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Mixing characteristics of vent slot mixer in supersonic flow
Aerospace Science and Technology 49 (2016) 250–258
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Aerospace Science and Technology www.elsevier.com/locate/aescte
Mixing characteristics of vent slot mixer in supersonic flow Chae-Hyoung Kim a , In-Seuck Jeung b,∗ a b
Engine Test and Evaluation Team, Korea Aerospace Research Institute, Daejeon 34133, Republic of Korea Department of Mechanical and Aerospace Engineering, Institute of Advanced Aerospace Technology, Seoul National University, Seoul 08826, Republic of Korea
a r t i c l e
i n f o
Article history: Received 23 April 2015 Received in revised form 3 October 2015 Accepted 7 December 2015 Available online 14 December 2015 Keywords: Vent slot mixer Stereoscopic PIV Counter-rotating vortex pair Turbulent structure
a b s t r a c t Non-reacting experiments were performed to show the mixing characteristics of the vent slot mixer by the injector location in Mach 2 supersonic flow. As the injectant such as hydrogen, helium, and air was injected into the supersonic main flow, flow structures were visualized by schlieren photography and stereoscopic particle image velocimetry. Pressure measurement and gas sampling were conducted in order to compare with their flowfield visualization. The mixing performance is highly sensitive to the injection position of the vent slot mixer. While the injection occurs under the vent slot mixer, the remnant injectant is evenly distributed toward the spanwise direction. In the meantime, the injection behind the vent slot mixer generates the jet plume containing a counter-rotating vortex pair which mainly affects the velocity field and turbulent motion around the jet plume. In the case of the vent slot mixer, because the jet plume is combined with the nearby shear layer, the injectant in the jet plume can be supplied into the nearby shear layer. © 2015 Elsevier Masson SAS. All rights reserved.
1. Introduction The supersonic combustion engine is a key to design hypersonic vehicle such as scramjet (supersonic combustion ramjet) engine and RBCC (Rocket Based Combined Cycle) engine [1–3]. However, it is believed to be very difficult to develop the supersonic combustion engine. The residence time of the fuel injectant is very short, resulting in not being well-mixed and not surely-ignited in the supersonic flow. Due to such difficulties, various mixing methods have been proposed during the last few decades [4]. Among them, transverse injection from a flat plate has the simplest configuration and induces an aerodynamic barrier, which is a bow shock, to give a chance of mixing fuel and air in the jet plume [5,6]. With the transverse injection, physical mixer models installed in the supersonic flow can enhance the mixing performance. Typically, step mixers have been extensively studied with an objective of extending the residence time of the fuel–air mixture with the simple configuration [7–9]. Upstream boundary layer is separated at the edge of the step mixer, creating the recirculation region behind the step mixer. If the fuel is injected in the recirculation region, the injectant can be sustained and slightly mixed in the recirculation region. However, because the step mixer indicates poor mass transfer in the recirculation region [8], a stirring device is required to mix the fuel–air mixture at macro- and micro-levels
*
Corresponding author. E-mail address: [email protected] (I.-S. Jeung).
http://dx.doi.org/10.1016/j.ast.2015.12.011 1270-9638/© 2015 Elsevier Masson SAS. All rights reserved.
in the recirculation region. For example, Helmholtz resonators [10] generate an acoustic oscillation and hyper mixers [11–13] composed of wedges and ramps produce streamwise vortices by pressure gradient. Based on these considerations, a new mixer model, vent slot mixer, was suggested in a previous work [14]. The step mixer was used to create a recirculation region which was augmented by adding an extended roof-plate at upper region of the step mixer. With the “well mixed” model [15], an active method for supplying air into the fuel–air mixing region was suggested by using a slot on the roof-plate. The main flow is considered to be entrained into the recirculation region through the slot due to the pressure gradient between the main flow and the recirculation region. Furthermore, the interaction of the inflow air in the recirculation region tends to induce some turbulent flow structures. This kind of the flow mechanism by the vent slot mixer was simulated with CFD (Computational Fluid Dynamics) analysis [14]. The inflow air through the slot into the recirculation region generated complex flow structures such as circulation bubbles and large-scale vortex structures. In addition, due to the inflow air interaction, the shear layer was gently extended and oscillated, increasing the mass transfer through the shear layer. While the fuel was normally injected toward the roof-plate in the recirculation region, it was scattered near the roof-plate. Some fuel was intruded into the main flow and others were widely dispersed downstream in the recirculation region. Needless to say, it is important that the injector location is placed in the recirculation region because the fuel remnant in the recirculation is
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Fig. 1. Schematic diagram of laboratory-scaled supersonic wind tunnel.
dependent on the injector position [16]. For such considerations, in this study, an injector was additionally mounted at a place which would be less affected by the vent slot mixer to compare with the mixing characteristics of the previous experiment with respect to the injector location. In addition, turbulent parameters influencing the micro-scale mixing performance were investigated using a stereoscopic-PIV (particle image velocimetry) method. 2. Experimental setup A laboratory-scaled supersonic wind-tunnel is presented in Fig. 1. A suction-type supersonic wind-tunnel was attached to the vacuum tank of 8 m3 . It is composed of a nozzle part, an isolator part and a test section. In this experimental study, non-reacting experiments were conducted to study mixing characteristics of a new mixer model compared with other mixer models [9,13]. Atmospheric air ( P 0 = 100 kPa, T 0 = 286 K) in the laboratory was inhaled and accelerated through a Mach 2 half nozzle. Several mixer models, injection ports, a plasma torch, and pressure ports were embedded in the lower wall. The isolator was a rectangular duct of 50 mm long, 30.7 mm high and 30 mm wide, and the test section was 210 mm long by 36.7 mm high with the same width. The unit Reynolds number at the mixer model was approximately 6.6 × 105 m. The side windows were comprised of Pyrex® glass and a Quartz window was used in the upper wall in order to pass the laser sheet. Two mixer models were used; one was a reference model (the step mixer) and the other was the vent slot mixer [14]. The vent slot mixer had 2 mm wide slot in the middle of the roof-plate, 2 mm thick by 6 mm long, extended from the step mixer of 6 mm height. To discern the difference of the mixing and the flow structure according to the injector location, two injection ports were located at 2 mm (injector 1) and 9 mm (injector 2) from the step wall, respectively. Pressure measurement and gas sampling were conducted through two port arrays which existed separately at 22 mm (span 1) and 30 mm (span 2) downstream from the step wall as shown in Fig. 2. Each port array had five holes with 5 mm interval. The wall pressure and the injection pressure were acquired using strain-gauge type pressure transducers, PDCR23D-200 psi (Scanivalve, Inc.) with ±1% accuracy and PABA200KP (Kyowa, Inc.) with ±2% accuracy, respectively. From the same port arrays, the gas was sampled using tubes of 2 mm diameter for 10 s, and then stored in small vacuum bottles. The sampled gas was examined with the gas chromatograph (CP-4900 Micro-GC: Varian, Inc.). The calculated uncertainty was less than 1% for N2 and 6% for O2 and H2 . Schlieren and stereoscopic-PIV techniques were utilized to visualize the flow structures. For the schlieren method, the light source was a stroboscope lamp of 180 ns pulse time and the images were captured by a digital camera, Cannon EOS-D30.
Fig. 2. Experimental measurement systems.
