Engineering topics

Chang, Chau-Lyan

Publications and source records attributed to Chang, Chau-Lyan.

At least 19 records

NASA NTRS2019

Effects of Wall Cooling on Supersonic Modes in High-Enthalpy Hypersonic Boundary Layers over a Cone

High-enthalpy hypersonic boundary-layer transition plays an important role in many entry/descent vehicles. Aerothermodynamic performance of these vehicles strongly depends on the transition location on the surface. However, detailed transition flow physics in these chemically reacting boundary layers are poorly understood and transition estimates during the design phase rely heavily on empirically-derived transition criteria such as 𝑹𝒆(𝜽)/𝑴(𝒆). One of the most intriguing characteristics in hypersonic boundary layers is the presence of unstable supersonic modes, first identified in the 1990s. Due to a recent surge in hypersonic applications, there has been renewed interest in studying the flow physics of supersonic modes using either theory or direct numerical simulations. This paper investigates the rise of supersonic modes in a high-enthalpy hypersonic flow over a 𝟓° half-angle cone at various wall temperatures using both quasiparallel linear stability theory and linear PSE. It was found that supersonic modes exist in all wall temperature conditions including the adiabatic wall case. Cooler wall temperature causes the second Mack mode to become an unstable supersonic mode naturally downstream of the upper-branch neutral location when the wall is sufficiently cooled. In terms of the integrated growth, the second mode is still the dominant mode. Nonetheless, supersonic modes can cause additional series of relatively weaker growth than that of the second mode beyond the peak amplitude location. According to the present linear PSE results, contrary to what was speculated in the literature, supersonic-mode pressure disturbance structure radiated into the freestream is nonacoustic in nature and the formation of unstable supersonic modes is mainly associated with the synchronization of phase speed between the instability and acoustic waves in a nonp ayer, not due to nonlinear modal interaction as suggested in the literature.

Chang, Chau-Lyan↗

NASA NTRS2019

Investigation of Transitional Shock-Wave/Boundary Layer Interactions Using Direct Numerical Simulations

Interaction of a transitional boundary layer with a normal-shock is investigated using unstructured tetrahedral meshes under the numerical framework of the space-time conservation element, solution element (CESE) method. The computations mimic recent experimental efforts at the University of Tennessee Space Institute, where a Mach 2.0 flow interacts with a tall cylinder attached to a flat plate. The location of the cylinder with respect to the flat plate leading edge determines if the incoming boundary layer is laminar, transitional or fully turbulent. Four representative flow conditions exemplifying laminar and transitional boundary layers are analyzed by direct numerical simulations. Similar to what was observed in the experiments for the case of transitional interaction, the computations reveal an intermittent upstream influence (UI) shock that repeatedly travels upstream from the lambda-foot toward the leading edge before vanishing. Through detailed unsteady flow analysis obtained using Fourier analysis and dynamic mode decomposition techniques, the presence of disturbances with similar frequencies as those measured in experiments were identified in the flow along with locations that appear to influence the dynamics of the flow.

Venkatachari, Balaji Shankar↗

NASA NTRS2019

Dynamic Smagorinsky Modeled Large-Eddy Simulations of Turbulence Using Tetrahedral Meshes

Eddy-resolving numerical computations of turbulent flows are emerging as viable alternatives to Reynolds Averaged Navier-Stokes (RANS) calculations for flows with an intrinsically steady mean state due to the advances in large-scale parallel computing. In these computations, medium to large turbulent eddies are resolved by the numerics while the smaller or subgrid scales are either modeled or taken care of by the inherent numerical dissipation. To advance the state of the art of unstructured-mesh turbulence simulation capabilities, large eddy simulations (LES) using the dynamic Smagorinsky model (DSM) on tetrahedral meshes are carried out with the space-time conservation element, solution element (CESE) method. In contrast to what has been reported in the literature, the present implementation of dynamic models allows for active backscattering without any ad-hoc limiting of the eddy viscosity calculated from the subgrid-scale model. For the benchmark problems involving compressible isotropic turbulence decay as well as the shock/turbulent boundary layer interaction benchmark problems, no numerical instability associated with kinetic energy growth is observed and the volume percentage of the backscattering portion accounts for about 38-40% of the simulation domain. A slip-wall model in conjunction with the implemented DSM is used to simulate a relatively high Reynolds number Mach 2.85 turbulent boundary layer over a 30° ramp with several tetrahedral meshes and a wall-normal spacing of either Δγ& = 10 or Δγ& = 20. The computed mean wall pressure distribution, separation region size, mean velocity profiles, and Reynolds stress agree reasonably well with experimental data.

