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Stability of compressible reacting mixing layer

Linear instability of compressible reacting mixing layers is analyzed with emphasis on the effects of heat release and compressibility. Laminar solutions of the compressible boundary-layer equations are used as the base flows. The parameters of this study are the adiabatic flame temperature, the Mach number of the upper stream, frequency, wavenumber, and the direction of propagation of the disturbance wave. Stability characteristics of the flow are presented. Three groups of unstable modes are found when the Mach number and/or heat release are large. Finally, it is shown that the unstable modes are two-dimensional for large heat release even in highly compressible flow.

Shin, D. S.↗

Theory on instability and transition

The fundamental fluid dynamics governing instability and transition to turbulence in boundary layers are considered, and attention is focused on the key aspects of nonlinear dynamics central to the transition process and to turbulent boundary-layer phenomena. Emphasis is placed on truly nonlinear theories, in which the boundary layer mean-flow profile is completely altered from its original form. Nonlinear TS transitions, Euler-stage interactions, and vortex/wave interactions are discussed, and compressible boundary layers are analyzed. Connections with experiments and computations are outlined, along with overall trends including the extension of the nonlinear theory and the advancement in the compressible and other flow regimes.

Smith, Frank T.↗

Real gas effects on hypersonic boundary-layer stability

High-temperature effects alter the physical and transport properties of a gas, air in particular, due to vibrational excitation and gas dissociation, and thus the chemical reactions have to be considered in order to compute the flow field. Linear stability of high-temperature boundary layers is investigated under the assumption of chemical equilibrium and this gas model is labeled here as real gas model. In this model, the system of stability equations remains of the same order as for the perfect gas and the effect of chemical reactions is introduced only through mean flow and gas property variations. Calculations are performed for Mach 10 and 15 boundary layers and the results indicate that real gas effects cause the first mode instability to stabilize while the second mode is made more unstable. It is also found that the second mode instability shifts to lower frequencies. There is a slight destabilizing influence of real gas on the Goertler instability as compared to the perfect gas results.

Malik, M. R.↗

Direct numerical simulation of laminar breakdown in high-speed, axisymmetric boundary layers

The compressible Navier-Stokes equations are solved using spectral collocation and high-order compact-difference techniques to simulate the laminar breakdown in high-speed, axisymmetric boundary-layer flow. Mach 4.5 flow along a hollow cylinder and Mach 6.8 flow along a sharp cone are considered. Data obtained replicate two previously unexplained phenomena, namely, the appearance of so-called 'rope-like waves' and 'the precursor transition effect', in which transitional flow originates near the critical layer well upstream of the transition location at the wall. The numerical data also reveal that neither of these effects can be explained, even qualitatively, by linear stability theory alone. It is shown that rope-like appearance arises from secondary instability. Certain features of the precursor transition effect also emerge from secondary instability but its nature is revealed to be fundamentally nonlinear.

Pruett, C. D.↗

A finite Reynolds-number approach for the prediction of boundary-layer receptivity in localized regions

Previous theoretical work on the boundary layer receptivity problem has utilized large Reynolds number asymptotic theories, thus being limited to a narrow part of the frequency-Reynolds number domain. An alternative approach is presented for the prediction of localized instability generation which has a general applicability, and also accounts for finite Reynolds number effects. This approach is illustrated for the case of Tollmien-Schlichting wave generation in a Blasius boundary layer due to the interaction of a free stream acoustic wave with a region of short scale variation in the surface boundary condition. The specific types of wall inhomogeneities studied are: regions of short scale variations in wall suction, wall admittance, and wall geometry (roughness). Extensive comparison is made between the results of the finite Reynolds number approach and previous asymptotic predictions, which also suggests an alternative way of using the latter at Reynolds numbers of interest in practice.

