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The effect of trailing edge geometry on cavity flow oscillation driven by a supersonic shear layer
Abstract
A computational analysis is performed of self-sustained oscillatory flow over a cavity driven by a shear layer at Mach 1·5. The unsteady flow is studied through solutions of the Reynolds-averaged Navier-Stokes equations with turbulence modelled by a two-equation k-ω model. The trailing edge (face) of a baseline rectangular cavity is modified using wedge and ramp shapes to investigate means for the suppression and attenuation of the self-sustained oscillation. Through modification of the shear layer impingement, both wedge and ramp are effective in reducing the level of oscillation. The time-averaged pressure (form) drag coefficient of the cavity is also reduced significantly. The main cause of the drag reduction is the elimination or reduction of the high pressure area near the down-stream corner of the cavity due to the presence of a vortex. Two types of unsteady flow exist when a curved ramp is employed: 'regular' and 'random'. The use of a h = 0·6D ramp generates a random type pressure fluctuation with lower rms pressure compared with the h = 0·2D and 0·4D ramps.
... Gruber et al.'s study [28] (Ma∞ = 3.0, L/H = 3) found that as θ decreases from 90° to 30° and 16°, the drag coefficients gradually increase. Zhang et al.'s study [27] (Ma∞ = 1.5, L/H = 3) found that as θ decreases from 90° to 67.5° and 45°, the drag coefficients gradually decrease. Barkar et al. [2] discovered this contradictory conclusion and speculated that the change in cavity drag with θ is not monotonic; possibly, there is a critical value (between θ = 45° and 16°) at which the drag penalties are minimal. ...
... In addition, as θ decreases, the drag coefficient first decreases and then increases. [27] (Ma ∞ = 1.5, L/H = 3) found that as θ decreases from 90 • to 67.5 • and 45 • , the drag coefficients gradually decrease. Barkar et al. [2] discovered this contradictory conclusion and speculated that the change in cavity drag with θ is not monotonic; possibly, there is a critical value (between θ = 45 • and 16 • ) at which the drag penalties are minimal. ...
A numerical study of supersonic cavity flows is conducted with different turbulent models, including RANS, LES, DES, DDES, and IDDES. Firstly, a supersonic cavity-ramp flow with Ma∞ = 2.92 is simulated numerically. It shows that the results of DDES and IDDES are nearly equivalent. The wall skin-friction coefficients obtained by these two models are in better agreement with the experimental measurement than those of DES. The reason is that the RANS region of DDES and IDDES is larger than that of DES, so it produces more turbulence in the near-wall region. In comparison, RANS cannot accurately predict large separation flows. The shear layer’s reattachment point on the ramp predicted by RANS is biased downstream compared to the experimental measurement, making its overall prediction accuracy worse than other models. The results obtained by LES are comparable to those obtained by DDES and IDDES except for the wall skin-friction coefficient, which is much smaller because the grid resolution is not high enough to accurately resolve the near-wall turbulent flow. Secondly, the effect of different aft-wall angles (θ) on the flow characteristics of the supersonic cavity is investigated numerically with IDDES. We find that as θ decreases, the oscillation intensity of the cavity flow continuously decreases. However, the change in cavity drag with θ is non-monotonic, which means that there might be a critical θ at which the drag penalties of a cavity are minimal. Therefore, an optimal design should be achieved when changing θ to control the oscillation intensity of supersonic cavity flows.
... 6,7 When the shear layer impinges on an angled wall, the acoustic wave would be deflected toward the outside of the cavity rather than the front wall, avoiding the interaction between shear-layer and acoustic wave and stabilizing the shear-layer. 8 Therefore, many studies have been focused on the cavity flame-holder with a slanted aft wall, both experimentally and numerically. Reviews of such efforts can be found from the papers of Ben-Yakar and Hanson 2 and Wang et al., 9 and we will only give a brief summary of the related numerical studies. ...
... It is also possible that the angled aft wall has an ability of stabilizing the shearlayer according to the previous research. 8 Therefore, the absence of the low-frequency characteristics could be due to the low Reynolds effect and the angled aft wall. Further analysis of the flow at different Reynolds numbers and geometry of the wall should be conducted to clarify this problem. ...
