1. 1
14th Annual CFD Symposium, August 10-11, 2012, Bangalore
Flow field studies over V-shaped rear face cavities at supersonic speed
G. Srinivasan*, K.P. Sinhamahapatra
Department of Aerospace Engineering, Indian Institute of Technology, Kharagpur, India
and
Sudip Das
Space Engineering and Rocketry, Birla Institute of Technology, Mesra, Ranchi, India
*E-mail: vasuaero1988@gmail.com
Abstract
Experimental and computational study at Mach 2.0 over cavities with V-notched rear face is carried
out. A different angle like 60, 75, 90 and 110 degrees has been applied for V-notches. Unsteady and static
pressure measurements were made on the walls and floor of the cavity. Data analysis was performed on the
experimental results using statistical methods. Attempt was also made to obtain oil flow and schlieren flow
visualisation photographs of the flow field. Three dimensional unsteady turbulent simulations were made using
fluent on a structured grid. It is observed that the OASPL at rear face of the cavity has high magnitude with
different modes of frequency and as the depth of rear face of cavity is increased i.e with decreasing V-notch
angle an increase in OASPL near rear face is observed. The pressure distribution on floor of the cavity showed
a good comparison between experiments and computations.
Nomenclature
f frequency in Hz
D depth of cavity
L length of cavity
L/D Length to Depth ratio of the cavity
n Mode number
SPL Sound pressure level (db)
OASPL Overall sound pressure level (db)
PSD Power Spectral Density
P Static pressure
P0 Total Pressure
X/L Non Dimensional Coordinate along length of the cavity
Y/D Non dimensional Coordinate along Depth of the cavity
CV180 Cavity with Flat rear face
CV110 Cavity with 1100
V-notch
CV90 Cavity with 900
V-notch
CV 75 Cavity with 750
V-notch
CV60 Cavity with 600
V-notch
I. Introduction
Cavities are finite width longitudinal slots on surfaces in a solid object. The cavities have wide
application areas, in particular they are used as a flame holding devices in scramjet combustors as well as it can
be seen as aircraft weapons bay etc. A supersonic airbreathing engine is a crucial propulsion unit of future high-
speed transportation vehicles. At flight speeds beyond Mach 6, air entering the combustor must be supersonic
and the time available for fuel injection, fuel–air mixing, and combustion is very short, of the order of 1ms. A
stable cavity can be used for flame-holding applications in the combustor whereas an unstable cavity can
provide enhancement in the turbulent mixing and combustion. In an effort to reduce the combustor length
required for efficient high-speed combustion, the scramjet community has proposed the use of wall cavities to
stabilize supersonic combustion. The main idea is to create a recirculation region inside the cavity. However, for
a stable combustion process, the cavity recirculation region has to be stable to provide a continuous ignition
source. Cavities are characterized based on its geometry i.e. the ratio of cavity length (L) to depth (D). A typical
sketch of geometry of cavity as well as its nomenclature is shown in figure 1. In general the flows over cavities

