55 resultados para Numerical Problems
Resumo:
Tämän työn tarkoituksena on koota yhteen selluprosessin mittausongelmat ja mahdolliset mittaustekniikat ongelmien ratkaisemiseksi. Pääpaino on online-mittaustekniikoissa. Työ koostuu kolmesta osasta. Ensimmäinen osa on kirjallisuustyö, jossa esitellään nykyaikaisen selluprosessin perusmittaukset ja säätötarpeet. Mukana on koko kuitulinja puunkäsittelystä valkaisuun ja kemikaalikierto: haihduttamo, soodakattila, kaustistamo ja meesauuni. Toisessa osassa mittausongelmat ja mahdolliset mittaustekniikat on koottu yhteen ”tiekartaksi”. Tiedot on koottu vierailemalla kolmella suomalaisella sellutehtaalla ja haastattelemalla laitetekniikka- ja mittaustekniikka-asiantuntijoita. Prosessikemian paremmalle ymmärtämiselle näyttää haastattelun perusteella olevan tarvetta, minkä vuoksi konsentraatiomittaukset on valittu jatkotutkimuskohteeksi. Viimeisessä osassa esitellään mahdollisia mittaustekniikoita konsentraatiomittausten ratkaisemiseksi. Valitut tekniikat ovat lähi-infrapunatekniikka (NIR), fourier-muunnosinfrapunatekniikka (FTIR), online-kapillaarielektroforeesi (CE) ja laserindusoitu plasmaemissiospektroskopia (LIPS). Kaikkia tekniikoita voi käyttää online-kytkettyinä prosessikehitystyökaluina. Kehityskustannukset on arvioitu säätöön kytketylle online-laitteelle. Kehityskustannukset vaihtelevat nollasta miestyövuodesta FTIR-tekniikalle viiteen miestyövuoteen CE-laitteelle; kehityskustannukset riippuvat tekniikan kehitysasteesta ja valmiusasteesta tietyn ongelman ratkaisuun. Työn viimeisessä osassa arvioidaan myös yhden mittausongelman – pesuhäviömittauksen – ratkaisemisen teknis-taloudellista kannattavuutta. Ligniinipitoisuus kuvaisi nykyisiä mittauksia paremmin todellista pesuhäviötä. Nykyään mitataan joko natrium- tai COD-pesuhäviötä. Ligniinipitoisuutta voidaan mitata UV-absorptiotekniikalla. Myös CE-laitetta voitaisiin käyttää pesuhäviön mittauksessa ainakin prosessikehitysvaiheessa. Taloudellinen tarkastelu pohjautuu moniin yksinkertaistuksiin ja se ei sovellu suoraan investointipäätösten tueksi. Parempi mittaus- ja säätöjärjestelmä voisi vakauttaa pesemön ajoa. Investointi ajoa vakauttavaan järjestelmään on kannattavaa, jos todellinen ajotilanne on tarpeeksi kaukana kustannusminimistä tai jos pesurin ajo heilahtelee eli pesuhäviön keskihajonta on suuri. 50 000 € maksavalle mittaus- ja säätöjärjestelmälle saadaan alle 0,5 vuoden takaisinmaksuaika epävakaassa ajossa, jos COD-pesuhäviön vaihteluväli on 5,2 – 11,6 kg/odt asetusarvon ollessa 8,4 kg/odt. Laimennuskerroin vaihtelee tällöin välillä 1,7 – 3,6 m3/odt asetusarvon ollessa 2,5 m3/odt.
Resumo:
This thesis studies the problems and their reasons a software architect faces in his work. The purpose of the study is to search and identify potential factors causing problens in system integration and software engineering. Under a special interest are non-technical factors causing different kinds of problems. Thesis was executed by interviewing professionals that took part in e-commerce project in some corporation. Interviewed professionals consisted of architects from technical implementation projects, corporation's architect team leader, different kind of project managers and CRM manager. A specific theme list was used as an guidance of the interviews. Recorded interviews were transcribed and then classified using ATLAS.ti software. Basics of e-commerce, software engineering and system integration is described too. Differences between e-commerce and e-business as well as traditional business are represented as are basic types of e-commerce. Software's life span, general problems of software engineering and software design are covered concerning software engineering. In addition, general problems of the system integration and the special requirements set by e-commerce are described in the thesis. In the ending there is a part where the problems founded in study are described and some areas of software engineering where some development could be done so that same kind of problems could be avoided in the future.
