Reduced-order analysis of buffet flow of space launchers

2017 ◽  
Vol 815 ◽  
pp. 1-25 ◽  
Author(s):  
Vladimir Statnikov ◽  
Matthias Meinke ◽  
Wolfgang Schröder
Keyword(s):  
Shear Layer ◽  
Vortex Shedding ◽  
Separation Bubble ◽  
Dynamic Mode Decomposition ◽  
Recirculation Region ◽  
Dynamic Mode ◽  
Main Body ◽  
Reduced Order ◽  
Order Analysis ◽  
Wall Pressure Fluctuations

A reduced-order analysis based on optimized dynamic mode decomposition (DMD) is performed on the turbulent wake of a generic axisymmetric space launcher configuration computed via a zonal large-eddy simulation at the free stream Mach number $Ma_{\infty }=0.8$ and the Reynolds number based on the main body diameter $Re_{D}=6\times 10^{5}$ to investigate the buffet phenomenon. The transonic wake is characterized by an unsteady recirculation region occurring around the nozzle due to the separation of the turbulent boundary layer at the main body shoulder and subsequent dynamic interaction of the unstable free-shear layer with the nozzle surface. This results in strongly periodic and antisymmetric wall pressure fluctuations, for which three distinct frequency ranges are identified using conventional spectral analysis, i.e. $Sr_{D}\approx 0.1$, $Sr_{D}\approx 0.2$ and $Sr_{D}\approx 0.35$. For the spatially integrated side (buffet) loads on the nozzle, the second range is found to be energetically most dominant. To clarify the origin of the detected wake dynamics, the underlying spatio-temporal coherent modes are extracted using DMD. Subsequent analysis of the reduced-order modelled flow field based on the identified DMD modes reveals that at $Sr_{D}\approx 0.1$ a longitudinal cross-pumping motion of the separation bubble takes place, caused by a harmonic antisymmetric oscillation of the main recirculation vortex in the streamwise direction. At $Sr_{D}\approx 0.2$, a cross-flapping motion of the shear layer is determined, triggered by antisymmetric vortex shedding which is in phase with the cross-pumping motion such that it occurs at twice the frequency value. The last range of $Sr_{D}\approx 0.35$ is attributed to a swinging motion of the shear layer caused by a higher harmonic of the vortex shedding mode. Conclusively, the controversial aspect of the true three-dimensional shape of the antisymmetric mode at $Sr_{D}\approx 0.2$ that dominates the buffet phenomenon is scrutinized. Inclined elongated closed-loop vortices are identified that are shed in alternating sequence from azimuthally opposite positions in a longitudinal plane of symmetry that changes its momentary orientation irregularly, maintaining an axisymmetric time-averaged field and spatially isotropic buffet loads.

Modeling the Turbulent Wake Behind a Wall-Mounted Square Cylinder

2020 ◽  
Author(s):  
Christian Amor ◽  
José M Pérez ◽  
Philipp Schlatter ◽  
Ricardo Vinuesa ◽  
Soledad Le Clainche
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Turbulent Wake ◽  
Orthogonal Decomposition ◽  
Dynamic Mode Decomposition ◽  
Dynamic Mode ◽  
Square Cylinder ◽  
Complex Flow ◽  
Reduced Order ◽  
Mode Decomposition ◽  
Proper Orthogonal

Abstract This article introduces some soft computing methods generally used for data analysis and flow pattern detection in fluid dynamics. These techniques decompose the original flow field as an expansion of modes, which can be either orthogonal in time (variants of dynamic mode decomposition), or in space (variants of proper orthogonal decomposition) or in time and space (spectral proper orthogonal decomposition), or they can simply be selected using some sophisticated statistical techniques (empirical mode decomposition). The performance of these methods is tested in the turbulent wake of a wall-mounted square cylinder. This highly complex flow is suitable to show the ability of the aforementioned methods to reduce the degrees of freedom of the original data by only retaining the large scales in the flow. The main result is a reduced-order model of the original flow case, based on a low number of modes. A deep discussion is carried out about how to choose the most computationally efficient method to obtain suitable reduced-order models of the flow. The techniques introduced in this article are data-driven methods that could be applied to model any type of non-linear dynamical system, including numerical and experimental databases.

scholarly journals Analysis of transonic buffet using dynamic mode decomposition

2021 ◽  
Vol 62 (4) ◽  
Author(s):  
Antje Feldhusen-Hoffmann ◽  
Christian Lagemann ◽  
Simon Loosen ◽  
Pascal Meysonnat ◽  
Michael Klaas ◽  
...  
Keyword(s):  
Shock Wave ◽  
Flow Field ◽  
Acoustic Waves ◽  
Feedback Loop ◽  
Measurement Data ◽  
Dynamic Mode Decomposition ◽  
Recirculation Region ◽  
Dynamic Mode ◽  
Mode Decomposition ◽  
Transonic Buffet

