Influence of wall roughness in particle-laden turbulent channel flows

U disertaciji se proučava uticaj hrapavosti zidova pri strujanju mešavine če- stica i gasa. Pri ovakvim strujanjima, sudar čestica sa hrapavim zidom je uvek trodimenzionalan (3D) usled prilaznih uglova čestica prema zidu kao i geomet- rije hrapavih zidova, dok su prema ranijim istraživanjima, modeli korišćeni za ovaj sudar u numeričkim simulacijama uglavnom dvodimenzionalan (2D) ili uprošćeni 3D. Kako bi se omogućio tačniji proračun strujanja mešavine čestica i gasa, cilj disertacije je razvoj modela za 3D sudar čestice i hrapavog zida. U di- sertaciji su analizirani sudari čestica sa izotropnim i anizotropnim hrapavim zidovima, putem determinističkih simulacija i izvedeni su odgovarajući stoha- stički modeli za te sudare, primenljivi u Ojler-Lagranž simulacijama strujanja mešavine čestica i gasa. Nalazi se da sa porastom prilaznog ugla čestica u od- nosu na makroskopski gladak zid, dolazi do porasta standardne devijacije bočnih uglova odbijanja čestica i u slučaju izotropne i anizotropne površine. Mehani- zam višestrukih sudara čestica sa zidom ostaje nepromenjen u odnosu na 2D model za sudar čestice i zida. Izvedeni stohastički modeli se porede se raspoloživim eksperimentalnim rezultatima i determinističkim simulacijama. Izvršene su LES simulacije strujanja čistog fluida (bez prisustva disperzne faze) u horizon- talnom kanalu pravougaonog poprečnog preseka koristeći različite SGS modele: model Smagorinskog, WALE i dinamički jedno-jednačinski model. Simulacije su izvedene u programskom paketu OpenFOAM. Uticaj zidova tog kanala, različite hrapavosti, na disperznu fazu, pri strujanju mešavine gasa i čestica istražen je putem LES-DPS simulacija. Međusobni sudari čestica se izračunavaju prime- nom modela mekih sfera. Kada se ovi sudari zanemare, što bi bilo opravdano pri strujanjima sa veoma malom koncentracijom disperzne faze, nalazi se da hra- pavost zida može biti značajan mehanizam za produkciju poprečnih fluktuacije čestica. Uzimanjem u obzir međusobnih sudara čestica, dolazi do porasta popreč- nih fluktuacija brzine čestica i pokazuje se da je u pogledu ovih fluktuacija uticaj međusobnog sudara čestica veći u odnosu na uticaj hrapavosti zidova ka- nala.Influence of wall roughness in turbulent particle-laden wall confined flows is studied in this thesis. In such a flow configuration, particle-wall collision is always three-dimensional (3D) owing to the particle incident angles and rough wall geometry, while according to the previous investigations, models for this collision in numerical simulations are mostly two-dimensional (2D) or simplified 3D. In order to enable more accurate calculation of wall confined particle-laden flows, the goal of the thesis is development of the model for 3D particle-rough wall collision. Particles collision with isotropic and anisotropic rough walls are analyzed using deterministic simulations and stochastic models for those collisions are developed in Euler-Lagrangian framework. It is found that with increase of particle incident angle a standard deviation of particle transverse angles increases, for cases of isotropic and anisotropic rough wall surface. Mechanism of multiple particlerough wall collision remains unchanged comparing to the 2D model for particle-rough wall collision. Derived stochastic models are compared to the available experimental measurements and results of deterministic simulations. LES of pure fluid flow (without disperse phase) in a horizontal channel are carried out, using different SGS models: Smagorinsky, WALE and dynamic one-equation model. Simulations are carried out in software package OpenFOAM. Also, LES-DPS is performed in turbulent particleladen flow in horizontal channel in order to estimate influence of walls roughness on disperse phase. Inter-particle collisions are calculated using soft-sphere model. When these collisions are neglected, which is justified at very diluted flows, it is shown that wall roughness can be significant mechanism for production of particle spanwise velocity fluctuations. When inter-particle collisions are accounted for, these fluctuations increase and the influence of inter-particle collisions on particle spanwise velocity fluctuations becomes larger than the influence of channel wall roughness

Rarefied gas flow in microtubes at low Reynolds numbers

U radu se proučava osnosimetrično, izotermsko, stišljivo strujanje gasa sa klizanjem, pri malim vrednostima Rejnoldsovog broja. Problem je rešen primenom jednačine kontinuiteta i Navije-Stoksovih jednačina, zajedno sa Maksvelovim graničnim uslovom prvog reda. Analitički rezultati su dobijeni primenom perturbacione metode. Dobijena rešenja se dobro slažu sa poznatim eksperimentalnim rezultatima drugih autora.Low Reynolds number, axisymmetric, isothermal, compressible, slip gas flow in microtubes is investigated in this paper. The problem is solved by the continuum equations, continuity and Navier-Stokes, along with Maxwell first order boundary condition. The analytical results are obtained by perturbation method. The solutions show a good agreement with experimental results

