A simulation study on the amplification of
cavity induced air-fuel mixing in scramjet
engine
Cite as: AIP Conference Proceedings 2292, 040003 (2020); https://doi.org/10.1063/5.0030626
Published Online: 27 October 2020
Minh Quang Chau, Xuan Phuong Nguyen, Hung Chien Do, et al.
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© 2020 Author(s).
2292, 040003
A Simulation Study on the Amplification of Cavity Induced
Air-Fuel Mixing in Scramjet Engine
Minh Quang Chau1, a) Xuan Phuong Nguyen2,b) Hung Chien Do2,c) and
Dinh Tuyen Nguyen2,d)
1
Industrial University of Ho Chi Minh city, Ho Chi Minh city, Vietnam.
Ho Chi Minh city University of Transport, Ho Chi Minh city, Vietnam.
2
a)
chauminhquang@iuh.edu.vn
b)
phuong@ut.edu.vn
Corresponding author:c)chien.do@ut.edu.vn
d)
nguyendinhtuyen8899@gmail.com
Abstract: The search for technical solutions to optimize the combustion chamber size as well as improve the combustion efficiency
of the scramjet engine has gained many benefits from optimizing the air-fuel supersonic mixing. Indeed, the technique of increasing
the mixture through optimizing the flow of air-fuel mixture by applying cavity technology is the outstanding solution. This present
work reports of a passive enhancement technique of supersonic mixing of air-fuel through amplification of cavity-induced flow field
oscillations. In this study, with the controlling-edge profile changes to assess the changing properties of an unstable flow on a shallow
cavity at the controlling-edge. This controlling-edge modification is used to augment the stimulating way in a shear surface, and that
may lead to the amplification of cavity-induced flow field oscillations. The ‘reactingFoam’ solver within the OpenFOAM was used to
simulate the supersonic cavity induced air-fuel mixing. The pressure changes over time with time and mixing indices at various
positions of cavity are analyzed. Changing the leading-edge profile of the combustion chamber has an important impact on the pressure
variation as well as the efficiency of the mixing process.
INTRODUCTION
Entering the 21st century, the universe sciences industry has made great progress in improving the efficiency of
supersonic vehicles. The scramjets engine is considered to be the generation of the most efficient supersonic engine being
researched [1]. The dominant advantage of scramjet engines is its simple construction and low weight. That has attracted
the attention of many scientists in optimizing the combustion process to improve performance. The improved combustion
efficiency in scramjets mainly depends on the fuel-air mixing quality. The reason is that the very high engine speed
required the ignition process to occur super-fast. Therefore, improving the fuel injection characteristics to ensure better
mixing quality is of great significance. This not only reduces fuel consumption, but also reduces the number of fuel tanks
and hypersonic equipment volume [2].
Much research has been done to improve the performance of scramjets by optimizing air-fuel mixing techniques. The
survey of mixing characteristics inside supersonic engines has been carried out by many modern techniques and methods.
Wang et al. [3] investigated the correlation of hypersonic currents in hydrogen jet engines with oblique shock waves to
increase mixing quality. Atmaca and Ezgi have shown that the properties of the transverse hypersonic field are improved
by optimizing the molecular weight and injector configuration parameters [4]. Sanchez et al. [5] used CFD techniques to
simulate and evaluate the impact of vortex jets on supersonic current mixed states. Measures to improve the supersonic
combustion chamber were investigated by Hoang [6]. The optimal solutions to shorten the length of supersonic
combustion chambers have been implemented such as ramp [7], aerodynamic-ramp [8], strut [9] or pylon [10] as well as
their combination [11]. A review of the factors affecting horizontal jet reaction was conducted by Hoang et al. [11]. The
solutions mentioned in the study include: Upstream, they have retrofitted shockwave transmitters; Downstream, an
increase in the mix quality has been achieved by micro air injection. Thus, the solution for enhancing the air-fuel mixture
in the downstream is to apply micro air jet injection technique. The mechanism determining the effectiveness of this
Proceedings of the 2020 2nd International Conference on Sustainable Manufacturing, Materials and Technologies
AIP Conf. Proc. 2292, 040003-1–040003-8; https://doi.org/10.1063/5.0030626
Published by AIP Publishing. 978-0-7354-4024-1/$30.00
040003-1
technique is the cavity flame holder. An experimental study for scramjet's supersonic combustion chamber using cavitybased flame holder was conducted by Juntao et al. [12]. By evaluating essential parameters such as aft ramp angles and
the length-to-depth ratio of the fuel flow feature in the cavity, they have demonstrated that at shallower ramp angles are
higher drag coefficients and shorter residence times.
