Wavelet Analysis in Turbulence

The objective of this thesis is to study wavelets and their role in turbulence applications. Under scrutiny in the thesis is the intermittency in turbulence models. Wavelets are used as a mathematical tool to study the intermittent activities that turbulence models produce. The first section generally introduces wavelets and wavelet transforms as a mathematical tool. Moreover, the basic properties of turbulence are discussed and classical methods for modeling turbulent flows are explained. Wavelets are implemented to model the turbulence as well as to analyze turbulent signals. The model studied here is the GOY (Gledzer 1973, Ohkitani & Yamada 1989) shell model of turbulence, which is a popular model for explaining intermittency based on the cascade of kinetic energy. The goal is to introduce better quantification method for intermittency obtained in a shell model. Wavelets are localized in both space (time) and scale, therefore, they are suitable candidates for the study of singular bursts, that interrupt the calm periods of an energy flow through various scales. The study concerns two questions, namely the frequency of the occurrence as well as the intensity of the singular bursts at various Reynolds numbers. The results gave an insight that singularities become more local as Reynolds number increases. The singularities become more local also when the shell number is increased at certain Reynolds number. The study revealed that the singular bursts are more frequent at Re ~ 107 than other cases with lower Re. The intermittency of bursts for the cases with Re ~ 106 and Re ~ 105 was similar, but for the case with Re ~ 104 bursts occured after long waiting time in a different fashion so that it could not be scaled with higher Re.

Computational and Experimental Analysis of Flow Field in the Diffusers of Centrifugal Compressors

Centrifugal compressors are widely used for example in process industry, oil and gas industry, in small gas turbines and turbochargers. In order to achieve lower consumption of energy and operation costs the efficiency of the compressor needs to be improve. In the present work different pinches and low solidity vaned diffusers were utilized in order to improve the efficiency of a medium size centrifugal compressor. In this study, pinch means the decrement of the diffuser flow passage height. First different geometries were analyzed using computational fluid dynamics. The flow solver Finflo was used to solve the flow field. Finflo is a Navier-Stokes solver. The solver is capable to solve compressible, incompressible, steady and unsteady flow fields. Chien's k-e turbulence model was used. One of the numerically investigated pinched diffuser and one low solidity vaned diffuser were studied experimentally. The overall performance of the compressor and the static pressure distribution before and after the diffuser were measured. The flow entering and leaving the diffuser was measured using a three-hole Cobra-probe and Kiel-probes. The pinch and the low solidity vaned diffuser increased the efficiency of the compressor. Highest isentropic efficiency increment obtained was 3\% of the design isentropic efficiency of the original geometry. It was noticed in the numerical results that the pinch made to the hub and the shroud wall was most beneficial to the operation of the compressor. Also the pinch made to the hub was better than the pinchmade to the shroud. The pinch did not affect the operation range of the compressor, but the low solidity vaned diffuser slightly decreased the operation range.The unsteady phenomena in the vaneless diffuser were studied experimentally andnumerically. The unsteady static pressure was measured at the diffuser inlet and outlet, and time-accurate numerical simulation was conducted. The unsteady static pressure showed that most of the pressure variations lay at the passing frequency of every second blade. The pressure variations did not vanish in the diffuser and were visible at the diffuser outlet. However, the amplitude of the pressure variations decreased in the diffuser. The time-accurate calculations showed quite a good agreement with the measured data. Agreement was very good at the design operation point, even though the computational grid was not dense enough inthe volute and in the exit cone. The time-accurate calculation over-predicted the amplitude of the pressure variations at high flow.

Computational Analysis and Optimization of Real Gas Flow In Small Centrifugal Compressors

