Discretized integral hydrodynamics

Using an interpolant form for the gradient of a function of position, we write an integral version of the conservation equations for a fluid. In the appropriate limit, these become the usual conservation laws of mass, momentum, and energy. We also discuss the special cases of the Navier-Stokes equations for viscous flow and the Fourier law for thermal conduction in the presence of hydrodynamic fluctuations. By means of a discretization procedure, we show how the integral equations can give rise to the so-called particle dynamics of smoothed particle hydrodynamics and dissipative particle dynamics.

Simulation of interface dynamics across pore discontinuities

We study the dynamics of a water-oil meniscus moving from a smaller to a larger pore. The process is characterised by an abrupt change in the configuration, yielding a sudden energy release. A theoretic study for static conditions provides analytical solutions of the surface energy content of the system. Although the configuration after the sudden energy release is energetically more convenient, an energy barrier must be overcome before the process can happen spontaneously. The energy barrier depends on the system geometry and on the flow parameters. The analytical results are compared to numerical simulations that solve the full Navier-Stokes equation in the pore space and employ the Volume Of Fluid (VOF) method to track the evolution of the interface. First, the numerical simulations of a quasi-static process are validated by comparison with the analytical solutions for a static meniscus, then numerical simulations with varying injection velocity are used to investigate dynamic effects on the configuration change. During the sudden energy jump the system exhibits an oscillatory behaviour. Extension to more complex geometries might elucidate the mechanisms leading to a dynamic capillary pressure and to bifurcations in final distributions of fluid phases in porous

A framework for hybrid simulations of two-phase flow in porous media

Rough a global coarse problem. Although these techniques are usually employed for problems in which the fine-scale processes are described by Darcy's law, they can also be applied to pore-scale simulations and used as a mathematical framework for hybrid methods that couples a Darcy and pore scales. In this work, we consider a pore-scale description of fine-scale processes. The Navier-Stokes equations are numerically solved in the pore geometry to compute the velocity field and obtain generalized permeabilities. In the case of two-phase flow, the dynamics of the phase interface is described by the volume of fluid method with the continuum surface force model. The MsFV method is employed to construct an algorithm that couples a Darcy macro-scale description with a pore-scale description at the fine scale. The hybrid simulations results presented are in good agreement with the fine-scale reference solutions. As the reconstruction of the fine-scale details can be done adaptively, the presented method offers a flexible framework for hybrid modeling.

Gravity-driven slug motion in capillary tubes

The velocity of a liquid slug falling in a capillary tube is lower than predicted for Poiseuille flow due to presence of menisci, whose shapes are determined by the complex interplay of capillary, viscous, and gravitational forces. Due to the presence of menisci, a capillary pressure proportional to surface curvature acts on the slug and streamlines are bent close to the interface, resulting in enhanced viscous dissipation at the wedges. To determine the origin of drag-force increase relative to Poiseuille flow, we compute the force resultant acting on the slug by integrating Navier-Stokes equations over the liquid volume. Invoking relationships from differential geometry we demonstrate that the additional drag is due to viscous forces only and that no capillary drag of hydrodynamic origin exists (i.e., due to hydrodynamic deformation of the interface). Requiring that the force resultant is zero, we derive scaling laws for the steady velocity in the limit of small capillary numbers by estimating the leading order viscous dissipation in the different regions of the slug (i.e., the unperturbed Poiseuille-like bulk, the static menisci close to the tube axis and the dynamic regions close to the contact lines). Considering both partial and complete wetting, we find that the relationship between dimensionless velocity and weight is, in general, nonlinear. Whereas the relationship obtained for complete-wetting conditions is found in agreement with the experimental data of Bico and Quere [J. Bico and D. Quere, J. Colloid Interface Sci. 243, 262 (2001)], the scaling law under partial-wetting conditions is validated by numerical simulations performed with the Volume of Fluid method. The simulated steady velocities agree with the behavior predicted by the theoretical scaling laws in presence and in absence of static contact angle hysteresis. The numerical simulations suggest that wedge-flow dissipation alone cannot account for the entire additional drag and that the non-Poiseuille dissipation in the static menisci (not considered in previous studies) has to be considered for large contact angles.

