Mixing enhancement via nozzle trailing edge modifications in a high speed rectangular jet

Transcription

1 PHYSICS OF FLUIDS VOLUME 11, NUMBER 9 SEPTEMBER 1999 Mixing enhancement via nozzle trailing edge modifications in a high speed rectangular jet J.-H. Kim and M. Samimy a) Department of Mechanical Engineering, The Ohio State University, Columbus, Ohio Received 20 October 1998; accepted 17 May 1999 An aspect ratio 3 rectangular nozzle with design Mach number 2 was used to investigate the effects of trailing edge modifications on mixing enhancement and to explore the sources of streamwise vorticity at the fully expanded jet Mach numbers 1.75, 2.0, and 2.5. The trailing edge modifications are simple cut-outs in the plane of the nozzle at the nozzle exit. The investigation of mixing and interaction between mixing layers and vortices was performed by the laser sheet illumination technique. Through surface flow visualizations and wall pressure measurements, the investigation of the major source of streamwise vorticity was carried out. In addition, the variation of thrust generated by the nozzle with modified trailing edges was investigated. In the underexpanded flow condition, the major source of streamwise vorticity was determined to be the spanwise surface pressure gradient on the modification. Substantial mixing enhancement was achieved in this flow regime. On the other hand, in the overexpanded flow regime, the role of streamwise vortices in mixing and the source of streamwise vorticity were unclear, and mixing enhancement was not substantial. No measurable thrust loss or gain was obtained for nozzles with trailing edge modifications, regardless of the type of modification American Institute of Physics. S I. INTRODUCTION A review of the characteristics of large-scale structures and their role in mixing was presented by Samimy et al. 1 As was discussed there, it is difficult to control mixing by using spanwise or ringlike vortical structures in highly compressible supersonic mixing layers because of their threedimensionality and lack of organization. In contrast to these large-scale structures, streamwise vortices do not seem to be much affected by compressibility. 2 5 Thus, generating streamwise vortices appears to be an effective way to enhance mixing in supersonic jets. In the past, several techniques have been explored to generate streamwise vortices and to enhance mixing. Tabs, as streamwise vortex generators, were found to be an effective device in reducing jet noise and enhancing mixing in both subsonic and supersonic axisymmetric jets. 3 6 The streamwise vortices generated by half delta-wings resulted in significantly enhanced mixing in Mach number 0.6 circular 7 and rectangular 8 jets. Although the use of tabs or vortex generators to enhance mixing is effective in subsonic and supersonic flows, it results in thrust losses due to the blockage effects of the tabs or vortex generators. 4 An alternative technique for generating streamwise vortices to enhance mixing is the use of trailing edge modifications. Longmire et al. 9 were able to generate streamwise vortices, which resulted in enhanced mixing, in incompressible circular jets by using crown-shaped attachments. Martens et al. 10 showed that mixing in a rectangular supersonic jet a Author to whom correspondence should be addressed. Electronic mail: samimy.1@osu.edu can be significantly enhanced in the underexpanded flow regime by trailing edge modifications. Samimy et al. 1,11,12 furthered the experiments and found that the use of trailing edge modifications enhanced mixing significantly in the underexpanded cases and moderately in the overexpanded cases. The enhanced mixing is most likely related to the generated streamwise vortices, which are responsible for the jet crosssectional deformations. 1,12 Their extended experiments also revealed that the trailing edge modifications which have the cut-out edge parallel to the jet axis, can generate stronger streamwise vortices than those which have oblique edges. However, the modifications did not significantly enhance mixing in the ideally expanded case. The purpose of the present experiments was to find answers to some questions raised in the previous experiments of Samimy et al. 1,11,12 and Kim et al. 13 The questions to be answered are the following: 1 What is the major source of streamwise vorticity?; 2 How does mixing vary with downstream location and with multiple trailing edges?; 3 How do the streamwise vortices develop or evolve with downstream location?; and 4 Is the thrust generated by a jet changed by the trailing edge modification? II. EXPERIMENTAL FACILITY AND TECHNIQUES The air supply system and jet facility used in the present experiments Fig. 1 are the same as those used in previous experiments, 1 except for additional nozzles and a thrustmeasuring system that will be described later. In the present experiments, the nozzle used for flow visualizations is a full nozzle, which is smaller will be referred to as smaller nozzle later than the one used in the previous /99/11(9)/2731/12/$ American Institute of Physics

