Effect of Axisymmetric Aft Wall Angle Cavity in Supersonic Flow Field
-
S. Jeyakumar
,
Shan M. Assis
Abstract
Cavity plays a significant role in scramjet combustors to enhance mixing and flame holding of supersonic streams. In this study, the characteristics of axisymmetric cavity with varying aft wall angles in a non-reacting supersonic flow field are experimentally investigated. The experiments are conducted in a blow-down type supersonic flow facility. The facility consists of a supersonic nozzle followed by a circular cross sectional duct. The axisymmetric cavity is incorporated inside the duct. Cavity aft wall is inclined with two consecutive angles. The performance of the aft wall cavities are compared with rectangular cavity. Decreasing aft wall angle reduces the cavity drag due to the stable flow field which is vital for flame holding in supersonic combustor. Uniform mixing and gradual decrease in stagnation pressure loss can be achieved by decreasing the cavity aft wall angle.
Introduction
Cavities gained attention in the application of supersonic flow fields like aircraft weapon bays, wheel wells, in-flight fueling ports, scramjet combustion chambers, etc. Various experimental and computational studies [1–4] are still carried out to understand the flow physics. The cavity flow field depends on significant features like, boundary layer separation, approaching Mach number of the flow, shock boundary layer interaction, shear layer instability, and length to depth ratio of the cavity. The cavities are classified open and closed based on the length to depth ratio of the cavity. The basic aspect of flow over cavity is the boundary layer separation at the leading edge to form a free shear layer. The separated shear layer may reattach either to the base of the cavity or to the aft edge of the cavity wall. The former type is termed as closed cavity (L/D > 10) and the latter one is referred as open cavity (L/D < 10).
Gruber et al. [5] investigated the non-reacting Mach 3.0 flow over cavities with different aft wall angles and offset ratios. Results showed that decreasing wall angle from 90 degree decreases cavity fore-wall pressure steadily with more stable flow field. Experimental studies [6] on axisymmetric tandem cavities in supersonic stream reveals that increase in cavity configuration enhances mixing with more stagnation pressure loss. Maurya et al. [7] performed experiments on aft wall cavities with different offset ratios at Mach 1.65. It is found that decreasing the cavity aft wall angle shows the reduction in static pressure level with more stable flow field in the vicinity of the cavity. Vikramaditya and Kurian [8] investigated on wall mounted cavities of different aft wall angles in a supersonic flow field. Their instantaneous shadowgraph images showed that cavities with higher aft wall angles cause instable shear layers than lower aft wall angles.
Takahrio et al. [9] performed experiments on rectangular cavity with dual upstream injection under the flow Mach number of 1.9. The flow characteristic is analyzed using high-speed schlieren flow visualization, PIV and surface oil flow techniques. Unstable flow over cavity is observed irrespective of the dual jet distance and long dual jets enhance the mixing rate than the short one. The flame stability using cavities in a varying supersonic reacting flow field was experimentally studied by Rasmussen et al. [10]. Their results revealed that flame stabilization was observed for cavity injection from the floor as well as at the aft wall.
In the present study, an attempt is made to investigate the behavior of axisymmetric aft wall cavities in a Mach 1.3 flow field. The cavities aft wall is inclined with two consecutive angles. The cavity aft wall entails three primary and secondary angles combined to form nine sets of cavity configurations. The performance of the cavity is analyzed based on wall static pressures along the axial direction of the flow, momentum flux distribution and total pressure loss of the flow at the exit of the combustor. The results of aft wall angle cavities are compared with rectangular cavity.
Experimental setup
The experiments are carried out in a blow-down type supersonic flow facility. The experiments are conducted non-reacting flow conditions. The facility consists of a supersonic nozzle which provides a flow Mach number of 1.3±0.03, operating with a stagnation pressure of 0.28 Mpa at atmospheric temperature. The flow conditions from the exit of the nozzle is shown in Table 1. A constant area circular cross sectional duct is attached at the exit of the nozzle which acts as a supersonic combustor. The schematic diagram of the combustor is shown in Figure 1. The diameter of the combustor is 26 mm with a constant length of 95 mm.
