Articles de revista
http://hdl.handle.net/2117/3191
2016-10-24T14:50:10ZTechno-economic performance evaluation of solar tower plants with integrated multilayered PCM thermocline thermal energy storage: a comparative study to conventional two-tank storage systems
http://hdl.handle.net/2117/90561
Techno-economic performance evaluation of solar tower plants with integrated multilayered PCM thermocline thermal energy storage: a comparative study to conventional two-tank storage systems
Guedéz, Rafael; Ferruzza, Davide; Arnaudo, Monica; Rodríguez Pérez, Ivette María; Pérez Segarra, Carlos David; Hassar, Zhor; Laumert, Björn
Solar Tower Power Plants with thermal energy storage are a promising technology for dispatchable renewable energy in the near future. Storage integration makes possible to shift the electricity production to more profitable peak hours. Usually two tanks are used to store cold and hot fluids, but this means both higher investment costs and difficulties during the operation of the variable volume tanks. Instead, another solution can be a single tank thermocline storage in a multi-layered configuration. In such tank both latent and sensible fillers are employed to decrease the related cost up to 30% and maintain high efficiencies. This paper analyses a multi-layered solid PCM storage tank concept for solar tower applications, and describes a comprehensive methodology to determine under which market structures such devices can outperform the more conventional two tank storage systems. A detail model of the tank has been developed and introduced in an existing techno-economic tool developed by the authors (DYESOPT). The results show that under current cost estimates and technical limitations the multi-layered solid PCM storage concept is a better solution when peaking operating strategies are desired, as it is the case for the two-tier South African tariff scheme.
Copyright 2016 AIP Publishing. This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing.
2016-10-05T16:19:16ZGuedéz, RafaelFerruzza, DavideArnaudo, MonicaRodríguez Pérez, Ivette MaríaPérez Segarra, Carlos DavidHassar, ZhorLaumert, BjörnSolar Tower Power Plants with thermal energy storage are a promising technology for dispatchable renewable energy in the near future. Storage integration makes possible to shift the electricity production to more profitable peak hours. Usually two tanks are used to store cold and hot fluids, but this means both higher investment costs and difficulties during the operation of the variable volume tanks. Instead, another solution can be a single tank thermocline storage in a multi-layered configuration. In such tank both latent and sensible fillers are employed to decrease the related cost up to 30% and maintain high efficiencies. This paper analyses a multi-layered solid PCM storage tank concept for solar tower applications, and describes a comprehensive methodology to determine under which market structures such devices can outperform the more conventional two tank storage systems. A detail model of the tank has been developed and introduced in an existing techno-economic tool developed by the authors (DYESOPT). The results show that under current cost estimates and technical limitations the multi-layered solid PCM storage concept is a better solution when peaking operating strategies are desired, as it is the case for the two-tier South African tariff scheme.Particulate immersed boundary method for complex fluid-particle interaction problems with heat transfer
http://hdl.handle.net/2117/86702
Particulate immersed boundary method for complex fluid-particle interaction problems with heat transfer
Zhang, Hao; Yuan, Haizhuan; Trias Miquel, Francesc Xavier; Yu, Aibing; Tan, Yuanqiang; Oliva Llena, Asensio
In our recent work (Zhang et al., 2015), a Particulate Immersed Boundary Method (PIBM) for simulating fluid-particle multiphase flow was proposed and assessed in both two- and three-dimensional applications. In this study, the PIBM was extended to solve thermal interaction problems between spherical particles and fluid. The Lattice Boltzmann Method (LBM) was adopted to solve the fluid flow and temperature fields, the PIBM was responsible for the no-slip velocity and temperature boundary conditions at the particle surface, and the kinematics and trajectory of the solid particles were evaluated by the Discrete Element Method (DEM). Four case studies were implemented to demonstrate the capability of the current coupling scheme. Firstly, numerical simulation of natural convection in a two-dimensional square cavity with an isothermal concentric annulus was carried out for verification purpose. The current results were found to have good agreement with previous references. Then, sedimentation of two-and three-dimensional isothermal particles in fluid was numerically studied, respectively. The instantaneous temperature distribution in the cavity was captured. The effect of the thermal buoyancy on particle behaviors was discussed. Finally, sedimentation of three-dimensional thermosensitive particles in fluid was numerically investigated. Our results revealed that the LBM-PIBM-DEM is a promising scheme for the solution of complex fluid-particle interaction problems with heat transfer.