The stereoscopic-PIV system in Fig. 2 was available by the Scheimpflug condition [17] to view clear velocity fields and turbulent structures in the y–z cross-plane. Our previous studies have demonstrated calibration works about the stereoscopic-PIV system in detail [13,18,19]. The light source was a double-pulsed Nd:YAG laser (532 nm; 12 mJ pulse; pulse width 5–7 ns; Y12-15E: TSI, Inc.), which was modified to a laser sheet of 1.5 mm thick and 50 mm wide through cylindrical lenses. A pulse generator was used to synchronize the laser signals with two CCD (chargecoupled device) cameras (1600 × 1200 pixels; 28.77 μm square pixels resolution) with a Scheimpflug lens mount of Nikon PCMicro 85 mm − f /2.8 lens. The interrogation window size was 33 × 33 pixels. Each tilt angle of the CCD cameras relative to the image plane was 30 degrees and the Scheimpflug lens mount was adjusted angularly to clear the images. The commercial software FtrPIV (Flowtech Research, Inc.) controlled the whole arrangement about the stereoscopic-PIV measurement. Droplets of dioctylsebacate (density 913.5 kg/m3 ) were added to working gas (air) by the Laskin nozzle; the mean diameter of the trace particles was of 1 μm [20]. With the correction method [19] based on the Basset–Bousinesq–Oseen equation [21], the Stokes drag coefficient was evaluated to confirm the flow tracer fidelity of the particle in the supersonic flow. In previous researches [19,20], the order of the Stokes number was approximately 10−1 for the normal injection in the
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Fig. 3. Schlieren visualization snapshots: (a) the step mixer without injection, (b) the step mixer for J = 1.6 from injector 1, (c) the step mixer for J = 1.6 from injector 2, (d) the step mixer for J = 3.1 from injector 1, (e) the step mixer for J = 3.1 from injector 2, (f) the vent slot mixer without injection, (g) the vent slot mixer for J = 1.6 from injector 1, (h) the vent slot mixer for J = 1.6 from injector 2, (i) the vent slot mixer for J = 3.1 from injector 1, and (j) the vent slot mixer for J = 3.1 from injector 2.
supersonic flow. The response time of the particle was roughly to be 10 μs in supersonic flow (500 m/s). In case of abrupt change of the velocity gradient and particle accumulation, the flow tracking accuracy of the particles largely decreases and the noise level increases. For this reason, to avoid the flow tracking disturbances due to shock waves and collisions, the laser sheet location, x = 24 mm from the step wall, was selected after several preliminary tests. A sequence of 600 image pairs obtained by the two CCD cameras were calculated through the post-processing work with the software FtrPIV. Previous uncertainty analysis [18] indicated that the error was about 3% for u-velocity and 1.5% for v-velocity and w-velocity. Here, the number of image pairs was adequate to calculate the mean velocities but insufficient to evaluate the turbulent components [22]; hence, the turbulent properties were qualitatively displayed in this article. In this study, three gases such as, helium, hydrogen and air were exploited as injectant and their conditions are listed in Table 1. Helium gas was used to depict the schlieren image of the flowfield in the mixing experiment. For the stereoscopic-PIV, the momentum flux ratio ( J ) was limited as J = 1.6 because the seeding particles of the dioctyl-sebacate were easily agglutinated to contaminate the side window. For the same momentum flux ratio J = 1.6, the gas sampling using hydrogen gas was conducted to compare with the velocity images obtained from the stereoscopic PIV.
Table 1 Injection conditions. Injectant
P [kPa]
J
R [J/Kg K]
γ
Helium
138 272
1.6 3.1
2077
1.7
Hydrogen
152
1.6
4124
1.4
Air
152
1.6
287
1.4
3. Results and discussions Instantaneous schlieren images are displayed for J = 1.6 in Fig. 3. The schlieren images of the step mixer are used to compare with those of the vent slot mixer for the injector location. In Fig. 3a, upstream boundary is separated at the edge of the step mixer. The expansion fan is observed as a dark fan shape. A dark thick line is the shear layer which scatters near the bottom wall. The accelerated flow through the expansion fan decreases by shock structures which are combined to be the recompression shock. When the helium is injected from the injector 1 for J = 1.6, the injectant passes through the shear layer which produces the bow shock in Fig. 3b. Some injectant also remains and mixes with the air in the downstream layer. The interruption by the bow shock generates large eddy structures in the downstream
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Fig. 4. Pressure distributions along span 1: (a) the step mixer with injector 1, (b) the step mixer with injector 2, (c) the vent slot mixer with injector 1, and (d) the vent slot mixer with injector 2.
layer, contributing to the inflected shock structures in the vicinity of the downstream layer. Compared with the injector 1 case in Fig. 3b, the bow shock developed by the injector 2 can be clearly seen in Fig. 3c. This is because the injectant from the injector 2 is little affected by the expansion fan. As a result, the interference of the bow shock has large effect on the wave motion of the downstream layer. Large-scale vortex structures are also observed in the downstream region, which creates the shock structures. In the schlieren images, the penetration of the injectant increases as the injection location is close to the wall of the step mixer. While the injection occurs in the recirculation region, the formation of the large eddy structures in the downstream layer is sensitive to the relative interaction between the bow shock by the injection and the expansion fan generated from the step mixer. The vent slot mixer has the slot on the roof-plate. From the slot, a small expansion fan (expansion fan 1) and an oblique shock is generated in Fig. 3f. With respect to the step mixer, weak shocks can be visible along the shear layer, which was studied with CFD in my previous research [13]. The main flow can be entrained into the recirculation region through the slot, which interacts with the shear layer. This disturbance of the shear layer contributes to developing many weak shocks, decreasing the pressure loss by the recompression shock. The position of the injection 1 induces the impingement of the injectant against the roof-plate, as can be seen in Fig. 3g. For J = 1.6, the shape of the expansion fan 1 is indistinct because the injectant is permeated into the main flow through the slot, leading to developing the shock structures by the flow interference and affecting the flow structure in the vicinity of the slot. The weak shocks are widely distributed, resulting to decreasing the recompression shock strength. The injector 2 has little effect on the upstream flow structures of the vent slot mixer in Fig. 3h. The bow shock formed by the injection can be found
on the shear layer behind of the roof-plate, thickening the downstream layer. Many shocks are also originated from the large-scale vortical structures in the downstream layer. As the injection rate increases from J = 1.6 to J = 3.1, for the step mixer with the injector 1, the bow shock moves upstream, which can be captured at the edge of the step mixer in Fig. 3d. The bow shock (white line) made by the injection is the threedimensional structure and the expansion fan at the edge of the step mixer is the two-dimensional structure. Thus, the two flow structures are overlapped and are not clearly distinguished in the schlieren image. For the injector 2, the bow shock becomes strong and the downstream layer is thick; hence, the root of the recompression shock is unclear and weak winding shocks are detected in Fig. 3e. In case of the vent slot mixer, the injectant from the injector 1 intrudes through the slot into the main flow, so the bow shock can be clearly perceived in Fig. 3i. Interestingly, the outline of the shear layer is parallel to the main flow direction, attributing to the disappearance of the shock structures. In Fig. 3j, the bow shock is stronger due to the injection rate increase and approaching to the oblique shock. By the disturbance of the bow shock, the downstream layer is strongly undulating, causing to the wavy shock structures. Moreover, for the injector 1 case, as the penetration trajectory is independent of the injectant molecular weight [23], the flowfield formed by the He gas injection shows little difference compared with that of H2 gas injection in the previous work [14]. The pressure distribution measured from the span 1 is displayed in Fig. 4. When the injectant is emitted, for the step mixer with the injector 1, the pressure around z = 0 mm corresponding to the injector position decreases due to the flow velocity of the jet plume. Except the center region, other pressure pattern is little modified by the injection rate in Fig. 4a. For the injector 1
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Fig. 5. Local equivalence ratio profiles: (a) sampling data measured from span 1, and (b) sampling data measured from span 2.
