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All sourcesNASA NTRSDOE OSTI
NASA NTRS1988

Onset of finger convection in a horizontal porous layer underlying a fluid layer

The problem of the onset of finger convection in a porous layer underlying a fluid layer is considered using linear stability analysis. The linear stability equations for the porous layer are formulated for temperature and salinity gradients existing in both layers. The eigenvalue problem is solved by a shooting method. The solution method and associated computer program are validated by comparison with the results of Sun (1973) for the thermal convection case. Results are also presented for the onset of salt-finger convection.

Chen, F.↗
NASA NTRS2008

Bounded Linear Stability Margin Analysis of Nonlinear Hybrid Adaptive Control

This paper presents a bounded linear stability analysis for a hybrid adaptive control that blends both direct and indirect adaptive control. Stability and convergence of nonlinear adaptive control are analyzed using an approximate linear equivalent system. A stability margin analysis shows that a large adaptive gain can lead to a reduced phase margin. This method can enable metrics-driven adaptive control whereby the adaptive gain is adjusted to meet stability margin requirements.

Nguyen, Nhan T.↗
NASA NTRS1982

Thresholds for the onset of fluid and magnetofluid turbulence

Linear stability calculations conducted in plasma physics are based on the theory of hydrodynamic stability of neutral fluids. The present investigation is concerned with the validity of procedures based on linear stability analysis in six much-studied situations. All have the property that the fluid goes from laminar to turbulent at critical values of some dimensionless number, such as the Reynolds number or the Rayleigh number. The question is, at what threshold values of the dimensionless number do the unstable motions set in, and can these thresholds be predicted by a linear analysis of the stability of the laminar state as the threshold is approached from the stable side. In three cases linear stability analysis clearly seems to fail. These cases include Plane Poiseuille Flow, Plane Couette Flow, and Cylindrical Pipe Flow (Hagen-Poiseuille Flow). Situations in which predictions provided by linear stability analysis are correct are related to Rotating Couette Flow, Thermally-Driven Convection, and Instability of Laminar Boundary Layers.

Montgomery, D.↗
NASA NTRS1984

Microsegregation during directional solidification

During the directional solidification of alloys, solute inhomogeneities transverse to the growth direction arise due to morphological instabilities (leading to cellular or dendritic growth) and/or due to convection in the melt. In the absence of convection, the conditions for the onset of morphological instability are given by the linear stability analysis of Mullins and Sekerka. For ordinary solidification rates, the predictions of linear stability analysis are similar to the constitutional supercooling criterion. However, at very rapid solidification rates, linear stability analysis predicts a vast increase in stabilization in comparison to constitutional supercooling.

Coriell, S. R.↗
NASA NTRS1987

A linear thermal stability analysis for the vertical structure of alpha model accretion disks

The linear equations that describe the thermal stability of the convective and radiative vertical structure of an alpha model accretion disk are derived. For a specific model chosen to be representative of a dwarf nova disk, it is found that the eigenfunction for the temperature shows large excursions in the zone of partial ionization, but that the eigenfunctions for the unstable fundamental mode perturbations of the vertical distance and flux are nearly constant over the vertical extent of the disk. The growth of any instability is thus nearly homologous and the stability criteria derived for vertically averaged structures represent an adequate approximation.

Saio, Hideyuki↗
NASA NTRS2002

Linear Temporal Stability Analysis of a Low-Density Round Gas Jet Injected into a High-Density Gas

It has been observed in previous experimental studies that round helium jets injected into air display a repetitive structure for a long distance, somewhat similar to the buoyancy-induced flickering observed in diffusion flames. In order to investigate the influence of gravity on the near-injector development of the flow, a linear temporal stability analysis of a round helium jet injected into air was performed. The flow was assumed to be isothermal and locally parallel; viscous and diffusive effects were ignored. The variables were represented as the sum of the mean value and a normal-mode small disturbance. An ordinary differential equation governing the amplitude of the pressure disturbance was derived. The velocity and density profiles in the shear layer, and the Froude number (signifying the effects of gravity) were the three important parameters in this equation. Together with the boundary conditions, an eigenvalue problem was formulated. Assuming that the velocity and density profiles in the shear layer to be represented by hyperbolic tangent functions, the eigenvalue problem was solved for various values of Froude number. The temporal growth rates and the phase velocity of the disturbances were obtained. The temporal growth rates of the disturbances increased as the Froude number was reduced (i.e. gravitational effects increased), indicating the destabilizing role played by gravity.

