Mathematical Modelling of a Reciprocating Piston Expander

Modern internal combustion (IC) engines reject around two thirds of the energy provided by the fuel as low-grade waste heat. Capturing a portion of this waste heat energy and transforming it into a more useful form of energy could result in a significant reduction in fuel consumption. By using the low-grade heat, an organic Rankine cycle (ORC) can produce mechanical work from a pressurised organic fluid with the use of an expander.
Ideal gas assumptions are shown to produce significant errors in expander performance predictions when using an organic fluid. This paper details the mathematical modelling technique used to accurately model the thermodynamic processes for both ideal and non-ideal fluids within the reciprocating expander. A comparison between the two methods illustrates the extent of the errors when modelling a reciprocating piston expander. Use of the ideal gas assumptions are shown to produce an error of 55% in the prediction of power produced by the expander when operating on refrigerant R134a.

Mathematical modelling of quantum yield enhancements of methyl orange photooxidation in aqueous TiO2 suspensions under controlled periodic UV LED illumination

Quantum yields of the photocatalytic degradation of methyl orange under controlled periodic illumination (CPI) have been modelled using existing models. A modified Langmuir-Hinshelwood (L-H) rate equation was used to predict the degradation reaction rates of methyl orange at various duty cycles and a simple photocatalytic model was applied in modelling quantum yield enhancement of the photocatalytic process due to the CPI effect. A good agreement between the modelled and experimental data was observed for quantum yield modelling. The modified L-H model, however, did not accurately predict the photocatalytic decomposition of the dye under periodic illumination.

Mathematical modelling of supercritical CO2 extraction of volatile oils from aromatic plants

The modelling of the experimental data of the extraction of the volatile oil from six aromatic plants (coriander, fennel, savoury, winter savoury, cotton lavender and thyme) was performed using five mathematical models, based on differential mass balances. In all cases the extraction was internal diffusion controlled and the internal mass transfer coefficienty (k(s)) have been found to change with pressure, temperature and particle size. For fennel, savoury and cotton lavender, the external mass transfer and the equilibrium phase also influenced the second extraction period, since k(s) changed with the tested flow rates. In general, the axial dispersion coefficient could be neglected for the conditions studied, since Peclet numbers were high. On the other hand, the solute-matrix interaction had to be considered in order to ensure a satisfactory description of the experimental data.

Mathematical Modelling of the Dynamics of Granular Materials in a Rotating Cylinder

The current study is aimed at the development of a theoretical simulation tool based on Discrete Element Method (DEM) to 'interpret granular dynamics of solid bed in the cross section of the horizontal rotating cylinder at the microscopic level and subsequently apply this model to establish the transition behaviour, mixing and segregation.The simulation of the granular motion developed in this work is based on solving Newton's equation of motion for each particle in the granular bed subjected to the collisional forces, external forces and boundary forces. At every instant of time, the forces are tracked and the positions velocities and accelarations of each partcle is The software code for this simulation is written in VISUAL FORTRAN 90 After checking the validity of the code with special tests, it is used to investigate the transition behaviour of granular solids motion in the cross section of a rotating cylinder for various rotational speeds and fill fraction.This work is hence directed towards a theoretical investigation based on Discrete Element Method (DEM) of the motion of granular solids in the radial direction of the horizontal cylinder to elucidate the relationship between the operating parameters of the rotating cylinder geometry and physical properties ofthe granular solid.The operating parameters of the rotating cylinder include the various rotational velocities of the cylinder and volumetric fill. The physical properties of the granular solids include particle sizes, densities, stiffness coefficients, and coefficient of friction Further the work highlights the fundamental basis for the important phenomena of the system namely; (i) the different modes of solids motion observed in a transverse crosssection of the rotating cylinder for various rotational speeds, (ii) the radial mixing of the granular solid in terms of active layer depth (iii) rate coefficient of mixing as well as the transition behaviour in terms of the bed turnover time and rotational speed and (iv) the segregation mechanisms resulting from differences in the size and density of particles.The transition behaviour involving its six different modes of motion of the granular solid bed is quantified in terms of Froude number and the results obtained are validated with experimental and theoretical results reported in the literature The transition from slumping to rolling mode is quantified using the bed turnover time and a linear relationship is established between the bed turn over time and the inverse of the rotational speed of the cylinder as predicted by Davidson et al. [2000]. The effect of the rotational speed, fill fraction and coefficient of friction on the dynamic angle of repose are presented and discussed. The variation of active layer depth with respect to fill fraction and rotational speed have been investigated. The results obtained through simulation are compared with the experimental results reported by Van Puyvelde et. at. [2000] and Ding et at. [2002].The theoretical model has been further extended, to study the rmxmg and segregation in the transverse direction for different particle sizes and their size ratios. The effect of fill fraction and rotational speed on the transverse mixing behaviour is presented in the form of a mixing index and mixing kinetics curve. The segregation pattern obtained by the simulation of the granular solid bed with respect to the rotational speed of the cylinder is presented both in graphical and numerical forms. The segregation behaviour of the granular solid bed with respect to particle size, density and volume fraction of particle size has been investigated. Several important macro parameters characterising segregation such as mixing index, percolation index and segregation index have been derived from the simulation tool based on first principles developed in this work.

