 All right, all right, my name is Emil Suhiro. I'm from the University of Arizona, and I work with Professors Lutz Taubert and Professor Izro Wognansky, and I'm gonna be talking about my research involving 3D mixing layers created from a lambda notch. So why a lambda notch? Well, a lambda notch represents a single wavelength of a Chevron nozzle. These Chevron nozzles are seen on many of today's modern aircraft for noise suppression and on military aircraft seen here for reduction of infrared signature. However, the mechanisms that govern the flow behavior are not well understood, and therefore these designs are purely empirical and not well optimized, and it could be enhanced for control by active means. And so the main focus of this experiment is to understand the fundamental effect that this lambda-shaped pattern has on the mixing and the turbulent evolution of this mixing layer downstream, in particular these swept trailing edges in conjunction with the notch, and how it affects the mixing layer, and also to be able to study the controllability of this flow by studying the sensitivity to span-wise periodic excitation, where we also lay a small flap on the trailing edges and study what the flow does to these small amplitude perturbations. And so a little bit about the experimental setup. We have a splitter plate with this lambda notch in here. We have the high speed flow coming out the top, the low speed flow coming out the bottom. We put these honeycombs and screens down here to get the desired velocity ratio. Here we can see the splitter plate with this lambda notch swept at 60 degrees. Also we have these holes here where we use suction to control the boundary layer thickness. Also we can inject smoke for flow visualization. Attached over here are these small flip runs hinged at the trailing edge and they oscillate. The mid-span of each trailing edge are these strings that are attached and these strings thread up and down outside of the tunnel test section connected to these speakers that oscillate in phase. And this is what provides us the perturbations. So the test conditions that we used was we ran out of velocity ratio fixed at 0.4. It's important to note that the boundary layer over the splitter plate was turbulent. So with a splitter plate here, we would have any quality of boundary layer thickness due to the increased length. And therefore it's important to note that we would have a expect to see a variable thickness across the span. The forcing parameters such as amplitude and frequency, the amount we displaced the flap is fixed at 2 millimeters and we use the given frequency shown. And these were determined from or selected by 2D experiments in order for us to get a direct comparison which I'll be going over later in the presentation. Additionally, we'd be forcing from a single side and also the other side and control the phase between these perturbations to understand any vortex interactions that might be seen in the center and this effect, to be able to study this effect, it has on the growth of the mixing layer downstream. So first of all, it was discovered that the center of the mixing layer was, or the mixing layer was distorted. We can see here the locations of the center of the mixing layer designated by the average of the two streams. We can see it varies for each span-wise location. I've put these span-wise locations on this map shown here. Opposed to a 2D mixing layer, which from vortex induction, the high speed will induce a downward motion and we see that a two-dimensional mixing layer would be inclined towards the low-speed stream. So what we would expect that we would see a similar thing for when we put a lambda notch in here. However, we actually see the opposite effect if we look at this center of the mixing layer, this actually is inclined towards the high-speed stream while the more outward locations are inclined more downwards. And this was actually confirmed with flow visualization images. When we took a cross-stream flow visualization image by an injecting smoke at the splitter plate, we can see the similar behavior of this sort of slight upwards bending in the center and downwards on the outward locations. And so explanation for this is the possibility of two counter-rotating vortices that could be causing this upward distortion of the mixing layer. And the way this is generated is if we were to take a traverse, horizontal traverse above the splitter plate outside of the boundary layer, we would see a profile shown here with a weight component shown in blue due to the merging of the two streams and the velocity deficit. And this weight would be inviscidly unstable and then therefore would create these vortices, a pair of vortices with its axis oriented in the vertical direction. And from here, it would be tilted by the mean shear shown in red such that its axis would be stream-wise and then counter-rotating. So this is what's believed to be causing this upwelling in the center and distorting the mixing layer. And so this was confirmed with PIV measurements, Particle Image Velocimetry measurements in the cross-stream plane. It confirms this upward bending, slight upward bending in the center. When we look at velocity contours and also when we look at stream lines, we can see the existence of these two vortex cores that are indeed counter-rotating. And so to provide further support for this idea, we actually did an experiment where we put little vortex generators angled like so at different distances apart and then from there we would create stronger vorticity components that are counter-rotating and then we can sort of see the flow visualization images shown here. For example, this is when the vortex generators are 80 millimeters apart and 160 and we can see it does indeed cause this upward distortion of the mixing