Choudhari, Meelan↗

Instability and transition in three-dimensional supersonic boundary layers

Linear stability of three-dimensional flow past a 5 deg semi-vertex sharp cone at 2 deg incidence in Mach 3.5 free-stream is studied. Computed laminar mean flow profiles along the leeward line of symmetry are highly inflectional and, hence, much more unstable than the profiles along the windward line of symmetry. Accordingly, transition occurs much earlier along the leeward line both in the present calculations (based upon eN approach) and in the experiments of King (1991) performed in NASA Langley 'quiet' tunnel. Boundary-layer transition in the region between the two symmetry lines is influenced by the crossflow generated due to the angle of attack and, as a consequence, it progressively moves upstream with increasing azimuthal angle measured from the windward line. The computed transition front is qualitatively similar to the experimental results, although some differences remain.

Malik, M. R.↗

On the three-dimensional instability of laminar boundary layers on concave walls

A study is made of the stability of laminar boundary-layer profiles on slightly curved walls relative to small disturbances that result from vortices whose axes are parallel to the principal direction of flow. The result is an eigenvalue problem by which, for a given undisturbed flow at a prescribed wall, the amplification or decay is computed for each Reynolds number and each vortex thickness. For neutral disturbances (zero amplification) a critical Reynolds number is determined for each vortex distribution. The numerical calculation produces amplified disturbances on concave walls only.

FLOW, LAMINAR↗

Crossflow instability control on a swept-wing: Preliminary studies

The pressure distribution on a swept wing causes the streamlines at the edge of the boundary layer to be curved. This pressure gradient normal to the external streamline creates a velocity component normal to the external streamline within the boundary layer which is referred to as the crossflow velocity. Because the crossflow velocity profile perpendicular to the wing surface has an inflection point, the profile is unstable. The stationary instability mode takes the form of crossflow vortices. Under these conditions, the boundary layer on the wing is extremely unstable and transition to turbulent flow takes place much closer to the leading edge of the wing than it would on an unswept wing. Higher skin friction drag is associated with turbulent flow, and so better aircraft performance could be obtained if the crossflow could be eliminated One method of controlling crossflow that is being investigated is boundary-layer suction. An extensive airfoil suction experiment in the 8 feet Transonic Pressure Tunnel (TPT) at NASA Langley Research Center will begin late in 1994. Because of the size, complexity, and expense associated with this test, a number of 'risk-reduction' tests are currently being conducted. The 20 x 28 in. Shear Flow Control Tunnel at NASA Langley is being used for some of these tests. Prior to the summer of 1994, a flat plate with a swept leading edge was installed in the 20 x 28 in. tunnel, with a displacement body mounted on the tunnel ceiling that created a pressure distribution on the plate similar to the pressure distribution on a swept wing. The flow over the plate was investigated during the summer of 1994 using a laser Doppler velocimeter (LDV) system. The LDV measurements indicated the possible presence of multiple disturbance modes, a rarely-seen phenomena since, in most tests, one disturbance mode dominates. The possible existence of multiple disturbance modes in the flat plate boundary layer, however, means that the flow in the 20 x 28 in. tunnel is of interest itself, and will be investigated more thoroughly in the future. With a view to these investigations, the boundary layer traverse mechanism in the 20 x 28 in. tunnel was modified to improve its performance, and strain gauges were mounted on the traverse in order to monitor its deflection during a test. Other preliminary work conducted in the 20 x 28 in. tunnel included the use of an infrared camera system. Previous work with this system showed that transition indeed could be detected, but the signal produced by the crossflow vortices was too weak to be detected. It was hoped that spraying the flat plate with naphthalene would augment the heat transfer associated with the crossflow vortices so that they would show up in a IR image; however, experiments showed that this would not work. Another set of tests was conducted in the 20 x 28 in. tunnel to determine the tripping requirements for a set of airfoil-shaped struts that will be used in the 8 feet TPT experiment. Since the Reynolds number associated with these struts is small, a laminar boundary layer would separate early, causing large fluctuations in the flow field. A turbulent boundary layer would remain attached further back, but tripping from laminar to turbulent flow at low Reynolds number is very difficult. However, trip strip configurations were found that should effectively trip the boundary layer at the required conditions. Currently underway is an investigation of the data acquisition requirements for the 8 feet TPT experiment, with the purpose of the finding the minimum amount of data needed to characterize sufficiently the swept-wing boundary layer. This study is being conducted using a numerically generated data set.