Mathematical modelling of decision making processes in construction projects

Many different individuals, who have their own expertise and criteria for decision making, are involved in making decisions on construction projects. Decision-making processes are thus significantly affected by communication, in which a dynamic performance of human intentions leads to unpredictable outcomes. In order to theorise the decision making processes including communication, it is argued here that the decision making processes resemble evolutionary dynamics in terms of both selection and mutation, which can be expressed by the replicator-mutator equation. To support this argument, a mathematical model of decision making has been made from an analogy with evolutionary dynamics, in which there are three variables: initial support rate, business hierarchy, and power of persuasion. On the other hand, a survey of patterns in decision making in construction projects has also been performed through self-administered mail questionnaire to construction practitioners. Consequently, comparison between the numerical analysis of mathematical model and the statistical analysis of empirical data has shown a significant potential of the replicator-mutator equation as a tool to study dynamic properties of intentions in communication.

Can the study of natural vegetation succession assist in the control of soil erosion on abandoned croplands on the Loess Plateau, China?

In the Loess Plateau, China, arable cultivation of slope lands is common and associated with serious soil erosion. Planting trees or grass may control erosion, but planted species may consume more soil water and can threaten long-term ecosystem sustainability. Natural vegetation succession is an alternative ecological solution to restore degraded land, but there is a time cost, given that the establishment of natural vegetation, adequate to prevent soil erosion, is a longer process than planting. The aims of this study were to identify the environmental factors controlling the type of vegetation established on abandoned cropland and to identify candidate species that might be sown soon after abandonment to accelerate vegetation succession and establishment of natural vegetation to prevent soil erosion. A field survey of thirty-three 2 × 2–m plots was carried out in July 2003, recording age since abandonment, vegetation cover, and frequency of species together with major environmental and soil variables. Data were analyzed using correspondence analysis, classification tree analysis, and species response curves. Four vegetation types were identified and the data analysis confirmed the importance of time since abandonment, total P, and soil water in controlling the type of vegetation established. Among the dominant species in the three late-successional vegetation types, the most appropriate candidates for accelerating and directing vegetation succession were King Ranch bluestem (Bothriochloa ischaemum) and Lespedeza davurica (Leguminosae). These species possess combinations of the following characteristics: tolerance of low water and nutrient availability, fibrous root system and strong lateral vegetative spread, and a persistent seed bank.

Mathematical modelling of competitive LDL/VLDL binding and uptake by hepatocytes

Elevated levels of low-density-lipoprotein cholesterol (LDL-C) in the plasma are a well-established risk factor for the development of coronary heart disease. Plasma LDL-C levels are in part determined by the rate at which LDL particles are removed from the bloodstream by hepatic uptake. The uptake of LDL by mammalian liver cells occurs mainly via receptor-mediated endocytosis, a process which entails the binding of these particles to specific receptors in specialised areas of the cell surface, the subsequent internalization of the receptor-lipoprotein complex, and ultimately the degradation and release of the ingested lipoproteins' constituent parts. We formulate a mathematical model to study the binding and internalization (endocytosis) of LDL and VLDL particles by hepatocytes in culture. The system of ordinary differential equations, which includes a cholesterol-dependent pit production term representing feedback regulation of surface receptors in response to intracellular cholesterol levels, is analysed using numerical simulations and steady-state analysis. Our numerical results show good agreement with in vitro experimental data describing LDL uptake by cultured hepatocytes following delivery of a single bolus of lipoprotein. Our model is adapted in order to reflect the in vivo situation, in which lipoproteins are continuously delivered to the hepatocyte. In this case, our model suggests that the competition between the LDL and VLDL particles for binding to the pits on the cell surface affects the intracellular cholesterol concentration. In particular, we predict that when there is continuous delivery of low levels of lipoproteins to the cell surface, more VLDL than LDL occupies the pit, since VLDL are better competitors for receptor binding. VLDL have a cholesterol content comparable to LDL particles; however, due to the larger size of VLDL, one pit-bound VLDL particle blocks binding of several LDLs, and there is a resultant drop in the intracellular cholesterol level. When there is continuous delivery of lipoprotein at high levels to the hepatocytes, VLDL particles still out-compete LDL particles for receptor binding, and consequently more VLDL than LDL particles occupy the pit. Although the maximum intracellular cholesterol level is similar for high and low levels of lipoprotein delivery, the maximum is reached more rapidly when the lipoprotein delivery rates are high. The implications of these results for the design of in vitro experiments is discussed.

Stochastic field processes in the mathematical modelling of damped transmission line vibrations

Wind-excited vibrations in the frequency range of 10 to 50 Hz due to vortex shedding often cause fatigue failures in the cables of overhead transmission lines. Damping devices, such as the Stockbridge dampers, have been in use for a long time for supressing these vibrations. The dampers are conveniently modelled by means of their driving point impedance, measured in the lab over the frequency range under consideration. The cables can be modelled as strings with additional small bending stiffness. The main problem in modelling the vibrations does however lay in the aerodynamic forces, which usually are approximated by the forces acting on a rigid cylinder in planar flow. In the present paper, the wind forces are represented by stochastic processes with arbitrary crosscorrelation in space; the case of a Kármán vortex street on a rigid cylinder in planar flow is contained as a limit case in this approach. The authors believe that this new view of the problem may yield useful results, particularly also concerning the reliability of the lines and the probability of fatigue damages. © 1987.

