Virtauslaskentaa ja energia-analyysiä hyödyntävä huoneilman lämpöolosuhteiden simulointimalli

Huonetilojen lämpöolosuhteiden hallinta on tärkeä osa talotekniikan suunnittelua. Tavallisesti huonetilan lämpöolosuhteita mallinnetaan menetelmillä, joissa lämpödynamiikkaa lasketaan huoneilmassa yhdessä laskentapisteessä ja rakenteissa seinäkohtaisesti. Tarkastelun kohteena on yleensä vain huoneilman lämpötila. Tämän diplomityön tavoitteena oli kehittää huoneilman lämpöolosuhteiden simulointimalli, jossa rakenteiden lämpödynamiikka lasketaan epästationaarisesti energia-analyysilaskennalla ja huoneilman virtauskenttä mallinnetaan valittuna ajanhetkenä stationaarisesti virtauslaskennalla. Tällöin virtauskentälle saadaan jakaumat suunnittelun kannalta olennaisista suureista, joita tyypillisesti ovat esimerkiksi ilman lämpötila ja nopeus. Simulointimallin laskentatuloksia verrattiin testihuonetiloissa tehtyihin mittauksiin. Tulokset osoittautuivat riittävän tarkoiksi talotekniikan suunnitteluun. Mallilla simuloitiin kaksi huonetilaa, joissa tarvittiin tavallista tarkempaa mallinnusta. Vertailulaskelmia tehtiin eri turbulenssimalleilla, diskretointitarkkuuksilla ja hilatiheyksillä. Simulointitulosten havainnollistamiseksi suunniteltiin asiakastuloste, jossa on esitetty suunnittelun kannalta olennaiset asiat. Simulointimallilla saatiin lisätietoa varsinkin lämpötilakerrostumista, joita tyypillisesti on arvioitu kokemukseen perustuen. Simulointimallin kehityksen taustana käsiteltiin rakennusten sisäilmastoa, lämpöolosuhteita ja laskentamenetelmiä sekä mallinnukseen soveltuvia kaupallisia ohjelmia. Simulointimallilla saadaan entistä tarkempaa ja yksityiskohtaisempaa tietoa lämpöolosuhteiden hallinnan suunnitteluun. Mallin käytön ongelmia ovat vielä virtauslaskennan suuri laskenta-aika, turbulenssin mallinnus, tuloilmalaitteiden reunaehtojen tarkka määritys ja laskennan konvergointi. Kehitetty simulointimalli tarjoaa hyvän perustan virtauslaskenta- ja energia-analyysiohjelmien kehittämiseksi ja yhdistämiseksi käyttäjäystävälliseksi talotekniikan suunnittelutyökaluksi.

Fluid dynamics simulation of right ventricular outflow tract oversizing.

OBJECTIVES: Repair of the right ventricular outflow tract (RVOT) in paediatric cardiac surgery remains challenging due to the high reoperation rate. Intimal hyperplasia and consequent arteriosclerosis is one of the most important limitation factors for graft durability. Since local shear stress and pressure are predictive elements for intimal hyperplasia and wall degeneration, we sought to determine in an oversized 12-mm RVOT model, with computed fluid dynamics simulation, the local haemodynamical factors that may explain intimal hyperplasia. This was done with the aim of identifying the optimal degree of oversizing for a 12-mm native RVOT. METHODS: Twenty domestic pigs, with a weight of 24.6 ± 0.89 kg and a native RVOT diameter of 12 ± 1.7 mm, had valve conduits of 12, 16, 18 and 20 mm implanted. Pressure and flow were measured at 75, 100 and 125% of normal flow at RVOT at the pulmonary artery, pulmonary artery bifurcation and at the left and right pulmonary arteries. Three-dimensional computed fluid dynamics (CFD) simulation in all four geometries in all flow modalities was performed. Local shear stress and pressure conditions were investigated. RESULTS: Corresponding to 75, 100 and 125% of steady-state flow, three inlet velocity profiles were obtained, 0.2, 0.29 and 0.36 m/s, respectively. At inflow velocity profiles, low shear stress areas, ranged from 0 to 2 Pa, combined with high-pressure areas ranging from 11.5 to 12.1 mmHg that were found at distal anastomosis, at bifurcation and at the ostia of the left and right pulmonary arteries in all geometries. CONCLUSIONS: In all three oversized geometries, the local reparation of shear stress and pressure in the 16-mm model showed a similar local profile as in the native 12 mm RVOT. According to these findings, we suggest oversizing the natural 12-mm RVOT by not more than 4 mm. The elements responsible for wall degeneration and intimal hyperplasia remain very similar to the conditions present in native RVOT.

