On the development of the convective boundary layer in a shear-free thermally forced stably stratified fluid setting: a 2D and 3D experimental investigation using image analysis techniques coupled with temperature measurements

Abstract

The motion of buoyancy driven plumes is, on all scales, the most common heat and momentum transfer mechanism in geophysical flows, well known as Free Convection. Similarly, density stratification due to heating inequalities is also an ordinary scenario in nature. Free Convection phenomenon coupled with a density stratified fluid setting leads to the so-called Penetrative Free Convection (PFC). When a fluid, in static equilibrium, is stably stratified a thermal forcing can produce an unstable configuration ensuing internal waves formation of increasing amplitude. If the perturbation is strong enough, it can definitely erode the initial stratification and cause the motion of turbulent buoyant updrafts, dome-shaped, compensated by denser downdrafts. The entrainment phenomenon occurring at the interface between the turbulent and non-turbulent region justifies the penetrative feature of convection and causes the non linear growth of the Convective Boundary Layer (CBL) of well mixed fluid against the adjacent stably stratified region. In addition to the wide engineering applications, the environmental impact mostly motivates PFC studies. The upper lakes and oceans, under calm conditions, usually exhibit a continuous, moderately stable density distribution. Turbulent convective flow can be generated both by the free-surface cooling and wind shear-stress, eroding the stable stratification on a daily or seasonal time scale. Domes with large downward velocities are generated at the free surface, balanced by updrafts with lower velocity but larger area. Because of the relatively rapid mixing, the density distribution is approximately uniform in the upper layer and it deepens with time as a result of the entrainment and erosion of the underlying denser water. An analogous phenomenon is observed in the lower troposphere when surface heating due to solar radiation results in a growing unstable layer adjacent to the ground which replaces a nocturnal inversion from below. In this case, the initially stable environment near the ground is affected by convection characterized by relatively narrow and fast plumes of rising horizontal surfaces balanced by larger regions of downward slower motion. Resulting internal waves generated within the stable layer take place at or below the Brunt-Väisälä frequency, which is related to the vertical temperature gradient. In nature, the dynamics of the CBL influences the transport and mixing features of a given stratified fluid-body. The amount of materials being mixed due to penetrative convection is a crucial issue both in water or air quality monitoring and forecast with important implications in environmentally-friendly studies. Focusing on the environmental aspect, the pollutant dispersion is a matter of particular importance. On one hand, mixing processes inside the CBL help increasing dispersion with some positive consequences: the concentration of potential harmful pollutants in high risk zones tends to decrease, the turnover and the redistribution of vital substances, like oxygen and nutrients, is guaranteed; the latter plays a major role in large water bodies. These advantages are essential for the safety of populations living close to urban or industrial areas, or for preserving coastal human activities and ecosystems. On the other hand each pollutant, released inside the CBL mainly by human activities, remains confined inside it because of the interface with the non-turbulent region, which acts as a barrier for outward transport. Considering the proximity of the CBL with biosphere, a deeper insight into dispersion and entrainment processes appears mandatory either for sustainable engineering design or for monitoring purposes. Given the great applicability of the topic in several scientific and engineering fields, large amount of experimental, theoretical and numerical investigations on CBL development in a continuously and linearly stratified fluid setting had been conducted in the past since sixties. It appears there is a lack of consensus about the dependence of integral parameters of convective entrainment (in particular the CBL growth rate) on the initial stratification strength and convective phenomenon evolution. Driven by all these premises the main aims of the present research are related to better understanding dispersion of a passive scalar inside the CBL with a lagrangian, non-local approach and a fully three-dimensional (3D 3C) experimental technique, which for the first time has been applied to the topic. When turbulent convection occurs, in fact, dispersion is mostly due to transport by large organized structures while molecular diffusion can be neglected. Given this assumption, a non local approach based on a fully advective-like behaviour of the tracer is necessary and a lagrangian description of flow may be more suitable. Moreover, the knowledge of the horizontal and vertical extension of the structures dominating the flow field appears to be mandatory. Furthermore, turbulence is fully three-dimensional on the scales of motion characterising the phenomena in nature. In order to better understanding and likely describing the evolution of turbulent structures inside the convective layer, a three dimensional experimental technique is strongly required. In the present work shear free convection experiments in a stably stratified environment were performed in a thermally controlled convection chamber. The experimental set up was arranged in different optical configurations to ensure the two components and three components of velocity to be measured in an illuminated plane and volume respectively through different image analysis techniques with sub-pixel accuracy. Temperature measurements were simultaneously acquired using thermocouples of accuracy less than 0.1 °C. The experiments highlighted the time evolution of the convective structure characteristic spatial scales (CBL height and horizontal spacing between thermals) and the non local description of transport and mixing inside the growing CBL. The main novelty of the present contribution covers the improvement of techniques and methods to achieve more reliable, statistically robust and likely results. The experimental effort based on image analysis techniques (mainly Feature Tracking and photogrammetric 3D-PTV) resulted suitable for reconstructing longer trajectories (always more than 103 trajectories longer than 20 consecutive snapshots) and analyzing larger particle density images (reliable results for more than 2000 particles in a volume of 15X15X15 cm3 for 3D-PTV). Velocity statistics are then more robust than those from classical Particle Tracking Velocimetry. Moreover, for the first time, a fully three-dimensional particle tracking technique has been applied to penetrative convection experiments. 