel atomization processes. The modeling effort proposed in this project is aimed at developing a realistic model to produce accurate predictions of fuel atomization parameters. The model involves application of the nonlinear stability theory to analyze the instability and subsequent disintegration of the liquid fuel sheet that is produced by fuel injection nozzles in gas turbine combustors. The fuel sheet is atomized into a multiplicity of small drops of large surface area to volume ratio to enhance the evaporation rate and combustion performance. The proposed model will effect predictions of fuel sheet atomization parameters such as drop size, velocity, and orientation as well as sheet penetration depth, breakup time and thickness. These parameters are essential for combustion simulation codes to perform a controlled and optimized design of gas turbine fuel injectors. Optimizing fuel injection processes is crucial to improving combustion efficiency and hence reducing fuel consumption and pollutants emissions.

Liu, Nan-Suey↗
NASA NTRS2000

Nonlinear Stability and Structure of Compressible Reacting Mixing Layers

The parabolized stability equations (PSE) are used to investigate issues of nonlinear flow development and mixing in compressible reacting shear layers. Particular interest is placed on investigating the change in flow structure that occurs when compressibility and heat release are added to the flow. These conditions allow the 'outer' instability modes- one associated with each of the fast and slow streams-to dominate over the 'central', Kelvin-Helmholtz mode that unaccompanied in incompressible nonreacting mixing layers. Analysis of scalar probability density functions in flows with dominant outer modes demonstrates the ineffective, one-sided nature of mixing that accompany these flow structures. Colayer conditions, where two modes have equal growth rate and the mixing layer is formed by two sets of vortices, offer some opportunity for mixing enhancement. Their extent, however, is found to be limited in the mixing layer's parameter space. Extensive validation of the PSE technique also provides a unique perspective on central- mode vortex pairing, further supporting the view that pairing is primarily governed perspective sheds insight on how linear stability theory is able to provide such an accurate prediction of experimentally-observed, fully nonlinear flow phenomenon.

Day, M. J.↗
NASA NTRS1989

Transition Flight Experiments on a Swept Wing with Suction

Flight boundary-layer transition experiments were conducted on a 30 degree swept wing with a perforated leading-edge suction panel. The transition location on the panel was changed by systematically varying the location and amount of suction. Transition from laminar to turbulent flow was due to leading-edge turbulence contamination or crossflow disturbance growth and/or Tollmien-Schlichting disturbance growth, depending on flight condition and suction variation. Amplification factor correlations with transition location were made for various suction configurations using a state-of-the-art linear stability theory which accounts for body and streamline curvature and compressibility.

Maddalon, D. V.↗
NASA NTRS2004

An Approach to V&V of Embedded Adaptive Systems

Rigorous Verification and Validation (V&V) techniques are essential for high assurance systems. Lately, the performance of some of these systems is enhanced by embedded adaptive components in order to cope with environmental changes. Although the ability of adapting is appealing, it actually poses a problem in terms of V&V. Since uncertainties induced by environmental changes have a significant impact on system behavior, the applicability of conventional V&V techniques is limited. In safety-critical applications such as flight control system, the mechanisms of change must be observed, diagnosed, accommodated and well understood prior to deployment. In this paper, we propose a non-conventional V&V approach suitable for online adaptive systems. We apply our approach to an intelligent flight control system that employs a particular type of Neural Networks (NN) as the adaptive learning paradigm. Presented methodology consists of a novelty detection technique and online stability monitoring tools. The novelty detection technique is based on Support Vector Data Description that detects novel (abnormal) data patterns. The Online Stability Monitoring tools based on Lyapunov's Stability Theory detect unstable learning behavior in neural networks. Cases studies based on a high fidelity simulator of NASA's Intelligent Flight Control System demonstrate a successful application of the presented V&V methodology. ,