CESE method↗

NASA NTRS2018

Tetrahedral-Mesh Simulations of Shock-Turbulence Interaction

Despite decades of development of unstructured mesh methods, direct numerical simulations (DNS) of turbulent flows are still predominantly performed on structured or unstructured hexahedral meshes with high-order finite-difference methods, weighted essentially nonoscillatory (WENO) schemes, or hybrid schemes formed by their combinations. Tetrahedral meshes offer easy mesh generation and adaptation around complex geometries and the potential of an orientation-free grid that would benefit the isotropic nature of small-scale dissipation, as well as the solution accuracy of intermediate scales. To advance the state of the art of unstructured-mesh simulation capabilities for shock/turbulence interaction, DNS using pure tetrahedral meshes are carried out with the space-time conservation element, solution element (CESE) method in this research. By its design, the CESE method is constructed based on a non-dissipative scheme and is a genuinely multidimensional numerical framework that is free from the use of an approximate Riemann-solver. The numerical framework also provides the ability to add numerical dissipation (the nondissipative scheme acts as the reference state like that of the reversible state in thermodynamics) when needed (with justification from mathematics/physics). The above-mentioned features along with the CESE method's consistent shock-capturing approach and strong enforcement of flux conservation in spacetime offers a novel method to accurately simulate turbulent flows and their interaction with shocks using tetrahedral meshes. Two canonical problems, namely, isotropic turbulence interaction with a normal shock and a Mach 2.9 turbulent boundary layer flow over a 24deg compression corner are investigated in this study. Computational results show reasonably good agreement with experimental data and results from structured-mesh, high-order simulations available in the literature. Successful validation of these canonical problems demonstrated here paves the way for future high-fidelity supersonic flow simulations involving complex-geometries.

Venkatachari, Balaji Shankar↗

NASA NTRS2017

Cause and Cure - Deterioration in Accuracy of CFD Simulations With Use of High-Aspect-Ratio Triangular Tetrahedral Grids

Traditionally high-aspect ratio triangular/tetrahedral meshes are avoided by CFD re-searchers in the vicinity of a solid wall, as it is known to reduce the accuracy of gradient computations in those regions and also cause numerical instability. Although for certain complex geometries, the use of high-aspect ratio triangular/tetrahedral elements in the vicinity of a solid wall can be replaced by quadrilateral/prismatic elements, ability to use triangular/tetrahedral elements in such regions without any degradation in accuracy can be beneficial from a mesh generation point of view. The benefits also carry over to numerical frameworks such as the space-time conservation element and solution element (CESE), where triangular/tetrahedral elements are the mandatory building blocks. With the requirement of the CESE method in mind, a rigorous mathematical framework that clearly identities the reason behind the difficulties in use of such high-aspect ratio triangular/tetrahedral elements is presented here. As will be shown, it turns out that the degree of accuracy deterioration of gradient computation involving a triangular element is hinged on the value of its shape factor Gamma def = sq sin Alpha1 + sq sin Alpha2 + sq sin Alpha3, where Alpha1; Alpha2 and Alpha3 are the internal angles of the element. In fact, it is shown that the degree of accuracy deterioration increases monotonically as the value of Gamma decreases monotonically from its maximal value 9/4 (attained by an equilateral triangle only) to a value much less than 1 (associated with a highly obtuse triangle). By taking advantage of the fact that a high-aspect ratio triangle is not necessarily highly obtuse, and in fact it can have a shape factor whose value is close to the maximal value 9/4, a potential solution to avoid accuracy deterioration of gradient computation associated with a high-aspect ratio triangular grid is given. Also a brief discussion on the extension of the current mathematical framework to the tetrahedral-grid case along with some of the practical results of this extension is also provided. Furthermore, through the use of numerical simulations of practical viscous problems involving high-Reynolds number flows, the effectiveness of the gradient evaluation procedures within the CESE framework (that have their basis on the analysis presented here) to produce accurate and stable results on such high-aspect ratio meshes is also showcased.

