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Large eddy simulation on using a cavity-jet controller for supersonic blunt base mixing layer control
Acta Astronautica 161 (2019) 57–65
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Large eddy simulation on using a cavity-jet controller for supersonic blunt base mixing layer control
T
Yong-yi Zhou, Rui Yang∗, Yu-xin Zhao Science and Technology on Scramjet Laboratory, College of Aerospace Science and Engineering, National University of Defense Technology, Changsha, Hunan, 410073, People's Republic of China
ARTICLE INFO
ABSTRACT
Keywords: Cavity-jet controller Supersonic mixing layer Blunt base Numerical simulation Power spectral density
In this study, a cavity-jet controller was used to control the supersonic blunt base mixing layer. This method is simple in structure, requires no external energy, and can utilize the pressure potential energy of the flow. A large eddy simulation was performed to numerically investigate the control effect. The Mach numbers of the upper and lower layers were 1.5 and 2.5, respectively, and the convective Mach number was 0.35. The simulation flow field structures and mean properties with and without the cavity-jet controller were compared. The results showed that this controller enhanced the turbulence intensity of the flow. The mixing thickness was used to quantify the mixing characteristics. The controller significantly improved the mixing performance. The flow fields were monitored at several points to record the pressure pulsation information, and the power spectral density was analyzed.
1. Introduction Rocket-based combined cycle (RBCC) engine technology is the current development trend for hypersonic aircraft propulsion systems [1]. The mixing process of supersonic air and fuel is a key point of the RBCC engine. Therefore, the supersonic mixing layer, which is a typical compressive shear flow [2], and its characteristics have received significant attention [3,4]. Because of limitations on the engine length, the flow in the engine has a short duration time. To enhance the combustion efficiency, the mixing process of air and fuel needs to be fastened. However, under the supersonic flow condition, the compressibility significantly affects the growth of the mixing layer [5]. Previous studies have shown that the mixing efficiency is strongly limited by the compressibility [6]. To enhance the mixing effect of air and fuel under the supersonic condition and improve the engine performance, various control methods have been introduced. These can be divided into active and passive methods [7,8]. Active control methods mainly change the characteristic structures of the flow field by actively injecting energy and momentum into the flow. Zhang et al. [9] set a vibrating reed upstream of the supersonic flow. The reed was then stimulated by the control system to control the flow field. Flow visualization showed that the laminar flow area of the mixing layer was shortened, and the opening angle increased. Different vibration frequencies varied the mixing enhancement performance.
∗
Zhou et al. [10] adopted a dual-frequency disturbance and reported that the growth rate of the mixing layer exceeded that of the singlefrequency layer. The synthetic jet is a control method that needs no external pressure source and has a simple structure [11]. Davis et al. [12,13] and Ritchie et al. [14,15] experimentally studied enhancing the mixing of air and fuel with a synthetic jet and demonstrated its effectiveness. However, the synthetic jet has limited energy, which makes it suitable for low-speed flows. Active control methods introduce external energy into the flow; under the actual working conditions of high temperature and pressure, the design and manufacture of movable parts is difficult. Unlike the active control methods, passive control methods use fixed-structure devices. Raman et al. [16] installed protuberances with various geometric configurations to generate disturbances at various frequencies. The disturbances generated a resonance that enhanced the mixing. Sunken cavities set in the wall of the flow have a similar effect. The flow past the cavity resonates to improve the fuel penetration performance [17,18]. Island et al. [19] reported that the growth rate of the supersonic mixing layer was increased by 45% through the use of small perturbations. Bradbury et al. [20] and Fernando et al. [21] experimentally studied the mixing enhancement and control effect of splitter plates. However, they observed a remarkable total pressure loss. In contrast to splitter plates, lobe supports can effectively generate high-intensity streamwise vortices to improve the mixing effect [22]. However, the increased divergence angle increases the loss of the total
Corresponding author. E-mail address: [email protected] (R. Yang).
https://doi.org/10.1016/j.actaastro.2019.05.019 Received 7 December 2018; Received in revised form 26 March 2019; Accepted 10 May 2019 Available online 15 May 2019 0094-5765/ © 2019 IAA. Published by Elsevier Ltd. All rights reserved.
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Fig. 1. Schematic for the flow structures of the supersonic blunt base mixing layer.
pressure, which is detrimental to the engine performance. Williams et al. [23] installed plasma polymer films in the flow to stimulate vibrations that enhance mixing by 150%–375%. However, they considered a laminar flow with a Reynolds number of only 10. The various control methods currently in use have their own characteristics and are suitable for a thin trailing-edge mixing layer. However, engineering applications have a high gas temperature, and a protective cooling mechanism is required. The thickness of the base is inevitably increased, which results in a supersonic blunt base mixing layer. This is quite different from the typical thin base in the flow field structure [24]; a flow diagram is shown in Fig. 1. The flow characteristics include a recirculation zone, a shear layer, expansion waves, and shock waves [24,25]. Control methods aimed at this type of mixing layer have rarely been reported. Reedy et al. [26] proposed a passive method that uses rudders to control the recirculation zone after a cylinder base, but the effects are not obvious. The most important feature of flow structures is the recirculation zone at the bottom of the blunt base, which has a significantly lower pressure than the surrounding area. In the present study, a control method was developed that is based on the low-pressure characteristics of the recirculation zone of the supersonic blunt base. The method is suitable for a supersonic blunt base mixing layer; it has a simple structure, requires no external energy, and achieves good control performance. Two layers of the base are introduced into a cavity that empties into the base and ejects into the recirculation zone under the action of the pressure potential energy generated in the low-pressure zone. The high-frequency disturbance generated by the cavity can easily lead to unstable flow control of the mixing layer, which is a characteristic of this method. The large eddy simulation (LES) method was used to evaluate the mixing control effects of the method and analyze the mechanism of the controller.
Fig. 2. Schematic of the cavity-jet controller.
Fig. 3. Diagram of the 2-D cavity-jet controller with size markings (length unit: mm).
The drainage port is a rectangular channel with a narrowing section from outside to the inside, which increases the amount of intake air. The jet port is a rectangular channel with an equal section, and the channels are inclined to the blunt base. The specific dimensions of the controller are shown in Fig. 3.
2. Physical model and numerical setup 2.1. Physical model
2.2. Numerical setup and verification
The supersonic blunt base mixing layer flow separates at the base, and the pressure at the bottom is much less than the incoming flow pressure. Fig. 2 shows the cavity-jet controller designed in this study to utilize this part of the pressure potential energy. The middle part of the controller is a cavity separated by a partition, and a drainage inlet opens at a specific position upstream of the upper and lower surfaces of the controller. Correspondingly, two jet outlets open at the bottom of the base. Under the action of the pressure potential energy, the flow enters the cavity through the drainage inlet and rushes out through the jet outlet. This is why the component is called a “cavity-jet” controller.
A compressible and finite-volume LES solver that is third order in space and second order in time was employed in this study. The subgrid model is used for kinetic energy transport. The governing equations [27] and kinetic energy transport equation of the sub-grid model [28] were previously developed. This solver has been extensively validated and used for many supersonic mixing layers [3,29,30]. To avoid shock waves from being generated at the entrance, the flow was assumed to be a plate boundary layer, and the velocity profile was determined according to the 1/7 power law 58
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layer velocity U1 and the base thickness h was ReML = 1.52 × 105 , which fits the simulation Reynolds number. The main flow field structure of the supersonic blunt base mixing layer could be obtained via the numerical simulation. Two layers formed free shear layers that intersected at the reattachment point to form a reattachment shock wave. At the same time, the vortex structure began to roll up behind the reattachment point. The simulation and experiment have similar flow structures. The basic structure of the flow field was simulated. However, the LES simulation is sensitive to the boundary layer, so there are some differences between the simulation and experiment results. The position of the reattachment point was behind the experimental result. The laser was mostly reflected at the sharp point of the upper base without passing through the glass partition. This is why the diagonal stripe appeared in Fig. 5(a) (marked in white dashed box). Note that this did not affect the investigation of the flow field structure. Fig. 6 compares the streamwise mean velocity profiles from the unforced case simulation and Wu's experiment [32]. The simulation result is in black solid line and the black circle symbols represent the experiment data. In the experiment, the design Mach numbers of the upper and lower layers were 1.5 and 2.5, and the Reynolds number ReML was ReML = 1.5 × 105 . The accuracy of the velocity measurements was ± 1%. The velocity profiles from the simulation showed the same tendency as those in the experiment. Though the velocity data at x/ H = 4 position near y/H = 0 have some difference, the simulation results fit the experiment well. Thus, the simulation results were demonstrated to be highly reliable.