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.

Virtauslaskennankäyttö keskipakopumpun eroosiokulumisen mallintamisessa

Diplomityössä kehitetään malli tiheän kaksifaasivirtauksen aiheuttaman eroosiokulumi-sen mallintamiseksi, ratkaistaan virtauskenttä kahdessa erilaisessa keskipakopumpussa, sovelletaan kehitettyä mallia, sekävertaillaan mallin antamia tuloksia käytännön kokeissa saavutettuihin tuloksiin. Työssä on erityisenä mielenkiinnon kohteena savukaasupesurin pumppu. Työn alkuosa sisältää tarkemman kuvauksen savukaasupesurin toi-minnasta. Numeerinen ratkaisu ja laskentahilan generointi suoritetaan ANSYS CFX- ja Turbo-Grid-ohjelmistoilla. Laskennassa virtauksen Navier-Stokesin yhtälöt on aikakeskiarvo-tettu ja ratkaistu käyttäen kontrollitilavuusmenetelmää. Tiheiden kaksifaasivirtausten eroosiokulumista on mallinnettu tekijän kehittämällä mallilla, jonka käytännön toteutus-ta ei kuitenkaan saateta julkiseksi, koodin kehittämisessä käytetty teoria on kuitenkin esitetty työssä. Työn piirissä tehtiin myös kulumiskokeita Sulzer Pumps Finlandin Karhulan tehtailla, sekä vertailtiin simuloinnin tuloksia aikaisemmissa kokeissa saavutettuihin. Koejärjestelyt kuvataan työssä.

Experimental and Numerical Analysis of Different Volutes in a Centrifugal Compressor

In a centrifugal compressor the flow around the diffuser is collected and led to the pipe system by a spiral-shaped volute. In this study a single-stage centrifugal compressor with three different volutes is investigated. The compressorwas first equipped with the original volute, the cross-section of which was a combination of a rectangle and semi-circle. Next a new volute with a fully circular cross-section was designed and manufactured. Finally, the circular volute wasmodified by rounding the tongue and smoothing the tongue area. The overall performance of the compressor as well as the static pressure distribution after the impeller and on the volute surface were measured. The flow entering the volute was measured using a three-hole Cobra-probe, and flow visualisations were carriedout in the exit cone of the volute. In addition, the radial force acting on theimpeller was measured using magnetic bearings. The complete compressor with thecircular volute (inlet pipe, full impeller, diffuser, volute and outlet pipe) was also modelled using computational fluid dynamics (CFD). A fully 3-D viscous flow was solved using a Navier-Stokes solver, Finflo, developed at Helsinki University of Technology. Chien's k-e model was used to take account of the turbulence. The differences observed in the performance of the different volutes were quite small. The biggest differences were at low speeds and high volume flows,i.e. when the flow entered the volute most radially. In this operating regime the efficiency of the compressor with the modified circular volute was about two percentage points higher than with the other volutes. Also, according to the Cobra-probe measurements and flow visualisations, the modified circular volute performed better than the other volutes in this operating area. The circumferential static pressure distribution in the volute showed increases at low flow, constant distribution at the design flow and decrease at high flow. The non-uniform static pressure distribution of the volute was transmitted backwards across the vaneless diffuser and observed at the impeller exit. At low volume flow a strong two-wave pattern developed into the static pressure distribution at the impeller exit due to the response of the impeller to the non-uniformity of pressure. The radial force of the impeller was the greatest at the choke limit, the smallest atthe design flow, and moderate at low flow. At low flow the force increase was quite mild, whereas the increase at high flow was rapid. Thus, the non-uniformityof pressure and the force related to it are strong especially at high flow. Theforce caused by the modified circular volute was weaker at choke and more symmetric as a function of the volume flow than the force caused by the other volutes.

