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Register a new userOn the noise in statistics of PIV measurements
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Added by
Michel Stanislas Pr.
Publication date
2020
fields
Physics
and research's language is
English
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It is argued herein that when PIV is used to measure turbulence, it can be treated as a time-dependent signal. The `output velocity consists of three primary contributions: the time-dependent velocity, a noise arising from the quantization (or pixelization), and a noise contribution from the fact that the velocity is not uniform inside the interrogation volume. For both of the latter their variances depend inversely on the average number of particles or images) in this interrogation volume. All three of these are spatially filtered by the finite extent of the interrogation window. Since the above noises are associated directly with the individual particles (or particle images), the noise between different realizations and different interrogation volumes is statistically independent.
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Viscoelastic flow through an abrupt planar contraction geometry above a certain Weissenberg number (Wi) is well known to become unstable upstream of the contraction plane via a central jet separating from the walls and forming vortices in the salient corners. Here, for the first time we consider three-dimensional (3D) viscoelastic contraction flows in a microfabricated glass square-square contraction geometry. We employ state-of-the-art microtomographic particle image velocimetry to produce time-resolved and volumetric quantification of the 3D viscoelastic instabilities arising in a dilute polymer solution driven through the geometry over a wide range of Wi but at negligible Reynolds number. Based on our observations, we describe new insights into the growth, propagation, and transient dynamics of an elastic vortex formed upstream of the 3D micro-contraction due to flow jetting towards the contraction. At low Wi we observe vortex growth for increasing Wi, followed by a previously unreported vortex growth plateau region. In the plateau region, the vortex circulates around the jet with a period that decreases with Wi but an amplitude that is independent of Wi. In addition, we report new out-of-plane asymmetric jetting behaviour with a phase-wise dependence on Wi. Finally, we resolve the rate-of-strain tensor D and ascribe local gradients in D as the underlying driver of circulation via strain-hardening of the fluid in the wake of the jet.
198 -
Harish N Mirajkar
, Sridhar Balasubramanian (Department of Mechanicaln Engineering
, IDP in Climate Studies
2016
The presence of stratified layer in atmosphere and ocean leads to buoyant vertical motions, commonly referred to as plumes. It is important to study the mixing dynamics of a plume at a local scale in order to model their evolution and growth. Such a characterization requires measuring the velocity and density of the mixing fluids simultaneously. Here, we present the results of a buoyant plume propagating in a linearly stratified medium with a density difference of 0.5%, thus yielding a buoyancy frequency of N=0.15 s^{-1}. To understand the plume behaviour, statistics such as centerline and axial velocities along varying downstream locations, turbulent kinetic energy, Reynolds stress, and buoyancy flux were measured. The centerline velocity was found to decrease with increase in height. The Reynolds stress and buoyancy flux profiles showed the presence of a unstable layer and the mixing associated within that layer.
In the past decade, advances in electronics technology have made larger imaging sensors available to the experimental fluid mechanics community. These advancements have enabled the measurement of 2-component 2-dimensional (2C-2D) velocity fields using particle image velocimetry (PIV) with much higher spatial resolution than previously possible. However, due to the large size of the sensor, the lens distortion needs to be taken into account as it will now have a more significant effect on the measurement quality that must be corrected to ensure accurate high-fidelity 2C-2D velocity field measurements. In this paper, two dewarping models, a second-order rational function (R2) and a bicubic polynomial (P3) are investigated with regards to 2C-2D PIV measurements of a turbulent boundary layer (TBL) using a large imaging sensor. Two approaches are considered and compared: (i) dewarping the images prior to the PIV cross-correlation analysis and (ii) undertaking the PIV cross-correlation analysis using the original recorded distorted images then followed by using the mapping functions derived for image dewarping to provide the correct spatial location of the velocity measurement point. The results demonstrate that the use of P3 dewarping model to correct lens distortion yields better results than the R2 dewarping model. Furthermore, both approaches for the P3 dewarping model yield results which are statistically indistinguishable.
An analytical framework for the propagation of velocity errors into PIV-based pressure calculation is extended. Based on this framework, the optimal spatial resolution and the corresponding minimum field-wide error level in the calculated pressure field are determined. This minimum error is viewed as the smallest resolvable pressure. We find that the optimal spatial resolution is a function of the flow features, geometry of the flow domain, and the type of the boundary conditions, in addition to the error in the PIV experiments, making a general statement about pressure sensitivity difficult. The minimum resolvable pressure depends on competing effects from the experimental error due to PIV and the truncation error from the numerical solver. This means that PIV experiments motivated by pressure measurements must be carefully designed so that the optimal resolution (or close to the optimal resolution) is used. Flows (Re=$1.27 times 10^4$ and $5times 10^4$) with exact solutions are used as examples to validate the theoretical predictions of the optimal spatial resolutions and pressure sensitivity. The numerical experimental results agree well with the rigorous predictions. Estimates of the relevant constants in the analysis are also provided.
High-spatial-resolution (HSR) two-component, two-dimensional particle-image-velocimetry (2C-2D PIV) measurements of a zero-pressure-gradient (ZPG) turbulent boundary layer (TBL) and an adverse-pressure-gradient (APG)-TBL were taken in the LMFL High Reynolds number Boundary Layer Wind Tunnel. The ZPG-TBL has a momentum-thickness based Reynolds number $Re_{delta_2} = delta_2 U_e/ u = 7,750$ while the APG-TBL has a $Re_{delta_2} = 16,240$ and a Clausers pressure gradient parameter $beta = delta_1 P_x/tau_w = 2.27$ After analysing the single-exposed PIV image data using a multigrid/multipass digital PIV (Soria, 1996) with in-house software, proper orthogonal decomposition (POD) was performed on the data to separate flow-fields into large- and small-scale motions (LSMs and SSMs), with the LSMs further categorized into high- and low-momentum events. Profiles of the conditionally averaged Reynolds stresses show that the high-momentum events contribute more to the Reynolds stresses than the low-momentum between wall to the end of the log-layer and the opposite is the case in the wake region. The cross-over point of the profiles of the Reynolds stresses from the high- and low-momentum LSMs always has a higher value than the corresponding Reynolds stress from the original ensemble at the same wall-normal location. Furthermore, the cross-over point in the APG-TBL moves further from the wall than in the ZPG-TBL. By removing the velocity fields with LSMs, the estimate of the Reynolds streamwise stress and Reynolds shear stress from the remaining velocity fields is reduced by up to $42 %$ in the ZPG-TBL. The reduction effect is observed to be even larger (up to $50%$) in the APG-TBL. However, the removal of these LSMs has a minimal effect on the Reynolds wall-normal stress in both the ZPG- and APG-TBL.
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