Energy efficiency of consecutive fragmentation processes

Motivated by a problem arising in the mining industry, we present a first study of the energy required to reduce a unit mass fragment by consecutively using several devices. Two devices are considered, which we represent as different stochastic fragmentation processes. Following the self-similar energy model introduced in Bertoin and Martínez (2005), we compute the average energy required to attain a size η0 with this two-device procedure. We then asymptotically compare, as η0 goes to 0 or 1, its energy requirement with that of individual fragmentation processes. In particular, we show that, for a certain range of parameters of the fragmentation processes and of their energy cost functions, the consecutive use of two devices can be asymptotically more efficient than using each of them separately, or vice versa.

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Operation of a CCHP System Using an Optimal Energy Dispatch Algorithm

ASME 2008 2nd International Conference on Energy Sustainability, Volume 1 ◽

10.1115/es2008-54096 ◽

2008 ◽

Cited By ~ 4

Author(s):

Heejin Cho ◽

Sandra D. Eksioglu ◽

Rogelio Luck ◽

Louay M. Chamra

Keyword(s):

Energy Efficiency ◽

Energy Cost ◽

Network Flow ◽

Flow Model ◽

Energy Requirement ◽

Optimal Operation ◽

Operational Conditions ◽

Optimal Energy ◽

Network Flow Model ◽

The Cost

The Combined Cooling, Heating, and Power (CCHP) systems have been widely recognized as a key alternative for thermal and electric energy generation because of the outstanding energy efficiency, reduced environmental emissions, and relative independence from centralized power grids. Nevertheless, the total energy cost of CCHP systems can be highly dependent on the operation of individual components and load balancing. The latter refers to the process of fulfilling the thermal and electrical demand by partitioning or “balancing” the energy requirement between the available sources of energy supply. The energy cost can be optimized through an energy dispatch algorithm which provides operational/control signals for the optimal operation of the equipment. The algorithm provides optimal solutions on decisions regarding generating power locally or buying power from the grid. This paper presents an initial study on developing an optimal energy dispatch algorithm that minimizes the cost of energy (i.e., cost of electricity from the grid and cost of natural gas into the engine and boiler) based on energy efficiency constrains for each component. A deterministic network flow model of a typical CCHP system is developed as part of the algorithm. The advantage of using a network flow model is that the power flows and efficiency constraints throughout the CCHP components can be readily visualized to facilitate the interpretation of the results. A linear programming formulation of the network flow model is presented. In the algorithm, the inputs include the cost of the electricity and fuel and the constraints include the cooling, heating, and electric load demands and the efficiencies of the CCHP components. This algorithm has been used in simulations of several case studies on the operation of an existing micro-CHP system. Several scenarios with different operational conditions are presented in the paper to demonstrate the economical advantages resulting from optimal operation.

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Fragmentations with self-similar branching speeds

Advances in Applied Probability ◽

10.1017/apr.2021.11 ◽

2021 ◽

Vol 53 (4) ◽

pp. 1149-1189

Author(s):

Jean-Jil Duchamps

Keyword(s):

Markov Processes ◽

Finite Time ◽

Sufficient Conditions ◽

Natural Generalization ◽

Nonnegative Real Number ◽

The Self ◽

Genealogical Tree ◽

Self Similar ◽

Fragmentation Processes

AbstractWe consider fragmentation processes with values in the space of marked partitions of $\mathbb{N}$, i.e. partitions where each block is decorated with a nonnegative real number. Assuming that the marks on distinct blocks evolve as independent positive self-similar Markov processes and determine the speed at which their blocks fragment, we get a natural generalization of the self-similar fragmentations of Bertoin (Ann. Inst. H. Poincaré Prob. Statist.38, 2002). Our main result is the characterization of these generalized fragmentation processes: a Lévy–Khinchin representation is obtained, using techniques from positive self-similar Markov processes and from classical fragmentation processes. We then give sufficient conditions for their absorption in finite time to a frozen state, and for the genealogical tree of the process to have finite total length.

