Numerical investigation on the extrusive and intrusive subcavity types and their location on the primary recirculation zone for the supersonic turbulent flow through cavity type flameholders

Highlights

• Base cavity geometry modifications with the extrusive and intrusive type of subcavities.

• Effect of subcavity aspect ratio and its location in the cavity on the primary recirculation zone.

• Significant increase in the strength of the primary recirculation zone for intrusive type of subcavities.

• Substantial decrease in the velocity magnitude of cavity fluid with increase in base cavity aspect ratio.

• Significant decrease in velocity magnitude with the decrease in closeout angle.

Abstract

Supersonic turbulent non-reacting flow through a cavity-type flameholder employed in scramjet engines with and without subcavities is numerically investigated. The governing equations describing the flow are solved by employing a density-based solver i.e., rhoCentralFoam which is an open-source computational fluid dynamics (CFD) code in OpenFOAM. The turbulence is modeled using the two-equation k-$\omega$ SST (shear stress transport) turbulence model. In the present study implication of subcavity types (i.e., extrusive and intrusive) on recirculation patterns and their strength at different subcavity aspect ratios (l/d) and subcavity locations at different inflow Mach numbers is investigated. A significant increase in the strength of the primary recirculation zone is observed for modified rectangle cavity 2 (MRC2) compared to the base rectangle cavity (BRC) and modified rectangle cavity 1 (MRC1). Results show a significant decrease in the size of the secondary recirculation zone for modified angle cavity 2 (MAC2) for all the subcavity aspect ratios and subcavity leading-edge distances (SLDs) at Mach 2. Results also indicate that at a fixed Mach number, the strength of the primary recirculation decreases with the increase in base cavity aspect ratio (L/D) for all the cavity types. Results show a substantial decrease in the velocity magnitude of cavity fluid with the decrease in cavity aft wall angle from 90° to 30°, which shows that the strength of the primary recirculation zone for BRC and MRC2 is higher compared to base angle cavity (BAC) and MAC2. Results show a 20.4776 % and 7.3822 % increase in the peak values of streamwise and normal velocities for MRC2 compared to BRC and MRC1 at Mach 2, and the corresponding increase in velocities for Mach 3 are 14.7979% and 5.6693% respectively for all the aspect rations and SLDs. Present results are validated with the experimental results available in the literature.

Introduction

The quest for an alternative propulsion system that not only reduces the weight penalty but also provides long-duration flights at hypersonic speeds led to the invention of air-breathing engines (viz., X-43, HiFiRE) [1]. One of the prominent technical challenges in designing these engines is to obtain sustainable and efficient combustion at supersonic speeds. Many innovative ideas have been proposed and tested in developing a combustor for air-breathing engines [2], [3], [4], [5], [6]. Attributes of successful combustor design are: shorter combustor length, efficient fuel injection system and enhanced air-fuel mixing (via direct, strut, ramp, or cavity injection), and sustainable and stable combustion (via flameholders). Hence, the selection of fuel injection strategies (transverse or angled) and flameholder geometries plays a significant role in combustor design for the air-breathing engines i.e., scramjet engines.

Flameholding (flameholding cycle) in the scramjet engine combustor is broadly achieved by employing three techniques: (a) by facilitating the mixture augmentation of fuel and air at low velocities (subsonic speed) by creating recirculation zones, (b) interaction of shock with this (low velocity) air-fuel mixture, and (c) formation of coherent structures constituting unmixed fuel and air [3], [7]. These techniques can be incorporated in different ways to achieve flameholding in the supersonic combustor. The flameholding methods that incorporate the aforementioned techniques and facilitates formation of subsonic recirculation zone are categorized into intrusive methods and non-intrusive methods viz. strut, simple backward-facing step/cavity in the flow path [8], [9]. In the intrusive method, fuel injection and flameholding are achieved by struts (wedge shaped) [10], ramps (compression and expansion), and pylons mounted on the combustor wall. On the other hand in the non-intrusive method wall mounted cavities are employed for fuel injection and flameholding. In the non-intrusive method, fuel injection and flameholding are achieved in three ways: (a) by direct injection (transverse or angle) from the combustor wall, (b) by wall mounted cavity with direct injection (transverse or angle) in the cavity, and (c) by the combination of any of these methods (i.e., a and b). Further, as it is apparent from the findings of Wang et al. [11] that stabilized combustion cannot be realized through jet-wake alone hence the cavities in the combustor employed for scramjet engine becomes indispensable. Therefore among the various types (intrusive and non-intrusive) of flameholders wall mounted cavities are considered as one of the ideal flameholder types for scramjet engine owing to their minimum drag and total pressure losses. However, the cavity-type flameholders suffer from large local wall heat flux as the flame remains close to the wall this requires an additional thermal protection system [9], [12].

