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Shape effect of cavity flameholder on mixing zoneof hydrogen jet at supersonic flow

Rasoul Moradi a, A. Mahyari b, M. Barzegar Gerdroodbary c,*,A. Abdollahi d, Younes Amini e

a Department of Chemical Engineering, School of Engineering & Applied Science, Khazar University, Baku,

Azerbaijanb Department of Chemical and Petroleum Engineering, Sharif University of Technology, Tehran, Iranc Department of Mechanical Engineering, Babol Noshirvani University of Technology, Babol, Irand Department of Mechanical Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Irane Department of Chemical Engineering, Isfahan University of Technology, Isfahan, Iran

a r t i c l e i n f o

Article history:

Received 16 May 2018

Received in revised form

20 June 2018

Accepted 27 June 2018

Available online 18 July 2018

Keywords:

Computational fluid dynamics

Mixing efficiency

Scramjets

Hydrogen mixing

Cavity flameholder

* Corresponding author.E-mail address: mbarzegarg@yahoo.com

https://doi.org/10.1016/j.ijhydene.2018.06.1660360-3199/© 2018 Hydrogen Energy Publicati

a b s t r a c t

Cavity flameholder is known as an efficient technique for providing the ignition zone. In

this research, computational fluid dynamic is applied to study the influence of the various

shapes of cavity as flameholder on the mixing efficiency inside the scramjet. To evaluate

different shapes of cavity flame holder, the Reynolds-averaged NaviereStokes equations

with (SST) turbulence model are solved to reveal the effect of significant parameters. The

influence of trapezoidal, circle and rectangular cavity on fuel distribution is expansively

analyzed. Moreover, the influence of various Mach numbers (M ¼ 1.2, 2 and 3) on mixing

rate and flow feature inside the cavity is examined. The comprehensive parametric studies

are also done. Our findings show that the trapezoidal cavity is more efficient than other

shapes in the preservation of the ignition zone within the cavity. In addition, the increase

of free stream Mach number intensifies the main circulations within cavity and this in-

duces a stable ignition zone within cavity.

© 2018 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.

Introduction

Scramjets are known as the most efficient engine for the

increasing of the flight speed. This engine is simple and low

cost and does not need high amount of fuel tank which is the

main challenge for the long flight. Development of the com-

bustion efficiency inside the cavity is a crucial for increasing

the performance of scramjets (supersonic combustion ramjet)

[1,2]. Since weight of this engine is low and the working

mechanism is simple, this type of engine is more recom-

mended. Hence, researchers have tried to increase the

(M. Barzegar Gerdroodba

ons LLC. Published by Els

efficiency of this engine. Among numerous subjects for

refining the scramjets, efficient mixing of fuel to air is crucial

for future development of these engines [3]. Since the velocity

of free stream inside themain chamber is high andmore than

sonic, the process of ignition is supersonic main stream oc-

curs very fast, and this augments the importance of mixing in

these engines [4e6].

In order to enhance the mixing rate inside the combustion

chamber, scholars and engineers have investigated different

methods [7e12]. Various techniques and geometries of

scramjets are proposed [13e16] and investigated to enhance

the efficiency [17,18]. It is important to note that the most

ry).

evier Ltd. All rights reserved.

Fig. 1 e Plan of three shapes of cavity (circle, rectangular

and trapezoidal).

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 4 3 ( 2 0 1 8 ) 1 6 3 6 4e1 6 3 7 2 16365

favorable approaches for the development of these engines

are geometrical modifications of the domain and applications

of different techniques such as multi jets injectors, micro air

jets and shock generators. In addition, combinations of these

methods are also considered to enhance the mixing efficiency

of the fuel within cavity. Since this topic is very significant,

several review papers have focused on many features of fuel

injection within supersonic free stream [19]. In our previous

works [20e26], computational techniques are applied for in-

vestigations of different possible mechanisms of fuel and air

injections. Among different geometries, cavity-based flame-

holder concept seems a good mechanism for supersonic

combustors [27].

