arXiv subjects

Zhao Pan

Publications and source records attributed to Zhao Pan.

29 records · Page 2Linked to original sources

arXiv2021

On the criteria of large cavitation bubbles in a tube during a transient process

Extreme cavitation scenarios such as water column separations in hydraulic systems during transient processes caused by large cavitation bubbles can lead to catastrophic destruction. In the present paper, we study the onset criteria and dynamics of large cavitation bubbles in a tube. A new cavitation number $Ca_2 = {l^*}^{-1} Ca_0$ is proposed to describe the maximum length $L_{\max}$ of the cavitation bubble, where $l^*$ is a non-dimensional length of the water column indicating its slenderness, and $Ca_0$ is the classic cavitation number. Combined with the onset criteria for acceleration-induced cavitation ($Ca_1<1$, Pan et al. (2017)), we show that the occurrence of large cylindrical cavitation bubbles requires both $Ca_2<1$ and $Ca_1<1$ simultaneously. We also establish a Rayleigh-type model for the dynamics of large cavitation bubbles in a tube. The bubbles collapse at a finite end speed, and the time from the maximum bubble size to collapse is $T_c=\sqrt{2}\sqrt{lL_{\max}}\sqrt{\fracρ{p_\infty}}$, where $l$ is the length of the water column, $L_{\max}$ is the maximum bubble length, $ρ$ is the liquid density, and $p_{\infty}$ is the reference pressure in the far field. The analytical results are validated against systematic experiments using a modified 'tube-arrest' apparatus, which can decouple acceleration and velocity. The results in the current work can guide design and operation of hydraulic systems encountering transient processes.

physics.flu-dyn↗

arXiv2020

Targeted particle delivery via vortex ring reconnection

A conceptual model for targeted particle delivery is proposed using controlled vortex ring reconnection. Entrained particles can be efficiently transported within the core of the vortex ring which is propelled via self-induction. A pair of these particle-transporting vortices travelling in the streamwise direction along parallel trajectories will mutually interact resulting in vortex reconnection. The reconnection causes a topological change to the vortex rings which is accompanied by a rapid repulsion in a perpendicular plane to the direction of travel; effectively, transporting the particles to the desired delivery site on the sidewalls. This work explains the physics of the process and the considerations for targeted delivery.

physics.flu-dyn↗

arXiv2020

Universal Model for Deposition of Entities from Molecular to Nanosizes on Nanofibers

Understanding the behavior of entities is critical to the development of new policies and technologies aiming at global health and wellbeing; this paper presents a unified model developed and validated for the deposition of entities, ranging from a few Angstroms to tens of nanometers,on nanofibers. The transport of entities is based on convective diffusion and interfacial interactive diffusion. As the size of entities decreases to intermediate sizes - between gas molecules and nanoparticles - adhesion probability on the surface is less than unity, which is determined by the interfacial interactions and kinetics of adhesion. Dimensionless surface coverage provides a better understanding of adhesion kinetic by considering the effects of initial concentration and time. The model is validated by available experimental data in the literature.

physics.flu-dyn↗

arXiv2020

Unscented Kalman filter (UKF) based nonlinear parameter estimation for a turbulent boundary layer: a data assimilation framework

A turbulent boundary layer is an essential flow case of fundamental and applied fluid mechanics. However, accurate measurements of turbulent boundary layer parameters (e.g., friction velocity $u_τ$ and wall shear $τ_w$), are challenging, especially for high speed flows (Smits et al., 2011). Many direct and/or indirect diagnostic techniques have been developed to measure wall shear stress (Vinuesa et al., 2017). However, based on different principles, these techniques usually give different results with different uncertainties. The current study introduces a nonlinear data assimilation framework based on the Unscented Kalman Filter that can fuse information from i) noisy and gappy measurements from Stereo Particle Image Velocimetry, a Preston tube, and a MEMS shear stress sensor, as well as ii) the uncertainties of the measurements to estimate the parameters of a turbulent boundary layer. A direct numerical simulation of a fully developed turbulent boundary layer flow at Mach 0.3 is used first to validate the data assimilation algorithm. The algorithm is then applied to experimental data of a flow at Mach 0.3, which are obtained in a blowdown wind tunnel facility. The UKF-based data assimilation algorithm is robust to uncertain and gappy experimental data and is able to provide accurate estimates of turbulent boundary layer parameters.