2 2732 Phys. Fluids, Vol. 11, No. 9, September 1999 J.-H. Kim and M. Samimy FIG. 1. Schematic of the flow facility with thrust measuring system. The nozzle, nozzle extension, two stagnation chamber supports, and vertical cantilever are attached and move together. experiments 1,11,12 and has the capability of trailing edge modifications on one or two sides. The exit dimensions of the smaller nozzle are 2.86 cm wide and 0.95 cm high (1-1/8 in. 3/8 in.), with an equivalent diameter D eq (4A exit / ) 1/2 of 1.86 cm in.. Schematics of the baseline nozzle and the trailing edge modified nozzles and modification types are shown in Fig. 2. The letter O or R in a modification name represents the shape of the cut-out; O for an oblique and R for a rectangular cut-out. The letter C or S stands for the location of a cut-out; C for a central and S for a side cut-out on the trailing edge. For example, modification RS means it has a rectangular side cut-out. The nozzle name represents the types of modifications on both sides. For example, nozzle RC RS has modifications RC on one side and RS on the other side. Based on previous results, 1,11,12 four types of modifications, OS, OC, RS, and RC, were selected because of their superior mixing performance. By combining any two types of modifications, six double trailing edge modified nozzles, nozzle OS-OS N33, OC-OS N43, OC-OC N44, RS-RS N65, RC-RS N65, and RC-RC N66, as depicted in Fig. 2, were selected as good candidates for mixing enhancement. The nozzle names in parentheses are those used in Ref. 13. Surface flow visualizations and wall pressure measurements were carried out for the larger nozzle, 1 whose exit dimensions are 7.6 cm wide and 2.5 cm (3 in. 1 in.) high, to take advantage of the thicker boundary layer. A more detailed description of the larger nozzle is found in Ref. 1. The instantaneous cross-sectional images are acquired by the laser sheet illumination technique as in previous experiments. 1,11,12 No seeding is required to visualize jet cross sections, since water particles, formed during the mixing process in the mixing layer, scatter the laser light. The FIG. 2. Schematics of the nozzles and the modified trailing edges. Letters O and R represent the shape of cut-outs; O for oblique and R for rectangular cut-outs. Letters C and S represent the position of cut-outs; C for central and S for side cut-outs in the trailing edge. For example, modification RC means that it has a rectangular-central cutout. Nozzle names bear all the modification types they have i.e., both sides. particles, with a diameter on the order of nm, are formed when the cold and dry jet air mixes with the humid and warm ambient air that is entrained into the jet plume. Only mixing regions are visualized because no condensate is formed outside the mixing layer. The visualizations of the jet cross section are performed at four downstream locations, i.e., x/d eq 1, 2, 4, and 8. The jet is operated at three fully expanded jet Mach numbers of 1.75 overexpanded, 2.0 design Mach number, and 2.5 underexpanded. Two additional Mach numbers, M j 1.5 and 2.2, were also used in surface flow visualizations and thrust measurements. All Mach numbers are nominal values since the measured design Mach number is The cross-sectional images are stored on the hard disk of a personal computer. Although the jet air is clean, the cross-sectional images were contaminated by some dust particles entrained into the jet from the ambient. The quality of the instantaneous images is improved by an image processing program. Since one of the primary objectives of the present work is to identify the major sources of streamwise vorticity, experiments were conducted using surface-flow visualizations and wall pressure measurements on the modified surfaces. Before measuring the wall pressure distribution on the modification, a surface flow pattern image was obtained by using the kerosene-lampblack surface streak method. 14 Contrary to the conventional surface flow visualization technique which

3 Phys. Fluids, Vol. 11, No. 9, September 1999 Mixing enhancement via nozzle trailing edge FIG. 3. The location of spanwise and streamwise pressure taps on modification RC. W shows the width of the nozzle which is 7.6 cm. uses an oil-pigment mixture, the surface streak trace by kerosene-lampblack mixtures is not affected by the tunnel shutdown since the kerosene evaporates completely before the airflow is stopped. The microscope observations of Settles and Teng 14 revealed that the deposited lampblack particles are typically on the order of a few m in diameter. Thus, the flow disturbance by the deposited pigment particles is expected to be negligible. Before each test, the lampblack-kerosene mixture was applied 12 mm upstream of the cut-out. Just after the shutdown, the modification was taken apart, and the surface flow pattern traced by the paint powder was recorded on a 4.9 cm wide piece of 3 M adhesive transparent tape. The image was imprinted on a sheet of white paper by pressing the tape on it. Even after being photocopied, the surface flow image quality is very good. Surface flow visualizations were performed for the baseline nozzle and nozzles OS, OC, RS, and RC denoted previously as nozzles N3, N4, N5, and N6, respectively, and showed comparable mixing enhancement in previous work 1,11,12. A detailed description of the nozzle is found in Refs. 1,11, and 12. The wall pressure distribution on the modifications was measured by placing spanwise and streamwise arrays of pressure taps, as shown in Fig. 3, for one of the two cases investigated. The static pressure is measured by a transducer housed in a 12-channel manual Scanivalve. The pressure is displayed by a Newport Model digital readout. The thrust-measuring system is shown in Fig. 1. To minimize the inlet flow effects on measured thrust, the compressed air is introduced into the stagnation chamber perpendicularly to the nozzle axis. The hoses stay flexible even after they are pressurized up to the maximum stagnation pressure at M j 2.5), so the effects of inlet flow on thrust are expected to be negligible. The stagnation chamber, two chamber supports, and two 5.08 cm diam shafts are assembled together and are free to move axially in four guiding and supporting Thomson linear bearings. The load cell is a Sensotec Model 13 with 445 N 100 lb. capacity; thrust values are displayed by a Sensotec Model GM readout. To prevent the stagnation chamber from slamming into the load cell at start up and to minimize frictional effects on thrust, a preload of approximately 60 N is used. Thrust is measured for the baseline nozzle and nozzles B-RC, B-OC, RS-RS, FIG. 4. Conjectured two-dimensional pressure distributions, spanwise pressure gradients on the inside wall of a nozzle