Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 17

Mathematical Modelling Related Abstracts

17 The Convection Heater Numerical Simulation

Authors: Cristian Patrascioiu, Loredana Negoita


This paper is focused on modeling and simulation of the tubular heaters. The paper is structured in four parts: the structure of the tubular convection section, the heat transfer model, the adaptation of the mathematical model and the solving model. The main hypothesis of the heat transfer modeling is that the heat exchanger of the convective tubular heater is a lumped system. In the same time, the model uses the heat balance relations, Newton’s law and criteria relations. The numerical program achieved allows for the estimation of the burn gases outlet temperature and the heated flow outlet temperature.

Keywords: Mathematical Modelling, heat exchanger, nonlinear equation system, Newton-Raphson algorithm

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16 Schedule a New Production Plan by Heuristic Methods

Authors: Hanife Merve Öztürk, Sıdıka Dalgan


In this project, a capacity analysis study is done at TAT A. Ş. Maret Plant. Production capacity of products which generate 80% of sales amount are determined. Obtained data entered the LEKIN Scheduling Program and we get production schedules by using heuristic methods. Besides heuristic methods, as mathematical model, disjunctive programming formulation is adapted to flexible job shop problems by adding a new constraint to find optimal schedule solution.

Keywords: Scheduling, Mathematical Modelling, flexible job shop problem, shifting bottleneck heuristic

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15 Thermal Barrier Coated Diesel Engine With Neural Networks Mathematical Modelling

Authors: Hanbey Hazar, Hakan Gul


In this study; piston, exhaust, and suction valves of a diesel engine were coated in 300 mm thickness with Tungsten Carbide (WC) by using the HVOF coating method. Mathematical modeling of a coated and uncoated (standardized) engine was performed by using ANN (Artificial Neural Networks). The purpose was to decrease the number of repetitions of tests and reduce the test cost through mathematical modeling of engines by using ANN. The results obtained from the tests were entered in ANN and therefore engines' values at all speeds were estimated. Results obtained from the tests were compared with those obtained from ANN and they were observed to be compatible. It was also observed that, with thermal barrier coating, hydrocarbon (HC), carbon monoxide (CO), and smoke density values of the diesel engine decreased; but nitrogen oxides (NOx) increased. Furthermore, it was determined that results obtained through mathematical modeling by means of ANN reduced the number of test repetitions. Therefore, it was understood that time, fuel and labor could be saved in this way.

Keywords: Mathematical Modelling, Artificial Neural Network, Diesel Engine, thermal barrier coating

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14 3D CFD Model of Hydrodynamics in Lowland Dam Reservoir in Poland

Authors: Aleksandra Zieminska-Stolarska, Ireneusz Zbicinski


Introduction: The objective of the present work was to develop and validate a 3D CFD numerical model for simulating flow through 17 kilometers long dam reservoir of a complex bathymetry. In contrast to flowing waters, dam reservoirs were not emphasized in the early years of water quality modeling, as this issue has never been the major focus of urban development. Starting in the 1970s, however, it was recognized that natural and man-made lakes are equal, if not more important than estuaries and rivers from a recreational standpoint. The Sulejow Reservoir (Central Poland) was selected as the study area as representative of many lowland dam reservoirs and due availability of a large database of the ecological, hydrological and morphological parameters of the lake. Method: 3D, 2-phase and 1-phase CFD models were analysed to determine hydrodynamics in the Sulejow Reservoir. Development of 3D, 2-phase CFD model of flow requires a construction of mesh with millions of elements and overcome serious convergence problems. As 1-phase CFD model of flow in relation to 2-phase CFD model excludes from the simulations the dynamics of waves only, which should not change significantly water flow pattern for the case of lowland, dam reservoirs. In 1-phase CFD model, the phases (water-air) are separated by a plate which allows calculations of one phase (water) flow only. As the wind affects velocity of flow, to take into account the effect of the wind on hydrodynamics in 1-phase CFD model, the plate must move with speed and direction equal to the speed and direction of the upper water layer. To determine the velocity at which the plate will move on the water surface and interacts with the underlying layers of water and apply this value in 1-phase CFD model, the 2D, 2-phase model was elaborated. Result: Model was verified on the basis of the extensive flow measurements (StreamPro ADCP, USA). Excellent agreement (an average error less than 10%) between computed and measured velocity profiles was found. As a result of work, the following main conclusions can be presented: •The results indicate that the flow field in the Sulejow Reservoir is transient in nature, with swirl flows in the lower part of the lake. Recirculating zones, with the size of even half kilometer, may increase water retention time in this region •The results of simulations confirm the pronounced effect of the wind on the development of the water circulation zones in the reservoir which might affect the accumulation of nutrients in the epilimnion layer and result e.g. in the algae bloom. Conclusion: The resulting model is accurate and the methodology develop in the frame of this work can be applied to all types of storage reservoir configurations, characteristics, and hydrodynamics conditions. Large recirculating zones in the lake which increase water retention time and might affect the accumulation of nutrients were detected. Accurate CFD model of hydrodynamics in large water body could help in the development of forecast of water quality, especially in terms of eutrophication and water management of the big water bodies.

