Numerical investigation of detonation wave propagation pulse engine with obstacles

1. International Conference on Sustainable Computing in Science, Technology & Management (SUSCOM-2019)
February 26 - 28, 2019 | Amity University Rajasthan, Jaipur, India Page 253
Numerical Investigation of Detonation Wave Propagation in Pulse
Detonation Engine with Obstacles
Noor Alam*, K. K. Sharma, and K. M. Pandey
Department of Mechanical Engineering, National Institute of Technology Silchar, Assam-788010, India
A R T I C L E I N F O
Article history:
Received 19 December 18
Received in revised form 02 January 19
Accepted 20 February 19
Keywords:
Obstacles
Detonation
Turbulent flame
Pulse Detonation Engine
Blockage ratio
DDT
Euler equation
A B S T R A C T
The numerical investigation of Detonation wave propagation and Deflagration-to-Detonation transition is
done in straight long tube of 1200 mm length and 60 mm internal circular diameter with stoichiometric
(ϕ=1) mixture of hydrogen-air at ambient pressure and temperature of 0.1 MPa and 293 K respectively.
The detonation tube contains obstacles having blockage ratio (BR) 0.5, 0.6 and 0.7, and having 60 mm
gap among them. The computation analysis is performed firstly on simple straight tube having no obstacle
(BR=0.0) and then obstructed channel. The combustion phenomena of fuel-air mixture are modeled by
one-step irreversible chemical reaction model. Three-dimensional Navier-Stokes equations along with
realizable k-ɛ turbulence model are solved by the commercial computation fluid dynamics software
ANSYS Fluent-14 code. The performance of pulse detonation engine (PDE) depends on blockage ratio
(BR) of obstacles. The simulation results show that the initiation and propagation of flame is due to
exothermic expansion of hot combustion gases. The obstacles generated turbulence at obstacle wakes,
which caused to increase flame surface area. Therefore, obstacles reduced the Deflagration-to-Detonation
transition (DDT) run-up length. The perturbation inside the combustor increases as increased the blockage
ratio of obstacle. The PDE Simulation results of with and without obstacles were analyzed and compared
with adiabatic flame temperature.
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1. Introduction
The research of detonation waves had been started from 1880s, but there are number of question not explained in detail yet. After the many experiment,
researcher reported that the detonation wave is generated after the transition of deflagration wave (Dzieminska & Hayashi). In recent year, it increases
attention to develop the existing technology of pulse detonation engine through experimental, computational and Analytical analysis with the variation of
different operating parameter, which offered potentially better performance of PDE. The process of turbojet engines is complicated due to complex
arrangements of turbine, compressor, and combustion, while as the PDE combustor generate high frequency detonation wave for propulsive thrust in
aerospace vehicles. The conventional turbine engine operates on constant pressure and the PDE combustor possess is quasi-steady state at constant volume
(New & Lu, 2006). The combustion waves are to produce high pressure around the reaction zone. The new turbomachinery combustors normally operate
in the subsonic mode and deflagration combustion wave produces low pressure throughout the chamber compared to the supersonic mode. The modern
design of a pulse detonation engine (PDE) is to improve combustion cycles by the using of detonation waves for complete burning of fuel and oxidizer
mixture at high operating frequencies. The pulse detonation engine is thermodynamically proficient system because there is detonation wave compressed
rapidly to the fresh mixture and adds heat at constant volume with low entropy generation. The cyclic process of pulse detonation engine generally
consisting of 5 phases: 1) Fill friction, 2) Ignition, 3) Deflagration-to-Detonation Transition (DDT), 4) Expansion/Exhaust and 5) Purge. The final phase is
used to flush the hot combustion products from the system to prevent auto ignition during the fill phase of the subsequent cycle. Theoretically PDE system
would be reduce the required energy and supersonic form of detonation waves is used to ignite the refiling charge (Driscoll& Gutmark, 2015). The overall
efficiency of the PDE is also depend on the DDT phase, as the DDT run-up length is reduced then the thermal efficiency of the PDE combustion cycle is
increased and the majority of the reactants are burnt during the highly reactive detonation wave propagation. The Deflagration-to-Detonation Transition
run-up length is normally reduced through the use of obstacles inside the PDE combustor, which cause turbulence in the flame and quick transition from
deflagration to detonation. Such devices can consist of orifice plates, ramps, or the more well-known Shchelkin spiral. Unfortunately, due to the physics
involved, these devices can produce a large pressure drop across the system (Driscoll& Gutmark, 2012,Nielsen & Hoke, 2002). The transition to
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2. International Conference on Sustainable Computing in Science, Technology & Management (SUSCOM-2019)
February 26 - 28, 2019 | Amity University Rajasthan, Jaipur, India Page 254
detonation numerically solved with obstacles including all relevant physical processes. The turbulent flame propagated in obstructed channels with
subsonic to supersonic deflagration mode without DDT (Veser &Dorofeev, 2002,Breitung & Baraldi, 2005).
From the literature, the combustion mechanism is analyzed by using different blockage ratio obstacles in different size of PDE tube. Therefore, the
authors want to analyze the effect of obstacles blockage ratio on the thermodynamic parameter comparison to without obstacle PDE tube. The present
research work, numerically investigate the combustion flame temperature and flame propagation for stoichiometric hydrogen-air mixtures at ambient
pressure and temperature. The numerical results of obstructed PDE tube has been compared with the simple straight (without obstacle) PDE tube.
Nomenclature
A Pre-exponential Factor