2016-05-06T12:54:06ZZhang, HaoYuan, HaizhuanTrias Miquel, Francesc XavierYu, AibingTan, YuanqiangOliva Llena, AsensioIn our recent work (Zhang et al., 2015), a Particulate Immersed Boundary Method (PIBM) for simulating fluid-particle multiphase flow was proposed and assessed in both two- and three-dimensional applications. In this study, the PIBM was extended to solve thermal interaction problems between spherical particles and fluid. The Lattice Boltzmann Method (LBM) was adopted to solve the fluid flow and temperature fields, the PIBM was responsible for the no-slip velocity and temperature boundary conditions at the particle surface, and the kinematics and trajectory of the solid particles were evaluated by the Discrete Element Method (DEM). Four case studies were implemented to demonstrate the capability of the current coupling scheme. Firstly, numerical simulation of natural convection in a two-dimensional square cavity with an isothermal concentric annulus was carried out for verification purpose. The current results were found to have good agreement with previous references. Then, sedimentation of two-and three-dimensional isothermal particles in fluid was numerically studied, respectively. The instantaneous temperature distribution in the cavity was captured. The effect of the thermal buoyancy on particle behaviors was discussed. Finally, sedimentation of three-dimensional thermosensitive particles in fluid was numerically investigated. Our results revealed that the LBM-PIBM-DEM is a promising scheme for the solution of complex fluid-particle interaction problems with heat transfer.Turbulent flow around a square cylinder at Reynolds number 22,000: A DNS study
http://hdl.handle.net/2117/86080
Turbulent flow around a square cylinder at Reynolds number 22,000: A DNS study
Trias Miquel, Francesc Xavier; Gorobets, Andrei; Oliva Llena, Asensio
The turbulent flow around a square cylinder at Reynolds number 22,000 (based on the cylinder diameter and the inflow velocity) is studied by means of direct numerical simulation. An overview of the numerical methods and the methodology used to verify the simulation is presented with special emphasis to determine the proper domain size and time-integration period. Then, the time-averaged flow results and turbulent statistics are discussed together with available experimental data showing a fairly good agreement. Finally, frequency analysis of velocity samples is used to analyze both the Kelvin-Helmholtz vortical structures produced by the flow separation at the leading edge of the cylinder and the Von Karman vortex shedding in the wake region. The former are observed more downstream compared with the experiments suggesting that transition to turbulence may occur later. However, comparison of the turbulent statistics in the near wall region indicates that transition is being well captured.
2016-04-21T16:00:15ZTrias Miquel, Francesc XavierGorobets, AndreiOliva Llena, AsensioThe turbulent flow around a square cylinder at Reynolds number 22,000 (based on the cylinder diameter and the inflow velocity) is studied by means of direct numerical simulation. An overview of the numerical methods and the methodology used to verify the simulation is presented with special emphasis to determine the proper domain size and time-integration period. Then, the time-averaged flow results and turbulent statistics are discussed together with available experimental data showing a fairly good agreement. Finally, frequency analysis of velocity samples is used to analyze both the Kelvin-Helmholtz vortical structures produced by the flow separation at the leading edge of the cylinder and the Von Karman vortex shedding in the wake region. The former are observed more downstream compared with the experiments suggesting that transition to turbulence may occur later. However, comparison of the turbulent statistics in the near wall region indicates that transition is being well captured.Direct numerical simulation of a fully developed turbulent square duct flow up to Re-tau=1200
http://hdl.handle.net/2117/86076
Direct numerical simulation of a fully developed turbulent square duct flow up to Re-tau=1200
Zhang, Hao; Trias Miquel, Francesc Xavier; Gorobets, Andrey; Tan, Yuanqiang; Oliva Llena, Asensio
Various fundamental studies based on a turbulent duct flow have gained popularity including heat transfer, magnetohydrodynamics as well as particle-laden transportation. An accurate prediction on the turbulent flow field is critical for these researches. However, the database of the mean flow and turbulence statistics is fairly insufficient due to the enormous cost of numerical simulation at high Reynolds number. This paper aims at providing available information by conducting several Direct Numerical Simulations (DNS) on turbulent duct flows at Re-tau = 300, 600, 900 and 1200. A quantitative comparison between current and previous DNS results was performed where a good agreement was achieved at Re-tau = 300. However, further comparisons of the present results with the previous DNS results at Re-tau = 600 obtained with much coarser meshes revealed some discrepancies which can be explained by the insufficient mesh resolution. At last, the mean flow and turbulent statistics at higher Re-tau was presented and the effect of Re-tau on the mean flow and flow dynamics was discussed.
