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REVIEW ARTICLES

Supersonic Flow Separation with Application to Rocket Engine Nozzles

[+] Author and Article Information
J. Östlund

Volvo-Aero Corporation, S-461 SI Trollhättan, Sweden Department of Mechanics, Royal Institute of Technology, S-144 00 Stockholm, Swedene-mail: jan.ostlund@Volvo.com

B. Muhammad-Klingmann

Department of Mechanics, Royal Institute of Technology, S-144 00 Stockholm, Swedene-mail: barbro@mech.kth.se

Appl. Mech. Rev 58(3), 143-177 (May 27, 2005) (35 pages) doi:10.1115/1.1894402 History: Online May 27, 2005
Copyright © 2005 by ASME
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Bollinger, L. E., Goldsmith, M., and Lemmon, Jr., A. W., 1960, Liquid Rockets and Propellants, Academic Press, New York, Progress in Astronautics and Rocketry, Vol. 2, pp. 617–645.
Smith-Kent, R., Loh, H., and Chawalowski, P., 1995, “Analytical Contouring of Pintle Nozzle Exit Cone Using Computational Aerodynamics,” 31st Joint Propulsion Conference and Exhibit, AIAA Paper No. 1995-2877.
Asbury, S. C., and Hunter, C. A., 1999, “Effects of Convoluted Divergent Flap Contouring on the Performance of a Fixed-Geometry Nonaxisymmetric Exhaust Nozzle,” NASA TP-1999-209093, Langley Research Center, Hampton.
Jameson, A., 1995, “The Present Status, Challenges and Future Developments in Computational Fluid Dynamics,” Proc. of 12th Australasian Conference on Fluid Dynamics, Sydney, pp. 1–47.