case, the jet plume size is thus restricted although the injection rate increases. Furthermore, in the schlieren images in Fig. 3b and 3d, the recompression shock shape is not altered, despite the injection rate increases. As the injection place is changed from the injector 1 to the injector 2, the pressure difference between the center and outer region becomes large in Fig. 4b. As the injection rate increases, the pressure of the outer place of z = ±10 mm is slightly raised because the perturbation by the bow shock affects the growth of the circumferential shear layer and the recompression shock becomes also unclear, as shown in Figs. 3c and 3e. For the vent slot mixer with the injector 1, interestingly, the pressure is gradually recovered with the injection rate growth in Fig. 4c. Furthermore, the pressure distribution is very uniform along the spanwise direction. It is thus considered that the jet plume is broken due to the collision of the injectant on the roof-plate. As the injection rate increases, the plateau pressure is gradually growing. In contrast, the injection from the injector 2 is not interacted with the vent slot mixer, as depicted in Figs. 3h and 3j, thus the jet plume tends to be created, leading to the pressure drop around the center region in Fig. 4d. In the outer region of z = ±10 mm, the pressure is recovered as the injection rate rises from J = 1.6 to J = 3.1, which is similar with the pressure values in the outer region of z = ±10 mm in Fig. 4c. In Fig. 3j, the bow shock appears to be close to the oblique shock, so it can be considered that the injectant intruding into the main flow is disturbed by the oblique shock, which is thickening the downstream shear layer. In comparison, the pressure recovery rate of the vent slot mixer based on the no injection case is higher than that of the step mixer. Therefore, it is believed that the injectant dispersion for higher injection has effect on the pressure recovery in the recompression region behind the mixer. For global equivalence ratio Φ = 0.02 ( J = 1.6), local equivalence ratio obtained along the span 1 is plotted in Fig. 5a. Note that the hydrogen injection rate is limited as Φ = 0.02 for the safety reason. Most cases show Gaussian distribution of the local equivalence ratio except the vent slot mixer with the injector 1. Fuel rich (Φ > 1) region is concentrated around z = 0 mm corresponding to the injection position, whereas other region is fuel lean (Φ < 1). For the step mixer, despite the difference of the downstream flow structure in Figs. 3b and 3c, the injector location has little effect on the fuel distribution on the bottom wall. On the other hand, the vent slot mixer with the injector 1 shows the plateau distribution above the peak value of the local equivalence ratio of the step mixer along the spanwise direction. This is because the interaction of the injectant from the injector 1 with the vent slot mixer enhances holding and dispersing the fuel toward the spanwise di-
rection with the fuel rich condition. For the injector 2, the injectant is directly injected into the main flow, as shown in Fig. 3h, which is little influenced by the vent slot mixer. In this sense, for the vent slot mixer, the equivalence ratio distribution of the injector 2 is lower than that of the injector 1. However, the local equivalence ratio of the vent slot mixer with the injector 2 in the outer region beyond z = ±5 mm shows somewhat higher values compared with the step mixer. It is considered that the inflow air from the vent slot mixer influences the injection and the injectant is also disturbed by the oblique shock, as seen in Fig. 3h. Thus the injectant can be dispersed toward the spanwise downstream layer. In the farfield region (span 2), the remnant fuel in the mixing layer is highly reduced and the local equivalence ratio of the step mixer shows the same distribution pattern regardless of the injector position in Fig. 5b. For the vent slot mixer, the injector 1 case still holds some fuel of approximately Φ = 0.4, and then the injector 2 shows lower local equivalence ratio distribution. Therefore, the fuel distribution pattern in the farfield region is significantly dependent on the fuel concentration in the upstream mixing region, which is also well matched with the reference [24]. Normalized velocity contour with velocity vectors is illustrated in Fig. 6. Due to the physical problem, the agglutination of the droplet seeding particle, the stereoscopic-PIV measurement can be applied only for the case of the injector 2 for J = 1.6. Note that black lines of Mach number 1 and 0.5 are used as reference lines which are displayed in the following images processed from the stereoscopic PIV data. The separation between the main flow and the shear layer (or jet plume) is based on the sonic line, i.e., Mach number is unity. For the step mixer in Fig. 6a, most of the velocity vectors in the main flow toward the bottom wall because the cross plane is located in the expansion region, referring to the flowfield near the span 1 in Fig. 3c. The velocity vector direction is initially changed through the bow shock and then modified along the peripheral region of the jet plume. Moreover, two circulation vortex configurations are symmetrically observed at the center axis of z = 0 mm, which is well known as the counter-rotating vortex pair. Although the sonic line is connected between the jet plume and the circumferential shear layer, the inner flow along M = 0.5 line is hardly circulated between the two regions. As a result, most injectant appears to be held in the jet plume from z = −5 mm to 5 mm and is hard to disperse toward the spanwise direction, which is well matched with the distribution of the local equivalence ratio in Fig. 5a. In contrast, for the vent slot mixer in Fig. 6b, it is difficult to discern the bow shock referring the velocity vectors due to the disturbance of the complex shock structure, as depicted in Fig. 3h. The counter-rotating vortex pair also can be seen in the jet plume and the circumferential shear layer appears to be thick which is in accordance with a half of the jet plume height. The ve-
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Fig. 6. Normalized velocity and vector fields: (a) u velocity and vector field of the step mixer, (b) u velocity and vector field of the vent slot mixer, (c) v velocity and vector field of the vent slot mixer, and (d) w velocity and vector field of the vent slot mixer.
locity vortex is moving down along the periphery of the jet plume and is separated into two regions: the jet plume and the circumferential shear layer. For this reason, the injectant in the jet plume can be run into the circumferential shear layer. The inner flow in the core region of the jet plume proceeds downstream with the high velocity of M = 0.5, but the u-velocity close to the bottom wall under the shear layer tends to be zero. On the other hand, the v-velocity field is well developed in the circumferential shear layer (red color contour), which tends to be affected by not only the counter-rotating vortex pair but also the inflow air from the vent slot mixer. The development of w-velocity component in the main flow is sensitive to the bow shock. The w-velocity field adjacent to the jet plume is symmetrically distributed according to the counter-rotating vortex pair. Furthermore the circulation motion by the counter-rotating vortex pair attributes to developing the w-velocity field. The normalized vorticity field is displayed in Fig. 7. For the normal injection, the vorticity, which is mathematically expressed by the curl of the velocity, proceeds spirally down-stream [24,25]. In this sense, the vorticity core is important factor to quantify the magnitude and position of the vortex structure in the y–z cross plane. With the vortex filament model [26], it is possible to derive the vorticity core from a few tangential velocity measurements in the vortex field. The peak value of the velocity profiles, extracted from three axes at z = −1 mm, 0 mm, and 1 mm in Fig. 7, respectively, indicates approximately y = 2.5 mm in Fig. 8. In addition, the two dimensional coordinates of the two vorticity cores can be acquired by calculating the path-line, as shown in Fig. 7, which are approximately ( y , z) = (2.7 mm, −2 mm) and (2.7 mm, 1.9 mm). The vorticity magnitude is naturally maximized at the vorticity core and the v-velocity distribution is symmetric with respect to
Fig. 7. Normalized vorticity contour.
the each vorticity core in Fig. 9. The counter-rotating vortex pair composed of the two vorticity cores appears to be filled in the jet plume. Therefore, the vorticity core is believed to be treated as the jet plume center, which is analogous to a half of the jet plume height. Turbulent quantities used in this work such as Reynolds stress and turbulence kinetic energy is referred to the reference [27]. For turbulent statistical analysis, the velocity u˜ i is decomposed into the mean velocity u i and the velocity fluctuation u i , depicted by:
u˜ ı = u i + u i
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Fig. 8. V -velocity profiles along z = 1 mm, 0 mm, and −1 mm axes.
The Reynolds stress is designated by the symbol
τi j and given
by:
τi j ∼ = −ρ u ı u j Time-averaged variable is expressed with over bar symbol. The right term −ρ u ı u j is mathematically derived as a consequence of time-averaging the xi -momentum transport equation for turbulence. Note that time variation of density is ignored in the exper-
Fig. 9. V -velocity and vorticity profiles along y = 2.7 mm axis.
iment work. The isotropic components (u 2 , v 2 , and w 2 ) of τi j are normal stresses. The summation of these normal stresses is called as the turbulent kinetic energy. These normal stresses exchange kinetic energy between the mean flow and the turbulent velocity fluctuation. On the contrary, the anisotropic components (−u v , −u w , and − v w ) of τi j are shear stresses, which causes the mean momentum transfer by turbulent motion. Here, the u 2 contour is mainly visible along the M = 1 line (sonic line) in Fig. 10a. The upper region of the jet plume is di-
Fig. 10. Normal stress contours: (a) normalized u 2 contour, (b) normalized v 2 contour, and (c) normalized w 2 contour.
