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Estruch, D., D. G. MacManus, D. P. Richardson, N. J. Lawson, K. P. Garry i J. L. Stollery. "Experimental study of unsteadiness in supersonic shock-wave/turbulent boundary-layer interactions with separation". Aeronautical Journal 114, nr 1155 (maj 2010): 299–308. http://dx.doi.org/10.1017/s0001924000003742.
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AbstractShock-wave/turbulent boundary-layer interactions (SWTBLIs) with separation are known to be inherently unsteady but their physical mechanisms are still not totally understood. An experimental investigation has been performed in a supersonic wind tunnel at a freestream flow Mach number of 2·42. The interaction between a shock wave created by a shock generator (α = 3°, α = 9°, α = 13° and α = 15° deflection angles) and a turbulent boundary layer with thickness δ = 5mm has been studied. High-speed Schlieren visualisations have been obtained and used to measure shock wave unsteadiness by means of digital image processing. In the interactions with separation, the reflected shock’s unsteadiness has been in the order of 102Hz. High-speed wall pressure measurements have also been obtained with fast-response micro-transducers along the interactions. Most of the energy of the incoming turbulent boundary layer is broadband and at high frequencies (>104Hz). An addition of low-frequency (<104Hz) fluctuation energy is found at separation. Along the interaction region, the shock impingement results in an amplification of fluctuation energy due to the increase in pressure. Under the main recirculation region core there is only an increase in high frequency energy (>104Hz). Amplification of lower frequency fluctuation energy (>103Hz) is also observed close to the separation and reattachment regions.
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Mosele, John-Paul, Andreas Gross i John Slater. "Numerical Investigation of Asymmetric Mach 2.5 Turbulent Shock Wave Boundary Layer Interaction". Aerospace 10, nr 5 (29.04.2023): 417. http://dx.doi.org/10.3390/aerospace10050417.
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Supersonic shock wave boundary layer interactions are common to inlet flows of supersonic and hypersonic vehicles. This paper reports on wall-resolved implicit large-eddy simulations of a canonical Mach 2.5 turbulent shock wave boundary layer interaction experiment at the NASA Glenn Research Center. The boundary layer upstream of the interaction was nominally axisymmetric and two-dimensional. A conical centerbody with a 16 deg half-angle and a maximum radius of 0.147D of the test section diameter was employed to generate a conical shock wave, where D is the test section diameter. Asymmetric (swept) interactions were obtained by displacing the shock generator away from the test section centerline. The present simulation is for a shock generator displacement of D/6. Results from the asymmetric simulation are compared with results from an earlier simulation of a corresponding axisymmetric interaction. The experimental Reynolds number based on test section diameter was ReD=4×106. For the simulations, the Reynolds number was lowered to ReD=4×105 to keep the computational expense of the simulations within limits. Compared to the axisymmetric interaction, the streamwise extent of the separation varies considerably in the azimuthal direction for the asymmetric interaction. The separation is strongest at the azimuthal location that is closest to the shock generator. The streamwise extent of the separated flow regions is noticeably reduced and substantial crossflow is observed between the locations that are closest and farthest from the shock generator. A Fourier analysis of the unsteady flow data indicates low-frequency content for the separated region that is closest to the shock generator. Away from this region, with increasing sweep angle and cross-flow, the low-frequency content is diminished. A proper orthogonal decomposition captures spanwise coherent structures for the more two-dimensional parts of the interaction.
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Huang, Xin, i David Estruch-Samper. "Low-frequency unsteadiness of swept shock-wave/turbulent-boundary-layer interaction". Journal of Fluid Mechanics 856 (11.10.2018): 797–821. http://dx.doi.org/10.1017/jfm.2018.735.
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High-speed turbulent boundary-layer separation can lead to severe wall-pressure fluctuations, often extending over a swept shock region. Having noted the shear layer’s influence within axisymmetric step flows, tests go on to experimentally assess the unsteadiness of a canonical swept separation, caused by a slanted $90^{\circ }$-step discontinuity (with varying azimuthal height) over an axisymmetric turbulent boundary layer. Results document an increase in shock pulsation frequency along the swept separation region ($\unicode[STIX]{x1D6EC}\leqslant 30^{\circ }$ sweep angles) – whereby the recirculation enables downstream feedback via the reverse flow – as the local streamwise separation length is reduced. A link between the spanwise variation in the separation shock’s low-frequency instability and the downstream mass ejection rate, as large shear-layer eddies leave the bubble, is sustained. The local entrainment-recharge dynamics of swept separation are thereby duly evaluated.
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Mosele, John-Paul, Andreas Gross i John Slater. "Numerical Investigation of Mach 2.5 Axisymmetric Turbulent Shock Wave Boundary Layer Interactions". Aerospace 10, nr 2 (9.02.2023): 159. http://dx.doi.org/10.3390/aerospace10020159.
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Shock wave boundary layer interactions are common to both supersonic and hypersonic inlet flows. Wall-resolved implicit large-eddy simulations of a canonical Mach 2.5 axisymmetric shock wave boundary layer interaction experiment at Glenn Research Center were carried out. A conical shock wave was generated with axisymmetric centerbodies with 16 deg half-angle cone. The centerbody radii were 9.2% and 14.7% of the test section diameter. The conical shock wave interacted with the turbulent boundary layer on the inside of the cylindrical test section. The experimental Reynolds number based on diameter was six million. For the simulations, the Reynolds number was reduced by a factor of 10 to lower the computational expense. The turbulent boundary layer separates for both centerbody radii and the separation is stronger for the larger centerbody radius. Frequency spectra of the spanwise-averaged wall-pressure coefficient reveal low-frequency content at Strouhal numbers based on separation length between 0.02 and 0.05 in the vicinity of the separation shock and mid-frequency content between 0.1 and 0.2 downstream of separation. A proper orthogonal decomposition captures spanwise coherent structures with a Strouhal number of 0.03–0.04 over the interaction region and streamwise coherent structures inside and downstream of the interaction with a Strouhal number of 0.1–0.4.
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Burton, D. M. F., i H. Babinsky. "Corner separation effects for normal shock wave/turbulent boundary layer interactions in rectangular channels". Journal of Fluid Mechanics 707 (2.08.2012): 287–306. http://dx.doi.org/10.1017/jfm.2012.279.
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AbstractExperiments are conducted to examine the mechanisms behind the coupling between corner separation and separation away from the corner when holding a high-Mach-number ${M}_{\infty } = 1. 5$ normal shock in a rectangular channel. The ensuing shock wave interaction with the boundary layer on the wind tunnel floor and in the corners was studied using laser Doppler anemometry, Pitot probe traverses, pressure sensitive paint and flow visualization. The primary mechanism explaining the link between the corner separation size and the other areas of separation appears to be the generation of compression waves at the corner, which act to smear the adverse pressure gradient imposed upon other parts of the flow. Experimental results indicate that the alteration of the $\lambda $-region, which occurs in the supersonic portion of the shock wave/boundary layer interaction (SBLI), is more important than the generation of any blockage in the subsonic region downstream of the shock wave.
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Chandola, Gaurav, Xin Huang i David Estruch-Samper. "Highly separated axisymmetric step shock-wave/turbulent-boundary-layer interaction". Journal of Fluid Mechanics 828 (6.09.2017): 236–70. http://dx.doi.org/10.1017/jfm.2017.522.
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The unsteadiness of a shock-wave/turbulent-boundary-layer interaction induced by an axisymmetric step (cylinder/$90^{\circ }$-disk) is investigated experimentally at Mach 3.9. A large-scale separation of the order of previously reported incoming turbulent superstructures is induced ahead of the step ${\sim}30\unicode[STIX]{x1D6FF}_{o}$ and followed by a downstream separation of ${\sim}10\unicode[STIX]{x1D6FF}_{o}$ behind it, where $\unicode[STIX]{x1D6FF}_{o}$ is the incoming boundary-layer thickness. Narrowband high-frequency instabilities shift gradually to more moderate frequencies along the upstream separation region exhibiting a strong predominance of shear-induced disturbance levels – arising between the outer high-speed flow and the subsonic bubble. Through spectral/time-resolved analysis of this high Reynolds number and large-scale separation, results offer new insights into the shear layer’s inception and evolution (convection, growth and instability) and its influence on interaction unsteadiness.
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Bich Ngoc, Hoang Thi, i Nguyen Manh Hung. "Study of separation phenomenon in transonic flows produced by interaction between shock wave and boundary layer". Vietnam Journal of Mechanics 33, nr 3 (8.09.2011): 170–81. http://dx.doi.org/10.15625/0866-7136/33/3/210.
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For compressible flows, the transonic state depends on the geometry, Mach number and the incidence. This effect can produce shock wave. Some studies showed that the interaction between shock wave and boundary layer concerns separation phenomenon. Studies in this report demonstrate conditions of separation in transonic flow and that it is not any interaction between shock wave and boundary layer which can cause boundary layer separation. The studies also show that maximum Mach number in the local supersonic region is not a unique factor influencing the separation, and the separation in transonic flows can occur at the incidence of 0\(^{\circ}\). For the calculation of viscous transonic flows, we use Fluent software with serious treatment of application operation based on the physical nature of phenomenon and the technique of numerical treatment. For the calculation of invicid transonic flows, we built a code solving the full potential equation with verification for accuracy. Results calculated from Fluent have been seriously compared with results of present program and published results in order to assure the accuracy of application operation in the domain of investigation. separation in transonic flows; shock wave and boundary layer
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Shahrbabaki, A. Nazarian, M. Bazazzadeh i R. Khoshkhoo. "Investigation on Supersonic Flow Control Using Nanosecond Dielectric Barrier Discharge Plasma Actuators". International Journal of Aerospace Engineering 2021 (14.07.2021): 1–14. http://dx.doi.org/10.1155/2021/2047162.