CESE Method↗

NASA NTRS2017

Cause and Cure - Deterioration in Accuracy of CFD Simulations with Use of High-Aspect-Ratio Triangular/Tetrahedral Grids

Traditionally high-aspect ratio triangular/tetrahedral meshes are avoided by CFD researchers in the vicinity of a solid wall, as it is known to reduce the accuracy of gradient computations in those regions. Although for certain complex geometries, the use of high-aspect ratio triangular/tetrahedral elements in the vicinity of a solid wall can be replaced by quadrilateral/prismatic elements, ability to use triangular/tetrahedral elements in such regions without any degradation in accuracy can be beneficial from a mesh generation point of view. The benefits also carry over to numerical frameworks such as the space-time conservation element and solution element (CESE), where simplex elements are the mandatory building blocks. With the requirement of the CESE method in mind, a rigorous mathematical framework that clearly identifies the reason behind the difficulties in use of such high-aspect ratio simplex elements is formulated using two different approaches and presented here. Drawing insights from the analysis, a potential solution to avoid that pitfall is also provided as part of this work. Furthermore, through the use of numerical simulations of practical viscous problems involving high-Reynolds number flows, how the gradient evaluation procedures of the CESE framework can be effectively used to produce accurate and stable results on such high-aspect ratio simplex meshes is also showcased.

CESE Method↗

NASA NTRS2017

Cause and Cure-Deterioration in Accuracy of CFD Simulations with Use of High-Aspect-Ratio Triangular/Tetrahedral Grids

In the multi-dimensional space-time conservation element and solution element16 (CESE) method, triangles and tetrahedral mesh elements turn out to be the most natural building blocks for 2D and 3D spatial grids, respectively. As such, the CESE method is naturally compatible with the simplest 2D and 3D unstructured grids and thus can be easily applied to solve problems with complex geometries. However, because (a) accurate solution of a high-Reynolds number flow field near a solid wall requires that the grid intervals along the direction normal to the wall be much finer than those in a direction parallel to the wall and, as such, the use of grid cells with extremely high aspect ratio (103 to 106) may become mandatory, and (b) unlike quadrilateral hexahedral grids, it is well-known that accuracy of gradient computations involving triangular tetrahedral grids tends to deteriorate rapidly as cell aspect ratio increases. As a result, the use of triangular tetrahedral grid cells near a solid wall has long been deemed impractical by CFD researchers. In view of (a) the critical role played by triangular tetrahedral grids in the CESE development, and (b) the importance of accurate resolution of high-Reynolds number flow field near a solid wall, as will be presented in the main paper, a comprehensive and rigorous mathematical framework that clearly identifies the reasons behind the accuracy deterioration as described above has been developed for the 2D case involving triangular cells. By avoiding the pitfalls identified by the 2D framework, and its 3D extension, it has been shown numerically.

CFD↗

NASA NTRS2016

The Space-Time Conservative Schemes for Large-Scale, Time-Accurate Flow Simulations with Tetrahedral Meshes

Despite decades of development of unstructured mesh methods, high-fidelity time-accurate simulations are still predominantly carried out on structured, or unstructured hexahedral meshes by using high-order finite-difference, weighted essentially non-oscillatory (WENO), or hybrid schemes formed by their combinations. In this work, the space-time conservation element solution element (CESE) method is used to simulate several flow problems including supersonic jet/shock interaction and its impact on launch vehicle acoustics, and direct numerical simulations of turbulent flows using tetrahedral meshes. This paper provides a status report for the continuing development of the space-time conservation element solution element (CESE) numerical and software framework under the Revolutionary Computational Aerosciences (RCA) project. Solution accuracy and large-scale parallel performance of the numerical framework is assessed with the goal of providing a viable paradigm for future high-fidelity flow physics simulations.

Venkatachari, Balaji Shankar↗

NASA NTRS2015

On the Comparison of the Long Penetration Mode (LPM) Supersonic Counterflowing Jet to the Supersonic Screech Jet

Classic tonal screech noise created by under-expanded supersonic jets; Long Penetration Mode (LPM) supersonic phenomenon -Under-expanded counter-flowing jet in supersonic free stream -Demonstrated in several wind tunnel tests -Modeled in several computational fluid dynamics (CFD) simulations; Discussion of LPM acoustics feedback and fluid interactions -Analogous to the aero-acoustics interactions seen in screech jets; Lessons Learned: Applying certain methodologies to LPM -Developed and successfully demonstrated in the study of screech jets -Discussion of mechanically induced excitation in fluid oscillators in general; Conclusions -Large body of work done on jet screech, other aero-acoustic phenomenacan have direct application to the study and applications of LPM cold flow jets