Reduction of Soil Erosion on Forest Roads

Results of onsite erosion control work from across the United States provide estimates of the amount of erosion reduction on forest roads from various treatments. Supplementary information includes the effects of slope gradient, soil characteristics, and ground cover. Estimates of sediment travel below fillslopes can be made, together with the combined effect of erosion control treatments of the running surface, road cut, and ditch.

Applying erosion damage mapping to asses and quantify off-site effects of soil erosion in Switzerland

In order to fill existing knowledge gaps in the temporal and spatial distribution of soil erosion, its sources and causes, as well as in relation to its off-site impacts, erosion damage mapping of all visible erosion features was carried out at three study sites in Switzerland. The data illustrate that about one-quarter of the cultivated land was affected by water erosion. Observed mean annual soil loss rates are considered rather low (0.7–2.3 t/ha/y) compared to other European countries. However, substantial losses of >70 t/ha were recorded on individual plots. This paper focuses on the spatial aspects of soil erosion, by observing and comparing the study areas in a 1-year period from October 2005 to October 2006. The analyses illustrate that the sites differ considerably in average soil loss rates, but show similar patterns of off-site effects. In about one-third of the damaged plots an external source of surface runoff upslope contributed to the damage (run-on). Similarly, more than 50 per cent of the soil eroded on arable land deposited downslope on adjacent plots, roads, public/private infrastructure, etc., and 20 per cent of it reached open water bodies. Large amounts of eroded soil which deposit off-site, often related to slope depressions, are considered muddy floods and were frequently observed in Switzerland. Mapping, in conclusion, helps to sheds light on some of the important challenges of today, in particular: to comprehensively assess socioeconomic and ecological off-site effects of soil erosion, to attribute off-site impacts to on-site causes, and to raise awareness of all stakeholders involved, in order to improve ongoing discussions on policy formulation and implementation at the national and international levels.

Assessment of soil erosion vulnerability in rural communities in the vicinity of Motozintla de Mendoza, Chiapas, Mexico : a physical and sociological approach

Soil erosion is a natural geological phenomenon resulting from removal and transportation of soil particles by water, wind, ice and gravity. As soil erosion may be affected from cultural factors as well. The physical and social phenomena of soil erosion are researched in six communities in the upper part of Rio Grijalva Basin in the vicinity of Motozintla de Mendoza, Chiapas, Mexico. For this study, the USDA RUSLE model was applied to estimate soil erosion rates in the six communities based on the available data. The RUSLE model is based on soil properties, topography, and land cover and management factors. These results showed that estimated soil erosion rates ranged from a high of 2,050 metric ton ha-1 yr-1 to a low of 100 metric ton ha-1 yr-1. A survey concerning knowledge, attitudes and practices (KAP) related to soil erosion was also conducted in all 236 households in the six communities. The main findings of the KAP survey were: 69% of respondents did not know what soil erosion was, while over 40% of the population perceived that hurricanes are the biggest factors that cause soil erosion, and about 20 % of the interviewees said that the landslides are the consequences of the soil erosion. People in communities did not perceive cultural factors as important in conservation efforts for reduce vulnerability to erosion; therefore, the results obtained are suggested to be useful for informing efforts to educate stakeholders.

Assessment of soil erosion and soil conservation practices in Angereb watershed, Ethiopia: Technological and land user context

Soil conservation technologies that fit well to local scale and are acceptable to land users are increasingly needed. To achieve this at small-holder farm level, there is a need for an understanding of specific erosion processes and indicators, the land users’ knowledge and their willingness, ability and possibilities to respond to the respective problems to decide on control options. This study was carried out to assess local erosion and performance of earlier introduced conservation terraces from both technological and land users’ points of view. The study was conducted during July to August 2008 at Angereb watershed on 58 farm plots from three selected case-study catchments. Participatory erosion assessment and evaluation were implemented along with direct field measurement procedures. Our focus was to involve the land users in the action research to explore with them the effectiveness of existing conservation measures against the erosion hazard. Terrace characteristics measured and evaluated against the terrace implementation guideline of Hurni (1986). The long-term consequences of seasonal erosion indicators had often not been known and noticed by farmers. The cause and effect relationships of the erosion indicators and conservation measures have shown the limitations and gaps to be addressed towards sustainable erosion control strategies. Less effective erosion control has been observed and participants have believed the gaps are to be the result of lack of landusers’ genuine participation. The results of both local erosion observation and assessment of conservation efficacy using different aspects show the need to promote approaches for erosion evaluation and planning of interventions by the farmers themselves. This paper describes the importance of human factor involving in the empirical erosion assessment methods towards sustainable soil conservation.