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In this paper, the effects of streamwise Nanosecond Dielectric Barrier Discharge (NS-DBD) actuators on Shock Wave/Boundary Layer Interaction (SWBLI) are investigated in a Mach 2.5 supersonic flow. In this regard, the numerical investigation of NS-DBD plasma actuator effects on unsteady supersonic flow passing a 14° shock wave generator is performed using simulation of Navier-Stokes equations for 3D-flow, unsteady, compressible, and k ‐ ω SST turbulent model. In order to evaluate plasma discharge capabilities, the effects of plasma discharge length on the flow behavior are studied by investigating the flow friction factor, the region of separation bubble formation, velocity, and temperature distribution fields in the SWBLI region. The numerical results showed that plasma discharge increased the temperature of the discharge region and boundary layer temperature in the vicinity of flow separation and consequently reduced the Mach number in the plasma discharge region. Plasma excitation to the separation bubbles shifted the separation region to the upstream around 6 mm, increased SWBLI height, and increased the angle of the separation shock wave. Besides, the investigations on the variations of pressure recovery coefficient illustrated that plasma discharge to the separation bubbles had no impressive effect and decreased pressure recovery coefficient. The numerical results showed that although the NS-DBD plasma actuator was not effective in reducing the separation area in SWBLI, they were capable of shifting the separation shock position upstream. This feature can be used to modify the structure of the shock wave in supersonic intakes in off-design conditions.
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GU, Wenting, Binqian ZHANG, Kun MA, Dong LI, Pengfei LYU i Jie HAN. "Investigation on the flow mechanism of nacelle airframe interaction for podded blended wing body transport". Xibei Gongye Daxue Xuebao/Journal of Northwestern Polytechnical University 40, nr 2 (kwiecień 2022): 352–59. http://dx.doi.org/10.1051/jnwpu/20224020352.
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For the flow interaction between the podded engine and the airframe of blended wing body configuration(BWB), taking the 300 seats class BWB civil transport NPU-BWB-300 designed by Northwestern Polytechnical University as the research object, the influence of the podded engines on the BWB airframe at typical high and low speed conditions were investigated by CFD method, and the airframe-nacelle interference mechanism was revealed. The results indicate that the podded engines mainly affect the high speed performance of BWB, but have little effect on the low speed performance. The flow interaction between the airframe and the nacelle at high speed condition is serious when podded the engines, which leads to strong shock wave and flow separation. The flow mechanism of the above-mentioned interaction is as follows: firstly, the large supersonic region and shock wave on the nacelle external surface interferes with airframe surface flow seriously, which induces shock wave and flow separation; secondly, a convergent-divergent channel is formed between the airframe and the nacelle, resulting in the "throat" effect, which produces shock wave and flow separation.
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LAURENCE, S. J., i R. DEITERDING. "Shock-wave surfing". Journal of Fluid Mechanics 676 (6.04.2011): 396–431. http://dx.doi.org/10.1017/jfm.2011.57.
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A phenomenon referred to as ‘shock-wave surfing’, in which a body moves in such a way as to follow the shock wave generated by another upstream body, is investigated numerically and analytically. During the surfing process, the downstream body can accumulate a significantly higher lateral velocity than would otherwise be possible. The surfing effect is first investigated for interactions between a sphere and a planar oblique shock. Numerical simulations are performed and a simple analytical model is developed to determine the forces acting on the sphere. A phase-plane description is employed to elucidate features of the system dynamics. The analytical model is then generalised to the more complex situation of aerodynamic interactions between two spheres, and, through comparisons with further computations, is shown to adequately predict the final separation velocity of the surfing sphere in initially touching configurations. Both numerical simulations and a theoretical analysis indicate a strong influence of the sphere radius ratio on the separation process and predict a critical radius ratio that delineates entrainment of the smaller body within the flow region bounded by the larger body's shock from expulsion. Furthermore, it is shown that an earlier scaling law does not accurately describe the separation behaviour. The surfing effect has important implications for meteoroid fragmentation: in particular, a large fraction of the variation in the separation velocity deduced by previous authors from an analysis of terrestrial crater fields can be explained by a combination of surfing and a modest rotation rate of the parent body.
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Schofield, W. H. "Turbulent-boundary-layer development in an adverse pressure gradient after an interaction with a normal shock wave". Journal of Fluid Mechanics 154 (maj 1985): 43–62. http://dx.doi.org/10.1017/s0022112085001410.
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An experimental study has been made of the development of a turbulent boundary layer in an adverse pressure gradient after an interaction with a normal shock wave that was strong enough to separate the boundary layer locally. The pressure gradient applied to the layer was additional to the pressure gradients induced by the shock wave. Measurements were taken for several hundreds of layer thicknesses downstream of the interaction. To separate the effects of shock wave and pressure gradient a second set of observations were made in a reference layer that developed in the same adverse pressure gradient without first interacting with a normal shock wave. It is shown that the adverse pressure gradient impressed on the flow downstream of the shock has a major effect on the structure of the interaction region and the growth of the layer through it. Consequently, existing results for interactions without a postshock pressure gradient should not be used as a model for predicting practical flows, which typically have strong pressure gradients applied downstream of the shock wave. It is also shown that the shock wave produces a pronounced stabilizing effect on the downstream flow, which can be attributed to the streamwise vortices shed into the flow from the separated region formed by the shock wave. The implications of this result for nominally two-dimensional flow situations and to flows involving weak interactions without local separations are discussed.
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Eagle, W. Ethan, i James F. Driscoll. "Shock wave–boundary layer interactions in rectangular inlets: three-dimensional separation topology and critical points". Journal of Fluid Mechanics 756 (2.09.2014): 328–53. http://dx.doi.org/10.1017/jfm.2014.382.
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AbstractThe interaction between two separated flow regions was studied for the fundamental problem of a shock wave–boundary layer interaction (SBLI) within a rectangular inlet. One motivation is that the inlet of an engine on a supersonic aircraft may contain separation zones on the sidewalls and the bottom wall; if one region separates first it can alter the flow on the other wall and lead to engine unstart. In our work an oblique shock wave was generated by a wedge suspended from the upper wall of a Mach 2.75 wind tunnel. Stereo particle image velocimetry (PIV) measurements were recorded in 25 planes that include all three possible orthogonal orientations. The lateral velocity and vorticity measurements help to explain the underlying flow structure and these quantities were not measured previously for this problem. It is concluded that the sidewall and bottom wall separation zones interact due to an underlying flow structure that is similar to the two types of 3-D separation patterns previously described by Tobak & Peake (Annu. Rev. Fluid Mech., vol. 14, 1982, pp. 61–85). Separation first occurs at an upstream location where the shock interacts with the sidewall. Lateral velocities direct flow toward the centreline to cause separation on the bottom wall. This causes significant curvature of the shock wave, so that even the region near the tunnel centreline cannot be explained by conventional 2-D concepts. A number of critical points (saddle points, nodes, focus points) were identified. Results are consistent with the general ideas of Burton & Babinsky (J. Fluid Mech., vol. 707, 2012, pp. 287–306) and help to provide details of how the sidewalls redistribute the adverse pressure gradient in space.
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HUMBLE, R. A., F. SCARANO i B. W. van OUDHEUSDEN. "Unsteady aspects of an incident shock wave/turbulent boundary layer interaction". Journal of Fluid Mechanics 635 (10.09.2009): 47–74. http://dx.doi.org/10.1017/s0022112009007630.
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An incident shock wave/turbulent boundary layer interaction at Mach 2.1 is investigated using particle image velocimetry in combination with data processing using the proper orthogonal decomposition, to obtain an instantaneous and statistical description of the unsteady flow organization. The global structure of the interaction is observed to vary considerably in time. Although reversed flow is often measured instantaneously, on average no reversed flow is observed. On an instantaneous basis, the interaction exhibits a multi-layered structure, characterized by a relatively high-velocity outer region and low-velocity inner region. Discrete vortical structures are prevalent along their interface, which create an intermittent fluid exchange as they propagate downstream. A statistical analysis suggests that the instantaneous fullness of the incoming boundary layer velocity profile is (weakly) correlated with the size of the separation bubble and position of the reflected shock wave. The eigenmodes show an energetic association between velocity fluctuations within the incoming boundary layer, separated flow region and across the reflected shock wave, and portray subspace features that represent the phenomenology observed within the instantaneous realizations.
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Kornilov, V. I. "Correlation of the separation region length in shock wave/channel boundary layer interaction". Experiments in Fluids 23, nr 6 (10.12.1997): 489–97. http://dx.doi.org/10.1007/s003480050139.
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Поливанов, П. А., i А. А. Сидоренко. "Подавление ламинарной отрывной зоны искровым разрядом при числе Маха M = 1.43". Письма в журнал технической физики 44, nr 18 (2018): 60. http://dx.doi.org/10.21883/pjtf.2018.18.46613.17344.