(1)
u/ ue = (y / )1/7
Here, ue is the incoming flow velocity, y is the distance from the base surface, and is the thickness of the boundary layer. The influence of the temperature boundary layer also needed to be considered. According to the approximation theory of the high-speed compressible boundary layer, the relationship between the temperature and velocity under the adiabatic condition and with Pr = 1 is given by
T / Te = 1 + (
1) Mae2 (1
u2/ ue2 )1/7 /2
(2)
The following specific conditions were used in this study: an upper air flow Mach number of 1.5, lower air flow Mach number of 2.5, and convective Mach number of 0.35 [5]. The total pressure of the incoming flow was p0 = 101325 Pa , and the total temperature was T0 = 300 K . The static pressure of the lower flow was solved based on the nozzle theory to be 5930.3151 Pa. In the case of pressure matching, the upper and lower flow static pressures were equal. The inflow temperature was determined by the nozzle theory to be 206.8966 K on the upper side and 133.3333 K on the lower side. The boundary layer was determined by the engineering 1/7 law and was 2 mm thick. The calculation time step was dt = 1 × 10 7s . The single-step iteration was performed 50 times and required an iteration error below 10−3 per step. The total calculation time was t = 6 × 10 3s . The Reynolds number ReML based on the lower layer stream velocity U1, and the base thickness h in this simulation was ReML = 1.51 × 105 . The velocity ratio r = U1/ U2 = 1.36 , where U2 was the upper layer velocity. Fig. 4 shows the pressure profiles in the unforced case at x/H = 5 resulting from different grid scales. The static pressure p was nondimensionalized by the incoming flow static pressure ps. The detailed information of the mesh is listed in Table 1. The profiles show the effect of different grids on the pressure in the recirculation regions. In the range of −1 < y/H < 1, the discrepancy between the computational results predicted by the moderate and refined grids was much less than that between the results predicted by the coarse and moderate grids. This may imply that the moderate grid system was sufficient for this study. Fig. 5 compares the typical flow field structures in the experiment [31] and simulation. In the experiment, the design Mach numbers the upper and lower layers were 1.5 and 2.5, which fits the simulation conditions. The experiment Reynolds number ReML based on the lower
2.3. Precision estimates Estimation of precision and error accumulation is necessary for large scale simulations of complex supersonic mixing layers. The error depends on the accuracy of the algorithm and grid and the number of time steps [33]. Accumulation of error takes place for successive time steps. In case of systematic error origination from the defect of algorithm or solver, accumulation of error is proportional to the number of time steps. Smirnov et al. [33,34] developed a method to estimate the simulation precision. The relative error of integration in the one dimensional case S1 is proportional to the mean ratio of the cell size L to the domain size L1 in the direction of integration of power depending on the scheme accuracy:
S1
L L1
k+1
(3)
The order of accuracy of the numerical scheme is k. The integration in several directions results in summation of the errors: 3
Serr =
Si
(4)
i=1
The allowable value of total error is defined as 1%. The maximal allowable number of time steps for solving the present problem could be determined by the following formula:
S max
n max = (S max /Serr ) 2
(5)
The ratio of maximal allowable number of time steps for the problem, and the actual number of time steps used to obtain the result can be introduced as another important characteristic for the results of supercomputer simulations:
RS = n max /n
(6)
This ratio characterizes the reliability of the results. The higher the value, the lower is the error [33]. Table 2 provides data on the present numerical simulation. The precision estimation of the simulation is within the expectation.
Fig. 4. Comparison of pressure profiles resulting from different grid scales for the unforced case at x/H = 5. 59
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Table 1 Detailed information of the mesh. Mesh
Size (unit: mm) Length × Height × Thickness
Resolution Length × Height × Thickness
y+ (end of the base wall) Upper Wall/Lower Wall
Coarse Moderate Fine
220 × 70 × 10 220 × 70 × 10 220 × 70 × 10
306 × 350 × 40 396 × 450 × 40 476 × 670 × 40
0.98/1.15 0.98/1.15 0.98/1.15
Fig. 7. Density grayscale contours of the instantaneous flow field: (a) unforced case and (b) with the cavity-jet controller. Fig. 5. Comparison of flow structures: (a) experiment [31] and (b) simulation.
Fig. 6. Comparison of streamwise mean velocity profiles from simulation and Wu's experiment [32].
Fig. 8. Diagrams of the velocity vector for the magnified red boundary area in Fig. 6 (with the upper-air concentration contour): (a) unforced case and (b) with the cavity-jet controller. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
Table 2 Data on numerical simulation. Number of cells
Number of time steps
Allowable number of time steps (1% accuracy)
RS
5.5 × 106
6.0 × 104
4.0 × 105
6.7
reattachment shock wave was clear, and the mixing layer was further developed, while the vortex structure remained small in scale. With the cavity-jet controller, the free shear layer was unstable upstream of the reattachment point, and the degree of instability gradually increased. The strong vortex structure interacted with the shock wave [35], which led to shocklets appearing near the reattachment point. The vortex structure continued to develop in the redeveloping mixing layer at a larger scale and in a more unstable state. Fig. 8 shows a magnification of the red boundary area in Fig. 7 and the velocity vector diagrams (the background is the upper-air concentration contour). The velocity vector distributions near the jet exit with and without the controller showed that the cavity-jet controller
3. Results and discussion 3.1. Flow structures Fig. 7 compares the instantaneous flow field density grayscale contours. In the unforced case, the free shear layer downstream of the base was relatively stable, and no obvious oscillation occurred. The 60
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Fig. 11. Transverse mean velocity profiles for the flow fields of the unforced case and with the cavity-jet controller.
Fig. 9. Instantaneous velocity contour of the mixing layer with the cavity-jet controller.
consistent with the results of Samimy et al. [36]; the Mach numbers of the upper and lower layers were 2.07 and 1.50, respectively. Fig. 11shows the transverse mean velocity profiles for a range of x/ H = 2–14. The sign convention used in this figure is consistent with the spatial coordinates. The positive values of the velocity were higher in the lower flow layer, which indicates that the region experienced stronger expansion. The signs of the velocity were opposite in the lower and upper parts of the flow, which indicates that both layers collided during the mixing process. The exits of the controller had two opposite directions, which decreased the absolute flow velocity in the y direction. Compared to the streamwise mean velocity, the controller affects the velocity less in the y direction than in the x direction. Fig. 12 shows the streamwise turbulence intensity profiles, which demonstrate intensive mixing enhancement because of interaction at the base. The absolute maximum turbulence intensity at each streamwise location occurred at the lower part of the flow, which means that a higher Mach number generated a higher turbulence intensity. This can be attributed to the effects of the Mach number, which indicates that a greater entrainment of the recirculation flow originated from a highly turbulent interaction zone. The relatively high streamwise turbulence intensity was nearly 30% at the 2 and 4 base-height locations, which were in the stage of reattachment and recompression. In the redeveloping mixing layer, the turbulence intensity profile was more uniform, which indicates weaker pulsation in the flow. The following can be concluded from the turbulence intensity in the two cases: with the cavity-jet controller, the streamwise turbulence intensity was enhanced almost 10 times in the recirculation zone, and the turbulence intensity continued to increase in the redeveloping mixing layer. The range where high turbulence intensity occurred, was broadened by the controller in the y direction, which indicates higher mixing enhancement in the wake of the blunt base. The effect of the enhancement could still be found downstream of the redeveloping mixing layer. The turbulence intensity profiles are similar to those reported by Andreopoulos et al. [37] for an incompressible wake over a plate, although the values of < u′ > /u were higher in the present study.