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Fig. 11. Turbulent kinetic energy contour. (For interpretation of the colors in this figure, the reader is referred to the web version of this article.)
rectly exposed to the supersonic flow, leading to the high velocity difference between the main flow and the inner flow of the jet plume. In this regard, the velocity difference induces the streamwise flow oscillation associated to the u 2 intensity adjacent to the upper region of the jet plume. The u 2 is well distributed around the circumferential shear layer with the same reason. The v 2 is highly contoured under the jet plume in Fig. 10b. The v-velocity in the jet plume is mainly related to the counter-rotating vortex pair, thus the v-velocity fluctuation occurs actively along the spiral mo-
257
tion of the counter-rotating vortex pair. However, the v 2 intensity is weak along the center line of z = 0 mm close the bottom wall due to the low velocity disturbance. In contrast to the v 2 contour, the w 2 contour in Fig. 10c is illustrated like an alphabet ‘U ’. In the jet plume, downwash flow of the counter-rotating vortex pair is impinged on the bottom wall and w-velocity in Fig. 6d is activated, increasing the w-velocity fluctuation w 2 . Moreover, as shown in Fig. 6d, the velocity vector is accumulated and disturbed in the vicinity of the hollow region between the jet plume and the circumferential shear layer, attributing to the development of the w 2 . Compared with the three normal stresses, the u 2 is generally developed around the jet plume and the shear layer, and then the v 2 and the w 2 appear comparatively around the jet plume. For that reason, the turbulent kinetic energy consisted of the three normal stresses is highly distributed in the periphery of the jet plume, which looks like a horse shoe in Fig. 11. In the end, the source of the turbulent kinetic energy is primarily originated from the interaction between the main flow (supersonic flow) and the jet plume, contributing to the active micro-scale mixing of the injectant and the air. In Fig. 12a, the −u v is generally found in the vicinity region of M = 1 and 0.5 lines. The high intensity of the −u v indicates that the turbulent momentum transfer is vigorous. In similar with the u 2 development in Fig. 10a, the −u v is significantly strengthened around the top area of the jet plume, which is expanded into the adjacent main flow due to the turbulent momentum transfer. The −u w contour in Fig. 12b is symmetrically observed along the periphery of the jet plume, which is analogous to the downwash
Fig. 12. Shear stress contours: (a) normalized −u v contour, (b) normalized −u w contour, and (c) normalized − v w contour.
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flow along the outside of the jet plume in Fig. 6c. The momentum transfer (or mass exchange) along the side region of the jet plume is dominated by the −u w term. In Fig. 12c, the − v w contour is very weak compared with other shear stress terms. In comparison, the −u w and the − v w are weakly contoured near the side periphery of the jet plume, and their magnitude is relatively weak. Therefore, it can be considered that the u 2 and the u v have significant influence on the turbulence generation and the momentum transfer (or mass exchange) around the jet plume. 4. Conclusions Mixing experiments supported by various measurement methods were carried out to understand the effect of the injector location for the vent slot mixer in a Mach 2 supersonic main flow. For the selection of two injector positions, one (injector 1) was located under the vent slot mixer, and the other (injector 2) was equipped behind the vent slot mixer. Flow and turbulent structures were visualized by using schlieren photography and stereoscopic particle image velocimetry. Furthermore, the wall pressure and the gas concentration were measured to compare with the flowfield visualization images. In the case of the injector 1 case, the injectant impinges on the roof plate of the vent slot mixer, which is dispersed widely toward spanwise direction. The local equivalence ratio in relation to the mixing characteristics shows the uniform distribution. As the injection rate increases, the pressure pattern is evenly recovered and shock structures originated from the recompression region disappear. In other words, the mixing layer behind the vent slot mixer is widely thick, approaching the height of the mixer. On the other hand, in the case of the injector 2 case, the injectant is slightly sensitive to the vent slot mixer. Each distribution of the pressure and local equivalence ration is similar with that of the step mixer, respectively. Although the difference is not noticeable, the mixing performance is improved in the shear layer adjacent to the jet plume, compared with the step mixer. In the velocity field of the vent slot mixer with the injector 2, the flowfield such as velocity components and vectors in the periphery of the jet plume is dominantly dependent on the counterrotating vortex pair. The shear layer in the vicinity of the jet plume is well developed by the vent slot mixer and is combined with the jet plume. As such, the injectant in the jet plume can be supplied into the circumferential shear layer. The u 2 and u v among turbulent intensities play major role in turbulent generation and momentum transfer. Particularly, turbulent motion corresponding to the micro-scale mixing is significantly activated along the boundary layer (sonic line) between the supersonic main flow and the jet plume. Conflict of interest statement No conflict of interest. Acknowledgements Authors appreciate for the technical and material supports of Prof. Goro Masuya and his staffs in Tohoku University, Japan. Financial support from the Advanced Research Center Program (NRF-2013R1A5A1073861) through the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) contracted through Advanced Space Propulsion Research Center at Seoul National University was appreciated. Author ISJ person-
ally supported by the Brain Korea 21 Plus Program through the National Research Foundation of Korea (NRF) by the Korea government (MOE, the Ministry of Education), and NALDA project by the Korea government (MOLIT, the Ministry of Land, Infrastructure and Transport). References [1] W.H. Heiser, D.T. Pratt, D.H. Daley, U.B. Mehta, Hypersonic Airbreathing Propulsion, American Institute of Aeronautics and Astronautics, Washington DC, 1994. [2] R. Daines, C. Seagal, Combined rocket and airbreathing propulsion systems for space-launch applications, J. Propuls. Power 14 (5) (1998) 605–612. [3] F.S. Billig, Research on supersonic combustion, J. Propuls. Power 9 (4) (1993) 499–514. [4] J.M. Seiner, S.M. Dash, D.C. Kenzakowski, Historical survey on enhanced mixing in scramjet engines, J. Propuls. Power 17 (6) (2001) 1273–1286. [5] A.D. Rothstein, P.J. Wantuck, A Study of the normal injection of hydrogen into a heated supersonic flow using planar laser-induced fluorescence, AIAA 1992-3423. [6] W. Huang, L. Yan, Progress in research on mixing techniques for transverse injection flow fields in supersonic crossflows, J. Zhejiang Univ. Sci. A 14 (8) (2013) 554–564. [7] A. Roshko, G.J. Thomke, Observations of turbulent reattachment behind an axisymmetric downstream-facing step in supersonic flow, AIAA J. 4 (6) (1996) 975–980. [8] E. Loth, K. Kailasanath, R. Lohner, Supersonic flow over an axisymmetric backward-facing step, J. Spacecr. Rockets 29 (3) (1992) 352–359. [9] C.-H. Kim, I.-S. Jeung, B. Choi, T. Kouchi, G. Masuya, Effect of fuel injection location on a plasma jet assisted combustion with a backward-facing step, Proc. Combust. Inst. 33 (2011) 2375–2382. [10] P.K. Tang, W.A. Sirignana, Theory of a generalized Helmholtz resonator, J. Sound Vib. 26 (2) (1973) 247–262. [11] J.C. Doster, P.I. King, M.R. Gruber, C.D. Carter, M.D. Ryan, K.