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Three-dimensional boundary-layer transition on a cone at Mach 3.5

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Abstract

A boundary-layer transition study on a sharp, 5° half-angle cone at various angles of attack was conducted at Mach 3.5. Transition data were obtained with and without significantly reduced freestream acoustic disturbance levels. A progressive downstream and upstream motion of the transition front on the windward and leeward rays, respectively, of the cone with angle of attack was observed for the high noise level data in agreement with data trends obtained in conventional (“noisy”) wind tunnels. However, the downstream movement was not observed to the same degree for the low noise level data in the present study. Transition believed to be crossflow dominated was found to be less receptive to freestream acoustic disturbances than first-mode (Tollmien-Schlichting) dominated transition. The previously-developed crossflow transition Reynolds number criterion, χ tr,max ≈200, was found to be inadequate for the current case. An improved criterion is offered, which includes compressibility and flow-geometry effects.

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Abbreviations

f :

frequency, kHz

M :

Mach number

P :

pressure, N/m2

P t :

Preston tube pressure, N/m2

Re ∞ :

freestream Reynolds number, V ∞ S/v ∞

S :

distance measured along cone surface from apex, cm

S p :

location of Preston tube measured from apex, cm

T :

temperature, °C

νmax :

maximum crossflow velocity (normal to edge inviscid streamline)

V :

resultant velocity

X :

axial distance measured along nozzle centerline from throat, cm

ΔX :

axial dimension of quiet test core, see Fig. 1

ΔY :

vertical dimension of quiet test core

ΔZ :

horizontal dimension of quiet test core

α :

angle of attack, deg

γ :

ratio of specific heats

δ :

laminar boundary-layer thickness, based on V/V e =0.995

ɛ i :

divergence angle between edge inviscid streamline and cone generator (ray), deg

ɛ s :

divergence angle between surface streamline and cone generator, deg

ɛ ν :

divergence angle between vortex and cone generator, deg

θ c :

cone half angle, deg

v :

kinematic viscosity

φ:

cone meridian angle (see Fig. 2), deg

χ :

crossflow Reynolds number, ν max δ/v e

χ* :

modified crossflow Reynolds number, \({\chi \mathord{\left/ {\vphantom {\chi {[1 + \tfrac{{\gamma - 1}}{2}M_e^2 ]}}} \right. \kern-\nulldelimiterspace} {[1 + \tfrac{{\gamma - 1}}{2}M_e^2 ]}}\)

e :

edge conditions

o :

tunnel stagnation conditions

tr :

conditions at transition onset

∞:

freestream conditions

−:

mean value

∼:

rms value

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  1. Experimental Flow Physics Branch, NASA Langley Research Center, 23665 — 5225, Hampton, VA, USA

    R. A. King

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King, R.A. Three-dimensional boundary-layer transition on a cone at Mach 3.5. Experiments in Fluids 13, 305–314 (1992). https://doi.org/10.1007/BF00209502

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