2. 2
are classified into three categories 1) Open 2) Closed and 3) Transitional. Figure 2 shows cavity with V-shaped
Rear face.
Figure 1: Geometry and classification of surfaces of cavity Figure 2: Cavity with V-shaped Rear Face
Research and studies on supersonic flow over wall mounted cavities have been carried out extensively
in the past decade. Earlier studies on flow over cavities were aimed at studying the self sustained oscillations
which are the source of flow noise and undesirable structural loading of aerodynamic configurations. Many
experimental and computational studies have been directed toward improving the understanding of the physics
of cavity flows and controlling their nature. In the current decade, attention is drawn on the flow over cavities
due to the possible role of the cavity oscillations for fuel-air mixing and flame holding in supersonic
combustors. Some of the work carried out by different scientists are presented in this chapter. Ritchie and
Knowles[17]
conducted computational investigation on rectangular cavity of L/D = 5. During his investigation on
various types of turbulence models available for numerical investigation he found that the realizable k-epsilon
model was showing better results than any other turbulence model. Zhang and Naguib [20]
investigated the effect
of Cavity width on the unsteady pressure at low Mach numbers. It was found that the increase of the cavity
width caused the cavity’s self-sustained oscillation to be attenuated or disappear altogether. At a high Reynolds
number, the increase in oscillation was accompanied by increased unsteadiness at very low frequencies.
Edwards et al[10]
performed computational analysis of self-sustained oscillatory flow over a cavity driven by
shear layer at Mach number 1.5. The unsteady flow was studied through solutions of the Reynolds-averaged
navier stokes equations with turbulence modelled by a two-equation k-omega model. Zhisong and Hamed [22]
investigated the effect of sidewall boundary conditions on the computed unsteady flow and sound pressure level
in a transonic open cavity. The solutions were obtained using a 3rd
order rossitier scheme and the shear-stress-
transport (SST) two-equation-based hybrid turbulence model. He compared the computational results with the
experimental results with prior LES results, and with previous results obtained using low Reynolds number two-
equation DES based model. Basu et al[15]
performed Detached Eddy Simulation (DES) for unsteady three-
dimensional supersonic flow over an open L/D = 5 cavity at free-stream Mach number of 1.19. Their results
revealed the basic flow features, including the vertex shedding, shock waves, and coupling of the acoustic and
vorticity fields. Their study demonstrated that DES formulation is an effective method for performing unsteady
simulations for cavity flow-fields compared to 3-D URANS simulations. 3D unsteady computations of
supersonic cavity flow was performed by Soemarwoto and Kok[13]
. He assessed with RANS equations with a K-
Omega turbulence model for the whole flowfield and a combination of an inviscid flow model using the Euler
equations for the domain outside the boundary layer and the RANS model for the boundary layer. ZhaoLin et
al[25]
conducted experimental and numerical investigation to obtain flow characteristics for three types of
rectangular cavities. The results indicate that the shear-layer expands over the cavity leading edge and impinges
on the cavity floor for closed cavity flow, whereas it bridges the open cavity. The static pressure distributions
are relatively uniform with the exception of a small adverse gradient occurring ahead of the rear face inside
open cavity. Vikram and kurian[24]
investigated on the effect of aft wall slope on cavity pressure oscillations in
supersonic flows. He investigated on cavities with aft wall angles of 90, 75, 60, 45,30 and 15 degrees by making
unsteady pressure measurement on their walls and floor. Higher amplitude oscillations were observed for
cavities with 90 and 75 degree aft wall angle while for cavities of aft angle 60 degrees and lower, sharp fall in
amplitudes were observed. Mode switching was seen to be clearly influenced by the change in angle for higher
angled cavities. Stallings and Wilcox[6]
conducted experimental investigation to define pressure distributions for
rectangular cavities over a range of free-stream Mach numbers 1.5 t0 2.86 and cavity dimensions with lengths
varied from 0.5 to 12in and depth from 0.5 to 2.5 in. Values of L/D ranged from 2 to 16. In his experiments he
observed that the effect of cavity width on cavity pressure distributions were much greater for cavities having
open flow field. A complete database of pressure distribution over cavities with various length to depth ratio has
been reported. Experimental studies on rectangular cavities at subsonic and transonic speeds were conduted by
Plentovich et. al[8]
. Cavity depths and widths were varied from 0.5 to 2.5 in. Values of L/D ranged from 1 to
17.5 and width to depth ratio 1 to 16. In his experiments he observed that the effect of cavity width on cavity
pressure distributions were much greater for cavities having open flow field.

3. 3
II. Geometric Details
Investigations were carried on a cavity with Length-to-Depth ratio of 5 with length of 50mm, Depth of
10mm and width of 10mm. Figure 3.2 shows the geometry of cavity made on the base plate. The cavity with
length of 110mm, depth of 10mm and width of 10mm was chosen for studies. In the present paper cavity with
different angled V-shaped rear face models are named as CV180, CV110, CV90, CV75 and CV60 where each
of the following corresponds to cavity with flat rear face, cavity with 1100
V-notch, cavity with 900
V-notch,
cavity with 750
V-notch and cavity with 600
V-notch respectively.
III. Experimental Setup
All the experiments were carried out using intermittent blow down Supersonic Wind Tunnel, available
in the Department of Space Engineering and Rocketry, Birla Institute of Technology, Mesra. It has a test section
size of 50mm x 100mm cross section. The Mach number inside the test section can be varied from 1.8 to 3.2 by
using different nozzle blocks. For the present study, nozzle block corresponding to Mach number of 2.0 is used.
Compressed air is supplied to the tunnel through a reservoir having 30m3
capacity and with a maximum storage
pressure capacity of 150psig. Compressed air from compressor passes through a dryer and stores in the
reservoir. The stored air is released using an electronic solenoid valve through pneumatic operations, to the
settling chamber and finally expanding through a C-D nozzle at the test section. The run time of the tunnel is
typically 15 sec.
Experiments were carried on a cavity that was made on an Aluminium base plate. The Length-to-Depth
ratio of the cavity is 5 with length of 50mm, Depth of 10mm and width of 10mm. Two base plates were
fabricated one for Unsteady pressure measurement and the other for static pressure measurement. In order to
change the rear face shapes and for mounting pressure sensors the entire model was made into three parts. The
cavity was made with length of 110mm, depth of 10mm and width of 10mm. Two rectangular blocks each of
30mm length, breadth of 10mm and height of 10mm were made. These two blocks were inserted into the base
plate cavity such that one acts as front face block and other being rear face block. The rear face with V-notches
was made with angles of 60, 75, 90 and 110 degree.
Model for static pressure measurement
Static pressure measurements were carried out on the models with different rear face notch angles. 18
pressure tap locations were identified in the region of interest.1.2 mm Diameter holes were drilled on the model
with 9 ports on the floor, 2 ports on the front face and 6 ports on the aft wall were made. For models of V-notch
rear face, pressure measurement were done only on the floor and front face. Stainless steel tubes were passed
through these holes and one side of the tubes were flushed with the cavity surface, the other ends were
connected to polythene tubes which were then connected to electronic pressure scanner tubing’s. The pressure
ports in the cavity are shown in figure 3. Details of these port locations are given in figure 4.
Figure 3 : Base plate cavity with static pressure ports seen on the cavity floor
a b c
Figure 4 : Static Pressure port locations a) Front face b) Floor c) Rear Face