Liu, Yan↗
NASA NTRS2003

Optimal Disturbances in Boundary Layers Subject to Streamwise Pressure Gradient

Laminar-turbulent transition in shear flows is still an enigma in the area of fluid mechanics. The conventional explanation of the phenomenon is based on the instability of the shear flow with respect to infinitesimal disturbances. The conventional hydrodynamic stability theory deals with the analysis of normal modes that might be unstable. The latter circumstance is accompanied by an exponential growth of the disturbances that might lead to laminar-turbulent transition. Nevertheless, in many cases, the transition scenario bypasses the exponential growth stage associated with the normal modes. This type of transition is called bypass transition. An understanding of the phenomenon has eluded us to this day. One possibility is that bypass transition is associated with so-called algebraic (non-modal) growth of disturbances in shear flows. In the present work, an analysis of the optimal disturbances/streamwise vortices associated with the transient growth mechanism is performed for boundary layers in the presence of a streamwise pressure gradient. The theory will provide the optimal spacing of the control elements in the spanwise direction and their placement in the streamwise direction.

Tumin, Anatoli↗
NASA NTRS2010

Instability of a Supersonic Boundary-Layer with Localized Roughness

A localized 3-D roughness causes boundary-layer separation and (weak) shocks. Most importantly, streamwise vortices occur which induce streamwise (low U, high T) streaks. Immersed boundary method (volume force) suitable to represent roughness element in DNS. Favorable comparison between bi-global stability theory and DNS for a "y-mode" Outlook: Understand the flow physics (investigate "z-modes" in DNS through sinuous spanwise forcing, study origin of the beat in DNS).

Marxen, Olaf↗
NASA NTRS2012

Crossflow Instability on a Wedge-Cone at Mach 3.5

As a follow-on activity to the HyBoLT flight experiment, a six degree half angle wedge-cone model at zero angle of attack has been employed to experimentally and computationally study the boundary layer crossflow instability at Mach 3.5 under low disturbance freestream conditions. Computed meanflow and linear stability analysis results are presented along with corresponding experimental Pitot probe data. Using a model-mounted probe survey apparatus, data acquired to date show a well defined stationary crossflow vortex pattern on the flat wedge surface. This effort paves the way for additional detailed, calibrated flow field measurements of the crossflow instability, both stationary and traveling modes, and transition-to-turbulence under quiet flow conditions as a means of validating existing stability theory and providing a foundation for dynamic flight instrumentation development.

Beeler, George B.↗
NASA NTRS2013

High-Order Simulation of Induced Disturbance in a Mach 6 Boundary Layer

Simulations of the early evolution of induced unstable disturbances in a Mach 6 hypersonic boundary layer are presented for the purposes of validating a high-order discontinuous Galerkin Navier-Stokes simulation code. The simulations are modeled after experiments performed in the Boeing/AFOSR Mach-6 Quiet Tunnel at Purdue University. In these experiments, a forcing mechanism was employed to induce reproducible disturbances in a hypersonic boundary layer providing for the controlled study of the growth and breakdown of these disturbances into turbulent spots. Simulations revealed that the form and strength of the excitation can greatly influence the growth of the disturbance. In particular, at large forcing amplitude, the simulated forcing produces large advecting transients that appear to enhance the growth of the wave packet, relative to that of low amplitude forcing. Simulation results with large amplitude forcing agree well with experimental results while results from low amplitude forcing agree with linear stability theory.

