The goal of the current research is to advance current turbulence modeling capabilities in the prediction of shockwaveturbulentboundarylayerinteractions and flows with mas- sive separation for complex configurations, relevant to NASA Johnson Space Center. The current methodology involves taking a baseline k − ω turbulence model and using it to define equilibrium turbulent values to drive the actual Reynolds Stresses towards. This is done with a simple ”lag” equation. The new aspect of this work is using actual modeled Reynolds stresses in a production CFD code and applying them to real geometries of in- terest in a URANS method. By actually solving for the Reynolds Stresses and not the turbulent eddy viscosity, the models are allowed to relax to their non-equilibrium values with more degrees of freedom.
FUNDERBURK, MORGAN LEE. Investigation of Three-Dimensional Shock-Wave/TurbulentBoundaryLayerInteractions. (Under the direction of Venkateswaran Narayanaswamy.)
Ramjet and scramjet type engines represent the future of high-speed air-breathing propul- sion, providing superior efficiency compared to conventional turbojet and rocket engines. This improved efficiency is the result of using a shock-wave train to produce the compression of the intake air necessary for combustion. However, the inlet/isolators of these systems are partic- ularly susceptible to the effects of turbulentshock-wave/boundarylayerinteractions (SBLIs) for flight Mach numbers less than 5. As the boundarylayer along the inlet wall is compressed by the shockwave, it thickens and in some situations may separate. In a time-averaged sense, separated SBLIs cause numerous undesireable effects, including increased flowpath distortion and reduced total pressure recovery. The shock-induced separation is also intensely unsteady, and can produce low-frequency transient wall pressure loads that couple with the underlying aerostructure leading to fatigue. In rare circumstances, the separated boundarylayer can cause a blockage of the inviscid core flow and induce the ejection of the oblique shock train in an event known as unstart.
interaction cases, 20 consecutive short-exposure shadow- grams in each run were averaged to one final picture, which corresponds to a time span of 20 ms. The vibration-related displacements from frame to frame were corrected by fit- ting the model edges from each shadowgram onto the ref- erence image taken before wind-tunnel start. In the cases with traveling interactions, no averaging was conducted and each single image was evaluated. The single images were positioned in relation to the reference image by using the stationary parts of the test section. In Fig. 3a a shadowgram of a stationary interaction case is shown as an example with the reference model edges presented as light-blue lines. For this task the edge detection function from the GNU Octave programming language is used. It is a multi-stage algorithm using the Canny method (Canny 1987; Adler and Hauberg 2019). The Prewitt operator was used as a filter to find the intensity gradient of the image in both horizontal and verti- cal direction and than to calculate the gradient direction for each pixel. The following steps of the Canny algorithm are as described in the literature. The model edges in the station- ary interaction cases are used to correct a possible image shift. The positioned shadowgrams are than used to gener- ate the averaged shadowgrams of stationary interactions for further analysis.
Flow velocities are measured using a two component Laser Doppler Velocimetry (LDV) system. Two pairs of coherent laser beams, with a wavelength of 561nm and 532nm respectively, are focused inside the working section to form the interference pattern of the ellipsoidal working volume, measuring 130µm in diameter.
Kerosene particles, with a diameter of approximately 0.5µm, 7 are used to seed the flow and allow velocity measurements to be recorded via a proprietary software. The laser emitting head and receiving optics are mounted on a traverse capable of moving in one direction with a user defined velocity. The signal is sampled at an optimised variable rate to exploit a full signal cycle leading to a typical measurement accuracy, as stated by the manufacturer, of ±0.1% of U max (∼580m/s). In addition the emitting head is oriented at an angle β = 8.5 ◦ to allow the surface to be reached by the incident beams. A component of the spanwise velocity, w, will now affect the measurement of vertical velocity component. The absence of strong span-wise pressure gradients, and the relatively high v, due to curved nature of the flow, suggest that w is one order of magnitude lower than v. As a consequence of this and of the small angle, the error is expected to be just above 1%. The horizontal velocity component is, on the other hand, unaffected by β. Proper seeding in the area of interest is crucial to maximise accuracy. The seeding density is consistently high in the free-stream but drops as the wall is approached. As a result, considering the aforementioned sources of error, the overall deviance of the measured values from the real one is estimated to be below ± 2%. However, this is higher in the proximity of the wall, within the inner-most portion of he boundarylayer. As a consequence, the near wall region is subject to greater uncertainty.