Here we discuss the mixing augmentation and combustion efficiency improvement owing to the geometry modifications and intrusive type of attachments to the cavity-type flameholders. Over the years, many researchers exploited the fact that a low-pressure area/zone can be created by employing a strut/pylon in a supersonic flow. The pylon placed at the leading edge of a cavity-type flameholder generates wakes behind the pylon (known as pylon wakes) these are the low-pressure zones. These low-pressure zones behind the pylon facilitate the upward movement of the cavity fluid, thus increases the mass exchange between the cavity and core flow. Further, the pylon enhances turbulence mixing. Interaction of the cavity-type flameholder with the core flow and mixing augmentation in the core flow is achieved by employing the intrusive type of devices (viz., pylons, struts) in conjunction with the cavity-type flameholder [9]. Freeborn et al. [13], [14] investigated the effect of a pylon placed at the leading edge of 22° angle cavity. They have modeled the turbulence using the two-equation k-$\omega$ SST (shear stress transport) turbulence model, and the governing equations are solved by employing the FLUENT solver. Their result showed a threefold increase in the mass flow passing through the cavity with pylon compared to the cavity without pylon. Their results indicate that for the cavity with pylon the primary recirculation zone occupies most of the cavity area, and the strength of the recirculation zone is higher compared to the cavity without pylon. Grady et al. [15] carried out experimental and LES (large eddy simulation) based numerical investigation of supersonic flow over a 22.5° angle cavity (i.e., ramped wall cavity) with an upstream strut placed at the leading edge of the cavity. Their results showed that under the influence of upstream strut the cavity shear layer grows faster, and its impingement on the cavity ramp is higher (i.e., lifted) compared to no strut case, owing to lifting of the cavity shear layer by the low pressure created behind the strut. Their results also highlight the enhancement in cavity and core flow interaction, owing to the higher propagation of the cavity shear layer into the core flow. They have also observed an increase in cavity recirculation.

In an experimental study of flameholding configurations for airflow at Mach 1.8, Owens et al. [16] compared the ramp vs. two-dimensional step and cavity vs. rearward-facing step. Their results showed that the flame stability in the recirculation region is nearly unaffected by the geometrical configurations. In an experimental and numerical investigation on pylon geometry implication on the performance parameters (i.e., mixing efficiency, total pressure loss, fuel jet penetration, and fuel plume area) Oamjee and Sadanandan [17], observed that the pylon geometry with inward and outward slanted structures shows significant improvement in performance parameters compared to other pylon geometries and base configuration. Wang et al. [18] numerically investigated the mixing enhancement of the swallowtail cavity employed as flameholders in the supersonic combustor. They have observed that the swallowtail cavity in the combustor wall sucks the supersonic flow into the cavity, and flow is ejected out through the lateral cavity ends as 3D (three-dimensional) vortices. This mechanism acts as a pumping effect. The mixing efficiency of the swallowtail cavity increases owing to the pumping effect. Further, they have observed the presence of a low-speed fluid region in the cavity and intensive mass exchange between the cavity and core flow. The aforementioned attributes are essential for efficient flameholder.

Landsberg and Veeraragavan [19] numerically investigated the implications of cavity fore wall (i.e., upstream cavity wall) modifications on the base drag and secondary vortex. They have modified the fore wall by replacing the rear-face step (90°) of the fore wall with the ramps (22.5° and 45°), streamtraced profile, and combination of streamtraced and ramp. Their results showed that among the four modifications of the fore wall, the combined profile shows 12% drag reduction. Further, their results highlighted the absence of a secondary vortex for all four modifications of the cavity fore wall. In an experimental and numerical investigation of fore wall modification Trudgian et al. [20] highlight the implications of fore wall modifications on base drag and secondary recirculation zone. They have varied the aspect ratio $\frac{L}{D}$ from 4 to 7 along with the fore wall angle (i.e., $\theta =90°$, 45°, and 22°). Their results showed that reducing the fore wall angle for aspect ratios 4 and 5 did not markedly affect the cavity shear layer separation, whereas for the aspect ratios equal to 6 and 7 deep penetration of cavity shear layer into the cavity was noticed. Further, their results showed that for 45° fore wall angle, the base drag was minimum, and drag reduction up to 21% was noticed as compared to 90° fore wall angle. Their results also showed the absence of the secondary recirculation zone owing to the modification to the cavity fore wall.