for the underexpanded case, and the induced streamwise vortices. RC-RS, and RC-RC. The letter B in the name of a nozzle represents the baseline plate, which does not have any cutout. III. RESULTS The present experiments are focused on identification of the major source of streamwise vorticity, which governs jet development and evolution, and on the mixing enhancement due to these vortices. In addition, the effects of trailing edge modifications on the jet thrust were investigated. The results presented here complement those reported in previous experiments 1 and further advance our understanding of these complex flows. A. Streamwise vorticity sources Since vortex dynamics govern jet development and mixing, some discussion of the topic, as a follow-up to previous work, 1,12 is warranted. Three main sources of streamwise vorticity in the supersonic jet with modified trailing edges are believed to be 1 the vorticity convected downstream in the boundary layer approaching the modified region; 2 the spanwise z-dir. pressure gradient on the nozzle inside surface as shown schematically in Fig. 4; and 3 the baroclinic torque due to the possible misalignment of pressure and density gradients. Kim et al. 13 conjectured that the spanwise pressure gradient may be the major source of the streamwise vorticity. However, they were not able to provide experimental results to support the conjecture. Below these three sources will be discussed further. 1. Three potential sources Source 1, the vorticity convected downstream in the boundary layer, experiences vortex stretching and reorientation. As was believed to be the case for the jet with tabs, 4 this source is much weaker than the vorticity generated by a spanwise pressure gradient in the vicinity of the modified

4 2734 Phys. Fluids, Vol. 11, No. 9, September 1999 J.-H. Kim and M. Samimy trailing edges. A pair of horseshoe vortices, which was observed in a tabbed jet for very low Reynolds number incompressible flow 5 and formed by wrapping the vorticity in the approaching boundary layer around a protruded object, is not expected in the present case, since the cutouts do not protrude into the jet stream. Strong support for this is the lack of any observable streamwise vortices in the cross-sectional images to be presented later for the ideally expanded case. The second streamwise vorticity source, source 2, is the spanwise pressure gradient on the modified trailing edge as schematically shown in Fig. 4. This source is similar to the streamwise vorticity due to the spanwise pressure gradient in front of a tab. 4 For incompressible flows, the vorticity flux due to the surface pressure gradient is given as, p z w x y, 1 w 1 p z y, 2 x w w where x, y, and z are for the streamwise, normal, and spanwise directions, respectively, as shown in Fig. 4. The subscript w represents the conditions at the wall. Equations 1 and 2 are valid not only for incompressible flow but also for compressible flow without significant heat transfer through the wall as in the present case. 18 Basically, Eqs. 1 and 2 were derived from the momentum equation and the no-slip condition on the wall. Spanwise and streamwise pressure gradients are expected in both the over- and underexpanded cases in the present experiments due to upstream influences through the subsonic region of the boundary layer and due to the spanwise propagation of disturbances caused by the cut-outs. The extent of the upstream influence zone in the underexpanded cases is expected to be on the same scale as the boundary layer thickness, which is on the order of a millimeter. On the other hand, the range of the spanwise disturbance propagation due to cut-outs is dependent on the design Mach number and the type of trailing edge modification in the underexpanded case. The expansion wave propagates at approximately 30 relative to the streamwise direction, since the design Mach number is 2.0. When the jet is overexpanded, the extent of upstream influences varies with the jet exit pressure as will be discussed later. The third source of streamwise vorticity is the baroclinic torque. The baroclinic torque is usually generated in compressible flows, and is present when the pressure and density gradients are not parallel. In the vorticity transport equation for the mean flow shown in Eq. 3, 19 the second term on the right-hand side represents the baroclinic torque, U U 1 1 p viscous terms, 3 where the boldface letters represent vectors and U,,, and p are velocity, vorticity, density, and pressure, respectively. If one assumes a simple two-dimensional expansion of a bounded flow Fig. 5, the baroclinic torque that would generate streamwise vorticity is zero as shown in Eq. 4, FIG. 5. Schematic of the pressure and density gradients in a boundary layer going through a two-dimensional expansion. The subscripts T and e represent the gradients due to temperature and expansion, respectively, while tot represents the total gradient by both of them. BC s 1 3 n p b p b n 0, where BC s represents the streamwise component of baroclinic torque, and b and n are for spanwise and normal coordinates, respectively. Misalignment of the pressure and density gradients in the boundary layer is due to the density gradient generated by the temperature variation across the boundary layer. Thus, the baroclinic torque is negligible for adiabatic incompressible and low Mach number subsonic boundary layer flows, where the temperature variations across the boundary layer are relatively small. On the other hand in very high-speed flows, this could be a strong source of vorticity. 