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NASA NTRS2021

Transition Analysis for Isolated Trips on BOLT-II Wind-Tunnel and Flight Configuration

The BOLT-II configuration designed for an upcoming flight experiment exemplifies the complexities of hypersonic boundary layer transition in the presence of multiple and potentially interacting instability mechanisms. The present paper is related to the NASA-led roughness experiment on the secondary side of the BOLT-II configuration. First, computations are performed to aid mean-flow based correlations for the transition measurements acquired during an experimental campaign in the Ludwieg Tube facility at the United States Air Force Academy. To that end, both laminar and turbulent flow computations are performed for selected conditions of the experiment with a 1:3 scale model of the slightly shorter BOLT configuration. The variation in well-known correlation parameters for transition due to isolated roughness elements with respect to element position, height, and flow Reynolds number is delineated. Furthermore, the wake instability theory is used to examine the amplification of unstable disturbances behind the centerline trip at the design conditions of the BOLT-II flight experiment and for its dynamically scaled version on the 1:3 scale model of the wind tunnel experiment. To our knowledge, this study represents the first analysis of the wake instabilities in the presence of a prominent entropy layer outside the boundary layer. At the nominal flight design condition of Re ∞ ) = 5.44 and Re ∞ = 2.5 x 10 6 /m, a diamond planform (“pizza-box”) trip with k/δ = 0.70 and planform-halfwidth-to-height ratio of b/k = 3.0 at X/L = 0.254 induces a strong distortion of the boundary-layer flow in the vicinity of the symmetry plane, such that the wake structure includes a centerline streak produced by the flow retardation behind the trip along with multiple additional, prominent vorticity structures representing the necklace vortex system. Stability results reveal that each of these streaks can support a strong amplification of wake instabilities within a frequency band of 95 kHz–255 kHz, with a peak N-factor of greater than 15 beyond X/L ≈ 0.42. The dynamically scaled wind tunnel configuration with Re ∞ = 20.25 x 10 6 /m is also found to support N > 15 at similar axial stations.

BOLT↗

NASA NTRS2016

Measurements in a Transitioning Cone Boundary Layer at Freestream Mach 3.5

An experimental study was conducted in the Supersonic Low-Disturbance Tunnel to investigate naturally-occurring instabilities in a supersonic boundary layer on a 7 deg half- angle cone. All tests were conducted with a nominal freestream Mach number of M(sub infinity) = 3:5, total temperature of T(sub 0) = 299:8 K, and unit Reynolds numbers of Re(sub infinity) x 10(exp -6) = 9:89, 13.85, 21.77, and 25.73 m(exp -1). Instability measurements were acquired under noisy- ow and quiet- ow conditions. Measurements were made to document the freestream and the boundary-layer edge environment, to document the cone baseline flow, and to establish the stability characteristics of the transitioning flow. Pitot pressure and hot-wire boundary- layer measurements were obtained using a model-integrated traverse system. All hot- wire results were single-point measurements and were acquired with a sensor calibrated to mass ux. For the noisy-flow conditions, excellent agreement for the growth rates and mode shapes was achieved between the measured results and linear stability theory (LST). The corresponding N factor at transition from LST is N 3:9. The stability measurements for the quiet-flow conditions were limited to the aft end of the cone. The most unstable first-mode instabilities as predicted by LST were successfully measured, but this unstable first mode was not the dominant instability measured in the boundary layer. Instead, the dominant instabilities were found to be the less-amplified, low-frequency disturbances predicted by linear stability theory, and these instabilities grew according to linear theory. These low-frequency unstable disturbances were initiated by freestream acoustic disturbances through a receptivity process that is believed to occur near the branch I locations of the cone. Under quiet-flow conditions, the boundary layer remained laminar up to the last measurement station for the largest Re1, implying a transition N factor of N greater than 8:5.

