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NASA NTRS2021

Modeling Laminar-to-Turbulent Transition in the Panel Test Facility Arcjet

A computational fluid dynamics (CFD) laminar-to-turbulence transition model was developed for the NASA Ames Research Center’s 20 MW Panel Test Facility (PTF). Surface pressure, heat flux to a water-cooled plate, and surface temperature on a tile plate coated with reaction-cured glass were measured across several conditions in the facility and compared with laminar and fully-turbulent CFD simulations. The potential for bypass transition in the PTF nozzle was assessed via application of the Langtry-Menter four-equation transitional shear-stress transport (SST) model. Results from the transition model were inconsistent with measurements. Flow interaction with a boundary conditioning plate feature inside the nozzle was also investigated as a potential source of laminar-to-turbulent transition using two turbulence models with specified transition locations. The Baldwin-Lomax turbulence model was configured to simulate a transition at the upstream edge of the boundary conditioning plate and produced results consistent with the surface pressure measurements but not the cold-wall heat flux. Finally, the SST turbulence model was calibrated to transition at the upstream edge of the boundary conditioning plate and produced results consistent with both the surface pressure and cold-wall heat flux measurements. The SST-based model demonstrated reasonable agreement with surface temperature measurements on the reaction-cured glass tile, albeit with some discrepancies.

Computational Fluid Dynamics↗
NASA NTRSDate not supplied

Toward Verification of the γ-Reθt Transition Model in OVERFLOW and FUN3D

The results of an ongoing assessment of the transition modeling capability in NASA's OVERFLOW and FUN3D programs are presented, with a focus on the Langtry-Menter γ-Reθt transition model in combination with the shear-stress transport (SST) turbulence model. While the effect of numerics and boundary conditions on the accuracy and iterative convergence of RANS solutions for fully turbulent flows has been well documented, especially in the context of canonical flow configurations, the same cannot be said for transport-equation-based transition models coupled with RANS-based turbulence models. Given the criticality of transition modeling for new aircraft design and optimization, there has been a renewed focus on the accuracy of such transition models and their inconsistent implementation across different flow solvers as seen from the AIAA and NATO-AVT workshops. In this work, we aim to establish the verification of such models via these two well established CFD codes with different numerics. The goal is to produce high-quality data, such as grids, solutions, and other auxiliary data, that may be utilized for code verification by others in the CFD community. As a first step, the work reported here is focused on the Langtry-Menter transition model as applied to two simple 2D configurations, namely the flat plate, and the NLF-0416, respectively. The paper also highlights how the boundary conditions and baseline turbulence model can affect the solutions from the SST-based Langtry-Menter transition model. A preliminary evaluation of the automatic mesh adaption capabilities of these solvers and potential benefits for flow configurations involving a mix of laminar, transitional, and fully turbulent flows is also reported.

CFD Modeling↗
NASA NTRSDate not supplied

Implementation of Two Local Correlation-Based Transition Models in OVERFLOW 2.3e

Accurate prediction of the laminar-to-turbulent boundary layer transition is highlighted as a vital component of NASA's CFD Vision 2030 Study. With an increased emphasis on greener air transports and sustainable aviation, transition modeling is anticipated to have an added significance, particularly in the applications related to laminar flow technology. However, unmanned aerial vehicles, crewed reentry vehicles, and ground-to-flight extrapolation all benefit from transition models. It is useful to incorporate a variety of models in CFD solvers because there isn't a single transition model that is ideal for the complete spectrum of applications. While the Langtry-Menter γ–Reθt model has been widely used for CFD predictions of flows with laminar, transitional, and turbulent boundary layers, it does not meet the criteria for Galilean invariance, a desirable attribute for rotorcraft applications. To help overcome that limitation, we have implemented Menter's SST-based γ transition model within NASA’s OVERFLOW Overset CFD code (version 2.3e). In addition, an SA-based implementation of the Langtry-Menter γ–Reθt transition model has also been implemented in view of the increased robustness of the SA-turbulence model for external aerodynamic applications. An initial assessment of the implemented models has been carried out using benchmark 2D test cases involving flat plates and the NLF-0416 airfoil, focusing on bypass, Tollmien-Schlichting, and laminar separation bubble-induced transition scenarios. In comparison to the Langtry-Menter γ–Reθt model, both models were found to produce increased computation efficiency, principally as a result of the decrease from four to three auxiliary transport equations. Results from the initial analysis will be presented, along with additional details pertaining to the deployment of these models.

