© Faculty of Mechanical Engineering, Belgrade. All rights reserved FME Transactions (2012) 40, 111-118 111
Received: September 2009, Accepted: June 2012
Correspondence to: Vladeta Zmijanović
École Polytechnique,
91128 Palaiseau cedex, France
E-mail: vladeta.zmijanovic@polytechnique.edu
Vladeta Zmijanović
Graduate student
Fluid Mechanics and Energetics
École Polytechnique
Boško Rašuo
Full Professor
University of Belgrade
Faculty of Mechanical Engineering
Amer Chpoun
Full Professor
Université Evry Val d'Essonne
Laboratoire de Mécanique et d'Energétique
Evry (Paris region), France
Flow Separation Modes and Side
Phenomena in an Overexpanded
Nozzle
As a part of an aerodynamics Ecole Polytechnique project, separation
modes which occur in supersonic nozzles at overexpanded regimes are
numerically investigated and compared with known effects. Different shock
generation and reflections in different nozzle types are observed and their
impact on the two main separation modes, namely Free and Restricted
Shock Separation (FSS & RSS) is explored. ONERA’ experimental thust-
optimized-contour (TOC) rocket nozzle was the reference case and it is
compared with the corresponding Vulcain 2 nozzle and analogues conical
and TIC nozzle contours. Strong lateral forces and side effects on the
nozzle wall caused by the RSS and by transition FSS to RSS are depicted in
terms of flow unsteadiness and presented in flow charts and diagrams.
Additionally, some design criteria for modern thrust optimized nozzles
according to these effects are proposed.
Keywords: launcher nozzle, TOC, TIC, conical contour, overexpanded
regime, free, restricted shock separation.
1. INTRODUCTION
The nozzle, an end-element of the propulsive process
cycle, represents a critical part of any aerospace vehicle.
The task of accelerating and efficiently exhausting
combusted and reactive gases according to the delivered
thrust represents the main objective of the propulsion
system design. As such, propulsive convergent-
divergent (C-D) axisymmetric rocket nozzles have
evolved since the early period of use till nowadays.
From technical and historical point of view, it is
possible to sort axisymmetric nozzle types by the shape
of their divergent profile as conical, ideal - de Laval,
truncated ideal contour (TIC) and sorts of modern thrust
optimized contour (TOC) nozzles.
In the space launcher engine design it is of
substantial importance to optimize and control flow
end-effects at the conventionally used nozzles. The
launcher nozzle, designed to work in extremely wide
range of pressure regimes has critical stress points at its
lower and upper limits of operation envelope. With the
high ambient pressure and thus, lower nozzle pressure
ratio (NPR) than the designed one, exhaust plume is
over-expanded and it is being recompressed through the
shock reflections to the ambient pressure. The nozzle
flow under certain circumstances generates critical side-
loads on the walls. This mainly occurs when the flow is
separated due to an overexpansion and during the start-
up transition processes. Different types of flow
separation are possible with the different nozzle types as
well within the same nozzle. At largely over-expanded
regime boundary-layer is detached from the nozzle wall
due to an adverse pressure gradient generating the
separation shock. This supersonic and separated flow
continues downstream and it may interact with the
recompression shocks, asymmetric jet portions and/or
possibly present internal shock, which can further lead
to the severe lateral loads. These lateral or side-loads of
uncontrolled flow separation are frequently present
during the transient processes of engine start-up and
shut-down operation. As the part of the Ecole
Polytechnique applied aerodynamics student-project
under the guidance of ONERA, the separation effects
and nature of such produced flow field are investigated.
2. STATE OF THE ART OF THE PROBLEM IN BRIEF
The presented study is motivated by the flow and
performance investigations of the contemporary nozzles
used in the space launcher technology. This implies use
of the thrust optimized and compressed parabolic
nozzles. The main reasons for the use of these nozzles
are higher thrust performance on the shorter nozzle
divergent section length and thus the smaller mass of
the launcher propulsion system.
Following the principles of the shockless de Laval
ideal nozzle, whose contour may be also numerically
obtained in respect to the method of characteristics
(MoC) procedure [1], it is possible to further optimize
this contour in the direction of thrust to mass ratio.
Optimization of the ideal nozzle would consider
subsonic and supersonic throat section curvature radius
but still with a smooth transition and calculation
according to Kliegel, Sauer or another method of sonic
line as an incipient point for further MoC calculation
process. The calculated divergent supersonic profile
with marching characteristic until the completely
parallel 0deg and uniform exit flow in the first optimal
derivation may be truncated according to the maximum
delivered thrust. In the usual design process optimal exit
angle of the truncated ideal contour (TIC) nozzle profile
is found between 4.5 and 7.5 deg but its naturally