The operating condition of nozzle.
| Parameter | Nozzle |
|---|---|
| Stagnation. Pr. | 0.28 MPa |
| Total temperature | 300 K |
| Mach no. | 1.3 |
| Mass flow rate | 0.2 Kg/s |
Schematic view of supersonic combustor.
Cavities are placed inside the combustor at a distance of 20 mm from the inlet. The cavities used for the study are open type and axisymmetric. Cavities of constant length “L” 50 mm, and depth “D” 10 mm and varying aft wall angles are used for the study. Cavity details are shown in Figure 2. The aft wall of the cavity is inclined with two angles. The primary angle (θ1) begins from the base of the cavity and the secondary angle (θ2) from half the depth of the cavity. The angles of 90, 60 and 30 degrees are used for primary angle and 45, 30 and 15 degrees for secondary aft wall angles. The details of the cavity configurations are listed in Table 2.
Schematic diagram of the cavity layout.
Geometrical details of cavity configurations.
| Notation | Cavity L/D | Effective cavity Le/D | Primary angle (θ1) | Secondary angle (θ2) |
|---|---|---|---|---|
| 90, 90 | 4 | 4.0 | 90 | 90 |
| 90, 45 | 4 | 4.4 | 90 | 45 |
| 90, 30 | 4 | 4.9 | 90 | 30 |
| 90, 15 | 4 | 6.0 | 90 | 15 |
| 60, 45 | 4.3 | 4.75 | 60 | 45 |
| 60, 30 | 4.3 | 5.1 | 60 | 30 |
| 60, 15 | 4.3 | 6.0 | 60 | 15 |
| 30, 45 | 4.9 | 5.3 | 30 | 45 |
| 30, 30 | 4.9 | 5.7 | 30 | 30 |
| 30, 15 | 4.9 | 6.65 | 30 | 15 |
Pressure ports of 1.0 mm diameter are placed along the combustor wall in the flow direction to observe the wall static pressure distribution. Static and stagnation pressures are measured at the exit of the combustor using long cone static probe and pitot pressure probe in order to examine the flow characteristics influenced by the cavities. Each experiment is conducted three times to check repeatability. The uncertainties are estimated which is less than 3 % over the pressure measurements. A traversing mechanism is used to move the probes in radial direction of the flow field.
Results and discussion
Static pressure distribution
Centre line wall static pressures for various aft wall cavities are plotted with respect to the axial length (x/L) of the combustor as shown in Figure 3. The figure shows the primary and secondary cavity aft wall angles associated with the rectangular cavity. The x denotes the axial distance of the pressure tap from the inlet of the combustor to the total length L. In a rectangular cavity (90, 90), the static pressure increases at the leading edge due to shear layer separation and gradually increases towards the aft wall. The static pressure reaches a peak value ahead of the aft wall due to shear layer reattachment which creates a compression zone. Moreover unstable shear layer formed at the trailing edge creates a flapping motion which are responsible for mass addition and rejection in the cavity [11]. The fore wall region of the cavity remains compressive in nature though the secondary aft wall angle is reduced to 45 degrees, Figure 3(a). The static pressure within the cavity appears to be similar to rectangular cavity with slightly reduced pressure at the bottom of the cavity. At x/Lc=0.68, the static pressure takes a higher value than rectangular cavity due to the recompression of shear layer occurs at the aft wall. For cavities of (90, 30) and (90, 15), at the separation corner the flow remain compressive in nature resulting increase in static pressure and relatively decreases towards the bottom/aft wall corner. A stronger recompression of shear layer occurs at the axial location of x/Lc=0.68. From the shadowgraph flow visualization of two dimensional cavity by Vikramathiya and Kurian [8] revealed that decreasing cavity secondary wall angle provides a more stable flow than higher wall angles. The stable shear layers are suitable for flame holding in scramjet combustors.