Small centrifugal compressors are more and more widely used in many industrialsystems because of their higher efficiency and better off-design performance comparing to piston and scroll compressors as while as higher work coefficient perstage than in axial compressors. Higher efficiency is always the aim of the designer of compressors. In the present work, the influence of four partsof a small centrifugal compressor that compresses heavy molecular weight real gas has been investigated in order to achieve higher efficiency. Two parts concern the impeller: tip clearance and the circumferential position of the splitter blade. The other two parts concern the diffuser: the pinch shape and vane shape. Computational fluid dynamics is applied in this study. The Reynolds averaged Navier-Stokes flow solver Finflo is used. The quasi-steady approach is utilized. Chien's k-e turbulence model is used to model the turbulence. A new practical real gas model is presented in this study. The real gas model is easily generated, accuracy controllable and fairly fast. The numerical results and measurements show good agreement. The influence of tip clearance on the performance of a small compressor is obvious. The pressure ratio and efficiency are decreased as the size of tip clearance is increased, while the total enthalpy rise keeps almost constant. The decrement of the pressure ratio and efficiency is larger at higher mass flow rates and smaller at lower mass flow rates. The flow angles at the inlet and outlet of the impeller are increased as the size of tip clearance is increased. The results of the detailed flow field show that leakingflow is the main reason for the performance drop. The secondary flow region becomes larger as the size of tip clearance is increased and the area of the main flow is compressed. The flow uniformity is then decreased. A detailed study shows that the leaking flow rate is higher near the exit of the impeller than that near the inlet of the impeller. Based on this phenomenon, a new partiallyshrouded impeller is used. The impeller is shrouded near the exit of the impeller. The results show that the flow field near the exit of the impeller is greatly changed by the partially shrouded impeller, and better performance is achievedthan with the unshrouded impeller. The loading distribution on the impeller blade and the flow fields in the impeller is changed by moving the splitter of the impeller in circumferential direction. Moving the splitter slightly to the suction side of the long blade can improve the performance of the compressor. The total enthalpy rise is reduced if only the leading edge of the splitter ismoved to the suction side of the long blade. The performance of the compressor is decreased if the blade is bended from the radius direction at the leading edge of the splitter. The total pressure rise and the enthalpy rise of thecompressor are increased if pinch is used at the diffuser inlet. Among the fivedifferent pinch shape configurations, at design and lower mass flow rates the efficiency of a straight line pinch is the highest, while at higher mass flow rate, the efficiency of a concave pinch is the highest. The sharp corner of the pinch is the main reason for the decrease of efficiency and should be avoided. The variation of the flow angles entering the diffuser in spanwise direction is decreased if pinch is applied. A three-dimensional low solidity twisted vaned diffuser is designed to match the flow angles entering the diffuser. The numerical results show that the pressure recovery in the twisted diffuser is higher than in a conventional low solidity vaned diffuser, which also leads to higher efficiency of the twisted diffuser. Investigation of the detailed flow fields shows that the separation at lower mass flow rate in the twisted diffuser is later than in the conventional low solidity vaned diffuser, which leads to a possible wider flow range of the twisted diffuser.

Comprehensive Study of Crystal Growth from Solution

Crystal growth is an essential phase in crystallization kinetics. The rate of crystal growth provides significant information for the design and control of crystallization processes; nevertheless, obtaining accurate growth rate data is still challenging due to a number of factors that prevail in crystal growth. In industrial crystallization, crystals are generally grown from multi-componentand multi-particle solutions under complicated hydrodynamic conditions; thus, it is crucial to increase the general understanding of the growth kinetics in these systems. The aim of this work is to develop a model of the crystal growth rate from solution. An extensive literature review of crystal growth focuses on themodelling of growth kinetics and thermodynamics, and new measuring techniques that have been introduced in the field of crystallization. The growth of a singlecrystal is investigated in binary and ternary systems. The binary system consists of potassium dihydrogen phosphate (KDP, crystallizing solute) and water (solvent), and the ternary system includes KDP, water and an organic admixture. The studied admixtures, urea, ethanol and 1-propanol, are employed at relatively highconcentrations (of up to 5.0 molal). The influence of the admixtures on the solution thermodynamics is studied using the Pitzer activity coefficient model. Theprediction method of the ternary solubility in the studied systems is introduced and verified. The growth rate of the KDP (101) face in the studied systems aremeasured in the growth cell as a function of supersaturation, the admixture concentration, the solution velocity over a crystal and temperature. In addition, the surface morphology of the KDP (101) face is studied using ex situ atomic force microscopy (AFM). The crystal growth rate in the ternary systems is modelled on the basis of the two-step growth model that contains the Maxwell-Stefan (MS) equations and a surface-reaction model. This model is used together with measuredcrystal growth rate data to develop a new method for the evaluation of the model parameters. The validation of the model is justified with experiments. The crystal growth rate in an imperfectly mixed suspension crystallizer is investigatedusing computational fluid dynamics (CFD). A solid-liquid suspension flow that includes multi-sized particles is described by the multi-fluid model as well as by a standard k-epsilon turbulence model and an interface momentum transfer model. The local crystal growth rate is determined from calculated flow information in a diffusion-controlled crystal growth regime. The calculated results are evaluated experimentally.

Lämmönsiirron numeerinen laskenta profiloidulle kanavalle.