The shape effect of the cavity in different applications

within the scramjets are studied by various scholars. Kum-

mitha et al. [28] applied CFDmethod for analyzing of fluid flow

behavior inside the scramjet combustor with different cavity-

based flame holders in presence of shock generator. In their

study, shock interactions and their effects on the flow pattern

inside the model are extensively explained. Investigated ef-

fects of passive methods for optimizing the performance of

scramjet combustor. He also presented numerical analysis of

hydrogen fuel scramjet combustor with different turbulence

models. Huang et al. [29e31] examined the result of geometric

constraints on the significant parameters of the cavity

flameholder such as drag and temperature based on the

variance analysis technique.

Though cavity flameholder has been applied as a well-

organized model for providing fuel in a combustor of the

scramjet [32e34], limited works studied the effects of flow

feature and shape of cavity on its performance. In fact,

analyzing and finding of the main parameters which is sig-

nificant on the hydrogen mass distribution inside the cavity

could present the valuable data and improve the knowledge of

the design of the future scramjets. In addition, the effect of the

free stream velocity on the shock effect on the fuel distribu-

tion inside the cavity was not investigated. Previous works

have always investigated the formation of the shock structure

on themain flow patterns as the key point for the analyzing of

the fuel distributions in supersonic combustion chamber.

Indeed, the formation and structure of the fuel jet with the

free stream reveal the main effective terms in the mixing ef-

ficiency of the various methods.

Our work has tried to comprehensively focused on these

deficiencies and explain the main advantages of each cavity

shapes on the performance of the scramjets. As shown in

Fig. 1, three different geometries of cavity such as circle,

rectangular and trapezoidal are investigated. Meanwhile, the

criteria of the ignition zone are displayed to clearly demon-

strate the effect of each parameter on this zone. Furthermore,

streamline patterns are compared for different models to

show the influence of the streamline on the various condi-

tions. It should be noted that circulations are the main results

of the cavity in the supersonic flow patterns. Hence, the for-

mation and effective term of this phenomena is crucial for the

recognition of the main parameters. It is clear that the injec-

tion of the fuel with sonic condition highly disturbs the main

circulation within the cavity. As it will be further explained in

the next sections, the injection of the hydrogen divides the

main circulation inside the cavity and the role of the cavity

shape is significant for the formation of the circulations inside

the cavity. This study also analyzes the flow pattern in the

downstream of the cavity. Hence, the obtained results could

be valuable for the next generation of the scramjets.

In order to analyze the shape effects of cavity, circle,

rectangular and trapezoidal cavities are examined to analyze

the role of the flow inside the cavity on feature and mixing

performance of scramjet. Furthermore, the result of free

stream Mach number on the mixing rate of hydrogen jet is

comprehensively investigated.

Numerical approach

In this work, geometry of the DLR experimental work [35,36] is

used as the main size for further investigations. Since the 2D

model is applied, the size of the domain in x and y direction is

300 and 50 mm, respectively. Fig. 2 shows the applied grid for

Fig. 2 e Grid generation.

i n t e rn a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 4 3 ( 2 0 1 8 ) 1 6 3 6 4e1 6 3 7 216366

the chosen domain for a rectangular cavity. In this research,

structured grid with high resolution inside the cavity are

generated. In order to reduce the numerical diffusion, chosen

efficient grid with high resolution in the model is essential.

Since the main interactions of the problems occurs inside the

cavity, the size of grid is very low in this region. In addition,

the grid should be uniform to avoid any discontinuity in the

results. The grid is densely clustered near the walls of the

combustor and in the vicinity of the injection slot, and the

height of the first row of cells is set at a distance to the wall of

0.001mm,which results in a value of wall yþ smaller than 10.0

for all of the flow field.

In this research, the main inflow Mach supersonic

airstream, stagnation pressure and stagnation temperature

are 2, of 1 atm and 300 K. In addition, other Mach numbers

M∞ ¼ 1:2 and 3 are investigated. Fig. 2 clearly demonstrates

the applied hydrodynamic boundary condition for our model.