Wall static pressure distribution for various axial distance of the combustor for different aft wall angles.
The data presented in Figure 3(b), are for the primary wall angle of 60o with varying secondary wall angles and compared with rectangular cavity. In these geometries, the static pressure profile reveals that the flow at the fore wall separation corner remains compressive in nature with relatively less magnitude than in rectangular cavity i. e. for primary angle of 90 degrees in Figure 3(a). Moreover, the static pressure gradually decreases along from the leading edge towards the cavity aft wall corner with decrease in secondary aft wall angles from 45 to 15 degrees. However stronger recompression occurs at x/Lc=0.68 resulting in peak static pressure. Similar trend is observed for cavity geometry of primary wall angle of 30 degrees, as seen in Figure 3(c), with relatively decrease in static pressure distribution throughout the cavity region showing a more stable flow than other cavity geometries. For cavity (30, 15), relatively less static pressure rise is observed in the cavity region showing less cavity drag and at x/Lc=0.68, stronger recompression is observed by the peak pressure value.
From the above observation, decreasing the primary and secondary aft wall angle plays a significant role in cavity drag and flame stabilization. As the flow is axisymmetric one, the flow visualization technique cannot be established within the cavity region. However the qualitative agreement with the wall static pressure measurement suggests the nature of flow in the vicinity of cavity.
Momentum flux distribution
The momentum flux distribution at the exit of the supersonic combustor in the radial direction is a measure of the extent of bulk mixing. The momentum flux is calculated as
where p is the measured value of static pressure and Mach number M is calculated from the measured values of static and stagnation pressures, using Rayleigh-Pitot formula. The measurements are made at the exit of the combustor from the centre towards the wall in the radial direction. Figure 4 shows the momentum flux distribution for various cavity configurations at different radial locations. In the plot, r/R denotes radial distance from the axis (r) normalized by the radius (R) of the supersonic combustor. Experimental results are presented for all cavity configurations operating under identical conditions and compared with rectangular cavity. Without cavity conditions, the momentum flux takes a high value at the centre and gradually reduces towards the wall due to higher stagnation pressure at the centre and reduces at the wall. The uniform momentum flux profile confirms the uniformity of mixing in the radial direction of the combustor.
Momentum flux distribution for various cavity aft wall angle.
The nature of momentum flux curve tends to be uniform from the centre to the wall of the combustor by placing the cavity in the flow field. In case of rectangular cavity, as seen in Figure 4(a), the momentum flux values is not uniform, as a result of the reattachment of shear layer at the trailing edge. Due to this reattachment of shear layers creates a flapping motion [11] resulting in unstable flow field in the cavity region. With the decrease in secondary aft wall angle to 15 degrees, the momentum flux value increases from the centre towards the wall. The shock waves emerges from the cavity aft wall due to reattachment of shear layers obstructs the main stream from the wall towards the centre of the combustor. However the momentum flux value is almost constant at the centre of the combustor reveals that main stream of the flow towards the axis of the combustor is undisturbed due to these cavities.
In the Figure 4(b), for cavity (60, 45) a uniform profile is observed from the radial distance r/R=0.62 to the wall, which shows a uniform mixing is achieved by this cavity geometry. Decreasing the secondary wall angle to 15 degrees increases the momentum flux value towards the wall showing an impact of cavity flow tends to penetrate the main stream to augment uniform mixing. Similar trend is observed by reducing the primary angle of the cavity to 30 degrees, as shown in Figure 4(c). For cavity (30, 30), an almost uniform profile is obtained from the centre to a radial distance of r/R=0.68, indicating an enhancement in mixing is obtained over this radial distance at the exit cross plane of the combustor.