physics.flu-dyn↗

arXiv2019

Giant Negative Thermal Expansion Induced by the Synergistic Effects of Ferroelectrostriction and Spin-Crossover in PbTiO3-Based Perovskites

The discovery of unusual negative thermal expansion (NTE) provides the opportunity to control the common but much desired property of thermal expansion, which is valuable not only in scientific interests but also in practical applications. However, most of the available NTE materials are limited to a narrow temperature range, and the NTE effect is generally weakened by means of various modifications. Here, we report an enhanced NTE effect that occurs over a wide temperature range (αV = -5.24 * 10-5 °C^-1, 25-575 ° C), and this NTE effect is accompanied by an abnormal enhanced tetragonality, a large spontaneous polarization, and a G-type antiferromagnetic ordering in the present perovskite-type ferroelectric of (1-x)PbTiO3-xBiCoO3. Specifically, for the composition of 0.5PbTiO3-0.5BiCoO3, an extensive volumetric contraction of ~4.8 % has been observed near the Curie temperature of 700 °C, which represents the highest level in PbTiO3-based ferroelectrics. According to our experimental and theoretical results, the giant NTE originates from a synergistic effect of the ferroelectrostriction and spin-crossover of cobalt on the crystal lattice. The actual NTE mechanism is contrasted with previous functional NTE materials, in which the NTE is simply coupled with one ordering such as electronic, magnetic, or ferroelectric ordering. The present study sheds light on the understanding of NTE mechanisms and it attests that NTE could be simultaneouslycoupled with different orderings, which will pave a new way toward the design of large NTE materials.

cond-mat.mtrl-sci↗

arXiv2019

Metamagnetism stabilized giant magnetoelectric coupling in ferroelectric \textit{x}BaTiO${_3}$-(1-\textit{x})BiCoO${_3}$ solid solution

In order to establish the correlation between the magnetoelectric coupling and magnetic instability, we have studied the structural, magnetic, and ferroelectric properties of \textit{x}BaTiO${_3}$-(1-\textit{x})BiCoO${_3}$ as a function of BaTiO$_3$ concentration ($x$) and volume.The $G-$type antiferromagnetic ordering is found to be energetically favorable for $x<$ 0.45 and higher concentrations stabilize with nonmagnetic states. We observe metamagnetic spin state transitions associated with paraelectric to ferrolectric transitions as a function of volume and $x$ using synchrotron diffraction and computational studies, indicating a strong magnetoelectric coupling. Specifically for $x=$ 0.33 composition, a pressure induced high spin (HS) to low spin (LS) transition occurs when the volume is compressed below 5\%. Our orbital$-$projected density of states show a HS state for Co$^{3+}$ in the ferroelectric ground state for $x<$ 0.45 and the corresponding paraelectric phase is stable in the nonmagnetic state due to the stabilization of LS state as evident from our fixed$-$spin$-$moment calculations and magnetic measurements. High values of spontaneous ferroelectric polarizations are predicted for lower $x$ values which inversely vary with $x$ because of the reduction of tetragonality ($c/a$) with increase in $x$. Moreover, we find that the HS$-$LS transition point and magnetoelectric coupling strength can be varied by $x$.

cond-mat.mtrl-sci↗

arXiv2018

Reducing water entry impact forces

The forces on an object impacting the water are extreme in the early moments of water entry and can cause structural damage to biological and man-made bodies alike. These early-time forces arise primarily from added mass, peaking when the submergence is much less than one body length. We experimentally investigate a means of reducing impact forces on rigid spheres by making a jet of water strike the quiescent water surface prior to the object impacting. The water jet accelerates the pool liquid and forms a cavity into which a sphere falls. Through on-board accelerometer measurements and high speed imaging, we quantify the force reduction compared to the case of a sphere entering a quiescent pool. Finally, we find the emergence of a critical jet volume required to maximize force reduction; the critical volume is rationalized using scaling arguments informed by near-surface particle image velocimetry (PIV) data.