Resumo:
The transport of macromolecules, such as low-density lipoprotein (LDL), and their accumulation in the layers of the arterial wall play a critical role in the creation and development of atherosclerosis. Atherosclerosis is a disease of large arteries e.g., the aorta, coronary, carotid, and other proximal arteries that involves a distinctive accumulation of LDL and other lipid-bearing materials in the arterial wall. Over time, plaque hardens and narrows the arteries. The flow of oxygen-rich blood to organs and other parts of the body is reduced. This can lead to serious problems, including heart attack, stroke, or even death. It has been proven that the accumulation of macromolecules in the arterial wall depends not only on the ease with which materials enter the wall, but also on the hindrance to the passage of materials out of the wall posed by underlying layers. Therefore, attention was drawn to the fact that the wall structure of large arteries is different than other vessels which are disease-resistant. Atherosclerosis tends to be localized in regions of curvature and branching in arteries where fluid shear stress (shear rate) and other fluid mechanical characteristics deviate from their normal spatial and temporal distribution patterns in straight vessels. On the other hand, the smooth muscle cells (SMCs) residing in the media layer of the arterial wall respond to mechanical stimuli, such as shear stress. Shear stress may affect SMC proliferation and migration from the media layer to intima. This occurs in atherosclerosis and intimal hyperplasia. The study of blood flow and other body fluids and of heat transport through the arterial wall is one of the advanced applications of porous media in recent years. The arterial wall may be modeled in both macroscopic (as a continuous porous medium) and microscopic scales (as a heterogeneous porous medium). In the present study, the governing equations of mass, heat and momentum transport have been solved for different species and interstitial fluid within the arterial wall by means of computational fluid dynamics (CFD). Simulation models are based on the finite element (FE) and finite volume (FV) methods. The wall structure has been modeled by assuming the wall layers as porous media with different properties. In order to study the heat transport through human tissues, the simulations have been carried out for a non-homogeneous model of porous media. The tissue is composed of blood vessels, cells, and an interstitium. The interstitium consists of interstitial fluid and extracellular fibers. Numerical simulations are performed in a two-dimensional (2D) model to realize the effect of the shape and configuration of the discrete phase on the convective and conductive features of heat transfer, e.g. the interstitium of biological tissues. On the other hand, the governing equations of momentum and mass transport have been solved in the heterogeneous porous media model of the media layer, which has a major role in the transport and accumulation of solutes across the arterial wall. The transport of Adenosine 5´-triphosphate (ATP) is simulated across the media layer as a benchmark to observe how SMCs affect on the species mass transport. In addition, the transport of interstitial fluid has been simulated while the deformation of the media layer (due to high blood pressure) and its constituents such as SMCs are also involved in the model. In this context, the effect of pressure variation on shear stress is investigated over SMCs induced by the interstitial flow both in 2D and three-dimensional (3D) geometries for the media layer. The influence of hypertension (high pressure) on the transport of lowdensity lipoprotein (LDL) through deformable arterial wall layers is also studied. This is due to the pressure-driven convective flow across the arterial wall. The intima and media layers are assumed as homogeneous porous media. The results of the present study reveal that ATP concentration over the surface of SMCs and within the bulk of the media layer is significantly dependent on the distribution of cells. Moreover, the shear stress magnitude and distribution over the SMC surface are affected by transmural pressure and the deformation of the media layer of the aorta wall. This work reflects the fact that the second or even subsequent layers of SMCs may bear shear stresses of the same order of magnitude as the first layer does if cells are arranged in an arbitrary manner. This study has brought new insights into the simulation of the arterial wall, as the previous simplifications have been ignored. The configurations of SMCs used here with elliptic cross sections of SMCs closely resemble the physiological conditions of cells. Moreover, the deformation of SMCs with high transmural pressure which follows the media layer compaction has been studied for the first time. On the other hand, results demonstrate that LDL concentration through the intima and media layers changes significantly as wall layers compress with transmural pressure. It was also noticed that the fraction of leaky junctions across the endothelial cells and the area fraction of fenestral pores over the internal elastic lamina affect the LDL distribution dramatically through the thoracic aorta wall. The simulation techniques introduced in this work can also trigger new ideas for simulating porous media involved in any biomedical, biomechanical, chemical, and environmental engineering applications.