-Y. Hsu, In-stream hypermixer fueling pylons in supersonic flow, J. Propuls. Power 25 (4) (2009) 885–901. [12] T. Sunami, K. Itoh, K. Sato, T. Komuro, Mach 8 ground tests of the hypermixer scramjet for HyShot-IV, flight experiment, AIAA 2006-8062. [13] C.-H. Kim, I.-S. Jeung, B. Choi, T. Kouchi, G. Masuya, Flowfield characteristics of a hypermixer interacting with transverse injection in supersonic flow, AIAA J. 50 (8) (2012) 1742–1753. [14] C.-H. Kim, K. Sung, I.-S. Jeung, B. Choi, T. Kouchi, G. Masuya, Flowfield characteristics on a vent slot mixer in supersonic flow, Shock Waves 20 (6) (2010) 559–569. [15] W.J. Thayer, R.C. Corlett, Gas dynamic and transport phenomena in the twodimensional jet interaction flowfield, AIAA J. 10 (4) (1972) 488–493. [16] A. Thakur, C. Segal, Concentration distribution in a supersonic flow recirculation region, J. Propuls. Power 24 (1) (2008) 64–73. [17] A.K. Prasad, K. Jensen, Scheimpflug stereocamera for particle image velocimetry in liquid flows, Appl. Opt. 34 (30) (1995) 7092–7099. [18] S. Uramoto, S. Tsuru, T. Kouchi, G. Masuya, Stereoscopic PIV measurement of supersonic injection flowfield and its error analysis, in: Asian Joint Conference on Propulsion and Power, 2010, pp. 733–740. [19] S. Koike, H. Takahishi, K. Tanaka, M. Hirota, K. Takita, G. Masuya, Correction method for particle velocimetry data based on the stokes drag law, AIAA J. 45 (11) (2007) 2770–2777. [20] S. Koike, K. Suzuki, E. Kitamura, M. Hirota, K. Takita, G. Masuya, M. Matsumoto, Measurement of vortices and shock waves produced by ramp and twin jets, J. Propuls. Power 22 (5) (2006) 1059–1067. [21] S.L. Soo, Fluid Dynamics of Multiphase Systems, Blaisdell Pub. Co, Waltham, MA, 1967. [22] S. Tsuru, S. Uramoto, T. Kouchi, G. Masuya, Stereoscopic PIV measurement of supersonic flow with normal injection, in: Proceedings of the 2010 Annual Meeting and the Eleventh Symposium on Propulsion System for Reusable Launch Vehicles, Sendai, Japan, 2010. [23] E.E. Zukoski, F.W. Spaid, Secondary injection of gases into a supersonic flow, AIAA J. 2 (10) (1964) 1689–1696. [24] W. Huang, S. Li, L. Yan, Z. Wang, Performance evaluation and parametric analysis on cantilevered ramp injector in supersonic flows, Acta Astron. 84 (2013) 141–152. [25] A.E. Perry, M.S. Chong, Topology of flow patterns in vortex motions and turbulence, Appl. Sci. Res. 53 (1994) 357–374. [26] R. Fearn, R.P. Weston, Vorticity associated with a jet in a cross flow, AIAA J. 12 (12) (1974) 1666–1671. [27] H. Tennekes, J.L. Lumley, A First Course in Turbulence, MIT Press, Cambridge, MA, 1972.
Contents lists available at ScienceDirect
Aerospace Science and Technology www.elsevier.com/locate/aescte
Mixing characteristics of vent slot mixer in supersonic flow Chae-Hyoung Kim a , In-Seuck Jeung b,∗ a b
Engine Test and Evaluation Team, Korea Aerospace Research Institute, Daejeon 34133, Republic of Korea Department of Mechanical and Aerospace Engineering, Institute of Advanced Aerospace Technology, Seoul National University, Seoul 08826, Republic of Korea
a r t i c l e
i n f o
Article history: Received 23 April 2015 Received in revised form 3 October 2015 Accepted 7 December 2015 Available online 14 December 2015 Keywords: Vent slot mixer Stereoscopic PIV Counter-rotating vortex pair Turbulent structure
a b s t r a c t Non-reacting experiments were performed to show the mixing characteristics of the vent slot mixer by the injector location in Mach 2 supersonic flow. As the injectant such as hydrogen, helium, and air was injected into the supersonic main flow, flow structures were visualized by schlieren photography and stereoscopic particle image velocimetry. Pressure measurement and gas sampling were conducted in order to compare with their flowfield visualization. The mixing performance is highly sensitive to the injection position of the vent slot mixer. While the injection occurs under the vent slot mixer, the remnant injectant is evenly distributed toward the spanwise direction. In the meantime, the injection behind the vent slot mixer generates the jet plume containing a counter-rotating vortex pair which mainly affects the velocity field and turbulent motion around the jet plume. In the case of the vent slot mixer, because the jet plume is combined with the nearby shear layer, the injectant in the jet plume can be supplied into the nearby shear layer. © 2015 Elsevier Masson SAS. All rights reserved.
1. Introduction The supersonic combustion engine is a key to design hypersonic vehicle such as scramjet (supersonic combustion ramjet) engine and RBCC (Rocket Based Combined Cycle) engine [1–3]. However, it is believed to be very difficult to develop the supersonic combustion engine. The residence time of the fuel injectant is very short, resulting in not being well-mixed and not surely-ignited in the supersonic flow. Due to such difficulties, various mixing methods have been proposed during the last few decades [4]. Among them, transverse injection from a flat plate has the simplest configuration and induces an aerodynamic barrier, which is a bow shock, to give a chance of mixing fuel and air in the jet plume [5,6]. With the transverse injection, physical mixer models installed in the supersonic flow can enhance the mixing performance. Typically, step mixers have been extensively studied with an objective of extending the residence time of the fuel–air mixture with the simple configuration [7–9]. Upstream boundary layer is separated at the edge of the step mixer, creating the recirculation region behind the step mixer. If the fuel is injected in the recirculation region, the injectant can be sustained and slightly mixed in the recirculation region. However, because the step mixer indicates poor mass transfer in the recirculation region [8], a stirring device is required to mix the fuel–air mixture at macro- and micro-levels
*
Corresponding author. E-mail address: [email protected] (I.-S. Jeung).
http://dx.doi.org/10.1016/j.ast.2015.12.011 1270-9638/© 2015 Elsevier Masson SAS. All rights reserved.
in the recirculation region. For example, Helmholtz resonators [10] generate an acoustic oscillation and hyper mixers [11–13] composed of wedges and ramps produce streamwise vortices by pressure gradient. Based on these considerations, a new mixer model, vent slot mixer, was suggested in a previous work [14]. The step mixer was used to create a recirculation region which was augmented by adding an extended roof-plate at upper region of the step mixer. With the “well mixed” model [15], an active method for supplying air into the fuel–air mixing region was suggested by using a slot on the roof-plate. The main flow is considered to be entrained into the recirculation region through the slot due to the pressure gradient between the main flow and the recirculation region. Furthermore, the interaction of the inflow air in the recirculation region tends to induce some turbulent flow structures. This kind of the flow mechanism by the vent slot mixer was simulated with CFD (Computational Fluid Dynamics) analysis [14]. The inflow air through the slot into the recirculation region generated complex flow structures such as circulation bubbles and large-scale vortex structures. In addition, due to the inflow air interaction, the shear layer was gently extended and oscillated, increasing the mass transfer through the shear layer. While the fuel was normally injected toward the roof-plate in the recirculation region, it was scattered near the roof-plate. Some fuel was intruded into the main flow and others were widely dispersed downstream in the recirculation region. Needless to say, it is important that the injector location is placed in the recirculation region because the fuel remnant in the recirculation is
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Fig. 1. Schematic diagram of laboratory-scaled supersonic wind tunnel.