Rarefied gas flow in microtubes at low Reynolds numbers

U radu se proučava osnosimetrično, izotermsko, stišljivo strujanje gasa sa klizanjem, pri malim vrednostima Rejnoldsovog broja. Problem je rešen primenom jednačine kontinuiteta i Navije-Stoksovih jednačina, zajedno sa Maksvelovim graničnim uslovom prvog reda. Analitički rezultati su dobijeni primenom perturbacione metode. Dobijena rešenja se dobro slažu sa poznatim eksperimentalnim rezultatima drugih autora.Low Reynolds number, axisymmetric, isothermal, compressible, slip gas flow in microtubes is investigated in this paper. The problem is solved by the continuum equations, continuity and Navier-Stokes, along with Maxwell first order boundary condition. The analytical results are obtained by perturbation method. The solutions show a good agreement with experimental results

Anisotropy analysis of turbulent swirl flow

U radu su primenjene dve vrste invarijantnih mapa kako bi se procenio stepen anizotropnosti turbulentnog vihornog strujanja. Korišćene su invarijantna mapa, koju su predložili Lamli i Njuman, kao i baricentrična mapa. Analizirane su razlike u vizuelnom predstavljanju stanja anizotropnosti i izvedene su matematičke osnove za obe mape. Analizom eksperimentalnih podataka je pokazano da postoji značajan uticaj vihora na anizotropnost turbulencije. Korišćenje mapa anizotropnosti pokazuje da su različite oblasti strujnog polja u vihornom strujanju okarakterisane različitim stanjima anizotropnosti.Anisotropy invariant map proposed by Lumley and Newman and barycentric map proposed by Banerjee et al. were used in order to estimate the degree of anisotropy in turbulent swirl flow. The differences in visual interpretations of anisotropy states in these two maps were analyzed and mathematical basis of these two maps was derived. Experimental data reveal that there is significant influence of swirl on the anisotropy of turbulence. Anisotropy invariant mapping shows that different flow regions of swirl flow are characterized by different anisotropy states

Anisotropy analysis of turbulent swirl flow

U radu su primenjene dve vrste invarijantnih mapa kako bi se procenio stepen anizotropnosti turbulentnog vihornog strujanja. Korišćene su invarijantna mapa, koju su predložili Lamli i Njuman, kao i baricentrična mapa. Analizirane su razlike u vizuelnom predstavljanju stanja anizotropnosti i izvedene su matematičke osnove za obe mape. Analizom eksperimentalnih podataka je pokazano da postoji značajan uticaj vihora na anizotropnost turbulencije. Korišćenje mapa anizotropnosti pokazuje da su različite oblasti strujnog polja u vihornom strujanju okarakterisane različitim stanjima anizotropnosti.Anisotropy invariant map proposed by Lumley and Newman and barycentric map proposed by Banerjee et al. were used in order to estimate the degree of anisotropy in turbulent swirl flow. The differences in visual interpretations of anisotropy states in these two maps were analyzed and mathematical basis of these two maps was derived. Experimental data reveal that there is significant influence of swirl on the anisotropy of turbulence. Anisotropy invariant mapping shows that different flow regions of swirl flow are characterized by different anisotropy states

Euler-Euler numerical simulations of upward turbulent bubbly flows in vertical pipes with low-Reynolds-number model

In this work, numerical simulations of upward turbulent bubbly flows in vertical pipes are conducted in the Euler-Euler framework with a low-Reynolds-number (LRN) model for liquid. It is found that the existing correlation for the drag coefficient of a single bubble in a shear flow, which has been successfully used along with the high-Reynolds-number (HRN) models, cannot be used with the LRN model. The reason is that drag forces of bubbles calculated using such correlation are enormous in near-wall cells (order of 10(12) N/m(3)), which causes a divergence of numerical simulations with LRN. Therefore, a modified correlation for the drag coefficient of a single bubble in shear flow, that can be used successfully with the LRN model, has been proposed. The results of numerical simulations, performed with a new correlation for the drag coefficient, are analysed and compared to selected experimental measurements for different pipe diameters and different flow conditions of gas and liquid. It is shown that the largest effect of the application of the new correlation for the drag coefficient of a single bubble in shear flow in numerical simulations can be achieved on the reduction of the relative velocity between gas and liquid. The degree of this reduction depends on the pipe diameter and liquid volumetric flux