Experiments have been performed in the supersonic wind tunnel No.1 in the Cambridge University Aerodynamics Laboratory. This tunnel is of the intermittent blow-down type driven by a high-pressure reservoir of dry air. A nominal freestream Mach number of 2.5 is used for all experiments with a unit Reynolds number of 40 ∗ 10 6 m −1 . The stagnation pressure is set to 380kP a (fluctuating by about 0.5% during a typical run) and the stagnation temperature is set at 296K ±3K. During tunnel runs the stagnation temperature in the settling chamber is observed to increase at a rate of 0.1Ks −1 , giving a maximum variation of 6K. The set-up for the working section and key dimensions are shown in figure 2. A half-liner configuration with a single nozzle block is used here. By blocking the lower half of the tunnel, the streamwise distance for observation through the sidewall window is almost doubled and the possible run time is increased. The resulting working section is 114mm wide and 86mm tall. A deployable wedge on the ceiling of the tunnel is lowered to 8 o to generate an oblique shock once the desired supersonic flow is developed. A gap of 5mm between the leading edge of the deployed shock-generator and the upper surface of the tunnel enables the boundarylayer on the nozzle block to disappear into the gap and therefore creates a ‘cleaner’ environment for the generation of the incident shock. A coordinate system following convention is used where x refers to the streamwise direction with x = 0mm corresponding to the end of the nozzle. The theoretical inviscid shock reflection location is at x = 135mm. y is measured vertically upwards with y = 0 referring to the tunnel floor. Spanwise position is denoted by z, measuring from the centreline of the tunnel floor with the sidewalls being at z = ±57mm.
Conclusion and Future Works
4.1 Concluding remarks
Experiments were performed to investigate the fluid structure interactions caused by a shockboundarylayer interaction unit placed over a rubber surface to explore the potential use of compliant materials towards unsteady shock load mitigation and separa- tion control. Compression ramps of different angles were employed to generate different strength SBLIs whose inviscid pressure ratio varied by over 50%. For all the cases, surface streakline visualization of the SBLI revealed that having a rubber surface beneath the SBLI displaced the separation line downstream by an average of almost 30% compared to the SBLI over rigid surfaces. Experiments over an acrylic surface ruled out differences in thermal conductivities as being the driving factor behind the observed reductions in separation, and experiments over a thin panel surface showed even greater extents of separation relative to that of the rigid surface.
• MC code is used to determine the significance limit c of the coherence estimate:
where P is the probability operator, and α is the significance level (here α=99.9%).
• Note: A coherence value of 0.25 is “equivalent” to a correlation coefficient of
sqrt(0.25) = 0.5, which would indicate a strong statistical link between the signals. • Physically, this would imply that the incoming boundarylayer plays an important
18) with strong fluctuant energy detached from the wall. The turbulent structures in this zone are similar with those in the mixing layer, in which the flow is also dominated by the free shear 41 . The third zone is the edge of the jet, in which the flow is also dominated by the free shear flow and some large-scale turbulent structures. The difference with the second zone is that, the jet flow is not fully turbulent in it beginning part. Therefore, we can observe the transition process and the generation of large-scale structures by the Kelvin–Helmholtz instability as shown in the instantaneous schlieren picture in Fig. 14. The forth zone is the reverse flow, where some quasi-streamwise structures existence. The structures in this zone is similar with the wall turbulence in the first zone, but the structures are restrained in a thin layer close to the wall, therefore no large-scale structures, such as the horseshoe vortex heads, can be located. The fifth zone is the low-turbulent zone, which includes the core of the jet and a gap between the second zone and the forth zone. The flow in the fifth zone is quiet and less organized, just like the close separation bubble in the 2D SWTBLI, where the flow is filled with less organized fluid.