A Mach 1.5 non-reactive flow in a cavity-stabilized combustor of a model scramjet is studied via a direct-numerical simulation approach, and the analysis is focused on the interaction among boundary layer, free shear-layer above the cavity and shock wave. It is found that the impingement of the free shear-layer on the aft wall of the cavity leads to strong turbulence kinetic energy, high local pressure, and a fan of compression waves. The compression waves evolve into an oblique shock, which reflects between the upper and lower walls and interacts with the boundary layers attached to the two walls. The analysis of the turbulence production reveals that the amplification of turbulence in the core of the shear-layer and around the reattachment point is mainly due to the shear production, but the deceleration production mechanism presents a significant impact in the regions above the aft wall of the cavity and around the shock interaction points. The very low frequency commonly observed in shock wave/boundary layer interactions is not observed in the present research, which might be due to the low Reynolds number of the studied case.
... The cavity leading edges are located 40 mm downstream from the combustor entrance, and the trailing edges are inclined at an angle of 45 o to enlarge the recirculation zone and suppress the unsteady behavior of the free shear layer. 23,25 Finite parallel air inlets with rearward-facing steps are adopted as the combustor entrance configuration as suggested by Ali et al. 16 Gaseous hydrogen jets are injected as fuel from two 2D slots of width 1 mm. The injectors are located 30 mm downstream from the combustor inlet and 10 upstream from the cavity leading edge. ...
This study numerically investigates the flow field of a non-reacting cavity-configured scramjet (Supersonic Combustion Ramjet) combustor at various fuel injection pressures by solving the 2D Reynolds-Averaged Navier-Stokes (RANS) equations , species transport equations, and Menter SST k-v model. The aim of this research is to reveal the effects of wall cavity insertion and fuel injection pressure (FIP) on the crucial performance parameters i.e., fuel-air mixing efficiency (MxE), total pressure recovery (TPR), and mass-averaged Mach number (MAMN). Accordingly, two trapezoidal cavities of aspect ratio 7 are introduced on the opposite walls of a rectangular combustor. The combustor entrance is configured with rearward-facing steps and it intakes finite parallel air streams through finite-width inlets. Gaseous hydrogen jets are injected 30 mm downstream from the combustor entrance and 10 mm upstream from the cavity leading edge. FIP is varied according to the fuel-to-freestream pressure ratios (FFPR) of 4.5, 9.0, 13.5, and 18.0. The results of the cavity-configured combustor are then compared with the performance of the combustor in the absence of the wall cavities. The results delineate the change in flow structures with the inclusion of wall cavities and variation in FIP. Insight physics of mixing, total pressure loss, and MAMN in different regions of the combustor are studied and the results are quantified for comparison. MxE in a cavity-configured combustor does not monotonically increase with decreasing FFPR as found in the combustor without wall cavities. The shock-shear layer interactions (SSLIs) play a dominant role in mixing inside the cavity-configured combustor. The results also demonstrate that the insertion of wall cavities can increase fuel-air MxE through the formation of cavity recirculation zones. In the cavity-configured combustor, a maximum of 45% MxE is achieved for FFPR 4.5, which is 4% higher than the value obtained from the combustor without the cavities with an expense of 3% greater total pressure loss.
... The geometry examined in this work is shown in Fig. 1(a) and involves supersonic flow over a cavity with a ramp-shaped trailing edge. The use of a ramp shape has been found to be advantageous compared to a rectangular shape with regard to reduction in drag and shear-layer oscillations [7]. We study direct fuel injection into this cavity at two different locations, labeled as cases C1 and C2. ...
This paper is associated with a video winner of a 2020 American Physical Society's Division of Fluid Dynamics (DFD) Gallery of Fluid Motion Award for work presented at the DFD Gallery of Fluid Motion. The original video is available online at the Gallery of Fluid Motion, https://doi.org/10.1103/APS.DFD.2020.GFM.V0026.