dependent on the injector position [16]. For such considerations, in this study, an injector was additionally mounted at a place which would be less affected by the vent slot mixer to compare with the mixing characteristics of the previous experiment with respect to the injector location. In addition, turbulent parameters influencing the micro-scale mixing performance were investigated using a stereoscopic-PIV (particle image velocimetry) method. 2. Experimental setup A laboratory-scaled supersonic wind-tunnel is presented in Fig. 1. A suction-type supersonic wind-tunnel was attached to the vacuum tank of 8 m3 . It is composed of a nozzle part, an isolator part and a test section. In this experimental study, non-reacting experiments were conducted to study mixing characteristics of a new mixer model compared with other mixer models [9,13]. Atmospheric air ( P 0 = 100 kPa, T 0 = 286 K) in the laboratory was inhaled and accelerated through a Mach 2 half nozzle. Several mixer models, injection ports, a plasma torch, and pressure ports were embedded in the lower wall. The isolator was a rectangular duct of 50 mm long, 30.7 mm high and 30 mm wide, and the test section was 210 mm long by 36.7 mm high with the same width. The unit Reynolds number at the mixer model was approximately 6.6 × 105 m. The side windows were comprised of Pyrex® glass and a Quartz window was used in the upper wall in order to pass the laser sheet. Two mixer models were used; one was a reference model (the step mixer) and the other was the vent slot mixer [14]. The vent slot mixer had 2 mm wide slot in the middle of the roof-plate, 2 mm thick by 6 mm long, extended from the step mixer of 6 mm height. To discern the difference of the mixing and the flow structure according to the injector location, two injection ports were located at 2 mm (injector 1) and 9 mm (injector 2) from the step wall, respectively. Pressure measurement and gas sampling were conducted through two port arrays which existed separately at 22 mm (span 1) and 30 mm (span 2) downstream from the step wall as shown in Fig. 2. Each port array had five holes with 5 mm interval. The wall pressure and the injection pressure were acquired using strain-gauge type pressure transducers, PDCR23D-200 psi (Scanivalve, Inc.) with ±1% accuracy and PABA200KP (Kyowa, Inc.) with ±2% accuracy, respectively. From the same port arrays, the gas was sampled using tubes of 2 mm diameter for 10 s, and then stored in small vacuum bottles. The sampled gas was examined with the gas chromatograph (CP-4900 Micro-GC: Varian, Inc.). The calculated uncertainty was less than 1% for N2 and 6% for O2 and H2 . Schlieren and stereoscopic-PIV techniques were utilized to visualize the flow structures. For the schlieren method, the light source was a stroboscope lamp of 180 ns pulse time and the images were captured by a digital camera, Cannon EOS-D30.
Fig. 2. Experimental measurement systems.
The stereoscopic-PIV system in Fig. 2 was available by the Scheimpflug condition [17] to view clear velocity fields and turbulent structures in the y–z cross-plane. Our previous studies have demonstrated calibration works about the stereoscopic-PIV system in detail [13,18,19]. The light source was a double-pulsed Nd:YAG laser (532 nm; 12 mJ pulse; pulse width 5–7 ns; Y12-15E: TSI, Inc.), which was modified to a laser sheet of 1.5 mm thick and 50 mm wide through cylindrical lenses. A pulse generator was used to synchronize the laser signals with two CCD (chargecoupled device) cameras (1600 × 1200 pixels; 28.77 μm square pixels resolution) with a Scheimpflug lens mount of Nikon PCMicro 85 mm − f /2.8 lens. The interrogation window size was 33 × 33 pixels. Each tilt angle of the CCD cameras relative to the image plane was 30 degrees and the Scheimpflug lens mount was adjusted angularly to clear the images. The commercial software FtrPIV (Flowtech Research, Inc.) controlled the whole arrangement about the stereoscopic-PIV measurement. Droplets of dioctylsebacate (density 913.5 kg/m3 ) were added to working gas (air) by the Laskin nozzle; the mean diameter of the trace particles was of 1 μm [20]. With the correction method [19] based on the Basset–Bousinesq–Oseen equation [21], the Stokes drag coefficient was evaluated to confirm the flow tracer fidelity of the particle in the supersonic flow. In previous researches [19,20], the order of the Stokes number was approximately 10−1 for the normal injection in the
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Fig. 3. Schlieren visualization snapshots: (a) the step mixer without injection, (b) the step mixer for J = 1.6 from injector 1, (c) the step mixer for J = 1.6 from injector 2, (d) the step mixer for J = 3.1 from injector 1, (e) the step mixer for J = 3.1 from injector 2, (f) the vent slot mixer without injection, (g) the vent slot mixer for J = 1.6 from injector 1, (h) the vent slot mixer for J = 1.6 from injector 2, (i) the vent slot mixer for J = 3.1 from injector 1, and (j) the vent slot mixer for J = 3.1 from injector 2.
supersonic flow. The response time of the particle was roughly to be 10 μs in supersonic flow (500 m/s). In case of abrupt change of the velocity gradient and particle accumulation, the flow tracking accuracy of the particles largely decreases and the noise level increases. For this reason, to avoid the flow tracking disturbances due to shock waves and collisions, the laser sheet location, x = 24 mm from the step wall, was selected after several preliminary tests. A sequence of 600 image pairs obtained by the two CCD cameras were calculated through the post-processing work with the software FtrPIV. Previous uncertainty analysis [18] indicated that the error was about 3% for u-velocity and 1.5% for v-velocity and w-velocity. Here, the number of image pairs was adequate to calculate the mean velocities but insufficient to evaluate the turbulent components [22]; hence, the turbulent properties were qualitatively displayed in this article. In this study, three gases such as, helium, hydrogen and air were exploited as injectant and their conditions are listed in Table 1. Helium gas was used to depict the schlieren image of the flowfield in the mixing experiment. For the stereoscopic-PIV, the momentum flux ratio ( J ) was limited as J = 1.6 because the seeding particles of the dioctyl-sebacate were easily agglutinated to contaminate the side window. For the same momentum flux ratio J = 1.6, the gas sampling using hydrogen gas was conducted to compare with the velocity images obtained from the stereoscopic PIV.
Table 1 Injection conditions. Injectant
P [kPa]
J
R [J/Kg K]
γ
Helium
138 272
1.6 3.1
2077
1.7
Hydrogen
152
1.6
4124
1.4
Air
152
1.6
287
1.4
3. Results and discussions Instantaneous schlieren images are displayed for J = 1.6 in Fig. 3. The schlieren images of the step mixer are used to compare with those of the vent slot mixer for the injector location. In Fig. 3a, upstream boundary is separated at the edge of the step mixer. The expansion fan is observed as a dark fan shape. A dark thick line is the shear layer which scatters near the bottom wall. The accelerated flow through the expansion fan decreases by shock structures which are combined to be the recompression shock. When the helium is injected from the injector 1 for J = 1.6, the injectant passes through the shear layer which produces the bow shock in Fig. 3b. Some injectant also remains and mixes with the air in the downstream layer. The interruption by the bow shock generates large eddy structures in the downstream
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Fig. 4. Pressure distributions along span 1: (a) the step mixer with injector 1, (b) the step mixer with injector 2, (c) the vent slot mixer with injector 1, and (d) the vent slot mixer with injector 2.