Atkins, Harold L.↗
NASA NTRS2015

Solid Rocket Motor Combustion Instability Modeling in COMSOL Multiphysics

Combustion instability modeling of Solid Rocket Motors (SRM) remains a topic of active research. Many rockets display violent fluctuations in pressure, velocity, and temperature originating from the complex interactions between the combustion process, acoustics, and steady-state gas dynamics. Recent advances in defining the energy transport of disturbances within steady flow-fields have been applied by combustion stability modelers to improve the analysis framework. Employing this more accurate global energy balance requires a higher fidelity model of the SRM flow-field and acoustic mode shapes. The current industry standard analysis tool utilizes a one dimensional analysis of the time dependent fluid dynamics along with a quasi-three dimensional propellant grain regression model to determine the SRM ballistics. The code then couples with another application that calculates the eigenvalues of the one dimensional homogenous wave equation. The mean flow parameters and acoustic normal modes are coupled to evaluate the stability theory developed and popularized by Culick. The assumption of a linear, non-dissipative wave in a quiescent fluid remains valid while acoustic amplitudes are small and local gas velocities stay below Mach 0.2. The current study employs the COMSOL Multiphysics finite element framework to model the steady flow-field parameters and acoustic normal modes of a generic SRM. This work builds upon previous efforts to verify the use of the acoustic velocity potential equation (AVPE) laid out by Campos. The acoustic velocity potential (psi) describing the acoustic wave motion in the presence of an inhomogeneous steady high-speed flow is defined by, del squared psi - (lambda/c) squared psi - M x [M x del((del)(psi))] - 2((lambda)(M)/c + M x del(M) x (del)(psi) - 2(lambda)(psi)[M x del(1/c)] = 0. with M as the Mach vector, c as the speed of sound, and λ as the complex eigenvalue. The study requires one way coupling of the CFD High Mach Number Flow (HMNF) and mathematics module. The HMNF module evaluates the gas flow inside of a SRM using St. Robert's law to model the solid propellant burn rate, slip boundary conditions, and the supersonic outflow condition. Results from the HMNF model are verified by comparing the pertinent ballistics parameters with the industry standard code outputs (i.e. pressure drop, axial velocity, exit velocity). These results are then used by the coefficient form of the mathematics module to determine the complex eigenvalues of the AVPE. The mathematics model is truncated at the nozzle sonic line, where a zero flux boundary condition is self-satisfying. The remaining boundaries are modeled with a zero flux boundary condition, assuming zero acoustic absorption on all surfaces. The one way coupled analysis is perform four times utilizing geometries determined through traditional SRM modeling procedures. The results of the steady-state CFD and AVPE analyses are used to calculate the linear acoustic growth rate as is defined by Flandro and Jacob. In order to verify the process implemented within COMSOL we first employ the Culick theory and compare the results with the industry standard. After the process is verified, the Flandro/Jacob energy balance theory is employed and results displayed.

Fischbach, S. R.↗
NASA NTRS2015

Solid Rocket Motor Combustion Instability Modeling in COMSOL Multiphysics

Combustion instability modeling of Solid Rocket Motors (SRM) remains a topic of active research. Many rockets display violent fluctuations in pressure, velocity, and temperature originating from the complex interactions between the combustion process, acoustics, and steady-state gas dynamics. Recent advances in defining the energy transport of disturbances within steady flow-fields have been applied by combustion stability modelers to improve the analysis framework [1, 2, 3]. Employing this more accurate global energy balance requires a higher fidelity model of the SRM flow-field and acoustic mode shapes. The current industry standard analysis tool utilizes a one dimensional analysis of the time dependent fluid dynamics along with a quasi-three dimensional propellant grain regression model to determine the SRM ballistics. The code then couples with another application that calculates the eigenvalues of the one dimensional homogenous wave equation. The mean flow parameters and acoustic normal modes are coupled to evaluate the stability theory developed and popularized by Culick [4, 5]. The assumption of a linear, non-dissipative wave in a quiescent fluid remains valid while acoustic amplitudes are small and local gas velocities stay below Mach 0.2. The current study employs the COMSOL multiphysics finite element framework to model the steady flow-field parameters and acoustic normal modes of a generic SRM. The study requires one way coupling of the CFD High Mach Number Flow (HMNF) and mathematics module. The HMNF module evaluates the gas flow inside of a SRM using St. Robert's law to model the solid propellant burn rate, no slip boundary conditions, and the hybrid outflow condition. Results from the HMNF model are verified by comparing the pertinent ballistics parameters with the industry standard code outputs (i.e. pressure drop, thrust, ect.). These results are then used by the coefficient form of the mathematics module to determine the complex eigenvalues of the Acoustic Velocity Potential Equation (AVPE). The mathematics model is truncated at the nozzle sonic line, where a zero flux boundary condition is self-satisfying. The remaining boundaries are modeled with a zero flux boundary condition, assuming zero acoustic absorption on all surfaces. The results of the steady-state CFD and AVPE analyses are used to calculate the linear acoustic growth rate as is defined by Flandro and Jacob [2, 3]. In order to verify the process implemented within COMSOL we first employ the Culick theory and compare the results with the industry standard. After the process is verified, the Flandro/Jacob energy balance theory is employed and results displayed.