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Hausdorff measure and Assouad dimension of generic self-conformal IFS on the line

Proceedings of the Royal Society of Edinburgh Section A Mathematics ◽

10.1017/prm.2020.89 ◽

2020 ◽

pp. 1-31

Author(s):

Balázs Bárány ◽

Károly Simon ◽

István Kolossváry ◽

Michał Rams

Keyword(s):

Hausdorff Measure ◽

Similar Case ◽

Iterated Function Systems ◽

The Self ◽

Dimensional Hausdorff Measure ◽

Assouad Dimension ◽

Iterated Function ◽

Self Similar ◽

Weak Separation ◽

Topological Sense

This paper considers self-conformal iterated function systems (IFSs) on the real line whose first level cylinders overlap. In the space of self-conformal IFSs, we show that generically (in topological sense) if the attractor of such a system has Hausdorff dimension less than 1 then it has zero appropriate dimensional Hausdorff measure and its Assouad dimension is equal to 1. Our main contribution is in showing that if the cylinders intersect then the IFS generically does not satisfy the weak separation property and hence, we may apply a recent result of Angelevska, Käenmäki and Troscheit. This phenomenon holds for transversal families (in particular for the translation family) typically, in the self-similar case, in both topological and in measure theoretical sense, and in the more general self-conformal case in the topological sense.

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A Comparative Study of Energy Efficiency in Tumbling Mills with the Use of Relo Grinding Media

Metals ◽

10.3390/met11050735 ◽

2021 ◽

Vol 11 (5) ◽

pp. 735

Author(s):

Nikolay Kolev ◽

Petar Bodurov ◽

Vassil Genchev ◽

Ben Simpson ◽

Manuel G. Melero ◽

...

Keyword(s):

Energy Efficiency ◽

Test Procedure ◽

Mining Industry ◽

Slight Modification ◽

Index Test ◽

Grinding Media ◽

Work Index ◽

Mineral Sample ◽

Tumbling Mills ◽

Bond Tests

An evaluation of Relo grinding media (RGM, Reuleaux tetrahedron-shaped bodies) performance versus standard grinding media (balls) was made through a series of grinding tests, including a slight modification of the standard Bond test procedure. Standard Bond tests showed a reduction in the Bond ball mill work index (wi) of the mineral sample used in this study when using Relo grinding media. The modified Bond test procedure is based on using the standard Bond ball work index test but changing the circulating loads (350%, 250%, 150%, 100%). The comparative tests with RGM were carried out at the same number of revolutions as the grinding tests with balls at respective circulating load. The RGM charge yielded a 14% higher net undersize product than balls, which hints at improving energy efficiency and the potential for significant mining industry benefits.

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Onset of the Mach Reflection of Zel’dovich–von Neumann–Döring Detonations

Entropy ◽

10.3390/e23030314 ◽

2021 ◽

Vol 23 (3) ◽

pp. 314

Author(s):

Tianyu Jing ◽

Huilan Ren ◽

Jian Li

Keyword(s):

Hot Spot ◽

Mach Reflection ◽

Near Field ◽

The Self ◽

Small Scale ◽

Mach Stem ◽

Self Similarity ◽

Von Neumann ◽

Similarity Problem ◽

Self Similar

The present study investigates the similarity problem associated with the onset of the Mach reflection of Zel’dovich–von Neumann–Döring (ZND) detonations in the near field. The results reveal that the self-similarity in the frozen-limit regime is strictly valid only within a small scale, i.e., of the order of the induction length. The Mach reflection becomes non-self-similar during the transition of the Mach stem from “frozen” to “reactive” by coupling with the reaction zone. The triple-point trajectory first rises from the self-similar result due to compressive waves generated by the “hot spot”, and then decays after establishment of the reactive Mach stem. It is also found, by removing the restriction, that the frozen limit can be extended to a much larger distance than expected. The obtained results elucidate the physical origin of the onset of Mach reflection with chemical reactions, which has previously been observed in both experiments and numerical simulations.

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