Kang et al. [21] studied the effect of cavity configuration on mixing augmentation and combustion efficiency at Mach 2.5 through experimental, numerical, and quasi-one-dimensional approaches. They have considered three cavity configurations viz., combustor with no cavity, with a plain cavity, and with a zigzag cavity. Their experimental results highlighted that the combustion induced pressure values are highest for the zigzag cavity. Numerical analysis shows the augmentation of mixing efficiency for the zigzag cavity owing to the transverse directional flow induced by the zigzag configuration compared to the other two configurations. Their quasi-one-dimensional analysis showed the highest combustion efficiency for the zigzag cavity. Results of Kang et al. [22] also corroborates that the presence of transverse directional non-uniformity in the air-breathed into the scramjet engine results in efficient air-fuel mixing and supersonic combustion. Shi et al. [23] carried out experimental and numerical investigations to assess the effect of cavity configuration on flameholding and combustion characteristics. Among the three combustor models, the model with tandem cavities having an aspect ratio of 9 shows the highest pressure recovery and combustion efficiency. In a tandem cavity-type arrangement, Sun et al. [4] observed that the fuel diffusion and its convection into the cavity are greatly influenced by the flow disturbances emanating from the upstream cavity, the divergence angle of the top wall, and the ignition process itself. In an experimental and numerical investigation of dual cavity-type flameholder, Yang et al. [5] found that for parallel dual cavity configuration high-pressure region is present in the core flow, owing to the bulging of the cavity entrapped recirculation zone. Whereas for tandem dual cavity configuration high-pressure region is present in the vicinity of the top wall. Their results also highlight a swift increase in combustion efficiency for the parallel dual cavity as compared to the tandem dual cavity owing to the concentrated combustion around the parallel dual cavity configuration. Wang et al. [24] performed a Large Eddy Simulation (LES) of parallel dual cavity-type flameholder at Mach 2.52. Their results indicate that the core flow over the parallel dual cavity undergoes compression and expansion (diverging flow). The throat of compression and expansion is located approximately over the midpoint of the cavities for the given cavity configuration and fuel injection strategy. They have also observed significant improvement in the mass exchange process between the core fluid and cavity fluid due to shock impingement on the cavity. Gruber et al. [25] investigated different geometrical configurations of the cavity-type flameholder at Mach 3 by experimental and FVM (Finite Volume Method) using k-$\omega$ SST turbulence model. They have noticed that the cavity residence time decreases with the decrease in closeout angle. Their results showed increase in pressure drag value with the decrease in closeout angle, and maximum pressure drag was noticed for 16° closeout angle. Kim et al. [26] numerically investigated the combustion characteristics of the cavity flameholder at Mach 2.5. They have shown that the combustion efficiency is maximum for 60° closeout angle, but this configuration has maximum total pressure losses. Cai et al. [27] performed one equation LES simulations to study the effect of cavity geometry (i.e., cavity aft wall height modifications) on the fuel transport and mixing process at Mach 2.91. They have employed scramjetFoam developed using OpenFOAM C++ [28] library. They have observed that the magnitude of fuel concentration in the cavity increases with an increase in expansion ratio (which represents cavity geometry with different aft wall heights) due to substantial entrainment of the upstream injected fuel into the cavity.