physics.flu-dyn↗

arXiv2017

Drop on a Bent Fibre

Inspired by the huge droplets attached on cypress tree leaf tips after rain, we find that a bent fibre can hold significantly more water in the corner than a horizontally placed fibre (typically up to three times or more). The maximum volume of the liquid that can be trapped is remarkably affected by the bending angle of the fibre and surface tension of the liquid. We experimentally find the optimal included angle ($\sim {36}{^\circ}$) that holds the most water. Analytical and semi-empirical models are developed to explain these counter-intuitive experimental observations and predict the optimal angle. The data and models could be useful for designing microfluidic and fog harvesting devices.

physics.flu-dyn↗

arXiv2016

On the Asymptotic Behavior of Variance of PLRS Decompositions

A positive linear recurrence sequence is of the form $H_{n+1} = c_1 H_n + \cdots + c_L H_{n+1-L}$ with each $c_i \ge 0$ and $c_1 c_L > 0$, with appropriately chosen initial conditions. There is a notion of a legal decomposition (roughly, given a sum of terms in the sequence we cannot use the recurrence relation to reduce it) such that every positive integer has a unique legal decomposition using terms in the sequence; this generalizes the Zeckendorf decomposition, which states any positive integer can be written uniquely as a sum of non-adjacent Fibonacci numbers. Previous work proved not only that a decomposition exists, but that the number of summands $K_n(m)$ in legal decompositions of $m \in [H_n, H_{n+1})$ converges to a Gaussian. Using partial fractions and generating functions it is easy to show the mean and variance grow linearly in $n$: $a n + b + o(1)$ and $C n + d + o(1)$, respectively; the difficulty is proving $a$ and $C$ are positive. Previous approaches relied on delicate analysis of polynomials related to the generating functions and characteristic polynomials, and is algebraically cumbersome. We introduce new, elementary techniques that bypass these issues. The key insight is to use induction and bootstrap bounds through conditional probability expansions to show the variance is unbounded, and hence $C > 0$ (the mean is handled easily through a simple counting argument).

math.NT↗

arXiv2016

New Behavior in Legal Decompositions Arising from Non-positive Linear Recurrences

Zeckendorf's theorem states every positive integer has a unique decomposition as a sum of non-adjacent Fibonacci numbers. This result has been generalized to many sequences $\{a_n\}$ arising from an integer positive linear recurrence, each of which has a corresponding notion of a legal decomposition. Previous work proved the number of summands in decompositions of $m \in [a_n, a_{n+1})$ becomes normally distributed as $n\to\infty$, and the individual gap measures associated to each $m$ converge to geometric random variables, when the leading coefficient in the recurrence is positive. We explore what happens when this assumption is removed in two special sequences. In one we regain all previous results, including unique decomposition; in the other the number of legal decompositions exponentially grows and the natural choice for the legal decomposition (the greedy algorithm) only works approximately 92.6\% of the time (though a slight modification always works). We find a connection between the two sequences, which explains why the distribution of the number of summands and gaps between summands behave the same in the two examples. In the course of our investigations we found a new perspective on dealing with roots of polynomials associated to the characteristic polynomials. This allows us to remove the need for the detailed technical analysis of their properties which greatly complicated the proofs of many earlier results in the subject, as well as handle new cases beyond the reach of existing techniques.

math.CO↗

arXiv2016

Error Propagation Dynamics of PIV-based Pressure Field Calculations: How well does the pressure Poisson solver perform inherently?

Obtaining pressure field data from particle image velocimetry (PIV) is an attractive technique in fluid dynamics due to its noninvasive nature. The application of this technique generally involves integrating the pressure gradient or solving the pressure Poisson equation using a velocity field measured with PIV. However, very little research has been done to investigate the dynamics of error propagation from PIV-based velocity measurements to the pressure field calculation. Rather than measure the error through experiment, we investigate the dynamics of the error propagation by examining the Poisson equation directly. We analytically quantify the error bound in the pressure field, and are able to illustrate the mathematical roots of why and how the Poisson equation based pressure calculation propagates error from the PIV data. The results show that the error depends on the shape and type of boundary conditions, the dimensions of the flow domain, and the flow type.

physics.flu-dyn↗