mainly caused the flow to have a smaller recirculation zone with no other particular effect. The mixing degree of both air layers in the recirculation zone was greater with the cavity-jet controller (Fig. 8 (b)) than without it (Fig. 8 (a)). The concentration distribution of the gas was not sufficiently uniform with the cavity-jet controller. The effect of the cavity-jet controller on the blunt base recirculation zone did not appear in the characteristics of the flow structure. Fig. 9 shows the instantaneous velocity contour of the tailing region with the cavity-jet controller. Both outlets at the base formed a jet with a velocity of nearly 200 m/s. The jets interacted with the separation free shear layer, which caused the flow at the reattachment point to produce a large oscillation. Therefore, a large vortex structure formed at the beginning of the redeveloping mixing layer. 3.2. Mean properties Fig. 10 shows the streamwise mean velocity profiles nondimensionalized by the lower layer incoming velocity u1. The streamwise and transverse distances were nondimensionalized by the thickness of the blunt base H. The vertical dashed dotted lines at each x/H value represent the streamwise locations of the profiles, while the scale plate at the top of the graph represents the scale of the velocity u/u1. The profiles in the unforced case are marked with a solid line, and the profiles of the cavity-jet controller are marked with a dashed line. The profiles revealed that a negative velocity appeared in the recirculation zone and that the velocity recovered as the flow developed. A significant change in velocity occurred at the edge of the free shear layer. The profiles showed that the velocity changed from a sharp gradient to a gentle gradient, which represents the process of recompression and reattachment. Furthermore, the profiles developed at a faster rate during the earlier stages of the wake. The profile differences between the unforced case and with the cavity-jet controller indicate that the jet at the bottom of the base yielded a less negative velocity and enabled the velocity to recover faster. The tendency of the velocity profiles was
Fig. 10. Streamwise mean velocity profiles for the flow fields of the unforced case and with the cavity-jet controller.
Fig. 12. Streamwise turbulence intensity profiles for the flow fields of the unforced case and with the cavity-jet controller. 61
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The development of the mixing thickness can be divided into three stages. In Fig. 15 (a), the stages of the unforced case and with the cavity-jet controller are marked in gray and red, respectively. In stage 1, the mixing thickness decreased in the streamwise direction, which shows that both flow layers in this region moved towards each other. At the jet exits, the recirculation zone narrowed (see Fig. 8). At the blunt base trailing edge, the mixing thickness was smaller with the cavity-jet controller than in the unforced case. With the controller, the reattachment point, which was the thinnest point of the mixing thickness, appeared earlier than in the unforced case. The position of the redeveloping mixing layer also advanced. Stages 2 and 3 represent the redeveloping mixing layer. At stage 2, the two flow layers collided, and the dominant mixing form was momentum mixing. The mixing process in this region was fast. Therefore, the mixing thickness grew faster in stage 2 than in stage 3. The kinetic energy of both flow layers decreased during stage 3, but vortex structures appeared and became the main form of mixing. With the controller, the mixing thickness was greater in stages 2 and 3 than in the unforced case. The mixing enhancement reached 1.3–5.1 times.
Fig. 13. Transverse turbulence intensity profiles for the flow fields of the unforced case and with the cavity-jet controller.
Fig. 13 presents the transverse turbulence intensity profiles. The transverse turbulence intensity showed the same tendency as the streamwise turbulence intensity but at lower levels. The maximum transverse turbulence intensity at each streamwise location occurred near the centerline of the transverse direction. Around the beginning of the interaction of both flow layers and afterwards, the transverse turbulence intensity reached a peak at different streamwise locations in both cases. The intensity reached a peak at a streamwise distance of 8 base-heights and 4 base-heights in the unforced case and with the cavity-jet controller, respectively. The difference between the profiles shown by the solid and dashed lines indicates that the controller increased the intensity, and the influence of the controller spread broadly across the transverse height. The computational data were similar to the results obtained by Kuntz et al. [38] and Samimy and Addy [36]. Currently, the main indices used to describe the degree of mixing include the velocity thickness, vortex thickness, and scalar thickness [6,39,40]. Compared to the experimental method, a simulation can more easily mark the components of the upper and lower fluids. In this study, the mixing thickness was used as an evaluation index to illustrate the effect of the cavity-jet controller. This can be defined as the longitudinal position difference between the lower-air concentrations of 0.1 and 0.9 at the same streamwise position, which can be regarded as a scalar measurement. Fig. 14 shows the profile and contour lines of the lower-air concentration in the unforced case. The center of the distribution profile is located at the dotted line. The 0.1 and 0.9 concentration contours indicate the edges of the defined mixing layer. Fig. 15 Illustrates the (a) mixing thickness and (b) mixing enhancement. The mixing enhancement as formulated as.
=(
cavity jet
unforced )/ unforced
3.3. Power spectral density analysis The unsteady spectral characteristics of the supersonic blunt base mixing layer were analyzed to explain the mechanism of the controller action. Several monitoring points were set in the wake to record the variation characteristics of the pressure during the unsteady calculation process. All the pressure data were collected from the simulation process. Fast Fourier transform (FFT) was performed to calculate the power spectral density (PSD) of the pressure pulsation and obtain the most unstable frequency and characteristic frequency of the flow. Fig. 16 shows the layout of the monitoring points, determined considering the flow characteristics, and the specific position coordinates are presented in Table 2. Probe-1 was only set in the uncontrolled flow field, Probe-3 was only set in the flow field with the cavity-jet controller, and the others were set in both flow fields (see Table 3). Fig. 17 demonstrates the PSD of the monitoring points (a) in the unforced case and (b) with the cavity-jet controller. In the uncontrolled flow field, Probe-1 was located in the boundary layer of the blunt base and was used to characterize the unsteady characteristics of the incoming boundary layer. The frequency of 166.7 Hz was dominant at Probe-1. Note that the PSD was only 0.03, which was the minimum value that could be identified via spectrum analysis. This indicates that, at the base position, the turbulence was very low, and the boundary layer had almost no transition. Probe-2 was at the initial stage of boundary layer separation. The PSD curve is basically identical to that at Probe-1, but the PSD increased by 102. High-frequency pulsation was dominant at Probe-4, where an obvious vortex occurred as shown in Fig. 16. The low-frequency pulsation strength weakened. At Probe-5, the intensity of the high-frequency signal further increased, and the pulsation with a frequency of f = 43 kHz gradually became dominant. Fig. 16 shows that the vortex structure at this time had also become fully developed, which indicates that f = 43 kHz was the characteristic frequency of the flow. The free shear layer did not change the pulsation frequency of the incoming stream but only amplifies the pulsation signal, while the development of the mixing layer produced a new frequency pulsation. This is correlated with the unrestricted development of the redeveloping mixing layer. Although the velocity gradient inside the free shear layer was large, as shown in Fig. 16, the shear layer was limited to the vicinity of the recirculation zone. Its action time was short and failed to affect the unsteady characteristics of the flow. Probe-3 in the flow field with the controller was located where the jet ejected and had not yet interacted with the free shear layer. Here, high-frequency pulsation occurred, which led to the transition of the free shear layer at this particular position and greatly enhanced the instability during the early stage of the flow. Compared to Probe-1 in the unforced case, the high-energy pressure pulsation frequencies were
(7)
Fig. 14. Profile and contour line of the lower-air concentration: (a) unforced case and (b) with the cavity-jet controller. 62
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Fig. 15. Mixing thickness and mixing enhancement rate.