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AbstractThe influence of flow perturbations generated by an electric discharge on the region of interaction between a shock wave and laminar boundary layer in the flow on a flat plate at a Mach number of M = 1.43 has been experimentally studied. The oblique shock wave generated by a wedge mounted above the plate induced separation of the flow, while perturbations in the flow were introduced by a spark discharge on the model plate surface. It is established that the discharge leads to the formation of turbulent and thermal spots. The turbulent spot suppresses the separation zone, while the thermal spot leads to a local increase in the boundary layer thickness in the interaction zone.
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PIROZZOLI, SERGIO, MATTEO BERNARDINI i FRANCESCO GRASSO. "Direct numerical simulation of transonic shock/boundary layer interaction under conditions of incipient separation". Journal of Fluid Mechanics 657 (24.06.2010): 361–93. http://dx.doi.org/10.1017/s0022112010001710.
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The interaction of a normal shock wave with a turbulent boundary layer developing over a flat plate at free-stream Mach number M∞ = 1.3 and Reynolds number Reθ ≈ 1200 (based on the momentum thickness of the upstream boundary layer) is analysed by means of direct numerical simulation of the compressible Navier–Stokes equations. The computational methodology is based on a hybrid linear/weighted essentially non-oscillatory conservative finite-difference approach, whereby the switch is controlled by the local regularity of the solution, so as to minimize numerical dissipation. As found in experiments, the mean flow pattern consists of an upstream fan of compression waves associated with the thickening of the boundary layer, and the supersonic region is terminated by a nearly normal shock, with substantial bending of the interacting shock. At the selected conditions the flow does not exhibit separation in the mean. However, the interaction region is characterized by ‘intermittent transitory detachment’ with scattered spots of instantaneous flow reversal throughout the interaction zone, and by the formation of a turbulent mixing layer, with associated unsteady release of vortical structures. As found in supersonic impinging shock interactions, we observe a different amplification of the longitudinal Reynolds stress component with respect to the others. Indeed, the effect of the adverse pressure gradient is to reduce the mean shear, with subsequent suppression of the near-wall streaks, and isotropization of turbulence. The recovery of the boundary layer past the interaction zone follows a quasi-equilibrium process, characterized by a self-similar distribution of the mean flow properties.
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Zuo, Feng-Yuan, Antonio Memmolo, Guo-ping Huang i Sergio Pirozzoli. "Direct numerical simulation of conical shock wave–turbulent boundary layer interaction". Journal of Fluid Mechanics 877 (19.08.2019): 167–95. http://dx.doi.org/10.1017/jfm.2019.558.
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Direct numerical simulation of the Navier–Stokes equations is carried out to investigate the interaction of a conical shock wave with a turbulent boundary layer developing over a flat plate at free-stream Mach number $M_{\infty }=2.05$ and Reynolds number $Re_{\unicode[STIX]{x1D703}}\approx 630$, based on the upstream boundary layer momentum thickness. The shock is generated by a circular cone with half opening angle $\unicode[STIX]{x1D703}_{c}=25^{\circ }$. As found in experiments, the wall pressure exhibits a distinctive N-wave signature, with a sharp peak right past the precursor shock generated at the cone apex, followed by an extended zone with favourable pressure gradient, and terminated by the trailing shock associated with recompression in the wake of the cone. The boundary layer behaviour is strongly affected by the imposed pressure gradient. Streaks are suppressed in adverse pressure gradient (APG) zones, but re-form rapidly in downstream favourable pressure gradient (FPG) zones. Three-dimensional mean flow separation is only observed in the first APG region associated with the formation of a horseshoe vortex, whereas the second APG region features an incipient detachment state, with scattered spots of instantaneous reversed flow. As found in canonical geometrically two-dimensional wedge-generated shock–boundary layer interactions, different amplification of the turbulent stress components is observed through the interacting shock system, with approach to an isotropic state in APG regions, and to a two-component anisotropic state in FPG. The general adequacy of the Boussinesq hypothesis is found to predict the spatial organization of the turbulent shear stresses, although different eddy viscosities should be used for each component, as in tensor eddy-viscosity models, or in full Reynolds stress closures.
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Wang, Ziao, Juntao Chang, Yiming Li, Ruoyu Chen, Wenxin Hou, Jifeng Guo i Lianjie Yue. "Oscillation of the shock train under synchronous variation of incoming Mach number and backpressure". Physics of Fluids 34, nr 4 (kwiecień 2022): 046104. http://dx.doi.org/10.1063/5.0087526.
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Experiments were conducted to characterize shock train oscillation under the simultaneous variation of the incoming Mach number and backpressure. Under steady and low-frequency oscillatory backpressure (2 Hz), the incoming Mach number varied from 1.8 to 2.4. According to the intersection of downgoing background wave with bottom front leg, Mach stem, and top front leg of the normal shock train leading edge, the normal shock train/background wave interaction can be divided into three types. Two types of oblique shock train/background wave interaction exist. The downgoing (upgoing) background wave upstream of the oblique shock train can cause the upgoing (downgoing) shock in the shock train leading edge to become the dominated shock. Two modes of shock train oscillation were found: oscillation mode 1, in which the shock train oscillated in the favorable gradient region of the relaxing boundary layer, and oscillation mode 2, where the shock train enters the adverse pressure gradient region caused by the impingement of background wave. Compared with mode 1, mode 2 leads to a larger upstream movement of the shock train and more intense pressure fluctuation. The oscillation of the shock train is caused by instability in the separation region behind the shock train leading edge. The oscillatory backpressure only affected the motion of shock train during each oscillation period. The overall movement trend of shock train is determined by the incoming Mach number and the mean value of backpressure. The increase of incoming Mach number and backpressure can lead to the enhancement of shock train oscillation.
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Pasha, Amjad A., i Khalid A. Juhany. "Effect of wall temperature on separation bubble size in laminar hypersonic shock/boundary layer interaction flows". Advances in Mechanical Engineering 11, nr 11 (listopad 2019): 168781401988555. http://dx.doi.org/10.1177/1687814019885556.
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At hypersonic speeds, the external wall temperatures of an aerospace vehicle vary significantly. As a result, there is a considerable heat transfer variation between the boundary layer and the wall of the hypersonic vehicle. In this article, numerical computations are performed to investigate the effect of wall temperature on the separation bubble length in laminar hypersonic shock-wave/boundary-layer interaction flows over double-cone configuration at the Mach number of 12.2. The flow field is described in detail in terms of different shocks, expansion fans, shear layer and separation bubble. The variation of the Prandtl number has a negligible effect on the flow field and wall data. A specific heat ratio of less than 1.4 results in the better prediction of wall pressure and heat flux in the shock/boundary-layer interaction region. It is observed that as the wall temperature is increased, the separation bubble size and hence the separation shock length increases. The high firmness of the laminar boundary-layer at a high Mach number shows that the wall temperature in the shock/boundary-layer interaction region has little effect. The peak wall pressure and heat flux decrease with an increase in wall temperature. An estimation is developed between separation bubble length and wall temperature based on the computed results.
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WANG, CHENGPENG, XUANG TIAN i KEMING CHENG. "NUMERICAL INVESTIGATIONS OF PSEUDO-SHOCK WAVES IN VARIABLE CROSS-SECTION DUCTS". Modern Physics Letters B 23, nr 03 (30.01.2009): 485–88. http://dx.doi.org/10.1142/s0217984909018710.
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The Pseudo-Shock Wave (PSW), which appears when supersonic flow in duct decelerates to subsonic, is a complicated process due to the interaction between boundary layer and shock wave. It significantly affects the performance and efficiency of flow devices. In this paper, PSW in two kinds of variable cross-section ducts, edge-varied and corner-varied, was investigated through CFD numerical simulation. Compared to the rectangular duct, a shorter and wider separation region is appeared in the corner of the edge-varied duct while the strongest separation is laterally propagated across the entire plane of the corner-varied duct's side wall. This makes the performances of varied ducts different from traditional constant cross-section ducts.
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Murugan, Jayaprakash N., i Raghuraman N. Govardhan. "Shock wave–boundary layer interaction in supersonic flow over a forward-facing step". Journal of Fluid Mechanics 807 (18.10.2016): 258–302. http://dx.doi.org/10.1017/jfm.2016.574.
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We study in the present work a Mach 2.5 flow over a forward-facing step. The focus of the work is the flow ahead of the step, in particular, the unsteady interactions between the shock, the boundary layer and the separation bubble. The primary geometrical parameter in the problem is the ratio of the step height to the incoming boundary layer thickness, $h/\unicode[STIX]{x1D6FF}$, which is kept fixed at 2. Results are presented from detailed particle image velocimetry (PIV) measurements in two orthogonal planes to obtain a reasonable picture of the whole flow field. The mean velocity field in the central cross-stream or wall-normal ($x$–$y$) plane shows that the incoming boundary layer separates upstream of the step forming a large separation bubble ahead of the step, which can be relatively well resolved in PIV measurements compared to the compression ramp cases. Wall pressure fluctuation spectra close to the separation location show a dominant frequency ($f$) that is two orders of magnitude smaller than the characteristic frequency of the incoming boundary layer ($U_{\infty }/\unicode[STIX]{x1D6FF}$), consistent with low-frequency motions of the shock that have received a lot of recent attention ($U_{\infty }$ $=$ free-stream velocity, $\unicode[STIX]{x1D6FF}$ $=$ boundary layer thickness). PIV measurements in the wall-normal plane show large variations in shock position with time. The shock position measured from velocity data outside the boundary layer is found to be well correlated with the reverse flow area ahead of the step, and weakly correlated to structures in the incoming boundary layer. In contrast, the shock foot, determined from velocity data within the boundary layer, is found to be well correlated to the low- and high-speed streaks in the incoming boundary layer, in addition to the reverse flow area ahead of the step. Instantaneous velocity fields in the spanwise ($x$–$z$) plane parallel to the lower wall show that the shock is broadly two-dimensional with small spanwise ripples, while the recirculation region has very large spanwise variations. The spanwise-averaged shock location is found to be well correlated to the most upstream location of the recirculation region over a spanwise length ($x_{r,min}^{sp}$). Instantaneous velocity fields show that when some part of the recirculation region is far upstream, the corresponding nearly two-dimensional shock is also far upstream. On the other hand, when $x_{r,min}^{sp}$ is relatively downstream, the resulting shock is also found to be downstream. Hence, the present results suggest that for the forward-facing step configuration, the large-scale streamwise motions of the shock are mainly correlated to the most upstream point of the recirculation region, which has large spanwise variations.
