In this investigation, the flow friction associated with laminar pulsating flows through porous media was numerically studied. The problem is of interest for understanding the regenerators of Stirling and pulse tube cryocoolers. Two-dimensional flow in a system composed of a number of unit cells of generic porous structures was simulated using a CFD tool, with sinusoidal variations of flow with time. Detailed numerical data representing the oscillating velocity and pressure variations for five different generic porous structure geometries in the porosity range of 0.64 to 0.84, with flow pulsation frequency of 40 Hz were obtained, and special attention was paid to the phase shift characteristics between the velocity and pressure waves. Based on these detailed numerical data, the standard unsteady volume-averaged momentum conservation equation for porous media was then applied in order to obtain the instantaneous as well as cycle-averaged permeability and Forchheimer coefficients. It was found that the cycle-averaged permeability coefficients were nearly the same as those for steady flow, but the cycle-averaged Forchheimer coefficients were about two times larger than those for steady flow. Significant phase lags were observed with respect to the volume-averaged velocity and pressure waves. The parametric trends representing the dependence of these phase lags on porosity and flow Reynolds number were discussed. The phase difference between pressure and velocity waves, which is important for pulse tube cryocooling, depended strongly on porosity and flow Reynolds number.

The work performed in this thesis explores new ways of reducing the drag of ground vehicles. Specifically, the effect of plasma actuators are investigated numerically with the intention to delay separation around a half-cylinder, a geometry chosen to represent a simplified A-pillar of a truck. The plasma actuators have to be included in turbulent flow simulations. Therefore, emphasis is first put on finding a numerical model that can reproduce the effect of the plasma without increasing the computational cost. This effect is modeled through a body force term added to the Navier-Stokes equations. To determine the strength and spatial extent of this body force, optimization was performed to minimize the difference between experimental and simulated profiles of plasma induced velocity.  The plasma actuator model is thereafter used in Large Eddy Simulations (LES) of the flow around a half-cylinder at Reynolds number Re=65*10^3 and Re=32*10^3. Two types of actuation cases are performed. In the first case, a single actuator is used. In the second case, a pair of consecutive actuators are used, and their position on the half-cylinder is changed. It is found that a drag reduction of up to 10% is achievable. Moreover, the ideal location for actuation is determined to be near the separation point of the non-actuated flow.  Finally, dynamic mode decomposition (DMD) is investigated as a tool to extract coherent dynamic structures from a turbulent flow field. The DMD is first used to analyze a channel flow where pulsations are imposed at a known frequency. It is found that DMD gives similar results to phase averaging done at the oscillation frequency. However, the presence of turbulence noise hinders the ability to identify modes at higher harmonics. The DMD is also used to post-process the half-cylinder flow case. There, it is found that the spectrum of the wake is broadband. Nevertheless, modes within distinct frequency ranges are found to be located in distinct spatial regions. / Arbetet som utförts i denna avhandling undersöker nya sätt att minska luftmotstånd hos markfordon. Speciellt undersöks numeriskt effekten av plasmaaktuatorer med avsikten att uppnå fördröjd separation av strömningen kring en halvcylinder, en geometri vald för att representera en förenklad A-stolpe på en lastbil.  För att kunna utföra studien behöver plasmaaktuatorer kunna ingå i beräkningar av turbulenta strömningsfält. Därför undersöks först sätt för att hitta en numerisk modell som kan reproducera effekten av plasma utan att öka beräkningskostnad. Plasmaaktuatorn  modelleras i detta arbete genom att ett källterm adderas till Navier-Stokes ekvationer. För att bestämma styrkan och den rumsliga utbredningen hos källtermen, utförs en optimering för att minimera skillnaden mellan experimentella och simulerade profiler av plasma inducerad strömningshastighet.  Plasmaaktuatormodellen används därefter i Large Eddy Simulations (LES) för att beräkna strömningen kring en halvcylinder med Reynolds tal Re=65*10^3 och Re=32*10^3. Två typer av fall studeras. I det första fallet används en enda aktuator. I det andra fallet, är ett par på varandra följande aktuatorer placerade, där aktuatorernas position på halvcylinder ändras. Resultaten visar att en luftmotståndsminskning på upp till 10% kan erhållas. Den idealiska platsen för aktuatorn bedöms vara nära den punkt där strömningen utan aktuator separerar. Slutligen undersöks Dynamic Mode Decomposition (DMD) som ett verktyg för att extrahera koherenta dynamiska strukturer i en turbulent strömning. DMD används först för att analysera pulserande kanalströmning där pulsationen har en känd frekvens. Resultaten visar att DMD ger liknande resultat som då fas-medelvärdesbildning görs vid oscillationsfrekvensen. Förekomsten av turbulens buller hindrar dock möjligheten att identifiera moder vid högre övertoner. DMD används också för att analysera strömningen kring halv-cylindern. I avhandlingen visas att spektrat i vaken är bredbandigt men att även moder inom distinkta frekvensintervall fanns vara belägna i avgränsade områden i vaken. / <p>QC 20170117</p>