20,21 According to Zaman et al., 4 the baroclinic term might be negligible in the tab case because the results for subsonic and supersonic jets with tabs showed similar overall results. In a Mach 2 flow, Donohue et al. 22 found that the streamwise vortex generated by a ramp in the authors opinion the source of the streamwise vorticity is a spanwise pressure gradient on the ramp is stronger than that generated by baroclinic torque. In addition, the effect of streamwise vortices generated by pure baroclinic torque on the mean flow was negligible. This supports the conjecture that the vorticity generated by baroclinic torque is perhaps negligible compared with that caused by the spanwise pressure gradient in the present case. 2. The effects of expansion or compression on vorticity Another issue to be addressed is whether vortex stretching or compression is important in supersonic jets in nonideally expanded conditions for which the vortices generated by the cut-outs go through significant expansion in the underexpanded flow regime and compression in the overexpanded flow regime. To investigate this issue, Eq. 3 is considered again. According to Bradshaw, 23 the viscous term is much smaller than the first term on the right-hand side, representing vortex stretching and reorientation. By neglecting the viscous term, Eq. 3 can be rewritten for the streamwise component as 4

5 Phys. Fluids, Vol. 11, No. 9, September 1999 Mixing enhancement via nozzle trailing edge V s s / s s / s / V b V b n n s V s s b V s b n V s n BC s, 5 where BC s is the baroclinic component for the s-direction and is zero as shown in Eq. 4 if the expansion is twodimensional. To focus on streamwise vorticity change through an expansion, a streamwise vortex tube ( s 0, b 0, and n 0) in a quasi-two-dimensional flow, a flow similar to that shown in Fig. 5, is considered. Because V b 0, ( s / )/ b 0, BC s 0, V s V n and ( s / )/ s ( s / )/ n, Eq. 5 is reduced to s / V s s V s s s, s const V s. 6 Thus, the streamwise vorticity decreases through an expansion for underexpanded jets due to the faster decrease of density in comparison with the increase in velocity. For the expansion from M j 2.0 to M j 2.5, the density decreases approximately 45%, and the velocity increases 15%. On the other hand, the streamwise vorticity increases through a compression owing to the compression of the vortex diameter, which is similar to vortex stretching in incompressible flows. For the compression from M j 2.0 to M j 1.75, the density increases approximately 31%, and the velocity decreases 8%. In fact, Eq. 6 implies that the circulation of a vortex is conserved when there are no vorticity sources. The same equation can be derived from the conservation law of circulation in a quasi-two-dimensional flow. 18 Note that this argument is for a two-dimensional expansion. The extent that this formulation will hold for the present case, which is not purely two-dimensional, is not clear at this time. 3. Surface flow visualization results Before measuring the spanwise pressure distribution on the modification, surface flow visualizations were performed to measure not only the surface flow direction on the modification, but also the range of the upstream influence zone. The acquired surface streak patterns for the modifications OS and RC are shown in Figs. 6 and 7, respectively. In these figures, the flow direction is from bottom to top of the page, with alternating black and white stripes representing the surface flow direction on the modification. When the jet is underexpanded, Fig. 6 c, the upstream influence zone is not significantly affected by the fully expanded jet Mach number M j. For modification OS at M j 2.3, the upstream influence zone was in the range of 2 mm as can be observed in Fig. 6 c. On the other hand for modification RC at M j 2.3, the zone is very wide as shown in Fig. 7 b. The disturbance initiated from the beginning of the cut-out propagates in the spanwise direction. Then the upstream influence zone is formed from the inside of the expansion waves with an angle of approximately 30 relative to FIG. 6. Surface flow streaklines on the inside wall of modification OS. The flow direction is from bottom to top of the page. The alternating black and white stripes represent the surface flow direction on the modification. the jet axis as depicted in Fig. 8, since the design Mach number is 2.0. The surface flow direction is significantly changed in the upstream influence zone. In contrast to the underexpanded case, the flow pattern was changed significantly with the fully expanded jet Mach number in the overexpanded cases, even for M j 1.75 with a relatively small adverse pressure gradient (P e /P a 0.7). For this jet Mach number, the separation line marked on the modification is relative to the jet axis for all modifications tested. Over the separation line on the modification, a separation shock is expected to exist at the upper edge of the boundary layer. As the fully expanded jet Mach number or the jet exit pressure decreases, the angle of the separation line increases and eventually becomes 90 relative to the jet axis at M j 1.5 as shown in Fig. 6 a and schematically in Fig. 8. Separation was two-dimensional at M j 1.5 for all the modifications tested and was located upstream of the cut-outs. 4. Wall pressure measurement results Based on the surface flow visualizations, the expected two-dimensional pressure distribution on the inside nozzle surface, as depicted in Fig. 4, was measured by spanwise and streamwise arrays of pressure taps for modifications RS and RC. However, results for only RC will be presented in this paper. The location of each tap on the modification is tabulated in Fig. 3. All surface flow visualizations and wall pressure measurements were carried out for the larger nozzle 1 to