2016-04-21T14:52:02ZZhang, HaoTrias Miquel, Francesc XavierGorobets, AndreyTan, YuanqiangOliva Llena, AsensioVarious fundamental studies based on a turbulent duct flow have gained popularity including heat transfer, magnetohydrodynamics as well as particle-laden transportation. An accurate prediction on the turbulent flow field is critical for these researches. However, the database of the mean flow and turbulence statistics is fairly insufficient due to the enormous cost of numerical simulation at high Reynolds number. This paper aims at providing available information by conducting several Direct Numerical Simulations (DNS) on turbulent duct flows at Re-tau = 300, 600, 900 and 1200. A quantitative comparison between current and previous DNS results was performed where a good agreement was achieved at Re-tau = 300. However, further comparisons of the present results with the previous DNS results at Re-tau = 600 obtained with much coarser meshes revealed some discrepancies which can be explained by the insufficient mesh resolution. At last, the mean flow and turbulent statistics at higher Re-tau was presented and the effect of Re-tau on the mean flow and flow dynamics was discussed.PIBM: Particulate immersed boundary method for fluid-particle interaction problems
http://hdl.handle.net/2117/85915
PIBM: Particulate immersed boundary method for fluid-particle interaction problems
Zhang, Hao; Trias Miquel, Francesc Xavier; Oliva Llena, Asensio; Yang, Dongmin; Tan, Yuanqiang; Shu, Shi; Sheng, Yong
It is well known that the number of particles should be scaled up to enable industrial scale simulation. The calculations are more computationally intensive when the motion of the surrounding fluid is considered. Besides the advances in computer hardware and numerical algorithms, the coupling scheme also plays an important role on the computational efficiency. In this study, a particulate immersed boundary method (PIBM) for simulating the fluid-particle multiphase flow was presented and assessed in both two- and three-dimensional applications. The idea behind PIBM derives from the conventional momentum exchange-based Immersed Boundary Method (IBM) by treating each Lagrangian point as a solid particle. This treatment enables Lattice Boltzmann Method (LBM) to be coupled with fine particles residing within a particular grid cell. Compared with the conventional IBM, dozens of times speedup in two-dimensional simulation and hundreds of times in three-dimensional simulation can be expected under the same particle and mesh number. Numerical simulations of particle sedimentation in Newtonian flows were canducted based on a combined LBM-PIBM-Discrete Element Method (DEM) scheme, showing that the PIBM can capture the feature of particulate flows in fluid and is indeed a promising scheme for the solution of the fluid-particle interaction problems.