King, Rudolph A.↗

NASA NTRS1984

Effect of curvature on three-dimensional boundary layer stability

The problem of the stability of a three-dimensional laminar boundary layer formed on a curved surface is considered. A calculation scheme, which takes account of the curvature of the flow streamlines and of the surface is proposed for the prediction of the development of small amplitude temporal disturbances. Computations have been performed for the flow over the windward face of an infinitely long yawed cylinder and comparisons have been made with experimental data. These indicate that the theory correctly predicts many of the features of the unstable laminar flow. The theory also suggests that transition, in this particular situation, is dominated by traveling disturbance waves and that, at the experimentally observed transition location, the wave which has undergone greatest total amplification has an amplitude ratio of approximately e to the 11th. When the effects of curvature are omitted the maximum amplitude ratio at transition is about e to the 17th.

Malik, M. R.↗

NASA NTRS1987

Spatially growing disturbances in a high velocity ratio two-stream, coplanar jet

The influence of cold and heated secondary flow on the instability of a two-stream, coplanar jet having a 0.7 Mach number heated primary jet for a nominal fan to primary velocity ratio of 0.68 was investigated by means of inviscid linearized stability theory. The instability properties of spatially growing axisymmetric and first order azimuthal disturbances were studied. The instability characteristics of the two-stream jet with a velocity ratio of 0.68 are very different from those of a single stream jet, and a two-stream, coplanar jet having a 0.9 Mach number heated primary jet and a cold secondary jet for a fan to primary velocity ratio of 0.30. For X/D = 1 and in comparison to the case where the velocity ratio was 0.3, the presence of the fan stream with a velocity ratio of 0.68 enhanced the instability of the jet and increased the unstable frequency range. However, the axisymmetric mode (m = 0) and the first order azimuthal mode (m = 1) have similar spatial growth rates where the velocity ratio is 0.68 while for a velocity ratio of 0.3 the growth rate of the first order azimuthal mode (m = 1) is greater. Comparing the cold and hot secondary flow results showed that for a velocity ratio of 0.68 the growth rate is greater for cold.

Miles, J. H.↗

NASA NTRS1987

Spatially growing disturbances in a high velocity ratio two-stream, coplanar jet

Miles, Jeffrey H.↗

NASA NTRS1986

Electromagnetic scattering theory

Electromagnetic scattering theory is discussed with emphasis on the general stochastic variational principle (SVP) and its applications. The stochastic version of the Schwinger-type variational principle is presented, and explicit expressions for its integrals are considered. Results are summarized for scalar wave scattering from a classic rough-surface model and for vector wave scattering from a random dielectric-body model. Also considered are the selection of trial functions and the variational improvement of the Kirchhoff short-wave approximation appropriate to large size-parameters. Other applications of vector field theory discussed include a general vision theory and the analysis of hydromagnetism induced by ocean motion across the geomagnetic field. Levitational force-torque in the magnetic suspension of the disturbance compensation system (DISCOS), now deployed in NOVA satellites, is also analyzed using the developed theory.

Bird, J. F.↗

NASA NTRS1983

Wave propagation in intense flux tubes

The nature of nonadiabatic wave propagation in a slender magnetic flux tube is explored. The results of the theory are compared with the observations of Giovanelli et al. (1978), and found to be in general agreement. Those observations, of tubes in the photosphere-chromosphere, show outwardly propagating waves, with periods of 300 s, which take some 19 s to propagate from one level of line formation to another level higher in the atmosphere. In sharp contrast to this, is the time of 7 s for a similar disturbance outside the tube to propagate between the same two levels of line formation, estimated to be some 600 km apart in the field-free atmosphere. It is argued that the sharply contrasting propagation times for the tube and its environment is principally due to the elasticity of the tube and its subsequent propensity for propagation. A nonadiabatic disturbance may be essentially propagating within the tube but essentially nonpropagating outside, with considerably slower phase speeds thus arising inside the tube. The theory suggests that the observed disturbances are nonadiabatic, acoustic-gravity waves channelled along a magnetic flux tube and modulated by external pressure variations.