Bridges, David H.↗

Combustion of solid fuel slabs with gaseous oxygen in a hybrid motor analog

Using a high-pressure, two-dimensional hybrid motor, an experimental investigation was conducted on fundamental processes involved in hybrid rocket combustion. HTPB (Hydroxyl-terminated- Polybutadiene) fuel cross linked with diisocyanate was burned with GOX under various operating conditions. Large amplitude pressure oscillations were encountered in earlier test runs. After identifying the source of instability and decoupling the GOX feed line system and combustion chamber, the pressure oscillations were drastically reduced from +/- 20% of the localized mean pressure to an acceptable range of +/- 1.5%. Embedded fine-wire thermocouples indicated that the surface temperature of the burning fuel was around 1000 K depending upon axial locations and operating conditions. Also, except near the leading-edge region, the subsurface thermal wave profiles in the upstream locations arc thicker than those in the downstream locations since the solid-fuel regression rate, in general, increases with distance along the fuel slab. The recovered solid fuel slabs in the laminar portion of the boundary layer exhibited smooth surfaces, indicating the existence of a liquid melt layer on the burning fuel surface in the upstream region. After the transition section, which displayed distinct transverse striations, the surface roughness pattern became quite random and very pronounced in the downstream turbulent boundary-layer region. Both real time X-ray radiography and ultrasonic pulse-echo techniques were used to determine the instantaneous web thicknesses and instantaneous solid-fuel regression rates over certain portions of the fuel slabs. Globally averaged and axially dependent but time-averaged regression rates were also obtained and presented. Several tests were conducted using, simultaneously, one translucent fuel slab and one fuel slab processed with carbon black powder. The addition of carbon black did not affect the measured regression rates or surface temperatures in comparison to the translucent fuel slabs.

Chiaverini, Martin J.↗

Combustion of solid fuel slabs with gaseous oxygen in a hybrid motor analog

Using a high-pressure, two-dimensional hybrid motor, an experimental investigation was conducted on fundamental processes involved in hybrid rocket combustion. HTPB (Hydroxyl-terminated Polybutadiene) fuel cross-linked with diisocyanate was burned with gaseous oxygen (GOX) under various operating conditions. Large-amplitude pressure oscillations were encountered in earlier test runs. After identifying the source of instability and decoupling the GOX feed-line system and combustion chamber, the pressure oscillations were drastically reduced from plus or minus 20% of the localized mean pressure to an acceptable range of plus or minus 1.5%. Embedded fine--wire thermocouples indicated that the surface temperature of the burning fuel was around 1000 K depending upon axial locations and operating conditions. Also, except near the leading edge region, the subsurface thermal wave profiles in the upstream locations are thicker than those in the downstream locations since the solid-fuel regression rate, in general, increases with distance along the fuel slab. The recovered solid fuel slabs in the laminar portion of the boundary layer exhibited smooth surfaces, indicating the existence of a liquid melt layer on the burning fuel surface in the upstream region. After the transition section, which displayed distinct transverse striations, the surface roughness pattern became quite random and very pronounced in the downstream turbulent boundary-layer region. Both real-time X-ray radiography and ultrasonic pulse echo techniques were used to determine the instantaneous web thicknesses and instantaneous solid-fuel regression rates over certain portions of the fuel slabs. Globally averaged and axially dependent but time-averaged regression rates were also obtained and presented. Several tests were conducted using, simultaneously, one translucent fuel slab and one fuel slab processed with carbon black powder. The addition of carbon black did not affect the measured regression rates or surface temperatures in comparison to the translucent fuel slabs.