This thesis deals with flow measuring techniques applied on steady and pulsatingflows. Specifically, it is focused on gas flows where density changes canbe significant, i.e. compressible flows. In such flows only the mass flow ratehas a significance and not the volume flow rate since the latter depends onthe pressure. The motivation for the present study is found in the use of flowmeters for various purposes in the gas exchange system for internal combustionengines. Applications can be found for instance regarding measurements of airflow to the engine, or measurements of the amount of exhaust gas recirculation.However the scope of thesis is wider than this, since the thesis aims toinvestigate the response of flow meters to pulsating flows. The study is mainlyexperimental, but it also includes an introduction and discussion of several inindustry, common flow measuring techniques.The flow meters were studied using a newly developed flow rig, designedfor measurement of steady and pulsating air flow of mass flow rates and pulsefrequencies typically found in the gas exchange system of cars and smallertrucks. Flow rates are up to about 200 g/s and pulsation frequencies from 0 Hz(i.e. steady flow) up to 80 Hz. The study included the following flow meters:hot-film mass flow meter, venturi flowmeter, Pitot tube, vortex flowmeter andturbine flowmeter. The performance of these meters were evaluated at bothsteady and pulsating conditions. Furthermore, the flow under both steady andpulsating conditions were characterized by means of a resistance-wire basedmass flow meter, with the ability to perform time resolved measurements ofboth the mass flux ρu, and the stagnation temperature T0.Experiments shows that, for certain flow meters, a quasi-steady assumptionis fairly well justified at pulsating flow conditions. This means that thefundamental equations describing the steady flow, for each instant of time,is applicable also in the pulsating flow. In the set-up, back-flow occurred atcertain pulse frequencies, which can result in highly inaccurate output fromcertain flow meters, depending on the measurement principle. For the purposeof finding means to determine when back flow prevails, LDV measurementswere also carried out. These measurements were compared with measurementsusing a vortex flow meter together with a new signal processing technique basedon wavelet analysis. The comparison showed that this technique may have apotential to measure pulsating flow rates accurately.Descriptors: Flow measuring, compressible flow, steady flow, pulsating flow,hot-wire anemometry, cold-wire anemometry. / QC 20101208

<div>Studying the motion of cells and investigating their migration patterns in inertial microchannels have been of great interest among researchers because of their numerous biological applications such as sorting, separating, and filtering them. A great drawback in conventional microfluidics is the inability to focus extremely small biological particles and pathogens in the order of sub-micron and nanometers due to the requirement of designing an impractically elongated microchannel, which could be in the order of a few meters in extreme cases. This restriction is because of the inverse correlation between the cube of the particle size and the theoretically required channel length. Exploiting an oscillatory flow is one solution to this issue where the total distance that the particle needs to travel to focus is virtually extended beyond the physical length of the device. Due to the present symmetry in such flow, the directions of the lift forces acting on the particle remain the same, making the particle focusing feasible. </div><div><br></div><div>Here, we present results of simulation of such oscillatory flows of a single capsule in a rectangular microchannel containing a Newtonian fluid. A 3D front-tracking method has been implemented to numerically study the dynamics of the capsule in the channel of interest. Several cases have been simulated to quantify the influence of the parameters involved in this problem such as the channel flow rate, capsule deformability, frequency of oscillation, and the type of applied mechanism for inducing flow oscillations. In all cases, the capsule