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NASA NTRS1973

Gaussian variational equations for osculating elements of an arbitrary separable reference orbit.

Lagrange-type equations are often used in planetary theory and sometimes in satellite theory. The equations express the variation of osculating Keplerian elements in terms of derivatives of a disturbing function or a perturbing potential. When the perturbing force is derivable from a potential, it is possible to convert the Lagrange-type equations to another form. This form, usually, attributed to Gauss, contains the perturbing forces instead of the derivatives of the potential. The case of an arbitrary separable reference orbit is discussed together with a lemma, a Keplerian check, and questions of the applicability of the equations to the spheroidal method.

Vinti, J. P.↗

NASA NTRS1973

Synthesis of oscillating adaptive feedback systems

A synthesis theory is developed which allows system design to proceed from practical specifications on system command and/or disturbance response to a design which is very nearly optimal in terms of feedback sensor noise effects. The approach taken is to replace the nonlinear element by a mean square error minimizing approximation (dual-input describing function), and then use linear frequency domain synthesis techniques subject to additional constraints imposed by the limit cycle and the approximator. Synthesis techniques are also developed for a similar system using an externally excited oscillating signal with the above approach. The results remove the design of the systems considered from the realm of simulation and experimentation, permitting true synthesis and the optimization that accompanies it.

Smay, J. W.↗

NASA NTRS1976

Acoustic disturbances produced by an unsteady spherical diffusion flame

The disturbances produced by a moving spherical diffusion flame are investigated within the framework of a linearized theory. After the flame position and species concentrations are determined, the problem of determining the associated density, pressure, temperature, and velocity fields is delineated. Explicit results for certain limiting situations are discussed.

Rasmussen, M. L.↗

NASA NTRS1980

Experimental analysis of the boundary layer transition with zero and positive pressure gradient

The influence of a positive pressure gradient on the boundary layer transition is studied. The mean velocity and turbulence profiles of four cases are examined. As the intensity of the pressure gradient is increased, the Reynolds number of the transition onset and the length of the transition region are reduced. The Tollmein-Schlichting waves disturb the laminar regime; the amplification of these waves is in good agreement with the stability theory. The three dimensional deformation of the waves leads finally to the appearance of turbulence. In the case of zero pressure gradient, the properties of the turbulent spots are studied by conditional sampling of the hot-wire signal; in the case of positive pressure gradient, the turbulence appears in a progressive manner and the turbulent spots are much more difficult to characterize.

Arnal, D.↗

NASA NTRS1989

Application of a full potential method to AGARD standard airfoils

One of the most important uses of method that calculate unsteady aerodynamic loads is to predict and analyze the aeroelastic responses of flight vehicles. Currently, methods based on transonic small disturbance potential aerodynamics are the primary tools for aeroelastic analysis. Flow solutions obtained using isentropic potential theory can be highly inaccurate and even multivalued, because they do not model the effects of entropy that is produced when shock waves are in the flow field. From the results that are presented, it is concluded that nonisentropic potential methods more accurately model Euler solutions than do isentropic methods. The primary effects of modeling shock generated entropy are: (1) to eliminate mulitple flow solutions when strong shock waves are in the flow field; and (2) to bring the strengths and locations of computed shock waves into better agreement with those calculated using Euler method and those measured during experiments.

Whitlow, Woodrow, Jr.↗

NASA NTRS1957

A discussion of cone and flat-plate Reynolds numbers for equal ratios of the laminar shear to the shear caused by small velocity fluctuations in a laminar boundary layer

By use of the linear theory of boundary-layer stability and Schlichting's formula for the maximum amplification of a disturbance, an approximate relation is derived between the Reynolds number on a cone and the Reynolds number on a flat plate for equal closeness to transition. The indication is that the ratio of the cone Reynolds number for transition, based on the distance to the cone apex, to the plate Reynolds number for transition, based on the distance to the leading edge, is not in general equal to 3, as has been suggested by other investigators, but varies from 3 when transition occurs at the minimum critical Reynolds number to unity when transition occurs at a large multiple of the critical Reynolds number.

FLOW, TURBULENT↗

NASA NTRS1994

Long-wavelength asymptotics of unstable crossflow modes, including the effect of surface curvature

Stationary vortex instabilities with wavelengths significantly larger than the thickness of the underlying three-dimensional boundary layer are studied with asymptotic methods. The long-wavelength Rayleigh modes are locally neutral and are aligned with the direction of the local inviscid streamline. For a spanwise wave number Beta much less than 1, the spatial growth rate of these vortices is O(Beta(exp 3/2)). When Beta becomes O(R(exp -1/7)), the viscous correction associated with a thin sublayer near the surface modifies the inviscid growth rate to the leading order. As Beta is further decreased through this regime, viscous effects assume greater significance and dominate the growth-rate behavior. The spatial growth rate becomes comparable to the real part of the wave number when Beta = O(R(exp -1/4)). At this stage, the disturbance structure becomes fully viscous-inviscid interactive and is described by the triple-deck theory. For even smaller values of Beta, the vortex modes become nearly neutral again and align themselves with the direction of the wall-shear stress. Thus, the study explains the progression of the crossflow-vortex structure from the inflectional upper branch mode to nearly neutral long-wavelength modes that are aligned with the wall-shear direction.