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Experimental and computational analysis has been carried out by many researchers on supersonic cavity flow, but detailed analysis based on Rossiter's model still requires some insight. In the current study an open rectangular cavity with a length to depth ratio of 2 (L/D = 2) and Mach number at the inlet as 1.71, was considered as a baseline configuration for experimental analysis. Statistical techniques such as power spectral density (PSD), correlation, and overall sound pressure level (OASPL) were carried out on the unsteady pressure data, to analyze the aero-acoustic flow physics. High-speed schlieren images were processed to obtain spatially coherent modes by proper orthogonal decomposition (POD). The analysis was extended for different dimensions of subcavities on the aft, floor, and front wall. This detailed analysis of these configurations with different dimensions and combinations revealed the various flow features and mode frequencies in supersonic cavity. As the front wall subcavity act as a passive control device, reducing the overall sound pressure level inside the cavity whereas, the aft wall subcavity acts as a passive resonator with distinct harmonic fluid-resonant modes, a similar phenomenon was observed for floor subcavity at different locations. A novel method was employed to analyze Rossiter's model and its applicability in estimating experimental modes was verified, as it accurately predicted the dominant frequencies with a maximum of 2.74% uncertainty among all the configurations.
Çalışmada, dikdörtgen kesitli kavite içinde akan akış nedeniyle oluşan gürültü seviyesi ve kavite etrafındaki akış yapıları sayısal olarak incelenmiştir. Araştırma bulgularına göre kavite kesitinde değişiklikler yapılarak gürültü seviyesinin azaltılması amaçlanmıştır. Öncelikle, dikdörtgen kesitli kavite uygulaması için sayısal analizler yapılarak elde edilen akış yapısı sonuçları literatürdeki çalışmalarla doğrulanmıştır. Daha sonra, en yüksek gürültü seviyesinin oluştuğu kavite çıkış kenarı için r/h=0.1, 0.2, 0.5, 0.75 ve 1.0 çap oranlarında beş farklı geometri tasarlanmıştır ve bu geometriler için sonuçları doğrulanan SST k-ω türbülans modeli ile 10-35 m/s hız aralığında sayısal analizler yapılmıştır. Dikdörtgen kesitli ve çıkış kenarı beş farklı çap oranı ile tasarlanmış kavite akış sonuçları görsel ve sayısal veriler halinde sunulmuştur. Elde edilen sonuçlara göre özellikle artan çap oranı ile gürültü seviyesinde azalma tespit edilmiştir. Artan çap oranıyla tüm hızlar için gürültü seviyelerinde en yüksek %26 en düşük %15 oranında azalmalar gözlemlenmiştir. Çalışma sonuçları, uygulamada kullanılan kavite geometrilerinin tasarımına bağlı olarak gürültü seviyesinin azaltılmasında araştırmacılar için yol gösterici nitelikte olacaktır.
Experimental and computational analysis has been already carried out by many researchers on supersonic flow past cavities, but detailed analysis of computational results still needs some insight. For this purpose, an open rectangular cavity with a length to depth ratio of 2 () and inlet Mach number 1.71 was considered for an unsteady computational analysis in ANSYS FLUENT, using SST turbulence model. The two dimensional structured grids were generated in Pointwise grid generation software. FFT using Power Spectral Density (PSD) was carried out on the unsteady pressure data for 10,000 time-steps, with a total flow time of 10 ms. Many modes were observed, with dominant frequency at 10.5 kHz. The mode frequencies obtained were validated from experimental results and from the corresponding Rossiter’s Modes. Correlation between the unsteady pressure data was also found to analyze the flow dynamics. Many flow visualization techniques were employed such as density gradient-based numerical schlieren, which revealed many flow features associated with the flow. Vortex Shedding Visualization was carried out in terms of the lambda 2 criterion, where the vortex core () can be observed moving downstream in the shear layer. Lastly in the acoustic pressure contour, an acoustic wave can be observed moving within the cavity. The analysis was extended for different shapes of subcavities on the front and aft wall. As the front wall subcavity act as a passive control device, reducing the overall sound pressure level inside the cavity, whereas the aft wall subcavity acts as a passive resonator with distinct harmonic fluid-resonant modes. A more detailed analysis on these configurations with different shapes will give a comparative and better understanding on the flow features, mode frequencies, Rossiter’s coefficients, and fluid-resonant oscillations in a supersonic cavity. Also, the applicability of Rossiter’s Modes has been compared with the Closed-Box acoustic model for different configurations.KeywordsSupersonic cavity flowFast Fourier transformNumerical SchlierenLambda 2 criterion
Owing to the safety concerns associated with the usage of hydrogen (H2) fuel in conducting experiments, the current study investigates the suitability of using helium (He) gas as a surrogate fuel for H2 for supersonic mixing studies. The study adopts a steady state computational approach to compare the mixing performance between the two injection cases, where a wall-based pylon-cavity aided flameholder configuration is used for the investigation. A common fuel injection location at the cavity floor is used for He and H2 injection cases with an injector hole diameter of 1 mm. An inflow Mach number of 2.2 with sonic transverse fuel injection is kept the same for all the cases. A steady Reynolds-averaged Navier–Stokes (RANS) based computational model for compressed real gas is used for the investigation. The governing equations are solved by an implicit, second-order upwind solver with a two-equation Menter's Shear Stress Transport (SST) turbulence model. The study shows a variation in near field mixing performance between He and H2 injection cases due to the difference in the molecular mass. As a result, a 10%–11% variation in the mixing efficiency is observed between the two cases. This makes He not suitable for micro-level mixing studies as a surrogate to H2. However, it is possible to closely predict the trend in global mixing performance parameters as in the H2 injection case.