blockage ratio and the initial location are the same, and it is tracked until it reaches its equilibrium position. The capability to focus the capsule in a short microchannel with oscillatory flow has been observed for capsule deformabilities and mechanisms to induce the oscillations used in our study. Nevertheless, there is a limit to the channel flow rate beyond which, there is no single focal point for the capsule. Another advantage of having an oscillatory microchannel flow is the ability to control the capsule focal point by changing the oscillation frequency according to the cases presented in the current study. The capsule focusing point also depends on its deformability, flow rate, and the form of the imposed periodic pressure gradient; more deformable capsules with lower maximum velocity focus closer to the channel center. Also, the difference between the capsule equilibrium point in steady and oscillatory flows is affected by the capsule stiffness and the device flow rate. Furthermore, increasing the oscillation frequency, capsule rigidity, and system flow rate shorten the essential device length. </div><div><br></div><div>Although the oscillation frequency can provide us with new particle equilibrium positions, especially ones between the channel center and wall that can be very beneficial for separation purposes, it has the shortcoming of having a zero net throughput. To address this restriction, a steady component has been added to the formerly defined oscillatory flow to make it pulsating. Furthermore, this type of flow adds more new equilibrium points because it behaves similarly to a pure oscillatory flow with an equivalent frequency in that regard. They also enable the presence of droplets at high Ca or Re that could break up in the steady or a very low-frequency regime. Therefore, we perform new numerical simulations of a deformable droplet suspended in steady, oscillatory, and pulsating microchannel flows. We have observed fluctuations in the trajectory of the drop and have shown that the amplitude of these oscillations, the average of the oscillatory deformation, and the average migration velocity decrease by increasing the frequency. The dependence of the drop focal point on the shape of the velocity profile has been investigated as well. It has been explored that this equilibrium position moves towards the wall in a plug-like profile, which is the case at very high frequencies. Moreover, due to the expensive cost of these simulations, a recursive version of the Multi Fidelity Gaussian processes (MFGP) has been used to replace the numerous high-fidelity (or fine-grid) simulations that cannot be afforded numerically. The MFGP algorithm is used to predict the equilibrium distance of the drop from the channel center for a wide range of the input parameters, namely Ca and frequency, at a constant Re. It performs exceptionally well by having an average R^2 score of 0.986 on 500 random test sets.</div><div><br></div><div>The presence of lift forces is the main factor that defines the dynamics of the drop in the microchannel. The last part of this work will be dedicated to extracting the active lift force profiles and identify their relationships with the parameters involved to shed light on the underlying physics. This will be based on a novel methodology that solely depends on the drop trajectory. Assuming a constant Re, we then compare steady lift forces at different Ca numbers and oscillatory ones at the same constant Ca. We will then define analytical equations for the obtained lift profiles using non-linear regression and predict their key coefficients over a continuous range of inputs using MFGP.</div>

Solid-fluid thermal interactions during unsteady flow in porous media play an important role in the regenerators of pulse tube cryocoolers. Pore-level thermal processes in porous media under unsteady flow conditions are poorly understood. The objective of this investigation is to study the pore-level thermal phenomena during pulsating flow through a generic, two-dimensional porous medium by numerical analysis. Furthermore, an examination of the effects of flow pulsations on the thermal dispersion and heat transfer coefficient that are encountered in the standard, volume-average energy equations for porous media are carried out. The investigated porous media are periodic arrays of square cylinders. Detailed numerical data for the porosity range of 0.64 to 0.84, with flow Reynold's numbers from 0-1000 are obtained. Based on these numerical data, the instantaneous as well as cycle-average thermal dispersion and heat transfer coefficients, to be used in the standard unsteady volume-average energy conservation equations for flow in porous media, are derived. Also, the adequacy of current applied cycle-average correlations for heat transfer coefficients and the inclusion of the thermal dispersion in the definition of an effective fluid thermal conductivity are investigated.