In our model, all thermal boundary condition of wall is

assumed constant temperature of 300 K. For turbulence and

species boundary condition, zero flux is applied on the walls.

As shown in Fig. 2, the hydrogen gas was injected from the

cavity front wall at three different pressures. The chosen

pressures are according to the total pressure of the free stream

condition. In this study, total pressure ratios (PR) of 0.25, 0.5

and 1 are investigated for the jet injection. It is worthy to note

that no chemical reactions and/or combustion processes are

taken into account in this work.

In order to simulate the chosen domain, implicit CFD code

is used to solve NaviereStokes equations with SST turbulence

model by using cell centered finite volume approach [37e42].

The details of the applied techniques and turbulence model

are explained in our previous works and other similar refer-

ences [43e46]. Previous studies showed that this is a good

model for this problem [47e53]. In evaluating the flame

holding capacity it is necessary providing estimates of ignition

delays for hydrogen-air mixture under the conditions of pre-

sent numerical experiment being compared with that pro-

vided by chemical kinetics model. The details on ignition

delays for different flow parameters can be found in Ref. [54].

Fig. 3 e Grid independency and validation of obtained

results for cavity a) without swept angle b) with swept

angle of 30.

Results and discussion

Validation

Validation is a first step for the simulation of the engineering

and scientific researches. In order to confirm the superiority of

the grid and analyze the precision of the obtained results,

experimental data of Gruber et al. [27] is chosen and three-

dimensional model of the cavity flameholder is used. Fig. 3

compares obtained results of the normalized pressure distri-

bution for two different shapes of cavity. Our findings show

that deviation is less than 10% for diverse models.

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 4 3 ( 2 0 1 8 ) 1 6 3 6 4e1 6 3 7 2 16367

Additionally, the results of the three different grids are also

compared and it is found that the number grid in fine grid is

reasonable for further simulations. Since two-dimensional

models presented reliable results and obtained validation

confirmed the applied numerical approaches, further simu-

lations will be done with two-dimensional models. For fine

grid resolution and great number of steps accumulation of

numerical stochastic error could exceed all acceptable values.

Special estimates are necessary. The method for those esti-

mates can be found, for example, in Refs. [55] and [56].

Effect of circle cavity on mixing of hydrogen

Fig. 4 illustrates the distribution of hydrogen gas within the

circle cavity with different pressure ratios. In PR ¼ 0.25, the

injected hydrogen remains in the cavity and the distribution

of the hydrogen in the downstream is approximately uniform.

As the Pressure ratio of the fuel jet increases, the interaction of

the jet with themain stream increases and the gradient of the

hydrogen percentage inside/outside the cavity varies. In order

to recognize the mixing rate of the hydrogen, the pattern of

streamline of these models should be investigated. Fig. 5

compares streamlines for various conditions.

According to the results of the flow patterns (Fig. 5), two

circulations covers the whole cavity. As observed from Fig. 4,

mass distribution of the hydrogen jet in the circle cavity with

PR ¼ 0.25 is approximately similar. Increasing the pressure of

the hydrogen jet effects on the interactions of the freestream

and jet outcomes and freestream intends to enter the cavity.

This declines the mass fraction in the left side of the cavity.

The flow pattern of Fig. 5 in PR ¼ 1 clearly confirms this

entrance of the main stream into the cavity.

Fig. 4 e Effect of various pressure ratio of hydrogen jet

Rectangular cavity

Figs. 6 and 7 illustrates the mass distribution and streamline

pattern inside the domain for the various PRs of hydrogen jet,

respectively. One of the main differences of this geometry

with circle geometry is the formation of the extra circulation

inside the cavity. As shown in the Fig. 7, two distinct circula-

tions are observed in the upstream of the fuel jet inside the

cavity. This confirms that the circulation inside the domain is

effective term on the distribution of the mass inside the cav-

ity. One of valuable results is the flow pattern of the hydrogen

in downstream outside the cavity. It is found that increasing

total pressure of the hydrogen intensifies the fluctuations in

the downstream.

