Saikumar Reddy Yeddula
Dynamics of the shock wave in supersonic air-intake systems
Background
With the advent of ambitious emission targets from the United Kingdom in achieving net-zero emissions by 2050 and rapidly growing air-traffic, there is a renewed interest in flying efficiently at speeds
much faster than the speed of sound. In particular, Reaction Engines Ltd. (UK) are involved with
developing a hydrogen-powered engine that can propel high-speed aircraft under the name SABRE
– Synergetic Air-Breathing Rocket Engine. By operating in the ram-jet mode, this new class engine
achieves the flow compression by establishing several shock waves (fluid discontinuities) over the airintake, unlike a turbojet, which uses a compressor. As shown in Figure 1, based on the flight Mach
number1 , these engines operate under either sub-critical or super-critical conditions.
I. Sub-critical
Normal Shock outside inlet plane.
Susceptible to buzz
Incoming supersonic flow,
with atmospheric disturbances
q
Obli
II. Super-critical.
Normal Shock inside the cowl.
Susceptible to un-start
I. Little buzz: Shock-shock
interaction vortex sheet
ho
ue S
ck
holes
Bleed
Acoustic waves
Acoustic
reflecting
boundary
Combustor.
Oscillation
`
Shock
expulsion
I. Big buzz: Shock induced
recirculation bubble
II. Unstart: Acoustic feedback
and shock induced separation.
Acoustic
waves from
combustor.
Figure 1: Unsteady phenomena in ram-jet intakes under sub-critical and super-critical conditions.
Ram-jet air-intakes are subjected to unsteady behavior, predominantly triggered by atmospheric
disturbances. This behavior is a significant problem for air-intakes operating under both the subcritical and super-critical operating conditions. Atmospheric disturbances, which are closely associated
with atmospheric turbulence, interact with the shock wave and generate acoustic disturbances2 . Under
super-critical conditions, the acoustic disturbances can trigger an un-start phenomenon, where the
normal shock (represented by vertical red line in Figure 1) expels out of the air-intake as a result
of large flow separation at the boundary layer, and positive acoustic feedback from the impinging
disturbances [1]. Un-start phenomenon is highly undesirable and results in (i) a sudden decrease in
the airflow to the engine and (ii) a significant rise in the drag force, affecting both the performance
and maneuverability of the ram-jet. .
The air-intake’s sub-critical operation is relatively stable but susceptible to self-sustained oscillations of the normal shock, occurring due to flow separation over the air-intake walls, triggered by the
atmospheric disturbances. This phenomenon is known as little buzz, or big buzz (shown in Figure 1),
depending on the criteria that govern their onset [2, 3].
For both the unsteady phenomena, un-start and buzz, the flow separation along the walls play
a dominant role. It occurs over a length-scale of O(mm). However, the acoustic and atmospheric
disturbances’ wavelengths are of O(m), suggesting a disparity among the length-scales. Capturing the
flow physics at these two distinct scales is computationally expensive. Hence, computational models
that couple separate treatments for the flow and the disturbances are envisaged. In this approach,
the mean flow is resolved using high fidelity numerical simulations, while lower-order network models
are employed for obtaining the response of the air-intake to disturbances. This multi-scale approach
is computationally fast and commendable when investigating several flow conditions of interest to
identify un-start.
Although attempts were made to model the buzz phenomenon by linking it with the air-intake
acoustic response [1, 3 – 5], none proceeded in explaining the un-start. Also, existing models assume
1
2
Mach number, denoted by M, is the ratio of flight speed to speed of sound in the atmosphere
Fluctuations in pressure
1
one or more of, (i) one-dimensional linear disturbances, (ii) very low forcing frequency, (iii) negligible
effects of fluid friction (viscosity) and flow separation, or, (iv) ignore area changes along the diffuser.
Objective
This project’s primary objective is to develop a simplified model that predicts a shock wave response to
impinging disturbances. A comprehensive study of the ram-jet air-intake will be performed to account
for the effects of 2D disturbances and other complex mean flow effects such as shock-boundary layer
interaction and boundary layer suction in the model under a linear or a weakly non-linear framework.
This model will then be used to identify the system’s susceptible frequencies that lead to un-start or
buzz of the SABRE air-intake, and there-by characterize its stability. The results thus obtained will
be validated both numerically and experimentally.
Choice of the institution: Validation of the proposed model requires excellent computational resources to accurately capture the unsteady dynamics at the two very different length scales mentioned
earlier. The High-Performance Computing (HPC) support at Imperial is nation-leading. It can offer
high productivity for the numerical validation of the model. Concurrently, well-established experimental facilities and high-speed wind tunnel availability that can operate up-to Mach 9 facilitate swift
experimental validation. Availability of prominent research groups working in high-speed aerodynamics, supervised by Dr. Paul Bruce, with comprehensive experience in experimental supersonic flows
[6, 7], will also be extremely crucial. Lastly, the Postdoc and Fellows Development Centre (PFDC)
is also unique to Imperial. Their courses, and the support they offer, ensure overall development for
an early-stage researcher like me. For these reasons, I have chosen to work in the Department of
Aeronautics at Imperial College London during the fellowship.
Methodology
References:
[1] Fincham JH. Unsteady shockwave motion in supersonic intakes (Doctoral dissertation, University of Bristol). [2] Hankey W, Shang J. In13th fluid and Plasma Dynamics conference
1980 (p. 1346). [3] Soltani MR, Sepahi-Younsi J. AIAA Journal. 2016 Mar;54(3):1040-53. [4] Culick
FE, Rogers T. AIAA journal. 1983 Oct;21(10):1382-90. [5] MacMartin DG. Journal of Aircraft.
2004 Jul;41(4):846-53. [6] Bruce PJ, Babinsky H. Aerospace Science and Technology. 2010 Mar
1;14(2):134-42. [7] Rabey PK, Jammy SP, Bruce PJ, Sandham ND. Journal of Fluid Mechanics. 2019
Jul 25;871. [8] Yeddula S, Morgans AS. Journal of Sound and Vibration. 2021 Apr 492:115770. [9]
Yang D, Guzmán-Iñigo J, Morgans AS. Journal of Fluid Mechanics. 2020 Dec;905. [10] Emmanuelli
A, Zheng J, Huet M, Giauque A, Le Garrec T, Ducruix S. Journal of Sound and Vibration. 2020 Apr
28;472:115163.
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