Characterisation of the unsteady wake of a square-back road vehicle

Square-back shapes are popular in the automotive market for their high level of practicality. These geometries, however, are usually characterised by high aerodynamic drag and their wake flow dynamics present many aspects, such as the coexistence of long- and short-time unsteady modes, whose full comprehension is still far from being achieved. The present work aims to provide some contributions to this field. An extensive experimental campaign consisting of balance, pressure tapping, particle image velocimetry and single point velocity measurements has been carried out in order to characterise the dynamic behaviour of the wake developing downstream of a simplified square-back geometry. Tests have been performed considering the Windsor body, at a Reynolds number (based on the model height) of ReH = 7.7 × 10^5. New insights on how the long-time instability develops are provided. The instability is shown to stem from the mutual interactions between the four shear layers bounding the wake rather than being the result of the state of perturbation of a single shear layer. Changes in the level of interaction between two or more shear layers are also reported to affect the short-time unsteady modes. A drag reduction is reported every time the symmetry of the wake is restored, as a consequence of the increased amount of reverse flow impinging on the base of the model. This seems to be true regardless of the configuration considered (with or without wheels) and the type of optimisation strategy adopted, although it does not necessarily imply the complete suppression of the long-time instability. In fact, a certain level of mobility in the flow reversal seems to be inevitable every time the symmetry of the wake is restored. Several elements that can alter this behaviour are also identified. A change in the curvature of at least one of the four shear layers is shown to increase the frequency of the switches between bi-stable states, until eventually the long-time instability disappears replaced by low frequency flapping or swinging motions. Such changes can be triggered by applying perturbations on either a global scale or a more local scale. Overall, the results presented in this work help to bridge the gap between simplified geometries and more realistic automotive shapes, as far as the characterisation of the time averaged and main unsteady features of the wake is concerned, and provide insights that may allow in the future the design of more effective flow control systems for drag reduction

Identification of large coherent structures in supersonic axisymmetric wakes

Direct numerical simulation data of supersonic axisymmetric wakes are analysed for the existence of large coherent structures. Wakes at Ma ¼ 2:46 are considered with results being presented for cases at Reynolds numbers ReD ¼ 30; 000 and 100,000. Criteria for identification of coherent structures in freeshear flows found in the literature are compiled and discussed, and the role of compressibility is addressed. In particular, the ability and reliability of visualisation techniques intended for incompressible shear-flows to educe meaningful structures in supersonic wakes is scrutinised. It is shown that some of these methods retain their usefulness for identification of vortical structures as long as the swirling rate is larger than the local compression and expansion rates in the flow field. As a measure for the validity of this condition in a given flow the ‘vortex compressibility parameter’ is proposed which is derived here. Best ‘visibility’ of coherent structures is achieved by employing visualisation techniques and proper orthogonal decomposition in combination with the introduction of artificial perturbations (forcing of the wake). The existence of both helical and longitudinal structures in the shear layer and of hairpin-like structures in the developing wake is demonstrated. In addition, elongated tubes of streamwise vorticity are observed to emanate from the region of recirculating flo

Evolution of the bi-stable wake of a square-back automotive shape

Square-back shapes are popular in the automotive market for their high level of practicality. These geometries, however, are usually characterised by high drag and their wake dynamics present aspects, such as the coexistence of a long-time bi-stable behaviour and short-time global fluctuating modes that are not fully understood. In the present paper, the unsteady behaviour of the wake of a generic square-back car geometry is characterised with an emphasis on identifying the causal relationship between the different dynamic modes in the wake. The study is experimental, consisting of balance, pressure, and stereoscopic PIV measurements. Applying wavelet and cross-wavelet transforms to the balance data, a quasi-steady correlation is demonstrated between the forces and bi-stable modes. This is investigated by applying proper orthogonal decomposition to the pressure and velocity data sets and a new structure is proposed for each bi-stable state, consisting of a hairpin vortex that originates from one of the two model’s vertical trailing edges and bends towards the opposite side as it merges into a single streamwise vortex downstream. The wake pumping motion is also identified and for the first time linked with the motion of the bi-stable vortical structure in the streamwise direction, resulting in out-of-phase pressure variations between the two vertical halves of the model base. A phase-averaged low-order model is also proposed that provides a comprehensive description of the mechanisms of the switch between the bi-stable states. It is demonstrated that, during the switch, the wake becomes laterally symmetric and, at this point, the level of interaction between the recirculating structures and the base reaches a minimum, yielding, for this geometry, a 7% reduction of the base drag compared to the time-averaged result