4. 4
Model for unsteady pressure measurement
Unsteady pressure measurements were carried on the models with different rear face V-notch and flat
wall. For model with flat wall 3 port location were identified in the region of interest one on the centre of front
face another on floor and the third on rear face. For models with V-notch rear face, the third port was near the
floor near to the rear face. 3mm diameter holes were drilled where the sensor is directly inserted into holes such
the sensor was flush with the surface of the cavity. Fig 5 shows the assembled model made for unsteady
pressure sensors mounted on the bottom face. Fig 6 gives the unsteady pressure port locations.
Figure 5 : Cavity with Unsteady Pressure sensors
a b c
Figure 6 : Unsteady pressure transducers locations a) front face b) Floor c) Aft wall (For flat face only)
Data acquisition of Static pressure
Pressures were measured using Scanivalve make electronic pressure scanner (Z0C 22b/32Px). This has
32 individual sensors having a range of 2.5 to 50 psig. The scanner module has two pneumatic control lines
which operate the 32 pressure sensors arranged in two blocks of 16 sensors. Each of 16 sensors has its own
calibration value. All these were calibrated prior to making test runs. Logic controls and the signal acquisition
from the scanner are programmed through LabVIEW. National Instruments make DAQ (PCI-M10-16E-1) and a
PC was used to acquire the signals. Calibration of the sensors of the scanner was done by providing different
pressures and by using a mercury manometer.
Data acquisition for unsteady pressure measurement
Unsteady pressure measurements were performed using Kulite XCL-100-25A pressure transducer
which was flush mounted on the cavity surface. These pressure transducers work on the principle of fully active
four arm Wheatstone bridge isolated silicon on silicon patented leadless technology. Three pressure transducers
were used to measure unsteady oscillations of pressure. For cavity flat face the first transducer was at front face,
second at floor and the third on the rear face. For cavity with V-notches, due to unavailability of space to
accommodate the transducer on rear face the third sensor was place on floor near to rear face. Data was acquired
using NI card and labview. Signals from the transducers were obtained in different modes with a sampling rate
of 30 KHz. FFT of the signal were done and results were analyzed using post processing software.
IV. Numerical Solver
Numerical simulations were performed using the commercially available software FLUENT where grid
is generated using GAMBIT. Based on certain preliminary performance analysis the realizable k-ε turbulence
model was used for all the simulations. Table 1 shows details of numerical simulation applied for computations.

