Turbulent Boundary Layer Features via Lagrangian Coherent Structures, Proper Orthogonal Decomposition and Dynamic Mode Decomposition

High-speed stereo PIV-measurements have been performed in a turbulent boundary layer at Reθ of 9800 in order to elucidate the coherent structures. Snapshot proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) are used to visualize the flow structure depending on the turbulent kinetic energy and frequency content. The first six POD and DMD modes show the largest and the lowest amount of energy and frequency, respectively. Lagrangian coherent structure (LCS) based on the algorithm developed using the variational theory is also applied to track the flow via attracting and repelling trajectories. The shapes and the length of the trajectories show variation with increasing advection time. LCS trajectories are overlayed with the individual POD and DMD modes. Repelling and attracting lines cover the structure of these modes. Reconstructed flow fields from individual POD modes are also used to generate new LCS trajectories. The energy and frequency content have a direct impact on the length of the trajectories, where the longest reconstructed trajectories associate with the higher energy and lower frequency modes, and vise verse. The multiple intersection points between the repelling and attracting lines marked the low momentum regions

Markovian properties of velocity increments in boundary layer turbulence

Markovian properties of the turbulent velocity increments in a flat plate boundary layer at Re = 19 100 are investigated using hot-wire anemometry measurements of the streamwise velocity component in a wind tunnel. Increments of the longitudinal velocities at di erent wall-normal positions show that the flow exhibits Markovian properties when the separation between di erent scales, or the Markov-Einstein coherence length, is on the order of the Taylor microscale, . The results indicate that Markovian nature of turbulence evolves across the boundary layer showing certain characteristics pertaining to the distance to the wall. The connection between the Markovian properties of turbulent boundary layer and existence of the spectral gap is explored. Markovianity of the process is also discussed in relation to the nonlocal nonlinear versus local nonlinear transfer of energy, triadic interactions and dissipation

A Historical Center in the Aspects of Identity/Culture/Space: Santa Ruins in the Context of Sustainability

In the historic environments located in rural areas, the difficulty of transportation and physical services causes the active use of these fields be difficult, and over time, these areas are faced with the danger of extinction. In this sense, “Santa Ruins” that is one of the important locations especially in terms of its historical importance, many architectural heritages that it contains and the mountain tourism is an important figure which faces extinction. Santa Ruins is considered as one of the areas to be protected when it’s examined in terms of its history, religious and cultural background, the character of rural settlement, its location at the intersection of important historic routes, the architectural / cultural heritages that it contains, having archaeological value, and the natural value of the region, etc. In the studies done specific to Piştoflu District, the necessary measurements of the buildings in the neighbourhood and the measurement drawings that belong to the buildings were obtained using photogrammetric and conventional methods after the historical researches, photography studies and obtaining the overall work plan. The considerations were done in the context of identity, culture and space by analysing the structural data, building material data, information about its conservation status, living conditions and the data related to in-service spaces and non-advanced spaces of the buildings that are located on this area

Structure of Zero Pressure Gradient High Reynolds Number Turbulent Boundary Layers

This thesis presents part of the large research program funded by the European Commission calledWallturb: A European synergy for the assessment of wall turbulence. The main aim of this researchprogram is to create new experimental and numerical databases on the characteristics of turbulent wall-bounded flows, especially turbulent boundary layers. The goal is that these databases will be used togain more insight into the physical mechanisms governing the dynamics of these flows. This knowledgeis deemed essential for the future development of efficient and physical turbulence modeling strategies,which are in turn crucial to aircraft and other industries for sustainable development, especially underthe pressure of high oil prices and operational costs. The signature experiment of Wallturb was the multi-investigator, multi-system, multi-point investigation carried out in the 20m test section of the boundary layer research facility at LML Lille, Francein 2006. This thesis is focused primarily on the part of that investigation which utilized the 143 probehot-wire array belonging to the Turbulence Research Laboratory of Chalmers, and only on the two zero-pressure gradient boundary layer experiments at Reθ of 9800 and 19 100. A new hot-wire calibration method was developed and utilized for this investigation. The method isbased on a polynomial curve fitting approximation which expresses the instantaneous velocity as a function of instantaneous voltage. The results showed that even a second order polynomial approximationyields very good agreement between the measured profiles (or computed profiles after the calibration)and the reference profiles used in the calibration. The method also provides an opportunity to do thecalibration on the fly as long as the convergence of the high order voltage statistics can be satisfied. The large scale motions of the turbulence were studied in detail using two-dimensional two-pointcross-correlations maps on different planes within the measurement domain. It was observed that theelongated correlations exist at every wall-normal position above the buffer layer. These elongated structures were relatively more significant in the log layer. The investigation using the proper orthogonal decomposition showed that the POD (in conjunctionwith Fourier analysis in the statistically homogeneous and stationary directions) can effectively representthe total kinetic energy with a small number of modes. At both Reynolds numbers, it was possible torecover almost 90% of the total turbulence kinetic energy within the entire boundary layer with onlyfour POD modes. The reconstructed velocity fluctuations on the spanwise-wall-normal plane show howorganized motions of turbulence with significant amounts of energy interact with each other across theboundary layer. It was also possible to observe the interaction between the inner and outer layers ofturbulence using these reconstructed velocity fields

Structure of Zero Pressure Gradient High Reynolds Number Turbulent Boundary Layers