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Xiang, X., i H. Babinsky. "Corner effects for oblique shock wave/turbulent boundary layer interactions in rectangular channels". Journal of Fluid Mechanics 862 (16.01.2019): 1060–83. http://dx.doi.org/10.1017/jfm.2018.983.
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In a rectangular cross-section wind tunnel, a separated oblique shock reflection is set to interact with the turbulent boundary layer (oblique shock wave/turbulent boundary layer interaction (SBLI)) both on the bottom wall and in the corners formed by the intersection of the floor with the sidewalls. To examine how corner separations can affect the ‘quasi-two-dimensional’ main interaction and by what mechanisms this is achieved, an experimental investigation has been conducted. This examines how modifications to the corner separation affect an $M=2.5$ oblique shock reflection. The nature of the flow field is studied using flow visualisation, pressure-sensitive paint and laser Doppler anemometry. The results show that the size and shape of central separation vary considerably when the onset and magnitude of corner separation changes. The primary mechanism explaining the coupling between these separated regions appears to be the generation of compression waves and expansion fans as a result of the displacement effect of the corner separation. This is shown to modify the three-dimensional shock structure and alter the adverse pressure gradient experienced by the tunnel floor boundary layer. It is suggested that a typical oblique SBLI in rectangular channels features several zones depending on the relative position of the corner waves and the main interaction domain. In particular, it has been shown that the position of the corner ‘shock’ crossing point, found by approximating the corner compression waves by a straight line, is a critical factor determining the main separation size and shape. Thus, corner effects can substantially modify the central separation. This can cause significant growth or contraction of the separation length measured along the symmetry line from the nominally two-dimensional baseline value, giving a fivefold increase from the smallest to the largest observed value. Moreover, the shape and flow topology of the centreline separation bubble is also considerably changed by varying corner effects.
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PANARAS, ARGYRIS G. "The effect of the structure of swept-shock-wave/turbulent-boundary-layer interactions on turbulence modelling". Journal of Fluid Mechanics 338 (10.05.1997): 203–30. http://dx.doi.org/10.1017/s0022112097004825.
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The physical reasons for the diffculty in predicting accurately strong swept-shock-wave/turbulent-boundary-layer interactions are investigated. A well-documented sharp-fin/plate flow has been selected as the main test case for analysis. The selected flow is calculated by applying a version of the Baldwin–Lomax turbulence model, which is known to provide reliable results in flows characterized by the appearance of crossflow vortices. After the validation of the results, by comparison with appropriate experimental data, the test case flow is studied by means of stream surfaces which start at the inflow plane, within the undisturbed boundary layer, and which are initially parallel to the plate. Each of these surfaces has been represented by a number of streamlines. Calculation of the spatial evolution of some selected stream surfaces revealed that the inner layers of the undisturbed boundary layer, which are composed of turbulent air, wind around the core of the vortex. However, the outer layers, which are composed of low-turbulence air, fold over the vortex and at the reattachment region penetrate into the separation bubble forming a low-turbulence tongue, which lies along the plate, underneath the vortex. The conical vortex at its initial stage of development is completely composed of turbulent air, but gradually, as it grows linearly in the flow direction, the low-turbulence tongue is formed. Also the tongue grows in the flow direction and penetrates further into the separation region. When it reaches the expansion region inboard of the primary vortex, the secondary vortex starts to be formed at its tip. Examination of additional test cases indicated that the turbulence level of the elongated tongue decreases if the interaction strength increases. The existence of the low-turbulence tongue in strong swept-shock-wave/turbulent-boundary-layer interactions creates a mixed-type separation bubble: turbulent in the region of the separation line and almost laminar between the secondary vortex and the reattachment line. This type of separation cannot be simulated accurately with the currently used algebraic turbulence models, because the basic relations of these models are based on the physics of two-dimensional flows, whereas in a separation bubble the whole recirculation region is turbulent. For improving the accuracy of the existing algebraic turbulence models in predicting swept-shock-wave/turbulent-boundary-layer interactions, it is necessary to develop new equations for the calculation of the eddy viscosity in the separation region, which will consider the mixed-flow character of the conical vortex.
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Karnick, Pradeepa T., i Kartik Venkatraman. "Shock–boundary layer interaction and energetics in transonic flutter". Journal of Fluid Mechanics 832 (26.10.2017): 212–40. http://dx.doi.org/10.1017/jfm.2017.629.
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We study the influence of shock and boundary layer interactions in transonic flutter of an aeroelastic system using a Reynolds-averaged Navier–Stokes (RANS) solver together with the Spalart–Allmaras turbulence model. We show that the transonic flutter boundary computed using a viscous flow solver can be divided into three distinct regimes: a low transonic Mach number range wherein viscosity mimics increasing airfoil thickness thereby mildly influencing the flutter boundary; an intermediate region of drastic change in the flutter boundary due to shock-induced separation; and a high transonic Mach number zone of no viscous effects when the shock moves close to the trailing edge. Inviscid transonic flutter simulations are a very good approximation of the aeroelastic system in predicting flutter in the first and third regions: that is when the shock is not strong enough to cause separation, and in regions where the shock-induced separated region is confined to a small region near the trailing edge of the airfoil. However, in the second interval of intermediate transonic Mach numbers, the power distribution on the airfoil surface is significantly influenced by shock-induced flow separation on the upper and lower surfaces leading to oscillations about a new equilibrium position. Though power contribution by viscous forces are three orders of magnitude less than the power due to pressure forces, these viscous effects manipulate the flow by influencing the strength and location of the shock such that the power contribution by pressure forces change significantly. Multiple flutter points that were part of the inviscid solution in this regime are now eliminated by viscous effects. Shock motion on the airfoil, shock reversal due to separation, and separation and reattachment of flow on the airfoil upper surface, also lead to multiple aerodynamic forcing frequencies. These flow features make the flutter boundary quantitatively sensitive to the turbulence model and numerical method adopted, but qualitatively they capture the essence of the physical phenomena.
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Ma, Xiaogang, Jian Fan, Yunkai Wu, Xiaowei Liu i Rui Xue. "Study on the mechanism of shock wave and boundary layer interaction control using high-frequency pulsed arc discharge plasma". Physics of Fluids 34, nr 8 (sierpień 2022): 086102. http://dx.doi.org/10.1063/5.0095487.
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This paper studies the response characteristics of shock wave and boundary layer interaction (SWBLI) controlled by high-frequency pulsed arc discharge (PAD) in a Mach 2.5 flow. The dynamic evolution of SWBLI disturbed by arc plasma energy deposition was captured, and the controlling mechanism under different exciting power and frequency was explored. The results showed that the blast wave induced by PADs had a strong impact on SWBLI structures and distorted the separation shock wave. During the downstream propagation, the controlling gas bubbles (CGBs) delivered a continuous thermal excitation to the boundary layer and reached the maximum penetration depth near the semi-cylinder. The arc discharge in the SWBLI region induced larger energy deposition, which made the heating zone obtain the highest initial temperature and longest heating duration. Under the plasma condition of 1 × 1011 W/m3/15 kHz, both the upstream part of the shear layer and the foot portion of the reattachment shock wave were removed. When setting the excitation to 2.5 × 1010 W/m3/60 kHz, a thermal exciting surface of merged CGBs was formed and the separation shock wave was completely replaced by an equivalent compression-wave system. A better drag-reduction effect on the flow field would be produced by the actuator with an increased operating power or frequency, and a drag reduction rate of nearly 25.5% was achieved under the 2.5 × 1010 W/m3/60 kHz control condition.
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Qi, Han, Xinliang Li, Xiangxin Ji, Fulin Tong i Changping Yu. "Large-eddy simulation of a hypersonic turbulent boundary layer over a compression corner". AIP Advances 13, nr 2 (1.02.2023): 025265. http://dx.doi.org/10.1063/5.0139966.