1.3 Technical Approach
To investigate the effect of 3-D relief on a sharp fin SBLI, a myriad of experimental techniques are employed to analyze both the surface and off-body mean flows of a fin placed on a cylindrical surface. Oil flow streaklines provide a qualitative picture of the shear contours and separation entities, while pressure sensitive paint (PSP) provides a quantitative picture of the surface pressure field. Moreover, planar laser scattering (PLS) and particle image velocimetry (PIV) are used to determine how the off-body flow corresponds to the patterns seen on the surface. A technique was developed to calibrate the PLS intensity fields to density fields to enhance its quantitative value, thus providing deeper insight into the physics at play. When possible, all processing is done with in-house codes developed in MATLAB; the notable exception being processing of the velocity fields, which was done in DaVis 8.4. Because extreme maneuvers of vehicles would represent a wide range of shock strengths, separation regimes, and distortion magnitudes, extensive work is presented in this manuscript in which the Mach number, fin angle, extent of 3-D relief, and perturbation size are varied. Complementary planar fin SBLI and computational RANS simulations are presented as well as a basis of comparison to the fin-on-cylinder configuration and to extend the results into regions unobtainable in the experiments. A consolidated list of all of the experimental and computational methods is provided in chapter 2.
This research study on micro-actuator array flow control is a collaborative effort between the AFRL Flight Vehicles Directorate (AFRL/VAAI) and NASA Glenn Research Center (NASA/GRC) to develop and demonstrate advanced flow control techniques for supersonic mixed compression inlets. The AFRL Flight Vehicles Directorate has focused recent effort on the advancement of propulsion integration technologies associated with LRSA (Long Range Strike Aircraft). The goal of this effort has been to define and develop high payoff advanced technology approaches for mixed compression inlets operating in the Mach 2.0 to 4.0 speed regime. In addition, NASA/GRC is also focusing a portion of its micro-flow control research effort on commercial and business type aircraft in the speed range Mach 1.6 to 2.0. Therefore, the collaborative effort also provides technology interchange between the military and commercial side of aerodynamic research. The collaboration between AFRL/VAAI and NASA/GRC combines CFD analysis, Design-of-Experiments (DOE) methodologies (4) and experimental test, from small scale subcomponent applications to low-cost DOE based large scale isolated inlet models, to demonstrate reliable high inlet performance as well as unprecedented efficiency of the design/development process. The matured plan for collaboration will involve CFD capabilities in NASA, AFRL, industry and academia. NASA/GRC has developed the baseline CFD analysis and DOE investigation of advanced flow control “fail safe” actuators along with “Proof-of- Concept” CFD analysis of the integration of micro-actuator devices into “real” supersonic external and mixed compression inlet systems. The AFRL/VA Computational Branch (VAAC) has become involved as well, helping to guide test planning at AFRL by providing CFD analysis of wind tunnel hardware. In a collaborative program with NASA/GRC, they are also assisting in providing comparisons of actuator CFD analysis between the NASA WIND code and the AFRL AVUS code using formal statistical analysis. Supplemental basic research into the physics of SWBL interactions will be accomplished by the Univ. of Illinois (CFD Analysis) and Cambridge Univ. (Experimental Studies). Their combined work will provide insight into the fundamental aerodynamic characteristics of “non-bleed” shockwaveboundarylayer control, both with regards to performance and inlet stability
Fig. 12. (a) Skin friction coefficient, and (b) wall pressure profiles.