Resumo:
This dissertation analyses the growing pool of copyrighted works, which are offered to the public using Creative Commons licensing. The study consist of analysis of the novel licensing system, the licensors, and the changes of the "all rights reserved" —paradigm of copyright law. Copyright law reserves all rights to the creator until seventy years have passed since her demise. Many claim that this endangers communal interests. Quite often the creators are willing to release some rights. This, however, is very difficult to do and needs help of specialized lawyers. The study finds that the innovative Creative Commons licensing scheme is well suited for low value - high volume licensing. It helps to reduce transaction costs on several le¬vels. However, CC licensing is not a "silver bullet". Privacy, moral rights, the problems of license interpretation and license compatibility with other open licenses and collecting societies remain unsolved. The study consists of seven chapters. The first chapter introduces the research topic and research questions. The second and third chapters inspect the Creative Commons licensing scheme's technical, economic and legal aspects. The fourth and fifth chapters examine the incentives of the licensors who use open licenses and describe certain open business models. The sixth chapter studies the role of collecting societies and whether two institutions, Creative Commons and collecting societies can coexist. The final chapter summarizes the findings. The dissertation contributes to the existing literature in several ways. There is a wide range of prior research on open source licensing. However, there is an urgent need for an extensive study of the Creative Commons licensing and its actual and potential impact on the creative ecosystem.
Resumo:
There is an increasing reliance on computers to solve complex engineering problems. This is because computers, in addition to supporting the development and implementation of adequate and clear models, can especially minimize the financial support required. The ability of computers to perform complex calculations at high speed has enabled the creation of highly complex systems to model real-world phenomena. The complexity of the fluid dynamics problem makes it difficult or impossible to solve equations of an object in a flow exactly. Approximate solutions can be obtained by construction and measurement of prototypes placed in a flow, or by use of a numerical simulation. Since usage of prototypes can be prohibitively time-consuming and expensive, many have turned to simulations to provide insight during the engineering process. In this case the simulation setup and parameters can be altered much more easily than one could with a real-world experiment. The objective of this research work is to develop numerical models for different suspensions (fiber suspensions, blood flow through microvessels and branching geometries, and magnetic fluids), and also fluid flow through porous media. The models will have merit as a scientific tool and will also have practical application in industries. Most of the numerical simulations were done by the commercial software, Fluent, and user defined functions were added to apply a multiscale method and magnetic field. The results from simulation of fiber suspension can elucidate the physics behind the break up of a fiber floc, opening the possibility for developing a meaningful numerical model of the fiber flow. The simulation of blood movement from an arteriole through a venule via a capillary showed that the model based on VOF can successfully predict the deformation and flow of RBCs in an arteriole. Furthermore, the result corresponds to the experimental observation illustrates that the RBC is deformed during the movement. The concluding remarks presented, provide a correct methodology and a mathematical and numerical framework for the simulation of blood flows in branching. Analysis of ferrofluids simulations indicate that the magnetic Soret effect can be even higher than the conventional one and its strength depends on the strength of magnetic field, confirmed experimentally by Völker and Odenbach. It was also shown that when a magnetic field is perpendicular to the temperature gradient, there will be additional increase in the heat transfer compared to the cases where the magnetic field is parallel to the temperature gradient. In addition, the statistical evaluation (Taguchi technique) on magnetic fluids showed that the temperature and initial concentration of the magnetic phase exert the maximum and minimum contribution to the thermodiffusion, respectively. In the simulation of flow through porous media, dimensionless pressure drop was studied at different Reynolds numbers, based on pore permeability and interstitial fluid velocity. The obtained results agreed well with the correlation of Macdonald et al. (1979) for the range of actual flow Reynolds studied. Furthermore, calculated results for the dispersion coefficients in the cylinder geometry were found to be in agreement with those of Seymour and Callaghan.