Separation between coherent and turbulent fluctuations. What can we learn from the Empirical Mode Decomposition?

The performances of a new data processing technique, namely the Empirical Mode Decomposition, are evaluated on a fully developed turbulent velocity signal perturbed by a numerical forcing which mimics a long-period flapping. First, we introduce a "resemblance" criterion to discriminate between the polluted and the unpolluted modes extracted from the perturbed velocity signal by means of the Empirical Mode Decomposition algorithm. A rejection procedure, playing, somehow, the role of a high-pass filter, is then designed in order to infer the original velocity signal from the perturbed one. The quality of this recovering procedure is extensively evaluated in the case of a "mono-component" perturbation (sine wave) by varying both the amplitude and the frequency of the perturbation. An excellent agreement between the recovered and the reference velocity signals is found, even though some discrepancies are observed when the perturbation frequency overlaps the frequency range corresponding to the energy-containing eddies as emphasized by both the energy spectrum and the structure functions. Finally, our recovering procedure is successfully performed on a time-dependent perturbation (linear chirp) covering a broad range of frequencies.Comment: 23 pages, 13 figures, submitted to Experiments in Fluid

Three dimensionality in the wake of the flow around a circular cylinder at Reynolds number 5000

The turbulent flow around a circular cylinder has been investigated at Re=5000Re=5000 using direct numerical simulations. Low frequency behavior, vortex undulation, vortex splitting, vortex dislocations and three dimensional flow within the wake were found to happen at this flow regime. In order to successfully capture the wake three dimensionality, different span-wise lengths were considered. It was found that a length LZ=2pDLZ=2pD was enough to capture this behavior, correctly predicting different aspects of the flow such as drag coefficient, Strouhal number and pressure and velocity distributions when compared to experimental values. Two instability mechanisms were found to coexist in the present case study: a global type instability originating in the shear layer, which shows a characteristic frequency, and a convective type instability that seems to be constantly present in the near wake. Characteristics of both types of instabilities are identified and discussed in detail. As suggested by Norberg, a resonance-type effect takes place in the vortex formation region, as the coexistence of both instability mechanisms result in distorted vortex tubes. However, vortex coherence is never lost within the wake.Peer ReviewedPostprint (author's final draft

Unsteady Cylinder Wakes from Arbitrary Bodies with Differentiable Physics-Assisted Neural Network

This work delineates a hybrid predictive framework configured as a coarse-grained surrogate for reconstructing unsteady fluid flows around multiple cylinders of diverse configurations. The presence of cylinders of arbitrary nature causes abrupt changes in the local flow profile while globally exhibiting a wide spectrum of dynamical wakes fluctuating in either a periodic or chaotic manner. Consequently, the focal point of the present study is to establish predictive frameworks that accurately reconstruct the overall fluid velocity flowfield such that the local boundary layer profile, as well as the wake dynamics, are both preserved for long time horizons. The hybrid framework is realized using a base differentiable flow solver combined with a neural network, yielding a differentiable physics-assisted neural network (DPNN). The framework is trained using bodies with arbitrary shapes, and then it is tested and further assessed on out-of-distribution samples. Our results indicate that the neural network acts as a forcing function to correct the local boundary layer profile while also remarkably improving the dissipative nature of the flowfields. It is found that the DPNN framework clearly outperforms the supervised learning approach while respecting the reduced feature space dynamics. The model predictions for arbitrary bodies indicate that the Strouhal number distribution with respect to spacing ratio exhibits similar patterns with existing literature. In addition, our model predictions also enable us to discover similar wake categories for flow past arbitrary bodies. For the chaotic wakes, the present approach predicts the chaotic switch in gap flows up to the mid-time range.Comment: codes to follow shortly: https://github.com/tum-pbs/DiffPhys-CylinderWakeFlow