Keywords: Hydrodynamics, CFD, Mathematical Modelling, dam reservoirs

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13 Modelling the Anaerobic Digestion of Esparto Paper Industry Wastewater Effluent in a Batch Digester Using IWA Anaerobic Digestion Model No. 1 (ADM1)

Authors: Boubaker Fezzani, Ridha Ben Cheikh, Tarek Rouissi


In this work the original ADM1, implemented in the simulation software package MATLAB/Simulink, was modified and adapted and applied to reproduce the experimental results of the mesophilic anaerobic digestion of Esperto paper industry wastewater in a batch digester. The data set from lab-scale experiment runs were used to calibrate and validate the model. The simulations’ results indicated that the modified ADM1 was able to predict reasonably well the steady state results of gas flows, methane and carbon dioxide contents, pH and total volatile fatty acids (TVFA) observed with all influents concentrations.

Keywords: Simulation, Mathematical Modelling, Anaerobic Digestion, ADM1, batch digester, esparto paper industry effluent, mesophilic temperature

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12 Multiscale Modelling of Citrus Black Spot Transmission Dynamics along the Pre-Harvest Supply Chain

Authors: Winston Garira, Muleya Nqobile


We presented a compartmental deterministic multi-scale model which encompass internal plant defensive mechanism and pathogen interaction, then we consider nesting the model into the epidemiological model. The objective was to improve our understanding of the transmission dynamics of within host and between host of Guignardia citricapa Kiely. The inflow of infected class was scaled down to individual level while the outflow was scaled up to average population level. Conceptual model and mathematical model were constructed to display a theoretical framework which can be used for predicting or identify disease pattern.

Keywords: Mathematical Modelling, epidemiological model, multi-scale modelling, immunological model

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11 Mathematical Modelling of Wastewater Collection System in Cha-Am Municipality Using PCSWMM

Authors: Thawtar Htun, Kim N. Irvine, Ranjna Jindal


This study aimed at modelling the wastewater collection system in Cha-Am Municipality using PCSWMM to investigate the quantity of combined sewage delivered to the aeration lagoon treatment system (ALTS). Cha-Am is a small sea resort town in Petchaburi Province located about 175 km southwest of Bangkok and is facing increasing development so it is important to understand current system performance and plan for future build out. PCSWMM was calibrated using observed ALTS inflow data for the period 15 June to 20 July 2015. The model was validated using observed ALTS inflow data for the periods 19 July to 20 October 2015 and 1 October to 31 December 2015, respectively. The 1:1 lines between modeled and observed peak flow and event volume for the calibration events qualitatively showed good correspondence. The r2 values between modeled and observed peak flow (99%) and event volume (89%) also were strong.

Keywords: Mathematical Modelling, combined sewer system, PCSWMM, wastewater collection system

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10 The Using of Liquefied Petroleum Gas (LPG) on a Low Heat Loss Si Engine

Authors: Hanbey Hazar, Hakan Gul


In this study, Thermal Barrier Coating (TBC) application is performed in order to reduce the engine emissions. Piston, exhaust, and intake valves of a single-cylinder four-cycle gasoline engine were coated with chromium carbide (Cr3C2) at a thickness of 300 µm by using the Plasma Spray coating method which is a TBC method. Gasoline engine was converted into an LPG system. The study was conducted in 4 stages. In the first stage, the piston, exhaust, and intake valves of the gasoline engine were coated with Cr3C2. In the second stage, gasoline engine was converted into the LPG system and the emission values in this engine were recorded. In the third stage, the experiments were repeated under the same conditions with a standard (uncoated) engine and the results were recorded. In the fourth stage, data obtained from both engines were loaded on Artificial Neural Networks (ANN) and estimated values were produced for every revolution. Thus, mathematical modeling of coated and uncoated engines was performed by using ANN. While there was a slight increase in exhaust gas temperature (EGT) of LPG engine due to TBC, carbon monoxide (CO) values decreased.