Roberts, B.↗

NASA NTRS1999

Development of a Three-Dimensional PSE Code for Compressible Flows: Stability of Three-Dimensional Compressible Boundary Layers

A program is developed to investigate the linear stability of three-dimensional compressible boundary layer flows over bodies of revolutions. The problem is formulated as a two dimensional (2D) eigenvalue problem incorporating the meanflow variations in the normal and azimuthal directions. Normal mode solutions are sought in the whole plane rather than in a line normal to the wall as is done in the classical one dimensional (1D) stability theory. The stability characteristics of a supersonic boundary layer over a sharp cone with 50 half-angle at 2 degrees angle of attack is investigated. The 1D eigenvalue computations showed that the most amplified disturbances occur around x(sub 2) = 90 degrees and the azimuthal mode number for the most amplified disturbances range between m = -30 to -40. The frequencies of the most amplified waves are smaller in the middle region where the crossflow dominates the instability than the most amplified frequencies near the windward and leeward planes. The 2D eigenvalue computations showed that due to the variations in the azimuthal direction, the eigenmodes are clustered into isolated confined regions. For some eigenvalues, the eigenfunctions are clustered in two regions. Due to the nonparallel effect in the azimuthal direction, the eigenmodes are clustered into isolated confined regions. For some eigenvalues, the eigenfunctions are clustered in two regions. Due to the nonparallel effect in the azimuthal direction, the most amplified disturbances are shifted to 120 degrees compared to 90 degrees for the parallel theory. It is also observed that the nonparallel amplification rates are smaller than that is obtained from the parallel theory.

Balakumar, P.↗

NASA NTRS1940

On the theory of unsteady planing and the motion of a wing with vortex separation

The disturbance imparted to water by a planing body give rise to a wave form of motion on the free surface, the length of the waves increasing indefinitely with increase in the Froude number and being directly proportional to the latter in the case of the plane or two-dimensional problem. At large Froude numbers the effect of the weight shows up to any appreciable extent only at some distance from the body, so that the flow near the body can be considered as part of a flow of an infinitely extending weightless fluid. This paper is a consideration of these characteristics as well as a formulation of the planing problem and its relation to the problem of a thin wing.

Sedov, L↗

NASA NTRS1961

The Theory of Artificial Satellites in Terms of the Orbital True Longitude

The author's previous theory of the artificial satellite is derived in terms of the. disturbed eccentric anomaly. The present development, in terms of the orbital true longitude, is a substantial improvement over the earlier work in that it leads to the faster convergence for large eccentricities and to a smaller number of terms in the series representing the perturbations. Moreover, each approximation of the radius vector and of the parameters determining the position of the orbit plane is obtained not in the form of a truncated infinite series but in the form of trigonometric polynomials in two arguments. These arguments are the mean true anomaly and the mean argument of the latitude. The present theory, like the previous one, permits the computation of perturbations of any desired order. Thus, any future information about earth's gravitational field can easily be included.

Musen, Peter↗

NASA NTRS1973

Linear viscous stability theory for stably stratified shear flow - A review.

In this paper the linear viscous stability theory for stably stratified parallel shear flow is reviewed and some new results are presented. Attention is focused on recent work on unbounded flows with emphasis placed on results which demonstrate apparent destabilizing effects of diffusivity which lie beyond the scope of inviscid theory. In particular it is shown that self-excited disturbances may exist with phase speeds lying outside the range of basic flow speed and that with strong thermal diffusivity, instability may occur even though the local Richardson number exceeds 0.25 throughout the flow.

Gage, K. S.↗

NASA NTRS1980

A two-dimensional potential flow model for ground-induced effects on jet and fan inlets

A free-streamline potential flow model is developed for the flowfield external to a stationary jet or fan inlet in proximity to a ground plane. It is assumed that the flow is steady, incompressible, and irrotational. A two-dimensional flat plate geometry models the inlet configuration, and free streamline theory is used to avoid unrealistic infinite flow velocities at the lips of the inlet, and to account somewhat for flow separation. A water table experiment is used to verify the analytical results. The fact that the solutions are found to be limited to only a certain range of diameter-height ratios implies an overdetermination of the problem by free streamline theory. Also studied are the convective properties of small vortical disturbances superimposed on the ideal flow solution.