Chiaverini, Martin J.↗

Some Effects of Leading-Edge Sweep on Boundary-Layer Transition at Supersonic Speeds

The effects of crossflow and shock strength on transition of the laminar boundary layer behind a swept leading edge have been investigated analytically and with the aid of available experimental data. An approximate method of determining the crossflow Reynolds number on a leading edge of circular cross section at supersonic speeds is presented. The applicability of the critical crossflow criterion described by Owen and Randall for transition on swept wings in subsonic flow was examined for the case of supersonic flow over swept circular cylinders. A wide range of applicability of the subsonic critical values is indicated. The corresponding magnitude of crossflow velocity necessary to cause instability on the surface of a swept wing at supersonic speeds was also calculated and found to be small. The effects of shock strength on transition caused by Tollmien-Schlichting type of instability are discussed briefly. Changes in local Reynolds number, due to shock strength, were found analytically to have considerably more effect on transition caused by Tollmien-Schlichting instability than on transition caused by crossflow instability. Changes in the mechanism controlling transition from Tollmien-Schlichting instability to crossflow instability were found to be possible as a wing is swept back and to result in large reductions in the length of laminar flow.

Chapman, Gray T.↗

Annual Research Briefs

This report contains the 1997 annual progress reports of the research fellows and students supported by the Center for Turbulence Research (CTR). Titles include: Invariant modeling in large-eddy simulation of turbulence; Validation of large-eddy simulation in a plain asymmetric diffuser; Progress in large-eddy simulation of trailing-edge turbulence and aeronautics; Resolution requirements in large-eddy simulations of shear flows; A general theory of discrete filtering for LES in complex geometry; On the use of discrete filters for large eddy simulation; Wall models in large eddy simulation of separated flow; Perspectives for ensemble average LES; Anisotropic grid-based formulas for subgrid-scale models; Some modeling requirements for wall models in large eddy simulation; Numerical simulation of 3D turbulent boundary layers using the V2F model; Accurate modeling of impinging jet heat transfer; Application of turbulence models to high-lift airfoils; Advances in structure-based turbulence modeling; Incorporating realistic chemistry into direct numerical simulations of turbulent non-premixed combustion; Effects of small-scale structure on turbulent mixing; Turbulent premixed combustion in the laminar flamelet and the thin reaction zone regime; Large eddy simulation of combustion instabilities in turbulent premixed burners; On the generation of vorticity at a free-surface; Active control of turbulent channel flow; A generalized framework for robust control in fluid mechanics; Combined immersed-boundary/B-spline methods for simulations of flow in complex geometries; and DNS of shock boundary-layer interaction - preliminary results for compression ramp flow.

Spinks, Debra↗

"Dust Devils": Gardening Agents on the Surface of Mars, and Hidden Hazards to Human Exploration?