Työn tavoitteena oli tutkia aaltomaisen profiloinnin vaikutusta suorien jäähdytyskanavien lämmönsiirtoon ja painehäviöön. Erilaisia profiileja oli kymmenen kappaletta ja ne olivat 5mm leveitä ja 30cm pitkiä kukin. Ne laskettiin kolmeulotteisina tapauksina FINFLO-virtausratkaisijalla kolmella eri Reynoldsin luvulla, jotka vastasivat laminaarista, osittain turbulenttista ja lähes kokonaan turbulenttista virtausta. Lämmönsiirtoaine oli kuiva +30°C ilma ja profiloinnin toteutustapa oli toisiaan sivuavat ympyräkaaret kolmella erilaisella säteen arvolla ja kolmella erilaisella aallonpituuden arvolla. Lisäksi laskettiin saman levyisen tasokanavan arvot jokaisella Reynoldsin luvulla kaksiulotteisina tapauksina. Näitä profiloimattomia kanavia pidettiin referenssitapauksina. Tuloksena havaittiin että profiloimalla saadaan yksiselitteisesti suurempi lämpöteho ulos samasta tilavuudesta. Lämmönsiirtokerroin kasvaa profiloinnin avulla parhaimmillaan n. 20% käytetystä turbulenssimallista tai lämmönsiirtokertoimen määritelmästä riippumatta. Painehäviö kasvaa myös aina, mutta kitkakerroin voi hieman pienentyä. Profiilin varsinaisena hyvyyskriteerinä pidettiin lämmönsiirtokertoimen ja kitkakertoimen suhdetta h/f. Se osoittautui riippuvaksi Reynoldsin luvusta ja turbulenssimallista; ASM ja Chien k-έ -mallit ennustavat transitioetäisyyden eri tavalla. Laminaarisilla virtauksilla h/f :n vaihtelu oli vähäistä; suhde vaihteli vain ±5% eri profiilien kesken. ASM-mallilla havaittiin sekundääripyörteilyä, ehkä siksi että se mallintaa anisotrooppisen turbulenssin. Chien k-έ malli ennusti suuremman ja aikaisemmin alkavan turbulenttisuuden kuin ASM. Lisäksi havaittiin mm. että tietyillä profiileilla muodostuu kanavan kapeimpaan kohtaan selvä virtausnopeuden paikallinen minimi seinämän läheisyyden takia.

Ilmanjaon päätelaitteen virtauskentän mallintaminen

Tässä työssä esitetään tuloilmalaitteen virtausten laskennallinen tarkastelu huonetilassa virtauslaskentaohjelmiston avulla. Tarkastelu suoritetaan kolmiulotteisena sekä isotermisille että termisille tapauksille, jolloin huonetilan joihinkin pintoihin asetetaan lämpövuo ja epäpuhtauslähde. Työn tarkoituksena on arvioida CFX -virtauslaskentaohjelmiston soveltuvuutta huonetilavirtausten mallintamiseen ja tarkastella huonetilan ilmanvaihdon tehokkuutta eri tapauksissa. Arviointi suoritetaan vertaamalla laskentatuloksia mittaustuloksiin. Turbulenssimallien vaikutusta on arvioitu käyttämällä nollan yhtälön ja standardi k-e turbulenssimalleja. CFX:n k-e turbulenssimallilla lasketut nopeuden alenemat eri tilavuusvirroilla vastasivat paremmin mittaustuloksia kuin nollan yhtälön turbulenssimallilla, jolla erot olivat huomattavia. Huonetilan ilmanvaihdon tehokkuus vaihteli suuresti tuloilmalaitteen sijoituspaikan ja lämpövuon mukaan.

Performance Improvement of Centrifugal Compressor Stage with Pinched Geometry or Vaned Diffuser