6 2736 Phys. Fluids, Vol. 11, No. 9, September 1999 J.-H. Kim and M. Samimy FIG. 8. Schematics of the zone of upstream influence and resultant surface flow patterns on modification RC for underexpanded top and overexpanded bottom cases. The flow direction is from left to right. FIG. 7. Surface flow streaklines on the inside surface of modification RC. The flow direction is from bottom to top of the page. take advantage of the thicker boundary layer, which makes the surface flow visualization and pressure measurements easier than that for the smaller nozzle. The measured spanwise pressure distributions for modification RC at five flow conditions, M j 1.5, 1.75, 2.0, 2.2, and 2.5, are shown in Fig. 9. The measured wall pressure was normalized with the ambient pressure of 99.3 kpa 14.4 psi. In addition, the spanwise distance z was normalized by the cut-out width W co, which is equal to 1/3 of the nozzle width of 76.2 mm 3 in.. As expected, no significant spanwise or streamwise pressure gradients were measured in the ideally expanded case. The negligible streamwise vorticity source for this case resulted in almost the same jet cross section regardless of the type of modifications as will be shown in the flow visualization section. Not surprisingly, the normalized pressure distributions for the underexpanded cases have a similar trend for different M j s of 2.2 and 2.5. This is due to the fact that the expansion fan initiated from the cut-out corners does not significantly depend on M j but does depend on the design Mach number. Because of the spanwise pressure gradient, a pair of counter-rotating streamwise vortices is formed with the same direction as a log rolling down the pressure hill 4,15,17 as shown in Fig. 4. The measured spanwise pressure gradients, p/ z, for both modifications RS and RC are strong enough to generate streamwise vorticity on the wall Eq. 1. However, Eqs. 1 and 2 do not show any direct connection between vorticity and the magnitude of the pressure gradient, but show a circulation flow rate into the jet flow per unit length from the wall by the pressure gradient, when the units of any side of Eq. 1 are considered. In contrast to the underexpanded cases, the pressure distribution on a modification varies with the fully expanded jet Mach number M j in the overexpanded cases, since the separation location and accompanying separation shock location significantly depend on M j as shown schematically in Fig. 8. Contrary to the case for underexpansion, the flow experiences an adverse pressure gradient, which in turn results in flow separation as shown in the surface flow images of Figs. 6 and 7. Because of the complex nature of the flow in the overexpanded case, the interpretation of the spanwise pressure gradient as a streamwise vorticity source is not straightforward. At M j 1.5 the spanwise pressure gradient was very small due to a two-dimensional separation shock generated well upstream of the cut-out as can be seen in Fig. 6. More detailed surface flow visualization and wall pressure measurement results are found in Ref. 18. Note that tabs were effective in mixing enhancement for ideally expanded and underexpanded flow conditions, but not for the overexpanded flow condition. 3,4 The underlying reason was not

7 Phys. Fluids, Vol. 11, No. 9, September 1999 Mixing enhancement via nozzle trailing edge FIG. 9. Spanwise pressure distributions for modification RC at five flow conditions. The wall pressure, p w, was normalized by ambient pressure, p amb. known at the time. But now it is obvious that flow separation within the nozzle for the overexpanded flow regime negates spanwise pressure gradients in front of tabs. B. Effects of trailing edge modifications on the jet cross section deformations In the previous experiments, 1,11,12 single-sided trailing edge modifications were used to investigate their effects on mixing and noise. The reason behind using single-sided trailing edge modifications was to avoid any potential interaction between vortices generated by different trailing edges, and to make the investigation of the development of vortices easier. In the current work, modifications on both trailing edges of the nozzle were used to investigate the interaction between the streamwise vortices generated by the two trailing edges, and the effects of the modifications on mixing enhancement. Based on the results obtained with the single-sided trailing edge modified nozzle experiments, 1,11,12 four of the modifications that produced better mixing and noise performance were used to form six nozzles with the trailing edges modified on both sides; four of them were symmetric and two others asymmetric as shown in Fig. 2. The double-sided modifications were combinations of modifications type OS, OC, RS, and RC Fig. 2 b. To obtain reference data, the baseline nozzle was also used. Figures show average images of the cross section of the jet at x/d eq 1, 4, and 8 for the baseline nozzle and FIG. 10. Average cross-sectional images at x/d eq 1. The physical size of each image is 6.8D eq wide and 4.1D eq high (126.7 mm 75.7 mm). six modified nozzles at the fully expanded jet Mach number of M j 1.75, 2.0, and 2.5. These images are obtained by averaging 50 instantaneous but time-uncorrelated images. As mentioned above, only mixing regions are visualized by water particles of approximately nm diam, which are formed when the cold and dry jet air mixes with the humid and warm ambient air which is entrained into the jet plume. The average images at x/d eq 2 are similar to those at x/d eq 1; thus they are not presented here, but can be found in Ref. 13. It should be mentioned that the degree of expansion for the underexpanded case, with the jet exit pressureto-ambient pressure ratio (P e /P a ) of approximately 2.2, is much stronger than the degree of compression for the overexpanded case, with the jet exit pressure to ambient pressure ratio (P e /P a ) of approximately 0.7. From a practical viewpoint, however, these are within the flight envelope for a Mach 2 jet. As was observed in the previous work for the ideally expanded flow condition, 1,11,12 the cutouts do not seem to affect the jet cross section in any significant fashion for this case. This is due to the lack of the main streamwise vorticity source of wall pressure gradients in the zone of upstream influence, as shown in Fig. 9. For the underexpanded case, M j 2.5, the streamwise structures due to the RS and RC type cut-outs Fig. 2 are very clearly shown at x/d eq 1. The streamwise structures due to the OS and OC type cut-outs can only be inferred from the jet cross-sectional deformation. These results are again consistent with previous resultsd 1,12 where it was con-