Dust devils are familiar sites in the and regions of the world: they can produce quite spectacular displays of dust lofting when the vortices scavenge very loose dust from a dry lake bed or from recently disturbed agricultural fields. If one were to arrive at the center of an arid region, take one photograph, or even a series of photographs over a period of several days, then return the images for laboratory analysis, it would be most likely concluded that the region was inactive from an aeolian perspective. No images of general dust movement were obtained, nor were any dust devils "caught on camera" owing to their ephemeral and unpredictable appearance, and the fact that there was deceptively little residue of their actions. If, however, a camera were to take a 360 degree continuous recording over a period of a year, and the film were then to be shown at high speed over a period a several minutes, the impression might be that of a region ravaged by air vorticity and dust movement. Extrapolate this over geological time, and it is possible to visualize dust devils as prime aeolian agents, rather than insignificant vagaries of nature, On Mars, the thin atmosphere permits the surface of the planet to be heated but it does not itself retain heat with the capacity of the earth's atmosphere. This gives rise to greater thermal instability near the surface of Mars as "warm" air pockets diapiritically inject themselves into higher atmospheric layers. Resulting boundary-layer vorticity on Mars might therefore be expected to produce dust devils in abundance, if only seasonally. The spectacular images of dust devils obtained by Pathfinder within its brief functional period on the planet testify to the probability of highly frequent surface vorticity in light of the above reasoning about observational probability. Notably, the Pathfinder devils appeared to be at least a kilometer in height. There are several consequences for the geology of Mars, and for human exploration, if dust devils are to be expected in reasonable abundance. First, from a geological perspective, the vortices will act as "gardening" agents for the top few centimeters of entrainable material. Over time (hundreds of millions, or billions of years being available), they will cover the surface with scouring paths, and the grain sizes that can be lofted by a vortex probably extends over the whole sand to dust range. The depositional paths are, of course, much larger, so that vortex-induced deposition is more widespread than vortex-induced erosion, and will without doubt, affect the whole region in which the dust devils occur (this might explain why rocks at the Viking site seemed oddly capped with dust in a region apparently subject to general aeolian scouring). On Mars, the lift forces in dust devils might be less than on earth owing to the much thinner atmosphere, but this may be counterbalanced by lower gravity and greater vortex velocities. Certainly, when active, other aeolian phenomena on Mars --sand motion and dust storms, seem no less energetic and no less capable of lofting sediments than equivalent terrestrial aeolian phenomena. Every several years, within the current climatic regime, the surface of Mars is subject to light dust fall from global dust storms. Over time, this should develop a very uniform surface layer, with commensurate uniformity in grain size, mineralogy, albedo, color, and general spectroscopic properties. Dust devils will disturb this situation by continually mixing the surface dust with underlying layers, perhaps composed of silt and sand. This size mixing will also involve compositional mixing. After some years, the thin layer of dust that may be difficult to entrain alone, becomes progressively mixed with coarser materials that could reduce the general aeolian threshold of the soil. Certainly the continual disturbance by vorticity will prevent surface stabilization that may bind or indurate grains (caused by slow cementation or ice welding at grain boundaries). If dust devils continually loft dust to kilometer heights, and the dust is sprayed into many cubic kilometers of atmosphere each time, could the devils produce a continual background of atmospheric dust that might be mistaken for the fallout of a distant large-scale dust storm? From a human exploration perspective, dust devils are unlikely to pose any, life- threatening situation for an astronaut unfortunate enough to encounter a momentary swirling cloud of loose soil. However, it is noted that pervasive dust is probably one of the greatest long-term hazards for a human encampment. The fineness and penetration capabilities of the dust, its electrostatic adhesive properties, and its complete ubiquity, render the material a persistent nuisance at best, but at worst, over a period of many months it is possible that space suits, machinery, habitat interiors, air filters, and so forth, could become jeopardized. Owing to dust penetration, the space suits used in the Apollo landings were rendered unusable after a few EVA activities. There will be a definite attempt to situate a human colony on Mars in an area that is far removed from the regions of the planet known for being the centers of major dust storms. At the heart of these storm systems, the dust lofting mechanics are unknown, but they are energetic and perhaps potentially life-threatening for an astronaut. Locating a colony in a region that appears from space to be meteorologically benign may lead to colony placement in a region prone to dust devils, but dust devils are not (or have not been) detectable from orbital observations: the region surveyed for placement will appear like the apparently inactive and area referred to earlier. The region may be spared from highly energetic weather systems, but it may not be necessarily immune from continual dust disturbance. Additional information is contained in the original.

Marshall, J.↗

Measurements in Separated and Transitional Boundary Layers Under Low-Pressure Turbine Airfoil Conditions