layer, contributing to the inflected shock structures in the vicinity of the downstream layer. Compared with the injector 1 case in Fig. 3b, the bow shock developed by the injector 2 can be clearly seen in Fig. 3c. This is because the injectant from the injector 2 is little affected by the expansion fan. As a result, the interference of the bow shock has large effect on the wave motion of the downstream layer. Large-scale vortex structures are also observed in the downstream region, which creates the shock structures. In the schlieren images, the penetration of the injectant increases as the injection location is close to the wall of the step mixer. While the injection occurs in the recirculation region, the formation of the large eddy structures in the downstream layer is sensitive to the relative interaction between the bow shock by the injection and the expansion fan generated from the step mixer. The vent slot mixer has the slot on the roof-plate. From the slot, a small expansion fan (expansion fan 1) and an oblique shock is generated in Fig. 3f. With respect to the step mixer, weak shocks can be visible along the shear layer, which was studied with CFD in my previous research [13]. The main flow can be entrained into the recirculation region through the slot, which interacts with the shear layer. This disturbance of the shear layer contributes to developing many weak shocks, decreasing the pressure loss by the recompression shock. The position of the injection 1 induces the impingement of the injectant against the roof-plate, as can be seen in Fig. 3g. For J = 1.6, the shape of the expansion fan 1 is indistinct because the injectant is permeated into the main flow through the slot, leading to developing the shock structures by the flow interference and affecting the flow structure in the vicinity of the slot. The weak shocks are widely distributed, resulting to decreasing the recompression shock strength. The injector 2 has little effect on the upstream flow structures of the vent slot mixer in Fig. 3h. The bow shock formed by the injection can be found
on the shear layer behind of the roof-plate, thickening the downstream layer. Many shocks are also originated from the large-scale vortical structures in the downstream layer. As the injection rate increases from J = 1.6 to J = 3.1, for the step mixer with the injector 1, the bow shock moves upstream, which can be captured at the edge of the step mixer in Fig. 3d. The bow shock (white line) made by the injection is the threedimensional structure and the expansion fan at the edge of the step mixer is the two-dimensional structure. Thus, the two flow structures are overlapped and are not clearly distinguished in the schlieren image. For the injector 2, the bow shock becomes strong and the downstream layer is thick; hence, the root of the recompression shock is unclear and weak winding shocks are detected in Fig. 3e. In case of the vent slot mixer, the injectant from the injector 1 intrudes through the slot into the main flow, so the bow shock can be clearly perceived in Fig. 3i. Interestingly, the outline of the shear layer is parallel to the main flow direction, attributing to the disappearance of the shock structures. In Fig. 3j, the bow shock is stronger due to the injection rate increase and approaching to the oblique shock. By the disturbance of the bow shock, the downstream layer is strongly undulating, causing to the wavy shock structures. Moreover, for the injector 1 case, as the penetration trajectory is independent of the injectant molecular weight [23], the flowfield formed by the He gas injection shows little difference compared with that of H2 gas injection in the previous work [14]. The pressure distribution measured from the span 1 is displayed in Fig. 4. When the injectant is emitted, for the step mixer with the injector 1, the pressure around z = 0 mm corresponding to the injector position decreases due to the flow velocity of the jet plume. Except the center region, other pressure pattern is little modified by the injection rate in Fig. 4a. For the injector 1
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Fig. 5. Local equivalence ratio profiles: (a) sampling data measured from span 1, and (b) sampling data measured from span 2.
case, the jet plume size is thus restricted although the injection rate increases. Furthermore, in the schlieren images in Fig. 3b and 3d, the recompression shock shape is not altered, despite the injection rate increases. As the injection place is changed from the injector 1 to the injector 2, the pressure difference between the center and outer region becomes large in Fig. 4b. As the injection rate increases, the pressure of the outer place of z = ±10 mm is slightly raised because the perturbation by the bow shock affects the growth of the circumferential shear layer and the recompression shock becomes also unclear, as shown in Figs. 3c and 3e. For the vent slot mixer with the injector 1, interestingly, the pressure is gradually recovered with the injection rate growth in Fig. 4c. Furthermore, the pressure distribution is very uniform along the spanwise direction. It is thus considered that the jet plume is broken due to the collision of the injectant on the roof-plate. As the injection rate increases, the plateau pressure is gradually growing. In contrast, the injection from the injector 2 is not interacted with the vent slot mixer, as depicted in Figs. 3h and 3j, thus the jet plume tends to be created, leading to the pressure drop around the center region in Fig. 4d. In the outer region of z = ±10 mm, the pressure is recovered as the injection rate rises from J = 1.6 to J = 3.1, which is similar with the pressure values in the outer region of z = ±10 mm in Fig. 4c. In Fig. 3j, the bow shock appears to be close to the oblique shock, so it can be considered that the injectant intruding into the main flow is disturbed by the oblique shock, which is thickening the downstream shear layer. In comparison, the pressure recovery rate of the vent slot mixer based on the no injection case is higher than that of the step mixer. Therefore, it is believed that the injectant dispersion for higher injection has effect on the pressure recovery in the recompression region behind the mixer. For global equivalence ratio Φ = 0.02 ( J = 1.6), local equivalence ratio obtained along the span 1 is plotted in Fig. 5a. Note that the hydrogen injection rate is limited as Φ = 0.02 for the safety reason. Most cases show Gaussian distribution of the local equivalence ratio except the vent slot mixer with the injector 1. Fuel rich (Φ > 1) region is concentrated around z = 0 mm corresponding to the injection position, whereas other region is fuel lean (Φ < 1). For the step mixer, despite the difference of the downstream flow structure in Figs. 3b and 3c, the injector location has little effect on the fuel distribution on the bottom wall. On the other hand, the vent slot mixer with the injector 1 shows the plateau distribution above the peak value of the local equivalence ratio of the step mixer along the spanwise direction. This is because the interaction of the injectant from the injector 1 with the vent slot mixer enhances holding and dispersing the fuel toward the spanwise di-
rection with the fuel rich condition. For the injector 2, the injectant is directly injected into the main flow, as shown in Fig. 3h, which is little influenced by the vent slot mixer. In this sense, for the vent slot mixer, the equivalence ratio distribution of the injector 2 is lower than that of the injector 1. However, the local equivalence ratio of the vent slot mixer with the injector 2 in the outer region beyond z = ±5 mm shows somewhat higher values compared with the step mixer. It is considered that the inflow air from the vent slot mixer influences the injection and the injectant is also disturbed by the oblique shock, as seen in Fig. 3h. Thus the injectant can be dispersed toward the spanwise downstream layer. In the farfield region (span 2), the remnant fuel in the mixing layer is highly reduced and the local equivalence ratio of the step mixer shows the same distribution pattern regardless of the injector position in Fig. 5b. For the vent slot mixer, the injector 1 case still holds some fuel of approximately Φ = 0.4, and then the injector 2 shows lower local equivalence ratio distribution. Therefore, the fuel distribution pattern in the farfield region is significantly dependent on the fuel concentration in the upstream mixing region, which is also well matched with the reference [24]. Normalized velocity contour with velocity vectors is illustrated in Fig. 6. Due to the physical problem, the agglutination of the droplet seeding particle, the stereoscopic-PIV measurement can be applied only for the case of the injector 2 for J = 1.6. Note that black lines of Mach number 1 and 0.5 are used as reference lines which are displayed in the following images processed from the stereoscopic PIV data. The separation between the main flow and the shear layer (or jet plume) is based on the sonic line, i.e., Mach number is unity. For the step mixer in Fig. 6a, most of the velocity vectors in the main flow toward the bottom wall because the cross plane is located in the expansion region, referring to the flowfield near the span 1 in Fig. 3c. The velocity vector direction is initially changed through the bow shock and then modified along the peripheral region of the jet plume. Moreover, two circulation vortex configurations are symmetrically observed at the center axis of z = 0 mm, which is well known as the counter-rotating vortex pair. Although the sonic line is connected between the jet plume and the circumferential shear layer, the inner flow along M = 0.5 line is hardly circulated between the two regions. As a result, most injectant appears to be held in the jet plume from z = −5 mm to 5 mm and is hard to disperse toward the spanwise direction, which is well matched with the distribution of the local equivalence ratio in Fig. 5a. In contrast, for the vent slot mixer in Fig. 6b, it is difficult to discern the bow shock referring the velocity vectors due to the disturbance of the complex shock structure, as depicted in Fig. 3h. The counter-rotating vortex pair also can be seen in the jet plume and the circumferential shear layer appears to be thick which is in accordance with a half of the jet plume height. The ve-
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Fig. 6. Normalized velocity and vector fields: (a) u velocity and vector field of the step mixer, (b) u velocity and vector field of the vent slot mixer, (c) v velocity and vector field of the vent slot mixer, and (d) w velocity and vector field of the vent slot mixer.