Keywords: Mathematical Modelling, Artificial Neural Network, thermal barrier coating, LPG fuel

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9 On Consolidated Predictive Model of the Natural History of Breast Cancer Considering Primary Tumor and Primary Distant Metastases Growth

Authors: Ella Tyuryumina, Alexey Neznanov


Finding algorithms to predict the growth of tumors has piqued the interest of researchers ever since the early days of cancer research. A number of studies were carried out as an attempt to obtain reliable data on the natural history of breast cancer growth. Mathematical modeling can play a very important role in the prognosis of tumor process of breast cancer. However, mathematical models describe primary tumor growth and metastases growth separately. Consequently, we propose a mathematical growth model for primary tumor and primary metastases which may help to improve predicting accuracy of breast cancer progression using an original mathematical model referred to CoM-IV and corresponding software. We are interested in: 1) modelling the whole natural history of primary tumor and primary metastases; 2) developing adequate and precise CoM-IV which reflects relations between PT and MTS; 3) analyzing the CoM-IV scope of application; 4) implementing the model as a software tool. The CoM-IV is based on exponential tumor growth model and consists of a system of determinate nonlinear and linear equations; corresponds to TNM classification. It allows to calculate different growth periods of primary tumor and primary metastases: 1) ‘non-visible period’ for primary tumor; 2) ‘non-visible period’ for primary metastases; 3) ‘visible period’ for primary metastases. The new predictive tool: 1) is a solid foundation to develop future studies of breast cancer models; 2) does not require any expensive diagnostic tests; 3) is the first predictor which makes forecast using only current patient data, the others are based on the additional statistical data. Thus, the CoM-IV model and predictive software: a) detect different growth periods of primary tumor and primary metastases; b) make forecast of the period of primary metastases appearance; c) have higher average prediction accuracy than the other tools; d) can improve forecasts on survival of BC and facilitate optimization of diagnostic tests. The following are calculated by CoM-IV: the number of doublings for ‘nonvisible’ and ‘visible’ growth period of primary metastases; tumor volume doubling time (days) for ‘nonvisible’ and ‘visible’ growth period of primary metastases. The CoM-IV enables, for the first time, to predict the whole natural history of primary tumor and primary metastases growth on each stage (pT1, pT2, pT3, pT4) relying only on primary tumor sizes. Summarizing: a) CoM-IV describes correctly primary tumor and primary distant metastases growth of IV (T1-4N0-3M1) stage with (N1-3) or without regional metastases in lymph nodes (N0); b) facilitates the understanding of the appearance period and manifestation of primary metastases.

Keywords: Mathematical Modelling, Breast Cancer, Survival, Primary tumor, exponential growth model, primary metastases

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8 A Biomechanical Model for the Idiopathic Scoliosis Using the Antalgic-Trak Technology

Authors: Joao Fialho


The mathematical modelling of idiopathic scoliosis has been studied throughout the years. The models presented on those papers are based on the orthotic stabilization of the idiopathic scoliosis, which are based on a transversal force being applied to the human spine on a continuous form. When considering the ATT (Antalgic-Trak Technology) device, the existent models cannot be used, as the type of forces applied are no longer transversal nor applied in a continuous manner. In this device, vertical traction is applied. In this study we propose to model the idiopathic scoliosis, using the ATT (Antalgic-Trak Technology) device, and with the parameters obtained from the mathematical modeling, set up a case-by-case individualized therapy plan, for each patient.

Keywords: Mathematical Modelling, idiopathic scoliosis, human spine, Antalgic-Trak technology

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7 Adsorptive Media Selection for Bilirubin Removal: An Adsorption Equilibrium Study

Authors: Vincenzo Piemonte


The liver is a complex, large-scale biochemical reactor which plays a unique role in the human physiology. When liver ceases to perform its physiological activity, a functional replacement is required. Actually, liver transplantation is the only clinically effective method of treating severe liver disease. Anyway, the aforementioned therapeutic approach is hampered by the disparity between organ availability and the number of patients on the waiting list. In order to overcome this critical issue, research activities focused on liver support device systems (LSDs) designed to bridging patients to transplantation or to keep them alive until the recovery of native liver function. In recirculating albumin dialysis devices, such as MARS (Molecular Adsorbed Recirculating System), adsorption is one of the fundamental steps in albumin-dialysate regeneration. Among the albumin-bound toxins that must be removed from blood during liver-failure therapy, bilirubin and tryptophan can be considered as representative of two different toxin classes. The first one, not water soluble at physiological blood pH and strongly bounded to albumin, the second one, loosely albumin bound and partially water soluble at pH 7.4. Fixed bed units are normally used for this task, and the design of such units requires information both on toxin adsorption equilibrium and kinetics. The most common adsorptive media used in LSDs are activated carbon, non-ionic polymeric resins and anionic resins. In this paper, bilirubin adsorption isotherms on different adsorptive media, such as polymeric resin, albumin-coated resin, anionic resin, activated carbon and alginate beads with entrapped albumin are presented. By comparing all the results, it can be stated that the adsorption capacity for bilirubin of the five different media increases in the following order: Alginate beads < Polymeric resin < Albumin-coated resin < Activated carbon < Anionic resin. The main focus of this paper is to provide useful guidelines for the optimization of liver support devices which implement adsorption columns to remove albumin-bound toxins from albumin dialysate solutions.