On the other hand, Jorge et al. [13] investigated the effect of parameters such as injection pressure, back pressure on
air-fuel mixture in a scramjet. The relationship between the dual injection distance and the mixing characteristics and the
flow path in the cavity of the supersonic flow have been shown by Heeseok et al. [14]. Ren et al. [15] sed a variance
analysis method to evaluate the impact of geometric parameters on cavity flame holder's traction. In addition to modeling
studies for the cavity flame holder, it is done through the optimal solution of air-fuel mixing efficiency inside the
combustion chamber [16] [17]. The research directions of mixing outside the cavity and spraying small air beams have
also been considered quite a lot. However, there are very few scientific publications about mixing fuels with microscopic
air jets. Figure 1 shows a schematic diagram of the working principle of a scramjet engine along with the mixing flow in
the cavity.
As a method of improving the mixing performance of air and fuel flowing at a supersonic speed in a scramjet engine,
it is considered to provide a cavity in the combustion chamber. Due to this cavity, the air entering at a supersonic velocity
collides with the cavity trailing edge and generates a compression wave, and this compression wave propagates and
collides with the cavity leading edge. By the reciprocation of this compression wave, the shear layer near the cavity
leading edge oscillates and results in the flow field pressure oscillation [18], which leads to the improvement of the mixing
of fuel and air [11][19].
The present study aims to investigate a technique to improve the supersonic mixing of air-fuel through the
amplification of cavity-induced flow field oscillations. In this study, the leading edge of the cavity was modified to
intensify the flow field oscillations. For the analysis, the OpenFOAM [20] was used as the CFD tool [21].
FIGURE 1. Scramjet engine [19]
NUMERICAL MODEL AND COMPUTATIONAL METHODS
Governing equations
The Navier-Stokes equations for unsteady, turbulent, compressible fluid simulation are used to model the present
problem, consists of the following three equations: continuity equation, momentum conservation law, and energy
conservation law [22].
(1)
(2)
(3)
(4)
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&
Here, t is an independent variable representing time, v is the velocity vector, Z T and qr denotes the heat release
due to combustion and radiative heat flux, respectively.
The last term on the right-hand side of the Eq. (4) represents the chemical source term. When turbulence is present,
the turbulence-chemistry interaction is modeled based on the PaSR approach [23] where the reactive volume fraction, N
is calculated as,
(5)
IJres, IJc, and IJmix represent the residence time, chemical reaction time, and mixing time, respectively. If the flow is laminar
and turbulent reaction does not exist, IJmix is automatically set to zero, yielding a N value of unity.
Numerical methods
A non-reacting flow was numerically simulated by using the ‘reactingFoam’ solver [24] in OpenFoam. In this
simulation, switching off the chemical reaction and assuming no combustion model, the mixing of two non-reacting
gases, such as air and fuel, were only simulated [25].
Computational conditions
In this study, the cavity is placed at the bottom wall of a channel as shown in Fig. 2. The depth and length of the
cavity are D=12mm and L = 2D, respectively. The height H of the channel in 2D. The inlet and outlet of the
computational domain are located at 5D and 10D upstream and downstream of the cavity, respectively. A fuel inlet is
placed at D upstream of the cavity leading edge. Several measuring points (point ‘a’ through ‘g’) was set to measure
the pressure history and mass fraction. The leading edge of the cavity was changed accordingly to Fig. 3, and the angle
ș with the front edge was varied as 15o, 30o, and 45o, respectively. This modified cavity is called a triangular cavity
in this study [26].
FIGURE 2. Schematics of the computational domain and boundary conditions
FIGURE 3. Schematics of the triangular cavity
First, considering no fuel injection to the system, the simulation was conducted by taking the mainstream airflow
Mach number of Ma=1.5 at the inlet of the domain. Secondly, considering a fuel (H2) injection to the system, the flow
Mach number of the fuel was taken as Mj=0.6, while the main flow Mach number was kept constant at Ma=1.5. The
domain meshed with the blockMesh utility of OpenFoam. The grids densely clustered near the boundary or in the
shear layer and the cavity, as shown in Fig. 4, to provide reasonable predictions. The grids used in the present work
are 300×100 in the channel and 200×80 in the cavity. The inlet total pressure and temperature were p0=101.3kPa and
T0=293K, respectively. The boundary conditions used were the inflow conditions and pressure outlet conditions at the
inlet and outlet boundaries of the computational domain, respectively. Adiabatic and no-slip wall conditions were
applied to the solid wall surfaces [16].
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(a) Rectangular cavity, ș=0o
(b) Triangular cavity, ș=30o
FIGURE 4. Typical grids
RESULTS AND DISCUSSION
Flow and pressure fields for airflow
Figure 5 shows the contour maps of density during one period of flow field oscillation for a rectangular cavity,
ș=0o. From this time sequence of figures, it can be seen that the shear layer from the cavity leading edge collides with
the rear edge of the cavity, and the compression wave (CW) is generated and propagates towards the leading edge.