CFD modeling↗
NASA NTRS1959

Effects of Nose Radius and Extreme Cooling on Boundary-Layer Transition for Three Smooth 15°-Cone-Cylinders in Free Flight at Mach Numbers to 8.50

Three highly polished 15°- included- angle cone- cylinders with hemispherical tips of several diameters ( 2, 3, and 4 in.) have been flown in order to obtain boundary- layer transition data at very low wall to local stream temperature ratios, and heat- transfer data. All surfaces had a 2-microinch average roughness height. Laminar flow existed over the entire hemispherical nose of the 2- and 3-inch-tip- diameter models throughout the complete flight history. Extreme cooling to wall to local stream temperature ratios at the sonic point as low as 0.20 did not cause transition on the nose for diameters as large as 3 inches. However, extreme cooling did cause early transition on the 4-inch model where it appears probable that transition occurred forward of the 45° station at a wall to local stream temperature ratio of about 0.26. Variations in tip diameter influenced transition downstream of the nose under conditions of extreme cooling. The 2-inch- tip model was laminar at all cone- cylinder stations at temperature ratios as low as 0.32 whereas the 3- and 4-inch-tip models were turbulent at the same local flow conditions but at higher wall to local temperature ratios. Transition on the cone and cylinder of the 3- and 4-inch- tip bodies appeared to be sensitive to local Mach number, and occurred at higher local temperature ratios when values of local Mach number were higher. Increasing the nose diameter from 2 to 3 inches significantly changed the local flow conditions for which laminar flow existed on the cone- cylinder afterbody. However, a further increase in tip size t o a 4-inch diameter had no discernable effect on the local flow conditions at transition. The transition results of the 3- and 4-inch-nose-diameter smooth bodies are similar to those observed on a 7/8-inch-nose-diameter body with roughened surfaces. Turbulent boundary layers resulted in both cases at very low wall to local stream temperature ratios. Both laminar and turbulent heat-transfer data were in good agreement with theoretical Stanton numbers when heat-transfer reduction due to tip blunting was considered.

CYLINDRICAL AFTERBODY↗
NASA NTRS1973

Transition radiation in astrophysics.

Transition radiation produced by relativistic electrons traversing cosmic grains is investigated as a possible source of celestial X rays. The detailed theory of transition radiation including the formation-zone effect is used to calculate the X-ray emissivity in interstellar space. It is found that the largest contribution of transition radiation to the observed X-ray emission from the galactic disk is at about 2 keV, where less than about 0.3% of the observed emissivity is due to transition radiation. At higher energies transition radiation is strongly suppressed by the formation-zone effect, while at lower energies the observed emissivity increases much faster with decreasing energy than does transition radiation. Transition radiation is also compared with bremsstrahlung, synchrotron emission, and Compton scattering. The comparison with synchrotron emission and bremsstrahlung relates X-ray production by transition radiation to radio emission and to approximately 100-MeV gamma-ray production, respectively.

Yodh, G. B.↗
NASA NTRS1990

Direct numerical simulation of the transitional zone

Properties of the transitional zone in channel and boundary-layer flow are determined from the results of direct numerical simulations of forced transition. Three channel flow cases produce similar behavior, particularly in the 'transition function' relevant for some algebraic eddy viscosity models of the transitional zone. Moreover, the transitional zone from the computed forced boundary-layer transition is qualitatively similar to experimental data for natural transition and to the computed channel flow transition.