distribution of the other frequencies was similar to that at Probe-4. However, the PSD at Probe-5 was significantly lower than that at Probe4, which indicates that the pulsation energy decreased between the monitoring points. The pressure pulsation energy was still 10 times higher than that in the unforced case. Fig. 18 shows the PSD distribution for the flow characteristic pulsation frequency of 43 kHz and cavity characteristic pulsation frequency of 21.7 kHz. The ordinate of Fig. 18 is in the logarithmic scale. The energies of both characteristic frequency pulsations were enhanced by the controller. In the recirculation zone with the controller flow field, the pulsating energy with a frequency of 43 kHz exceeded that of the unforced case. However, for the redeveloping mixed layer, the energy was relatively close in both cases, which indicates that the controller enhanced the flow characteristic pulsation. Meanwhile, the pulsating energy with a frequency of 21.7 kHz was continuously strengthened in the flow field with the controller. It far exceeded the pulsation at the same frequency in the uncontrolled flow field, which indicates that the controller stimulated the pulsation of the characteristic frequency of the flow field.
Fig. 16. Positions of the monitoring points. Table 3 Coordinates of the monitoring points. Monitoring Point
Coordinates
Probe-1 Probe-2 Probe-3 Probe-4 Probe-5
(0.0, 0.55) (0.05, 0.5) (0.05, 0.38) (5.0, 0.0) (8.0, 0.0)
4. Conclusions A control method that effectively improves the mixing efficiency of the supersonic blunt base mixing layer is presented. The drainage inlet and jet outlet are set in the controller. The controller features a simple structure and requires no external energy. The proposed method can directly control the redeveloping mixing layer by using the pressure potential energy of the blunt base recirculation zone. The flow velocity of the jet exit of the controller is nearly 200 m/s. The jet interacts with the free shear layer formed by the separation, which results in large vibration characteristics of the flow near the reattachment point. A large vortex structure is induced at the initial stage of the redeveloping mixing layer. The strong vortex structure interacts with the shock wave and produces a series of shocklet structures. The controller enhances the turbulence intensity of the flow field and enlarges the transverse interaction region. The mixing thickness data indicate that the controller can increase the thickness of the redeveloping mixing layer by 1.3–5.1 times, which is a significant enhancement. Analysis of the unsteady spectral characteristics shows that the unstable characteristics are mainly concentrated in the initial stage of the redeveloping mixing layer. The broken vortex structure reduces the flow stability. The characteristic frequency of the flow field is 43 kHz. With the controller, the flow has strong vibration characteristics in the free shear layer stage, which enhances instability. The pulsation caused
higher here and reached 10.2 and 21.7 kHz. The energy was two orders of magnitude greater. The pulsation energy generated by the cavity carried by the airflow at the jet exit far exceeded the pulsation energy of the flow itself. Both pulsating frequencies with the highest energy at Probe-2 were identical to those at Probe-3, and the pulsation energy at f = 21.7 kHz was significantly increased. At the same time, two more high-frequency pulsations also developed. Among them was the flow characteristic frequency f = 43 kHz, which indicates that the instability enhancement by the controller originated from the blunt base. At Probe-4, a pulsation with a frequency of 21.7 kHz still existed, and the PSD intensity reached 1000. This indicates that the pulsation generated by the cavity was propagated and strengthened through the flow, and flow instability was induced. Therefore, with the controller, the mixing thickness still achieved a high growth rate during the later stages of the redeveloping mixing layer. The high-frequency pulsation had more frequencies here, and the pulsation energy exceeded that without controller. This indicates that the flow was more unstable, and the turbulence was greater. Note that pulsation with a frequency of 43 kHz still existed here, and the energy reached more than three times that of the unforced case. This indicates that the pulsation at the flow characteristic frequency was also enhanced. At Probe-5, the most powerful pulsation was still at a frequency of 21.7 kHz, and the pulsation energy 63
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Fig. 17. Power spectral densities of the monitoring points: (a) unforced case and (b) with the cavity-jet controller.
by the cavity of the controller is accompanied by the development of the flow field. The pulsation propagates downstream and is continuously strengthened, which stimulates the instability of the flow field. The pulsation energy of the flow field itself is also strengthened by
the controller. The mixing effect of the controller on the recirculation zone is not sufficiently strong but can increase the instability of the recirculation zone and positively affect the mixing enhancement in the redeveloping mixing layer. 64
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[14] [15] [16] [17] [18] [19] [20] [21] [22]
Fig. 18. PSD streamwise distributions of 21.7 and 43 kHz frequencies in the unforced case and with the cavity-jet controller.
[23]
Acknowledgment
[25]
[24]
[26]
Funding: This work was supported by the National Natural Science Foundation of China (Grant No. 11472304).
[27] [28]
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synthetic jet actuators, 38th Aerospace Sciences Meeting and Exhibit, AIAA, Reston, VA, 2000paper no. 0403. B. Ritchie, J. Seitzman, Mixing control of fuel jets using synthetic jet technology: scalar field measurements, 37th Aerospace Sciences Meeting and Exhibit, AIAA, Reston, VA, 1999paper no. 0448. B. Ritchie, D. Mujumdar, J. Seitzman, Mixing in coaxial jets using synthetic jet actuators, 38th Aerospace Sciences Meeting and Exhibit, AIAA, Reston, VA, 2000paper no. 0404. G. Raman, E.J. Rice, Supersonic jet mixing enhancement using impingement tones from obstacles of various geometries, AIAA J. 33 (1995) 454–462. R. Burnes, T. Parr, K. Wilson, K. Yu, Investigation of supersonic mixing control using cavities - effect of fuel injection location, 36th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, AIAA, Reston, Virginia, 2000paper no. 3618. A. Zang, T. Tempel, K. Yu, S. Buckley, Experimental characterization of cavityaugmented supersonic mixing, 43rd AIAA Aerospace Sciences Meeting and Exhibit, AIAA, Reston, Virginia, 2005paper no. 1423. T. Island, W. Urban, M. Mungal, Small-perturbation mixing enhancement in compressible shear layers, 35th Aerospace Sciences Meeting and Exhibit, AIAA, Reston, VA, 1997paper no. 395. L.J.S. Bradbury, A.H. Khadem, The distortion of a jet by tabs, J. Fluid Mech. 70 (1975) 801–813. E.M. Fernando, S. Menon, Mixing enhancement in compressible mixing layers – an experimental study, AIAA J. 31 (1993) 278–285. P. Gerlinger, P. Stoll, M. Kindler, F. Schneider, M. Aigner, Numerical investigation of mixing and combustion enhancement in supersonic combustors by strut induced streamwise vorticity, Aerosp. Sci. Technol. 12 (2008) 159–168. A.M. Williams, D.J. Griffiths, P.P. Vlachos, Laminar mixing using oscillating cantilevered ionic polymer actuators, Sens. Actuators A Phys. 153 (2009) 105–113. V.A. Amatucci, J.C. Dutton, D.W. Kuntz, A.L. Addy, Two-stream, supersonic, wake flowfield behind a thick base. I - general features, AIAA J. 30 (1992) 2039–2046. F. Scarano, B.W.V. Oudheusden, Planar velocity measurements of a two-dimensional compressible wake, Exp. Fluids. 34 (2003) 430–441. T.M. Reedy, G.S. Elliott, J.C. Dutton, Y. Lee, Passive control of high-speed separated flows using splitter plates, AIAA J. 50 (2012) 1586–1595. B. Vreman, B. Geurts, H. Kuerten, Large-eddy simulation of the turbulent mixing layer, J. Fluid Mech. 339 (1997) 357–390. X. Chai, K. Mahesh, Dynamic-equation model for large-eddy simulation of compressible flows, J. Fluid Mech. 699 (2012) 385–413. B.M.F. Chalot, M. Ravachol, F. Ducros, T. Poinsot, Large eddy simulation of a compressible mixing layer - study of the mixing enhancement, 14th Computational Fluid Dynamics Conference, AIAA, Reston, VA, 1999paper no. 3358. A. Sharma, R. Bhaskaran, S. Lele, Large-eddy simulation of supersonic, turbulent mixing layers downstream of a splitter plate, 49th AIAA Aerospace Sciences Meeting, AIAA, Reston, VA, 2011paper no. 208. R. Yang, Investigations on Characteristics of Supersonic Blunt Trailing Edge Mixing Layer and its Active Control, Master's Thesis, National University of Defense Technology, Changsha, China, 2017. J. Wu, H. Zhang, J. Chen, Investigation of large-scale structures in supersonic planar non-reactive shear layer with a base flow region, J. Vis. 21 (2018) 613–624. N.N. Smirnov, V.B. Betelin, R.M. Shagaliev, V.F. Nikitin, I.M. Belyakov, Yu.N. Deryuguin, S.V. Aksenov, D.A. Korchazhkin, Hydrogen fuel rocket engines simulation using LOGOS code, Int. J. Hydrogen Energy 39 (2014) 10748–10756. N.N. Smirnov, V.B. Betelin, V.F. Nikitin, L.I. Stamov, D.I. Altoukhov, Accumulation of errors in numerical simulations of chemically reacting gas dynamics, Acta Astronaut. 