Kuumailmapolttolaitteiston numeerinen virtausmallinnus

Tämä diplomityö perustuu Lappeenrannan teknillisen yliopiston Uusiutuvien energiajärjestelmien laboratorion koelaitteistoon, jolla tutkitaan voimakkaan savukaasunkierrätyksen ja kuumailmapolton soveltuvuutta pienen kokoluokan energiantuotantoprosesseihin. Työn teoriaosassa esitellään tavanomaisesta palamisesta eroavaa kuumailmapolttoa ja tarkastellaan sen ominaisuuksia. Myös työssä käytetyn tutkimusmenetelmän, numeerisen virtauslaskennan, periaatteita ja ominaisuuksia tarkastellaan. Työssä tutkitaan numeerisella virtausmallinnuksella kuumailmapolttolaitteiston virtauskentän käyttäytymistä, kun takaisin tulipesään kierrätettävän savukaasun määrä sekä tulipesän lämpöhäviöiden suuruus vaihtelevat. Virtauskentän tarkastelu on tärkeää, sillä palamisilman ja kierrätetyn savukaasun täytyy sekoittua kuumailmapolton aikaansaamiseksi. Työn virtausmallinnus suoritettiin Finflo-virtausratkaisijalla kaksiulotteisena palamisreaktioita mallintamatta. Vaikka työssä käytetyt mallit olivat kaksiulotteisia ja niissä käytettiin yksinkertaistuksia, virtausten käyttäytymisestä tulipesässä saatiin olennaista tietoa, jota voidaan mahdollisesti hyödyntää jatkotutkimuksissa.

Kuulakekoreaktorin sydämen jäähdytevirtauksen CFD-mallinnus

Kandidaatintyössä luotiin CFD-malli mallintamaan jäähdytevirtausta kuulakekoreaktorin sydämessä käyttämällä Ansys Fluent -ohjelmaa. Mallin avulla tarkasteltiin virtauksen käyttäymistä ja painehäviötä ja saatuja tuloksia verrattiin aiempiin tutkimuksiin. Kandidaatin työssä on myös kerrottu mallintamisen etenemisestä ja laskentateoriaa.

From Fluid Dynamics to Human Psychology.What Drives Financial Markets Towards Extreme Events

For decades researchers have been trying to build models that would help understand price performance in financial markets and, therefore, to be able to forecast future prices. However, any econometric approaches have notoriously failed in predicting extreme events in markets. At the end of 20th century, market specialists started to admit that the reasons for economy meltdowns may originate as much in rational actions of traders as in human psychology. The latter forces have been described as trading biases, also known as animal spirits. This study aims at expressing in mathematical form some of the basic trading biases as well as the idea of market momentum and, therefore, reconstructing the dynamics of prices in financial markets. It is proposed through a novel family of models originating in population and fluid dynamics, applied to an electricity spot price time series. The main goal of this work is to investigate via numerical solutions how well theequations succeed in reproducing the real market time series properties, especially those that seemingly contradict standard assumptions of neoclassical economic theory, in particular the Efficient Market Hypothesis. The results show that the proposed model is able to generate price realizations that closely reproduce the behaviour and statistics of the original electricity spot price. That is achieved in all price levels, from small and medium-range variations to price spikes. The latter were generated from price dynamics and market momentum, without superimposing jump processes in the model. In the light of the presented results, it seems that the latest assumptions about human psychology and market momentum ruling market dynamics may be true. Therefore, other commodity markets should be analyzed with this model as well.