Fischbach, Sean R.↗
NASA NTRS1961

Concerning Certain Collisionless Plasma-Shock Wave Models

A shock-wave model proposed by both Kahn and Parker for the collision of two interstellar gas clouds or of the solar wind with the ionized gas around the earth is re-evaluated in the light of recent developments in plasma stability theory. It is shown that the instability which was supposed to arrest the counter-streaming of the ions and to transfer much of their kinetic energy to the electrons does not occur in many important examples. Specifically, it is absent if the initial ion thermal energy exceeds 4.2 x 10 (sup -4) times their translational energy. While other plausible shock structures are known which yield supra-thermal electrons, they depend on magnetic fields, leaving no satisfactory theory in the limit of zero magnetic field.

Noerdlinger, Peter D.↗
NASA NTRS2018

On the Development of Shell Buckling Knockdown Factors for Stiffened Metallic Launch Vehicle Cylinders

From the 1920s to the early 1970s, many shell buckling experiments were conducted in an effort to understand the complex buckling behavior exhibited by thin-walled cylindrical shells, to provide data to correlate with new shell stability theories, and provide design guidelines. Typically, the experiments yielded buckling loads that were substantially lower than the corresponding analytical predictions, which were based on simplified linear bifurcation analyses of geometrically perfect shells with nominal dimensions and idealized boundary conditions. The seminal works by von Kármán and Tsien, by Donnell and Wan, and by Koiter identified small deviations from the idealized geometry of a shell, known as initial geometric imperfections, as a primary source of the discrepancy between corresponding analytical predictions and experimental results. However, the computational tools and capabilities at that time could not perform the nonlinear analyses needed to assess the effects of these imperfections on the buckling behavior of thin-walled shells. Thus, buckling design allowables were determined by establishing lower bounds to test data. Specifically, empirical design factors, that have become known as knockdown factors, were determined and were to be used in conjunction with linear bifurcation analyses for simply supported shells; that is, these empirical factors were used to "knock down" the value of the unconservative simplified analytical prediction. This approach to shell buckling design has proved satisfactory for most design purposes and remains prominent in industry practice, as evidenced by the extensive use of the NASA space vehicle design criteria and recommendations. Unfortunately, the current design guidelines have not been updated since they were first published in the late 1960s and may not be able to take full advantage of modern materials, precision manufacturing processes, and new structural concepts.

Hilburger, Mark W.↗
NASA NTRSDate not supplied

Supersonic Traveling Crossflow Wave Characteristics in Ground and Flight Tests

This paper continues analysis of data acquired in a series of supersonic crossflow transition experiments on a 65° swept- wing model tested in both wind tunnel and flight. Flow visualization data are summarized to provide context for the swept-wing instability mechanisms of interest. Unsteady pressure measurements obtained near the wing model leading edge (LE) are studied using 2nd- and 3rd-order statistical methods to extract traveling crossflow wave characteristics from these data. Comparisons between tunnel and flight data with boundary-layer (BL) Linear Stability Theory (LST) predictions provide insights into BL transition phenomena similarities and differences observed in tests using the same swept-wing model configurations. Comparisons of unsteady pressure data results for wing LE configurations with and without distributed-roughness-element (DRE) patterns installed, suggest traveling crossflow disturbance growth is reduced when this type of flow control is applied. A brief stud y of different background surface roughness levels on the wing LE suggests the potential for another flow control approach to promote laminar flow on swept wings using streamwise-biased surface finishes.