Resumo:
Learning of preference relations has recently received significant attention in machine learning community. It is closely related to the classification and regression analysis and can be reduced to these tasks. However, preference learning involves prediction of ordering of the data points rather than prediction of a single numerical value as in case of regression or a class label as in case of classification. Therefore, studying preference relations within a separate framework facilitates not only better theoretical understanding of the problem, but also motivates development of the efficient algorithms for the task. Preference learning has many applications in domains such as information retrieval, bioinformatics, natural language processing, etc. For example, algorithms that learn to rank are frequently used in search engines for ordering documents retrieved by the query. Preference learning methods have been also applied to collaborative filtering problems for predicting individual customer choices from the vast amount of user generated feedback. In this thesis we propose several algorithms for learning preference relations. These algorithms stem from well founded and robust class of regularized least-squares methods and have many attractive computational properties. In order to improve the performance of our methods, we introduce several non-linear kernel functions. Thus, contribution of this thesis is twofold: kernel functions for structured data that are used to take advantage of various non-vectorial data representations and the preference learning algorithms that are suitable for different tasks, namely efficient learning of preference relations, learning with large amount of training data, and semi-supervised preference learning. Proposed kernel-based algorithms and kernels are applied to the parse ranking task in natural language processing, document ranking in information retrieval, and remote homology detection in bioinformatics domain. Training of kernel-based ranking algorithms can be infeasible when the size of the training set is large. This problem is addressed by proposing a preference learning algorithm whose computation complexity scales linearly with the number of training data points. We also introduce sparse approximation of the algorithm that can be efficiently trained with large amount of data. For situations when small amount of labeled data but a large amount of unlabeled data is available, we propose a co-regularized preference learning algorithm. To conclude, the methods presented in this thesis address not only the problem of the efficient training of the algorithms but also fast regularization parameter selection, multiple output prediction, and cross-validation. Furthermore, proposed algorithms lead to notably better performance in many preference learning tasks considered.
Resumo:
The article describes some concrete problems that were encountered when writing a two-level model of Mari morphology. Mari is an agglutinative Finno-Ugric language spoken in Russia by about 600 000 people. The work was begun in the 1980s on the basis of K. Koskenniemi’s Two-Level Morphology (1983), but in the latest stage R. Beesley’s and L. Karttunen’s Finite State Morphology (2003) was used. Many of the problems described in the article concern the inexplicitness of the rules in Mari grammars and the lack of information about the exact distribution of some suffixes, e.g. enclitics. The Mari grammars usually give complete paradigms for a few unproblematic verb stems, whereas the difficult or unclear forms of certain verbs are only superficially discussed. Another example of phenomena that are poorly described in grammars is the way suffixes with an initial sibilant combine to stems ending in a sibilant. The help of informants and searches from electronic corpora were used to overcome such difficulties in the development of the two-level model of Mari. The variation of the order of plural markers, case suffixes and possessive suffixes is a typical feature of Mari. The morphotactic rules constructed for Mari declensional forms tend to be recursive and their productivity must be limited by some technical device, such as filters. In the present model, certain plural markers were treated like nouns. The positional and functional versatility of the possessive suffixes can be regarded as the most challenging phenomenon in attempts to formalize the Mari morphology. Cyrillic orthography, which was used in the model, also caused problems. For instance, a Cyrillic letter may represent a sequence of two sounds, the first being part of the word stem while the other belongs to a suffix. In some cases, letters for voiced consonants are also generalized to represent voiceless consonants. Such orthographical conventions distance a morphological model based on orthography from the actual (morpho)phonological processes in the language.
Resumo:
The general striving to bring down the number of municipal landfills and to increase the reuse and recycling of waste-derived materials across the EU supports the debates concerning the feasibility and rationality of waste management systems. Substantial decrease in the volume and mass of landfill-disposed waste flows can be achieved by directing suitable waste fractions to energy recovery. Global fossil energy supplies are becoming more and more valuable and expensive energy sources for the mankind, and efforts to save fossil fuels have been made. Waste-derived fuels offer one potential partial solution to two different problems. First, waste that cannot be feasibly re-used or recycled is utilized in the energy conversion process according to EU’s Waste Hierarchy. Second, fossil fuels can be saved for other purposes than energy, mainly as transport fuels. This thesis presents the principles of assessing the most sustainable system solution for an integrated municipal waste management and energy system. The assessment process includes: · formation of a SISMan (Simple Integrated System Management) model of an integrated system including mass, energy and financial flows, and · formation of a MEFLO (Mass, Energy, Financial, Legislational, Other decisionsupport data) decision matrix according to the selected decision criteria, including essential and optional decision criteria. The methods are described and theoretical examples of the utilization of the methods are presented in the thesis. The assessment process involves the selection of different system alternatives (process alternatives for treatment of different waste fractions) and comparison between the alternatives. The first of the two novelty values of the utilization of the presented