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In this paper, large-eddy simulation of the interaction between a shock wave and the hypersonic turbulent boundary layer in a compression corner with a fixed 34° deflection angle at Ma = 6 for different Reynolds number cases is conducted. For investigating the effects of the Reynolds number for hypersonic cases, three cases where the free-stream Reynolds numbers are 14000, 20000, and 30000/mm are selected. The averaged statistics, such as the mean velocity, the skin friction, the heat flux, and the wall pressure, are used in this paper. The flow structures in the compression ramp including the shock wave and interaction region are discussed. The decomposition of the mean skin-friction drag for the flat flow is extended to be used in the compression corner. In addition, the turbulent kinetic energy is studied through the decomposition of the mean skin-friction drag for the flat-plate region and the corner region. It is found that higher Reynolds numbers would increase the turbulent kinetic energy by turbulent dissipation at the interaction region, while higher Reynolds numbers would decrease the turbulent kinetic energy by turbulent dissipation after reattachment. In addition, it is also found that the turbulent kinetic energy is larger with a higher Reynolds number and higher turbulent kinetic energy inhibits the movement from the separation point to the inflection point (x = 0 mm), which deduces larger separation bubbles.
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Beketaeva, Asel, Amr H. Abdalla i Yekaterina Moisseyeva. "Investigation of Vortex Structures for Supersonic Jet Interaction Flowfield". Applied Mechanics and Materials 798 (październik 2015): 546–50. http://dx.doi.org/10.4028/www.scientific.net/amm.798.546.
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The three-dimensional supersonic turbulent flow in presence of symmetric transverse injection of round jet is simulated numerically. The simulation is based on the Favre-averaged Navier-Stokes equations coupled with Wilcox’s turbulence model. The numerical solution is performed using ENO scheme and is validated with the experimental data that include the pressure distribution on the wall in front of the jet in the plane symmetry. The numerical simulation is used to investigate in detail the flow physics for a range of the pressure ratio . The well-known primary shock formations are observed (a barrel shock, a bow shock, and the system of λ-shock waves), and the vortices are identified (horseshoe vortex, an upper vortex, two trailing vortices formed in the separation region and aft of the bow shock wave, two trailing vortices that merge together into one single rotational motion). During the experiment the presence of the new vortices near the wall behind the jet for the pressure ratio is revealed.
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Pasha, Amjad A., Khalid A. Juhany i Subramania N. Pillai. "One-equation turbulence models applied to practical scramjet inlet". International Journal of Turbo & Jet-Engines 39, nr 2 (4.06.2021): 241–49. http://dx.doi.org/10.1515/tjj-2021-0013.
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Abstract Reynolds-averaged Navier–Stokes equations are used to simulate a practical scramjet inlet geometry using the shock-unsteadiness modified Spalart–Allmaras (SA) turbulence model. The geometry consists of fore-body ramps, expansion corners, and inlet ducts. The focus is to study the impingement of the cowl shock on the opposite wall boundary-layer. The resulting separation bubble can lead to blockage and inlet unstarts. The shock-unsteadiness correction is employed and is found to improve the computational fluid dynamics (CFD) prediction of flow separation in shock/boundary-layer interactions. The shock-unsteadiness parameter is calibrated against available experimental data of canonical flows, and the predicted flow-field is analyzed in detail. A large separation bubble size normalized to the upstream boundary-layer thickness of 4.6 is observed in the interaction region. Across the reattachment region in the interaction region, a peak value of wall pressure is observed. The inlet performance parameters are also calculated. The total pressure losses of 62% are observed across different shock waves, with an additional loss of 15% due to viscous boundary-layer effects.
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Li, Xin, Yue Zhang, Hang Yu, Zheng-Kang Lin, Hui-Jun Tan i Shu Sun. "Görtler vortices behavior and prediction in dual-incident shock-wave/turbulent-boundary-layer interactions". Physics of Fluids 34, nr 10 (październik 2022): 106103. http://dx.doi.org/10.1063/5.0100718.
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Görtler vortices (GVs) in dual-incident shock-wave/turbulent-boundary-layer interactions (dual-ISWTBLIs) are experimentally investigated in a Mach 2.48 flow. A double-wedge shock generator with two deflection angles of 8° and 5° is used to produce two incident shock waves (ISWs). Flow structures of the experiments with three different shock-wave distances were visualized by the ice-cluster-based planar laser scattering technique at two orthogonal planes ( x– y and x– z planes). The images in the x– y plane present three types of flow patterns of dual-ISWTBLIs corresponding to the first type with a triangle-like separation, the second type with a quadrilateral-like separation, and the third type with two isolated interactions induced by the two ISWs. The images in the x– z plane indicate that the GVs exist in the first type of dual-ISWTBLI originating in the vicinity of the apex of the separation region and cover nearly the whole spanwise range of the reattachment region. By comparison, the GVs intermittently occur in the limited spanwise range of the reattachment region in the second type of dual-ISWTBLI. No GVs are observed in the third type of dual-ISWTBLI because no visible separation is induced under the experimental conditions considered in this situation. In addition, based on the wall-pressure distribution in the former two types of dual-ISWTBLIs, this paper proposes a method to estimate the mean-flow streamline curvature in the reattachment region, thereby obtaining the criteria for the existence of GVs, according to which reasonable explanations for the different distributions of GVs in the two types of dual-ISWTBLIs are provided.
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Brusniak, Leon, i David S. Dolling. "Physics of unsteady blunt-fin-induced shock wave/turbulent boundary layer interactions". Journal of Fluid Mechanics 273 (25.08.1994): 375–409. http://dx.doi.org/10.1017/s0022112094001989.
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Fluctuating wall-pressure measurements have been made on the centreline upstream of a blunt fin in a Mach 5 turbulent boundary layer. By examining the ensemble-averaged wall-pressure distributions for different separation shock foot positions, it has been shown that local fluctuating wall-pressure measurements are due to a distinct pressure distribution, [weierp ]i, which undergoes a stretching and flattening effect as its upstream boundary translates aperiodically between the upstream-influence and separation lines. The locations of the maxima and minima in the wall-pressure standard deviation can be accurately predicted using this distribution, providing quantitative confirmation of the model. This model also explains the observed cross-correlations and ensemble-average measurements within the interaction. Using the [weierp ]i model, wall-pressure signals from under the separated flow region were used to reproduce the position–time history of the separation shock foot. The unsteady behaviour of the primary horseshoe vortex and its relation to the unsteady separation shock is also described. The practical implications are that it may be possible to predict some of the unsteady aspects of the flowfield using mean wall-pressure distributions obtained from either computations or experiments; also, to minimize the fluctuating loads caused by the unsteadiness, flow control methods should focus on reducing the magnitude of the [weierp ]i gradient (∂[weierp ]i/∂x).
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Pasquariello, Vito, Stefan Hickel i Nikolaus A. Adams. "Unsteady effects of strong shock-wave/boundary-layer interaction at high Reynolds number". Journal of Fluid Mechanics 823 (22.06.2017): 617–57. http://dx.doi.org/10.1017/jfm.2017.308.
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We analyse the low-frequency dynamics of a high Reynolds number impinging shock-wave/turbulent boundary-layer interaction (SWBLI) with strong mean-flow separation. The flow configuration for our grid-converged large-eddy simulations (LES) reproduces recent experiments for the interaction of a Mach 3 turbulent boundary layer with an impinging shock that nominally deflects the incoming flow by $19.6^{\circ }$. The Reynolds number based on the incoming boundary-layer thickness of $Re_{\unicode[STIX]{x1D6FF}_{0}}\approx 203\times 10^{3}$ is considerably higher than in previous LES studies. The very long integration time of $3805\unicode[STIX]{x1D6FF}_{0}/U_{0}$ allows for an accurate analysis of low-frequency unsteady effects. Experimental wall-pressure measurements are in good agreement with the LES data. Both datasets exhibit the distinct plateau within the separated-flow region of a strong SWBLI. The filtered three-dimensional flow field shows clear evidence of counter-rotating streamwise vortices originating in the proximity of the bubble apex. Contrary to previous numerical results on compression ramp configurations, these Görtler-like vortices are not fixed at a specific spanwise position, but rather undergo a slow motion coupled to the separation-bubble dynamics. Consistent with experimental data, power spectral densities (PSD) of wall-pressure probes exhibit a broadband and very energetic low-frequency component associated with the separation-shock unsteadiness. Sparsity-promoting dynamic mode decompositions (SPDMD) for both spanwise-averaged data and wall-plane snapshots yield a classical and well-known low-frequency breathing mode of the separation bubble, as well as a medium-frequency shedding mode responsible for reflected and reattachment shock corrugation. SPDMD of the two-dimensional skin-friction coefficient further identifies streamwise streaks at low frequencies that cause large-scale flapping of the reattachment line. The PSD and SPDMD results of our impinging SWBLI support the theory that an intrinsic mechanism of the interaction zone is responsible for the low-frequency unsteadiness, in which Görtler-like vortices might be seen as a continuous (coherent) forcing for strong SWBLI.
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Ji, Xiangxin, Xinliang Li, Fulin Tong i Changping Yu. "Large eddy simulation of shock wave/turbulent boundary layer interaction under incipient and fully separated conditions". Physics of Fluids 35, nr 4 (kwiecień 2023): 046106. http://dx.doi.org/10.1063/5.0147829.
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Large eddy simulations of shock wave/turbulent boundary layer interaction on a compression ramp at the Mach number [Formula: see text] and Reynolds number [Formula: see text] are performed to investigate the impact of the incipient and fully separated conditions on the development of the flow field. The quasi-dynamic subgrid-scale kinetic energy equation model, which combines the benefits of the gradient model with the eddy-viscosity model, has been applied. Compared with the previous experimental and numerical results, the simulation was validated. The flow structures, turbulence properties, vortex structures, and low-frequency unsteadiness are all investigated. The flow field of the incipient separation is attached and rarely impacted by shock. An evident separation bubble and localized high wall temperatures in fully separated flow are caused by the separation shock's significant reverse pressure gradient. The Reynolds stress components exhibit significant amplification in both cases, and the peak outward shifts from the near-wall region to the center of the free shear layer. Turbulent kinetic energy terms were analyzed, and the two scenarios show a significant difference. The power spectral density of the wall pressure fluctuations shows that the low-frequency motion of the incipient separation is not apparent relative to the fully separated flow.