 Temperature Exponent
C-J Chapman Jouguet
CFD Computational Fluid Dynamics
E Activation Energy
e Total Energy
 Heat ratio
f
K  Reaction Rate
PDE Pulse Detonation Engine
P pressure
R Gas Constant
Y Fuel Mass Fraction
2. Numerical Methodology
The numerical simulation was based on the Navier-Stokes equations (Eq.1) coupled with compressible ideal gas equation of state. The pressure-based,
standard k-ε turbulence model were used to analyze the stoichiometric Hydrogen-air mixture (Alam & Pandey, 2018, Rudy &Teodorczyk, 2011).
Therefore, this turbulence model is solved by the commercial computation fluid dynamics software ANSYS Fluent-14 code.
2.1. Governing Equations
The general form of 3-D Euler equation expressed as:
E F G S
t x y z

   
   
   
(1)
where:
s
Y
u
v
e


 


 
 
 
 

 
 
 
 
,

2
s
u
uY
u p
E
uv
p
u e






 
 
 
 

  
 
 
 

 
 
, 2
s
v
vY
vu
F
v p
p
v e






 
 
 
 
 


 
 
 
 

 
 
 
 
, 2
( )
s
w
uwY
vw
G
w P
P
w e






 
 
 
 
  

 
 
 

 
 
0
0
0
0
s
w
S
 
 

 
 

 
 
 
 
(2)
The above equation can be solved by split method.
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3. International Conference on Sustainable Computing in Science, Technology & Management (SUSCOM-2019)
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0,
E
t x

 
 
 
0,
F
t y

 
 
 
0,
G
t w

 
 
 
( )
s
s
Y
t



 
 (3)
and p RT

 (4)
2 2
1
( )
1 2
P
e u v
 

  
 (5)
where ρ, T , P, u, v, e, and Y are the density, temperature, pressure, stream-wise velocity, transverse velocity, specific energy, and fuel mass fraction of
the gas mixture, respectively.
The ρ is calculated as sum of mass fraction (Yi) and density ( i) of each species,
1
n
i i
i
y
 

  (6)
where, i= 1 to nth
species
The equations of state can be defined,
1
1
1
n
n i
i
Y y


   (7)
The one-step Arrhenius chemical irreversible reactions are employed in the detonation calculations (Wei & Feng, 2015). Thus the reaction rate is
defined as,
( / )
,
E RT
f
K AT e
 