methods is the perspective selected for the formation of the SISMan model. Normally waste management and energy systems are operated separately according to the targets and principles set for each system. In the thesis the waste management and energy supply systems are considered as one larger integrated system with one primary target of serving the customers, i.e. citizens, as efficiently as possible in the spirit of sustainable development, including the following requirements: · reasonable overall costs, including waste management costs and energy costs; · minimum environmental burdens caused by the integrated waste management and energy system, taking into account the requirement above; and · social acceptance of the selected waste treatment and energy production methods. The integrated waste management and energy system is described by forming a SISMan model including three different flows of the system: energy, mass and financial flows. By defining the three types of flows for an integrated system, the selected factor results needed in the decision-making process of the selection of waste management treatment processes for different waste fractions can be calculated. The model and its results form a transparent description of the integrated system under discussion. The MEFLO decision matrix has been formed from the results of the SISMan model, combined with additional data, including e.g. environmental restrictions and regional aspects. System alternatives which do not meet the requirements set by legislation can be deleted from the comparisons before any closer numerical considerations. The second novelty value of this thesis is the three-level ranking method for combining the factor results of the MEFLO decision matrix. As a result of the MEFLO decision matrix, a transparent ranking of different system alternatives, including selection of treatment processes for different waste fractions, is achieved. SISMan and MEFLO are methods meant to be utilized in municipal decision-making processes concerning waste management and energy supply as simple, transparent and easyto- understand tools. The methods can be utilized in the assessment of existing systems, and particularly in the planning processes of future regional integrated systems. The principles of SISMan and MEFLO can be utilized also in other environments, where synergies of integrating two (or more) systems can be obtained. The SISMan flow model and the MEFLO decision matrix can be formed with or without any applicable commercial or free-of-charge tool/software. SISMan and MEFLO are not bound to any libraries or data-bases including process information, such as different emission data libraries utilized in life cycle assessments.
Resumo:
This thesis concentrates on developing a practical local approach methodology based on micro mechanical models for the analysis of ductile fracture of welded joints. Two major problems involved in the local approach, namely the dilational constitutive relation reflecting the softening behaviour of material, and the failure criterion associated with the constitutive equation, have been studied in detail. Firstly, considerable efforts were made on the numerical integration and computer implementation for the non trivial dilational Gurson Tvergaard model. Considering the weaknesses of the widely used Euler forward integration algorithms, a family of generalized mid point algorithms is proposed for the Gurson Tvergaard model. Correspondingly, based on the decomposition of stresses into hydrostatic and deviatoric parts, an explicit seven parameter expression for the consistent tangent moduli of the algorithms is presented. This explicit formula avoids any matrix inversion during numerical iteration and thus greatly facilitates the computer implementation of the algorithms and increase the efficiency of the code. The accuracy of the proposed algorithms and other conventional algorithms has been assessed in a systematic manner in order to highlight the best algorithm for this study. The accurate and efficient performance of present finite element implementation of the proposed algorithms has been demonstrated by various numerical examples. It has been found that the true mid point algorithm (a = 0.5) is the most accurate one when the deviatoric strain increment is radial to the yield surface and it is very important to use the consistent tangent moduli in the Newton iteration procedure. Secondly, an assessment of the consistency of current local failure criteria for ductile fracture, the critical void growth criterion, the constant critical void volume fraction criterion and Thomason's plastic limit load failure criterion, has been made. Significant differences in the predictions of ductility by the three criteria were found. By assuming the void grows spherically and using the void volume fraction from the Gurson Tvergaard model to calculate the current void matrix geometry, Thomason's failure criterion has been modified and a new failure criterion for the Gurson Tvergaard model is presented. Comparison with Koplik and Needleman's finite element results shows that the new failure criterion is fairly accurate indeed. A novel feature of the new failure criterion is that a mechanism for void coalescence is incorporated into the constitutive model. Hence the material failure is a natural result of the development of macroscopic plastic flow and the microscopic internal necking mechanism. By the new failure criterion, the critical void volume fraction is not a material constant and the initial void volume fraction and/or void nucleation parameters essentially control the material failure. This feature is very desirable and makes the numerical calibration of void nucleation parameters(s) possible and physically sound. Thirdly, a local approach methodology based on the above two major contributions has been built up in ABAQUS via the user material subroutine UMAT and applied to welded T joints. By using the void nucleation parameters calibrated from simple smooth and notched specimens, it was found that the fracture behaviour of the welded T joints can be well predicted using present methodology. This application has shown how the damage parameters of both base material and heat affected zone (HAZ) material can be obtained in a step by step manner and how useful and capable the local approach methodology is in the analysis of fracture behaviour and crack development as well as structural integrity assessment of practical problems where non homogeneous materials are involved. Finally, a procedure for the possible engineering application of the present methodology is suggested and discussed.