The increasing use of turbochargers is leading to an outstanding research to understand the internal flow in turbomachines. In this frame, computational fluid dynamics (CFD) is one of the tools that can be applied to contribute to the analysis of the fluid-dynamic processes occurring in a turbine. The objective of this thesis is the development of a methodology for performing simulations of radial turbomachinery optimizing the available computational resources. This methodology is used for the characterization of a vaned-nozzle turbine under steady and pulsating flow conditions. An important effort has been devoted in adjusting the case configuration to maximize the accuracy achievable with a certain computational cost. Concerning the cell size, a local mesh independence analysis is proposed as a procedure to optimize the distribution of cells in the domain, thus allowing to use a finer mesh in the most suitable places. Particularly important in turbomachinery simulations is the influence of the approach for simulating rotor motion. In this thesis two models have been compared: multiple reference frame and sliding mesh. The differences obtained using both methods were found to be significant in off-design regions. Steady flow CFD results have been validated against global measurements taken on a gas-stand. The modeling of a turbine, installed either on a turbocharger test rig or an engine, requires the calculation of the flow in the ducts composing the system. Those ducts could be simulated assuming a one-dimensional (1D) approximation, and thus reducing the computational cost. In this frame of ideas, two CFD boundary conditions have been developed. The first one allows performing coupled 1D-3D simulations, communicating the flow variables from each domain through the boundary. The second boundary condition is based in a new formulation for a stand-alone anechoic end, which intends to represent the flow behavior of an infinite duct. Finally, the turbine was simulat / Fajardo Peña, P. (2012). Methodology for the Numerical Characterization of a Radial Turbine under Steady and Pulsating Flow [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/16878 / Palancia

At the end of the 19th Century, the invention of the Internal Combustion Engine (ICE) marked the beginning of our current lifestyle. Soon after the first ICE patent, the importance of increasing air pressure upstream the engine cylinders was revealed. At the beginning of the 20th Century turbo-machinery developments (which had started time before), met the ICE what represented the beginning of turbocharged engines. Since that time, the working principle has not fundamentally changed. Nevertheless, stringent emissions standards and oil depletion have motivated engine developments; among them, turbocharging coupled with downsized engines has emerged as the most feasible way to increase specific power while reducing fuel consumption. Turbocharging has been traditionally a complex problem due to the high rotational speeds, high temperature differences between working fluids (exhaust gases, compressed air, lubricating oil and cooling liquid) and pulsating flow conditions. To improve current computational models, a new procedure for turbochargers characterization and modelling has been presented in this Thesis. That model divides turbocharger modelling complex problem into several sub-models for each of the nonrecurring phenomenon; i.e. heat transfer phenomena, friction losses and acoustic non-linear models for compressor and turbine. A series of ad-hoc experiments have been designed to aid identifying and isolating each phenomenon from the others. Each chapter of this Thesis has been dedicated to analyse that complex problem proposing different sub-models. First of all, an exhaustive literature review of the existing turbocharger models has been performed. Then a turbocharger 1-D internal Heat Transfer Model (HTM) has been developed. Later geometrical models for compressor and turbine have been proposed to account for acoustic effects. A physically based methodology to extrapolate turbine performance maps has been developed too. That model improves turbocharged engine prediction since turbine instantaneous behaviour moves far from the narrow operative range provided in manufacturer maps. Once each separated model has been developed and validated, a series of tests considering all phenomena combined have been performed. Those tests have been designed to check model accuracy under likely operative conditions. The main contributions of this Thesis are the development of a 1-D heat transfer model to account for internal heat fluxes of automotive turbochargers; the development of a physically-based turbine extrapolation methodology; the several tests campaigns that have been necessary to study each phenomenon isolated from others and the integration of experiments and models in a comprehensive characterization procedure designed to provide 1-D predictive turbocharger models for ICE calculation. / Reyes Belmonte, MÁ. (2013). Contribution to the Experimental Characterization and 1-D Modelling of Turbochargers for IC Engines [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/34777 / TESIS