Radiaalikompressorin spiraalivirtauksen numeerinen mallinnus

Diplomityössä mallinnetaan numeerisesti radiaalikompressorin spiraalin virtaus. Spiraalin tarkoituksena radiaalikompressorissa on kerätä tasaisesti virtaus diffuusorin kehältä. Spiraaliin on viime aikoina kiinnitetty enemmän huomiota, koska on havaittu, että kompressorin hyötysuhdetta voidaan parantaa spiraalia optimoimalla. Spiraalin toimintaa tarkastellaan kolmella eri massavirralla. Työn alussa käsitellään spiraalin toimintaperiaatteita. Numeerisena ratkaisijana käytetään Teknillisessä korkeakoulussa kehitettyä FIN-FLO -koodia. FINFLO -laskentaohjelmassa ratkaistaan Navier-Stokes yhtälöt kolmeulotteiselle laskenta-alueelle. Diskretointi perustuu kontrollitilavuus menetelmään. Työssä käsitellään laskentakoodin toimintaperiaatteitta. Turbulenssia mallinnetaan algebrallisella Baldwin-Lomaxin ja kahden yhtälön Chienin k-e turbulenssimalleilla. Laskentatuloksia verrataan Lappeenrannan teknillisessä korkeakoulussa tehtyihin mittauksiin kyseessä olevasta kompressorin spiraalista. Myös eri turbulenssimalleilla ja hilatasoilla saatuja tuloksia verrataan keskenään. Laskentatuloksien jälkikäsittelyä varten ohjelmoitiin neljä eri tietokoneohjelmaa. Laskennalla pyritään saamaan lisäselvyyttä virtauksen käyttäytymiseen spiraalissa ja erityisesti ns. kielen alueella. Myös kahden eri turbulenssimallin toimivuutta kompressorin numeerisessa mallinnuksessa tutkitaan.

Fluid flow in T-junction of pipes

The aim of this work is to study flow properties at T-junction of pipe, pressure loss suffered by the flow after passing through T-junction and to study reliability of the classical engineering formulas used to find head loss for T-junction of pipes. In this we have compared our results with CFD software packages with classical formula and made an attempt to determine accuracy of the classical formulas. In this work we have studies head loss in T-junction of pipes with various inlet velocities, head loss in T-junction of pipes when the angle of the junction is slightly different from 90 degrees and T-junction with different area of cross-section of the main pipe and branch pipe. In this work we have simulated the flow at T-junction of pipe with FLUENT and Comsol Multiphysics and observed flow properties inside the T-junction and studied the head loss suffered by fluid flow after passing through the junction. We have also compared pressure (head) losses obtained by classical formulas by A. Vazsonyi and Andrew Gardel and formulas obtained by assuming T-junction as combination of other pipe components and observations obtained from software experiments. One of the purposes of this study is also to study change in pressure loss with change in angle of T-junction. Using software we can have better view of flow inside the junction and study turbulence, kinetic energy, pressure loss etc. Such simulations save a lot of time and can be performed without actually doing the experiment. There were no real life experiments made, the results obtained completely rely on accuracy of software and numerical methods used.

Transient shear banding in time-dependent fluids

We study the dynamics of shear-band formation and evolution using a simple rheological model. The description couples the local structure and viscosity to the applied shear stress. We consider in detail the Couette geometry, where the model is solved iteratively with the Navier-Stokes equation to obtain the time evolution of the local velocity and viscosity fields. It is found that the underlying reason for dynamic effects is the nonhomogeneous shear distribution, which is amplified due to a positive feedback between the flow field and the viscosity response of the shear thinning fluid. This offers a simple explanation for the recent observations of transient shear banding in time-dependent fluids. Extensions to more complicated rheological systems are considered.