Here we present the implications of different injection strategies such as pylon assisted cavity injection, cavity upstream injection, direct cavity injection, and a combination of these injections on the air-fuel mixing augmentation in the scramjet combustor. Pylon assisted injection techniques are employed for air-fuel mixing augmentation. A pylon positioned upstream of fuel injection and cavity flameholder can shield the injectant from the oncoming supersonic flow as a result, the injectant injected by the injector will penetrate deeper into the supersonic crossflow. The air-fuel mixing augmentation is achieved in three stages: (a) the pressure behind the pylon facilitates the instantaneous penetration of the injectant and widening of the injectant plume, (b) transfer of injectant (fuel) concentration away from the wall, and (c) settling of the injectant in the wider upper area of the injectant plume. Gruber et al. [29] studied the mixing augmentation of a pylon-aided ethylene injection at Mach 2 in conjunction with an angled cavity flameholder. Performance analysis of the three geometries viz., medium, tall, and wide pylons indicate that the wide pylon geometry provides the best overall mixing enhancement. Oamjee and Sadanandan [30] have numerically investigated the implications of cavity injection and pylon upstream injection in a pylon cavity flameholder on the mixing enhancement, flameholding, fuel jet penetration, and total pressure loss (all these are known as performance parameters). They found that the counter-rotating vortex pair (i.e., primary and secondary recirculation zone) in the cavity plays a vital role in facilitating fuel dispersion and fuel jet penetration. Further, their results showed a 55% enhancement in fuel dispersion for the injection locations in the cavity as compared to the injection location upstream of the pylon.

Ebrahimi et al. [31] carried out numerical simulations to investigate the different jet injection possibilities in cavity-type flameholder. Their results showed that among the different injection possibilities, vertical injection from the cavity floor was found to influence the cavity recirculation markedly. Further, their results show that an injection strategy that facilitates the enhancement of intrinsic circulation patterns of the cavity is superior to one that opposes it. Cai et al. [32] performed the LES based simulations at Mach 2.52 to access the effect of cavity direct injection (i.e., aft wall injection) on the mixing efficiency. Their results showed enhancement in the mixing process for the cavity direct injection owing to the increase in local turbulent intensity because of fuel jet injection directly into the cavity.

Here we discuss the implications of heat release rate, base cavity geometry, and subcavity location on the cavity induced pressure oscillations. Davis and Bowersox [33] conducted a numerical investigation on flameholding capabilities of angle cavities. Their results showed suppression in the cavity oscillations owing to combustion. It was also observed that the combustion process (heat release) acts as a mass addition process and leads to the lifting of cavity shear layer impinging on the cavity aft wall thus reducing cavity oscillations. In a similar study on rectangular cavities, Rasmussen [34] highlighted the suppression of cavity oscillations due to the combined effect of direct fuel injection and heat release due to combustion. Vikramaditya and Kurian [35] experimentally investigated the effect of aft wall angle on cavity pressure oscillations at an inflow Mach number of 1.63. They have varied the aft wall angle from 90° to 15°. Their result showed that the acoustic wave strength decreases with the decrease in angle. They have also observed a substantial reduction in the amplitude of oscillations for cavities with aft wall angle 60° and below. Wang et al. [36] carried out experimental investigations on pressure and flame oscillations in the scramjet combustor at Mach 2.52. Their results highlight that for the non-reacting flow (i.e., cold flow) conditions the cavity oscillations are dominated by Rossiter mode. They have also observed that the cavity flame holders with higher aft wall angles are more prone to flame oscillations. Experimental studies on fuel injection strategies on the low-frequency combustion oscillations in an ethylene fuel scramjet combustor indicate strong coupling between oscillation mode and mixing efficiency. Further, the study highlights the presence of thermo-acoustic type oscillation for the fixed shock train condition in the combustor [37]. Panigrahi et al. [38] conducted experimental and numerical investigations on the attenuation and magnification of cavity pressure oscillations influenced by the location of subcavity on the fore and aft walls at Mach number 1.71.Their results showed that the presence of subcavity reduces overall cavity pressure oscillations.

The comprehensive understanding of different geometrical configurations of the cavity-type flameholder, including a subcavity in the base cavity, location of subcavity from the fore wall, and its aspect ratio on the recirculation zones and its strength analysis is limited in the literature. Further, as per the authors’ knowledge, a detailed analysis of the flow patterns and formation of recirculation zones for an extrusive and intrusive type of subcavities in the base cavities as a function of Mach number is not available, these points have been the motivation for the present work. In the present work, base cavities viz. rectangle base cavity and angle base cavity geometries are modified by introducing the extrusive and intrusive type of subcavities having a different length (l) to depth (d) ratios in the base cavity. The present work emphasizes the behavior of recirculation patterns and their strength associated with the modified base cavities. Further, the current work brings out the implications of subcavity locations in the modified base cavities on the recirculation patterns and their strength at two inflow Mach numbers. Finally, the present work aims to identify the modified cavity geometry that facilitates the formation of the stronger and large primary recirculation zone in it.