Flow simulations in a small bulb turbine using two-equation turbulence models

U radu su urađene numeričke simulacije strujanja u maloj cevnoj turbini primenom softvera Ansys CFX. Simulacije su izvedene primenom tri različita modela turbulencije koji su bazirani na Rejnoldsovom osrednjavanju Navije-Stoksovih jednačina: k-ε , k-ω i SST. Za svaki od navedenih modela razmotreno je sedam različitih radnih režima turbine. Da bi se smanjilo korišćenje računarskih resursa izvedene su stacionarne simulacije strujanja. Za sve slučajeve dobijena je dobra numerička stabilnost i konvergencija rešenja. Radne krive turbine formirane su za svaki od izabranih modela turbulencije na osnovu rezultata izvedenih simulacija u različitim radnim režimima. Za optimalni radni režim turbine, u proizvoljno izabranom poprečnom preseku difuzora izračunati su profili brzina za svaki model turbulencije, kao i raspodela statičkog pritiska po konturama loptatica radnog kola turbine. Izvršeno je upoređivanje dobijenih performansi turbine i data je analiza dobijenih profila brzine i raspodele statičkog pritiska za izabrane modele turbulencije.Numerical flow simulations in a small bulb turbine by the use of Ansys CFX software were performed in this paper. Simulations were performed for three different RANS-based models: k-ε , k-ω and SST. For each of these models, seven different operating regimes were considered. In order to reduce computational effort, steady state simulations were performed. In all cases, good numerical stability and convergence of solution were obtained. Based on the obtained results, performance curves for each of selected turbulence models in different operating regimes are formed. In turbine's optimal operating regime, velocity profiles in a selected cross section of the draft tube were calculated, as well as the static pressure distribution on runner blades. Comparison of obtained performance curves was performed. Analysis of the velocity profiles and distribution of static pressure are given for each of the selected turbulence model

Flow simulations in a small bulb turbine using two-equation turbulence models

U radu su urađene numeričke simulacije strujanja u maloj cevnoj turbini primenom softvera Ansys CFX. Simulacije su izvedene primenom tri različita modela turbulencije koji su bazirani na Rejnoldsovom osrednjavanju Navije-Stoksovih jednačina: k-ε , k-ω i SST. Za svaki od navedenih modela razmotreno je sedam različitih radnih režima turbine. Da bi se smanjilo korišćenje računarskih resursa izvedene su stacionarne simulacije strujanja. Za sve slučajeve dobijena je dobra numerička stabilnost i konvergencija rešenja. Radne krive turbine formirane su za svaki od izabranih modela turbulencije na osnovu rezultata izvedenih simulacija u različitim radnim režimima. Za optimalni radni režim turbine, u proizvoljno izabranom poprečnom preseku difuzora izračunati su profili brzina za svaki model turbulencije, kao i raspodela statičkog pritiska po konturama loptatica radnog kola turbine. Izvršeno je upoređivanje dobijenih performansi turbine i data je analiza dobijenih profila brzine i raspodele statičkog pritiska za izabrane modele turbulencije.Numerical flow simulations in a small bulb turbine by the use of Ansys CFX software were performed in this paper. Simulations were performed for three different RANS-based models: k-ε , k-ω and SST. For each of these models, seven different operating regimes were considered. In order to reduce computational effort, steady state simulations were performed. In all cases, good numerical stability and convergence of solution were obtained. Based on the obtained results, performance curves for each of selected turbulence models in different operating regimes are formed. In turbine's optimal operating regime, velocity profiles in a selected cross section of the draft tube were calculated, as well as the static pressure distribution on runner blades. Comparison of obtained performance curves was performed. Analysis of the velocity profiles and distribution of static pressure are given for each of the selected turbulence model

Comparison of novel variable area convergent-divergent nozzle performances obtained by analytic, computational and experimental methods

Different applications of a variable area convergent-divergent nozzle are found in various parts of the industry. This paper presents the development of a new design methodology for a variable area convergent-divergent nozzle, to maintain constant nozzle area ratio for different values of mass flow rates. The validation of the presented model was carried out on an example supersonic ejector using experimental, numerical and analytical data. Analytical (one dimensional) and computational fluid dynamics models showed satisfactory prediction performance in comparison with the experiment. The average entrainment ratio error was between 10% and 7%, respectively. Results confirmed that the velocity of the primary fluid at the nozzle outlet is in accordance with the one dimensional analysis. Although disturbances (strong and weak shock waves) are visible, their effects are negligible. Also, supersonic ejector performances are presented through relations between entrainment ratio, outlet pressure and spindle position. Disadvantages of variable area nozzle utilization in ejector applications are emphasized

Comparison of novel variable area convergent-divergent nozzle performances obtained by analytic, computational and experimental methods

Different applications of a variable area convergent-divergent nozzle are found in various parts of the industry. This paper presents the development of a new design methodology for a variable area convergent-divergent nozzle, to maintain constant nozzle area ratio for different values of mass flow rates. The validation of the presented model was carried out on an example supersonic ejector using experimental, numerical and analytical data. Analytical (one dimensional) and computational fluid dynamics models showed satisfactory prediction performance in comparison with the experiment. The average entrainment ratio error was between 10% and 7%, respectively. Results confirmed that the velocity of the primary fluid at the nozzle outlet is in accordance with the one dimensional analysis. Although disturbances (strong and weak shock waves) are visible, their effects are negligible. Also, supersonic ejector performances are presented through relations between entrainment ratio, outlet pressure and spindle position. Disadvantages of variable area nozzle utilization in ejector applications are emphasized