3D-PTV allows a more realistic description of the velocity field, which occurs during the evolution of the convective mixed layer, than more traditional 2D techniques. Furthermore, photogrammetric 3D-PTV rather than “scanning” 3D-PTV results in more accuracy when the tracer particle density is high, because particles may be tracked directly in the 3D space rather than through matching of 2D projections. The broader impact of the research mainly refers to the prediction of the CBL growth as a function of initial and boundary conditions with better accuracy than conventional and well established techniques. The experimental study can thus give a positive contribution on real pollutant dispersion studies in urban and natural environments for environmental protection and sustainable design purposes. Field experiments aimed at measuring the turbulence budget of the CBL have shown that the mechanical generation of kinetic energy by wind shear is often confined close to the heat source supporting the validity of laboratory models in which no wind is present. According to this assumption, the similarity proposed by Deardorff (1970) is employed to compute scaling parameters and to make results comparable with real scales. Through normalizing the quantities measured at different stages of the experiment, the phenomenon can be considered as a succession of steady states, according to an evolution of the variables of interest that may be defined quasi-steady state. The experimental apparatus employed to run the experiments is the same as in Cenedese and Querzoli (1994), Querzoli (1996), Cenedese and Querzoli (1997) and Moroni and Cenedese (2006). The spatial resolution of velocity data is largely increased here by means of 2D and 3D image analysis techniques (Feature Tracking, FT, and 3D Particle Tracking Velocimetry, 3D-PTV) used instead of Laser-Doppler Anemometry or 2D Particle Tracking Velocimetry as in Cenedese and Querzoli, 1994; Querzoli, 1996 and Cenedese and Querzoli, 1997. Moreover the photogrammetric 3D-PTV here applied allows fully three-dimensional descriptions of both the Eulerian velocity field and Lagrangian particle trajectories for a more likely understanding of the phenomenon than through the 2D approach used in Moroni and Cenedese (2006). Furthermore, the combined use of thermocouples and flow visualization techniques allows cross-validating different methods to estimate the evolutions of the key parameters and the plume characteristic dimensions. Two different experimental arrangements were set-up, 2D and a 3D models. A large set of data were firstly acquired using a 2D model and employing FT. The preliminary investigation was mainly focused on better understanding the physics of the phenomenon, finding a time scaling law, testing different methods to compute the variables of interest and comparing results with classical methods found in literature. When 2D techniques are employed to detect the velocity field, the flow is illuminated with a thin light sheet and only the velocity components within this sheet can be evaluated. Driven by the idea that only a fully three-dimensional technique can significantly improve our laboratory model in term of a more likely description of free convection structures we run a second set of experiments, by using a stereoscopic arrangement of cameras focused on an illuminated volume. Although some methods do exist for reconstructing 3D velocities in a point (3D laser Doppler Anemometry; Hinsch and Hinrichs, 1996) or plane (3D stereo-PIV; Stuer et al., 1999), only a fully 3D technique based on the illumination of a flow volume rather than a flow sheet will give the information needed to construct the instantaneous 3D velocity fields. A number of imaging-based measurement techniques exist for determining 3D velocity fields in an observation volume. Among these are: scanning, photogrammetric, holographic or photogrammetric techniques dependending on which principle is recalled to reconstruct the third dimension from a 2D image/s: The present study was focused on 3D-PTV which is a 3D extension of the 2D particle-tracking methods. 3D-PTV is based on reconstructing 3D trajectories of reflecting tracer particles through a photogrammetric recording of image sequences. The 3D particle trajectories obtained can be used to calculate the 3D velocity field. The 3D-PTV optical system has been designed with the following capabilities: image a volume far away the boundary walls, lengthen the trajectories, and improve the accuracy of the procedure through a careful test on synthetically generated data. A physically-based photogrammetric calibration of the stereoscopic arrangement was employed and its accuracy tested. The effects of multimedia geometry on calibration parameters were taken into account. The combination of image- and object-space based information was employed to establish the correspondences between particle positions (structure from stereo reconstruction). A particle tracking algorithm was then employed to reconstructed 3D trajectories. Sensitivity tests conducted on the matching algorithm proved that the calibration accuracy is fundamental to obtain the correct matching and particle tracking; small errors in calibration parameters or neglecting water refraction effects reduce matching performance. On the other hand, accuracy less than 1 pixel was reached with our calibration procedure ensuring good results in the matching procedure. Tests on synthetic data demonstrated a multi-choice strategy with a 3 camera arrangement is the best solution for matching data. It is less sensitive to errors in the calibration data set when both the percentage of correctly matched triplets and the number of outputs of the algorithm were considered. Original and cross-validating methods to compute the CBL height and horizontal scale of thermals were applied based on temperature, velocity and fluorescence imaging. The spatial covariance of the velocity field, providing the plume horizontal spacing, allows the spatial extension of the mixed region to be determined. Dome characteristic vertical dimension is of the same order of magnitude as the mixing layer height, while their horizontal dimension becomes similar to the vertical one at the end of the experiment when the structure dimensions are comparable to the test section side and border effects are no longer negligible. The mixing layer growth was computed by exploiting both temperature and velocity data. Outputs were then compared to more classical methods as the zero-order mixed-layer model and the zero-heat flux level method. The accuracy of our methods was computed as well. Present results, normalized accordingly to the Deardorff similarity for free convection, were compared with literature data and LES meteorological models. Outcomes from different experimental configurations, literature and LES models are in fairly good agreement. The comparison with literature data at real scale demonstrates the validity of our experimental task and its applicability for the study of the real atmospheric boundary layer and its monitoring for environmental purposes. On the other hand the agreement with LES models at different boundary conditions and domain aspect ratios proves that both scale and border effects of the experimental model are negligible if data are not processed for too long time