AbstractThe buffet flow field around supercritical airfoils is dominated by self-sustained shock wave oscillations on the suction side of the wing. Theories assume that this unsteadiness is driven by a feedback loop of disturbances in the flow field downstream of the shock wave whose upstream propagating part is generated by acoustic waves. High-speed particle-image velocimetry measurements are performed to investigate this feedback loop in transonic buffet flow over a supercritical DRA 2303 airfoil. The freestream Mach number is $$M_{\infty } = 0.73$$ M ∞ = 0.73 , the angle of attack is $$\alpha = 3.5^{\circ }$$ α = 3 . 5 ∘ , and the chord-based Reynolds number is $${\mathrm{Re}}_{c} = 1.9\times 10^6$$ Re c = 1.9 × 10 6 . The obtained velocity fields are processed by sparsity-promoting dynamic mode decomposition to identify the dominant dynamic features contributing strongest to the buffet flow field. Two pronounced dynamic modes are found which confirm the presence of two main features of the proposed feedback loop. One mode is related to the shock wave oscillation frequency and its shape includes the movement of the shock wave and the coupled pulsation of the recirculation region downstream of the shock wave. The other pronounced mode represents the disturbances which form the downstream propagating part of the proposed feedback loop. The frequency of this mode corresponds to the frequency of the acoustic waves which are generated by these downstream traveling disturbances and which form the upstream propagating part of the proposed feedback loop. In this study, the post-processing, i.e., the DMD, is highlighted to substantiate the existence of this vortex mode. It is this vortex mode that via the Lamb vector excites the shock oscillations. The measurement data based DMD results confirm numerical findings, i.e., the dominant buffet and vortex modes are in good agreement with the feedback loop suggested by Lee. Graphic abstract

scholarly journals Analysis of V-Gutter Reacting Flow Dynamics Using Proper Orthogonal and Dynamic Mode Decompositions

Energies ◽  
2020 ◽  
Vol 13 (18) ◽  
pp. 4886 ◽  
Author(s):  
Yang Yang ◽  
Xiao Liu ◽  
Zhihao Zhang
Keyword(s):  
Shear Layer ◽  
Large Scale ◽  
Dynamic Mode Decomposition ◽  
Dynamic Mode ◽  
Reacting Flow ◽  
Eddy Simulation ◽  
Mode Decomposition ◽  
Wake Instability ◽  
Shedding Frequency ◽  
Proper Orthogonal

The current work is focused on investigating the potential of data-driven post-processing techniques, including proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) for flame dynamics. Large-eddy simulation (LES) of a V-gutter premixed flame was performed with two Reynolds numbers. The flame transfer function (FTF) was calculated. The POD and DMD were used for the analysis of the flame structures, wake shedding frequency, etc. The results acquired by different methods were also compared. The FTF results indicate that the flames have proportional, inertial, and delay components. The POD method could capture the shedding wake motion and shear layer motion. The excited DMD modes corresponded to the shear layer flames’ swing and convect motions in certain directions. Both POD and DMD could help to identify the wake shedding frequency. However, this large-scale flame oscillation is not presented in the FTF results. The negative growth rates of the decomposed mode confirm that the shear layer stabilized flame was more stable than the flame possessing a wake instability. The corresponding combustor design could be guided by the above results.

scholarly journals An efficient computational framework for naval shape design and optimization problems by means of data-driven reduced order modeling techniques

2020 ◽  
Author(s):  
Nicola Demo ◽  
Giulio Ortali ◽  
Gianluca Gustin ◽  
Gianluigi Rozza ◽  
Gianpiero Lavini
Keyword(s):  
Optimization Problems ◽  
Computational Cost ◽  
Gaussian Process Regression ◽  
Dynamic Mode Decomposition ◽  
Data Driven ◽  
Free Form ◽  
Dynamic Mode ◽  
Two Phase ◽  
Initial Shape ◽  
Reduced Order

Abstract This contribution describes the implementation of a data-driven shape optimization pipeline in a naval architecture application. We adopt reduced order models in order to improve the efficiency of the overall optimization, keeping a modular and equation-free nature to target the industrial demand. We applied the above mentioned pipeline to a realistic cruise ship in order to reduce the total drag. We begin by defining the design space, generated by deforming an initial shape in a parametric way using free form deformation. The evaluation of the performance of each new hull is determined by simulating the flux via finite volume discretization of a two-phase (water and air) fluid. Since the fluid dynamics model can result very expensive—especially dealing with complex industrial geometries—we propose also a dynamic mode decomposition enhancement to reduce the computational cost of a single numerical simulation. The real-time computation is finally achieved by means of proper orthogonal decomposition with Gaussian process regression technique. Thanks to the quick approximation, a genetic optimization algorithm becomes feasible to converge towards the optimal shape.