5. 5
Table 1: Details of Numerical simulation applied for computations
Cavity Geometry L/D = 5
Mesh type Hexahedral, Map
Total Number of cells 5,26,000
Cell Refinement in Cavity (length x depth x width) 60 x 40 x 10
Flow solver Type Unsteady Coupled Solver
Turbulence Model Realizable K- ε
Time Step Size 0.0002
Total Number of time steps 10000
Solution Flow time (s) 5
Realizable K-ε model
The realizable k-ε model is a relatively recent development and differs from the standard k-ε model in
two important ways. The realizable k-ε model contains a new formulation for the turbulent viscosity. A new
transport equation for the dissipation rate, ε, has been derived from an exact equation for the transport of the
mean-square vorticity fluctuation. The modelled transport equations for k and ε in the realizable k-ε model are
and
where
Table 2: Free stream conditions
Total pressure 308145 Pa
Static pressure 39382.32 Pa
Mach Number 2
Figure 7 shows the full view of domain and grid. Figure 8 shows the close view of structured grid
inside the cavity. Figure 9 shows three dimensional cavity domain with different Rear face V-notch angles.
Figure 7: Domain Dimensions and its Boundary conditions Figure 8: Close up view of Cell distribution inside the cavity
(A)CV180 (B) CV60 (C) CV75 (D) CV90 (E) CV110
Figure 9: Three dimensional cavity domain with different Rear face V-notch angles

6. 6
Boundary Conditions
Pressure inlet boundary condition was used for the inflow, and the free stream conditions were
specified. Pressure outlet boundary condition was set to the outflow, where the variables are extrapolated from
the interior cells. Wall boundary condition was given for cavity bottom floor and side walls.
V. Results and Discussions
Experimental Results
Static pressure distribution along the floor of the cavity has been plotted in figure 10. The Cp values
between x/l = 0.1 to 0.5 are very similar suggesting that the pressure field for the first 50% is uniform along the
length of the cavity floor. However, the later 50% shows a slight decrease moving downstream which reaches a
minimum at x/l = 0.8 with a marginally negative Cp value. The last pressure tapping along the cavity length at
x/l = 0.9, which is near the rear face of the cavity recorded a high cp value. Sudden increase in the Cp at x/l =
0.9 is due to the deflected shear layer flowing towards the floor of the cavity.
Figure 10: Static Pressure distribution inside cavity CV180
Power spectra in the form of power spectral density (PSD) vs. frequency for transducers positioned at
different locations inside the cavity is shown in figure 11. One clear observation from the plot is that, the
dominant frequency exists with frequencies of 2500 Hz, 5000 Hz and 13000 Hz.
The OASPL plot for cavity faces has been plotted in figure 12. On observing the plot, the lowest value
occurs at the front face with 166 db and the highest value occurs at the rear face with amplitude of 171 db. This
indicates high magnitude unsteadiness near the rear face compared to any other location on the floor and front
face. The SPL data on the aft wall and near the aft wall on floor are shown in figure 13.
Front Face Rear FaceFloor
Figure 11: Power Spectra at different
locations inside cavity CV180
Figure 12: OASPL at different location inside cavity
CV180

7. 7
A B
Figure 13: SPL inside the cavity A) rear face B) On floor near rear face
Figure 14: Static pressure distribution inside cavity CV110
Figure 17: SPL of CV110 on the floor near rearface
Figure 15: Power spectra at different
locations inside cavity CV110
Figure 16: OASPL at different location inside cavity
CV110

8. 8
Figure 18: Static pressure distribution inside cavity CV90
Figure 19: SPL of CV90 on the floor near rear face
Figure 22: Static pressure distribution inside cavity CV75
Figure 21: OASPL at different location inside cavity
CV90
Figure 20: Power spectra at different
locations inside cavity CV90

9. 9
Figure 23: SPL of CV75 on the floor near rear face
Figure 26: Static pressure distribution inside cavity CV60
Figure 28: OASPL at different location inside cavity
CV60
Figure 25: OASPL at different location inside cavity
CV75
Figure 24: Power spectra at different
locations inside cavity CV75
Figure 27: Power spectra at different
locations inside cavity CV60

10. 10
Figure 29: SPL of CV60 on the floor near rear face
Effect of Notch angles
Table 3 show the comparison of dominant modes observed for of all Cavity models with V-notched
rear face.
Table 3: Dominating frequencies at rear face of the cavity with different V-notch angles
MODEL MODE FREQUENCY(Hz) STROUHAL
NUMBER
CV180
1 2500 0.242
2 5200 0.503
3 13000 1.26
CV110
1 5500 0.532
2 13000 1.26
CV90
1 5500 0.532
2 13000 1.26
CV75
1 6000 0.58
2 13000 1.26
CV60
1 5900 0.571
2 13200 1.276
It is seen that for different angles of the V-notch the dominant mode has variations. To clearly
understand the Intensity of variations in the power spectra the comparative plot showing OASPL at all surfaces
of the cavities has been plotted. Figure 21 shows the plot of OASPL recorded near Rear face for all cavity
models. It is observed that Cavity model CV60 has shown the highest OASPL value of 169.7 db near rear face
whereas CV180 has the least value of 166.7 db. On the centre of the floor CV180 has the highest OASPL and
CV110 has the least value. CV60 recorded least OASPL on the front face with 162.5db whereas CV180 has the
highest value.
Figure 30: OASPL near the aft wall for cavities with different V-Notch angles

