Studies of spatial clustering of inertial particles in turbulence

We present studies of the spatial clustering of inertial particles embedded in turbulent flow. A major part of the thesis is experimental, involving the technique of Phase Doppler Interferometry (PDI). The thesis also includes significant amount of simulation studies and some theoretical considerations. We describe the details of PDI and explain why it is suitable for study of particle clustering in turbulent flow with a strong mean velocity. We introduce the concept of the radial distribution function (RDF) as our chosen way of quantifying inertial particle clustering and present some original works on foundational and practical considerations related to it. These include methods of treating finite sampling size, interpretation of the magnitude of RDF and the possibility of isolating RDF signature of inertial clustering from that of large scale mixing. In experimental work, we used the PDI to observe clustering of water droplets in a turbulent wind tunnel. From that we present, in the form of a published paper, evidence of dynamical similarity (Stokes number similarity) of inertial particle clustering together with other results in qualitative agreement with available theoretical prediction and simulation results. We next show detailed quantitative comparisons of results from our experiments, direct-numerical-simulation (DNS) and theory. Very promising agreement was found for like-sized particles (mono-disperse). Theory is found to be incorrect regarding clustering of different-sized particles and we propose a empirical correction based on the DNS and experimental results. Besides this, we also discovered a few interesting characteristics of inertial clustering. Firstly, through observations, we found an intriguing possibility for modeling the RDF arising from inertial clustering that has only one (sensitive) parameter. We also found that clustering becomes saturated at high Reynolds number.

"Brethren upon the same level" : membership and class in Calumet's Masonic Lodge

The Keweenaw Peninsula of Upper Michigan was a ethnic conglomerate of cultures and ideas, with people attracted to the area by the mineral wealth found along the Copper Range. The center of copper mining from the mid 1860s to 1968 was in the vicinity of Calumet Township, home to the world-famous Calumet and Hecla Mining Company. The township depended on the mines and the company’s president Agassiz’s strove to make the area a “model community,” that included groups such as the Free and Accepted Masons. Men from myriad backgrounds arrived in Calumet from the British Isles, Germany, Finland, Eastern and Southern Europe and the Eastern United States. As in other communities from the time period these men formed common interest groups like Masonic Lodge 271, which received its charter in 1870. Gentlemen joined with merchants and craftsmen. They became “brethren upon the same level,” and were elevated to the status of Master Mason. This symbolic transformation within the Lodge removed the men from the “profane world” outside the sanctity of Masonry, and in the ritualistic transformation of the meeting they were reborn into Masonry’s sacred mysteries. Masonry acted as a means of moral guidance to men and gave them access to a larger social and economic community through a common connection of brotherhood. As the candidates moved through the three Blue Lodge degrees of Entered Apprentice, Fellowcraft, and Master Mason they saw each other as “brethren upon the same level” – all economic classes equal within the Masonic Lodge. To examine equality within Lodge 271, this study sorted workers into classes to allow a comparison of Lodge 271’s membership. Possibly a comparison between other lodges can be drawn from the membership. The Union Building in Calumet, MI will be examined for its role in the ritualistic transformation of Masonry as it housed Masonic activities and transformations. This transformation brought men into the lodge of brothers. While Masonry professed equality between members however, to what extent did the membership of the lodge reflect this between the brethren? To what extent did economic class determine who was made “brethren upon the same level? 1 Arthur Thurner, Calumet Copper and People: History of a Michigan Mining Community, 1864-1970 (Hancock, MI: Book Concern, 1974), 122.

VOLUME YIELDS OF SMALLHOLDER Eucalyptus grandis W. HILL EX MAIDEN STANDS IN EASTERN PARAGUAY

Smallholders in eastern Paraguay plant small stands of Eucalyptus grandis W. Hill ex Maiden intended for sale on the local market. Smallholders have been encouraged to plant E. grandis by local forestry extension agents who offer both forestry education and incentive programs. Smallholders who practice recommended forestry techniques geared towards growing large diameter trees of good form are financially rewarded by the local markets which desire saw log quality trees. The question was posed, are smallholders engaging in recommended silvicultural practices and producing reasonable volume yields? It was hypothesized that smallholders, having received forestry education and having financial incentives from the local market, would engage in silvicultural practices resulting in trees of good form and volume yields that were reasonable for the local climate and soil characteristics. Yield volume results from this study support this hypothesis. Mean volume yield was estimated at 70 cubic meters per hectare at age four and 225 cubic meters per hectare at age eight. These volume yields compare favorably to volume yields from other studies of E. grandis grown in similar climates, with similar stocking levels and site qualities.