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Register a new userError propagation dynamics of PIV-based pressure field calculation (3): What is the minimum resolvable pressure in a reconstructed field?
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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.
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A recent study investigated the propagation of error in a Velocimetry-based Pressure (V-Pressure) field reconstruction problem by directly analyzing the properties of the pressure Poisson equation (Pan et al., 2016). In the present work, we extend these results by quantifying the effect of the error profile in the data field (shape/structure of the error in space) on the resultant error in the reconstructed pressure field. We first calculate the mode of the error in the data that maximizes error in the pressure field, which is the most dangerous error (called the worst error in the present work). This calculation of the worst error is equivalent to finding the principle mode of, for example, an Euler-Bernoulli beam problem in one-dimension and the Kirchhoff-Love plate in two-dimensions, thus connecting the V-Pressure problem from experimental fluid mechanics to buckling elastic bodies from elastic mechanics. Taking advantage of this analogy, we then analyze how the error profile (e.g., spatial frequency of the error and the location of the most concentrated error) in the data field coupled with fundamental features of the flow domain (i.e., size, shape, and dimension of the domain, and the configuration of boundary conditions) significantly affects the error propagation from data to the reconstructed pressure. Our analytical results lend to practical applications in two ways. First, minimization of error propagation can be achieved by avoiding low-frequency error profiles in data similar to the worst case scenarios and error concentrated at sensitive locations. Second, small amounts of the error in the data, if the error profile is similar to the worst error case, can cause significant error in the reconstructed pressure field; such a synthetic error can be used to benchmark V-Pressure algorithms.
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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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.
Airflow through the nasal cavity exhibits a wide variety of fluid dynamicsbehaviour due to the intricacy of the nasal geometry. The flow is naturallyunsteady and perhaps turbulent, despite CFD in the literature that assumesa steady laminar flow. Time-dependent simulations can be used to generatedetailed data with the potential to uncover new flow behaviour, although theyare more computationally intensive compared with steady-state simulations. Furthermore, verification of CFD results has relied on reported pressure drop(e.g. nasal resistance) across the nasal airway although the geometries usedare different. This study investigated the unsteady nature of inhalation atflow rates of 10, 15, 20, and 30 L/min. A scale resolving CFD simulationusing a hybrid RANS-LES model was used and compared with experimentalmeasurements of the pressure distribution and the overall pressure drop in thenasal cavity. The experimental results indicated a large pressure drop acrossthe nasal valve, as well as across the nasopharynx with the latter attributedto a narrow cross-sectional area. At a flowrate of 30 L/min, the CFD simula-tions showed that the anterior half of the nasal cavity displayed dominantlylaminar but disturbed flow behaviour in the form of velocity fluctuations. Theposterior half of the nasal cavity displayed turbulent activity, characterised byerratic fluctuating velocities, which was enhanced by the wider cross-sectionalareas in the coronal plane. At 15L/min, the flow field was laminar dominantwith very little disturbance confirming a steady-state laminar flow assumptionis viable at this flow rate.
Wettability is a pore-scale property that has an important impact on capillarity, residual trapping, and hysteresis in porous media systems. In many applications, the wettability of the rock surface is assumed to be constant in time and uniform in space. However, many fluids are capable of altering the wettability of rock surfaces permanently and dynamically in time. Experiments have shown wettability alteration can significantly decrease capillarity in CO$_2$ storage applications. For these systems, the standard capillary-pressure model that assumes static wettability is insufficient to describe the physics. In this paper, we develop a new dynamic capillary-pressure model that takes into account changes in wettability at the pore-level by adding a dynamic term to the standard capillary pressure function. We simulate the dynamic system using a bundle-of-tubes (BoT) approach, where a mechanistic model for time-dependent contact angle change is introduced at the pore scale. The resulting capillary pressure curves are then used to quantify the dynamic component of the capillary pressure function. This study shows the importance of time-dependent wettability for determining capillary pressure over timescales of months to years. The impact of wettability has implications for experimental methodology as well as macroscale simulation of wettability-altering fluids.
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