Centrifugal compressors are widely used for example in refrigeration processes, the oil and gas industry, superchargers, and waste water treatment. In this work, five different vaneless diffusers and six different vaned diffusers are investigated numerically. The vaneless diffusers vary only by their diffuser width, so that four of the geometries have pinch implemented to them. Pinch means a decrease in the diffuser width. Four of the vaned diffusers have the same vane turning angle and a different number of vanes, and two have different vane turning angles. The flow solver used to solve the flow fields is Finflo, which is a Navier-Stokes solver. All the cases are modeled with the Chien's k – έ- turbulence model, and selected cases are modeled also with the k – ώ-SST turbulence model. All five vaneless diffusers and three vaned diffusers are investigated also experimentally. For each construction, the compressor operating map is measured according to relevant standards. In addition to this, the flow fields before and after the diffuser are measured with static and total pressure, flow angle and total temperature measurements. When comparing the computational results to the measured results, it is evident that the k – ώ-SST turbulence model predicts the flow fields better. The simulation results indicate that it is possible to improve the efficiency with the pinch, and according to the numerical results, the two best geometries are the ones with most pinch at the shroud. These geometries have approximately 4 percentage points higher efficiency than the unpinched vaneless diffusers. The hub pinch does not seem to have any major benefits. In general, the pinches make the flow fields before and after the diffuser more uniform. The pinch also seems to improve the impeller efficiency. This is down to two reasons. The major reason is that the pinch decreases the size of slow flow and possible backflow region located near the shroud after the impeller. Secondly, the pinches decrease the flow velocity in the tip clearance, leading to a smaller tip leakage flow and therefore slightly better impeller efficiency. Also some of the vaned diffusers improve the efficiency, the increment being 1...3 percentage points, when compared to the vaneless unpinched geometry. The measurement results confirm that the pinch is beneficial to the performance of the compressor. The flow fields are more uniform with the pinched cases, and the slow flow regions are smaller. The peak efficiency is approximately 2 percentage points and the design point efficiency approximately 4 percentage points higher with the pinched geometries than with the un- pinched geometry. According to the measurements, the two best geometries are the ones with the most pinch at the shroud, the case with the pinch only at the shroud being slightly better of the two. The vaned diffusers also have better efficiency than the vaneless unpinched geometries. However, the pinched cases have even better efficiencies. The vaned diffusers narrow the operating range considerably, whilst the pinch has no significant effect on the operating range.

Separation of Gas Bubbles from Circulation Waters and Pulp Suspensions in Open Channel Flow

The objective of this thesis was to study the removal of gases from paper mill circulation waters experimentally and to provide data for CFD modeling. Flow and bubble size measurements were carried out in a laboratory scale open gas separation channel. Particle Image Velocimetry (PIV) technique was used to measure the gas and liquid flow fields, while bubble size measurements were conducted using digital imaging technique with back light illumination. Samples of paper machine waters as well as a model solution were used for the experiments. The PIV results show that the gas bubbles near the feed position have the tendency to escape from the circulation channel at a faster rate than those bubbles which are further away from the feed position. This was due to an increased rate of bubble coalescence as a result of the relatively larger bubbles near the feed position. Moreover, a close similarity between the measured slip velocities of the paper mill waters and that of literature values was obtained. It was found that due to dilution of paper mill waters, the observed average bubble size was considerably large as compared to the average bubble sizes in real industrial pulp suspension and circulation waters. Among the studied solutions, the model solution has the highest average drag coefficient value due to its relatively high viscosity. The results were compared to a 2D steady sate CFD simulation model. A standard Euler-Euler k-ε turbulence model was used in the simulations. The channel free surface was modeled as a degassing boundary. From the drag models used in the simulations, the Grace drag model gave velocity fields closest to the experimental values. In general, the results obtained from experiments and CFD simulations are in good qualitative agreement.

Numerical modelling of small supersonic axial flow turbines

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.

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.

Application and development of numerical methods for the modelling of innovative gas cooled fission reactors