 
 (8)
where Aγ is the pre-exponential factor, R is the gas constant, Eγ is the activation energy for the reaction and βγ is temperature exponent.
2.2. Turbulence model
The standard k-ε model based on transport equation model for turbulent kinetic energy (k) and dissipation rate (ε):
( ) ( ) t
i k b M k
i j k j
k
k ku G G Y S
t x x x

   

 
 
   
       
 
 
   
 
 
 
(9)
 
2
1 3 2
( ) ( ) t
i k b k
i j j
u C G C G C S
t x x x k k
  

   
   

 
 
   
      
 
 
   
 
 
 
(10)
were, G and Gb are the turbulence kinetic energy generation due to the mean velocity gradients and buoyancy respectively. YMis fluctuating dilatation in
compressible turbulence for overall dissipation rate. C1, C2 and C3 are constants.  and  are the turbulent Prandtl numbers for k and ε, respectively S
and S are source terms.
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2.3. Computational model and boundary condition
The computational domain of three dimensional detonation tube of inner diameter (D) 60 mm and length 1200 mm with the obstacles of 0.5 blockage ratio
is shown by Fig.1. The obstacles inside the combustor having 1D spacing (60 mm) among them. The grid independent test was optimizing the mesh
element size for good resolution of results. The mesh was generated 3 mm element size as shown in Fig. 2, so that accurate analysis of combustion
phenomena occurred. There was 3-D standard k-ɛ turbulence model used along with finite rate chemistry as well as eddy dissipation reaction model.
Single step chemical reaction model was used for their simplicity and complete burning of oxidizer species of stoichiometric hydrogen-air fuel mixture.
There was SIMPLEC algorithms used to simulate combustion physics in the PDE combustion computational model. There are three types of boundaries
employed: inflow, outflow and fixed wall. The inflow boundary condition of hydrogen and air for present simulation are illustrate in Table 1. At the
outflow, pressure outlet condition applied and no-slip condition are employed to the fixed wall.
Fig. 1- Physical model of 3-D PDE detonation tube with obstacles of blockage ratio 0.5.
Fig. 2- Mesh generation of detonation tube of BR-0.5.
Table 1–Inlet boundary conditions of stoichiometric hydrogen-air mixture for PDE tube.
Inlet parameters Air Hydrogen
Pressure (MPa) 0.1 0.1
Temperature (K) 293 293
Mass flow rate (Kg/s) 0.655 0.019269
O2 mass fraction 0.23 0
H2 mass fraction 0 1
H2O mass fraction 0.032 0
3. Results and discussion
The computational analysis of flow and flame acceleration from deflagration state to detonation state in with and without (BR=0.0) obstructed channel of
pulse detonation engine has been done at initial boundary condition of 293 K temperature and 0.1 MPa pressure, which was increased the DDT and energy
release rate due to complete burning of fuel mixture. The burning mechanisms of mixture was effected to the growth of the flame surface area. There were
obstacles of different blockage ratio such as: BR=0.5, BR=0.6 and BR=0.7 fixed inside the PDE combustor at specified space 60 mm between the
obstacles. These obstacles created perturbation in the flow field of combustion region. The propagating flame interacts with the obstacles and generate
large flame surface area, which was immediate burn all fuel particles and reduces the deflagration-to-detonation run-up distance.
In initially, Fig. 3 shows that the flame increases very fast in flow in the form of leading flame edge and propagates towards the open end of tube. The
unburned hot mixture particles near to the obstacles was initiated auto ignition in the tube and generate a reaction zone. Another mechanism for increasing
of flame surface was the interaction of detonation-flame to the Richtmyer–Meshkov instabilities and recirculation flow near the obstacles. The shock-
flame accelerated and generate a fully developed flame at far from inlet in the simple tube (without obstacles BR=0.0). however, in case of obstructed
channel, when flame passed over the obstacle it stretched and wrinkled. Due to this, flame was recirculated near the obstacles that results turbulence in the
flame and fast propagation of flame. As blockage ratio increases the flame velocity increases up to certain limit and further increase of blockage ratio the
