Influence of periodic pressure on dendritic morphology and sidebranching

The influence of periodic pressure with low and high frequencies on microstructure and dendritic sidebranching was studied by using 3-D phase field method. In both low and high frequency cases, the variation trend of SDAS (secondary dendritic arm spacing) with increasing pressure frequency is opposite to that of sidebranching frequency, while the variation trend of the average length of secondary arms is consistent with that of sidebranching frequency. The high sidebranching frequency indicates that more secondary arms share the whole driving force of dendrite growth, resulting in lower driving force for each one and leading to less developed secondary arms. The smallest SDAS is obtained when perturbed by the periodic pressure with the frequency of 0.157/τ0 (τ0 is the physical unit of time in the dimensionless phase field model) and 2.200/τ0 in low and high frequency cases, respectively. Comparisons of dendritic morphology and secondary arms are made between the low and high frequency cases. Firstly, in the low frequency case, secondary arms are luxuriant especially when pressure frequency is low, with many high-order side branches stretching out. Secondly, the average length of secondary arms in primary dendrite is longer in the low frequency case than that without pressure, and much longer than that in the high frequency case. Thirdly, the dendrite tip without side branches in the high frequency case is much longer than that in the low frequency case. All of the differences in dendritic morphology and sidebranching in the two cases can be attributed to the different modulation mechanism. In the low frequency case, periodic pressure determines tip velocity and then modulates sidebranching directly. While in the high frequency case, periodic pressure cannot determine sidebranching directly, but via modulating tiny protuberances in dendrite tip, part of which evolves into side branch. In this case, the tiny protuberances take part of the whole driving force, leading to less developed secondary arms.

Distinctions of dendritic behavior influenced by constant pressure and periodic pressure

The distinctions of dendritic morphology and sidebranching behavior when solidified under atmosphere pressure,constant pressure which is higher than atmosphere pressure (hereinafter referred to as constant pressure) and periodic pressure were investigated using 3-D phase field method.When growing at atmosphere pressure,side branches (secondary dendritic arms) are irregular.When solidified under constant pressure with a relatively high value,side branches are much more luxuriant,with more developed high-order side branches.When applied with periodic pressure,resonant sidebranching happens,leading to many more regular side branches and the smallest secondary dendritic arm spacing (SDAS) in the three cases.The significant difference in dendritic morphology is associated with tip velocity modulated by total undercooling including pressure and temperature undercooling.In the case of constant pressure,tip velocity increases linearly with total undercooling,and it varies periodically in periodic pressure case.The different variation trend in tip velocity is the reason for the distinct dendrite growth behavior in different cases.Unlike the phenomenon in constant pressure case where the dendrite grows faster with higher pressure,the dendrite grows slower under periodic pressure with higher amplitude,resulting in less developed primary dendrite and side branches.This is influenced by tip remelting due to low undercooling or even negative undercooling.It is revealed that the accelerated velocity of tip remelting increases with the decline of undercooling.The greater the amplitude of periodic pressure,the faster the tip remelting velocity during one period.This is the reason why the average tip velocity decreases with the rise of amplitude of periodic pressure.

The mechanical response of piles with consideration of pile-soil interactions under a periodic wave pressure

The pile-soil interaction under wave loads is an extremely complex and difficult issue in engineering. In this study, a physical model test is designed based on the principle of the gravity similarity to obtain time histories of wave forces of unsteady regular waves, and to measure the magnitude and the distribution of wave forces acting on the piles. A numerical model and relevant numerical methods for the pile-soil contact surface are adopted based on the principles of elastic dynamics. For a practical project, the time histories of wave forces on the piles are obtained through physical model tests. The deformations of the piles in the pile-soil interactions and the distribution of the bending moment on the piles are studied. It is shown that, with the increase of the period of wave pressures, the absolute value of the horizontal displacement of the piles increases, the embedment depth of the piles increases, and the scope of influence of soils increases. The change of the bending moment on the piles is consistent with that of its theoretical results, and the proposed numerical method can very well simulate the properties of the piles.

Mass transport in a thin layer of power-law fluid in an Eulerian coordinate system

The mass transport velocity in a thin layer of muddy fluid is studied theoretically. The mud motion is driven by a periodic pressure load on the free surface, and the mud is described by a power-law model. Based on the key assumptions of the shallowness and the small deformation, a perturbation analysis is conducted up to the second order to find the mean Eulerian velocity in an Eulerian coordinate system. The numerical iteration method is adopted to solve these non-linear equations of the leading order. From the numerical results, both the first-order flow fields and the second-order mass transport velocities are examined. The verifications are made by comparing the numerical results with experimental results in the literature, and a good agreement is confirmed.