11. 11
Figure 31: Static pressure distribution on floor of the cavities with
different V-notch angles
Computational Results
Unsteady computation was carried out with time step size of Δt = 10-5
sec. Unsteady pressure data were
recorded at a point on the rear face. This definitely shows a fluctuation in the range P/P0 = 0.123-0.127. The
power spectra obtained from computations is plotted in figure 23 which shows dominating frequency peaks. The
comparison between experimental and computational results for the dominating frequencies captured is shown
in table 4.
Figure 34: Oil flow path lines on different faces of cavity CV180
Figure 35: Pressure history at the rear face of the cavity CV180 with time step size of 0.0002
Figure 32: Power spectra at rear face of cavity
CV180 obtained from computations
Figure 33: Mach contours inside cavity
CV180

12. 12
Table 4: Frequency mode comparison chart for CV180
Frequency (Hz) Mode (n)
Experiment Computation
2000 2000 1
4000 4100 2
7000 6400 3
10000 7500 4
(A) CV180 (B) CV110
(C) CV90 (D) CV75
Figure 36: Comparison of floor pressure distribution
of CV110
Figure 37: Comparison of floor pressure distribution
of CV90
Figure 38: Comparison of floor pressure distribution
of CV75
Figure 39: Comparison of floor pressure distribution
of CV60

13. 13
(D) CV60
Figure 40: Mach contours inside cavities with different V-Notch angles
Conclusion
Cavities with V-notched rear face of angles 180, 110, 90, 75 and 60 degrees are studied using experiments
and computations. Flow visualisation include oil flow and quantative measurement include static and unsteady
pressure measurements. Similar results were obtained also from the computations. From the results obtained,
number of conclusions are made which are listed as follows.
1) Oil flow over cavity revealed a complex flow pattern on all the faces.
2) The static pressure distribution on the floor of the cavity was taken during experiments which shows
that, as the angle of the V-notch was decreased there was decrease in pressure on the floor. Compared
to CV180 and all other angles CV180 had positive Cp values whereas other angles had negative Cp on
the floor of the cavity. The model CV90 recorded lowest Cp on the floor.
3) Analysis of spectra of oscillations generated by different V-notches showed that as the angle was
decreased there was increase in the amplitude of pressure oscillation near the rear face of the cavity.
High amplitude oscillation was observed for 60 degrees.
4) The magnitude of the OASPL increased as the angle was decreased. The OASPL near the rear face
CV180 was much less compared to the model CV60.
5) Three dimensional simulation using a time step size of 0.0002 was applied which showed that the floor
pressure distribution had good comparison with experiments.
6) Two dimensional simulations with a combination of steady and unsteady simulation with a time step
size of 1e-5 was attempted which showed the expected pressure history at rear face during simulations.
This method was not applied for three dimensional models due to computational power limitations.
References
1) Heller, H.H., Donald, B.B., “Aerodynamically induced pressure oscillations in cavities – Physical
Mechanisms and suppression concepts”, Technical report, Air Force Flight Dynamics Laboratory,
Febraury 1975, pp. 1-167
2) Sarohia, V., and Massier, P. F., “Control of cavity noise”, Journal of Aircraft, Vol. 14, No. 9, 1977, pp.
833-837
3) Shaw, L.L., “Suppression of aerodynamically induced cavity pressure oscillations”, Nasa Technical
report 3119, November 1979, pp. 1-62
4) Heller, H.H., Holmes, G., Covert, E.E., “Flow induced pressure oscillation in shallow cavities”, Air
Force Flight Dynamics Laboratory Technocal Report, Aug 1979, pp. 1-148
5) Kaufman, L.G., and Rodney L clark., “Mach 0.6 to 0.3 flows over rectangular cavities”, Air force
wrigth aeronautical laboratories report, June 1980, pp. 1-297
6) Stallings, R., Wilcox, F., “Experimental Cavity Pressure Distributions at Supersonic Speeds”, NASA
Technical Paper 2683, June 1987, pp.1-77
7) Zhang, X., and Edwards, J.A., “An investigation of supersonic oscillatory cavity flows driven by thick
shear layers”, The Aeronautical Journal, December 1990, Vol 16, pp. 355-364
8) Plentovich, E.B., Stallings, R., and Tracy, M.B., “Experimental cavity pressure measurements at
subsonic and transonic speeds”, NASA Technical paper 3358, December 1993, pp. 1-132
9) Tracy, M.B., and Plentovich, E. B., “Cavity Unsteady-Pressure Measurements at Subsonic and
Transonic Speeds”, NASA Technical report 3669, December 1997, pp. 1-76