117 (2015) 338–355. S.H. Yi, Y.X. Zhao, L. He, L.F. Tian, Z.Y. Cheng, A flow control study of a supersonic mixing layer via NPLS, Sci. China Ser. A G. 52 (2009) 2001–2006. M. Samimy, A.L. Addy, Interaction between two compressible, turbulent free shear layers, AIAA J. 24 (1986) 1918–1923. J. Andreopoulos, P. Bradshaw, Measurements of interacting turbulent shear layers in the near wake of a flat plat, J. Fluid Mech. 100 (1980) 639–668. D.W. Kuntz, N. Albuquerque, V.A. Amatucci, A.L. Addy, The turbulent boundary layer properties downstream of the shock wave-boundary layer interaction, 24th Aerospace Sciences Meeting, AIAA, Reston, Virginia, 1986paper no. 348. G.L. Brown, A. Roshko, On density effects and large structure in turbulent mixing layers, J. Fluid Mech. 64 (1974) 775–816. A.W. Vreman, N.D. Sandham, K.H. Luo, Compressible mixing layer growth rate and turbulence characteristics, J. Fluid Mech. 320 (1996) 235–258.
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Large eddy simulation on using a cavity-jet controller for supersonic blunt base mixing layer control
T
Yong-yi Zhou, Rui Yang∗, Yu-xin Zhao Science and Technology on Scramjet Laboratory, College of Aerospace Science and Engineering, National University of Defense Technology, Changsha, Hunan, 410073, People's Republic of China
ARTICLE INFO
ABSTRACT
Keywords: Cavity-jet controller Supersonic mixing layer Blunt base Numerical simulation Power spectral density
In this study, a cavity-jet controller was used to control the supersonic blunt base mixing layer. This method is simple in structure, requires no external energy, and can utilize the pressure potential energy of the flow. A large eddy simulation was performed to numerically investigate the control effect. The Mach numbers of the upper and lower layers were 1.5 and 2.5, respectively, and the convective Mach number was 0.35. The simulation flow field structures and mean properties with and without the cavity-jet controller were compared. The results showed that this controller enhanced the turbulence intensity of the flow. The mixing thickness was used to quantify the mixing characteristics. The controller significantly improved the mixing performance. The flow fields were monitored at several points to record the pressure pulsation information, and the power spectral density was analyzed.
1. Introduction Rocket-based combined cycle (RBCC) engine technology is the current development trend for hypersonic aircraft propulsion systems [1]. The mixing process of supersonic air and fuel is a key point of the RBCC engine. Therefore, the supersonic mixing layer, which is a typical compressive shear flow [2], and its characteristics have received significant attention [3,4]. Because of limitations on the engine length, the flow in the engine has a short duration time. To enhance the combustion efficiency, the mixing process of air and fuel needs to be fastened. However, under the supersonic flow condition, the compressibility significantly affects the growth of the mixing layer [5]. Previous studies have shown that the mixing efficiency is strongly limited by the compressibility [6]. To enhance the mixing effect of air and fuel under the supersonic condition and improve the engine performance, various control methods have been introduced. These can be divided into active and passive methods [7,8]. Active control methods mainly change the characteristic structures of the flow field by actively injecting energy and momentum into the flow. Zhang et al. [9] set a vibrating reed upstream of the supersonic flow. The reed was then stimulated by the control system to control the flow field. Flow visualization showed that the laminar flow area of the mixing layer was shortened, and the opening angle increased. Different vibration frequencies varied the mixing enhancement performance.
∗
Zhou et al. [10] adopted a dual-frequency disturbance and reported that the growth rate of the mixing layer exceeded that of the singlefrequency layer. The synthetic jet is a control method that needs no external pressure source and has a simple structure [11]. Davis et al. [12,13] and Ritchie et al. [14,15] experimentally studied enhancing the mixing of air and fuel with a synthetic jet and demonstrated its effectiveness. However, the synthetic jet has limited energy, which makes it suitable for low-speed flows. Active control methods introduce external energy into the flow; under the actual working conditions of high temperature and pressure, the design and manufacture of movable parts is difficult. Unlike the active control methods, passive control methods use fixed-structure devices. Raman et al. [16] installed protuberances with various geometric configurations to generate disturbances at various frequencies. The disturbances generated a resonance that enhanced the mixing. Sunken cavities set in the wall of the flow have a similar effect. The flow past the cavity resonates to improve the fuel penetration performance [17,18]. Island et al. [19] reported that the growth rate of the supersonic mixing layer was increased by 45% through the use of small perturbations. Bradbury et al. [20] and Fernando et al. [21] experimentally studied the mixing enhancement and control effect of splitter plates. However, they observed a remarkable total pressure loss. In contrast to splitter plates, lobe supports can effectively generate high-intensity streamwise vortices to improve the mixing effect [22]. However, the increased divergence angle increases the loss of the total
Corresponding author. E-mail address: [email protected] (R. Yang).
https://doi.org/10.1016/j.actaastro.2019.05.019 Received 7 December 2018; Received in revised form 26 March 2019; Accepted 10 May 2019 Available online 15 May 2019 0094-5765/ © 2019 IAA. Published by Elsevier Ltd. All rights reserved.
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Fig. 1. Schematic for the flow structures of the supersonic blunt base mixing layer.
pressure, which is detrimental to the engine performance. Williams et al. [23] installed plasma polymer films in the flow to stimulate vibrations that enhance mixing by 150%–375%. However, they considered a laminar flow with a Reynolds number of only 10. The various control methods currently in use have their own characteristics and are suitable for a thin trailing-edge mixing layer. However, engineering applications have a high gas temperature, and a protective cooling mechanism is required. The thickness of the base is inevitably increased, which results in a supersonic blunt base mixing layer. This is quite different from the typical thin base in the flow field structure [24]; a flow diagram is shown in Fig. 1. The flow characteristics include a recirculation zone, a shear layer, expansion waves, and shock waves [24,25]. Control methods aimed at this type of mixing layer have rarely been reported. Reedy et al. [26] proposed a passive method that uses rudders to control the recirculation zone after a cylinder base, but the effects are not obvious. The most important feature of flow structures is the recirculation zone at the bottom of the blunt base, which has a significantly lower pressure than the surrounding area. In the present study, a control method was developed that is based on the low-pressure characteristics of the recirculation zone of the supersonic blunt base. The method is suitable for a supersonic blunt base mixing layer; it has a simple structure, requires no external energy, and achieves good control performance. Two layers of the base are introduced into a cavity that empties into the base and ejects into the recirculation zone under the action of the pressure potential energy generated in the low-pressure zone. The high-frequency disturbance generated by the cavity can easily lead to unstable flow control of the mixing layer, which is a characteristic of this method. The large eddy simulation (LES) method was used to evaluate the mixing control effects of the method and analyze the mechanism of the controller.