Resumo:
This work is devoted to the development of numerical method to deal with convection diffusion dominated problem with reaction term, non - stiff chemical reaction and stiff chemical reaction. The technique is based on the unifying Eulerian - Lagrangian schemes (particle transport method) under the framework of operator splitting method. In the computational domain, the particle set is assigned to solve the convection reaction subproblem along the characteristic curves created by convective velocity. At each time step, convection, diffusion and reaction terms are solved separately by assuming that, each phenomenon occurs separately in a sequential fashion. Moreover, adaptivities and projection techniques are used to add particles in the regions of high gradients (steep fronts) and discontinuities and transfer a solution from particle set onto grid point respectively. The numerical results show that, the particle transport method has improved the solutions of CDR problems. Nevertheless, the method is time consumer when compared with other classical technique e.g., method of lines. Apart from this advantage, the particle transport method can be used to simulate problems that involve movingsteep/smooth fronts such as separation of two or more elements in the system.
Resumo:
Supersonic axial turbine stages typically exhibit lower efficiencies than subsonic axial turbine stages. One reason for the lower efficiency is the occurrence of shock waves. With higher pressure ratios the flow inside the turbine becomes relatively easily supersonic if there is only one turbine stage. Supersonic axial turbines can be designed in smaller physical size compared to subsonic axial turbines of same power. This makes them good candidates for turbochargers in large diesel engines, where space can be a limiting factor. Also the production costs are lower for a supersonic axial turbine stage than for two subsonic stages. Since supersonic axial turbines are typically low reaction turbines, they also create lower axial forces to be compensated with bearings compared to high reaction turbines. The effect of changing the stator-rotor axial gap in a small high (rotational) speed supersonic axial flow turbine is studied in design and off-design conditions. Also the effect of using pulsatile mass flow at the supersonic stator inlet is studied. Five axial gaps (axial space between stator and rotor) are modeled using threedimensional computational fluid dynamics at the design and three axial gaps at the off-design conditions. Numerical reliability is studied in three independent studies. An additional measurement is made with the design turbine geometry at intermediate off-design conditions and is used to increase the reliability of the modelling. All numerical modelling is made with the Navier-Stokes solver Finflo employing Chien’s k ¡ ² turbulence model. The modelling of the turbine at the design and off-design conditions shows that the total-to-static efficiency of the turbine decreases when the axial gap is increased in both design and off-design conditions. The efficiency drops almost linearily at the off-design conditions, whereas the efficiency drop accelerates with increasing axial gap at the design conditions. The modelling of the turbine stator with pulsatile inlet flow reveals that the mass flow pulsation amplitude is decreased at the stator throat. The stator efficiency and pressure ratio have sinusoidal shapes as a function of time. A hysteresis-like behaviour is detected for stator efficiency and pressure ratio as a function of inlet mass flow, over one pulse period. This behaviour arises from the pulsatile inlet flow. It is important to have the smallest possible axial gap in the studied turbine type in order to maximize the efficiency. The results for the whole turbine can also be applied to some extent in similar turbines operating for example in space rocket engines. The use of a supersonic stator in a pulsatile inlet flow is shown to be possible.
Resumo:
Transitional flow past a three-dimensional circular cylinder is a widely studied phenomenon since this problem is of interest with respect to many technical applications. In the present work, the numerical simulation of flow past a circular cylinder, performed by using a commercial CFD code (ANSYS Fluent 12.1) with large eddy simulation (LES) and RANS (κ - ε and Shear-Stress Transport (SST) κ - ω! model) approaches. The turbulent flow for ReD = 1000 & 3900 is simulated to investigate the force coefficient, Strouhal number, flow separation angle, pressure distribution on cylinder and the complex three dimensional vortex shedding of the cylinder wake region. The numerical results extracted from these simulations have good agreement with the experimental data (Zdravkovich, 1997). Moreover, grid refinement and time-step influence have been examined. Numerical calculations of turbulent cross-flow in a staggered tube bundle continues to attract interest due to its importance in the engineering application as well as the fact that this complex flow represents a challenging problem for CFD. In the present work a time dependent simulation using κ – ε, κ - ω! and SST models are performed in two dimensional for a subcritical flow through a staggered tube bundle. The predicted turbulence statistics (mean and r.m.s velocities) have good agreement with the experimental data (S. Balabani, 1996). Turbulent quantities such as turbulent kinetic energy and dissipation rate are predicted using RANS models and compared with each other. The sensitivity of grid and time-step size have been analyzed. Model constants sensitivity study have been carried out by adopting κ – ε model. It has been observed that model constants are very sensitive to turbulence statistics and turbulent quantities.