Wake Dynamics and Passive Flow Control of a Blunt Trailing Edge Profiled Body

Wake flows behind two-dimensional bodies are dominated mainly by two types of coherent structures, namely, the Karman Benard vortices and the streamwise vortices, also referred to as rolls and ribs respectively. The three-dimensional wake instabilities lead to distinct instability modes (mode-A, mode-B and mode-C or mode S) depending on the flow Reynolds number and geometric shape. The present investigation explores the mechanism by which the flow transitions take place to three-dimensionality in the near wake of a profiled leading edge and blunt trailing edge body. Experiments consisting of a combination of Planar Laser Induced Fluorescence visualizations and Particle Image Velocimetry measurements are conducted for Reynolds numbers ranging from 250 to 46000. The results indicate that three instability modes, denoted by mode-A, mode-B and mode-C, appear in the wake transition to three-dimensionality, but their order of appearance does not occur through the traditional route as observed in circular cylinder flows. It is found that mode-C instability with a spanwise spacing varying between 1.2 to 2.8D (D being the trailing edge thickness) dominates the near wake development. This result is explored further with the aim to devise a simple passive control method to mitigate vortex shedding for blunt trailing edge bodies. The effect of a trailing edge spanwise sinusoidal perturbation (SSP) is investigated for a range of Reynolds numbers (ReD) spanning the transition range from ReD = 550 up to 46000. PIV measurements at different vertical and horizontal locations are performed to study changes in the streamwise and spanwise vortices. The base drag and strength of vortex shedding decrease with wavy trailing edge compared to the straight trailing edge. Proper Orthogonal Decomposition (POD) of the obtained PIV data indicates that the spanwise sinusoidal perturbation redistributes the relative energy, enhancing the streamwise vortices and, as a result, suppressing the Karman Benard rolls

Analysis of stationary and non-stationary phenomena in turbulent subcritical flow behind two parallel cylinders