Lawson, Anthony L.↗
NASA NTRS1980

Transition prediction using three dimensional stability analysis

Several methods of transition prediction by linear stability analysis are compared. The spectral stability analysis code SALLY is used to analyze flows over laminar flow control wings. It is shown that transition by the envelope method and a new modified wave packet method are comparable in reliability but that the envelope method is more efficient computationally.

Malik, M. R.↗
NASA NTRS1995

Stability Analysis of Bow Shocks

We present a linear stability analysis of bow shocks created by the interaction of a spherical wind moving with respect to its surrounding medium. The bounding shocks are assumed isothermal and with Mach number M = infinity. Following Soker (1990) we study the evolution of short wavelength perturbations. We find that the motion is unstable in this limit. Moreover, the ratio of the wind velocity v(sub w) to the star velocity v(sub *) characterizes the stability properties. Bow shocks with fast winds for which v(sub *)/v(sub w)<<1 are more stable than bow sho with slow winds i.e. v(sub *)/v(sub w)>>1.

Bow Shocks↗
NASA NTRS1976

Stability of elastic bending and torsion of uniform cantilever rotor blades in hover with variable structural coupling

The stability of elastic flap bending, lead-lag bending, and torsion of uniform, untwisted, cantilever rotor blades without chordwise offsets between the elastic, mass, tension, and areodynamic center axes is investigated for the hovering flight condition. The equations of motion are obtained by simplifying the general, nonlinear, partial differential equations of motion of an elastic rotating cantilever blade. The equations are adapted for a linearized stability analysis in the hovering flight condition by prescribing aerodynamic forces, applying Galerkin's method, and linearizing the resulting ordinary differential equations about the equilibrium operating condition. The aerodynamic forces are obtained from strip theory based on a quasi-steady approximation of two-dimensional unsteady airfoil theory. Six coupled mode shapes, calculated from free vibration about the equilibrium operating condition, are used in the linearized stability analysis. The study emphasizes the effects of two types of structural coupling that strongly influence the stability of hingeless rotor blades. The first structural coupling is the linear coupling between flap and lead-lag bending of the rotor blade. The second structural coupling is a nonlinear coupling between flap bending, lead-lag bending, and torsion deflections. Results are obtained for a wide variety of hingeless rotor configurations and operating conditions in order to provide a reasonably complete picture of hingeless rotor blade stability characteristics.

Hodges, D. H., Roberta.↗
NASA NTRS1995

Linear Stability Regime Analysis of the Compressible Reacting Mixing Layer

Previous investigations have shown that a compressible reacting mixing layer can develop two peaks in the mean density weighted vorticity profile. Linear stability analyses show that at these peaks two distinct 'outer' instability modes appear in addition to the more common central mode, which exists unaccompanied in incompressible nonreacting flows. The present study parametrically analyzes the effects of compressibility, heat release, stoichiometry, and density ratio on the amplification rate and obliquity of each stability mode. The mean profiles used in the spatial stability calculation are generated by self-similar solutions of the compressible boundary layer equations combined with the assumption of infinitely fast chemistry. It is shown that the influence of stoichiometry and density ratio on the peaks of the density weighted vorticity profile determines which modes will dominate. Of particular interest are the conditions where two modes are equally amplified, causing the mixing layer to develop into a 'colayer' structure.