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Schreiber, H. A., i H. Starken. "An Investigation of a Strong Shock-Wave Turbulent Boundary Layer Interaction in a Supersonic Compressor Cascade". Journal of Turbomachinery 114, nr 3 (1.07.1992): 494–503. http://dx.doi.org/10.1115/1.2929170.
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Experiments have been performed in a supersonic cascade facility to elucidate the fluid dynamic phenomena and loss mechanism of a strong shock-wave turbulent boundary layer interaction in a compressor cascade. The cascade geometry is typical for a transonic fan tip section that operates with a relative inlet Mach number of 1.5, a flow turning of about 3 deg, and a static pressure ratio of 2.15. The strong oblique and partly normal blade passage shock-wave with a preshock Mach number level of 1.42 to 1.52 induces a turbulent boundary layer separation on the blade suction surface. The free-stream Reynolds number based on chord length was about 2.7 × 106. Cascade overall performance, blade surface pressure distributions, Schlieren photographs, and surface visualizations are presented. Detailed Mach number and flow direction profiles of the interaction region (lambda shock) and the corresponding boundary layer have been determined using a Laser-2-Focus anemometer. The obtained results indicated that the axial blade passage stream sheet contraction (axial velocity density ratio) has a significant influence on the mechanism of strong interaction and the resulting total pressure losses.
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Simeonides, G., i W. Haase. "Experimental and computational investigations of hypersonic flow about compression ramps". Journal of Fluid Mechanics 283 (25.01.1995): 17–42. http://dx.doi.org/10.1017/s0022112095002229.
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Comprehensive results of a joint experimental and computational study of the two-dimensional flow field over flat plate/compression ramp configurations at Mach 14 are presented. These geometries are aimed to simulate, in a simplified manner, the region around deflected control surfaces of hypersonic re-entry vehicles. The test cases considered cover a range of realistic flow conditions with Reynolds numbers to the hinge line varying between 4.5 × 105 and 2.6 × 106 (with a reference length taken as the distance between the leading edge and the hinge line) and a wall-to-total-temperature ratio of 0.12. The combination of flow and geometric parameters gives rise to fully laminar strong shock wave/boundary layer interactions with extensive separation, and transitional interactions with transition occurring near the reattachment point. A fully turbulent interaction is also considered which, however, was only approximately achieved in the experiments by means of excessive tripping of the oncoming hypersonic laminar boundary layer. Emphasis has been placed upon the quality and level of confidence of both experiments and computations, including a discussion on the laminar-turbulent transition process and the associated striation phenomenon. The favourable comparison between the experimental and computational results has profided the grounds for an enhanced understanding of the relevant flow processes and their modelling. Particularly in relation to transitional shock wave/boundary layer interactions, where laminar-turbulent transition is promoted by the adverse pressure gradient and flow concavity in the reattachment region, a method is proposed to compute extreme adverse effects in the interaction region avoiding such inhibiting requirements as transition modelling or turbulence modelling over separated regions.
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RUBAN, A. I., D. ARAKI, R. YAPALPARVI i J. S. B. GAJJAR. "On unsteady boundary-layer separation in supersonic flow. Part 1. Upstream moving separation point". Journal of Fluid Mechanics 678 (15.04.2011): 124–55. http://dx.doi.org/10.1017/jfm.2011.104.
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This study is concerned with the boundary-layer separation from a rigid body surface in unsteady two-dimensional laminar supersonic flow. The separation is assumed to be provoked by a shock wave impinging upon the boundary layer at a point that moves with speed Vsh along the body surface. The strength of the shock and its speed Vsh are allowed to vary with time t, but not too fast, namely, we assume that the characteristic time scale t ≪ Re−1/2/Vw2. Here Re denotes the Reynolds number, and Vw = −Vsh is wall velocity referred to the gas velocity V∞ in the free stream. We show that under this assumption the flow in the region of interaction between the shock and boundary layer may be treated as quasi-steady if it is considered in the coordinate frame moving with the shock. We start with the flow regime when Vw = O(Re−1/8). In this case, the interaction between the shock and boundary layer is described by classical triple-deck theory. The main modification to the usual triple-deck formulation is that in the moving frame the body surface is no longer stationary; it moves with the speed Vw = −Vsh. The corresponding solutions of the triple-deck equations have been constructed numerically. For this purpose, we use a numerical technique based on finite differencing along the streamwise direction and Chebyshev collocation in the direction normal to the body surface. In the second part of the paper, we assume that 1 ≫ Vw ≫ O(Re−1/8), and concentrate our attention on the self-induced separation of the boundary layer. Assuming, as before, that the Reynolds number, Re, is large, the method of matched asymptotic expansions is used to construct the corresponding solutions of the Navier–Stokes equations in a vicinity of the separation point.
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Kaldellis, J. K. "Parametrical Investigation of the Interaction Between Turbulent Wall Shear Layers and Normal Shock Waves, Including Separation". Journal of Fluids Engineering 115, nr 1 (1.03.1993): 48–55. http://dx.doi.org/10.1115/1.2910112.
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The existence of strong shock waves plays a major role in the performance of modern aero-mechanical devices, since it is primarily responsible not only for the shock induced total pressure drop, but also for the increased shear layer losses due to flow separation. In this paper a fast energy-type integral method along with an approximate shock-turbulent shear layer interaction procedure are presented. This integral method, based on the two-zone model, is able to predict attached and fully detached shear flows. An extended turbulence model is also used in order to take the influence of the turbulence inside the interaction region better into account. The external flow pressure distribution results from an improved and extended form of an approximate small disturbance theory. A detailed investigation is carried out to estimate the influence of the inlet Mach number, the shear layer characteristics and the confinement of the geometry upon the static pressure field. The resulting method has been successfully applied to several test cases including ones where separation appears. Comparison between results of previous calculations, experimental data and results of the proposed method is also presented, along with the convergence history of the shear layer—shock wave interaction procedure. Finally, the method has been applied to one-stage high pressure supersonic flow compressor with normal shock appearance inside the rotor of the machine. The major conclusion drawn from the present work is that the shear layer characteristics (e.g., displacement thickness and form factor) have a dominant effect upon the flow field near the interaction region. Additionally, the proposed method requires no more than five overall iterations to reproduce the real flow field for all cases examined.
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Song, Mo-Ru, i Bo Yang. "Analysis on the unsteady flow structures in the tip region of axial compressor". Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy 235, nr 6 (14.02.2021): 1272–87. http://dx.doi.org/10.1177/0957650921995111.
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The unsteady characteristic in the tip region of an axial compressor has been numerically studied with the help of the dynamic mode decomposition analysis. The characteristics of frequency and dynamic modes are compared and discussed under different operating points and different parameters, such as tip clearance and rotating speeds. For the flowfield structures in the tip region, such as tip leakage flow, separation flow and shock wave, their relationships with the unsteadiness are studied in detail. Except for the unsteadiness caused by the interaction between rotating rotor and the stationary boundaries, it is found that the unsteadiness is attributed to the moving of the low-velocity cell. Based on the generation and the development of the low-velocity cell, the unsteady characteristics in tip region are divided into 4 types: BPF-dominated, shedding-dominated, self-induced and separation-dominated. When the tip leakage flow is weak, the unsteadiness in the tip region is only triggered by the blade sweeping. As the tip leakage flow gets stronger to a certain extent, the low-velocity cell is shed into the flow passage and mixed with the main-flow. When the main-flow is weaker under the low flowrate condition, the interaction between the low-velocity cell and the pressure side occurs and generates a new low-velocity cell near the leading-edge of the neighboring blade. The frequency of the new cell generation is actually the self-induced frequency. In the zero and small clearance model, the low-velocity is shed by the separation in the leading-edge and the casing-suction corner. By understanding these unsteady characteristics, the change tendency of the leading frequency in the rotor tip is easily explained and forecasted. Furthermore, under the transonic operation condition, the low-velocity cell is decelerated and eliminated by the shock wave in the unsteadiness of the self-induced type and the separation-dominated type, respectively. Thus, the leading frequency in the tip flow field is moderated.
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Bonne, N., V. Brion, E. Garnier, R. Bur, P. Molton, D. Sipp i L. Jacquin. "Analysis of the two-dimensional dynamics of a Mach 1.6 shock wave/transitional boundary layer interaction using a RANS based resolvent approach". Journal of Fluid Mechanics 862 (16.01.2019): 1166–202. http://dx.doi.org/10.1017/jfm.2018.932.