2016-04-19T14:57:07ZZhang, HaoTrias Miquel, Francesc XavierOliva Llena, AsensioYang, DongminTan, YuanqiangShu, ShiSheng, YongIt is well known that the number of particles should be scaled up to enable industrial scale simulation. The calculations are more computationally intensive when the motion of the surrounding fluid is considered. Besides the advances in computer hardware and numerical algorithms, the coupling scheme also plays an important role on the computational efficiency. In this study, a particulate immersed boundary method (PIBM) for simulating the fluid-particle multiphase flow was presented and assessed in both two- and three-dimensional applications. The idea behind PIBM derives from the conventional momentum exchange-based Immersed Boundary Method (IBM) by treating each Lagrangian point as a solid particle. This treatment enables Lattice Boltzmann Method (LBM) to be coupled with fine particles residing within a particular grid cell. Compared with the conventional IBM, dozens of times speedup in two-dimensional simulation and hundreds of times in three-dimensional simulation can be expected under the same particle and mesh number. Numerical simulations of particle sedimentation in Newtonian flows were canducted based on a combined LBM-PIBM-Discrete Element Method (DEM) scheme, showing that the PIBM can capture the feature of particulate flows in fluid and is indeed a promising scheme for the solution of the fluid-particle interaction problems.On the flow past a circular cylinder from critical to super-critical Reynolds numbers: Wake topology and vortex shedding
http://hdl.handle.net/2117/85914
On the flow past a circular cylinder from critical to super-critical Reynolds numbers: Wake topology and vortex shedding
Rodríguez Pérez, Ivette María; Lehmkuhl Barba, Oriol; Chiva Segura, Jorge; Borrell Pol, Ricard; Oliva Llena, Asensio
Large-eddy simulations (LES) of the flow past a circular cylinder are used to investigate the flow topology and the vortex shedding process at Reynolds numbers Re=2.5×105-8.5×105Re=2.5×105-8.5×105. This range encompasses both the critical and super-critical regimes. As the flow enters the critical regime, major changes occur which affect the flow configuration. Asymmetries in the flow are found in the critical regime, whereas the wake recovers its symmetry and stabilizes in the super-critical regime. Wake characteristic lengths are measured and compared between the different Reynolds numbers. It is shown that the super-critical regime is characterised by a plateau in the drag coefficient at about CD˜0.22CD˜0.22, and a quasi-stable wake which has a non-dimensional width of dw/D˜0.4dw/D˜0.4. The periodic nature of the flow is analysed by means of measurements of the unsteady drag and lift coefficients. Power spectra of the lift fluctuations are computed. Wake vortex shedding is found to occur for both regimes investigated, although a jump in frequencies is observed when the flow enters the super-critical regime. In this regime, non-dimensional vortex-shedding frequency is almost constant and equal to St=fvsD/Uref˜0.44St=fvsD/Uref˜0.44. The analysis also shows a steep decrease in the fluctuating lift when entering the super-critical regime. The combined analysis of both wake topology and vortex shedding complements the physical picture of a stable and highly coherent flow in the super-critical regime.
2016-04-19T14:15:46ZRodríguez Pérez, Ivette MaríaLehmkuhl Barba, OriolChiva Segura, JorgeBorrell Pol, RicardOliva Llena, AsensioLarge-eddy simulations (LES) of the flow past a circular cylinder are used to investigate the flow topology and the vortex shedding process at Reynolds numbers Re=2.5×105-8.5×105Re=2.5×105-8.5×105. This range encompasses both the critical and super-critical regimes. As the flow enters the critical regime, major changes occur which affect the flow configuration. Asymmetries in the flow are found in the critical regime, whereas the wake recovers its symmetry and stabilizes in the super-critical regime. Wake characteristic lengths are measured and compared between the different Reynolds numbers. It is shown that the super-critical regime is characterised by a plateau in the drag coefficient at about CD˜0.22CD˜0.22, and a quasi-stable wake which has a non-dimensional width of dw/D˜0.4dw/D˜0.4. The periodic nature of the flow is analysed by means of measurements of the unsteady drag and lift coefficients. Power spectra of the lift fluctuations are computed. Wake vortex shedding is found to occur for both regimes investigated, although a jump in frequencies is observed when the flow enters the super-critical regime. In this regime, non-dimensional vortex-shedding frequency is almost constant and equal to St=fvsD/Uref˜0.44St=fvsD/Uref˜0.44. The analysis also shows a steep decrease in the fluctuating lift when entering the super-critical regime. The combined analysis of both wake topology and vortex shedding complements the physical picture of a stable and highly coherent flow in the super-critical regime.Numerical evaluation of multi-layered solid-PCM thermocline-like tanks as thermal energy storage systems for CSP applications
http://hdl.handle.net/2117/85680
Numerical evaluation of multi-layered solid-PCM thermocline-like tanks as thermal energy storage systems for CSP applications
Galione Klot, Pedro Andrés; Pérez Segarra, Carlos David; Rodríguez Pérez, Ivette María; Torras Ortiz, Santiago; Rigola Serrano, Joaquim
The two-tank system is the technology used for thermal energy storage (TES) in current concentrating solar power (CSP) plants. Thermocline storage concept has been considered for more than a decade as a possible solution to reduce the high cost of the storage system in these plants. In previous works, multi-layered solid-PCM (MLSPCM) thermocline-like storage tank configurations has been introduced and studied, giving promising results for their use as thermal energy storage systems for CSP. In this work, further analysis is performed in the use of this new concept of TES, by considering variable inlet conditions, and simulating the tank shell and the foundation. The numerical simulations are based on a modular object-oriented methodology. Energetic and exergetic results are presented and compared against a reference 2-tank case and against different thermocline configurations with either solid or phase change filler materials. Again, promising results are obtained for the tested MLSPCM concept.