Keywords: Mathematical Modelling, adsorption equilibrium, bilirubin, adsorptive media, artificial liver devices

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6 Passive Neutralization of Acid Mine Drainage Using Locally Produced Limestone

Authors: Tumisang Seodigeng, Hilary Rutto, Haleden Chiririwa, Reneiloe Seodigeng, Malwandla Hanabe


Neutralisation of acid-mine drainage (AMD) using limestone is cost effective, and good results can be obtained. However, this process has its limitations; it cannot be used for highly acidic water which consists of Fe(III). When Fe(III) reacts with CaCO3, it results in armoring. Armoring slows the reaction, and additional alkalinity can no longer be generated. Limestone is easily accessible, so this problem can be easily dealt with. Experiments were carried out to evaluate the effect of PVC pipe length on ferric and ferrous ions. It was found that the shorter the pipe length the more these dissolved metals precipitate. The effect of the pipe length on the hydrogen ions was also studied, and it was found that these two have an inverse relationship. Experimental data were further compared with the model prediction data to see if they behave in a similar fashion. The model was able to predict the behaviour of 1.5m and 2 m pipes in ferric and ferrous ion precipitation.

Keywords: Mathematical Modelling, limestone, acid mine drainage, neutralisation

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5 Two-Channels Thermal Energy Storage Tank: Experiments and Short-Cut Modelling

Authors: M. Capocelli, A. Caputo, M. De Falco, D. Mazzei, V. Piemonte


This paper presents the experimental results and the related modeling of a thermal energy storage (TES) facility, ideated and realized by ENEA and realizing the thermocline with an innovative geometry. Firstly, the thermal energy exchange model of an equivalent shell & tube heat exchanger is described and tested to reproduce the performance of the spiral exchanger installed in the TES. Through the regression of the experimental data, a first-order thermocline model was also validated to provide an analytical function of the thermocline, useful for the performance evaluation and the comparison with other systems and implementation in simulations of integrated systems (e.g. power plants). The experimental data obtained from the plant start-up and the short-cut modeling of the system can be useful for the process analysis, for the scale-up of the thermal storage system and to investigate the feasibility of its implementation in actual case-studies.

Keywords: Mathematical Modelling, Thermal Energy Storage, thermocline, experimental data, CSP plants

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4 The Effects of Plantation Size and Internal Transport on Energy Efficiency of Biofuel Production

Authors: Olga Orynycz, Andrzej Wasiak


Mathematical model describing energetic efficiency (defined as a ratio of energy obtained in the form of biofuel to the sum of energy inputs necessary to facilitate production) of agricultural subsystem as a function of technological parameters was developed. Production technology is characterized by parameters of machinery, topological characteristics of the plantation as well as transportation routes inside and outside of plantation. The relationship between the energetic efficiency of agricultural and industrial subsystems is also derived. Due to the assumed large area of the individual field, the operations last for several days increasing inter-fields routes because of several returns. The total distance driven outside of the fields is, however, small as compared to the distance driven inside of the fields. This results in small energy consumption during inter-fields transport that, however, causes a substantial decrease of the energetic effectiveness of the whole system.

Keywords: Production System, biofuel, Mathematical Modelling, energetic efficiency, EROEI

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3 Experimental Study and Numerical Modelling of Failure of Rocks Typical for Kuzbass Coal Basin