Day, M. J.↗
NASA NTRS2022

The Harmonic Linearized Navier-Stokes Equations for Transition Prediction in Three-Dimensional Flows

The conventional method to predict the onset of laminar-turbulent transition in convectively unstable boundary-layer flows is based on the logarithmic amplification ratio, the so-called N-factor, of the linear instability waves. To calculate the N-factor, the flow variables are decomposed into a laminar basic state solution and the linear disturbances, which are assumed to be harmonic in time. The most commonly used linear stability analysis approaches include the locally parallel linear stability theory (LST) and the nonlocal, weakly nonparallel parabolized stability equations (PSE). However, these methods do not account for strong streamwise gradients that are encountered in several configurations of interest, such as those in the vicinity of roughness elements, steps, gaps, or corners. To compute the linear evolution of disturbances along such strongly nonparallel regions, the harmonic linearized Navier-Stokes equations (HLNSE) need to be solved. The discretization of the HLNSE for spanwise/azimuthally inhomogeneous laminar basic states yields a linear system of complex arithmetic with a leading dimension of the order of 10^(7) to 10^(8) even in relatively simple flows. A combined multithread and multiprocessor algorithm is implemented for the direct solution of such linear systems. Results for a supersonic boundary layer over a three-dimensional roughness patch show good agreement with experimental measurements when the evolution of the instability waves over the roughness patch is included via the HLNSE. Additionally, inflow-resolvent analysis based on the HLNSE for discrete-roughness-induced disturbances in the nose tip of a blunt cone at Mach 6 demonstrates the importance of including the disturbance amplification along the near vicinity of the roughness element and separation region.

Boundary Layer Stability↗
NASA NTRS1998

Numerical Simulations of Unsteady Low-Reynolds-Number Flows Over the APEX Airfoil

Laminar and transitional separation bubbles are an important feature of low-Reynolds-number flows over airfoils. The separation bubbles are unsteady and have a significant impact on the aerodynamic properties of the airfoils. In this paper unsteady low-Reynolds-number separated flows over the APEX airfoil are calculated using a Navier-Stokes solver. The numerical results show the presence of unsteady separation bubbles in the flowfield. An analysis of the numerical results shows that flowfield disturbances are amplified significantly in the separation bubble, leading to periodic vortex shedding. A linear stability analysis of the separated boundary layer is performed and the results show that the dominant wavenumber and frequency in the numerical simulations agree with the most unstable wavenumber and frequency from the linear stability analysis. The numerical results also show the growth and interaction of disturbance waves in the separation bubble. For transonic flows over the APEX airfoil, the calculations show that the presence of shocks causes significant changes in the separation location and consequently, the overall flowfield.

Tatineni, Mahidhar↗
NASA NTRS2022

The Harmonic Linearized Navier-Stokes Equations for Transition Prediction in Three-Dimensional Flows

The conventional method to predict the onset of laminar-turbulent transition in convectively unstable boundary-layer flows is based on the logarithmic amplification ratio, the so-called N-factor, of the linear instability waves. To calculate the N-factor, the flow variables are decomposed into a laminar basic state solution and the linear disturbances, which are assumed to be harmonic in time. The most commonly used linear stability analysis approaches include the locally parallel linear stability theory (LST) and the non-local, weakly nonparallel parabolized stability equations (PSE). However, these methods do not account for strong streamwise gradients that are encountered in several configurations of interest, as roughness elements, steps, gaps, or corners. To solve the linear evolution of disturbances along such strongly nonparallel regions, the harmonic linearized Navier-Stokes equations (HLNSE) need to be solved. The discretization of the HLNSE for spanwise/azimuthally inhomogeneous laminar basic states yields a linear system of complex arithmetic with a leading dimension of the order of 107 to 108. A combined multithread and multiprocessor algorithm is implemented for the direct solution of such linear system. Results for a supersonic boundary layer over a three-dimensional roughness patch show good agreement with experimental measurements when the evolution of the instability waves over the roughness patch is included via the HLNSE.

Boundary Layer Stability↗
DOE OSTI2024

Aeroelastic code comparison using the IEA 22MW reference turbine

Reference wind turbine designs and the associated aeroelastic models are widely used in both research and industry. Reference models representing future concepts are of particular interest. Current state of the art aeroelastic tools are relied upon to design the next generation of large wind turbines. However, modelling assumptions may be invalidated by upcoming very large turbines, and different aeroelastic tools may give inconsistent results. A 22MW turbine model has been defined as part of International Energy Agency (IEA) Wind Task 55 on Reference Wind Turbines and Farms to represent future turbines to be deployed in the 2030s. In this study, an aeroelastic model of this turbine has been created in four tools; Bladed, HAWC2, OpenFAST, and QBlade. Code comparisons are presented for steady state operation, linear stability analysis, and time domain power production simulations in steady and turbulent wind. Generally, the codes show a good agreement, but with some differences present in the linear stability analysis, periodic azimuthal variation, and time domain simulations. The models are a good basis for further study with the IEA 22MW turbine, and further code comparison exercises.

