Gradual wavelet reconstruction of the velocity increments for turbulent wakes

This work explores the properties of the velocity increment distributions for wakes of contrasting local Reynolds number and nature of generation (a cylinder wake and a multiscale-forced case, respectively). It makes use of a technique called gradual wavelet reconstruction (GWR) to generate constrained randomizations of the original data, the nature of which is a function of a parameter, ϑ. This controls the proportion of the energy between the Markov-Einstein length (∼ 0.8 Taylor scales) and integral scale that is fixed in place in the synthetic data. The properties of the increments for these synthetic data are then compared to the original data as a function of ϑ. We write a Fokker-Planck equation for the evolution of the velocity increments as a function of spatial scale, r, and, in line with previous work, expand the drift and diffusion terms in terms up to fourth order in the increments and find no terms are relevant beyond the quadratic terms. Only the linear contribution to the expansion of the drift coefficient is non-zero and it exhibits a consistent scaling with ϑ for different flows above a low threshold. For the diffusion coefficient, we find a local Reynolds number independence in the relation between the constant term and ϑ for the multiscale-forced wakes. This term characterizes small scale structure and can be contrasted with the results for the Kolmogorov capacity of the zero-crossings of the velocity signals, which measures structure over all scales and clearly distinguishes between the types of forcing. Using GWR shows that results for the linear and quadratic terms in the expansion of the diffusion coefficient are significant, providing a new means for identifying intermittency and anomalous scaling in turbulence datasets. All our data showed a similar scaling behavior for these parameters irrespective of forcing type or Reynolds number, indicating a degree of universality to the anomalous scaling of turbulence. Hence, these terms are a useful metric for testing the efficacy of synthetic turbulence generation schemes used in large eddy simulation, and we also discuss the implications of our approach for reduced order modeling of the Navier-Stokes equations

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

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

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

Turbulent/turbulent Entrainment: a detailed examination of entrainment, and the behaviour of the outer interface as affected by background turbulence

This thesis presents an experimental investigation into the effects of free-stream turbulence on entrainment and examines the outer boundaries of fluidic regions with turbulence present on both sides of the interface. Simultaneous particle image velocimetry (PIV) and planar laser induced fluorescence (PLIF) experiments are conducted in the wake of a circular cylinder subjected to grid generated turbulence. The turbulent/turbulent interface (TTI) is identified for the first time. Analogous to the classical case of a turbulent/non-turbulent interface (TNTI), it facilitates the change in the enstrophy level between one region to the other. The TTI is seen to persist even at the most extreme background turbulence conditions. In the far wake of a circular cylinder, free-stream turbulence is seen to reduce the net entrainment into the wake relative to a non-turbulent background. This behaviour is driven by infrequent yet powerful, intermittent detrainment events. It is found that the intensity of the background turbulence is most important in determining this behaviour, whereas the length scale is seen to have, only a second order effect. The mechanism of this entrainment process is investigated and it is observed that role of viscosity in this process is insignificant when turbulence is present on both sides of the fluidic boundary. This is possible, since the availability of turbulent strain (and vorticity) on both sides of the interface in a TTI, allows the inertial term to take over the responsibilities of enstrophy production. Finally, in the near-field of a cylinder wake, the influence of length scale is more important. Unlike in the far-field, coherent structures play a vital role in near wake development. The traditional increase in a bluff body wake width in the near field is reproduced and the effects of both wake meandering as well as wake growth through entrainment are investigated.Open Acces

Densely distributed and real-time scour hole monitoring using piezoelectric rod sensors

This study aims to validate a piezoelectric driven-rod scour monitoring system that can sense changes in scour depth along the entire rod at its instrumented location. The proposed sensor is a polymeric slender rod with a thin strip of polyvinylidene fluoride that runs through its midline. Extraction of the fundamental frequency allows the direct calculation of the exposed length (or scour depth) of the slender rod undergoing fluid flow excitation. First, laboratory validation in dry conditions is presented. Second, hydrodynamic testing of the sensor system in a soil-bed flume is discussed. Each rod was installed using a three-dimensional-printed footing designed for ease of installation and stabilization during testing. The sensors were installed in a layout designed to capture symmetric scour conditions around a scaled pier. In order to analyze the system out of steady-state conditions, water velocity was increased in stages during testing to induce different degrees of scour. As ambient water flow excited the portion of the exposed rods, the embedded piezoelectric element outputted a time-varying voltage signal. Different methods were then employed to extract the fundamental frequency of each rod, and the results were compared. Further testing was also performed to characterize the relationship between frequency outputs and flow velocity, which were previously thought to be independent. In general, the proposed driven-rod scour monitoring system successfully captured changing frequencies under varied flow conditions

Constant-frequency time cells in the vortex-shedding from a square cylinder in accelerating flows

An extensive experimental campaign has been carried out in a multiple-fan wind tunnel to study the effects of flow acceleration on a sectional model of a sharp-edged square cylinder. Different levels of positive and negative acceleration are reproduced, which are compatible with those induced by full-scale thunderstorm outflows. Various initial and final conditions are also explored and, in all conditions, multiple test repeats are carried out in order to obtain satisfactory ensemble averages. Particular attention is devoted to the acquisition of signals associated with vortex-shedding, for which tailored time-frequency analyses, based on the continuous wavelet and Hilbert transforms, are introduced. Sensitivity analyses are carried out on a selection of the relevant pa-rameters that better allow the tracing of the temporal variation of the shedding frequency. Time intervals in which the shedding frequency is constant, separated by discontinuities, are found during the transients. The number and extent of such constant-frequency time cells and discontinuities seem to be connected with the flow acceleration, but are not strictly repetitive. For higher levels of acceleration the ensemble mean of the Strouhal number is found to be comparable with or moderately lower than the steady-flow value corresponding to the instantaneous velocity