Zang, Thomas A.↗
NASA NTRS1994

Physical description of boundary-layer transition: Experimental evidence

The problems of understanding the origins of turbulent flow and transition to turbulent flow are the most important unsolved problems of fluid mechanics and aerodynamics. It is well known that the stability, transition, and turbulent characteristics of bounded shear layers are fundamentally different from those of free shear layers. Likewise, the stability, transition, and turbulent characteristics of open systems are fundamentally different from those of closed systems. Because of the influence of indigenous disturbances, surface geometry and roughness, sound, heat transfer, and ablation, it is not possible to develop general prediction schemes for transition location and the nature of turbulent structures in boundary-layer flows. At the present time no mathematical model exists that can predict the transition Reynolds number on a flat plate. The recent progress in this area is encouraging, in that a number of distinct transition mechanisms have been found experimentally. The theoretical work finds them to be amplitude and Reynolds-number dependent. The theory remains rather incomplete with regard to predicting transition. Amplitude and spectral characteristics of the disturbances inside the laminar viscous layer strongly influence which type of transition occurs. The major need in this area is to understand how freestream disturbances are entrained into the boundary layer, i.e., to answer the question of receptivity. We refer receptivity to the mechanism(s) that cause freestream disturbances to enter the boundary layer and create the initial amplitudes for unstable waves.

Saric, William S.↗
NASA NTRS1994

Modeling the transition region

The calculation of engineering flows undergoing laminar-turbulent transition presents special problems. Mean-flow quantities obey neither the fully laminar nor the fully turbulent correlations. In addition, local maxima in skin friction, wall temperature, and heat transfer often occur near the end of the transition region. Traditionally, modeling this region has been important for the design of turbine blades, where the transition region is long in relation to the chord length of the blade. More recently, the need for better transition-region models has been recognized by designers of hypersonic vehicles where the high Mach number, the low Reynolds number, and the low-disturbance flight environment emphasize the importance of the transition region. Needless to say, a model that might work well for the transitional flows typically found in gas turbines will not necessarily work well for the external surface of a hypersonic vehicle. In Section 2 of this report, some of the important flow features that control the transition region will be discussed. In Section 3, different approaches to the modeling problem will be summarized and cataloged. Fully turbulent flow models will be discussed in detail in Section 4; models specifically designed for transitional flow, in Section 5; and the evaluation of models, in Section 6.

Singer, Bart A.↗
NASA NTRS1995

The transition regions of Capella

We have used the Goddard High Resolution Spectrometer (GHRS) to observe the spectoscopic binary system Capella (G8 III + G1 III). Exposures with the G140L, G140M, G160M, G200M, and echelle gratings provide emission line profiles with unprecedented signal-to-noise and spectral resolving power (lambda/Delta-lambda) up to 92,000. Multi-Gaussin fits to the line profiles show that the hotter star contributes 60%-70% of the total flux in the chromospheric O I and Mg II resonance lines, but about 90% of the flux in the Si III, Si IV, and C IV lines formed in the transition region at T less than or = 10(exp 5) K. We find clear evidence that the emission lines from the hotter star are systemtically redshifted relative to the photosphere with Doppler shifts of 5 +/- 1 km/s for the +9 +/- 3 km/s in the chromospheric Mg II and O I lines, respectively, increasing to +24 +/- 5 km/s for the transition region Si IV 1393.8A line. The multi-Gaussian fits to permitted transition region lines of SI III, Si IV, C IV, and N V indicate the presence of three components: moderately broad lines formed in the transition region of the hotter star (component H), narrow lines formed in the transition region of the cooler star (component C), and very broad lines that we think are formed in microflares on the hotter star (component B). The He II 1640.4 A feature has an broad profile, which indicates that it is formed by collisional excitation primarily from the hotter star, and a weak narrow component that we interpret as due to radiative recombination on the cooler star. We observed spin-forbidden emission lines of C III), O III), Si III), O IV), O V), and S IV) that are sensitive to electron density. Fainter members of the O IV) multiplet and all of the S IV) lines have never before been seen in any star than the Sun. We determine electron densities in the transition regions of the Capella stars using lines ratios of O IV) lines and emission measure analysis. The emission measures are self-consistent only when the fluxes from each emitting component are considered separately. In particular, the transition region abundance distributions appear to be different on the two stars, and the spin-forbidden lines were not detected in the B component. The emission measures for component H (the G1 star) are consistent with a constant electron pressure (or hydrostatic equilibrium) transition region with P(sub e) = 10(exp 15 + 0.1)/cu cm K and possibly solar 'coronal' abundances.