Farr, Rebecca A.↗

NASA NTRS2015

Numerical Experiments of Counterflowiing Jet Effects on Supersonic Slender-Body Configurations

Previous studies have demonstrated that the use of counterflowing jets can greatly reduce the drag and heat loads on blunt-body geometries, especially when the long penetration mode jet condition can be established. Previously, the authors had done some preliminary numerical studies to determine the ability to establish long penetration mode jets on a typical Mach 1.6 slender configuration, and study its impact on the boom signature. The results indicated that a jet with a longer penetration length was required to achieve any impact on the boom signature of a typical Mach 1.6 slender configuration. This paper focuses on an in-depth parametric study, done using the space-time conservation element solution element Navier-Stokes flow solver, for investigating the effect of various counterflowing jet conditions/configurations on two supersonic slender-body models (cone-cylinder and quartic body of revolution). The study is aimed at gaining a better understanding of the relationship between the shock penetration length and reduction of drag and boom signature for these two supersonic slender-body configurations. Different jet flow rates, Mach numbers, nozzle jet exit diameters and jet-to-base diameter ratios were examined. The results show the characteristics of a short-to-long-to-short penetration-mode pattern with the increase of jet mass flow rates, observed across various counterflowing jet nozzle configurations. Though the optimal shock penetration length for potential boom-signature mitigation is tied to the long penetration mode, it often results in a very unsteady flow and leads to large oscillations of surface pressure and drag. Furthermore, depending on the geometry of the slender body, longer jet penetration did not always result in maximum drag reduction. For the quartic geometry, the maximum drag reduction corresponds well to the longest shock penetration length, while this was not the case for the cone-cylinder-as the geometry was already optimized for drag. Numerical results and assessments obtained from this parametric study along with the recommendation for future implementation of counterflowing jets as a means for drag and noise reduction are detailed in this paper.

Venkatachari, Balaji Shankar↗

NASA NTRS2015

Tetrahedral-Mesh Simulation of Turbulent Flows with the Space-Time Conservative Schemes

Direct numerical simulations of turbulent flows are predominantly carried out using structured, hexahedral meshes despite decades of development in unstructured mesh methods. Tetrahedral meshes offer ease of mesh generation around complex geometries and the potential of an orientation free grid that would provide un-biased small-scale dissipation and more accurate intermediate scale solutions. However, due to the lack of consistent multi-dimensional numerical formulations in conventional schemes for triangular and tetrahedral meshes at the cell interfaces, numerical issues exist when flow discontinuities or stagnation regions are present. The space-time conservative conservation element solution element (CESE) method - due to its Riemann-solver-free shock capturing capabilities, non-dissipative baseline schemes, and flux conservation in time as well as space - has the potential to more accurately simulate turbulent flows using unstructured tetrahedral meshes. To pave the way towards accurate simulation of shock/turbulent boundary-layer interaction, a series of wave and shock interaction benchmark problems that increase in complexity, are computed in this paper with triangular/tetrahedral meshes. Preliminary computations for the normal shock/turbulence interactions are carried out with a relatively coarse mesh, by direct numerical simulations standards, in order to assess other effects such as boundary conditions and the necessity of a buffer domain. The results indicate that qualitative agreement with previous studies can be obtained for flows where, strong shocks co-exist along with unsteady waves that display a broad range of scales, with a relatively compact computational domain and less stringent requirements for grid clustering near the shock. With the space-time conservation properties, stable solutions without any spurious wave reflections can be obtained without a need for buffer domains near the outflow/farfield boundaries. Computational results for the isotropic turbulent flow decay, at a relatively high turbulent Mach number, show a nicely behaved spectral decay rate for medium to high wave numbers. The high-order CESE schemes offer very robust solutions even with the presence of strong shocks or widespread shocklets. The explicit formulation in conjunction with a close to unity theoretical upper Courant number bound has the potential to offer an efficient numerical framework for general compressible turbulent flow simulations with unstructured meshes.