Analysis and validation of space averaged drag model for numerical simulations of gas-solid flows in fluidized beds

This thesis presents an approach for formulating and validating a space averaged drag model for coarse mesh simulations of gas-solid flows in fluidized beds using the two-fluid model. Proper modeling for fluid dynamics is central in understanding any industrial multiphase flow. The gas-solid flows in fluidized beds are heterogeneous and usually simulated with the Eulerian description of phases. Such a description requires the usage of fine meshes and small time steps for the proper prediction of its hydrodynamics. Such constraint on the mesh and time step size results in a large number of control volumes and long computational times which are unaffordable for simulations of large scale fluidized beds. If proper closure models are not included, coarse mesh simulations for fluidized beds do not give reasonable results. The coarse mesh simulation fails to resolve the mesoscale structures and results in uniform solids concentration profiles. For a circulating fluidized bed riser, such predicted profiles result in a higher drag force between the gas and solid phase and also overestimated solids mass flux at the outlet. Thus, there is a need to formulate the closure correlations which can accurately predict the hydrodynamics using coarse meshes. This thesis uses the space averaging modeling approach in the formulation of closure models for coarse mesh simulations of the gas-solid flow in fluidized beds using Geldart group B particles. In the analysis of formulating the closure correlation for space averaged drag model, the main parameters for the modeling were found to be the averaging size, solid volume fraction, and distance from the wall. The closure model for the gas-solid drag force was formulated and validated for coarse mesh simulations of the riser, which showed the verification of this modeling approach. Coarse mesh simulations using the corrected drag model resulted in lowered values of solids mass flux. Such an approach is a promising tool in the formulation of appropriate closure models which can be used in coarse mesh simulations of large scale fluidized beds.

Oxidation rates of carbon and nitrogen in char residues from solid fuels

Computational fluid dynamics (CFD) modeling is an important tool in designing new combustion systems. By using CFD modeling, entire combustion systems can be modeled and the emissions and the performance can be predicted. CFD modeling can also be used to develop new and better combustion systems from an economical and environmental point of view. In CFD modeling of solid fuel combustion, the combustible fuel is generally treated as single fuel particles. One of the limitations with the CFD modeling concerns the sub-models describing the combustion of single fuel particles. Available models in the scientific literature are in many cases not suitable as submodels for CFD modeling since they depend on a large number of input parameters and are computationally heavy. In this thesis CFD-applicable models are developed for the combustion of single fuel particles. The single particle models can be used to improve the combustion performance in various combustion devices or develop completely new technologies. The investigated fields are oxidation of carbon (C) and nitrogen (N) in char residues from solid fuels. Modeled char-C oxidation rates are compared to experimental oxidation rates for a large number of pulverized solid fuel chars under relevant combustion conditions. The experiments have been performed in an isothermal plug flow reactor operating at 1123-1673 K and 3-15 vol.% O2. In the single particle model, the char oxidation is based on apparent kinetics and depends on three fuel specific parameters: apparent pre-exponential factor, apparent activation energy, and apparent reaction order. The single particle model can be incorporated as a sub-model into a CFD code. The results show that the modeled char oxidation rates are in good agreement with experimental char oxidation rates up to around 70% of burnout. Moreover, the results show that the activation energy and the reaction order can be assumed to be constant for a large number of bituminous coal chars under conditions limited by the combined effects of chemical kinetics and pore diffusion. Based on this, a new model based on only one fuel specific parameter is developed (Paper III). The results also show that reaction orders of bituminous coal chars and anthracite chars differ under similar conditions (Paper I and Paper II); reaction orders of bituminous coal chars were found to be one, while reaction orders of anthracite chars were determined to be zero. This difference in reaction orders has not previously been observed in the literature and should be considered in future char oxidation models. One of the most frequently used comprehensive char oxidation models could not explain the difference in the reaction orders. In the thesis (Paper II), a modification to the model is suggested in order to explain the difference in reaction orders between anthracite chars and bituminous coal chars. Two single particle models are also developed for the NO formation and reduction during the oxidation of single biomass char particles. In the models the char-N is assumed to be oxidized to NO and the NO is partly reduced inside the particle. The first model (Paper IV) is based on the concentration gradients of NO inside and outside the particle and the second model is simplified to such an extent that it is based on apparent kinetics and can be incorporated as a sub-model into a CFD code (Paper V). Modeled NO release rates from both models were in good agreement with experimental measurements from a single particle reactor of quartz glass operating at 1173-1323 K and 3-19 vol.% O2. In the future, the models can be used to reduce NO emissions in new combustion systems.