velocity of detonation flame has been reduced. The deflagration-to-detonation transition (DDT) distance vary with blockage ratio of obstacles and spacing
between them. As obstacles increases per unit length, the flame surface has been increased abruptly and DDT run-up distance reduces.
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0.0 0.2 0.4 0.6 0.8 1.0 1.2
0
500
1000
1500
2000
2500
Static
Temperature
(K)
Distance (m)
BR=0.0
BR=0.5
BR=0.6
BR=0.7
Fig. 3- Plot temperature contour of PDE combustion tube (a) without obstacles, (b) with obstacles of (c) BR=0.5, (d) BR=0.6, and (e) BR=0.7.
Fig. 4- Plot variation of Static Temperature in the combustion flow field
The temperature contours shown the propagation of flame and generated maximum temperature 2285 k in simple tube for fully developed flame.
While as obstacle laden tube of BR-0.5 generated fully developed flame at 2483 K and other obstructed channel of BR-0.6, 0.7 were generated fully
developed flame at 2493 k and 2525 k respectively. In the obstructed channel flame generation begins near the inlet instead of simple channel shown in
Fig. 4, because obstacles used to promote DDT. The variation in temperature was less but shock-flame was affected by blockage ratio. As increase in
blockage ratio, the run-up distance of fully developed flame was reduced. The obstacles were also generated velocity deficit near the wake of obstacles
shown in Fig. 5, but it is less and caused for high velocity generation at outlet. The velocity variation shown in Fig. 6, in case of without obstacle tube,
initially fuel burning very slow till 400 mm distance from inlet and then increases towards the open end. This caused to increases the DDT run-up
distance. On the other hand, obstacle of Blockage ratio 0.5 achieved maximum velocity compared to the other BR=0.6 and BR=0.7, because of limitation
of velocity deficit and production of strong Mach stem between the obstacles.
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0.0 0.2 0.4 0.6 0.8 1.0 1.2
0
200
400
600
800
1000
1200
1400
1600
1800
2000
Flame
Velocity
(m/s)
Distance (m)
BR=0.0
BR=0.5
BR=0.6
BR=0.7
Fig. 5- Plot velocity contours of PDE combustion tube (a) without obstacles, (b) with obstacles of (c) BR=0.5, (d) BR=0.6, and (e) BR=0.7.
Fig. 6- Plot variation of flame velocity of combustion in the PDE tube.
4. Conclusions
The computational investigation of detonation wave propagation in obstructed channel with stoichiometric ratio of Hydrogen-air mixture has been
reported at atmospheric temperature and pressure. The shock-flame interacts with the obstacles and reduces flame run-up distance, which causes fully
developed detonation wave shortly. The results of ideal PDE tube at blockage ratio (BR) 0.0, 0.5, 0.6, and 0.7, the temperatures 2285 K, 2483 K, 2493 K,
and 2525 K were obtained. The temperature of Plain tube (without obstacle i.e. BR=0.0) was less than the adiabatic temperature (2400 K) of Hydrogen-air
mixture, as the perturbation is not generated in the leading flame. The temperatures of obstructed channel were slightly above the adiabatic temperature of
Hydrogen-air mixture, due to perturbation occurred at obstacle. The speed of combustion flame is also depended on the perturbation. In simple
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combustion tube flame speed is very low about 1050 m/s. However, in obstructed combustion tube flame speed increases as increase of obstacle blockage
ratio. The blockage ratio of 0.7 shows that the detonation speed of flame is reached up to Chapman-Jouguet (C-J) detonation velocity.
In addition, further investigation of the combustion phenomena and performance of PDE, may depends on the inlet boundary condition of fuel-air
mixture such as pre heated limit of air as well as inlet pressure. the gap between obstacles are also highly affected to the formation of strong Mach stems
and obstacle blockage ratio has limitation of velocity deficit near the wake of obstacles. The overall optimization of above parameters along with pressure
drop would be calculate in further extended paper.
Acknowledgements
The authors would like to express gratitude to the Dept. of Mechanical Engineering, NIT Silchar, Assam, India for providing CFD lab facilities, and
also, thankful to TEQIP III for providing financial support to carry out the research work.
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