layer as we can see shown here. And when we change the distance between them, we can get a feel for how these vortices or the placement of them when they form on the splitter plate. And we can show the comparison with no vortex generators and we can see the similarities between the images to show that it's likely that, very likely that it is caused by a pair of stream-wise counter-rotating vortices. So when we look at the growth rates of the unforced mixing layer, we can see here I'm showing the momentum thickness with relative distance from the trailing edge. So I show these on the map here. And as we can see, these points collapse nicely onto a single curve which corresponds to a plane parallel to the trailing edge, these momentum thicknesses are more or less constant with the exception of these outboard locations shown here. They have a greater initial momentum thickness at the outboard locations likely due to the boundary there growing more over the increased distance and also possibly some span-wise flow at the more outboard locations. But however, when we subtract off the initial momentum thickness, we see that it all grows at the same rate and this rate is comparable to a 2D mixing layer. And so since we know that there's the inequality of momentum thickness across the span, especially at the outboard locations, we did an experiment where we used the suction holes to provide suction, non-uniform suction to equate the boundary layer across the trailing edge and to determine whether or not this boundary layer had an effect on the asymptotic rate of spread downstream. So we can see here without suction, particularly at this outboard location, we can see a thicker boundary layer. And when we applied suction, it showed to be effective in equating it across the trailing edge shown here. But however, in the application of suction and equating the boundary layer, it showed that there wasn't a significant effect in the growth rate. And so we concluded that the initial thickness of the boundary layer was not an important factor in determining the growth rate. And so since we know that the growth rate grew linearly and compared to the 2D and was independent of span, the boundary layer independence principle which was thought to have not been valid for turbulent flows for many years, appears to apply here. So if we decompose the flow into two components of flow perpendicular to the trailing edge and a flow parallel to the trailing edge, such that when we saw that the momentum thickness was constant, this would yield no variation in a plane parallel to the trailing edge. And so the momentum equations would reduce to the ones shown here. And this form was taken from just multiplying the continuity equation by the respective velocity component and adding it to the momentum equation to yield this form. So by looking at these two equations, we see that if the normal component is parallel, is proportional to the parallel component, then their corresponding Reynolds stress would also be proportional. And therefore, in this case, this equation would be identical to this equation and can be solved independently. And this is the independence principle. And this is what we're seeing here because when we look at measured profiles, we show that the normal component is proportional to the parallel component as well as their corresponding Reynolds stress. And so it shows that the independence principle can be applied for turbulent flows and mixing layers. But for this case, it's only within a narrow region where the momentum thickness is constant. And so that was in the absence of forcing. Now what happens when we start to force? For example, if we start oscillating one flap of the trailing edge, we take the same location, the velocity profile. What happens? Well, we see these large distortions in the mean velocity profile now that the normal component and parallel component are no longer proportional. So therefore, the independence principle no longer applies. And in addition, when we look at the vorticity profiles, we can see additional inflection points and note that they're just opposite of each other. And this creates or suggests that the mixing layer is susceptible to amplification of other frequencies at this point and other instabilities in the flow. So now when we wanna look at the stream-wise rate of growth and its effect from changing the forcing frequency, it's important to understand what a two-dimensional mixing layer, force mixing layer does. At first, when we look at these non-dimensional parameters, take the strewell number or the non-dimensional momentum thickness and also this distance from the virtual origin with a non-dimensional velocity ratio. The frequency is the counter form when we look at this wavelength of perturbation. Now what happens in a 2D mixing layer is that at high amplitude, take the two millimeter case, for example, we see this sort of step-wise behavior. And this corresponds to the coherent structures that amplify, which cause an increased rate of growth and they're followed by a decay which causes this plateau on here. And then it resumes to go at a rate slightly less than the initial region here. And what was characteristic about this is that throughout this range, the Reynolds stress was dominated by the coherent motion or from the direct action of the flap. And beyond, at this point, the incoherent or the random turbulence begins to dominate. And so when we lower the amplitude in a two-dimensional mixing layer, it's not very clear this sort of step-wise behavior. And this is because the incoherent or the random turbulence becomes more dominant. So what happens in a 3D mixing layer? In our case, well, we don't see a clear step-wise behavior. We do see some changes in the growth rates. And we can look at, we can correlate this to