Linsky, Jeffrey L.↗
NASA NTRS1959

Boundary-Layer-Transition Measurements on Hemispheres of Various Surface Roughness in a Wind Tunnel at Mach Numbers from 2.48 to 3.55

Wind-tunnel tests have been made to determine the location of the boundary-layer transition on three hemispheres having surface roughness (absolute) values of 50, 580, and 2760 microinches. After the initial test run of the smoothest (50 microinch) hemisphere, holes ranging in depth from 1500 to 2500 microinches were noticed in the meridian where transition was observed. The holes were believed to be caused by particles in the air stream. Shadowgraph pictures were obtained of all hemispheres and surface temperature measurements were made on one hemisphere (580 microinches). Tests at high Reynolds numbers (6.4 to 7.5 x 10(exp 6) and a Mach number of 2.48 did not indicate any transition on the 50-microinch surface hemisphere before the holes appeared. However, after the holes were noticed, transition locations as low as 50 deg(measured from the stagnation point) were observed at similar Reynolds numbers and Mach numbers. It is felt the transition resulted from the holes. Similar transition locations of approximately 500 were also observed in the tests of hemispheres with surface roughness values of 580 and 2760 microinches at high Reynolds numbers (6.4 x 10(exp 6) to 7.5 x 10(exp 6)) and at a Mach number of 2.48. The results at a Mach number of 2.48 indicate that an absolute surface roughness value of 50 microinches was not critical in causing boundary-layer tran sition at Reynolds numbers of 6.4 to 7.5 x 10(exp 6) whereas roughness values of 580 and 2760 microinches were greater than critical. Transition Reynolds numbers based on momentum thickness, R(sub phi T) varied over a range of approximately 480 to 300 for transition locations, alpha, on the hemisphere from 880 to 410 (measured from the stagnation point). A maximum value of R(phi) of 660 (based on alpha = 90 deg) was obtained with the 50-microinch surface hemisphere at a Mach number of 2.48.

Bandettini, Angelo↗
NASA NTRS2000

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.↗
NASA NTRS1961

Effects of Cone Angle, Mach Number, and Nose Blunting on Transition at Supersonic Speeds

An investigation has been made to determine the transition characteristics of a group of blunt cones which varied in included apex angle from 27 deg to 60 deg over a Mach number range from 1.61 to 2.20 and a range of tunnel Reynolds number per foot from about 1.5 x 10(exp 6) to 8.0 x 10(exp 6). The tests were made at zero angle of attack and with zero heat transfer. The results indicate that the general level of transition Reynolds number based on boundary-layer momentum thickness and local flow conditions just outside the boundary layer varied between 600 and 1,100. Changes in Mach number had little effect on transition distance and transition Reynolds number for the near-sharp or very small bluntnesses. The effect of Mach number variation on the larger hemispherical bluntnesses was much stronger, with the strongest Mach number effect occurring for Mach numbers between 1.61 and 1.82. With an increase in nose radius, there was a strong decrease in transition distance and transition Reynolds number at the lower Mach numbers. This adverse effect tended to become weaker with increase in Mach number. An increase in cone angle at a constant Mach number caused a reduction in transition distance and transition Reynolds number for the blunt configurations which had approximately the same values of nose radius.

Czarnecki, K. R.↗
NASA NTRS2004

Transition from Forward Smoldering to Flaming in Small Polyurethane Foam Samples

Experimental observations are presented of the effect of the flow velocity and oxygen concentration, and of a thermal radiant flux, on the transition from smoldering to flaming in forward smoldering of small samples of polyurethane foam with a gas/solid interface. The experiments are part of a project studying the transition from smolder to flaming under conditions encountered in spacecraft facilities, i.e., microgravity, low velocity variable oxygen concentration flows. Because the microgravity experiments are planned for the International Space Station, the foam samples had to be limited in size for safety and launch mass reasons. The feasible sample size is too small for smolder to self propagate because of heat losses to the surrounding environment. Thus, the smolder propagation and the transition to flaming had to be assisted by reducing the heat losses to the surroundings and increasing the oxygen concentration. The experiments are conducted with small parallelepiped samples vertically placed in a wind tunnel. Three of the sample lateral-sides are maintained at elevated temperature and the fourth side is exposed to an upward flow and to a radiant flux. It is found that decreasing the flow velocity and increasing its oxygen concentration, and/or increasing the radiant flux enhances the transition to flaming, and reduces the delay time to transition. Limiting external ambient conditions for the transition to flaming are reported for the present experimental set-up. The results show that smolder propagation and the transition to flaming can occur in relatively small fuel samples if the external conditions are appropriate. The results also indicate that transition to flaming occurs in the char left behind by the smolder reaction, and it has the characteristics of a gas-phase ignition induced by the smolder reaction, which acts as the source of both gaseous fuel and heat.