Newman, W. H.↗

NASA NTRS1982

An assessment of preliminary aerodynamic analysis methods for supersonic speeds including high angle-of-attack flow

The problems associated with predicting the aerodynamic loads for moderate supersonic Mach number, high angle-of-attack flows and for high supersonic Mach number flows are addressed. For these large disturbance-type flows, commonly used prediction methods based on linearized theory or on the tangent-wedge method are shown to be generally inadequate. For the preliminary analysis of aerodynamic shapes subjected to these type flows, two methods have recently been developed by combining features of the linearized theory and tangent-wedge method. These two new methods are discussed, and through extensive comparisons with experimental data, are shown to offer an improved prediction capability.

Pittman, J. L.↗

NASA NTRS1986

Unsteady transonics of a wing with tip store

The presence of tip stores influences both the aerodynamic and the aeroelastic performance of wings. Such effects are more pronounced in the transonic regime. In this study, a theoretical method is developed, for the first time, to compute unsteady transonics of oscillating wings with tip stores. The method is based on the small-disturbance, aerodynamic equations of motion from the potential-flow theory. To validate the method, subsonic and transonic aerodynamic computations are made for a lower-aspect-ratio wing, and they are compared with the available experimental data. Comparisons are favorable. The strong effects of the tip store on the transonic aerodynamics of the wing are also illustrated. The method developed in this steady can be used for transonic, aeroelastic computations of wings with tip stores.

Guruswamy, G. P.↗

NASA NTRS1986

Aerodynamics via acoustics - Application of acoustic formulas for aerodynamic calculations

Prediction of aerodynamic loads on bodies in arbitrary motion is considered from an acoustic point of view, i.e., in a frame of reference fixed in the undisturbed medium. An inhomogeneous wave equation which governs the disturbance pressure is constructed and solved formally using generalized function theory. When the observer is located on the moving body surface there results a singular linear integral equation for surface pressure. Two different methods for obtaining such equations are discussed. Both steady and unsteady aerodynamic calculations are considered. Two examples are presented, the more important being an application to propeller aerodynamics. Of particular interest for numerical applications is the analytical behavior of the kernel functions in the various integral equations.

Farassat, F.↗

NASA NTRS1989

Optimization of structure and control system

The objective of this study is the simultaneous design of the structural and control system for space structures. This study is focused on considering the effect of the number and the location of the actuators on the minimum weight of the structure, and the total work done by the actuators for specified constraints and disturbance. The controls approach used is the linear quadratic regulator theory with constant feedback. At the beginning collocated actuators and sensors are provided in all the elements. The actuator doing the least work is removed one at a time, and the structure is optimized for the specified constraints on the closed-loop eigenvalues and the damping parameters. The procedure of eliminating an actuator is continued until an acceptable design satisfying the constraints is obtained. The study draws some conclusions on the trade between the total work done by the actuators, and the optimum weight and the number of actuators.

Khot, N. S.↗

NASA NTRS1990

An LQR controller design approach for a Large Gap Magnetic Suspension System (LGMSS)

Two control approaches for a Large Gap Magnetic Suspension System (LGMSS) are investigated and numerical results are presented. The approaches are based on Linear Quadratic Regulator (LQR) control theory and include a nonzero set point regulator with constant disturbance input and an integral feedback regulator. The LGMSS provides five degree of freedom control of a cylindrical suspended element which is composed of permanent magnet material. The magnetic actuators are air core electromagnets mounted in a planar way.

Groom, Nelson J.↗

NASA NTRS1991

Development of a perturbation generator for vortex stability studies

Theory predicts vortex instability when subjected to certain types of disturbances. It was desired to build a device which could introduce controlled velocity perturbations into a trailing line vortex in order to study the effects on stability. A perturbation generator was designed and manufactured which can be attached to the centerbody of an airfoil type vortex generator. Details of design tests and manufacturing of the perturbation generator are presented. The device produced controlled perturbation with frequencies in excess of 250 Hz. Preliminary testing and evaluation of the perturbation generator performance was conducted in a 4 inch cylindrical pipe. Observations of vortex shedding frequencies from a centerbody were measured. Further evaluation with the perturbation generator attached to the vortex generator in a 2 x 3 foot wind tunnel were also conducted. Hot-wire anemometry was used to confirm the perturbation generator's ability to introduce controlled frequency fluctuations. Comparison of the energy levels of the disturbances in the vortex core was made between locations 42 chord lengths and 15 chord lengths downstream.

Riester, J. E.↗