, M. Barzegar Gerdroodbary

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

Rasoul Moradi

^a

, A. Mahyari

^b

, M. Barzegar Gerdroodbary

^c,^*

, A. Abdollahi

^d

, Younes Amini

^e

aDepartment of Chemical Engineering, School of Engineering&Applied Science, Khazar University, Baku, Azerbaijan

bDepartment of Chemical and Petroleum Engineering, Sharif University of Technology, Tehran, Iran

cDepartment of Mechanical Engineering, Babol Noshirvani University of Technology, Babol, Iran

dDepartment of Mechanical Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran

eDepartment 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

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 (M¼1.2, 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 induces a stable ignition zone within cavity.

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 combustion 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

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 the main chamber is high and more than sonic, the process of ignition is supersonic main stream occurs 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

*Corresponding author.

E-mail address:[email protected](M. Barzegar Gerdroodbary).

Available online atwww.sciencedirect.com

ScienceDirect

journal home page: www.elsevier.com/loca te/he

https://doi.org/10.1016/j.ijhydene.2018.06.166

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vestigations of different possible mechanisms of fuel and air injections. Among different geometries, cavity-based flameholder 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 CFD method 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 effects 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 significant 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 distribution inside the cavity was not investigated. Previous works have always investigated the formation of the shock structure on the main 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 efficiency 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 conditions. It should be noted that circulations are the main results of the cavity in the supersonic flow patterns. Hence, the formation and effective term of this phenomena is crucial for the recognition of the main parameters. It is clear that the injection 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. 2shows the applied grid for Fig. 1ePlan of three shapes of cavity (circle, rectangular and trapezoidal).

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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 0.001 mm, which results in a value of wall y^þsmaller 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 1atm and 300K. In addition, other Mach numbers M_∞¼1:2and3 are investigated. Fig. 2clearly 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 inFig. 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 present 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].

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 distribution for two different shapes of cavity. Our findings show that deviation is less than 10% for diverse models.

Fig. 2eGrid generation.

Fig. 3eGrid independency and validation of obtained results for cavity a) without swept angle b) with swept angle of 30.

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

Effect of circle cavity on mixing of hydrogen

Fig. 4illustrates the distribution of hydrogen gas within the circle cavity with different pressure ratios. In PR¼0.25, 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 the main 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 fromFig. 4, mass distribution of the hydrogen jet in the circle cavity with PR¼0.25 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.

effective term on the distribution of the mass inside the cavity. 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 trapezoidal 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 ¼0.25, 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 circulations remains for different PRs.

The comparisons of these three shapes of cavity flameholder show that trapezoidal cavity is more efficient in preservation of the ignition zone in downstream of the hydrogen

Fig. 4eEffect of various pressure ratio of hydrogen jet on hydrogen mixing rate inside the circle cavity.

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Fig. 6eMass distribution of the hydrogen jet in the rectangular cavity.

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

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

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

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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 influence of the various Mach number (M¼1.2 and 3) on the mass transfer and ignition zone is investigated.Fig. 10compares the

effect of Mach number on the mass concentration and flow feature of trapezoidal cavity when hydrogen jet with PR¼0.5 is injected. The results clearly show that ignition zone fluctuated in low Mach number (M¼1.2) while the uniform mass distribution of hydrogen is noticed at M¼3. In fact, the circulation is limited to the cavity in high Mach number due to high mo- mentum of the free stream. However, the effect of the hydrogen in more pronounced when the free Mach number is 1.2.

Fig. 10eEffect of Mach number on the flow feature and mixing zone inside trapezoidal cavity.

Fig. 9eComparison of the flow feature inside the cavity flameholder (M¼2) for different PRs (PR-¼0.25, 0.5 and 1).

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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 influences 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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