The propagating compressed wave then collides with the leading edge and reflects towards the trailing edge of the
cavity. During the returning phase, the reflected compression wave excites the shear layer, and the shear layer collides
again with the trailing edge [32]. Thus, a new compressed wave generates, and it creates a feedback loop [27]. Laterally,
it results in a fluctuation in the pressure field. When the frequencies of shear layer excitation and compression wave
match a resonance may occur [28]. While Fig. 6 shows the contour maps of density during one period of flow field
oscillation for a triangular cavity, ș=30o. From these figures, it can be mentioned that a similar phenomenon as the
rectangular cavity, ș=0o occurred in the case of the triangular cavities. Unlike the ș=0o, the cavity at ș=30o, the
compression waves propagate obliquely upwards, and it greatly pushes up the flow field pressure oscillation.
(a) t = 0.25T
(c) t = 0.75T
(b) t= 0.5T
(a) t=0.25T
(c) t=0.75T
(d) t = T
FIGURE 5. Density contours during one period of flow field
oscillation (Rectangular cavity, ș=0o)
(b) t=0.5T
(d) t=T
FIGURE 6. Density contours during one period of flow field
oscillation (Triangular cavity, ș=30o)
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To investigate the flow field pressure oscillation, the pressure was measured at the measurement points (point ‘a’
through ‘g’) shown in Fig. 2. A fast Fourier transform (FFT) was then performed to analyze the time-dependent
pressure data. The results are plotted graphically in Fig. 7. In this study, as the compression wave generates close to
the point of ‘b’, and the results of pressure histories and power spectra are shown as a reference [29]. From this figure,
it can be seen that the amplitude of pressure fluctuation increases with the increase of leading slant angle ș i.e. for
triangular cavities. Moreover, the peaks of power spectra for triangular cavities are high compared with the rectangular
cavity. Here, it is mentioned that the high peak in power spectra implies that the energy of turbulent fluctuation in the
flow field is high. Besides, the dominant frequency of the flow field pressure oscillation was found at about 400 Hz.
(a) Pressure histories
(b) Power spectra
FIGURE 7. Pressure histories and power spectra of pressure at point ‘b’
Flow and pressure fields for the air-fuel flow
Figure 8 shows the contour maps of pressure during one period of flow field oscillation for air-fuel flow over a
rectangular cavity, ș=0o; while the contour maps of mass fraction of H2 during one period of flow field oscillation for
air-fuel flow over a rectangular cavity, ș=0o are shown in Fig. 9.
(a) t=0.25T
(c) t=0.75T
(b) t=0.5T
(d) t=T
FIGURE 8. Pressure contours of air-fuel flow during one period of flow oscillation (Ma=1.5, Mj= 0.6, ș=0o)
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(a) t=0.25T
(b) t=0.5T
(c) t=0.75T
(d) t=T
FIGURE 9. Contours of mass fraction of H2 one period of flow field oscillation (Ma=1.5, Mj= 0.6, ș=0o)
From Fig. 8, it can be seen that a similar change is experienced in the flow fields unlike the shock wave generates
at fuel inlet downstream of the cavity leading edge, and this shock wave then reflects from the upper wall of the
channel and creates a shock train [30]. On the other hand, from the contours of mass fraction shown in Fig. 9, it can
be seen that the H2 gets mixed with the air on account of flow field pressure oscillation [31].
Figure 10 shows pressure history at point ‘b’ and mixing indices at different cross-sections in the channel, while the
H2 is injected at a Mach number of Mj=0.6 to the airflow at Ma=1.5. Here, the mixing index implies the mixing
performance, and at the highest performance, the mixing index is to be unity. From Fig. 10(a), it can be seen that the
pressure history shows a similar change in the pressure with time, unlike a high amplitude that may results in the flow
field due to the occurrence of a shock wave at fuel inlet. On the other hand, from Fig. 10(b), the cavity induced oscillation
can have a significant influence in air-fuel mixing.
(a) Pressure history at ‘b’
(b) Mixing index
FIGURE 10. Pressure history at point ‘b’ and mixing indices at different cross-sections in the channel (Ma=1.5, ș=0o)
CONCLUSIONS
In the present study, a numerical work was carried out to investigate a passive technique to improve the air-fuel
mixture in a cavity-based scramjet engine. The leading edge of the cavity was modified to intensify the shear layer
excitation, and that may lead to the amplification of cavity-induced flow field oscillations. Laterally, it results in the
improvement of the mixing of air-fuel. As a result, a slant at the leading edge i.e. a triangular cavity showed a high
amplitude of pressure oscillation compared with the rectangular cavity. Moreover, a triangular cavity showed a higher
peak in the power spectra. Besides, it can be mentioned that the cavity induced pressure oscillation can have a significant
influence on the air-fuel mixing improvement.
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