Choudhari, Meelan↗

NASA NTRS2012

Secondary Instability of Second Modes in Hypersonic Boundary Layers

Second mode disturbances dominate the primary instability stage of transition in a number of hypersonic flow configurations. The highest amplification rates of second mode disturbances are usually associated with 2D (or axisymmetric) perturbations and, therefore, a likely scenario for the onset of the three-dimensionality required for laminar-turbulent transition corresponds to the parametric amplification of 3D secondary instabilities in the presence of 2D, finite amplitude second mode disturbances. The secondary instability of second mode disturbances is studied for selected canonical flow configurations. The basic state for the secondary instability analysis is obtained by tracking the linear and nonlinear evolution of 2D, second mode disturbances using nonlinear parabolized stability equations. Unlike in previous studies, the selection of primary disturbances used for the secondary instability analysis was based on their potential relevance to transition in a low disturbance environment and the effects of nonlinearity on the evolution of primary disturbances was accounted for. Strongly nonlinear effects related to the self-interaction of second mode disturbances lead to an upstream shift in the upper branch neutral location. Secondary instability computations confirm the previously known dominance of subharmonic modes at relatively small primary amplitudes. However, for the Purdue Mach 6 compression cone configuration, it was shown that a strong fundamental secondary instability can exist for a range of initial amplitudes of the most amplified second mode disturbance, indicating that the exclusive focus on subharmonic modes in the previous applications of secondary instability theory to second mode primary instability may not have been fully justified.

Li, Fei↗

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 NTRS2018

Numerical Investigation of Roughness Effects on Transition on Spherical Capsules

The state of the boundary layer on space re-entry vehicles significantly affects the design of the thermal protection system. However, the physical mechanism that leads to the laminar-turbulent boundary-layer transition on blunt spherical capsules remains an open question in literature. This work numerically assesses the potential of roughness-induced non-modal disturbance growth on re-entry capsules with a spherical-section forebody by optimal transient-growth theory and direct numerical simulation. Two different sets of wind-tunnel experiments are considered. Optimal transient-growth studies have been performed for the blunt capsule experiments at Mach 5.9 in the Hypersonic Ludwieg tube Braunschweig (HLB) of the Technische Universitat Braunschweig. In some of these measurements, the capsule model was equipped with a specifically designed patch of distributed micron-sized surface roughness. The transient-growth results for the HLB capsule are compared to corresponding numerical data for a Mach 6 blunt capsule experiment in the Adjustable Contour Expansion (ACE) facility of the Texas A&M University (TAMU) at lower Reynolds number. Similar trends are observed for both configurations. In particular, a rather low maximum energy gain is noted for the surface temperature conditions of the experiments. It is shown that the surface temperature dependence of the optimal transient-growth results is very similar for both capsule configurations. Moreover, the generation of stationary disturbances by well-defined roughness patches on the capsule surface is studied for the conditions of the HLB experiment using direct numerical simulations (DNS). To help explain the observed laminar-turbulent transition downstream of the roughness patch in some of the HLB capsule experiments, additional simulations were carried out to study the evolution of unsteady perturbations within the steady disturbance flow field due to the roughness patch. However, the DNS did not provide any indication of modal or non-modal disturbance growth in the wake of the roughness patch, and hence, the physical mechanism underlying the observed onset of transition remains unknown.

Hein, Stefan↗

NASA NTRS1989

Calculation of steady and unsteady pressures at supersonic speeds with CAP-TSD

A finite difference technique is used to solve the transonic small disturbance flow equation making use of shock capturing to treat wave discontinuities. Thus the nonlinear effects of thickness and angle of attack are considered. Such an approach is made feasible by the development of a new code called CAP-TSD (Computational Aeroelasticity Program - Transonic Small Disturbance), and is based on a fully implicit approximate factorization (AF) finite difference method to solve the time dependent transonic small disturbance equation. The application of the CAP-TSD code to the calculation of low to moderate supersonic steady and unsteady flows is presented. In particular, comparisons with exact linear theory solutions are made for steady and unsteady cases to evaluate shock capturing and other features of the current method. In addition, steady solutions obtained from an Euler code are used to evaluate the small disturbance aspects of the code. Steady and unsteady pressure comparisons are made with measurements for an F-15 wing model and for the RAE tailplane model.

Bennett, Robert M.↗

NASA NTRS1996

Hypersonic Boundary Layer Stability over a Flared Cone in a Quiet Tunnel

Hypersonic boundary layer measurements were conducted over a flared cone in a quiet wind tunnel. The flared cone was tested at a freestream unit Reynolds number of 2.82x106/ft in a Mach 6 flow. This Reynolds number provided laminar-to-transitional flow over the model in a low-disturbance environment. Point measurements with a single hot wire using a novel constant voltage anemometry system were used to measure the boundary layer disturbances. Surface temperature and schlieren measurements were also conducted to characterize the laminar-to-transitional state of the boundary layer and to identify instability modes. Results suggest that the second mode disturbances were the most unstable and scaled with the boundary layer thickness. The integrated growth rates of the second mode compared well with linear stability theory in the linear stability regime. The second mode is responsible for transition onset despite the existence of a second mode sub-harmonic. The sub-harmonic wavelength also scales with the boundary layer thickness. Furthermore, the existence of higher harmonics of the fundamental suggests that non-linear disturbances are not associated with high free stream disturbance levels.