Chang, Chau-Lyan↗

NASA NTRS2014

Nonlinear Development and Secondary Instability of Traveling Crossflow Vortices

Transition research under NASA's Aeronautical Sciences Project seeks to develop a validated set of variable fidelity prediction tools with known strengths and limitations, so as to enable "sufficiently" accurate transition prediction and practical transition control for future vehicle concepts. This paper builds upon prior effort targeting the laminar breakdown mechanisms associated with stationary crossflow instability over a swept-wing configuration relevant to subsonic aircraft with laminar flow technology. Specifically, transition via secondary instability of traveling crossflow modes is investigated as an alternate scenario for transition. Results show that, for the parameter range investigated herein, secondary instability of traveling crossflow modes becomes insignificant in relation to the secondary instability of the stationary modes when the relative initial amplitudes of the traveling crossflow instability are lower than those of the stationary modes by approximately two orders of magnitudes or more. Linear growth predictions based on the secondary instability theory are found to agree well with those based on PSE and DNS, with the most significant discrepancies being limited to spatial regions of relatively weak secondary growth, i.e., regions where the primary disturbance amplitudes are smaller in comparison to its peak amplitude. Nonlinear effects on secondary instability evolution is also investigated and found to be initially stabilizing, prior to breakdown.

Li, Fei↗

NASA NTRS2013

Recent Development in the CESE Method for the Solution of the Navier-Stokes Equations Using Unstructured Triangular or Tetrahedral Meshes With High Aspect Ratio

In the multidimensional CESE development, triangles and tetrahedra turn out to be the most natural building blocks for 2D and 3D spatial meshes. As such the CESE method is compatible with the simplest unstructured meshes and thus can be easily applied to solve problems with complex geometries. However, because the method uses space-time staggered stencils, solution decoupling may become a real nuisance in applications involving unstructured meshes. In this paper we will describe a simple and general remedy which, according to numerical experiments, has removed any possibility of solution decoupling. Moreover, in a real-world viscous flow simulation near a solid wall, one often encounters a case where a boundary with high curvature or sharp corner is surrounded by triangular/tetrahedral meshes of extremely high aspect ratio (up to 106). For such an extreme case, the spatial projection of a space-time compounded conservation element constructed using the original CESE design may become highly concave and thus its centroid (referred to as a spatial solution point) may lie far outside of the spatial projection. It could even be embedded beyond a solid wall boundary and causes serious numerical difficulties. In this paper we will also present a new procedure for constructing conservation elements and solution elements which effectively overcomes the difficulties associated with the original design. Another difficulty issue which was addressed more recently is the wellknown fact that accuracy of gradient computations involving triangular/tetrahedral grids deteriorates rapidly as the aspect ratio of grid cells increases. The root cause of this difficulty was clearly identified and several remedies to overcome it were found through a rigorous mathematical analysis. However, because of the length of the current paper and the complexity of mathematics involved, this new work will be presented in another paper.

Chang, Sin-Chung↗

NASA NTRS2013

Towards Bridging the Gaps in Holistic Transition Prediction via Numerical Simulations

The economic and environmental benefits of laminar flow technology via reduced fuel burn of subsonic and supersonic aircraft cannot be realized without minimizing the uncertainty in drag prediction in general and transition prediction in particular. Transition research under NASA's Aeronautical Sciences Project seeks to develop a validated set of variable fidelity prediction tools with known strengths and limitations, so as to enable "sufficiently" accurate transition prediction and practical transition control for future vehicle concepts. This paper provides a summary of selected research activities targeting the current gaps in high-fidelity transition prediction, specifically those related to the receptivity and laminar breakdown phases of crossflow induced transition in a subsonic swept-wing boundary layer. The results of direct numerical simulations are used to obtain an enhanced understanding of the laminar breakdown region as well as to validate reduced order prediction methods.

Choudhari, Meelan M.↗

NASA NTRS2013

Time-Accurate Local Time Stepping and High-Order Time CESE Methods for Multi-Dimensional Flows Using Unstructured Meshes

With the wide availability of affordable multiple-core parallel supercomputers, next generation numerical simulations of flow physics are being focused on unsteady computations for problems involving multiple time scales and multiple physics. These simulations require higher solution accuracy than most algorithms and computational fluid dynamics codes currently available. This paper focuses on the developmental effort for high-fidelity multi-dimensional, unstructured-mesh flow solvers using the space-time conservation element, solution element (CESE) framework. Two approaches have been investigated in this research in order to provide high-accuracy, cross-cutting numerical simulations for a variety of flow regimes: 1) time-accurate local time stepping and 2) highorder CESE method. The first approach utilizes consistent numerical formulations in the space-time flux integration to preserve temporal conservation across the cells with different marching time steps. Such approach relieves the stringent time step constraint associated with the smallest time step in the computational domain while preserving temporal accuracy for all the cells. For flows involving multiple scales, both numerical accuracy and efficiency can be significantly enhanced. The second approach extends the current CESE solver to higher-order accuracy. Unlike other existing explicit high-order methods for unstructured meshes, the CESE framework maintains a CFL condition of one for arbitrarily high-order formulations while retaining the same compact stencil as its second-order counterpart. For large-scale unsteady computations, this feature substantially enhances numerical efficiency. Numerical formulations and validations using benchmark problems are discussed in this paper along with realistic examples.