8 2738 Phys. Fluids, Vol. 11, No. 9, September 1999 J.-H. Kim and M. Samimy FIG. 11. Average cross-sectional images at x/d eq 4. The physical size of each image is 6.4D eq wide and 3.8D eq high (120.0 mm 70.8 mm). FIG. 12. Average cross-sectional images at x/d eq 8. The physical size of each image is 9.5D eq wide and 5.6D eq high (176.8 mm mm). jectured that the streamwise vorticity shed due to the surface pressure gradients in the zone of upstream influence by the cut-outs are aligned in the streamwise direction for RS and RC type cut-outs. On the other hand, for the OS and OC type cut-outs, the shed vorticity, originally aligned with the 45 cut-out edge, must go through a reorientation process by V s / b Eq. 5 to form streamwise vorticity. Thus, the streamwise vortices seem to be stronger and better defined for the former cases. As the jet cross section is expanding from the original cross section in the underexpanded case, the structures imparted by each modified trailing edge seem to develop almost independently even beyond x/d eq of 4 in the present experiments. For example, the left side of the jet cross sections for nozzles RC-RS and RC-RC at x/d eq 4 Fig. 11, due to the trailing edge modification RC, are very similar, even though the other sides of the cut-outs have trailing edges RS and RC, respectively. The implication is that for this flow condition, at downstream locations up to x/d eq 4, where the interaction from the two sides begins, each cut-out acts almost independently, and the effect should be almost additive. A kidney-type pair of counter-rotating vortices was observed in the underexpanded case for modifications OS and RS, while a mushroom-type pair of vortices was observed for modifications OC and RC Ref. 12 as shown in instantaneous images at x/d eq 4 in Fig. 13. The kidney-type pair of vortices entrains ambient air into the jet plume. As can be observed in Figs , the kidney-type pair of vortices experiences destructive unfavorable interaction between vortex mates. The unfavorable interaction begins at a further upstream location for a shorter center-to-center vortex distance (r 0 ). For example, the unfavorable interaction for nozzle RS RS, which has a shorter r 0, started at a downstream location between x/d eq 1 and 2, while that for nozzle OS OS, which has a longer r 0, started at a downstream location between x/d eq 4 and 8. In addition, the mutually induced velocity V i for the kidney-type pair of vortices is toward the jet center entraining or pumping ambient air into the jet. This obviously retards the jet spreading. On the other hand, the mushroom-type pair of counter-rotating vortices, that eject the jet air into the ambient, do not experience any unfavorable interaction between vortex mates up to x/d eq 8. For the overexpanded case, even though the pressure ratio is small (P e /P a 0.7), the compression in the jet cross section causes the modifications from two sides to interact very early in the jet development. For example, this interaction is obvious for OC OS, OC OC, RC RS, and RC RC, even at x/d eq 1 Fig. 10. The jet flow experiences an adverse pressure gradient in the overexpanded flow regime. As a result, the flow separates as marked on the modification shown in Figs. 6 and 7, and this makes it difficult to interpret the pressure data. Thus, the development and role of streamwise vortices for the overexpanded case are not conclusive because of complex features of the flow, including separation inside the nozzle. The instantaneous visualizations, with 9 ns exposure time, of the jet cross section at x/d eq 1 and 2 not pre-

9 Phys. Fluids, Vol. 11, No. 9, September 1999 Mixing enhancement via nozzle trailing edge FIG. 13. Two different pairs of vortices generated by different trailing edge modifications; one, kidney-type, has a pair of vortices which entrains the ambient air a and the other, mushroom-type, has a pair vortices that ejects the jet air into the ambient air b in the underexpanded flow regime. The images are instantaneous cross-sectional images at x/d eq 4. sented here show results similar to the average results shown in Figs. 10 and 6 in Ref. 13, as the structures at these locations are spatially quite stationary. The only difference is that in the instantaneous images, unlike the average images, small-scale structures are embedded in large-scale structures. Figures 14 and 15 show typical instantaneous images at x/d eq 4 and 8 for all the cut-out types and fully expanded jet Mach numbers. As can be seen, the mixing layers in these locations are dominated by large-scale structures in the flow, but the jet core is still apparent for the fully expanded and underexpanded flow regimes, even at x/d eq 8 Fig. 15. C. Overall mixing Mixing areas, an indication of mixing layer thickness, were calculated from 50 instantaneous images in the same way as described by Samimy et al. 1,12 In an instantaneous image, a pixel with an intensity greater than a threshold value was counted as a part of the mixing region. After calculating the mixing area for each instantaneous image, ensemble averages of 50 images were obtained. In previous experiments, it was determined that to obtain an accurate measure of the mixing region, a reference mixing region is required to take into account the change in room temperature and humidity during experimentation, because these parameters affect the condensation process in the jet mixing region. The reference mixing area for each nozzle was acquired at FIG. 14. Instantaneous cross-sectional images at x/d eq 4. The physical size of each image is 6.4D eq wide and 3.8D eq high (120.0 mm 70.8 mm). M j 2.0 ideally expanded using the baseline nozzle after flow visualizations for the nozzle operated at three flow conditions were performed. All the mixing areas were normalized by the associated reference value. With this normalization process, mixing areas are expected to be repeatable for different weather and, thus, moisture condensation conditions. 