This thesis presents part of the large research program funded by the European Commission calledWallturb: A European synergy for the assessment of wall turbulence. The main aim of this researchprogram is to create new experimental and numerical databases on the characteristics of turbulent wall-bounded flows, especially turbulent boundary layers. The goal is that these databases will be used togain more insight into the physical mechanisms governing the dynamics of these flows. This knowledgeis deemed essential for the future development of efficient and physical turbulence modeling strategies,which are in turn crucial to aircraft and other industries for sustainable development, especially underthe pressure of high oil prices and operational costs. The signature experiment of Wallturb was the multi-investigator, multi-system, multi-point investigation carried out in the 20m test section of the boundary layer research facility at LML Lille, Francein 2006. This thesis is focused primarily on the part of that investigation which utilized the 143 probehot-wire array belonging to the Turbulence Research Laboratory of Chalmers, and only on the two zero-pressure gradient boundary layer experiments at Reθ of 9800 and 19 100. A new hot-wire calibration method was developed and utilized for this investigation. The method isbased on a polynomial curve fitting approximation which expresses the instantaneous velocity as a function of instantaneous voltage. The results showed that even a second order polynomial approximationyields very good agreement between the measured profiles (or computed profiles after the calibration)and the reference profiles used in the calibration. The method also provides an opportunity to do thecalibration on the fly as long as the convergence of the high order voltage statistics can be satisfied. The large scale motions of the turbulence were studied in detail using two-dimensional two-pointcross-correlations maps on different planes within the measurement domain. It was observed that theelongated correlations exist at every wall-normal position above the buffer layer. These elongated structures were relatively more significant in the log layer. The investigation using the proper orthogonal decomposition showed that the POD (in conjunctionwith Fourier analysis in the statistically homogeneous and stationary directions) can effectively representthe total kinetic energy with a small number of modes. At both Reynolds numbers, it was possible torecover almost 90% of the total turbulence kinetic energy within the entire boundary layer with onlyfour POD modes. The reconstructed velocity fluctuations on the spanwise-wall-normal plane show howorganized motions of turbulence with significant amounts of energy interact with each other across theboundary layer. It was also possible to observe the interaction between the inner and outer layers ofturbulence using these reconstructed velocity fields

Anisotropic character of low-order turbulent flow descriptions through the proper orthogonal decomposition

Proper orthogonal decomposition (POD) is applied to distinct data sets in order to characterize the propagation of error arising from basis truncation in the description of turbulence. Experimental data from stereo particle image velocimetry measurements in a wind turbine array and direct numerical simulation data from a fully developed channel flow are used to illustrate dependence of the anisotropy tensor invariants as a function of POD modes used in low-order descriptions. In all cases, ensembles of snapshots illuminate a variety of anisotropic states of turbulence. In the near wake of a model wind turbine, the turbulence field reflects the periodic interaction between the incoming flow and rotor blade. The far wake of the wind turbine is more homogenous, confirmed by the increased magnitude of the anisotropy factor. By contrast, the channel flow exhibits many anisotropic states of turbulence. In the inner layer of the wall-bounded region, one observes one-component turbulence at the wall; immediately above, the turbulence is dominated by two components, with the outer layer showing fully three-dimensional turbulence, conforming to theory for wall-bounded turbulence. The complexity of flow descriptions resulting from truncated POD bases can be greatly mitigated by severe basis truncations. However, the current work demonstrates that such simplification necessarily exaggerates the anisotropy of the modeled flow and, in extreme cases, can lead to the loss of three-dimensionality. Application of simple corrections to the low-order descriptions of the Reynolds stress tensor significantly reduces the residual root-mean-square error. Similar error reduction is seen in the anisotropy tensor invariants. Corrections of this form reintroduce three-dimensionality to severe truncations of POD bases. A threshold for truncating the POD basis based on the equivalent anisotropy factor for each measurement set required many more modes than a threshold based on energy. The mode requirement to reach the anisotropy threshold after correction is reduced by a full order of magnitude for all example data sets, ensuring that economical low-dimensional models account for the isotropic quality of the turbulence field

Experimental study of dispersed oil-water flow in a horizontal pipe with enhanced inlet mixing, Part 2: In-situ droplet measurements

acceptedVersio

Identification of Markov Process Within a Wind Turbine Array Boundary Layer

The Markovian properties within a wind turbine array boundary layer are explored for data taken in a wind tunnel containing a model wind turbine array. A stochastic analysis of the data is carried out using the mathematics of Markov processes. The data were obtained using hot-wire anemometry thus providing point velocity statistics. The theory of Markov process is applied to obtain a statistical description of longitudinal velocity increments inside the turbine wake. Comparison of two- and three-scale conditional probability density functions indicates the existence of Markovian properties in longitudinal velocity increments for scale differences larger than the Taylor microscale. This result is quantified by use of the Wilcoxon rank-sum test which verifies that this relationship holds independent of initial scale selection outside of the near-wake region behind a wind turbine. Furthermore, at the locations which demonstrate Markovian properties, there appears to be a well defined inertial subrange which follows Kolmogorov\u27s −5/3 scaling behavior. The results show that directly behind the tips of the rotor and the hub, the complex turbulent interactions and large scale structures of the near-wake affect the Markovian nature of the field. The presence of a Markov process in the remaining locations leads to characterization of the development multiscale statistics of the wind turbine wakes using the most recent states of the flow