Fig. 2. Schematic of the cavity-jet controller.
Fig. 3. Diagram of the 2-D cavity-jet controller with size markings (length unit: mm).
The drainage port is a rectangular channel with a narrowing section from outside to the inside, which increases the amount of intake air. The jet port is a rectangular channel with an equal section, and the channels are inclined to the blunt base. The specific dimensions of the controller are shown in Fig. 3.
2. Physical model and numerical setup 2.1. Physical model
2.2. Numerical setup and verification
The supersonic blunt base mixing layer flow separates at the base, and the pressure at the bottom is much less than the incoming flow pressure. Fig. 2 shows the cavity-jet controller designed in this study to utilize this part of the pressure potential energy. The middle part of the controller is a cavity separated by a partition, and a drainage inlet opens at a specific position upstream of the upper and lower surfaces of the controller. Correspondingly, two jet outlets open at the bottom of the base. Under the action of the pressure potential energy, the flow enters the cavity through the drainage inlet and rushes out through the jet outlet. This is why the component is called a “cavity-jet” controller.
A compressible and finite-volume LES solver that is third order in space and second order in time was employed in this study. The subgrid model is used for kinetic energy transport. The governing equations [27] and kinetic energy transport equation of the sub-grid model [28] were previously developed. This solver has been extensively validated and used for many supersonic mixing layers [3,29,30]. To avoid shock waves from being generated at the entrance, the flow was assumed to be a plate boundary layer, and the velocity profile was determined according to the 1/7 power law 58
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layer velocity U1 and the base thickness h was ReML = 1.52 × 105 , which fits the simulation Reynolds number. The main flow field structure of the supersonic blunt base mixing layer could be obtained via the numerical simulation. Two layers formed free shear layers that intersected at the reattachment point to form a reattachment shock wave. At the same time, the vortex structure began to roll up behind the reattachment point. The simulation and experiment have similar flow structures. The basic structure of the flow field was simulated. However, the LES simulation is sensitive to the boundary layer, so there are some differences between the simulation and experiment results. The position of the reattachment point was behind the experimental result. The laser was mostly reflected at the sharp point of the upper base without passing through the glass partition. This is why the diagonal stripe appeared in Fig. 5(a) (marked in white dashed box). Note that this did not affect the investigation of the flow field structure. Fig. 6 compares the streamwise mean velocity profiles from the unforced case simulation and Wu's experiment [32]. The simulation result is in black solid line and the black circle symbols represent the experiment data. In the experiment, the design Mach numbers of the upper and lower layers were 1.5 and 2.5, and the Reynolds number ReML was ReML = 1.5 × 105 . The accuracy of the velocity measurements was ± 1%. The velocity profiles from the simulation showed the same tendency as those in the experiment. Though the velocity data at x/ H = 4 position near y/H = 0 have some difference, the simulation results fit the experiment well. Thus, the simulation results were demonstrated to be highly reliable.
(1)
u/ ue = (y / )1/7
Here, ue is the incoming flow velocity, y is the distance from the base surface, and is the thickness of the boundary layer. The influence of the temperature boundary layer also needed to be considered. According to the approximation theory of the high-speed compressible boundary layer, the relationship between the temperature and velocity under the adiabatic condition and with Pr = 1 is given by
T / Te = 1 + (
1) Mae2 (1
u2/ ue2 )1/7 /2
(2)
The following specific conditions were used in this study: an upper air flow Mach number of 1.5, lower air flow Mach number of 2.5, and convective Mach number of 0.35 [5]. The total pressure of the incoming flow was p0 = 101325 Pa , and the total temperature was T0 = 300 K . The static pressure of the lower flow was solved based on the nozzle theory to be 5930.3151 Pa. In the case of pressure matching, the upper and lower flow static pressures were equal. The inflow temperature was determined by the nozzle theory to be 206.8966 K on the upper side and 133.3333 K on the lower side. The boundary layer was determined by the engineering 1/7 law and was 2 mm thick. The calculation time step was dt = 1 × 10 7s . The single-step iteration was performed 50 times and required an iteration error below 10−3 per step. The total calculation time was t = 6 × 10 3s . The Reynolds number ReML based on the lower layer stream velocity U1, and the base thickness h in this simulation was ReML = 1.51 × 105 . The velocity ratio r = U1/ U2 = 1.36 , where U2 was the upper layer velocity. Fig. 4 shows the pressure profiles in the unforced case at x/H = 5 resulting from different grid scales. The static pressure p was nondimensionalized by the incoming flow static pressure ps. The detailed information of the mesh is listed in Table 1. The profiles show the effect of different grids on the pressure in the recirculation regions. In the range of −1 < y/H < 1, the discrepancy between the computational results predicted by the moderate and refined grids was much less than that between the results predicted by the coarse and moderate grids. This may imply that the moderate grid system was sufficient for this study. Fig. 5 compares the typical flow field structures in the experiment [31] and simulation. In the experiment, the design Mach numbers the upper and lower layers were 1.5 and 2.5, which fits the simulation conditions. The experiment Reynolds number ReML based on the lower
2.3. Precision estimates Estimation of precision and error accumulation is necessary for large scale simulations of complex supersonic mixing layers. The error depends on the accuracy of the algorithm and grid and the number of time steps [33]. Accumulation of error takes place for successive time steps. In case of systematic error origination from the defect of algorithm or solver, accumulation of error is proportional to the number of time steps. Smirnov et al. [33,34] developed a method to estimate the simulation precision. The relative error of integration in the one dimensional case S1 is proportional to the mean ratio of the cell size L to the domain size L1 in the direction of integration of power depending on the scheme accuracy:
S1
L L1
k+1
(3)
The order of accuracy of the numerical scheme is k. The integration in several directions results in summation of the errors: 3
Serr =
Si
(4)
i=1
The allowable value of total error is defined as 1%. The maximal allowable number of time steps for solving the present problem could be determined by the following formula:
S max
n max = (S max /Serr ) 2
(5)
The ratio of maximal allowable number of time steps for the problem, and the actual number of time steps used to obtain the result can be introduced as another important characteristic for the results of supercomputer simulations:
RS = n max /n
(6)
This ratio characterizes the reliability of the results. The higher the value, the lower is the error [33]. Table 2 provides data on the present numerical simulation. The precision estimation of the simulation is within the expectation.
Fig. 4. Comparison of pressure profiles resulting from different grid scales for the unforced case at x/H = 5. 59
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Table 1 Detailed information of the mesh. Mesh
Size (unit: mm) Length × Height × Thickness
Resolution Length × Height × Thickness
y+ (end of the base wall) Upper Wall/Lower Wall
Coarse Moderate Fine
220 × 70 × 10 220 × 70 × 10 220 × 70 × 10
306 × 350 × 40 396 × 450 × 40 476 × 670 × 40
0.98/1.15 0.98/1.15 0.98/1.15
Fig. 7. Density grayscale contours of the instantaneous flow field: (a) unforced case and (b) with the cavity-jet controller. Fig. 5. Comparison of flow structures: (a) experiment [31] and (b) simulation.