14. 14
10) Zhang, X., Rona, A., and Edwards, J.A., “The effect of trailing edge geometry on cavity flow
oscillation driven by a supersonic shear layer”, The Aeronautical Journal, March 1998, pp. 129-136
11) Perng, S.W., and Dolling, D.S., “Suppression of Pressure Oscillations in High Mach Number
Turbulent, Cavity Flow”, AIAA Journal, Vol. 38, No. 02, 2001, pp. 248-256
12) Yakar, A.B., Hanson, R.K., ”Cavity Flame-Holders for Ignition and Flame Stabilization in Scramjets:
An Overview”, Journal of propulsion and Power, Vol. 17, No. 4, July–August 2001, pp. 869-877
13) Soemarwoto, B.I., Kok, J.C., “Computations of three-dimensional unsteady supersonic cavity flow to
study the effect of different downstream geometries”, RTO AVT symposium on “ Ageing Mechanisms
and control : Part A- Developments in Computational Aero-and Hydro-Acoustics” Manchester, UK, 8-
11 October 2001 pp. 1-14
14) Nayyar, P., Barakos, G.N., Badcock, K.J., “Numerical and Experimental Analysis of Transonic cavity
flows”, AIAA Journal, Vol 4, no 2, June 2002, pp. 56-66
15) Hamed, A., Basu, D., Das, K., “Detached eddy simulations of supersonic flow over cavities” AIAA
Journal, Vol. 5, 2003, pp. 45-54
16) Sahoo, D., and Annaswamy, A., “Control of cavity tones in supersonic flow”, AIAA aerospace
sciences and exhibit, January 2005, pp. 1-17
17) Knowles K., Lawson N.J., Ritchie S.A., ”An Experimental and Computational Investigation of a 3D,
l/h=5 Transonic Cavity Flow”, 3rd International Symposium on Integrating CFD and Experiments in
Aerodynamics 20-21 June 2007, U.S. Air Force Academy, CO, USA
18) Zhuang, A., Alkislar, F.S., and Shih, C., supersonic cavity flows and their control, AIAA Journal,
September 2006, Vol 44, pp 2118-2128
19) Lazer, E., Elliott, G., Glumac, G., “Control of the shear layer above a supersonic cavity using energy
deposition”, AIAA Journal, Vol.46, No.12, December 2008, pp.2987-2997
20) Zhang, Ke., Naguib, A.M., “Effect of cavity width on the unsteady pressure in a
low mach number cavity”, AIAA Journal, vol. 46, July 2008, pp.1878-1880
21) Charyulu, B.V.N., Manoj, R., Rajinikant, B., Tripathi, D,K., Rolex, A., Ramanujachari, V.,
Panneerselvam, S., “Experimental Investigation of Ramp-cavity based supersonic combustor”,
proceedings of the international conference on aerospace science and technology 26-28 june, 2008,
Bangalore, India pp.1-11
22) Zhisong L., Hamed, A., “Effect of sidewall boundary condition on unsteady high speed cavity flow and
acoustics”, Computers and Fluids 37(2008), Science direct pp. 584-592
23) Vikramaditya N.S., Kurian, J., “Pressure Oscillations from Cavities with Ramp”, AIAA Journal, Vol.
47, No. 12, December 2009, pp 2974-2984
24) Vikramaditya N.S., Kurian,J., “Effect of aft wall slope on cavity pressure oscillations in supersonic
flows”, The Aeronautical Journal, May2009,volume113, no1143, pp 291-300
25) Yang, D., JianQiang, L., ZhaoLin, F., Yao, D., “Aerodynamoc characteristics of transonic and
supersonic flow over rectangular cavities”, Flow Turbulence Combust(2010), springer publisher, pp.
639-652
26) Lawson S.J., and Barakos G.N., “Review of numerical simulations for high-speed turbulent cavity
flows”, Progress in Aerospace Sciences, 2010 pp. 1-31
27) Mahbudul, A., Shigeru, M., Teramoto, K., Toshiaki, S., Kim, D., “A computational investigation on the
control of cavity-induced pressure oscillations using sub-cavity”, Journal of Thermal sciences, Vol 15,
No. 3 pp. 213-219