Development of a process for the direct synthesis of hydrogen peroxide in a novel microstructured reactor

Microreactors have proven to be versatile tools for process intensification. Over recent decades, they have increasingly been used for product and process development in chemical industries. Enhanced heat and mass transfer in the reactors due to the extremely high surfacearea- to-volume ratio and interfacial area allow chemical processes to be operated at extreme conditions. Safety is improved by the small holdup volume of the reactors and effective control of pressure and temperature. Hydrogen peroxide is a powerful green oxidant that is used in a wide range of industries. Reduction and auto-oxidation of anthraquinones is currently the main process for hydrogen peroxide production. Direct synthesis is a green alternative and has potential for on-site production. However, there are two limitations: safety concerns because of the explosive gas mixture produced and low selectivity of the process. The aim of this thesis was to develop a process for direct synthesis of hydrogen peroxide utilizing microreactor technology. Experimental and numerical approaches were applied for development of the microreactor. Development of a novel microreactor was commenced by studying the hydrodynamics and mass transfer in prototype microreactor plates. The prototypes were designed and fabricated with the assistance of CFD modeling to optimize the shape and size of the microstructure. Empirical correlations for the mass transfer coefficient were derived. The pressure drop in micro T-mixers was investigated experimentally and numerically. Correlations describing the friction factor for different flow regimes were developed and predicted values were in good agreement with experimental results. Experimental studies were conducted to develop a highly active and selective catalyst with a proper form for the microreactor. Pd catalysts supported on activated carbon cloths were prepared by different treatments during the catalyst preparation. A variety of characterization methods were used for catalyst investigation. The surface chemistry of the support and the oxidation state of the metallic phase in the catalyst play important roles in catalyst activity and selectivity for the direct synthesis. The direct synthesis of hydrogen peroxide was investigated in a bench-scale continuous process using the novel microreactor developed. The microreactor was fabricated based on the hydrodynamic and mass transfer studies and provided a high interfacial area and high mass transfer coefficient. The catalysts were prepared under optimum treatment conditions. The direct synthesis was conducted at various conditions. The thesis represents a step towards a commercially viable direct synthesis. The focus is on the two main challenges: mitigating the safety problem by utilization of microprocess technology and improving the selectivity by catalyst development.

Turbulenssimallien soveltuminen syklonien numeeriseen virtauslaskentaan

Tässä työssä tutkittiin miten totuudenmukaisia tuloksia syklonierottimen virtauskentästä saadaan numeerisella laskennalla, kun käytetään eri turbulenssimalleja. Tarkoitus oli myös selvittää yleisesti syklonin toimintaperiaatteita, haasteita sen käytössä sekä syklonin numeerisen virtauslaskennan perusteita. Numeerisen virtauslaskennan teoria selitetään pääpiirteittäin, samoin turbulenssin mallinnus. Työn laskentaosiossa simuloitiin Fluent-ohjelmalla syklonin virtauskenttää kuumalla ilmalla sekä kahdella eri turbulenssimallilla ja verrattiin tuloksia kirjallisuudesta löytyviin mittaustuloksiin. Simuloinnit suoritettiin sekä ajasta riippuvana että ajasta riippumattomana ja kahdella eri laskentahilalla. Simulointien tulokset osoittivat, että RNG k-ε turbulenssimalli ei kykene tuottamaan totuu-denmukaista virtauskenttää. Toisen käytetyn turbulenssimallin, Reynolds-jännitysmallin tulokset vastasivat enemmän mittaustuloksia. Reynolds-jännitysmallia voidaan pitää käyttökelpoisena syklonin simuloinnissa tämän työn ja kirjallisuuden perusteella. Mallissa oli yksinkertaistuksia, esimerkiksi kiinteää ainetta ei otettu huomioon lainkaan.

Working fluid selection and design of small-scale waste heat recovery systems based on organic Rankine cycles