Lewis R Owens↗
NASA NTRS1992

Effect of Cooling on Boundary-Layer Stability at Mach Number 3

This paper describes the calculation of the effect of wall cooling on the instability of a two-dimensional, flat-plate supersonic boundary layer under stratospheric flight conditions at Mach 3 using both the inviscid and viscous linear stability theories.

wall↗
NASA NTRS2021

Boundary-layer Instability Measurements on a Cone at Freestream Mach 3.5

An experimental study was conducted in the NASA (National Aeronautics and Space Administration) Langley Supersonic Low-Disturbance Tunnel to investigate naturally-occurring instabilities in a supersonic boundary layer on a 7◦ half-angle cone at nominal freestream conditions: Mach 3.5, total temperature of 299.8K, and unit Reynolds numbers (millions per m) of 9.89, 13.85, 21.77, and 25.73. Instability measurements were acquired under noisy-flow and quiet-flow conditions. Pitot-pressure and calibrated hot-wire measurements were obtained using a model-integrated traverse system to document the model flow field. In noisy-flow conditions, growth rates and mode shapes achieved good agreement between the measured results and linear stability theory (LST). The corresponding N factor at transition from LST is N ≈ 3.9. Under quiet-flow conditions, the most unstable first-mode instabilities as predicted by LST were measured, but this mode was not the dominant instability measured in the boundary layer. Instead, the dominant instabilities were less-amplified, low-frequency disturbances predicted by LST, and grew according to linear theory. These low-frequency unstable disturbances were initiated by freestream acoustic disturbances through a receptivity process believed to occur near the branch I location of the cone. Under quiet-flow conditions, the boundary layer remained laminar up to the last measurement station for the largest unit Reynolds number, implying a transition N factor of N > 8.5.

Boundary Layer↗
NASA NTRS2023

Chemical Thermodynamics and the Mathematical Integration of Reaction Kinetics

Key advances in the development of numerical methods for non-reacting compressible flows have been enabled by translating physical requirements into concrete numerical guidelines, such as the satisfaction of entropy inequalities for shock-capturing techniques [Lax, Contributions to Nonlinear Functional Analysis (1971) 603-634]. In the present work, we present nonlinear numerical analysis tools that draw from Chemical Thermodynamics , the branch of Nonequilibrium Thermodynamics that deals with chemical reactions. Through Gibbs formalism, chemical thermodynamics provides a well-known theoretical expression for the chemical equilibrium constant of a reaction in terms of reduced chemical potentials. A less-known, yet extremely valuable result, due to [Krambeck, Arch. Ration. Mech. Anal. , 38 (1970) 317], states that when this expression is implemented, mass-action kinetic models are consistent with the dynamical prescriptions of the 2nd law of thermodynamics. For fixed-temperature ordinary differential equations modeling constant-volume reacting gas mixtures, this leads to a decreasing Helmholtz free energy. If the temperature is allowed to vary in accordance with conservation of energy (1st law), this leads to the statement of increasing entropy. These nonlinear prescriptions can, and should be, used to further develop temporal integration techniques for reaction kinetics. We demonstrate that Krambeck's result holds even when the equilibrium constants are approximated from data. We prove this result by constructing the implicit free energy and the implicit entropy inherent to a given approximation. This is first done for a 5-species, 17-reaction model problem for air. With this structure established, elements of discrete entropy-stability theory [Tadmor, Acta Numer. , 12 (2003) 451] are leveraged to examine the consistency of time-integration schemes with these prescriptions. Using chemical potentials, one can compute the respective contributions of the kinetics model and of the temporal scheme to free energy/entropy variations. We introduce a nonlinear-stable version of the Discontinuous-Galerkin (DG) scheme in time which shows robustness improvements over the standard linearly-stable version. Most notably, the maximum timestep that can be resolved with the nonlinearly-stable variant tends to grow with polynomial order, in contrast to the linearly-stable variant. We generalize our constructions to arbitrary systems of reversible chemical reactions, ultimately showing that the compressible reacting Euler system admits the opposite of the implicitly constructed thermodynamic entropy as a mathematical entropy . This lays important theoretical foundations towards robust scheme development [Harten, J. Comput. Phys. 49 (1983) 151-164].