Fig. 6. Comparison of streamwise mean velocity profiles from simulation and Wu's experiment [32].
Fig. 8. Diagrams of the velocity vector for the magnified red boundary area in Fig. 6 (with the upper-air concentration contour): (a) unforced case and (b) with the cavity-jet controller. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
Table 2 Data on numerical simulation. Number of cells
Number of time steps
Allowable number of time steps (1% accuracy)
RS
5.5 × 106
6.0 × 104
4.0 × 105
6.7
reattachment shock wave was clear, and the mixing layer was further developed, while the vortex structure remained small in scale. With the cavity-jet controller, the free shear layer was unstable upstream of the reattachment point, and the degree of instability gradually increased. The strong vortex structure interacted with the shock wave [35], which led to shocklets appearing near the reattachment point. The vortex structure continued to develop in the redeveloping mixing layer at a larger scale and in a more unstable state. Fig. 8 shows a magnification of the red boundary area in Fig. 7 and the velocity vector diagrams (the background is the upper-air concentration contour). The velocity vector distributions near the jet exit with and without the controller showed that the cavity-jet controller
3. Results and discussion 3.1. Flow structures Fig. 7 compares the instantaneous flow field density grayscale contours. In the unforced case, the free shear layer downstream of the base was relatively stable, and no obvious oscillation occurred. The 60
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Fig. 11. Transverse mean velocity profiles for the flow fields of the unforced case and with the cavity-jet controller.
Fig. 9. Instantaneous velocity contour of the mixing layer with the cavity-jet controller.
consistent with the results of Samimy et al. [36]; the Mach numbers of the upper and lower layers were 2.07 and 1.50, respectively. Fig. 11shows the transverse mean velocity profiles for a range of x/ H = 2–14. The sign convention used in this figure is consistent with the spatial coordinates. The positive values of the velocity were higher in the lower flow layer, which indicates that the region experienced stronger expansion. The signs of the velocity were opposite in the lower and upper parts of the flow, which indicates that both layers collided during the mixing process. The exits of the controller had two opposite directions, which decreased the absolute flow velocity in the y direction. Compared to the streamwise mean velocity, the controller affects the velocity less in the y direction than in the x direction. Fig. 12 shows the streamwise turbulence intensity profiles, which demonstrate intensive mixing enhancement because of interaction at the base. The absolute maximum turbulence intensity at each streamwise location occurred at the lower part of the flow, which means that a higher Mach number generated a higher turbulence intensity. This can be attributed to the effects of the Mach number, which indicates that a greater entrainment of the recirculation flow originated from a highly turbulent interaction zone. The relatively high streamwise turbulence intensity was nearly 30% at the 2 and 4 base-height locations, which were in the stage of reattachment and recompression. In the redeveloping mixing layer, the turbulence intensity profile was more uniform, which indicates weaker pulsation in the flow. The following can be concluded from the turbulence intensity in the two cases: with the cavity-jet controller, the streamwise turbulence intensity was enhanced almost 10 times in the recirculation zone, and the turbulence intensity continued to increase in the redeveloping mixing layer. The range where high turbulence intensity occurred, was broadened by the controller in the y direction, which indicates higher mixing enhancement in the wake of the blunt base. The effect of the enhancement could still be found downstream of the redeveloping mixing layer. The turbulence intensity profiles are similar to those reported by Andreopoulos et al. [37] for an incompressible wake over a plate, although the values of < u′ > /u were higher in the present study.
mainly caused the flow to have a smaller recirculation zone with no other particular effect. The mixing degree of both air layers in the recirculation zone was greater with the cavity-jet controller (Fig. 8 (b)) than without it (Fig. 8 (a)). The concentration distribution of the gas was not sufficiently uniform with the cavity-jet controller. The effect of the cavity-jet controller on the blunt base recirculation zone did not appear in the characteristics of the flow structure. Fig. 9 shows the instantaneous velocity contour of the tailing region with the cavity-jet controller. Both outlets at the base formed a jet with a velocity of nearly 200 m/s. The jets interacted with the separation free shear layer, which caused the flow at the reattachment point to produce a large oscillation. Therefore, a large vortex structure formed at the beginning of the redeveloping mixing layer. 3.2. Mean properties Fig. 10 shows the streamwise mean velocity profiles nondimensionalized by the lower layer incoming velocity u1. The streamwise and transverse distances were nondimensionalized by the thickness of the blunt base H. The vertical dashed dotted lines at each x/H value represent the streamwise locations of the profiles, while the scale plate at the top of the graph represents the scale of the velocity u/u1. The profiles in the unforced case are marked with a solid line, and the profiles of the cavity-jet controller are marked with a dashed line. The profiles revealed that a negative velocity appeared in the recirculation zone and that the velocity recovered as the flow developed. A significant change in velocity occurred at the edge of the free shear layer. The profiles showed that the velocity changed from a sharp gradient to a gentle gradient, which represents the process of recompression and reattachment. Furthermore, the profiles developed at a faster rate during the earlier stages of the wake. The profile differences between the unforced case and with the cavity-jet controller indicate that the jet at the bottom of the base yielded a less negative velocity and enabled the velocity to recover faster. The tendency of the velocity profiles was
Fig. 10. Streamwise mean velocity profiles for the flow fields of the unforced case and with the cavity-jet controller.
Fig. 12. Streamwise turbulence intensity profiles for the flow fields of the unforced case and with the cavity-jet controller. 61
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The development of the mixing thickness can be divided into three stages. In Fig. 15 (a), the stages of the unforced case and with the cavity-jet controller are marked in gray and red, respectively. In stage 1, the mixing thickness decreased in the streamwise direction, which shows that both flow layers in this region moved towards each other. At the jet exits, the recirculation zone narrowed (see Fig. 8). At the blunt base trailing edge, the mixing thickness was smaller with the cavity-jet controller than in the unforced case. With the controller, the reattachment point, which was the thinnest point of the mixing thickness, appeared earlier than in the unforced case. The position of the redeveloping mixing layer also advanced. Stages 2 and 3 represent the redeveloping mixing layer. At stage 2, the two flow layers collided, and the dominant mixing form was momentum mixing. The mixing process in this region was fast. Therefore, the mixing thickness grew faster in stage 2 than in stage 3. The kinetic energy of both flow layers decreased during stage 3, but vortex structures appeared and became the main form of mixing. With the controller, the mixing thickness was greater in stages 2 and 3 than in the unforced case. The mixing enhancement reached 1.3–5.1 times.
Fig. 13. Transverse turbulence intensity profiles for the flow fields of the unforced case and with the cavity-jet controller.
Fig. 13 presents the transverse turbulence intensity profiles. The transverse turbulence intensity showed the same tendency as the streamwise turbulence intensity but at lower levels. The maximum transverse turbulence intensity at each streamwise location occurred near the centerline of the transverse direction. Around the beginning of the interaction of both flow layers and afterwards, the transverse turbulence intensity reached a peak at different streamwise locations in both cases. The intensity reached a peak at a streamwise distance of 8 base-heights and 4 base-heights in the unforced case and with the cavity-jet controller, respectively. The difference between the profiles shown by the solid and dashed lines indicates that the controller increased the intensity, and the influence of the controller spread broadly across the transverse height. The computational data were similar to the results obtained by Kuntz et al. [38] and Samimy and Addy [36]. Currently, the main indices used to describe the degree of mixing include the velocity thickness, vortex thickness, and scalar thickness [6,39,40]. Compared to the experimental method, a simulation can more easily mark the components of the upper and lower fluids. In this study, the mixing thickness was used as an evaluation index to illustrate the effect of the cavity-jet controller. This can be defined as the longitudinal position difference between the lower-air concentrations of 0.1 and 0.9 at the same streamwise position, which can be regarded as a scalar measurement. Fig. 14 shows the profile and contour lines of the lower-air concentration in the unforced case. The center of the distribution profile is located at the dotted line. The 0.1 and 0.9 concentration contours indicate the edges of the defined mixing layer. Fig. 15 Illustrates the (a) mixing thickness and (b) mixing enhancement. The mixing enhancement as formulated as.