Stagnation pressure loss
The enhancement in mixing provide by the cavities causing stagnation pressure loss due to cavity drag. The Stagnation pressure loss across the combustor is defined as the difference in stagnation pressures at the inlet over axial distance is considered, which is normalized by the inlet stagnation pressure measured at the inlet and exit sections of the combustor along the radial direction. The changes in stagnation pressure loss for various cavity configurations are shown in Figure 5. From the experimental results the stagnation pressure loss for the rectangular cavity is calculated to be 25.34 %. Decreasing the aft wall angle of the cavity reduces the stagnation pressure loss. For rectangular cavity, large scale instable shear layer are formed in the cavity region which interferes the main flow resulting increased stagnation pressure loss. The effect of instability of shear layers reduces with decrease in aft wall angle [8] thereby reduces the stagnation pressure loss. In the plot, cavity (30, 15) provides less stagnation pressure loss than other cavity configurations.
Stagnation pressure loss for various secondary wall angles.
Conclusion
The characteristics of non-reacting supersonic flow past cavities are experimentally investigated in a blow-down type facility. Axisymmetric cavities of twin aft wall angle cavities are tested in a Mach 1.3 flow. The wall static pressure distribution along the combustor reveals that decrease in the aft wall angle of the cavity reduces the static pressure along the cavity base and increases at the aft wall due to stronger recompression which indicates a more stable flow is obtained in the cavity region compared to rectangular cavity. The momentum flux profile indicates the enhancement in mixing is achieved with decrease in cavity aft wall angles. Decreasing cavity aft wall angles reduce the stagnation pressure loss due to stable flow field in the cavity region. The flow stability in the cavity region plays a vital role for flame holding in scramjet engine combustors.
Funding statement: This work is supported by Department of Science and Technology under the Grant No: SR/FTP/ETA-55.
Nomenclature
- L
length of the cavity (mm)
- D
Depth of the cavity (mm)
- θ
aft wall angle (degrees)
- µ
Momentum flux (N/m2)
- p
static pressure (N/m2)
- M
Mach number
- R
radius of the combustor (mm)
- r
incremental radial distance (mm)
- x
incremental axial distance (mm)
- γ
specific heat ratio
- Subscripts
- 1
primary angle
- 2
secondary angle
- e
effective length
- c
combustor
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© 2018 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Mechanism of Film Cooling with One Inlet and Double Outlet Hole Injection at Various Turbulence Intensities
- State of Aircraft Turboshaft Engines by Means of Tribotechnical Diagnostic
- Theoretical Study of the Vibration Suppression on a Mistuned Bladed Disk Using a Bi-periodic Piezoelectric Network
- Effect of Axisymmetric Aft Wall Angle Cavity in Supersonic Flow Field
- A Generalized Method for the Comparable and Rigorous Calculation of the Polytropic Efficiencies of Turbocompressors
- Sliding Mode Fault Tolerant Control with Adaptive Diagnosis for Aircraft Engines
- Numerical Study on the Improvement of Oil Return Structure in Aero-Engine Bearing Chambers
- Numerical Investigation of Fuel Distribution Effect on Flow and Temperature Field in a Heavy Duty Gas Turbine Combustor
- A Novel Quasi-3D Method for Cascade Flow Considering Axial Velocity Density Ratio
Artikel in diesem Heft
- Frontmatter
- Mechanism of Film Cooling with One Inlet and Double Outlet Hole Injection at Various Turbulence Intensities
- State of Aircraft Turboshaft Engines by Means of Tribotechnical Diagnostic
- Theoretical Study of the Vibration Suppression on a Mistuned Bladed Disk Using a Bi-periodic Piezoelectric Network
- Effect of Axisymmetric Aft Wall Angle Cavity in Supersonic Flow Field
- A Generalized Method for the Comparable and Rigorous Calculation of the Polytropic Efficiencies of Turbocompressors
- Sliding Mode Fault Tolerant Control with Adaptive Diagnosis for Aircraft Engines
- Numerical Study on the Improvement of Oil Return Structure in Aero-Engine Bearing Chambers
- Numerical Investigation of Fuel Distribution Effect on Flow and Temperature Field in a Heavy Duty Gas Turbine Combustor
- A Novel Quasi-3D Method for Cascade Flow Considering Axial Velocity Density Ratio