locity vortex is moving down along the periphery of the jet plume and is separated into two regions: the jet plume and the circumferential shear layer. For this reason, the injectant in the jet plume can be run into the circumferential shear layer. The inner flow in the core region of the jet plume proceeds downstream with the high velocity of M = 0.5, but the u-velocity close to the bottom wall under the shear layer tends to be zero. On the other hand, the v-velocity field is well developed in the circumferential shear layer (red color contour), which tends to be affected by not only the counter-rotating vortex pair but also the inflow air from the vent slot mixer. The development of w-velocity component in the main flow is sensitive to the bow shock. The w-velocity field adjacent to the jet plume is symmetrically distributed according to the counter-rotating vortex pair. Furthermore the circulation motion by the counter-rotating vortex pair attributes to developing the w-velocity field. The normalized vorticity field is displayed in Fig. 7. For the normal injection, the vorticity, which is mathematically expressed by the curl of the velocity, proceeds spirally down-stream [24,25]. In this sense, the vorticity core is important factor to quantify the magnitude and position of the vortex structure in the y–z cross plane. With the vortex filament model [26], it is possible to derive the vorticity core from a few tangential velocity measurements in the vortex field. The peak value of the velocity profiles, extracted from three axes at z = −1 mm, 0 mm, and 1 mm in Fig. 7, respectively, indicates approximately y = 2.5 mm in Fig. 8. In addition, the two dimensional coordinates of the two vorticity cores can be acquired by calculating the path-line, as shown in Fig. 7, which are approximately ( y , z) = (2.7 mm, −2 mm) and (2.7 mm, 1.9 mm). The vorticity magnitude is naturally maximized at the vorticity core and the v-velocity distribution is symmetric with respect to
Fig. 7. Normalized vorticity contour.
the each vorticity core in Fig. 9. The counter-rotating vortex pair composed of the two vorticity cores appears to be filled in the jet plume. Therefore, the vorticity core is believed to be treated as the jet plume center, which is analogous to a half of the jet plume height. Turbulent quantities used in this work such as Reynolds stress and turbulence kinetic energy is referred to the reference [27]. For turbulent statistical analysis, the velocity u˜ i is decomposed into the mean velocity u i and the velocity fluctuation u i , depicted by:
u˜ ı = u i + u i
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Fig. 8. V -velocity profiles along z = 1 mm, 0 mm, and −1 mm axes.
The Reynolds stress is designated by the symbol
τi j and given
by:
τi j ∼ = −ρ u ı u j Time-averaged variable is expressed with over bar symbol. The right term −ρ u ı u j is mathematically derived as a consequence of time-averaging the xi -momentum transport equation for turbulence. Note that time variation of density is ignored in the exper-
Fig. 9. V -velocity and vorticity profiles along y = 2.7 mm axis.
iment work. The isotropic components (u 2 , v 2 , and w 2 ) of τi j are normal stresses. The summation of these normal stresses is called as the turbulent kinetic energy. These normal stresses exchange kinetic energy between the mean flow and the turbulent velocity fluctuation. On the contrary, the anisotropic components (−u v , −u w , and − v w ) of τi j are shear stresses, which causes the mean momentum transfer by turbulent motion. Here, the u 2 contour is mainly visible along the M = 1 line (sonic line) in Fig. 10a. The upper region of the jet plume is di-
Fig. 10. Normal stress contours: (a) normalized u 2 contour, (b) normalized v 2 contour, and (c) normalized w 2 contour.
C.-H. Kim, I.-S. Jeung / Aerospace Science and Technology 49 (2016) 250–258
Fig. 11. Turbulent kinetic energy contour. (For interpretation of the colors in this figure, the reader is referred to the web version of this article.)
rectly exposed to the supersonic flow, leading to the high velocity difference between the main flow and the inner flow of the jet plume. In this regard, the velocity difference induces the streamwise flow oscillation associated to the u 2 intensity adjacent to the upper region of the jet plume. The u 2 is well distributed around the circumferential shear layer with the same reason. The v 2 is highly contoured under the jet plume in Fig. 10b. The v-velocity in the jet plume is mainly related to the counter-rotating vortex pair, thus the v-velocity fluctuation occurs actively along the spiral mo-
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tion of the counter-rotating vortex pair. However, the v 2 intensity is weak along the center line of z = 0 mm close the bottom wall due to the low velocity disturbance. In contrast to the v 2 contour, the w 2 contour in Fig. 10c is illustrated like an alphabet ‘U ’. In the jet plume, downwash flow of the counter-rotating vortex pair is impinged on the bottom wall and w-velocity in Fig. 6d is activated, increasing the w-velocity fluctuation w 2 . Moreover, as shown in Fig. 6d, the velocity vector is accumulated and disturbed in the vicinity of the hollow region between the jet plume and the circumferential shear layer, attributing to the development of the w 2 . Compared with the three normal stresses, the u 2 is generally developed around the jet plume and the shear layer, and then the v 2 and the w 2 appear comparatively around the jet plume. For that reason, the turbulent kinetic energy consisted of the three normal stresses is highly distributed in the periphery of the jet plume, which looks like a horse shoe in Fig. 11. In the end, the source of the turbulent kinetic energy is primarily originated from the interaction between the main flow (supersonic flow) and the jet plume, contributing to the active micro-scale mixing of the injectant and the air. In Fig. 12a, the −u v is generally found in the vicinity region of M = 1 and 0.5 lines. The high intensity of the −u v indicates that the turbulent momentum transfer is vigorous. In similar with the u 2 development in Fig. 10a, the −u v is significantly strengthened around the top area of the jet plume, which is expanded into the adjacent main flow due to the turbulent momentum transfer. The −u w contour in Fig. 12b is symmetrically observed along the periphery of the jet plume, which is analogous to the downwash
Fig. 12. Shear stress contours: (a) normalized −u v contour, (b) normalized −u w contour, and (c) normalized − v w contour.
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flow along the outside of the jet plume in Fig. 6c. The momentum transfer (or mass exchange) along the side region of the jet plume is dominated by the −u w term. In Fig. 12c, the − v w contour is very weak compared with other shear stress terms. In comparison, the −u w and the − v w are weakly contoured near the side periphery of the jet plume, and their magnitude is relatively weak. Therefore, it can be considered that the u 2 and the u v have significant influence on the turbulence generation and the momentum transfer (or mass exchange) around the jet plume. 4. Conclusions Mixing experiments supported by various measurement methods were carried out to understand the effect of the injector location for the vent slot mixer in a Mach 2 supersonic main flow. For the selection of two injector positions, one (injector 1) was located under the vent slot mixer, and the other (injector 2) was equipped behind the vent slot mixer. Flow and turbulent structures were visualized by using schlieren photography and stereoscopic particle image velocimetry. Furthermore, the wall pressure and the gas concentration were measured to compare with the flowfield visualization images. In the case of the injector 1 case, the injectant impinges on the roof plate of the vent slot mixer, which is dispersed widely toward spanwise direction. The local equivalence ratio in relation to the mixing characteristics shows the uniform distribution. As the injection rate increases, the pressure pattern is evenly recovered and shock structures originated from the recompression region disappear. In other words, the mixing layer behind the vent slot mixer is widely thick, approaching the height of the mixer. On the other hand, in the case of the injector 2 case, the injectant is slightly sensitive to the vent slot mixer. Each distribution of the pressure and local equivalence ration is similar with that of the step mixer, respectively. Although the difference is not noticeable, the mixing performance is improved in the shear layer adjacent to the jet plume, compared with the step mixer. In the velocity field of the vent slot mixer with the injector 2, the flowfield such as velocity components and vectors in the periphery of the jet plume is dominantly dependent on the counterrotating vortex pair. The shear layer in the vicinity of the jet plume is well developed by the vent slot mixer and is combined with the jet plume. As such, the injectant in the jet plume can be supplied into the circumferential shear layer. The u 2 and u v among turbulent intensities play major role in turbulent generation and momentum transfer. Particularly, turbulent motion corresponding to the micro-scale mixing is significantly activated along the boundary layer (sonic line) between the supersonic main flow and the jet plume. Conflict of interest statement No conflict of interest. Acknowledgements Authors appreciate for the technical and material supports of Prof. Goro Masuya and his staffs in Tohoku University, Japan. Financial support from the Advanced Research Center Program (NRF-2013R1A5A1073861) through the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) contracted through Advanced Space Propulsion Research Center at Seoul National University was appreciated. Author ISJ person-
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