Demand for the use of energy systems, entailing high efficiency as well as availability to harness renewable energy sources, is a key issue in order to tackling the threat of global warming and saving natural resources. Organic Rankine cycle (ORC) technology has been identified as one of the most promising technologies in recovering low-grade heat sources and in harnessing renewable energy sources that cannot be efficiently utilized by means of more conventional power systems. The ORC is based on the working principle of Rankine process, but an organic working fluid is adopted in the cycle instead of steam. This thesis presents numerical and experimental results of the study on the design of small-scale ORCs. Two main applications were selected for the thesis: waste heat re- covery from small-scale diesel engines concentrating on the utilization of the exhaust gas heat and waste heat recovery in large industrial-scale engine power plants considering the utilization of both the high and low temperature heat sources. The main objective of this work was to identify suitable working fluid candidates and to study the process and turbine design methods that can be applied when power plants based on the use of non-conventional working fluids are considered. The computational work included the use of thermodynamic analysis methods and turbine design methods that were based on the use of highly accurate fluid properties. In addition, the design and loss mechanisms in supersonic ORC turbines were studied by means of computational fluid dynamics. The results indicated that the design of ORC is highly influenced by the selection of the working fluid and cycle operational conditions. The results for the turbine designs in- dicated that the working fluid selection should not be based only on the thermodynamic analysis, but requires also considerations on the turbine design. The turbines tend to be fast rotating, entailing small blade heights at the turbine rotor inlet and highly supersonic flow in the turbine flow passages, especially when power systems with low power outputs are designed. The results indicated that the ORC is a potential solution in utilizing waste heat streams both at high and low temperatures and both in micro and larger scale appli- cations.

Two-phase flow measurements with spacer grid in a rod bundle geometry

Heat transfer effectiveness in nuclear rod bundles is of great importance to nuclear reactor safety and economics. An important design parameter is the Critical Heat Flux (CHF), which limits the transferred heat from the fuel to the coolant. The CHF is determined by flow behaviour, especially the turbulence created inside the fuel rod bundle. Adiabatic experiments can be used to characterize the flow behaviour separately from the heat transfer phenomena in diabatic flow. To enhance the turbulence, mixing vanes are attached to spacer grids, which hold the rods in place. The vanes either make the flow swirl around a single sub-channel or induce cross-mixing between adjacent sub-channels. In adiabatic two-phase conditions an important phenomenon that can be investigated is the effect of the spacer on canceling the lift force, which collects the small bubbles to the rod surfaces leading to decreased CHF in diabatic conditions and thus limits the reactor power. Computational Fluid Dynamics (CFD) can be used to simulate the flow numerically and to test how different spacer configurations affect the flow. Experimental data is needed to validate and verify the used CFD models. Especially the modeling of turbulence is challenging even for single-phase flow inside the complex sub-channel geometry. In two-phase flow other factors such as bubble dynamics further complicate the modeling. To investigate the spacer grid effect on two-phase flow, and to provide further experimental data for CFD validation, a series of experiments was run on an adiabatic sub-channel flow loop using a duct-type spacer grid with different configurations. Utilizing the wire-mesh sensor technology, the facility gives high resolution experimental data in both time and space. The experimental results indicate that the duct-type spacer grid is less effective in canceling the lift force effect than the egg-crate type spacer tested earlier.

Large-eddy simulation of wind flows over complex terrains for wind energy applications