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A two-dimensional analysis of the resolvent spectrum of a Mach 1.6 transitional boundary layer impacted by an oblique shock wave is carried out. The investigation is based on a two-dimensional mean flow obtained by a RANS model that includes a transition criterion. The goal is to evaluate whether such a low cost RANS based resolvent approach is capable of describing the frequencies and physics involved in this transitional boundary layer/shock-wave interaction. Data from an experiment and a companion large eddy simulation (LES) are utilized as reference for the validation of the method. The flow is characterized by a laminar boundary layer upstream, a laminar separation bubble (LSB) in the interaction region and a turbulent boundary layer downstream. The flow exhibits low amplitude unsteadiness in the LSB and at the reflected shock wave with three particular oscillation frequencies, qualified as low, medium and high in reference to their range in Strouhal number, here based on free stream velocity and LSB length ($S_{t}=0.03{-}0.11$, 0.3–0.4 and 2–3 respectively). Through the resolvent analysis this dynamics is found to correspond to an amplifier behaviour of the flow. The resolvent responses match the averaged Fourier mode of the time dependent flow field, here described by the LES, with a close agreement in frequency and spatial distribution, thereby validating the resolvent approach. The low frequency dynamics relates to a pseudo-resonance process that sequentially implies the amplification in the separated shear layer of the LSB, an excitation of the shock foot and a backward travelling density wave. As this wave hits back the separation point the amplification in the shear layer starts again and loops. The medium and high frequency modes relate to the periodic expansion/reduction of the bubble and to the turbulent fluctuations at the reattachment point of the bubble, respectively.
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Pickles, J. D., B. R. Mettu, P. K. Subbareddy i V. Narayanaswamy. "On the mean structure of sharp-fin-induced shock wave/turbulent boundary layer interactions over a cylindrical surface". Journal of Fluid Mechanics 865 (18.02.2019): 212–46. http://dx.doi.org/10.1017/jfm.2019.53.
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Interactions between an oblique shock wave generated by a sharp fin placed on a cylindrical surface and the incoming boundary layer are investigated to unravel the mean features of the resulting shock/boundary layer interaction (SBLI) unit. This fin-on-cylinder SBLI unit has several unique features caused by the three-dimensional (3-D) relief offered by the cylindrical surface that noticeably alter the shock structure. Complementary experimental and computational studies are made to delineate both the surface and off-body flow features of the fin-on-cylinder SBLI unit and to obtain a detailed understanding of the mechanisms that dictate the mean flow and wall pressure features of the SBLI unit. Results show that the fin-on-cylinder SBLI exhibits substantial deviation from quasi-conical symmetry that is observed in planar fin SBLI. Furthermore, the separated flow growth rate appears to decrease with downstream distance and the separation size is consistently smaller than the planar fin SBLI with the same inflow and fin configurations. The causes for the observed diminution of the separated flow and its downstream growth rate were investigated in the light of changes caused by the cylinder curvature on the inviscid as well as separation shock. It was found that the inviscid shock gets progressively weakened in the region close to the triple point with downstream distance due to the 3-D relief effect from cylinder curvature. This weakening of the inviscid shock feeds into the separation shock, which is also independently impacted by the 3-D relief, to result in the observed modifications in the fin-on-cylinder SBLI unit.
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Priebe, Stephan, Jonathan H. Tu, Clarence W. Rowley i M. Pino Martín. "Low-frequency dynamics in a shock-induced separated flow". Journal of Fluid Mechanics 807 (20.10.2016): 441–77. http://dx.doi.org/10.1017/jfm.2016.557.
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The low-frequency unsteadiness in the direct numerical simulation of a Mach 2.9 shock wave/turbulent boundary layer interaction with mean flow separation is analysed using dynamic mode decomposition (DMD). The analysis is applied both to three-dimensional and spanwise-averaged snapshots of the flow. The observed low-frequency DMD modes all share a common structure, characterized by perturbations along the shock, together with streamwise-elongated regions of low and high momentum that originate at the shock foot and extend into the downstream flow. A linear superposition of these modes, with dynamics governed by their corresponding DMD eigenvalues, accurately captures the unsteadiness of the shock. In addition, DMD analysis shows that the downstream regions of low and high momentum are unsteady and that their unsteadiness is linked to the unsteadiness of the shock. The observed flow structures in the downstream flow are reminiscent of Görtler-like vortices that are present in this type of flow due to an underlying centrifugal instability, suggesting a possible physical mechanism for the low-frequency unsteadiness in shock wave/turbulent boundary layer interactions.
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Wu, Yanhui, Guangyao An, Zhiyang Chen i Bo Wang. "Computational analysis of vortices near casing in a transonic axial compressor rotor". Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering 233, nr 2 (5.12.2017): 710–24. http://dx.doi.org/10.1177/0954410017740922.
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Complicated flowfields near casing in a transonic axial flow compressor rotor have been numerically investigated in this paper. Two vortex identification methods, namely the Eigenvector Method and Lambda 2 Method, are introduced as important tools for the graphical representation of the concentrated vortices arising from tip leakage flow and blade boundary layer separation. The analysis of the numerical results reveals that multiple tip vortices whose development are dependent on the variation of shock wave configuration are observed at conditions around the peak efficiency point. However, with the decrease of the massflow rate, only the well-known tip leakage vortex and the second tip vortex are left in the tip region due to the disappearance of the second shock wave. Then when the massflow rate further decreases to the stall limit, an deceleration flow region emerges downstream of the shock wave due to an increasing interaction between the first shock wave and the well-known tip leakage vortex. The tip leakage vortex further experiences a bubble-type and then spiral-type breakdown at near stall flow conditions. In addition, the validity of the two vortex identification methods is also discussed in this paper. It is found that both methods are able to identify and accentuate the concentrated streamwise vortices near casing when a vortex is not disrupted. However, if the vortex breakdown occurs, only Eigenvector Method can describe the breakdown region in a deep view.
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CHEN, LI-WEI, CHANG-YUE XU i XI-YUN LU. "Numerical investigation of the compressible flow past an aerofoil". Journal of Fluid Mechanics 643 (17.12.2009): 97–126. http://dx.doi.org/10.1017/s0022112009991960.
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Numerical investigation of the compressible flow past an 18% thick circular-arc aerofoil was carried out using detached-eddy simulation for a free-stream Mach number M∞ = 0.76 and a Reynolds number Re = 1.1 × 107. Results have been validated carefully against experimental data. Various fundamental mechanisms dictating the intricate flow phenomena, including moving shock wave behaviours, turbulent boundary layer characteristics, kinematics of coherent structures and dynamical processes in flow evolution, have been studied systematically. A feedback model is developed to predict the self-sustained shock wave motions repeated alternately along the upper and lower surfaces of the aerofoil, which is a key issue associated with the complex flow phenomena. Based on the moving shock wave characteristics, three typical flow regimes are classified as attached boundary layer, moving shock wave/turbulent boundary layer interaction and intermittent boundary layer separation. The turbulent statistical quantities have been analysed in detail, and different behaviours are found in the three flow regimes. Some quantities, e.g. pressure-dilatation correlation and dilatational dissipation, have exhibited that the compressibility effect is enhanced because of the shock wave/boundary layer interaction. Further, the kinematics of coherent vortical structures and the dynamical processes in flow evolution are analysed. The speed of downstream-propagating pressure waves in the separated boundary layer is consistent with the convection speed of the coherent vortical structures. The multi-layer structures of the separated shear layer and the moving shock wave are reasonably captured using the instantaneous Lamb vector divergence and curl, and the underlying dynamical processes are clarified. In addition, the proper orthogonal decomposition analysis of the fluctuating pressure field illustrates that the dominated modes are associated with the moving shock waves and the separated shear layers in the trailing-edge region. The results obtained in this study provide physical insight into the understanding of the mechanisms relevant to this complex flow.
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GANAPATHISUBRAMANI, B., N. T. CLEMENS i D. S. DOLLING. "Low-frequency dynamics of shock-induced separation in a compression ramp interaction". Journal of Fluid Mechanics 636 (25.09.2009): 397–425. http://dx.doi.org/10.1017/s0022112009007952.
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The low-frequency dynamics of the shock-induced separation region in a Mach 2 compression ramp interaction is investigated by performing high-speed particle image velocimetry (HSPIV) measurements, at a rate of 6kHz, in a streamwise–spanwise plane. The HSPIV measurements made in the upstream turbulent boundary layer indicate the presence of spanwise strips of elongated regions of uniform streamwise velocity that extend to lengths greater than 30δ, validating previous results based on planar laser scattering measurements obtained by Ganapathisubramani, Clemens & Dolling (J. Fluid Mech., vol. 585, 2007, p. 369). At a wall normal-location of y/δ=0.2, a surrogate for separation based on a velocity threshold is found to fluctuate over a streamwise range of ±1.2δ, consistent with previous studies. The amplitude of unsteadiness has contributions from at least two sources that are related to the incoming boundary layer. First, the velocity threshold based surrogate separation line exhibits large-scale undulations along the spanwise direction that conform to the passage of elongated low- and high-speed regions in the upstream boundary layer. This motion is classified as the local influence of the upstream boundary layer. Second, the spanwise-averaged surrogate separation is found to respond to the overall change in streamwise velocity in the incoming boundary layer and is classified as the global influence of the upstream boundary layer. However, this global influence includes the contributions from the elongated low- and high-speed regions. Preliminary findings based on statistical analysis suggest that the local influence contributes nearly 50% more than the global influence. Regardless, the low-frequency unsteadiness of the separation-region can be attributed to the local and global influences of the incoming boundary layer.
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He, Z. W., i S. Y. Zhang. "Lip Separate Flow Blowing and Analysis of Coherence of Inlet". Journal of Engineering for Gas Turbines and Power 108, nr 3 (1.07.1986): 562–65. http://dx.doi.org/10.1115/1.3239947.