Bar-Ilan, A.↗
NASA NTRS2006

Shuttle Damage/Repair from the Perspective of Hypersonic Boundary Layer Transition - Experimental Results

An overview is provided of the experimental wind tunnel program conducted at the NASA Langley Research Center Aerothermodynamics Laboratory in support of an agency-wide effort to prepare the Shuttle Orbiter for Return-to-Flight. The effect of an isolated protuberance and an isolated rectangular cavity on hypersonic boundary layer transition onset on the windward surface of the Shuttle Orbiter has been experimentally characterized. These experimental studies were initiated to provide a protuberance and cavity effects database for developing hypersonic transition criteria to support on-orbit disposition of thermal protection system damage or repair. In addition, a synergistic experimental investigation was undertaken to assess the impact of an isolated mass-flow entrainment source (simulating pyrolysis/outgassing from a proposed tile repair material) on boundary layer transition. A brief review of the relevant literature regarding hypersonic boundary layer transition induced from cavities and localized mass addition from ablation is presented. Boundary layer transition results were obtained using 0.0075-scale Orbiter models with simulated tile damage (rectangular cavities) of varying length, width, and depth and simulated tile damage or repair (protuberances) of varying height. Cavity and mass addition effects were assessed at a fixed location (x/L = 0.3) along the model centerline in a region of near zero pressure gradient. Cavity length-to-depth ratio was systematically varied from 2.5 to 17.7 and length-to-width ratio of 1 to 8.5. Cavity depth-to-local boundary layer thickness ranged from 0.5 to 4.8. Protuberances were located at several sites along the centerline and port/starboard attachment lines along the chine and wing leading edge. Protuberance height-to-boundary layer thickness was varied from approximately 0.2 to 1.1. Global heat transfer images and heating distributions of the Orbiter windward surface using phosphor thermography were used to infer the state of the boundary layer (laminar, transitional, or turbulent). Test parametrics include angles-of-attack of 30 deg and 40 deg, sideslip angle of 0 deg, freestream Reynolds numbers from 0.02x106 to 7.3x106 per foot, edge-to-wall temperature ratio from 0.4 to 0.8, and normal shock density ratios of approximately 5.3, 6.0, and 12 in Mach 6 air, Mach 10 air, and Mach 6 CF4, respectively. Testing to simulate the effects of ablation from a proposed tile repair concept indicated that transition was not a concern. The experimental protuberance and cavity databases highlighted in this report were used to formulate boundary layer transition correlations that were an integral part of an analytical process to disposition observed Orbiter TPS damage during STS- 114.

Horvath, Thomas J.↗
NASA NTRS2007

Analysis of Crossflow Transition Flight Experiment aboard the Pegasus Launch Vehicle

The Pegasus wing-glove flight experiment was designed to provide crossflow transition data at high Mach numbers, specifically to help validate stability based predictions for transition onset in a flight environment. This paper provides an analysis of the flight experiment, with emphasis on computational results for crossflow disturbances and the correlation of disturbance growth factors with in-flight transition locations via the e(sup N) method. Implications of the flight data for attachment line stability are also examined. Analysis of the thermocouple data reveals that transition (from turbulent to laminar flow) was first detected during the ascending flight of the rocket when the free stream Mach number exceeded about 4. Therefore, computations have been performed for flight Mach numbers of 4.13, 4.35, 4.56 and 4.99. Due to continually decreasing unit Reynolds number at higher altitudes, the entire wing-glove boundary layer became laminar at the highest flight Mach number computed above. In contrast, the boundary layer flow over the inboard tile region remained transitional up to and somewhat beyond the time of laminarization over the instrumented glove region. Linear stability predictions confirmed that the tile boundary layer is indeed more unstable to crossflow disturbances than the much colder stainless steel glove boundary layer. The transition locations based on thermocouple data from both the glove and the tile regions are found to correlate with stationary-crossflow N-factors within the range of 7 to 12.4 and with traveling mode N-factors between 7.6 and 14.1. Data from the thermocouples and hot film sensors indicates that transition from turbulent to laminar flow (i.e., laminarization) at a fixed point over the glove is generally completed within a flight time interval of 3 seconds. However, the times at which transition begins and ends as inferred from the hot film sensors are found to differ by about 2 seconds from the corresponding estimates based on the thermocouple data.