This study presents the analysis of the bistable phenomenon for turbulent flows around two cylinders side-by-side using two methods for data analysis and chaos theory for dynamic analysis. The experimental data were acquired for various Reynolds numbers and pitch-todiameter ratio p/D of 1.16, 1.26, and 1.60, cylinders diameter was 25.1 mm. The experimental technique consists of measuring the velocity fluctuations in an aerodynamic channel using hot-wire anemometry. The study presents the application of the Hilbert-Huang transform (HHT) as a tool of analysis for non-stationary and non-linear signals. The method was first validated using single cylinders and then extended for two cylinders side-by-side. Results show that the HHT method may provide information about particular events in timefrequency space and about the physics of flow scales. The statistical analysis of the experimental data is performed to identify statistical patterns that can be used to characterize the bistable flow. The signals are scanned by a moving window for the statistical analysis, creating blocks of probability density functions (PDFs). The four first statistical moments of each PDF are calculated, and a tendency of behavior based on their variations is established. The dynamics of the bistable flow system are studied applying chaos theory tools, like the largest Lyapunov exponent. The strange attractors of the velocity-time series are reconstructed, and their topology is useful to understand the physics of the bistable system. Each flow wake mode is analyzed separately. A general model of the bistable flow is reconstructed using probability functions. The application of a set of tools in the analysis of the turbulent wake behind cylinders is useful for the comprehension of turbulent phenomena, producing meaningful results and allowing the identification of turbulent structures and flow scales, and a better understanding of the system dynamics.Este estudo apresenta a análise do fenômeno da biestabilidade no escoamento em torno de dois cilindros lado a lado usando dois métodos para análise de sinais, e teoria do caos para a análise da dinâmica. Os dados experimentais foram adquiridos para vários números de Reynolds e várias razões de aspecto p/D de 1,16, 1,26 e 1,60, o diâmetro dos cilindros é de 25,1 mm. A técnica experimental utilizada consiste em medir as flutuações de velocidade em um canal aerodinâmico utilizando anemometria de fio quente. O estudo apresenta a aplicação da transformada de Hilbert-Huang (HHT) como ferramenta de análise para sinais não estacionários e não lineares. O método é primeiramente validado utilizando sinais experimentais para um cilindro sobre escoamento turbulento e após aplicado ao escoamento sobre dois cilindros lado a lado. Resultados mostram que o método de HHT fornece não só uma definição mais precisa de eventos específicos no espaço tempo-frequência, mas também permite uma interpretação física mais significativa dos processos dinâmicos das escalas do escoamento. A análise estatística dos dados experimentais é feita com o objetivo de identificar padrões estatísticos que possam ser utilizados para caracterização do escoamento biestável. Para a análise estatística os dados são varridos por uma janela móvel, criando blocos de funções densidade de probabilidade (PDFs). Os quatro primeiros momentos estatísticos são calculados e é possível estabelecer uma tendência de comportamento baseada em suas variações. A dinâmica do sistema biestável é estudada aplicando ferramentas da teoria do caos, como o maior expoente de Lyapunov. O atrator estranho da série temporal da velocidade é reconstruído e sua topologia é utilizada para melhor compreensão do comportamento físico do fenômeno da biestabilidade. Cada esteira do escoamento biestável é analisada separadamente. Um modelo geral do escoamento biestável é reconstruído utilizando funções de probabilidade. A aplicação de um conjunto de ferramentas para a análise da turbulência das esteiras dos cilindros é útil para a melhor compreensão de fenômenos turbulentos, produzindo resultados significativos e permitindo a identificação de estruturas turbulentas e escalas do escoamento e um entendimento sobre a dinâmica do sistema

Revisit the intrinsic features of flip-flopping flow behind side-by-side circular cylinders

As one of the most intriguing wake patterns of two side-by-side circular cylinders at an intermediate gap spacing, the flip-flopping (FF) flow has attracted great attention of fundamental research interest. This FF flow is featured by the intermittently and randomly switching gap flow with correspondingly changing forces of the two cylinders. In this paper, we first present a partition map of the wake patterns behind two side-by-side circular cylinders and briefly introduce intrinsic features of each flow pattern. We focus on the FF flow aiming to explain: (i) the origin of the FF flow between laminar and turbulent regimes, (ii) their connections in different flow regimes, and (iii) mechanisms of the significantly varying flip-over time scale of the FF flows. In the laminar regime, we further divide the FF flow into the sub-classed I (FF1) and II (FF2), based on their different origins from the in-phase and anti-phase synchronized vortex shedding instabilities, respectively. By exploring the vortex interactions, we show that the FF flow in the turbulent regime has the same origin and similar vortex dynamics as the FF2 wake in the laminar regime, despite some minor disparities. Thus, a connection is established between the FF2 pattern in the laminar flow and the FF pattern in the turbulent flow. For the FF flow in the laminar regime (Re < 150-200), the mildly decreasing switching time, is several vortex shedding periods. However, for the FF flow in the weak turbulence regime (150-200 < Re < 1000-1700), the switching time scale increases significantly with Re owing to the increased vortex formation length. The FF in the strong turbulence regime (Re > 1000-1700) has a switching time scale of several orders of magnitude longer than the vortex shedding period, where the switching scale decreases gradually with Re due to the stronger Kelvin-Helmholtz vortices