Innovative gas cooled reactors, such as the pebble bed reactor (PBR) and the gas cooled fast reactor (GFR) offer higher efficiency and new application areas for nuclear energy. Numerical methods were applied and developed to analyse the specific features of these reactor types with fully three dimensional calculation models. In the first part of this thesis, discrete element method (DEM) was used for a physically realistic modelling of the packing of fuel pebbles in PBR geometries and methods were developed for utilising the DEM results in subsequent reactor physics and thermal-hydraulics calculations. In the second part, the flow and heat transfer for a single gas cooled fuel rod of a GFR were investigated with computational fluid dynamics (CFD) methods. An in-house DEM implementation was validated and used for packing simulations, in which the effect of several parameters on the resulting average packing density was investigated. The restitution coefficient was found out to have the most significant effect. The results can be utilised in further work to obtain a pebble bed with a specific packing density. The packing structures of selected pebble beds were also analysed in detail and local variations in the packing density were observed, which should be taken into account especially in the reactor core thermal-hydraulic analyses. Two open source DEM codes were used to produce stochastic pebble bed configurations to add realism and improve the accuracy of criticality calculations performed with the Monte Carlo reactor physics code Serpent. Russian ASTRA criticality experiments were calculated. Pebble beds corresponding to the experimental specifications within measurement uncertainties were produced in DEM simulations and successfully exported into the subsequent reactor physics analysis. With the developed approach, two typical issues in Monte Carlo reactor physics calculations of pebble bed geometries were avoided. A novel method was developed and implemented as a MATLAB code to calculate porosities in the cells of a CFD calculation mesh constructed over a pebble bed obtained from DEM simulations. The code was further developed to distribute power and temperature data accurately between discrete based reactor physics and continuum based thermal-hydraulics models to enable coupled reactor core calculations. The developed method was also found useful for analysing sphere packings in general. CFD calculations were performed to investigate the pressure losses and heat transfer in three dimensional air cooled smooth and rib roughened rod geometries, housed inside a hexagonal flow channel representing a sub-channel of a single fuel rod of a GFR. The CFD geometry represented the test section of the L-STAR experimental facility at Karlsruhe Institute of Technology and the calculation results were compared to the corresponding experimental results. Knowledge was gained of the adequacy of various turbulence models and of the modelling requirements and issues related to the specific application. The obtained pressure loss results were in a relatively good agreement with the experimental data. Heat transfer in the smooth rod geometry was somewhat under predicted, which can partly be explained by unaccounted heat losses and uncertainties. In the rib roughened geometry heat transfer was severely under predicted by the used realisable k − epsilon turbulence model. An additional calculation with a v2 − f turbulence model showed significant improvement in the heat transfer results, which is most likely due to the better performance of the model in separated flow problems. Further investigations are suggested before using CFD to make conclusions of the heat transfer performance of rib roughened GFR fuel rod geometries. It is suggested that the viewpoints of numerical modelling are included in the planning of experiments to ease the challenging model construction and simulations and to avoid introducing additional sources of uncertainties. To facilitate the use of advanced calculation approaches, multi-physical aspects in experiments should also be considered and documented in a reasonable detail.

CFD modeling of dispersion water feed in wastewater cleaning application

Fluid particle breakup and coalescence are important phenomena in a number of industrial flow systems. This study deals with a gas-liquid bubbly flow in one wastewater cleaning application. Three-dimensional geometric model of a dispersion water system was created in ANSYS CFD meshing software. Then, numerical study of the system was carried out by means of unsteady simulations performed in ANSYS FLUENT CFD software. Single-phase water flow case was setup to calculate the entire flow field using the RNG k-epsilon turbulence model based on the Reynolds-averaged Navier-Stokes (RANS) equations. Bubbly flow case was based on a computational fluid dynamics - population balance model (CFD-PBM) coupled approach. Bubble breakup and coalescence were considered to determine the evolution of the bubble size distribution. Obtained results are considered as steps toward optimization of the cleaning process and will be analyzed in order to make the process more efficient.

Korkeapainevesisumusuuttimen virtaustekninen laadunhallinta

Tämä työ vastaa tarpeeseen hallita korkeapainevesisumusuuttimen laatua virtausmekaniikan työkalujen avulla. Työssä tutkitaan suutinten testidatan lisäksi virtauksen käyttäytymistä suuttimen sisällä CFD-laskennan avulla. Virtausmallinnus tehdään Navier-Stokes –pohjaisella laskentamenetelmällä. Työn teoriaosassa käsitellään virtaustekniikkaa ja sen kehitystä yleisesti. Lisäksi esitetään suuttimen laskennassa käytettävää perusteoriaa sekä teknisiä ratkaisuja. Teoriaosassa käydään myös läpi laskennalliseen virtausmekaniikkaan (CFD-laskenta) liittyvää perusteoriaa. Tutkimusosiossa esitetään käsitellyt suutintestitulokset sekä mallinnetaan suutinvirtausta ajasta riippumattomaan virtauslaskentaan perustuvalla laskentamenetelmällä. Virtauslaskennassa käytetään OpenFOAM-laskentaohjelmiston SIMPLE-virtausratkaisijaa sekä k-omega SST –turbulenssimallia. Tehtiin virtausmallinnus kaikilla paineilla, joita suuttimen testauksessa myös todellisuudessa käytetään. Lisäksi selvitettiin mahdolliset kavitaatiokohdat suuttimessa ja suunniteltiin kavitaatiota ehkäisevä suutingeometria. Todettiin myös lämpötilan ja epäpuhtauksien vaikuttavan kavitaatioon sekä mallinnettiin lämpötilan vaikutusta. Luotiin malli, jolla suuttimen suunnitteluun liittyviin haasteisiin voidaan vastata numeerisella laskennalla.

Numerical Investigation of Flow Past a Circular Cylinder and in a Staggered Tube Bundle Using Various Turbulence Models

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.