Malik, Mujeeb R.↗
NASA NTRS2008

Implementation and Validation of a Laminar-to-Turbulent Transition Model in the Wind-US Code

A bypass transition model has been implemented in the Wind-US Reynolds Averaged Navier-Stokes (RANS) solver. The model is based on the Shear Stress Transport (SST) turbulence model and was built starting from a previous SST-based transition model. Several modifications were made to enable (1) consistent solutions regardless of flow field initialization procedure and (2) fully turbulent flow beyond the transition region. This model is intended for flows where bypass transition, in which the transition process is dominated by large freestream disturbances, is the key transition mechanism as opposed to transition dictated by modal growth. Validation of the new transition model is performed for flows ranging from incompressible to hypersonic conditions.

Denissen, Nicholas A.↗
NASA NTRS1940

Boundary-Layer Transition on the N.A.C.A. 0012 and 23012 Airfoils in the 8-Foot High-Speed Wind Tunnel, Special Report

Determinations of boundary-layer transition on the NACA 0012 and 2301 airfoils were made in the 8-foot high-speed wind tunnel over a range of Reynolds Numbers from 1,600,000 to 16,800,000. The results are of particular significance as compared with flight tests and tests in wind tunnels of appreciable turbulence because of the extremely low turbulence in the high-speed tunnel. A comparison of the results obtained on NACA 0012 airfoils of 2-foot and 5-foot chord at the same Reynolds Number permitted an evaluation of the effect of compressibility on transition. The local skin friction along the surface of the NACA 0012 airfoil was measured at a Reynolds Number of 10,000,000. For all the lift coefficient at which tests were made, transition occurred in the region of estimated laminar separation at the low Reynolds Numbers and approach the point of minimum static pressure as a forward limit at the high Reynolds Numbers. The effect of compressibility on transition was slight. None of the usual parameters describing the local conditions in the boundary layer near the transition point served as an index for locating the transition point. As a consequence of the lower turbulence in the 8-foot high-speed tunnel, the transition points occurred consistently farther back along the chord than those measured in the NACA full-scale tunnel. An empirical relation for estimating the location of the transition point for conventional airfoils on the basis of static-pressure distribution and Reynolds Number is presented.

Becker, John V.↗
NASA NTRS2009

Transition Analysis for the Mars Science Laboratory Entry Vehicle

Viscous Laminar-turbulent transition plays an important role in the design of the Mars Science Laboratory (MSL) entry vehicle. The lift-to-drag ratio required for the precision landing trajectory will be achieved via an angle of attack equal to 16 degrees. At this relatively high angle of attack, the boundary layer flow near the leeward meridian is expected to transition early in the trajectory, resulting in substantially increased heating loads. This paper presents stability calculations and transition correlations for a series of wind tunnel models of the MSL vehicle. Experimentally measured transition onset locations are used to correlate with the N-factor calculations for various wind tunnel conditions. Due to relatively low post-shock Mach numbers near the edge of the boundary layer, the dominant instability waves are found to be of the first mode type. The N-factor values correlating with measured transition onset at selected test points from the Mach 6 conventional facility experiments fall between 3.5 and 4.5 and apparently vary linearly with the wind tunnel unit Reynolds number, indicating strong receptivity effect. The small transition N value is consistent with previous correlations for second-mode dominant transition in the same wind tunnel facility. Stability calculations for stationary and traveling crossflow instability waves in selected configurations indicate that an N value of 4 and 6, respectively, correlates reasonably well with transition onset discerned from one experimentally measured thermographic image.

Chang, Chau-Lyan↗