2016-04-14T13:13:55ZGalione Klot, Pedro AndrésPérez Segarra, Carlos DavidRodríguez Pérez, Ivette MaríaTorras Ortiz, SantiagoRigola Serrano, JoaquimThe two-tank system is the technology used for thermal energy storage (TES) in current concentrating solar power (CSP) plants. Thermocline storage concept has been considered for more than a decade as a possible solution to reduce the high cost of the storage system in these plants. In previous works, multi-layered solid-PCM (MLSPCM) thermocline-like storage tank configurations has been introduced and studied, giving promising results for their use as thermal energy storage systems for CSP. In this work, further analysis is performed in the use of this new concept of TES, by considering variable inlet conditions, and simulating the tank shell and the foundation. The numerical simulations are based on a modular object-oriented methodology. Energetic and exergetic results are presented and compared against a reference 2-tank case and against different thermocline configurations with either solid or phase change filler materials. Again, promising results are obtained for the tested MLSPCM concept.Numerical simulation of non-adiabatic capillary tubes. Special emphasis on the near-saturation zone
http://hdl.handle.net/2117/85629
Numerical simulation of non-adiabatic capillary tubes. Special emphasis on the near-saturation zone
Ablanque Mejía, Nicolás; Oliet Casasayas, Carles; Rigola Serrano, Joaquim; Oliva Llena, Asensio
The aim of this article is to present a distributed numerical model that simulates the thermal and fluid-dynamic phenomena inside non-adiabatic capillary tubes. The resolution approach is based on a two-phase flow model where the fluid domain is discretized in a one-dimensional way, and the governing equations (continuity, momentum, and energy) are solved by means of a step-by-step algorithm. The model explained herein consists of an improved and extended version of previous works (Escanes et al., 1995; García-Valladares et al., 2002a,b; Ablanque et al., 2010) including two additional features. On the one hand, it allows the simulation of the two typical geometric arrangements found in capillary-tube/suction-line heat exchangers (i.e. concentric and lateral). On the other hand, it has an enhanced capability to address the convergence difficulties found in distributed models at the near-saturation zone. This document presents the major numerical adaptations done to the model, a comprehensive validation of the two geometric configurations, the model performance when tackling the aforementioned numerical difficulties and finally, some numerical studies.
2016-04-13T16:22:34ZAblanque Mejía, NicolásOliet Casasayas, CarlesRigola Serrano, JoaquimOliva Llena, AsensioThe aim of this article is to present a distributed numerical model that simulates the thermal and fluid-dynamic phenomena inside non-adiabatic capillary tubes. The resolution approach is based on a two-phase flow model where the fluid domain is discretized in a one-dimensional way, and the governing equations (continuity, momentum, and energy) are solved by means of a step-by-step algorithm. The model explained herein consists of an improved and extended version of previous works (Escanes et al., 1995; García-Valladares et al., 2002a,b; Ablanque et al., 2010) including two additional features. On the one hand, it allows the simulation of the two typical geometric arrangements found in capillary-tube/suction-line heat exchangers (i.e. concentric and lateral). On the other hand, it has an enhanced capability to address the convergence difficulties found in distributed models at the near-saturation zone. This document presents the major numerical adaptations done to the model, a comprehensive validation of the two geometric configurations, the model performance when tackling the aforementioned numerical difficulties and finally, some numerical studies.Building proper invariants for eddy-viscosity subgrid-scale models
http://hdl.handle.net/2117/85302
Building proper invariants for eddy-viscosity subgrid-scale models
Trias Miquel, Francesc Xavier; Folch, David; Gorobets, Andrei; Oliva Llena, Asensio
Direct simulations of the incompressible Navier-Stokes equations are limited to relatively low-Reynolds numbers. Hence, dynamically less complex mathematical formulations are necessary for coarse-grain simulations. Eddy-viscosity models for large-eddy simulation is probably the most popular example thereof: they rely on differential operators that should properly detect different flow configurations (laminar and 2D flows, near-wall behavior, transitional regime, etc.). Most of them are based on the combination of invariants of a symmetric tensor that depends on the gradient of the resolved velocity field, . In this work, models are presented within a framework consisting of a 5D phase space of invariants. In this way, new models can be constructed by imposing appropriate restrictions in this space. For instance, considering the three invariants P GG T , Q GG T , and R GG T of the tensorGG T , and imposing the proper cubic near-wall behavior, i.e., , we deduce that the eddy-viscosity is given by . Moreover, only R GG T -dependent models, i.e., p > - 5/2, switch off for 2D flows. Finally, the model constant may be related with the Vreman’s model constant via ; this guarantees both numerical stability and that the models have less or equal dissipation than Vreman’s model, i.e., . The performance of the proposed models is successfully tested for decaying isotropic turbulence and a turbulent channel flow. The former test-case has revealed that the model constant, C s3pqr , should be higher than 0.458 to obtain the right amount of subgrid-scale dissipation, i.e., C s3pq = 0.572 (p = - 5/2), C s3pr = 0.709 (p = - 1), and C s3qr = 0.762 (p = 0).