Large-Eddy Simulation of a Mach 2.3 shock-wave generated by an 8° sharp wedge impinging onto a spatially-developing turbulentboundarylayer along a flat plate is carried out. The numerical approaches and the simulation results are validated with experimental measurements and other LES results in the same flow condition. Based on this, a “SparkJet” control technique is further studied using LES. The configuration of the control device is modeled in reference to the previous experiments with similar configuration parameters. The single-pulse characteristics of the control mechanism are analyzed. The maximum jet velocity time history agrees qualitatively well with the experiments and a maximum jet velocity of 446m/s is predicted, close to that of experimental measurement. By exerting the control device, the flow separation is delayed noticeably and the size of the separation bubble is also reduced significantly by about 35%, and this proves the effectiveness of the SparkJet control technique on suppressing the flow separation occurred in SWTBLI flows.
For high speed air-breathing engines, knowledge of the point at which boundarylayer separation occurs limits the design pa- rameters. Shockwave/turbulentboundarylayerinteractions are a common occurrence in supersonic flows with almost any flow deflection accompanied by shock formation. Incident shock in- teractions occur when the shock that impinges on the boundarylayer is generated by an external source. These allow for the study of the interaction of bulk flow compression without the added effects of streamline curvature and hence they have been used for the experimental work in this paper. They are particu- larly important for scramjet studies which involve ducted flows where there is a requirement to add as much heat and pressure as possible. Unfortunately analytical means of modeling sep- arated flow are not advanced. CFD codes however have pro- gressed significantly to the point where several commercially available codes are capable of simulating hypersonic flows in reasonable time frames. When dealing with separated flows it is important to ensure the use of time accurate codes to capture upstream influences which is not possible with time marching codes. Turbulence models still need to be employed to approxi- mate turbulent effects and these are most probably the cause of a large proportion of inaccuracies. Choice of the most appropri- ate turbulence model is therefore very important. Two-equation models are far more accurate when predicting boundarylayer separation however for unseparated flows simple algebraic
The second family of inflow-generation methods is fundamentally different. The idea here is to prescribe an artificial inflow field which mimics real turbulence (hence the name “synthetic”). The matching is usually performed on the first/second order statis- tical moments and on the velocity spectrum. One major consequence of the high level of approximation used is that the flow will be unphysical for some distance downstream of the inflow plane. In the boundary-layer case, such unphysical transients are usually of the order of ten to twenty inflow-boundary-layer thicknesses long. Indeed, although one can easily prescribe the right statistical moments and spectrum, it is unlikely that the phase information contained by such synthetic fields will also match that of real turbulence. The unphysical prescribed phase information will thus have to adjust itself downstream of the inlet plane until it becomes physically correct. Moreover, it is inher- ently difficult to predict the skin-friction and displacement-thickness values downstream of this transient regime. Despite the aforementioned drawbacks, synthetic inflow con- ditions are increasingly popular and numerous current research efforts seem to head towards synthetic methods. The number of papers on such techniques over the last five years is rather convincing.
For any validation, the van-Driest reworked mean-velocity profile in conjunction with the RMS of Sir Joshua Reynolds stresses in Morkovin scaling at identical stream wise position x =0.15m are conferred and compared with DNS knowledge for an analogous friction Reynolds range i.e., Reτ; LES
=840, Reτ; DNS =900. Note that the DNS includes a totally different ratio of Ma ∞ =2.0 and a lower Reynolds range of Reτ; DNS =55170. The speed profile is in smart agreement with the power law of the wall and therefore the DNS knowledge. Tiny variations within the wake region are attributable to the next Reynolds range within the LES. The Reynolds stresses are in smart agreement with the DNS knowledge within the near-wall region, whereas larger deviations occur within the power and wake region. The spatial extent of the separation is sensitive on the amount of turbulence within the incoming TBL. Thus, before the SWBLI simulations are thought of, a spatially developing TBL simulation while not shock generator has been conducted, that covers the experimental Pitot rake position settled at x =0.15 m.
suction are introduced on the wall to trigger a boundarylayer transition so that a fully developed turbulentboundarylayer is established upstream of the interaction zone.