Authors: Mikhail O. Eremin


Present work is devoted to experimental study and numerical modelling of failure of rocks typical for Kuzbass coal basin (Russia). The main goal was to define strength and deformation characteristics of rocks on the base of uniaxial compression and three-point bending loadings and then to build a mathematical model of failure process for both types of loading. Depending on particular physical-mechanical characteristics typical rocks of Kuzbass coal basin (sandstones, siltstones, mudstones, etc. of different series – Kolchuginsk, Tarbagansk, Balohonsk) manifest brittle and quasi-brittle character of failure. The strength characteristics for both tension and compression are found. Other characteristics are also found from the experiment or taken from literature reviews. On the base of obtained characteristics and structure (obtained from microscopy) the mathematical and structural models are built and numerical modelling of failure under different types of loading is carried out. Effective characteristics obtained from modelling and character of failure correspond to experiment and thus, the mathematical model was verified. An Instron 1185 machine was used to carry out the experiments. Mathematical model includes fundamental conservation laws of solid mechanics – mass, impulse, energy. Each rock has a sufficiently anisotropic structure, however, each crystallite might be considered as isotropic and then a whole rock model has a quasi-isotropic structure. This idea gives an opportunity to use the Hooke’s law inside of each crystallite and thus explicitly accounting for the anisotropy of rocks and the stress-strain state at loading. Inelastic behavior is described in frameworks of two different models: von Mises yield criterion and modified Drucker-Prager yield criterion. The damage accumulation theory is also implemented in order to describe a failure process. Obtained effective characteristics of rocks are used then for modelling of rock mass evolution when mining is carried out both by an open-pit or underground opening.

Keywords: Mathematical Modelling, Failure, Damage Accumulation, three-point bending, uniaxial compression, Drucker-Prager yield criterion

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2 Mathematical Modelling of Ultrasound Pre-Treatment in Microwave Dried Strawberry (Fragaria L.) Slices

Authors: Hilal Uslu, Salih Eroglu, Betul Ozkan, Ozcan Bulantekin, Alper Kuscu


In this study, the strawberry (Fragaria L.) fruits, which were pretreated with ultrasound (US), were worked on in the microwave by using 90W power. Then mathematical modelling was applied to dried fruits by using different experimental thin layer models. The sliced fruits were subjected to ultrasound treatment at a frequency of 40 kHz for 10, 20, and 30 minutes, in an ultrasonic water bath, with a ratio of 1:4 to fruit/water. They are then dried in the microwave (90W). The drying process continued until the product moisture was below 10%. By analyzing the moisture change of the products at a certain time, eight different thin-layer drying models, (Newton, page, modified page, Midilli, Henderson and Pabis, logarithmic, two-term, Wang and Singh) were tested for verification of experimental data. MATLAB R2015a statistical program was used for the modelling, and the best suitable model was determined with R²adj (coefficient of determination of compatibility), and root mean square error (RMSE) values. According to analysis, the drying model that best describes the drying behavior for both drying conditions was determined as the Midilli model by high R²adj and low RMSE values. Control, 10, 20, and 30 min US for groups R²adj and RMSE values was established as respectively; 0,9997- 0,005298; 0,9998- 0,004735; 0,9995- 0,007031; 0,9917-0,02773. In addition, effective diffusion coefficients were calculated for each group and were determined as 3,80x 10⁻⁸, 3,71 x 10⁻⁸, 3,26 x10⁻⁸ ve 3,5 x 10⁻⁸ m/s, respectively.

Keywords: Mathematical Modelling, Ultrasound, microwave drying, strawberry

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1 Heat and Mass Transfer Modelling of Industrial Sludge Drying at Different Pressures and Temperatures

Authors: Layth Al Ahmad, Christelle Lattrille, Delphine Hainos, Denise Blanc, Marc Clausse


A two-dimensional finite volume axisymmetric model is developed to predict the simultaneous heat and mass transfers during the drying of industrial sludge. The simulations were run using COMSOL-Multiphysics 3.5a. The input parameters of the numerical model were acquired from a preliminary experimental work. Results permit to establish correlations describing the evolution of the various parameters as a function of the drying temperature and the sludge water content. The selection and coupling of the equation are validated based on the drying kinetics acquired experimentally at a temperature range of 45-65 °C and absolute pressure range of 200-1000 mbar. The model, incorporating the heat and mass transfer mechanisms at different operating conditions, shows simulated values of temperature and water content. Simulated results are found concordant with the experimental values, only at the first and last drying stages where sludge shrinkage is insignificant. Simulated and experimental results show that sludge drying is favored at high temperatures and low pressure. As experimentally observed, the drying time is reduced by 68% for drying at 65 °C compared to 45 °C under 1 atm. At 65 °C, a 200-mbar absolute pressure vacuum leads to an additional reduction in drying time estimated by 61%. However, the drying rate is underestimated in the intermediate stage. This rate underestimation could be improved in the model by considering the shrinkage phenomena that occur during sludge drying.

Keywords: Heat Transfer, Mathematical Modelling, mass transfer, industrial sludge drying

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