1. Underexpanded case Figure 16 shows variations of mixing area with x/d eq for three flow regimes for all the nozzles. The results at x/d eq 1 are less accurate than the other locations as light reflection from the nozzle, due to the close proximity of the laser sheet to the nozzle at this location, made the background subtraction and thresholding of the images more difficult. 12 One could get both the normalized mean mixing area normalized mixing layer thickness and normalized mixing rate or growth rate of the mixing layer from the slope in this figure. Note that the results are normalized, at each x/d eq, with the mixing area for the baseline nozzle at M j 2.0 at this location. The mixing area for the underexpanded jet, shown in Fig. 16 a, is substantially larger than that of the reference case at all locations. The normalized mixing level for nozzles OC OC and RC RC are much higher than the baseline case in every streamwise location, and also show higher growth rates. The higher mixing growth rate of nozzles OC OC and RC RC is because of the favorable fluid pumping action of the mushroom-type pair of streamwise vortices in these

10 2740 Phys. Fluids, Vol. 11, No. 9, September 1999 J.-H. Kim and M. Samimy FIG. 15. Instantaneous cross-sectional images at x/d eq 8. The physical size of each image is 9.5D eq wide and 5.6D eq high (176.8 mm mm). nozzles. Since no destructive interaction between vortex mates occurs, as mentioned earlier, the good mixing performance is sustained for longer downstream distances. The mixing level for the modifications in nozzle RC RC is higher than that of OC OC because the streamwise vortices for RC RC are stronger due to their initial alignment with the streamwise direction, as discussed earlier. The initial mixing levels for nozzles RS RS and OS OS are much higher than the baseline, but the growth rate for RS RS is similar to the baseline case in the downstream locations. Contrary to nozzles OC OC and RC RC, the mixing performance for nozzles OS OS and RS RS deteriorated with downstream distance as shown in Fig. 16 a because of the unfavorable interaction between vortex mates. Each one of the modifications for these nozzles generates a kidney-type pair of vortices that entrain ambient air into the mixing region. Similar to the difference between nozzles RC RC and OC OC, the modifications for nozzle RS RS generate stronger streamwise vortices than nozzle OS OS. However, as shown in Figs , the pair of streamwise vortices generated by each cut-out in RS RS are much closer to each other than those in OS OS. While the pair of vortices in OS OS does not interact until x/d eq 4, and thus keeps entraining a large amount of ambient air into the jet, the pair of vortices in RS RS starts interacting beyond x/d eq 1, which limits their entrainment capabilities as observed in Fig. 16 a. The nozzles OC OS and RC RS, have characteristics in between OS OS and OC OC, and RS RS and RC RC, respectively. FIG. 16. Variations of the normalized mixing area with downstream locations for underexpanded a, ideally expanded b, and overexpanded c flow regimes. 2. Ideally expanded case As in the nozzles with single-sided trailing edges, 1,11,12 the mixing enhancement by ideally expanded nozzles with double-sided trailing edges is negligible as shown in Fig. 16 b. The growth rates of trailing edge modified nozzles are the same as that for the baseline nozzle for this flow regime. 3. Overexpanded case When the jet is overexpanded, Fig. 16 c, the baseline case has higher mixing level than half of the modified nozzles at x/d eq 8. In addition, the growth rate of the baseline nozzle is higher than that of any other nozzles beyond x/d eq 4. There are three main reasons for this; 1 the jet for the baseline nozzle case is flapping, which provides significant mixing enhancement for the baseline case, 2 no strong streamwise vortical structures are generated due to flow separation inside the nozzle for the overexpanded flow condition, and 3 unlike the underexpanded cases, where a pair of vortices on one side of the jet did not interact with the pair of vortices on the other side until x/d eq 4, or even until x/d eq 8 in certain cases, the mixing layers for the overexpanded case interact immediately due to compression, owing

11 Phys. Fluids, Vol. 11, No. 9, September 1999 Mixing enhancement via nozzle trailing edge to the smaller cross section of the jet. For these reasons, comparisons and conclusions in this flow regime are not straightforward. D. Thrust measurement results Thrust generated by the jet is measured at four flow conditions, M j 1.75, 2.0, 2.2, and 2.5, by the thrust measuring system shown schematically in Fig. 1. The thrust value at a given M j was repeatable within 1.15% and 0.35% for M j 1.75 and 2.5, respectively. In a given nozzle operated in supersonic flow regimes, theoretical thrust (T th ) for an ideal gas and inviscid flow is a function of the stagnation pressure (p 0 ) and ambient pressure (p a ) as shown in Eq. 7, 13,18 T th ṁv e A e p e p a, A* M d p 2/ 1 1 / 1 0 A* M d M 2 d 2 p M d 1/ 2 1 / 1 M d 2 p a, 7 FIG. 17. Variations of thrust and thrust coefficient with the fully expanded jet Mach number. where is the specific heat ratio of the jet fluid, A* is the nozzle throat area, and M d is the design Mach number of the nozzle. Although vortex generating tabs are an effective way of enhancing mixing not only for the underexpanded cases but also for the ideally expanded case, they result in thrust loss. 3,4 It was expected that the thrust loss associated with cut-outs would be negligible since the cut-outs did not protrude into the flow. 11,12 The measured and theoretical thrust results are depicted in Fig. 17 for six nozzles at four fully expanded jet Mach numbers. The thrust coefficient is also depicted in Fig. 17. The thrust coefficient is defined as the ratio of measured thrust to the stagnation pressure (p 0 ) times the nozzle throat area (A throat ): thrust coefficient measured thrust /(p 0 A throat ). 