Detailed velocity measurements were made along a flat plate subject to the same dimensionless pressure gradient as the suction side of a modern low-pressure turbine airfoil. Reynolds numbers based on wetted plate length and nominal exit velocity were varied from 50,000 to 300,000, covering cruise to takeoff conditions. Low and high inlet free-stream turbulence intensities (0.2% and 7%) were set using passive grids. The location of boundary-layer separation does not depend strongly on the free-stream turbulence level or Reynolds number, as long as the boundary layer remains non-turbulent prior to separation. Strong acceleration prevents transition on the upstream part of the plate in all cases. Both free-stream turbulence and Reynolds number have strong effects on transition in the adverse pressure gradient region. Under low free-stream turbulence conditions transition is induced by instability waves in the shear layer of the separation bubble. Reattachment generally occurs at the transition start. At Re = 50,000 the separation bubble does not close before the trailing edge of the modeled airfoil. At higher Re, transition moves upstream, and the boundary layer reattaches. With high free-stream turbulence levels, transition appears to occur in a bypass mode, similar to that in attached boundary layers. Transition moves upstream, resulting in shorter separation regions. At Re above 200,000, transition begins before separation. Mean velocity, turbulence and intermittency profiles are presented.

Volino, Ralph J.↗

Flap Edge Aeroacoustic Measurements and Predictions

An aeroacoustic model test has been conducted to investigate the mechanisms of sound generation on high-lift wing configurations. This paper presents an analysis of flap side-edge noise, which is often the most dominant source. A model of a main element wing section with a half-span flap was tested at low speeds of up to a Mach number of 0.17, corresponding to a wing chord Reynolds number of approximately 1.7 million. Results are presented for flat (or blunt), flanged, and round flap-edge geometries, with and without boundary-layer tripping, deployed at both moderate and high flap angles. The acoustic database is obtained from a Small Aperture Directional Array (SADA) of microphones, which was constructed to electronically steer to different regions of the model and to obtain farfield noise spectra and directivity from these regions. The basic flap-edge aerodynamics is established by static surface pressure data, as well as by Computational Fluid Dynamics (CFD) calculations and simplified edge flow analyses. Distributions of unsteady pressure sensors over the flap allow the noise source regions to be defined and quantified via cross-spectral diagnostics using the SADA output. It is found that shear layer instability and related pressure scatter is the primary noise mechanism. For the flat edge flap, two noise prediction methods based on unsteady-surface-pressure measurements are evaluated and compared to measured noise. One is a new causality spectral approach developed here. The other is a new application of an edge-noise scatter prediction method. The good comparisons for both approaches suggest that much of the physics is captured by the prediction models. Areas of disagreement appear to reveal when the assumed edge noise mechanism does not fully define, the noise production. For the different edge conditions, extensive spectra and directivity are presented. Significantly, for each edge configuration, the spectra for different flow speeds, flap angles, and surface roughness were successfully scaled by utilizing aerodynamic performance and boundary layer scaling method developed herein.

Brooks, Thomas F.↗

Flap Edge Aeroacoustic Measurements and Predictions

An aeroacoustic model test has been conducted to investigate the mechanisms of sound generation on high-lift wing configurations. This paper presents an analysis of flap side-edge noise, which is often the most dominant source. A model of a main element wing section with a half-span flap was tested at low speeds of up to a Mach number of 0.17, corresponding to a wing chord Reynolds number of approximately 1.7 million. Results are presented for flat (or blunt), flanged, and round flap-edge geometries, with and without boundary-layer tripping, deployed at both moderate and high flap angles. The acoustic database is obtained from a Small Aperture Directional Array (SADA) of microphones, which was constructed to electronically steer to different regions of the model and to obtain farfield noise spectra and directivity from these regions. The basic flap-edge aerodynamics is established by static surface pressure data, as well as by Computational Fluid Dynamics (CFD) calculations and simplified edge flow analyses. Distributions of unsteady pressure sensors over the flap allow the noise source regions to be defined and quantified via cross-spectral diagnostics using the SADA output. It is found that shear layer instability and related pressure scatter is the primary noise mechanism. For the flat edge flap, two noise prediction methods based on unsteady surface pressure measurements are evaluated and compared to measured noise. One is a new causality spectral approach developed here. The other is a new application of an edge-noise scatter prediction method. The good comparisons for both approaches suggest that much of the physics is captured by the prediction models. Areas of disagreement appear to reveal when the assumed edge noise mechanism does not fully define the noise production. For the different edge conditions, extensive spectra and directivity are presented. Significantly, for each edge configuration, the spectra for different flow speeds, flap angles, and surface roughness were successfully scaled by utilizing aerodynamic performance and boundary layer scaling methods developed herein.

