Uncertainty of PIV/PTV based pressure, using velocity uncertainty

Pressure reconstruction from velocity measurements using particle image velocimetry (PIV) and particle tracking velocimetry (PTV) has drawn significant attention as it can provide instantaneous pressure fields without altering the flow. Previous studies have found that the accuracy of the calcualted pressure field depends on several factors including the accuarcy of the velocity measurement, the spatiotemporal resolutions, the method for calculating pressure-gradient, the algorithm for pressure-gradient integration, the pressure boundary condition, etc. Therefore, it is critical and challenging to quantify the uncertainty of the reconstructed pressure field. The recent development of the uncertainty quantification algorithms for PIV and PTV allows for the local and instantaneous uncertainty estimation of velocity measurement, which can be used to infer the pressure uncertainty. In this study, we introduce a framework that propagates the standard velocity uncertainty defined as the standard deviation of the velocity error distribution through the pressure reconstruction process to obtain the uncertainty of the pressure field. The uncertainty propagations through the calculation of the pressure-gradient and the pressure-gradient integration were modeled as linear transformations, which can reproduce the effects of the spatiotemporal resolutions, the numerical schemes, the integration algorithms, and the pressure boundary condition on the accuracy of the resulting pressure fields. The proposed uncertainty estimation approach also considers the effect of the spatiotemporal and componentwise correlation of the velocity errors in common PIV/PTV measurements on the pressure uncertainty.

A Solution to Pressure Equation with Its Boundary Condition of Combining Tangential and Normal Pressure Relations

Pressure is a physical quantity that is indispensable in the study of transport phenomena. Previous studies put forward a pressure constitutive law and constructed a partial differential equation on pressure to study the convection with or without heat and mass transfer. In this paper, a numerical algorithm was proposed to solve this pressure equation by coupling with the Navier-Stokes equation. To match the pressure equation, a method of dealing with pressure boundary condition was presented by combining the tangential and normal direction pressure relations, which should be updated dynamically in the iteration process. Then, a solution to this pressure equation was obtained to bridge the gap between the mathematical model and a practical numerical algorithm. Through numerical verification in a circular tube, it is found that the proposed boundary conditions are applicable. The results demonstrate that the present pressure equation well describes the transport characteristics of the fluid.

Plate-impact-driven ring expansion test (PIDRET) for dynamic fragmentation

A new experimental set-up mounted at the muzzle of a singlestage gas gun has been designed in order to study the fragmentation of metallic rings under dynamic radial expansion. This concept takes advantage of the quasi-incompressibility of HDPE whose radial flow under plate impact-like loading is used to apply a pressure boundary condition at the ring’s inner surface. For the experimental configurations considered in the present work, the average strain rate in the ring reaches values close to 104 s-1. The repeatability and the reliability of the experiments are verified for rings made of steel and aluminium.

A New Deterministic Model for Mixed Lubricated Point Contact With High Accuracy

Mixed lubrication is a major lubrication regime in the presence of surface roughness. A deterministic model is established to solve mixed lubricated point contact in this paper, using a new method to solve asperity contact region in mixed lubrication. Treatment of pressure boundary condition between elastohydrodynamic lubrication region and asperity contact region is discussed. The new model is capable of calculating typical Stribeck curve and analyzing transition of lubrication regime, from full film lubrication to boundary lubrication. Moreover, final result of the model is independent of pressure initialization. High performance in accuracy and convergence has been achieved, which is of great importance for further lubrication modelling with consideration of nano-scale roughness, intermolecular and surface forces.

On the steady posture of conical spindle distribution used in ball piston pump

Conical spindle distribution is a new type of hydraulic pump distribution, its steady working conditions refer to a stable position of the shaft and lubrication state under constant operating condition, which directly influences the hydraulic pump efficient and reliable work. In this paper, the Reynolds equation of the tapered flow field is used to establish the lubrication model. The static pressure boundary condition of the distribution pair is obtained by the hydraulic resistance network method. The finite difference method is employed to solve the model. The static and dynamic lubricating performances including the shaft eccentricity and the distribution gap height are obtained by solving the model with a numerical method. Accordingly, the influences of structural parameters and operating parameters on the steady state are investigated, and an experimental test rig is built to validate the model. The experimental results show that the model can predict the higher working pressure which leads to higher distribution gap and eccentricity; the higher the rotational speed is, the smaller the distribution gap and the eccentricity will become, which provides theoretical support for further guidance of the distribution design.

A variational principle for fluid sloshing with vorticity, dynamically coupled to vessel motion

A variational principle is derived for two-dimensional incompressible rotational fluid flow with a free surface in a moving vessel when both the vessel and fluid motion are to be determined. The fluid is represented by a stream function and the vessel motion is represented by a path in the planar Euclidean group. Novelties in the formulation include how the pressure boundary condition is treated, the introduction of a stream function into the Euler–Poincaré variations, the derivation of free surface variations and how the equations for the vessel path in the Euclidean group, coupled to the fluid motion, are generated automatically.