An open rectangular cavity with a length to depth ratio of 2 (L/D = 2) and inlet Mach number 1.71 was considered as a baseline configuration for an unsteady computational analysis. Fast Fourier transform using power spectral density, correlation, and overall sound
pressure level (OASPL) was carried out on the unsteady pressure data, to analyze the flow dynamics. Many flow visualization techniques
were employed such as density gradient-based numerical schlieren, vorticity contour, and streamlines for revealing major features associated with the flow. Vortex shedding visualization was carried out in terms of the Lambda 2 (k2) criterion, where the vortex core can be observed moving downstream in the shear layer. In the acoustic pressure contours and OASPL contours, the characteristics of the acoustic waves can be distinctly observed traversing within the cavity. The analysis was extended for different flow conditions and configurations. The front wall subcavity with a ratio of subcavity length (l) to cavity length (L) l/L = 0.20 has already been established as a passive control device experimentally whereas the aft wall subcavity with l/L = 0.20 was found to behave like a passive resonator with distinct harmonic fluid-resonant modes. A more detailed investigation of these configurations with different dimensions and combinations resulted in a comparative and better understanding of the flow features, mode frequencies, and fluid-resonant oscillations in a supersonic cavity flow. Further, a method for designing front wall subcavity for passive control device has been applied to a variety of test cases and has been proven effective in suppressing the oscillations for cavity configurations with longitudinal oscillation mechanisms.
Several numerical schemes for the solution of hyperbolic conservation laws are based on exploiting the information obtained by considering a sequence of Riemann problems. It is argued that in existing schemes much of this information is degraded, and that only certain features of the exact solution are worth striving for. It is shown that these features can be obtained by constructing a matrix with a certain “Property U.” Matrices having this property are exhibited for the equations of steady and unsteady gasdynamics. In order to construct thems it is found helpful to introduce “parameter vectors” which notably simplify the structure of the conservation laws.
Supersonic cavity flows driven by a thick shear layer at Mach 1.5 and 2.5 are studied by solving the two-dimensional unsteady compressible Navier-Stokes equations in terms of mass-averaged variables. The length to depth ratio of the rectangular cavity is three. The numerical scheme used is the finite-difference algorithm by I.Yu. Brailovskaya. A two-layer eddy-viscosity turbulence model is used. The computations show the self-sustained oscillations at Mach 1.5 and 2.5. The continuous formation and downstream shedding of leading edge vortices is demonstrated. The oscillatory modes are correctly predicted. The first mode is attributed to a large unsteady trailing edge vortex moving in the transverse direction. Based on the analysis, it is considered that the oscillation in the length to depth ratio three cavity is a longitudinal one and is controlled by a fluid-dynamic mechanism rather than a purely acoustic one.
A comprehensive and critical review of closure approximations for two-equation turbulence models has been made. Particular attention has focused on the scale-determining equation in an attempt to find the optimum choice of dependent variable and closure approximations. Using a combination of singular perturbation methods and numerical computations, this paper demonstrates that: (1) conventional κ-ε and κ-ω+2$/ formulations generally are inaccurate for boundary layers in adverse pressure gradient; (2) using 'wall functions' tends to mask the shortcomings of such models; and (3) a more suitable choice of dependent variables exists that is much more accurate for adverse pressure gradient. Based on the analysis, a two-equation turbulence model is postulated that is shown to be quite accurate for attached boundary layers in adverse pressure gradient, compressible boundary layers, and free shear flows.