Accounting for adsorption and desorption in Lattice Boltzmann simulations

We report a Lattice-Boltzmann scheme that accounts for adsorption and desorption in the calculation of mesoscale dynamical properties of tracers in media of arbitrary complexity. Lattice Boltzmann simulations made it possible to solve numerically the coupled Navier-Stokes equations of fluid dynamics and Nernst-Planck equations of electrokinetics in complex, heterogeneous media. With the moment propagation scheme, it became possible to extract the effective diffusion and dispersion coefficients of tracers, or solutes, of any charge, e.g., in porous media. Nevertheless, the dynamical properties of tracers depend on the tracer-surface affinity, which is not purely electrostatic and also includes a species-specific contribution. In order to capture this important feature, we introduce specific adsorption and desorption processes in a lattice Boltzmann scheme through a modified moment propagation algorithm, in which tracers may adsorb and desorb from surfaces through kinetic reaction rates. The method is validated on exact results for pure diffusion and diffusion-advection in Poiseuille flows in a simple geometry. We finally illustrate the importance of taking such processes into account in the time-dependent diffusion coefficient in a more complex porous medium.

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.

Simulació de vent en temps real per paisatges

La simulació de la realitat és un fenomen que va sorgir fa uns anys per tal de predir esdeveniments sense haver de malbaratar recursos. El problema inicial de la simulació va ser la necessitat de simplificar la realitat a causa de la manca de capacitat dels ordinadors de l’època. Amb aquest projecte volem ajudar, per exemple, a estudis científics sobre la difusió de la contaminació en grans nuclis a causa de l’efecte del vent, càlculs de trajectòries amb forces externes degudes al vent, o incorporar en el món de la multimèdia efectes realistes de vent. El principal objectiu d’aquest projecte és desenvolupar un sistema que permeti realitzar simulacions realistes de vent per un paisatge 2D, i estudiar com el vent és veu afectat per la geometria de l’escena. Un punt important, és que tot ha de ser en temps real. Per aconseguir-ho, utilitzarem tècniques basades en el mètode de Lattice-Boltzmann, el qual consisteix en una xarxa regular que representa el fluid en posicions discretes, i estudiar com flueix. Escollint els paràmetres correctes de la simulació, es pot demostrar que aquest mètode convergeix a les equacions continues de Navier-Stokes, les qual són les més importants per descriure el comportament macroscòpic d’un fluid. Per accelerar tots els càlculs, utilitzarem la capacitat i la potencia de les targes gràfiques, ajustarem l’algorisme per poder-lo utilitzar en paral•lel, tot tenint en compte les restriccions de les GPUs. També haurem de generar un sistema per poder llegir les escenes 2D sobre les que realitzarem la simulació. Finalment, haurem de “pintar” el vent per tal de poder visualitzar el resultat de la simulació

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.

Dynamics of coherent vortices in mixing layers using direct numerical and large-eddy simulations

Coherent vortices in turbulent mixing layers are investigated by means of Direct Numerical Simulation (DNS) and Large-Eddy Simulation (LES). Subgrid-scale models defined in spectral and physical spaces are reviewed. The new "spectral-dynamic viscosity model", that allows to account for non-developed turbulence in the subgrid-scales, is discussed. Pseudo-spectral methods, combined with sixth-order compact finite differences schemes (when periodic boundary conditions cannot be established), are used to solve the Navier- Stokes equations. Simulations in temporal and spatial mixing layers show two types of pairing of primary Kelvin-Helmholtz (KH) vortices depending on initial conditions (or upstream conditions): quasi-2D and helical pairings. In both cases, secondary streamwise vortices are stretched in between the KH vortices at an angle of 45° with the horizontal plane. These streamwise vortices are not only identified in the early transitional stage of the mixing layer but also in self-similar turbulence conditions. The Re dependence of the "diameter" of these vortices is analyzed. Results obtained in spatial growing mixing layers show some evidences of pairing of secondary vortices; after a pairing of the primary Kelvin-Helmholtz (KH) vortices, the streamwise vortices are less numerous and their diameter has increased than before the pairing of KH vortices.