Copyright 2015 AIP Publishing. This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing.
2016-04-06T12:57:30ZTrias Miquel, Francesc XavierFolch, DavidGorobets, AndreiOliva Llena, AsensioDirect simulations of the incompressible Navier-Stokes equations are limited to relatively low-Reynolds numbers. Hence, dynamically less complex mathematical formulations are necessary for coarse-grain simulations. Eddy-viscosity models for large-eddy simulation is probably the most popular example thereof: they rely on differential operators that should properly detect different flow configurations (laminar and 2D flows, near-wall behavior, transitional regime, etc.). Most of them are based on the combination of invariants of a symmetric tensor that depends on the gradient of the resolved velocity field, . In this work, models are presented within a framework consisting of a 5D phase space of invariants. In this way, new models can be constructed by imposing appropriate restrictions in this space. For instance, considering the three invariants P GG T , Q GG T , and R GG T of the tensorGG T , and imposing the proper cubic near-wall behavior, i.e., , we deduce that the eddy-viscosity is given by . Moreover, only R GG T -dependent models, i.e., p > - 5/2, switch off for 2D flows. Finally, the model constant may be related with the Vreman’s model constant via ; this guarantees both numerical stability and that the models have less or equal dissipation than Vreman’s model, i.e., . The performance of the proposed models is successfully tested for decaying isotropic turbulence and a turbulent channel flow. The former test-case has revealed that the model constant, C s3pqr , should be higher than 0.458 to obtain the right amount of subgrid-scale dissipation, i.e., C s3pq = 0.572 (p = - 5/2), C s3pr = 0.709 (p = - 1), and C s3qr = 0.762 (p = 0).Parametric study of two-tank TES systems for CSP plants
http://hdl.handle.net/2117/83029
Parametric study of two-tank TES systems for CSP plants
Torras Ortiz, Santiago; Pérez Segarra, Carlos David; Rodríguez Pérez, Ivette María; Rigola Serrano, Joaquim; Oliva Llena, Asensio
The two-tank thermal energy storage (TES) system is the most used technology for storage in concentrating solar power (CSP) plants. This work focuses on a parametric study, which aims to identify the most important parameters on TES system, in order to improve the design and increase the performance of the plant. Three parameters have been considered: meteorological data, insulation thickness of the storage tank, and configuration of the foundation of the storage tank. The effect of each parameter is evaluated using numerical simulations based on a modular object-oriented methodology. The main issues related to the mathematical models and its numerical methodology are also presented in this paper.
2016-02-16T16:10:22ZTorras Ortiz, SantiagoPérez Segarra, Carlos DavidRodríguez Pérez, Ivette MaríaRigola Serrano, JoaquimOliva Llena, AsensioThe two-tank thermal energy storage (TES) system is the most used technology for storage in concentrating solar power (CSP) plants. This work focuses on a parametric study, which aims to identify the most important parameters on TES system, in order to improve the design and increase the performance of the plant. Three parameters have been considered: meteorological data, insulation thickness of the storage tank, and configuration of the foundation of the storage tank. The effect of each parameter is evaluated using numerical simulations based on a modular object-oriented methodology. The main issues related to the mathematical models and its numerical methodology are also presented in this paper.