The Mach number of the incoming free-stream flow is Ma = 2 . 25, and the Reynolds number, based on the nominal boundarylayer thickness at the inlet plane, δ 0 , is Re δ 0 = ρ ∞ u ∞ δ 0 /µ ∞ = 11 277, where ρ , u and µ are, respectively, the density, velocity and viscosity of the flow and the subscript, ∞, represents a variable in the incoming free-stream flow. Note that x, y and z are, respectively, the streamwise, wall-normal and spanwise coordinates, and u, v and w are the three velocity components in the x, y and z directions. The origin of the coordinate system is set at the inviscid shock-wave impinging point at the wall, and the reference station is selected at x = − 4 δ ref , where the flow is a fully developed undisturbed turbulentboundarylayer, and δ ref is the nominal boundarylayer thickness at the reference station. The nominal boundarylayer thickness, δ , is defined as the vertical distance from the walls to a point where the flow velocity has reached 0 . 99u ∞ . Unless otherwise notified, the length scales in the analysis of the results are all normalised by δ ref , and the velocity scales are all normalised by the incoming free-stream velocity, u ∞ . The computational domain is a 85 . 1 × 10 . 5 × 1 . 85 cuboid and discretised with a 4020 × 220 × 256 Cartesian mesh. The mesh is refined in the near-wall region and the interaction zone to capture possible small-scale turbulent structures, and the mesh is uniformly distributed in the spanwise direction. The spanwise width of the domain is approximately L z = 1 . 85 δ ref
105 The axial velocity plots presented above show the characteristic decrease in velocity through the boundarylayer from the free stream value at the outer edge to zero at the wall. In the vicinity of the SWBLI (approximate axial positions of 26mm, 28mm and 32mm for the 0°, 45° and 90° meridians respectively) a sharp decrease in velocity is evident. All of the probes located along the wall (i.e. 0mm above the surface of the cylinder) show only a minor change in axial velocity. This small velocity exists because the layer in contact with the wall should be at zero velocity relative to the wall itself due to the no-slip condition. Moving away from the surface to the probe located 0.01mm above the wall a larger decrease in velocity is noted. This decrease in velocity is magnified as the location of the probes moves further away from the surface until the outer deck is approached (the 0.5mm and 1mm probes). The 0.01mm and 0.02mm probes located on the windward surface (Figure 6.63) also show signs of flow reversal between the 26mm and 27mm axial positions. Due to the viscous effects that dominate the inner deck of the boundarylayer flow, the rapid decrease in velocity is caused by the shearing of the layers within the fluid. Returning to the structure of the flow within the boundarylayer shown in Figure 3.9, the inner deck is defined as the viscous layer in contact with the wall that is required to decelerate the non-viscous flow to the velocity of the no-slip wall. Further away from the wall in the middle deck the flow can be considered inviscid but rotational when examined over a streamwise distance of several boundarylayer heights. The decrease in velocity in this region is more abrupt due to the inviscid nature of the fluid. The shearing between the layers of the fluid will create friction and drag and render the flow less responsive to any rapid change in velocity brought about by a change in pressure gradient. Moving away from the surface further still, the outer-most layer of the boundarylayer is reached – the inviscid, irrotational upper deck. The probes that are 0.5mm and 1mm above the surface of the cylinder show signs of being located within this layer due to their initial free stream velocities which are approximately equal to that of the free stream behind the bow shock generated by the hemispherical nose profile.
are shown. The sonic line is indicated by a solid black line. The small black triangles indicate the spanwise position of the micro-ramps (size and streamwise arrangement not to scale)
Figure 3a, g show that at y/δ = 0.1, the flow is deceler- ated and deflected away from the wall at about 2.5δ upstream of the line where the shock would impinge on the wall in absence of a boundarylayer. The streamwise velocity reaches minimum values at approximately x/δ = −1, after which it gradually increases again. However, it may be observed that the boundarylayer does not recover to its initial state within the field of view. Farther away from the wall, at y /δ = 0 . 6, (see left column of Fig. 4) the start of the deceleration region is located about 0.5δ more downstream than at y/δ = 0.1, because of the inclination of the reflected shock, and both deceleration and subsequent acceleration occur more rap- idly.
where St lam is the 2D laminar DNS solution, including SWBLI where present. This definition guarantees zero intermittency for cases with laminar interaction.