17 WIND ENERGY↗
NASA NTRS2001

Numerical Study of Buoyancy and Different Diffusion Effects on the Structure and Dynamics of Triple Flames

Numerical simulations of 2-D triple flames under gravity force have been implemented to identify the effects of gravity on triple flame structure and propagation properties and to understand the mechanisms of instabilities resulting from both heat release and buoyancy effects. A wide range of gravity conditions, heat release, and mixing widths for a scalar mixing layer are computed for downward-propagating (in the same direction with the gravity vector) and upward-propagating (in the opposite direction of the gravity vector) triple flames. Results of numerical simulations show that gravity strongly affects the triple flame speed through its contribution to the overall flow field. A simple analytical model for the triple flame speed, which accounts for both buoyancy and heat release, is developed. Comparisons of the proposed model with the numerical results for a wide range of gravity, heat release and mixing width conditions, yield very good agreement. The analysis shows that under neutral diffusion, downward propagation reduces the triple flame speed, while upward propagation enhances it. For the former condition, a critical Froude number may be evaluated, which corresponds to a vanishing triple flame speed. Downward-propagating triple flames at relatively strong gravity effects have exhibited instabilities. These instabilities are generated without any artificial forcing of the flow. Instead disturbances are initiated by minute round-off errors in the numerical simulations, and subsequently amplified by instabilities. A linear stability analysis on mean profiles of stable triple flame configurations have been performed to identify the most amplified frequency in spatially developed flows. The eigenfunction equations obtained from the linearized disturbance equations are solved using the shooting method. The linear stability analysis yields reasonably good agreements with the observed frequencies of the unstable triple flames. The frequencies and amplitudes of disturbances increase with the magnitude of the gravity vector. Moreover, disturbances appear to be most amplified just downstream of the premixed branches. The effects of mixing width and differential diffusion are investigated and their roles on the flame stability are studied.

Chen, Jyh-Yuan↗
NASA NTRS1993

Calculation of AGARD Wing 445.6 Flutter Using Navier-Stokes Aerodynamics

The flutter characteristics of the first AGARD standard aeroelastic configuration for dynamic response, Wing 445.6, are studied using an unsteady Navier-Stokes algorithm in order to investigate a previously noted discrepancy between Euler flutter characteristics and the experimental data. The algorithm, which is a three-dimensional, implicit, upwind Euler/Navier-Stokes code (CFL3D Version 2.1), was previously modified for the time-marching, aeroelastic analysis of wings using the unsteady Euler equations. These modifications include the incorporation of a deforming mesh algorithm and the addition of the structural equations of motion for their simultaneous time integration with the governing flow equations. In this paper, the aeroelastic method is extended and evaluated for applications that use the Navier- Stokes aerodynamics. The paper presents a brief description of the aeroelastic method and presents unsteady calculations which verify this method for Navier-Stokes calculations. A linear stability analysis and a time-marching aeroelastic analysis are used to determine the flutter characteristics of the isolated 45 deg. swept-back wing. Effects of fluid viscosity, structural damping, and number of modes in the structural model are investigated. For the linear stability analysis, the unsteady generalized aerodynamic forces of the wing are computed for a range of reduced frequencies using the pulse transfer-function approach. The flutter characteristics of the wing are determined using these unsteady generalized aerodynamic forces in a traditional V-g analysis. This stability analysis is used to determine the flutter characteristics of the wing at free-stream Mach numbers of 0.96 and 1.141 using the generalized aerodynamic forces generated by solving the Euler equations and the Navier-Stokes equations. Time-marching aeroelastic calculations are performed at a free-stream Mach number of 1.141 using the Euler and Navier-Stokes equations to compare with the linear V-g flutter analysis method. The V-g analysis, which is used in conjunction with the time-marching analysis, indicates that the fluid viscosity has a significant effect on the supersonic flutter boundary for this wing while the structural damping and number of modes in the structural model have a lesser effect.

Lee-Rausch, Elizabeth M.↗