Chang, Chau-Lyan↗

NASA NTRS2013

Wake Instabilities Behind Discrete Roughness Elements in High Speed Boundary Layers

Computations are performed to study the flow past an isolated, spanwise symmetric roughness element in zero pressure gradient boundary layers at Mach 3.5 and 5.9, with an emphasis on roughness heights of less than 55 percent of the local boundary layer thickness. The Mach 5.9 cases include flow conditions that are relevant to both ground facility experiments and high altitude flight ("cold wall" case). Regardless of the Mach number, the mean flow distortion due to the roughness element is characterized by long-lived streamwise streaks in the roughness wake, which can support instability modes that did not exist in the absence of the roughness element. The higher Mach number cases reveal a variety of instability mode shapes with velocity fluctuations concentrated in different localized regions of high base flow shear. The high shear regions vary from the top of a mushroom shaped structure characterizing the centerline streak to regions that are concentrated on the sides of the mushroom. Unlike the Mach 3.5 case with nearly same values of scaled roughness height k/delta and roughness height Reynolds number Re(sub kk), the odd wake modes in both Mach 5.9 cases are significantly more unstable than the even modes of instability. Additional computations for a Mach 3.5 boundary layer indicate that the presence of a roughness element can also enhance the amplification of first mode instabilities incident from upstream. Interactions between multiple roughness elements aligned along the flow direction are also explored.

Choudhari, Meelan↗

NASA NTRS2012

Computational Investigation of Supersonic Boundary Layer Transition Over Canonical Fuselage Nose Configurations

Boundary layer transition over axisymmetric bodies at non-zero angle of attack in supersonic flow is numerically investigated as part of joint research between the National Aeronautics and Space Administration (NASA) and Japan Aerospace Exploration Agency (JAXA). Transition over four axisymmetric bodies (namely, Sears-Haack body, semi-Sears-Haack body, 5-degree straight cone and flared cone) with different axial pressure gradients has been studied at Mach 2 in order to understand the effect of axial pressure gradient on instability amplification along the leeward symmetry plane and in the region of nonzero crossflow away from it. Comparisons are made with measured transition data in Mach 2 facilities as well as with predicted and measured transition characteristics for a 5-degree straight cone in a Mach 3.5 low disturbance tunnel. Limitations of using linear stability correlations for predicting transition over axisymmetric bodies at angle of attack are pointed out.

Choudhari, Meelan M.↗

NASA NTRS2012

Transition Within Leeward Plane of Axisymmetric Bodies at Incidence in Supersonic Flow

Boundary layer transition along the leeward symmetry plane of axisymmetric bodies at nonzero angle of attack in supersonic flow was investigated experimentally and numerically as part of joint research between the Japan Aerospace Exploration Agency (JAXA) and National Aeronautics and Space Administration (NASA). Transition over four axisymmetric bodies (namely, Sears-Haack body, semi-Sears-Haack body, straight cone and flared cone) with different axial pressure gradients was measured in two different facilities with different unit Reynolds numbers. The semi-Sears-Haack body and flared cone were designed at JAXA to broaden the range of axial pressure distributions. For a body shape with an adverse pressure gradient (i.e., flared cone), the experimentally measured transition patterns show an earlier transition location along the leeward symmetry plane in comparison with the neighboring azimuthal locations. For nearly zero pressure gradient (i.e.,straight cone), this feature is only observed at the larger unit Reynolds number. Later transition along the leeward plane was observed for the remaining two body shapes with a favorable pressure gradient. The observed transition patterns are only partially consistent with the numerical predictions based on linear stability analysis. Additional measurements are used in conjunction with the stability computations to explore the phenomenon of leeward line transition and the underlying transition mechanism in further detail.

Tokugawa, Naoko↗