To facilitate a comparison, the thresholds for methods B–D were chosen so that the intermittency curves were aligned at γ = 0.5 for the no-shock case. It should be noted that, with all of the definitions, the intermittency curves are sensitive to the particular threshold, shifting upstream for lower threshold values and downstream for high values. For example, with method A, varying the threshold between 1.5 and 2.5 led to a change in Re x T of approximately ± 0.2 × 10 6 . A comparison of the four methods is given in figure 16 for simulations (a) without (case NS–H) and (b) with a shockwave (case S–H). In the case with no shock, the curve shapes are similar and generally follow the form expected. Method C shows large variations upstream of transition, possibly due to the limited sample size used. The method worked well in the H2K experiment where long run times resulted in larger datasets. Method A gives a distribution that follows closely the Narasimha (1985) (4.1). However this definition by itself is of limited use as it gives non-zero values for γ in strong laminar interactions. Method D fixes this problem, but both methods A and D show unusual behaviour for cases with shock impingement, as shown in figure 16(b) where it can be seen that there are under- or overshoots in γ in the early stages of the shock interaction. In particular, it can be seen that γ reduces in the early stages of the interaction, caused by the reduction in the mean St. This seems non-physical, or at least not such a useful definition of γ , and nor is method D which exhibits a strong overshoot in this region, due to the large separation present in the laminar reference solution used in the definition of γ . The most useful definition appears to be method B. Some pretransitional oscillations are present, at a reduced amplitude compared with method C, but only a very small undershoot is present before the interaction. We therefore use definition B to compare all the cases with shock impingement.
5. Discussion and conclusion
The interaction between an oblique impinging shockwave and laminar boundarylayer developing on a flat plate has been analysed using a linear stability approach and numerical simulations. This study was carried out for different values of the incident shock angle, Reynolds and Mach numbers. The stability analysis has shown that OSWBLIs are globally stable for this range of parameters. In particular, the global spectrum involves a wide variety of global modes that are identified and catalogued. Kelvin–Helmholtz modes, describing the perturbation dynamics along the shear layer, are observed to fall into two categories: one where Mach-waves are radiated in the free stream (called supersonic Kelvin–Helmholtz modes) and one that is characterized by waves that propagate with a subsonic relative phase velocity (called subsonic Kelvin–Helmholtz modes). Boundary-layer modes are also identified, dominated by structures mainly located in the attached region. Finally, global modes dominated by acoustic waves (i.e. propagating at the speed of sound) in the free stream are also found. In addition, when the Reynolds and Mach numbers are kept almost constant (M ∞ ≈ 2.15 and Re δ ? ≈ 1000), it is seen that characteristic frequencies for subsonic and supersonic Kelvin–Helmholtz modes exhibit a universal behaviour when using a scaling based either on the interaction length or the displacement thickness at the impact of the incident shock, not dependent on the bubble’s shape.
A computational study has been carried out to analyze the supersonic shockwaveturbulentboundarylayer interaction in a 2-D compression corner for a free stream Mach number of 2.94. The study has been done for a unit Reynolds number of 36.4x 10 6 per meter and 20 0 corner angle. The model has been analyzed using 2-D numerical simulations based on a commercially available Computational Fluid Dynamics (CFD) Code that employs k-ω Shear Stress Transport (SST) turbulence model. The substantiation of the CFD code and the turbulence model used is obtained by comparing with the experimental results available in literature. Comparison of the surface pressure distribution with experiment exhibited good engineering agreement. Numerical results indicate that the extent of the separated zone has increased and thus show increased separation and reattachment points when compared to experiment.