Brooks, Thomas F.↗

Experimental Investigation of Separated and Transitional Boundary Layers Under Low-Pressure Turbine Airfoil Conditions

Modern low-pressure turbine airfoils are subject to increasingly stronger pressure gradients as designers impose higher loading in an effort to improve efficiency and to reduce part count. The adverse pressure gradients on the suction side of these airfoils can lead to boundary-layer separation, particularly under cruise conditions. Separation bubbles, notably those which fail to reattach, can result in a significant degradation of engine efficiency. Accurate prediction of separation and reattachment is hence crucial to improved turbine design. This requires an improved understanding of the transition flow physics. Transition may begin before or after separation, depending on the Reynolds number and other flow conditions, has a strong influence on subsequent reattachment, and may even eliminate separation. Further complicating the problem are the high free-stream turbulence levels in a real engine environment, the strong pressure gradients along the airfoils, the curvature of the airfoils, and the unsteadiness associated with wake passing from upstream stages. Because of the complicated flow situation, transition in these devices can take many paths that can coexist, vary in importance, and possibly also interact, at different locations and instances in time. The present work was carried out in an attempt to systematically sort out some of these issues. Detailed velocity measurements were made along a flat plate subject to the same nominal dimensionless pressure gradient as the suction side of a modern low-pressure turbine airfoil ('Pak-B'). The Reynolds number based on wetted plate length and nominal exit velocity, Re, was varied from 50;000 to 300; 000, covering cruise to takeoff conditions. Low, 0.2%, and high, 7%, inlet free-stream turbulence intensities were set using passive grids. These turbulence levels correspond to about 0.2% and 2.5% turbulence intensity in the test section when normalized with the exit velocity. The Reynolds number and free-stream turbulence level do not have a significant effect on the location of boundary-layer separation unless they are high enough to induce transition upstream of separation. The location and extent of the transition zone, in contrast, depend strongly on Re and TI. The beginning of reattachment closely follows the onset of transition. Under low free-stream turbulence conditions the boundary layer is laminar at separation and then begins to exhibit fluctuations in a finite frequency band in the shear layer over the separation bubble. These fluctuations are due to instability waves. The fluctuations grow in magnitude, higher harmonics are generated, and finally lead to a breakdown to turbulence. Transition begins in the shear layer, but quickly spreads to the near wall region and causes the boundary layer to reattach. The transition is rapid and the resulting turbulence contains a full range of high and low frequencies. Under high free-stream turbulence conditions, slowly growing low-frequency fluctuations are induced in the pretransitional boundary layer by the free-stream. The separation bubbles are considerably thinner than in the low TI cases, resulting in thinner boundary layers at the end of the test wall. At Re=50,000 and 100,000, the pre-transitional boundary layer separates at about the same location as in the low TI cases. Transition occurs through a bypass mode, begins upstream of the corresponding low-TI location, and proceeds in a manner similar to that of an attached boundary layer. Under high TI at Re=200,000 and 300,000, transition begins before separation. The boundary layer may separate, but if it does the separation bubble is very short and does not significantly affect the downstream development of the boundary layer. A comparison is made to previous work in a simulated cascade.

Hultgren, Lennart S.↗

Effect of Far-Field Boundary Conditions on Boundary-Layer Transition

The effect of far-field boundary conditions on the evolution of a finite-amplitude two-dimensional wave in the Blasius boundary layer is assessed. With the use of the parabolized stability equations (PSE) theory for the numerical computations, either asymptotic, Dirichlet, Neumann or mixed boundary conditions are imposed at various distances from the wall. The results indicate that asymptotic and mixed boundary conditions yield the most accurate mean-flow distortion and unsteady instability modes in comparison with the results obtained with either Dirichlet or Neumann conditions.

Bertolotti, Fabio P.↗