Research on the Inertial Migration Characteristics of Bi-Disperse Particles in Channel Flow

The inertial focusing effect of particles in microchannels shows application potential in engineering practice. In order to study the mechanism of inertial migration of particles with different scales, the motion and distribution of two particles in Poiseuille flow are studied by the lattice Boltzmann method. The effects of particle size ratio, Reynolds number, and blocking rate on particle inertial migration are analyzed. The results show that, at a high blocking rate, after the same scale particles are released at the same height of the channel, the spacing between the two particles increases monotonically, and the change in the initial spacing has little effect on the final spacing of inertial migration. For two different size particles, when the smaller particle is downstream, the particle spacing will always increase and cannot remain stable. When the larger particle is downstream, the particle spacing increases firstly and then decreases, and finally tends to be stable.

Comparison of various growth functions for predicting long-term stand development associated with different initial spacing in 64-year-old Japanese cedar (Cryptomeria japonica (L.f.) D. Don) plantations

Establishing a plantation with varied distances between trees is one way to control stand density in an initial growth stage. Understanding how stand growth patterns are influenced by initial spacing can help maximize growth and yield. The purpose of this study was to examine the long-term effects of different patterns of initial tree spacing on stand development. A spacing trial with five initial distances, namely, treatments I: 1×1 m, II: 2×2 m, III: 3×3 m, IV: 4×4 m, and V: 5×5 m, was established in 1950 in Japanese cedar (Cryptomeria japonica (L.f.) D. Don) plantations in central Taiwan, managed by the Experimental Forest of National Taiwan University. Each treatment had three repetitions, and all plots were surveyed from 1955 to 2014, with eight records for each time series. We simultaneously employed six growth functions to predict stand basal area growth for each plot and assessed their predictability using the root mean square error (RMSE) as a criterion. Consequently, a total of twelve plots covering all treatments except treatment I, each with six RMSEs resulting from various models, were obtained. The repeated measures analysis of variance approach was adopted to compare predictability among models. The Richards growth function performed the best compared to all the other models. As a result, this model was used to analyse stand development following different initial spacing. We found that the predicted curves could effectively exhibit the growth patterns resulting from different initial spacing. Moreover, the parameters help explain some characteristics of stand development, such as growth potential and maximum growth rate achieved (t max). As a result, a clear trend emerged, showing that, with decreasing initial spacing, the growth potential increased and the t max decreased. These results provided valuable information for managing the stand density of this conifer.

Wood density and wood shrinkage in relation to initial spacing and tree growth in black spruce (Picea mariana)

This study has quantified basic wood density and various types of wood shrinkage in relation to initial spacing (or initial planting density) and tree growth based on a 48-year-old black spruce (Picea mariana) spacing trial in eastern Canada. A total of 139 sample trees were collected from four initial spacings (3086, 2500, 2066, 1372 trees/ha) for this study. Analyses of variance (ANOVA) show that initial spacing is the most important parameter affecting wood density significantly, followed by tree diameter at breast height (DBH) class. With increasing spacing, wood density, radial and volumetric shrinkage tend to decrease, whereas longitudinal shrinkage tends to increase gradually. The largest spacing has the lowest wood density, the smallest transverse shrinkage and the largest longitudinal shrinkage. Path analysis indicates that wood density is the most important parameter affecting transverse shrinkage, followed by the distance from the pith. Furthermore, much of the variation of the transverse shrinkage with wood density may be due to the initial spacing and tree DBH class. Path analysis also reveals that longitudinal shrinkage is mainly related to log height and tree DBH class. With increasing log height, longitudinal shrinkage tends to increase, and transverse shrinkage tends to decrease. With increasing DBH class, the trees tend to have an increasing longitudinal shrinkage and a decreasing transverse shrinkage. Overall, this study suggests that a large increase in the initial spacing (e.g., 1372 trees/ha) might lead to a significant reduction in both wood density and transverse shrinkage, and a significant increase in longitudinal shrinkage in black spruce.

Dynamics of initial spacing on the diameter of hybrid Eucalyptus grandis x Eucalyptus urophylla in a systematic design

We evaluated the effect of initial spacing on the distribution of Eucalyptus grandis x Eucalyptus urophylla tree diameters in a Nelder wheel design. The study area was in west-central Brazil. A Nelder wheel design with three repetitions was used. This design provides 432 planting spots per plot/repetition. Planting density varied from 0.50 m² to 41.25 m². The diameter at breast height was measured for all plants every four months until 36 months of age, totaling eight measurements. The description of the diameter distribution was developed by fitting probability density functions for each spacing and age. The quality of fit was evaluated using the root mean square error percentage, Pearson’s correlation coefficient, and the Kolmogorov-Smirnov test (α < 0.05). The spacings up to 1.17 m² must be harvested in less than two years, since it is noted that in the third year the increment in diameter is static and the mortality rate increases. The spacing highly affects the diameter structure of the population, impelling the forester to consider different uses for the wood. For wood requiring larger diameters, spacing above 8.69 m² per tree is recommended

Managing plantation density through initial spacing and commercial thinning: Yield results from a 60-year-old red pine spacing trial experiment

We report on a 60-year-old Pinus resinosa spacing trial experiment located in Ontario (Canada) that included the combinations between six initial spacings (from 1.2–3.0 m) and the presence/absence of a commercial thinning (CT) regime, and their impacts on quadratic mean diameter (QMD) and stand volume yield. The CT regime, initiated at age 30, targeted a residual basal area (BA) of 38 m2 ha-1 after each of four entries. Without thinning, as initial spacing increased, QMD increased; gross and net volume production peaked in the 2.1–2.4 m spacings. With thinning, similar trends with spacing were evident for QMD, although piece sizes were larger and differences between spacing were lower. The immediate increase of average tree size caused by tree selection explained most of the differences in QMD between thinned and unthinned plots. Thinning to a common target BA resulted in similar standing volume across spacings. Cumulative gross yield was similar between spacings <2.1 m for both unthinned/thinned stands and decreased for thinned plots for wider spacings. Greater net volume production in thinned stands with the narrower spacings confirmed that mortality was captured. Lower gross and net production for wider spacings suggested that thinning resulted in under-utilized growing space.