Open cavities on aircraft exposed to high-speed flow, such as weapon bays, can give rise to intense self-induced pressure oscillations. The amplitude of these oscillations, under certain flight conditions, can cause structural damage. Substantial experimental and analytical efforts have investigated these pressure fluctuations, resulting in some understanding of the complex interaction of the external shear layer and cavity acoustical disturbances. However, no numerical computations have been obtained for the complete governing fluid mechanical equations. The purpose of this study is to obtain numerical solutions of the Navier-Stokes equations for an open cavity in order to provide a new tool for the analysis of this phenomenon.
A numerical solution is presented for the unsteady flow over a three-dimensional cavity at a freestream Mach number of 1.5 and Reynolds number of 1.09×106. The self-sustained oscillatory motion within the cavity is generated numerically by integration of the time-dependent compressible three-dimensional Reynolds averaged Navier-Stokes equations. Effects of fine-scale turbulence are simulated via a simple algebraic closure model. Details of the flowfield structure are elucidated, and it is verified that the fundamental behavior of the unsteady phenomena is two-dimensional. Comparison with experimental data is made in terms of the mean static pressure and overall acoustic sound pressure levels within the cavity, as well as with the acoustic frequency spectra of the oscillation along the cavity floor and rear bulkhead.
A numerical procedure is developed for the simultaneous implicit
numerical solution of the coupled k-epsilon and Navier-Stokes equations
for compressible viscous flows. The numerical algorithm is based on the
approximate factorization scheme of Beam and Warming for the strongly
coupled set of equations. The scheme incorporates a new second-order
Jameson type damping model that enhances the stability and relieves the
stiffness associated with the solution to the k-epsilon equations. The
model, which is based on the changes in both pressure and turbulent
kinetic energy, eliminates the need to use subiteration techniques.
Unsteady calculations were performed for supersonic flow over an open
cavity at a freestream Mach number of 1.5 and Reynolds number of 1.09 x
10(exp 6). The computed results are compared with experiments and
predictions from computations using uncoupled k-epsilon and
Navier-Stokes equations.
Some aspects of the numerical analysis of a supersonic cavity flow, including the effects of length scale, computational grid and time scale have been studied. A turbulent flow over a two-dimensional cavity has been analysed through solutions of the Reynolds-averaged Navier-Stokes equations. The effects of turbulence were modelled through a coupled solution of a k-ω turbulence model using compressibility corrections. A Riemann solver numerical scheme was employed. An adaptive mesh refinement technique has been used to capture the salient features of the transient fluid flow. Computational solutions have been obtained for cavities of length to depth ratios () of 1, 3, and 5, and freestream Mach numbers of 1.5 and 2.5; conditions corresponding to experimental data. It has been found that a single mode dominated oscillation existed at = 1 and that multiple mode dominated flows in the longer cavities. Frequency staging was observed for the long cavities. When the oscillation was weak at = 1, the predicted modes could be affected by the selection of the computational grid. The calculations were less sensitive to the grid characteristics for the longer cavities when the oscillation was strong.
This paper analyzes dilatation-dissipation based compressibility corrections for advanced turbulence models. Numerical computations verify that the dilatation-dissipation corrections devised by Sarkar and Zeman greatly improve both the k-omega and k-epsilon model predicted effect of Mach number on spreading rate. However, computations with the k-gamma model also show that the Sarkar/Zeman terms cause an undesired reduction in skin friction for the compressible flat-plate boundary layer. A perturbation solution for the compressible wall layer shows that the Sarkar and Zeman terms reduce the effective von Karman constant in the law of the wall. This is the source of the inaccurate k-gamma model skin-friction predictions for the flat-plate boundary layer. The perturbation solution also shows that the k-epsilon model has an inherent flaw for compressible boundary layers that is not compensated for by the dilatation-dissipation corrections. A compressibility modification for k-gamma and k-epsilon models is proposed that is similar to those of Sarkar and Zeman. The new compressibility term permits accurate predictions for the compressible mixing layer, flat-plate boundary layer, and a shock separated flow with the same values for all closure coefficients.