Figures

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Performance versus altitude
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Mach number distribution in a 15° conical, TIC, TOC, TOP nozzle with ε=43.4 (from top to bottom). The thick line indicates the approximate position of the internal shock.
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Initial expansion region, kernel
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Basic flow structures in an ideal nozzle
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(a) Ideal nozzle contours and (b) Truncation point to obtain maximum performance for a given constraint on expansion ratio (A), surface area (B), or length (C)
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Thrust-optimized nozzle contour
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Illustration of exhaust plume patterns at different operational conditions
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Exhaust plume patterns. Overexpanded flow: (a) Vulcain, with classical Mach disc. (b) Vulcain, with cap-shock pattern. (c) RL10-A5, with apparent regular reflection. Underexpanded flow: (d) Saturn 1-B photographed during launch (from 27; Courtesy photos: SNECMA, CNES, NASA).
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Exhaust plume patterns for subscale nozzles. Parabolic nozzles with cap-shock pattern: (a) VOLVO S1. (b) TOP ONERA. (c) P6 TOP DLR. (d) TIC nozzle with Mach disc: VOLVO S6. (e) sketch of cap-shock pattern. (f) sketch of Mach disc pattern (Courtesy photos: DLR and ONERA).
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Basic shock/boundary layer interactions in supersonic flow: (a) ramp flow, (b) step-induced separation, and (c) shock reflection (adopted from 53).
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Typical static wall pressure distribution observed in ramp, shock reflection and step flow (adopted from 4254).
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Generalized wall pressure correlation function F(s) for uniform turbulent flow, by Erdos and Pallone 55
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Separation pressure obtained with the free interaction theory for uniform flow. “Effective separation”: F=6 (point P); “True separation” (point S):F=4.22 (from 56).
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Influence of Reynolds number and ramp angle on separation length (a) at low to moderate Reδi,Lsi increases with Re (data from 43), (b) at high Reδi,Lsi decreases with Re (data from 39).
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Influence of wall cooling on the separation length in a ramp flow. Mi=2.9, ramp angles 7.52 deg≤α≤19.7 deg, 2.18×104≤Reδi≤5.92×104 and 0.474≤Tw/Tr≤1.05 (data from 43).
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Typical distribution of the fluctuation pressure in the interaction region near separation 444548.
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Sketch of the time variation of the pressure within the interaction domain according to Kistler [cf. 4548] .
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Fluctuating pressure in the intermittent region, computed according to Eqs. (17) and (18). Symbols are test data of Kistler 48 from flow over a step with height h.
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Conditional ensemble average of the wall pressure upstream of a 28°, Mach 5 compression ramp (based on test data from 46).
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Normalized power spectra in the intermittent region in a 28°, Mach 5 compression ramp flow (adopted from 46). (a) sketch of the streamwise evolution of the rms wall pressure and locations where the spectra have been evaluated, (b) definition of fmax, (c)–(f) spectra at different streamwise locations.
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Phenomenological sketch of free shock separation (FSS, top), and restricted shock separation (RSS, bottom).
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Pressure signals at different positions through the interaction region in the VOLVO S7 short nozzle. Measurements made during down ramping of p0. (cf. 5676). (a): attached flow; (b), (c), and (d): separation zone; (e): recirculation zone downstream of separation.
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Statistical evaluation of pressure in the VOLVO S7 short nozzle during down ramping of p0. The axial positions correspond to a wall Mach number of M=3.8 in the full flowing nozzle. Upper figure, rms values; lower figure, skewness and kurtosis. Each symbol is based on 800 samples collected during 0.2 s. (From 5676.)
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Side loads in a truncated ideal nozzle (VOLVO S6) at free shock condition (from 77).
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Calculated Mach number contours in the VOLVO S1 nozzle at different operational conditions, n=0.07–0.45, from 56
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Wall pressure profiles in the VOLVO S1 nozzle during start-up, see also Östlund et al. 32
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Wall pressure profiles in the VOLVO S1 nozzle during shutdown, from 56
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Comparison between wall pressure profile at FSS and RSS condition at n=0.12, from 56
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Side loads due to transition in separation pattern in the VOLVO S1 nozzle (from 32)
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Comparison of simple separation prediction models for pi/pa with experimental results. The symbol shape in the legend indicates from which investigation the data is taken and the gray scale of the symbol corresponds to different nozzle configurations tested (see 28). Also published in 27.
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(a) Wall pressure correlation and (b) separation length for Fs=4.22, according to the generalized free interaction theory for nonuniform flow by 86
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Fit of generalized pressure correlation curve by Carrière et al. to VOLVO S6 data; xi and ls varied, 2.82≤Mi≤3.25,−0.9≤p×103≤−0.5,n=0.04−0.24, from 56
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Interaction length correlation to separation point (ls) and plateau point (lp), respectively. Symbols indicate calculated values based on VOLVO S6 nozzle test data (from 56).
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Predicted and measured wall pressure profile in the VOLVO S7 short nozzle (from 56)
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Experimental results for the pressure rise pp/pa as function of separation location. The symbol shape in the legend indicates from which investigation the data is taken, and the gray scale of the symbol corresponds to different nozzle configurations tested (see 28). Also published in 27.
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Principle idea of a tilted separation line
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Distribution of the rms pressure fluctuations at two different axial locations in the VOLVO S7 short nozzle during down ramping of p0. The axial positions correspond to M=3.8 and M=4.1 in the full flowing nozzle. Each symbol is based on 800 samples collected during 0.2 s (from 5676).
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rms pressure fluctuations in the LEA TIC nozzle, comparison between measured and values calculated with the Kistler approach (test data taken from 100, figure from 56)
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The three Space Shuttle Main Engines SSME at transient start-up process (courtesy of NASA)
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FSS-RSS transition model; principle of model together with comparison of predicted and measured values for the VOLVO S3 nozzle (from 56)
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Schematic representation of the eight first nozzle mode shapes: (a) pendulum-, (b) bending-, (c) ovalisation-, (d) triangular-, (e) square-, (f) penta-, (g) hexa-, and (h) hepta-mode
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VOLVO S6 nozzle bending mode eigenfrequency versus operational condition (from 77)
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Nozzle and flow separation geometry
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Comparison between measured and calculated frequency shift for the S6 nozzle, from 77
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Aeroelastic stability of the S1 nozzle for the different spring set-ups, from 277
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Aeroelastic stability relation for the S1 nozzle, flexibly hinged with the “super weak” spring, from 77
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Wall pressure in the VOLVO S6 nozzle; comparison between Menter SST and test data (from 56)
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Mach number distribution in the VOLVO S6 nozzle at n=0.20 (from 56)
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Comparison of shock system position at n=0.20. The simulated value is compared to a Schlieren photo from the test (from 56).
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Schematic representation of different concepts for flow separation control: (a) dual-bell, (b) trip-rings, (c) vented nozzle, (d) secondary gas injection, (e) ejectible insert, (f) ablative insert, (g) two-position nozzle, (h) nozzle with pintle, (i) convoluted nozzle, and (j) polygon nozzle

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