=(
cavity jet
unforced )/ unforced
3.3. Power spectral density analysis The unsteady spectral characteristics of the supersonic blunt base mixing layer were analyzed to explain the mechanism of the controller action. Several monitoring points were set in the wake to record the variation characteristics of the pressure during the unsteady calculation process. All the pressure data were collected from the simulation process. Fast Fourier transform (FFT) was performed to calculate the power spectral density (PSD) of the pressure pulsation and obtain the most unstable frequency and characteristic frequency of the flow. Fig. 16 shows the layout of the monitoring points, determined considering the flow characteristics, and the specific position coordinates are presented in Table 2. Probe-1 was only set in the uncontrolled flow field, Probe-3 was only set in the flow field with the cavity-jet controller, and the others were set in both flow fields (see Table 3). Fig. 17 demonstrates the PSD of the monitoring points (a) in the unforced case and (b) with the cavity-jet controller. In the uncontrolled flow field, Probe-1 was located in the boundary layer of the blunt base and was used to characterize the unsteady characteristics of the incoming boundary layer. The frequency of 166.7 Hz was dominant at Probe-1. Note that the PSD was only 0.03, which was the minimum value that could be identified via spectrum analysis. This indicates that, at the base position, the turbulence was very low, and the boundary layer had almost no transition. Probe-2 was at the initial stage of boundary layer separation. The PSD curve is basically identical to that at Probe-1, but the PSD increased by 102. High-frequency pulsation was dominant at Probe-4, where an obvious vortex occurred as shown in Fig. 16. The low-frequency pulsation strength weakened. At Probe-5, the intensity of the high-frequency signal further increased, and the pulsation with a frequency of f = 43 kHz gradually became dominant. Fig. 16 shows that the vortex structure at this time had also become fully developed, which indicates that f = 43 kHz was the characteristic frequency of the flow. The free shear layer did not change the pulsation frequency of the incoming stream but only amplifies the pulsation signal, while the development of the mixing layer produced a new frequency pulsation. This is correlated with the unrestricted development of the redeveloping mixing layer. Although the velocity gradient inside the free shear layer was large, as shown in Fig. 16, the shear layer was limited to the vicinity of the recirculation zone. Its action time was short and failed to affect the unsteady characteristics of the flow. Probe-3 in the flow field with the controller was located where the jet ejected and had not yet interacted with the free shear layer. Here, high-frequency pulsation occurred, which led to the transition of the free shear layer at this particular position and greatly enhanced the instability during the early stage of the flow. Compared to Probe-1 in the unforced case, the high-energy pressure pulsation frequencies were
(7)
Fig. 14. Profile and contour line of the lower-air concentration: (a) unforced case and (b) with the cavity-jet controller. 62
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Fig. 15. Mixing thickness and mixing enhancement rate.
distribution of the other frequencies was similar to that at Probe-4. However, the PSD at Probe-5 was significantly lower than that at Probe4, which indicates that the pulsation energy decreased between the monitoring points. The pressure pulsation energy was still 10 times higher than that in the unforced case. Fig. 18 shows the PSD distribution for the flow characteristic pulsation frequency of 43 kHz and cavity characteristic pulsation frequency of 21.7 kHz. The ordinate of Fig. 18 is in the logarithmic scale. The energies of both characteristic frequency pulsations were enhanced by the controller. In the recirculation zone with the controller flow field, the pulsating energy with a frequency of 43 kHz exceeded that of the unforced case. However, for the redeveloping mixed layer, the energy was relatively close in both cases, which indicates that the controller enhanced the flow characteristic pulsation. Meanwhile, the pulsating energy with a frequency of 21.7 kHz was continuously strengthened in the flow field with the controller. It far exceeded the pulsation at the same frequency in the uncontrolled flow field, which indicates that the controller stimulated the pulsation of the characteristic frequency of the flow field.
Fig. 16. Positions of the monitoring points. Table 3 Coordinates of the monitoring points. Monitoring Point
Coordinates
Probe-1 Probe-2 Probe-3 Probe-4 Probe-5
(0.0, 0.55) (0.05, 0.5) (0.05, 0.38) (5.0, 0.0) (8.0, 0.0)
4. Conclusions A control method that effectively improves the mixing efficiency of the supersonic blunt base mixing layer is presented. The drainage inlet and jet outlet are set in the controller. The controller features a simple structure and requires no external energy. The proposed method can directly control the redeveloping mixing layer by using the pressure potential energy of the blunt base recirculation zone. The flow velocity of the jet exit of the controller is nearly 200 m/s. The jet interacts with the free shear layer formed by the separation, which results in large vibration characteristics of the flow near the reattachment point. A large vortex structure is induced at the initial stage of the redeveloping mixing layer. The strong vortex structure interacts with the shock wave and produces a series of shocklet structures. The controller enhances the turbulence intensity of the flow field and enlarges the transverse interaction region. The mixing thickness data indicate that the controller can increase the thickness of the redeveloping mixing layer by 1.3–5.1 times, which is a significant enhancement. Analysis of the unsteady spectral characteristics shows that the unstable characteristics are mainly concentrated in the initial stage of the redeveloping mixing layer. The broken vortex structure reduces the flow stability. The characteristic frequency of the flow field is 43 kHz. With the controller, the flow has strong vibration characteristics in the free shear layer stage, which enhances instability. The pulsation caused
higher here and reached 10.2 and 21.7 kHz. The energy was two orders of magnitude greater. The pulsation energy generated by the cavity carried by the airflow at the jet exit far exceeded the pulsation energy of the flow itself. Both pulsating frequencies with the highest energy at Probe-2 were identical to those at Probe-3, and the pulsation energy at f = 21.7 kHz was significantly increased. At the same time, two more high-frequency pulsations also developed. Among them was the flow characteristic frequency f = 43 kHz, which indicates that the instability enhancement by the controller originated from the blunt base. At Probe-4, a pulsation with a frequency of 21.7 kHz still existed, and the PSD intensity reached 1000. This indicates that the pulsation generated by the cavity was propagated and strengthened through the flow, and flow instability was induced. Therefore, with the controller, the mixing thickness still achieved a high growth rate during the later stages of the redeveloping mixing layer. The high-frequency pulsation had more frequencies here, and the pulsation energy exceeded that without controller. This indicates that the flow was more unstable, and the turbulence was greater. Note that pulsation with a frequency of 43 kHz still existed here, and the energy reached more than three times that of the unforced case. This indicates that the pulsation at the flow characteristic frequency was also enhanced. At Probe-5, the most powerful pulsation was still at a frequency of 21.7 kHz, and the pulsation energy 63
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Fig. 17. Power spectral densities of the monitoring points: (a) unforced case and (b) with the cavity-jet controller.
by the cavity of the controller is accompanied by the development of the flow field. The pulsation propagates downstream and is continuously strengthened, which stimulates the instability of the flow field. The pulsation energy of the flow field itself is also strengthened by
the controller. The mixing effect of the controller on the recirculation zone is not sufficiently strong but can increase the instability of the recirculation zone and positively affect the mixing enhancement in the redeveloping mixing layer. 64
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[14] [15] [16] [17] [18] [19] [20] [21] [22]
Fig. 18. PSD streamwise distributions of 21.7 and 43 kHz frequencies in the unforced case and with the cavity-jet controller.
[23]
Acknowledgment
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[24]
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Funding: This work was supported by the National Natural Science Foundation of China (Grant No. 11472304).
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