Trapezoidal cavity

The mass distribution and streamline patterns of the trape-

zoidal cavity for M ¼ 2 is illustrated in the Figs. 8 and 9,

respectively. As depicted in the figures, increasing the PRs of

the fuel intensifies the mass distribution on downstream of

the cavity inside the cavity. Unlike the rectangular cavity, the

mass fraction of the hydrogen jet in the upstream of the

hydrogen jet within the cavity remains constant.

Fig. 9 illustrates the streamline within the cavity for

various PRs (PR ¼ 0.25, 0.5 and 1). The figure confirms that

there are three circulations within the cavity. Two of these

circulations are upstream of the hydrogen jet and these cir-

culations remains for different PRs.

The comparisons of these three shapes of cavity flame-

holder show that trapezoidal cavity is more efficient in pres-

ervation of the ignition zone in downstream of the hydrogen

on hydrogen mixing rate inside the circle cavity.

Fig. 6 e Mass distribution of the hydrogen jet in the rectangular cavity.

Fig. 5 e Flow pattern of hydrogen and main stream inside the circle cavity.

i n t e rn a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 4 3 ( 2 0 1 8 ) 1 6 3 6 4e1 6 3 7 216368

Fig. 8 e Effect of trapezoidal cavity on the mass distribution in different PRs.

Fig. 7 e Comparison of the streamlines within the rectangular cavity for different PRs.

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 4 3 ( 2 0 1 8 ) 1 6 3 6 4e1 6 3 7 2 16369

Fig. 9 e Comparison of the flow feature inside the cavity flameholder (M ¼ 2) for different PRs (PR- ¼ 0.25, 0.5 and 1).

i n t e rn a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 4 3 ( 2 0 1 8 ) 1 6 3 6 4e1 6 3 7 216370

jet within cavity. This effect is significant due to importance of

the hydrogen concentration within cavity.

Effect of freestream Mach number

In order to recognize the shape effect of shape cavity, the in-

fluenceof thevariousMachnumber (M¼ 1.2 and3) on themass

transfer and ignition zone is investigated. Fig. 10 compares the

Fig. 10 e Effect of Mach number on the flow featu

effect of Mach number on the mass concentration and flow

feature of trapezoidal cavitywhenhydrogen jetwith PR¼ 0.5 is

injected. The results clearly show that ignition zone fluctuated

in low Mach number (M ¼ 1.2) while the uniform mass distri-

bution of hydrogen is noticed atM¼ 3. In fact, the circulation is

limited to the cavity in high Mach number due to high mo-

mentumof the freestream.However, theeffectof thehydrogen

in more pronounced when the free Mach number is 1.2.

re and mixing zone inside trapezoidal cavity.

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Conclusion

In this study, comprehensive computational studies are per-

formed to investigate the geometric effect of the cavity shape

on the fuel distribution and mixing efficiency of the hydrogen

jet in the supersonic free stream. In order to do this, three

different shapes of circle, rectangular and trapezoidal cavity

are chosen and investigated when the hydrogen jet is injected

from the bottom of the cavity. In this study, two dimensional

CFD approach is used with SST turbulence model to simulate

the flow inside the cavity.

The obtained results show that the trapezoidal cavity is the

most efficient cavity shape for the generation of the wide and

stable ignition point. In fact, the presence of large circulation

in downstream within trapezoidal cavity significantly in-

fluences on preservation of the hydrogen mass concentration

in this region. The comparison of the various free stream

Mach number shows that the ignition zone tends to remains

within the cavity as the Mach number of inlet flow increases.

Indeed, hydrogen jet becomes dominant in low Mach number

and this induces unstable ignition zone within cavity. Our

findings also show that flow of fuel is more stable in down

stream of trapezoidal cavity rather than other geometries in

high PRs. In fact, the formation of the large circulation inside

the trapezoidal cavity reduces the destabilization of the fuel in

the downstream and it is very significant for the flame

stability.

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