24 The agreement between the experimental and theoretical thrust results is very good. Small disagreements are due to the inviscid flow assumption within the nozzle in the theoretical calculations. The variations of the measured thrust values for all modified nozzles tested, in a given operating condition, are within the repeatability range of the baseline nozzle, indicating no thrust loss due to the trailing edge modifications. If the cut-out was placed on the contoured nozzle wall, thrust loss would not be negligible. According to Eq. 7, theoretical thrust increases until the design Mach number is equal to the fully expanded jet Mach number for a given stagnation pressure, and has a maximum when the two Mach numbers are equal. If a part of the contoured nozzle wall is cut out in the present case, the cut-out region will have a design Mach number between 1 and 2 while the other region has a design Mach number of 2. When a nozzle, with a cut-out on the contoured nozzle wall, is operated at M j 2.5, the thrust by this nozzle will be smaller than the baseline nozzle because of a reduced effective design Mach number around the cut-out. However, in the present case, the design Mach number near the cut-outs is not altered since the cut-outs are placed on extended trailing edges as shown in Fig. 2. Thus, thrust loss due to cut-outs was not expected in the present case as shown in Fig. 17. IV. CONCLUSIONS The jet cross section was visualized, using the laser sheet lighting technique, at four downstream locations at the fully expanded Mach numbers of M j 1.75,2.0 design Mach number, and 2.5 for double-sided trailing edge modified nozzles. Also, surface flow visualizations and surface pressure measurements were carried out in the vicinity of cutouts. Detailed discussions of the sources of streamwise vorticity were provided. In the underexpanded cases, the measured spanwise pressure gradient was significant enough to generate strong streamwise vortices, which were clearly observed for modifications RS and RC, and is believed to be the major source of streamwise vorticity. However, the interpretation of the measured pressure gradients is not straightforward in the overexpanded cases due to the complex flow features, including flow separation on the modified trailing edges. In the underexpanded flow regime with double-sided trailing edge modifications, the nature of mixing enhancement over the baseline nozzle strongly depends on the type of streamwise vortices generated by the modifications. At upstream locations, the mixing enhancement is more significant for nozzles which generate a kidney-type pair of counter-rotating streamwise vortices that entrain ambient air into the jet plume, as in nozzles with modifications OS or RS

12 2742 Phys. Fluids, Vol. 11, No. 9, September 1999 J.-H. Kim and M. Samimy nozzles OS OS and RS RS. The mushroom-type pair of vortices, which was generated for nozzles with modifications OC and RC nozzles OC OC and RC RC, acted like a fluid pump resulting in enhanced mixing performance sustained with downstream distance. The mixing level for the modifications in nozzles RS RS and RC RC is better than that of OS OS and OC OC, respectively, because the streamwise vortices for the former are stronger than those for the latter due to their initial alignment with the streamwise direction. In the underexpanded case, the spanwise pressure gradients in the vicinity of the cut-outs, are due to upstream influences through the subsonic region of the boundary layer and due to the spanwise propagation of disturbances from the cut-out corners. For this flow regime, it was found that the pair of streamwise vortices generated by the modified trailing edge at one side of the nozzle did not interact with the pair of streamwise vortices generated by the modified trailing edge on the other side for a large downstream distance, due to the expansion of the jet cross section at the nozzle exit. As a result, each modified trailing edge acted almost independently; thus, substantial mixing enhancement was achieved using the double-sided trailing edge modifications. On the other hand, for the overexpanded case, the streamwise vortices were much weaker, as expected, and the vortex pairs from the two modified trailing edges interacted immediately, owing to the smaller jet cross section due to the compression of the jet cross section at the nozzle exit. Thus, mixing enhancement was not substantial, and comparison and conclusions in this flow regime were not as straightforward. Thrust generated by the jet was measured at four flow conditions of M j 1.75, 2.0, 2.2, and 2.5. The thrust for nozzles with different single- and double-trailing edge modifications was within the repeatability range of the baseline nozzle, indicating that there is no thrust loss or gain due to the trailing edge modifications. Therefore, mixing can be significantly enhanced by generating pairs of streamwise vortices via trailing edge modifications with minimal thrust loss, especially in the underexpanded flow regime. ACKNOWLEDGMENTS The support of this research by NASA Lewis Research Center with Dr. Khairul Zaman and by the Air Force Office of Scientific Research with Dr. Steven Walker and Dr. Mark Glauser is very much appreciated. The authors are thankful for the assistance of William R. Erskine, Charles W. Kerechanin, and Brian S. Thurow in conducting experiments and in preparing this manuscript. 1 M. Samimy, J.-H. Kim, P. S. Clancy, and S. 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