Lachowicz, Jason T.↗

NASA NTRS1991

A finite-element perturbation approach to fluid/rotor interaction in turbomachinery elements. I - Theory. II - Application

The vibrational characteristics of a rotor that is in contact with a fluid in an annular clearance gap are investigated. The disturbance under consideration involves the axis of rotation, and includes a virtual lateral eccentricity, together with a whirling motion around the housing centerline. The fluid reaction components arise from infinitesimally small deformations with varied magnitudes which are experienced by an assembly of finite elements in the rotor-to-housing gap. A perturbation model is presented in which the perturbation equations emerge from the flow-governing equations in their discrete finite-element form. It is concluded that restrictions on the rotor-to-housing gap geometry, or the manner in which the rotor virtual eccentricity occurs are practically nonexisting. This model is used to compute the rotordynamic coefficients of an annular seal. The rotordynamic behavior of a hydraulic seal with a clearance gap depth/length ratio of 0.01 is analyzed under a cylindrical type of rotor whirl and several running speeds.

Baskharone, E. A.↗

NASA NTRS1972

Lorentz-invariant formulation of Cherenkov radiation by tachyons

Previous treatments of Cherenkov radiation, electromagnetic and gravitational, by tachyons were in error because the prescription employed to cut off the divergent integral over frequency is not a Lorentz invariant procedure. The resulting equation of motion for the tachyon is therefore not covariant. The proper procedure requires an extended, deformable distribution of charge or mass and yields a particularly simple form for the tachyon's world line, one that could be deduced from simple invariance considerations. It is shown that Cherenkov radiation by tachyons implys their ultimate annihilation with an antitachyon and demonstrates a disturbing property of tachyons, namely the impossibility of specifying arbitrary Cauchy data even in a purely classical theory.

Jones, F. C.↗

NASA NTRS1978

Interplanetary gas. XXII - Interaction of comet Kohoutek's ion tail with the compression region of a solar-wind corotating stream

An apparently successful identification of a comet-tail feature with a solar-wind event is presented. Photographs of comet Kohoutek 1973f show a large-scale disturbance in the middle and outer regions of the ion tail early on January 20 of 1974. On the previous and succeeding days the comet had, however, a 'normal' and less active appearance. The peculiar tail structure is linked to an encounter with rapidly changing solar-wind conditions on the forward edge of the high-velocity solar-wind stream which encountered the earth late on January 24. The stream produced a geomagnetic storm of the recurrent type. The high-speed stream appears to have been associated with a large near-equatorial coronal hole which underwent central meridian passage on January 22. It is proposed that the comet was in the compression region on the stream forward edge at the time of formation of the tail disturbance. The accuracy of the time delays is actually tested by an application of the wind shock theory of ionic tail orientations.

Niedner, M. B., Jr.↗

NASA NTRS1981

Nonparallel stability of three-dimensional flows

The linear stability of three-dimensional incompressible, isothermal, nonparallel boundary-layer flows has been investigated. The method of multiple scales is used to derive the partial-differential equations that describe the spatial modulations of the amplitude, phase and wavenumber of a disturbance. Group velocities are used to determine the disturbance growth direction. The envelope method is used to calculate the logarithmic amplitude growth rate N. The theory is applied to the flows over a swept-back tapered wing with boundary-layer suction. Results of such analysis for the X-21 wing are discussed. It is found that the nonparallel effects for this wing is substantial.

Padhye, A. R.↗

NASA NTRS1985

Thermocapillary Motion Research

Fundamental microgravity research on interfacial surface tension driven motion by a linear temperature gradient was conducted. A vertical linear temperature gradient will be established within a test container filled with a host fluid. The thermal gradient will be positive in the upward vertical direction to avoid any free convective currents. With minimal disturbance, a single immisible fluid droplet will be introduced into the host fluid. As predicted by existing theory, the droplet will move in the direction of higher temperature due to tangential shear stresses created by surface tension variations along the periphery of the droplet.

Peterson, T. T.↗

NASA NTRS1999

Receptivity of Flat-Plate Boundary Layer in a Non-Uniform Free Stream (Vorticity Normal to the Plate)

Experimental and theoretical studies of low speed leading edge boundary layer receptivity to free-stream vorticity produced by upstream wires normal to the leading edge are discussed. Data include parametric variations in leading edge configuration and details of the incident disturbance field including single and multiple wakes. The induced disturbance amplitude increases with increases in the leading edge diameter and wake interactions. Measurements agree with the theory of M. E. Goldstein.

Kogan, M. N.↗