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It is found experimentally that blowing at the lip separation of an inlet obviously reduces the turbulence at the inlet exit, and apparently reduces the intensity of pressure fluctuations caused by the shock-boundary layer interaction downstream of the throat. The coherence between pressure in the interaction region and total pressure at the exit is also reduced. The coherence between the pressure in the lip separation region and total pressure at the exit is 0.32. If, in addition, there is a stronger shock downstream of the throat, the abovementioned coherence is reduced to 0.06.
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Sansica, Andrea, Neil D. Sandham i Zhiwei Hu. "Instability and low-frequency unsteadiness in a shock-induced laminar separation bubble". Journal of Fluid Mechanics 798 (31.05.2016): 5–26. http://dx.doi.org/10.1017/jfm.2016.297.
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Three-dimensional direct numerical simulations (DNS) of a shock-induced laminar separation bubble are carried out to investigate the flow instability and origin of any low-frequency unsteadiness. A laminar boundary layer interacting with an oblique shock wave at $M=1.5$ is forced at the inlet with a pair of monochromatic oblique unstable modes, selected according to local linear stability theory (LST) performed within the separation bubble. Linear stability analysis is applied to cases with marginal and large separation, and compared to DNS. While the parabolized stability equations approach accurately reproduces the growth of unstable modes, LST performs less well for strong interactions. When the modes predicted by LST are used to force the separated boundary layer, transition to deterministic turbulence occurs near the reattachment point via an oblique-mode breakdown. Despite the clean upstream condition, broadband low-frequency unsteadiness is found near the separation point with a peak at a Strouhal number of $0.04$, based on the separation bubble length. The appearance of the low-frequency unsteadiness is found to be due to the breakdown of the deterministic turbulence, filling up the spectrum and leading to broadband disturbances that travel upstream in the subsonic region of the boundary layer, with a strong response near the separation point. The existence of the unsteadiness is supported by sensitivity studies on grid resolution and domain size that also identify the region of deterministic breakdown as the source of white noise disturbances. The present contribution confirms the presence of low-frequency response for laminar flows, similarly to that found in fully turbulent interactions.
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KNIGHT, D., M. GNEDIN, R. BECHT i A. ZHELTOVODOV. "Numerical simulation of crossing-shock-wave/turbulent-boundary-layer interaction using a two-equation model of turbulence". Journal of Fluid Mechanics 409 (25.04.2000): 121–47. http://dx.doi.org/10.1017/s0022112099007764.
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A crossing-shock-wave/turbulent-boundary-layer interaction is investigated using the k–ε turbulence model with a new low-Reynolds-number model based on the approach of Saffman (1970) and Speziale et al. (1990). The crossing shocks are generated by two wedge-shaped fins with wedge angles α1 and α2 attached normal to a flat plate on which an equilibrium supersonic turbulent boundary layer has developed. Two configurations, corresponding to the experiments of Zheltovodov et al. (1994, 1998a, b), are considered. The free-stream Mach number is 3.9, and the fin angles are (α1, α2) = (7°, 7°) and (7°, 11°). The computed surface pressure displays very good agreement with experiment. The computed surface skin friction lines are in close agreement with experiment for the initial separation, and are in qualitative agreement within the crossing shock interaction region. The computed heat transfer is in good agreement with experiment for the (α1, α2) = (7°, 7°) configuration. For the (α1, α2) = (7°, 11°) configuration, the heat transfer is significantly overpredicted within the three-dimensional interaction. The adiabatic wall temperature is accurately predicted for both configurations.
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GANAPATHISUBRAMANI, B., N. T. CLEMENS i D. S. DOLLING. "Effects of upstream boundary layer on the unsteadiness of shock-induced separation". Journal of Fluid Mechanics 585 (7.08.2007): 369–94. http://dx.doi.org/10.1017/s0022112007006799.
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The relationship between the upstream boundary layer and the low-frequency, large-scale unsteadiness of the separated flow in a Mach 2 compression ramp interaction is investigated by performing wide-field particle image velocimetry (PIV) and planar laser scattering (PLS) measurements in streamwise–spanwise planes. Planar laser scattering measurements in the upstream boundary layer indicate the presence of spanwise strips of elongated regions of uniform momentum with lengths greater than 40δ. These long coherent structures have been observed in a Mach 2 supersonic boundary layer (Ganapathisubramani, Clemens & Dolling 2006) and they exhibit strong similarities to those that have been found in incompressible boundary layers (Tomkins & Adrian 2003; Ganapathisubramani, Longmire & Marusic 2003). At a wall-normal location of y/δ=0.2, the inferred instantaneous separation line of the separation region is found to oscillate between x/δ=−3 and −1 (where x/δ=0 is the ramp corner). The instantaneous spanwise separation line is found to respond to the elongated regions of uniform momentum. It is shown that high- and low-momentum regions are correlated with smaller and larger size of the separation region, respectively. Furthermore, the instantaneous separation line exhibits large-scale undulations that conform to the low- and high-speed regions in the upstream boundary layer. The low-frequency unsteadiness of the separation region/shock foot observed in numerous previous studies can be explained by a turbulent mechanism that includes these elongated regions of uniform momentum.
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Wang, Lican, Yilong Zhao, Qiancheng Wang, Yuxin Zhao, Ruoling Zhang i Li Ma. "Three-dimensional characteristics of crossing shock wave/turbulent boundary layer interaction in a double fin with and without micro-ramp control". AIP Advances 12, nr 9 (1.09.2022): 095309. http://dx.doi.org/10.1063/5.0102986.
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The three-dimensional (3D) interactions between crossing shock waves and a turbulent boundary layer (CSWBLI) inside a symmetric double fin are experimentally studied using nanoparticle-based planar laser scattering, supersonic particle image velocimetry, and surface oil visualization. The possibility of controlling the separated flow generated by CSWBLI is considered by employing micro-ramp vortex generators. First, the fractal dimension, velocity profile, and logarithmic law of the incoming turbulent boundary layer at Mach number 2.8 are examined. Then, the flow structure and velocity distribution, which have seldom been presented in previous experiments, are measured in high resolution. The 3D behavior of the boundary layer after CSWBLI shows that the boundary layer becomes thicker behind the shock wave and converges toward the symmetry plane of the double fin. The converged effect contributes to the largest thickness of the boundary layer in the symmetry plane accompanied with a separation region near the wall. Introduction of seven equidistant micro-ramps upstream of the double fin is proved to suppress the separation region, where the arc-like vortices generated by the middle micro-ramps are found to be more sustainable along the streamwise direction. The micro-ramps can increase the momentum exchange between the boundary layer and the surrounding mainstream. At the same time, the momentum exchange induced by the micro-ramps decreases the flow velocity outside the converged region in comparison with the configuration without micro-ramps. The results obtained in this paper can provide an experimental insight into the 3D physical phenomena existing in the CSWBLI and its flow control.
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Hung, Nguyen Manh, i Hoang Thi Bich Ngoc. "Experimental study of laminar separation phenomenon combining with numerical calculations". Vietnam Journal of Mechanics 33, nr 2 (10.06.2011): 95–104. http://dx.doi.org/10.15625/0866-7136/33/2/41.
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The separation is much more sensitive for laminar flow than for turbulent flow. These remarks have been attested for both subsonic and supersonic flows. However, they are not applicable to transonic flows when there are interactions between boundary layer and shock wave. Along with the Reynolds number, the Mach number is a necessary dimensionless parameter for the condition and the mechanism of separations. The report presents one part of studies on laminar separation with Mach number of incompressible flow. The laminar regimes correspond to flows through wind turbine blades. Our experimental work for laminar separation phenomenon was carried out in a subsonic open circuit wind tunnel by taking photographs. The accuracy of experimental results basically depends on the accuracy of wind tunnel and the quality of smoke on density and constitutive materials. Experimental results permit to determine the position of separation and the form of turbulent region followed from the separation point. Numerical studies were simultaneously realized. Based on obtained experimental and numerical results, the report presents also the comparison between the laminar separation and the turbulent separation.
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Vanstone, Leon, Mustafa Nail Musta, Serdar Seckin i Noel Clemens. "Experimental study of the mean structure and quasi-conical scaling of a swept-compression-ramp interaction at Mach 2". Journal of Fluid Mechanics 841 (19.02.2018): 1–27. http://dx.doi.org/10.1017/jfm.2018.8.
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This study investigates the mean flow structure of two shock-wave boundary-layer interactions generated by moderately swept compression ramps in a Mach 2 flow. The ramps have a compression angle of either $19^{\circ }$ or $22.5^{\circ }$ and a sweep angle of $30^{\circ }$. The primary diagnostic methods used for this study are surface-streakline flow visualization and particle image velocimetry. The shock-wave boundary-layer interactions are shown to be quasi-conical, with the intermittent region, separation line and reattachment line all scaling in a self-similar manner outside of the inception region. This is one of the first studies to investigate the flow field of a swept ramp using particle image velocimetry, allowing more sensitive measurements of the velocity flow field than previously possible. It is observed that the streamwise velocity component outside of the separated flow reaches the quasi-conical state at the same time as the bulk surface flow features. However, the streamwise and cross-stream components within the separated flow take longer to recover to the quasi-conical state, which indicates that the inception region for these low-magnitude velocity components is actually larger than was previously assumed. Specific scaling laws reported previously in the literature are also investigated and the results of this study are shown to scale similarly to these related interactions. Certain limiting cases of the scaling laws are explored that have potential implications for the interpretation of cylindrical and quasi-conical scaling.