integrating the shear production across the flow. So we can see here, take the 20, when we force that 20 Hertz, we can see as the coherent production increases, we can see a slight increase in the growth rate here. For 50 Hertz, the blue, it's already decaying and that's why we don't see as much of a change in growth rate here. And forcing at 40 Hertz, this is the only case where it actually goes through an amplification cycle and that's why we see a change, enhanced growth rate here followed by a decreasing. And so this is taken at the center of the notch. And so if we were to change the span-wise location to somewhere outboard, we can see that it behaves somewhat differently. We can see, because we know that the initial momentum thickness is thicker, we can see for the same frequency of 20 Hertz, we can start to see a decay as well as the 40 and 50 are already decaying and that's why we don't see a very much change in the growth rate at that location. So it just shows the dependency on frequency as well as span-wise location. So now if we want to get a feel for the coherent structures occurring in the flow, we can look at vorticity contours. For example, if I force from one side of the trailing edge, also leading at two millimeters and look at vorticity contour on that side, we can see these structures that are occurring and notice this inclination angle with respect to the mean shear. And this inclination angle corresponds to coherent structures that have already undergone their amplification cycle and are already decaying. Now if we compare that to in the center, we can look at these structures. Notice that these angles are opposite and these angles correspond to the coherent structures that are still undergoing their amplification cycle and notice that the change in angle as we move downstream. And so this coherent structures at this location is extracting momentum and energy from the mean flow. And when we look at the opposite side of where the forcing flap is inputting its perturbations, we don't see much coherent structure occurring. So this sort of suggests that these coherent structures don't propagate too deeply into the other side. So now that was all forcing from one side. So what happens when we start forcing from both sides? For example, if we were to oscillate the two flip runs simultaneously at the same phase, how does the growth rate affect it? So we can see here that forcing in phase, there's a significant increase in the growth rate versus if we were to keep the same amplitude but flip the phase so it's 180 degrees apart, we can see a different effect where it's actually compares more to forcing a single side and maybe even slightly less as you get more downstream. So it inhibits this growth rate just to show the dependence on this phase relation and the coherent structure interaction that takes place in the center that affects this rate of growth. So now when we wanna get an understanding of how these coherent structures are affected by forcing, we can look at phase lock velocity profiles as well as the three components of velocity fluctuations. So we can see here that forcing from a single side produces some distortions in the phase lock velocity profile which correspond to these streamlined fluctuations shown here and forcing from a single side will actually produce fluctuations in all three components of U, V and W. And so keeping that in mind, when we force from both sides simultaneously in phase, we can see these large distortions of velocity, phase lock velocity profiles and we can see an increase in the streamwise fluctuation and an increase in the vertical fluctuation. However, we do see the normal to the tonal wall fluctuations being suppressed and this increases that rental stress and the coherent structures to see this amplification of vortices shown there. And when we look at forcing 180 degrees out of phase, we don't see any distortions in the phase lock velocity profile and this is because the streamwise velocity fluctuations are now suppressed and we do see vertical but however the normal to the tonal wall, the W component has been increased. And so how do these compare? Well, forcing from a single side we have shown here. And then so what we see here is just a constructive interference from forcing in phase and a destructive interference from forcing 180 degrees out of phase. And so this is what causes the growth rate to be effective. So just to conclude that this lambda notch creates these pair of counter rotating vortices that bend the mixing layer up in the center. We showed that the unforced mixing layer grows linearly and independent of span and therefore the boundary layer independence principle is valid. However, it becomes invalid as soon as you start forcing from a side. We showed that the mixing layer growth rate did not show any plateaus and this is due to the forcing from a slanted trailing edge but would have resulted in a slower amplitude of perturbation compared to a 2D case. And lastly, we showed that altering the phase of the flip bronze also leading from the trailing edges shows to increase the growth rate and shows that there are considerable vortex interaction and shows the importance of the phase relation and not just the amplitude beat from the perturbations that generate these coherent structures. Thank you. No, this is incompressible and it's mainly to understand really fundamentally what the notch does to a mixing layer. Yeah. So I guess you have to consider like the convective Mach number and the compressibility effects but yeah, this was more to understand fundamentally what this does to the flow and these counter-rotating vortices and this effect on growth rates and even mixing processes and things like that. So university? Yes, yes, 10 meters a second and four meters a second for the bottom.