STMD↗
NASA NTRSDate not supplied

Aerodynamic Design Optimization for Natural Laminar Flow Airfoils

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

Transition↗
DOE OSTI2020

Data-driven modeling and control of dynamical systems using Koopman and Perron-Frobenius operators

This dissertation studies the data-driven modeling and control problem of nonlinear systems by exploiting the linear operator theoretic framework involving Koopman and Perro-Frobenius operator. A systematic linear-operator based controller design procedure has been established, which can be used to solve a variety of nonlinear control problems, including feedback stabilization using control Lyapunov functions, optimal quadratic regulation using Koopman eigenfunctions and convex optimization formulation of optimal control problem using P-F and Koopman operator approximation. As the core of data-driven modeling, we first propose a new algorithm for the finite-dimensional approximation of the linear transfer Koopman and Perron-Frobenius operator from time-series data. We argue that the existing approach for the finite-dimensional approximation of these transfer operators such as Dynamic Mode Decomposition (DMD) and Extended Dynamic Mode Decomposition (EDMD) do not capture two important properties of these operators, namely positivity and Markov property. The algorithm we propose preserves these two properties. We call the proposed algorithm as naturally structured DMD (NSDMD) since it retains the inherent properties of these operators. Naturally structured DMD algorithm leads to a better approximation of the steady-state dynamics of the system regarding computing Koopman and Perron- Frobenius operator eigenfunctions and eigenvalues. However, preserving positivity property is critical for capturing the real transient dynamics of the system. This positivity property of the transfer operators and it's finite-dimensional approximation play an important role for controller and estimator design of nonlinear systems. To solve the feedback stabilization problem for nonlinear control systems, we tried to take advantage of the Koopman operator framework. The Koopman operator approach provides a linear representation for a nonlinear dynamical system and a bilinear representation for a nonlinear control system. The problem of feedback stabilization of a nonlinear control system is then transformed to the stabilization of a bilinear control system. We propose a control Lyapunov function (CLF)-based approach for the design of stabilizing feedback controllers for the bilinear system. The search for finding a CLF for the bilinear control system is formulated as a convex optimization problem. This leads to a schematic procedure for designing CLF-based stabilizing feedback controllers for the bilinear system and hence the original nonlinear system. Another advantage of the proposed controller design approach outlined in this dissertation is that it does not require explicit knowledge of system dynamics. In particular, the bilinear representation of a nonlinear control system in the Koopman eigenfunction space can be obtained from time-series data. Next, we study the optimal quadratic regulation problem for nonlinear systems. The linear operator theoretic framework involving the Koopman operator is used to lift the dynamics of nonlinear control system to an infinite-dimensional bilinear system. The optimal quadratic regulation problem for nonlinear system is formulated in terms of the finite-dimensional approximation of the bilinear system. A convex optimization-based approach is proposed for solving the quadratic regulator problem for bilinear system. We applied a variety of examples and compared the simulation results between our framework and conventional LQR control using linearized model. For more general optimal control problems, we provide a density-function based convex formulation for the optimal control problem of the nonlinear system. The convex formulation relies on the duality result in the stability theory of a dynamical system involving density function and Perron-Frobenius operator. The optimal control problem is formulated as an infinite-dimensional convex optimization program. The finite-dimensional approximation of the optimization problem relies on the recent advances made in the data-driven computation of the Koopman operator, which is dual to the Perron-Frobenius operator. Simulation results are presented to demonstrate the application of the developed framework.

Huang, Bowen↗