Wind energy has obtained outstanding expectations due to risks of global warming and nuclear energy production plant accidents. Nowadays, wind farms are often constructed in areas of complex terrain. A potential wind farm location must have the site thoroughly surveyed and the wind climatology analyzed before installing any hardware. Therefore, modeling of Atmospheric Boundary Layer (ABL) flows over complex terrains containing, e.g. hills, forest, and lakes is of great interest in wind energy applications, as it can help in locating and optimizing the wind farms. Numerical modeling of wind flows using Computational Fluid Dynamics (CFD) has become a popular technique during the last few decades. Due to the inherent flow variability and large-scale unsteadiness typical in ABL flows in general and especially over complex terrains, the flow can be difficult to be predicted accurately enough by using the Reynolds-Averaged Navier-Stokes equations (RANS). Large- Eddy Simulation (LES) resolves the largest and thus most important turbulent eddies and models only the small-scale motions which are more universal than the large eddies and thus easier to model. Therefore, LES is expected to be more suitable for this kind of simulations although it is computationally more expensive than the RANS approach. With the fast development of computers and open-source CFD software during the recent years, the application of LES toward atmospheric flow is becoming increasingly common nowadays. The aim of the work is to simulate atmospheric flows over realistic and complex terrains by means of LES. Evaluation of potential in-land wind park locations will be the main application for these simulations. Development of the LES methodology to simulate the atmospheric flows over realistic terrains is reported in the thesis. The work also aims at validating the LES methodology at a real scale. In the thesis, LES are carried out for flow problems ranging from basic channel flows to real atmospheric flows over one of the most recent real-life complex terrain problems, the Bolund hill. All the simulations reported in the thesis are carried out using a new OpenFOAM® -based LES solver. The solver uses the 4th order time-accurate Runge-Kutta scheme and a fractional step method. Moreover, development of the LES methodology includes special attention to two boundary conditions: the upstream (inflow) and wall boundary conditions. The upstream boundary condition is generated by using the so-called recycling technique, in which the instantaneous flow properties are sampled on aplane downstream of the inlet and mapped back to the inlet at each time step. This technique develops the upstream boundary-layer flow together with the inflow turbulence without using any precursor simulation and thus within a single computational domain. The roughness of the terrain surface is modeled by implementing a new wall function into OpenFOAM® during the thesis work. Both, the recycling method and the newly implemented wall function, are validated for the channel flows at relatively high Reynolds number before applying them to the atmospheric flow applications. After validating the LES model over simple flows, the simulations are carried out for atmospheric boundary-layer flows over two types of hills: first, two-dimensional wind-tunnel hill profiles and second, the Bolund hill located in Roskilde Fjord, Denmark. For the twodimensional wind-tunnel hills, the study focuses on the overall flow behavior as a function of the hill slope. Moreover, the simulations are repeated using another wall function suitable for smooth surfaces, which already existed in OpenFOAM® , in order to study the sensitivity of the flow to the surface roughness in ABL flows. The simulated results obtained using the two wall functions are compared against the wind-tunnel measurements. It is shown that LES using the implemented wall function produces overall satisfactory results on the turbulent flow over the two-dimensional hills. The prediction of the flow separation and reattachment-length for the steeper hill is closer to the measurements than the other numerical studies reported in the past for the same hill geometry. The field measurement campaign performed over the Bolund hill provides the most recent field-experiment dataset for the mean flow and the turbulence properties. A number of research groups have simulated the wind flows over the Bolund hill. Due to the challenging features of the hill such as the almost vertical hill slope, it is considered as an ideal experimental test case for validating micro-scale CFD models for wind energy applications. In this work, the simulated results obtained for two wind directions are compared against the field measurements. It is shown that the present LES can reproduce the complex turbulent wind flow structures over a complicated terrain such as the Bolund hill. Especially, the present LES results show the best prediction of the turbulent kinetic energy with an average error of 24.1%, which is a 43% smaller than any other model results reported in the past for the Bolund case. Finally, the validated LES methodology is demonstrated to simulate the wind flow over the existing Muukko wind farm located in South-Eastern Finland. The simulation is carried out only for one wind direction and the results on the instantaneous and time-averaged wind speeds are briefly reported. The demonstration case is followed by discussions on the practical aspects of LES for the wind resource assessment over a realistic inland wind farm.

Kalman filter for computational market dynamics

Kalman filter is a recursive mathematical power tool that plays an increasingly vital role in innumerable fields of study. The filter has been put to service in a multitude of studies involving both time series modelling and financial time series modelling. Modelling time series data in Computational Market Dynamics (CMD) can be accomplished using the Jablonska-Capasso-Morale (JCM) model. Maximum likelihood approach has always been utilised to estimate the parameters of the JCM model. The purpose of this study is to discover if the Kalman filter can be effectively utilized in CMD. Ensemble Kalman filter (EnKF), with 50 ensemble members, applied to US sugar prices spanning the period of January, 1960 to February, 2012 was employed for this work. The real data and Kalman filter trajectories showed no significant discrepancies, hence indicating satisfactory performance of the technique. Since only US sugar prices were utilized, it would be interesting to discover the nature of results if other data sets are employed.

Computational Market Dynamics of Virtual Economies

The last two decades have provided a vast opportunity to live and explore the compulsive imaginary world or virtual world through massively multiplayer online role-playing games (MMORPGs). MMORPG gives a wide range of opportunities to its users to participate with multi-players on the same platform, to communicate and to do real time actions. There is a virtual economy in these games which is largely player-driven. In-game currency provides its users to build up their Avatars, to buy or sell the necessary goods to play, survive in the games and so on. As a part of virtual economies generated through EVE Online, this thesis mainly focuses on how the prices of the minerals in EVE Online behave by applying the Jabłonska- Capasso-Morale (JCM) mathematical simulation model. It is to verify up to what degree the model can reproduce the virtual economy behavior. The model is applied to buy and sell prices of two minerals namely, isogen and morphite. The simulation results demonstrate that JCM model ts reasonably well to the mineral prices, which lets us conclude that virtual economies behave similarly to the real ones.