Reduced-Order Modeling for Dynamic Mode Decomposition Without an Arbitrary Sparsity Parameter

AIAA Journal ◽  
2020 ◽  
Vol 58 (9) ◽  
pp. 3919-3931 ◽  
Author(s):  
John Graff ◽  
Matthew J. Ringuette ◽  
Tarunraj Singh ◽  
Francis D. Lagor
Keyword(s):  
Reduced Order Modeling ◽  
Dynamic Mode Decomposition ◽  
Dynamic Mode ◽  
Reduced Order ◽  
Mode Decomposition

scholarly journals From snapshots to modal expansions – bridging low residuals and pure frequencies

2016 ◽  
Vol 802 ◽  
pp. 1-4 ◽  
Author(s):  
Bernd R. Noack
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Orthogonal Decomposition ◽  
Operating Conditions ◽  
Dynamic Mode Decomposition ◽  
Dynamic Mode ◽  
Simple Method ◽  
Reduced Order ◽  
Mode Decomposition ◽  
Optimality Property ◽  
Proper Orthogonal

Data-driven low-order modelling has been enjoying rapid advances in fluid mechanics. Arguably, Sirovich (Q. Appl. Maths, vol. XLV, 1987, pp. 561–571) started these developments with snapshot proper orthogonal decomposition, a particularly simple method. The resulting reduced-order models provide valuable insights into flow physics, allow inexpensive explorations of dynamics and operating conditions, and enable model-based control design. A winning argument for proper orthogonal decomposition (POD) is the optimality property, i.e. the guarantee of the least residual for a given number of modes. The price is unpleasant frequency mixing in the modes which complicates their physical interpretation. In contrast, temporal Fourier modes and dynamic mode decomposition (DMD) provide pure frequency dynamics but lose the orthonormality and optimality property of POD. Sieber et al. (J. Fluid Mech., vol. 792, 2016, pp. 798–828) bridge the least residual and pure frequency behaviour with an ingenious interpolation, called spectral proper orthogonal decomposition (SPOD). This article puts the achievement of the TU Berlin authors in perspective, illustrating the potential of SPOD and the challenges ahead.

A numerical study of shear layer characteristics of low-speed transverse jets

2016 ◽  
Vol 790 ◽  
pp. 275-307 ◽  
Author(s):  
Prahladh S. Iyer ◽  
Krishnan Mahesh
Keyword(s):  
Velocity Profile ◽  
Shear Layer ◽  
Convective Instability ◽  
Numerical Study ◽  
Velocity Ratio ◽  
Mixing Layer ◽  
Three Dimensional ◽  
Dynamic Mode Decomposition ◽  
Dynamic Mode ◽  
Dominant Frequencies

Direct numerical simulation (DNS) and dynamic mode decomposition (DMD) are used to study the shear layer characteristics of a jet in a crossflow. Experimental observations by Megerian et al. (J. Fluid Mech., vol. 593, 2007, pp. 93–129) at velocity ratios ($R=\overline{v}_{j}/u_{\infty }$) of 2 and 4 and Reynolds number ($Re=\overline{v}_{j}D/{\it\nu}$) of 2000 on the transition from absolute to convective instability of the upstream shear layer are reproduced. Point velocity spectra at different points along the shear layer show excellent agreement with experiments. The same frequency ($St=0.65$) is dominant along the length of the shear layer for $R=2$, whereas the dominant frequencies change along the shear layer for $R=4$. DMD of the full three-dimensional flow field is able to reproduce the dominant frequencies observed from DNS and shows that the shear layer modes are dominant for both the conditions simulated. The spatial modes obtained from DMD are used to study the nature of the shear layer instability. It is found that a counter-current mixing layer is obtained in the upstream shear layer. The corresponding mixing velocity ratio is obtained, and seen to delineate the two regimes of absolute or convective instability. The effect of the nozzle is evaluated by performing simulations without the nozzle while requiring the jet to have the same inlet velocity profile as that obtained at the nozzle exit in the simulations including the nozzle. The shear layer spectra show good agreement with the simulations including the nozzle. The effect of shear layer thickness is studied at a velocity ratio of 2 based on peak and mean jet velocity. The dominant frequencies and spatial shear layer modes from DNS/DMD are significantly altered by the jet exit velocity profile.

Sign in / Sign up

Export Citation Format

Share Document