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Shock unsteadiness in a thrust optimized parabolic nozzle

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Abstract

This paper discusses the nature of shock unsteadiness, in an overexpanded thrust optimized parabolic nozzle, prevalent in various flow separation modes experienced during start up \({(\delta P_{0} /\delta t > 0)}\) and shut down \({(\delta P_{0}/\delta t < 0)}\) sequences. The results are based on simultaneously acquired data from real-time wall pressure measurements using Kulite pressure transducers, high-speed schlieren (2 kHz) of the exhaust flow-field and from strain-gauges installed on the nozzle bending tube. Shock unsteadiness in the separation region is seen to increase significantly just before the onset of each flow transition, even during steady nozzle operation. The intensity of this measure (rms level) is seen to be strongly influenced by relative locations of normal and overexpansion shock, the decrease in radial size of re-circulation zone in the back-flow region, and finally, the local nozzle wall contour. During restricted shock separation, the pressure fluctuations in separation region exhibit periodic characteristics rather than the usually observed characteristics of intermittent separation. The possible physical mechanisms responsible for the generation of flow unsteadiness in various separation modes are discussed. The results are from an experimental study conducted in P6.2 cold-gas subscale test facility using a thrust optimized parabolic nozzle of area-ratio 30.

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Abbreviations

G(f):

power spectral density

f :

sampling frequency, Hz

P 0 :

stagnation chamber pressure, bar

P a :

ambient pressure, bar

P w :

local mean wall pressure, bar

P pl :

plateau pressure after separation, bar

r t :

radius of nozzle throat, mm

X :

co-ordinate along nozzle axis, mm

X sep :

point of physical separation, mm

X inc :

point of incipient separation, mm

X exit :

X-location of nozzle exit, mm

\({\in}\) :

area ratio of the nozzle

\({\sigma_{\rm pw}}\) :

rms of the local wall pressure

\({(\sigma_{w}/P_{w})_{\max }}\) :

non-dimensionalized maximum value of rms pressure fluctuation

θ w_exit :

nozzle exit wall angle

θ w :

nozzle wall angle

C O :

Overexpansion shock

C R :

Reflected shock

FSS:

Free shock separation

NPR:

Nozzle pressure ratio, P 0 / P a

pRSS:

Partially restricted shock separation

qRSS:

Quasi-restricted shock separation

RSS:

Restricted shock separation

Tq:

Triple point

TOP:

Thrust optimized parabolic

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Authors and Affiliations

  1. Experimental Aerodynamics Division, National Aerospace Laboratories (NAL), Bangalore, 560017, India

    S. B. Verma

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Correspondence to S. B. Verma.

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Communicated by A. Hadjadj.

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Verma, S.B. Shock unsteadiness in a thrust optimized parabolic nozzle. Shock Waves 19, 193–212 (2009). https://doi.org/10.1007/s00193-008-0180-8

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