This thesis is motivated by the application of active flow control on the cabin of trucks, thereby providing a new means of drag reduction. Particularly, the work presented strives to identify how plasma actuators can be used to reduce the drag caused by the detachment of the flow around the A-pillars. This is achieved by conducting numerical simulations, and is part of a larger project that also includes experimental. The effect of plasma actuators is modeled through a body force, which adds very little computational cost and is suitable for implementation in most CFD solvers. The spatial distribution of this force is described by coefficients which have been optimized against experimental data, and the model was shown to be able to accurately reproduce the wall jet created by a single plasma actuator in a no-flow condition. A half cylinder geometry - a simplified geometry for the A-pillar of a truck - was used in a preliminary Large Eddy Simulation (LES) study that showed that the actuator alone, operated continuously, was not sufficient to achieve a significant reduction of the drag. Nevertheless, a significant drag reduction was obtained by simply increasing the strength of the body force to a higher value, showing that this type of actuation remains relevant for the reduction of drag. In the course of finding ways to improve the efficiency of the actuator, dynamic mode decomposition was investigated as a post-processing tool to extract structures in the flow. Such structures are identified by their spatial location and frequency, and might help to understand how the actuator should be used to maximize drag reduction. Thus a parallel code for dynamic mode decomposition was developed in order to facilitate the treatment of the large amounts of data obtained by LES. This code and LES itself were thereafter evaluated in the case of a pulsating channel flow. By using the dynamic mode decomposition it was possible to accurately extract oscillating profiles at the forcing frequency, although harmonics with lower amplitude compared to the turbulence intensity could not be obtained. / Denna avhandling behandlar tillämpningen av aktiv strömningskontroll för lastbilshytter, vilket är en ny metod för minskning av luftmotståndet. Mer i detalj är det övergripande målet att visa på hur plasmaaktuatorer kan användas för att minska luftmotståndet orsakat av avlösningen runt A-stolparna. In denna avhandling studeras detta genom numeriska simuleringar. Arbetet är en del av ett projekt där även experimentella försök görs. Effekten av plasmaaktuatorer modelleras genom en masskraft, vilket inte ger nämnvärd ökning av beräkningstiden och är lämplig för implementering i de flesta CFD-lösare. Den rumsliga fördelningen av kraften bestäms av koefficienter vilka i detta arbete beräknades utifrån experimentella data. Modellen har visat sig kunna återskapa en stråle nära väggen med god noggrannhet av en enskild plasmaaktuator för en halvcylinder utan strömning. Samma geometri - en halvcylinder som här används som förenklad geometri av A-stolpen på en lastbil - användes i en preliminär LES studie som visade att enbart aktuatorn vid kontinuerlig drift inte var tillräckligt för att uppnå en signifikant minskning av luftmotståndet. En signifikant minskning av luftmotståndet erhölls genom att helt enkelt öka styrkan på kraften, vilket visats att denna typ av strömningskontroll är relevant för minskning av luftmotståndet. I syfte att förbättra effektiviteten hos aktuatorn, studerades dynamic mode decomposition, som ett verktyg för efterbehandling för att få fram flödesstrukturer. Dessa strukturer identifieras genom deras rumsupplösning och frekvens och kan hjälpa till att förstå hur aktuatorerna bör användas för att minska luftmotståndet. En parallelliserad kod för dynamic mode decomposition utvecklades för att underlätta efterbehandlingen av de stora datamängder som fås från LES-beräkningarna. Slutligen, utvärderades denna kod och LES-beräkningar på ett strömningsfall med pulserande kanalflöde. Metoden, dynamic mode decomposition, visade sig kunna extrahera de oscillerande flödesprofilerna med hög noggrannhet för den påtvingade frekvensen. Övertoner med lägre amplitud jämfört med turbulensintensiteten kunde dock inte erhållas. / <p>QC 20150312</p>

The behaviour of particles in pulsating and oscillating flows is of practical interest in devices such as pulsation reactors and ultrasonic elevators. In addition to the resulting flow patterns, the influence of the flow on heat and mass transfer is often important. The state of the art in this area is already quite well developed with many different models, theories, and experiments published. However, only small parameter ranges of the behaviour of particles in pulsating and oscillating flows are considered, while an overarching theoretical framework does not yet exist. Therefore, this work presents a three-stage model for the behaviour of solid single particles in oscillating (pulsating) flows. The relative velocity between particle and fluid as well as the flow patterns around the particle, together with the heat and mass transfer at the particle are considered. The model levels build on top of each other, with the introduced ϵ-Re plain as a common connection between the levels. The number of input parameters could be limited to the five most important ones (fluid velocity amplitude, fluid oscillation frequency, fluid temperature, particle diameter, particle density), but these are considered in very large ranges. The relative velocity is largely calculated analytically using various flow resistance approaches. Direct numerical simulations were carried out to qualitatively estimate the flow patterns around the particle. The quantitative determination of a meta correlation for the entire ϵ-Re plane was carried out using 33 data sets from the literature. Conditions in pulsation reactors are particularly emphasized and their influence investigated.:Chapter 1. Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Chapter 2. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Chapter 3. State of the Art . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3.1. Material Treatment in the Pulsation Reactor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.2. Particle Motion in an Oscillating Fluid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.3. Steady Streaming (Flow Pattern). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 3.4. Heat and Mass Transfer in Oscillating Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 3.5. Heat and Mass Transfer in Pulsating Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 3.6. Non-continuum Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 Chapter 4. Basic Assumptions and Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 4.1. Input Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 4.2. Pulsating Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 4.3. Forces on the Particle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 4.4. Motion of Particles - Stokes Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 4.5. Harmonic Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 4.6. Dimensionless Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 4.7. The ϵ-Re Plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 Chapter 5. Motion of the Particle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 5.1. Drag Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 5.2. Slip Velocity Amplitude . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 5.3. Particle Relaxation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 5.4. Navigation in the ϵ-Re Plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 5.5. Extension of the Stokes Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 5.6. Additional Effects at Micro Scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 5.7. Analytical Particle Motion - Summary and Conclusion . . . . . . . . . . . . . . . . . . . . 61 Chapter 6. Flow Patterns in the Vicinity of the Particle . . . . . . . . . . . . . . . . . . . . . . . . . . 63 6.1. Creeping Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 6.2. Quasi-steady Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 6.3. Steady Streaming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 Chapter 7. Heat and Mass Transfer to Particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 7.1. Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 7.2. The Quasi-Steady HMT Area of the Plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 7.3. Models for Oscillating Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 7.4. Meta Correlation Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 7.5. Deviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 7.6. Quasi-Steady Assumption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 7.7. Heat and Mass Transfer to Small Particles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 7.8. Conclusion of Heat and Mass Transfer to Particles . . . . . . . . . . . . . . . . . . . . . . . . . 83 Chapter 8. Summary & Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 8.1. Model Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 8.2. Inŕuence of input parameters on the HMT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 8.3. The ϵ-Re Plane in the Special Case of the Pulsation Reactor . . . . . . . . . . . . . . 91 8.4. Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 Chapter 9. Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 Appendix A. Derivation and Solution of Particle Motion in the Stokes Model . . . . . i Appendix B. Derivation and Solution of Particle Motion in the Landau & Lifshitz Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii Appendix C. Derivation of Deviation between Stokes and Schiller & Naumann . . . . x Appendix D. Parameters and Algorithm of the Direct Numerical Simulation and Flow Pattern Visualisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii Appendix E. Conducted Data Preparation for HMT Models . . . . . . . . . . . . . . . . . . . . . . xv / Das Verhalten von Partikeln in pulsierenden und oszillierenden Strömungen findet praktisches Interesse in Apparaten wie Pulsationsreaktoren und Ultraschalllevitatoren. Dabei ist neben den entstehenden Strömungsmustern oft der Einfluss der Strömung auf den Wärme- und Stoffübergang von Bedeutung. Der Stand der Technik in der Literatur in diesem Bereich ist bereits recht weit entwickelt mit vielen verschiedenen Modellen, Theorien und Experimenten. Dabei werden jedoch stets nur kleine Parameterbereiche des Verhaltens von Partikeln in pulsierenden und oszillierenden Strömungen betrachtet, während ein übergreifender theoretischer Rahmen noch nicht existiert. Deshalb wird in dieser Arbeit ein dreistufiges Modell vorgestellt für das Verhalten von festen Einzelpartikeln in oszillierenden (pulsierenden) Fluidströmungen. Sowohl die Relativgeschwindigkeit zwischen Partikel und Fluid als auch die Strömungsmuster um das Partikel und der Wärme- und Stoffübergang am Partikel werden hierbei betrachtet. Die Modellebenen bauen aufeinander auf, wobei die eingeführte ϵ-Re-Ebene die Modellebenen miteinander verbinden. Die Anzahl der Eingangsparameter konnte auf die wichtigsten fünf (Fluidgeschwindigkeitsamplitude, Fluidoszillationsfrequenz, Fluidtemperatur, Partikeldurchmesser, Partikeldichte) begrenzt werden, diese werden jedoch in sehr großen Bereichen betrachtet. Die Relativgeschwindigkeit wird mittels verschiedener Strömungswiderstandsansätze größtenteils analytisch berechnet. Zur qualitativen Abschätzung der Strömungsmuster um das Partikel wurden direkte numerische Simulationen durchgeführt. Die quantitative Bestimmung einer Metakorrelation für die gesamte ϵ-Re-Ebene wurde mittels 33 Datensätze aus der Literatur durchgeführt. Dabei werden Bedingungen in Pulsationsreaktoren besonders herausgestellt und deren Einfluss untersucht.:Chapter 1. Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Chapter 2. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Chapter 3. State of the Art . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3.1. Material Treatment in the Pulsation Reactor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.2. Particle Motion in an Oscillating Fluid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.3. Steady Streaming (Flow Pattern). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 3.4. Heat and Mass Transfer in Oscillating Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 3.5. Heat and Mass Transfer in Pulsating Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 3.6. Non-continuum Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 Chapter 4. Basic Assumptions and Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 4.1. Input Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 4.2. Pulsating Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 4.3. Forces on the Particle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 4.4. Motion of Particles - Stokes Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 4.5. Harmonic Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 4.6. Dimensionless Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 4.7. The ϵ-Re Plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 Chapter 5. Motion of the Particle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 5.1. Drag Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 5.2. Slip Velocity Amplitude . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 5.3. Particle Relaxation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 5.4. Navigation in the ϵ-Re Plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 5.5. Extension of the Stokes Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 5.6. Additional Effects at Micro Scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 5.7. Analytical Particle Motion - Summary and Conclusion . . . . . . . . . . . . . . . . . . . . 61 Chapter 6. Flow Patterns in the Vicinity of the Particle . . . . . . . . . . . . . . . . . . . . . . . . . . 63 6.1. Creeping Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 6.2. Quasi-steady Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 6.3. Steady Streaming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 Chapter 7. Heat and Mass Transfer to Particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 7.1. Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 7.2. The Quasi-Steady HMT Area of the Plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 7.3. Models for Oscillating Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 7.4. Meta Correlation Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 7.5. Deviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 7.6. Quasi-Steady Assumption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 7.7. Heat and Mass Transfer to Small Particles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 7.8. Conclusion of Heat and Mass Transfer to Particles . . . . . . . . . . . . . . . . . . . . . . . . . 83 Chapter 8. Summary & Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 8.1. Model Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 8.2. Inŕuence of input parameters on the HMT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 8.3. The ϵ-Re Plane in the Special Case of the Pulsation Reactor . . . . . . . . . . . . . . 91 8.4. Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 Chapter 9. Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 Appendix A. Derivation and Solution of Particle Motion in the Stokes Model . . . . . i Appendix B. Derivation and Solution of Particle Motion in the Landau & Lifshitz Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii Appendix C. Derivation of Deviation between Stokes and Schiller & Naumann . . . . x Appendix D. Parameters and Algorithm of the Direct Numerical Simulation and Flow Pattern Visualisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii Appendix E. Conducted Data Preparation for HMT Models . . . . . . . . . . . . . . . . . . . . . . xv

Die Abgasturboaufladung erweist sich als sinnvolles Hilfsmittel den Kraftstoffverbrauch eines Hubkolbenverbrennungsmotors bei gleichbleibender Fahrdynamik zu verringern und somit die Effizienz des Motors zu erhöhen. Zur optimalen Nutzung der im Abgas enthaltenen Energie werden Abgassysteme moderner Pkw – Motoren äußerst kompakt ausgeführt, um der Abgasturboladerturbine ein möglichst hohes Enthalpiegefälle zur Verfügung zu stellen. Diese Umstände, sowie zunehmend kleinere Zylinderzahlen mit großen Zündabständen führen dazu, dass sich die Eintrittsbedingungen von Radialturbinen von Abgasturboladern heutiger Motoren periodisch ändern. Die Strömungsmaschine kann aufgrund ihrer Trägheit dem Druckanstieg nicht unverzögert folgen und wird vorwiegend bei niedrigen Schnelllaufzahlen betrieben. Die Entwicklung von Abgasturboladern und deren Anpassung an den Verbrennungsmotor erfolgen überwiegend auf Grundlage von messtechnisch ermittelten Kennfeldern von Verdichter und Turbine. Diese werden an stationär betriebenen Heißgasprüfständen ermittelt. Aufgrund der stationären Leistungsbilanz zwischen beiden Strömungsmaschinen an diesen Prüfständen beschreiben stationär gemessene Turbinenkennfelder nicht den gesamten motorrelevanten Betriebsbereich der Turbine. Für die Entwicklung innovativer Turboladerturbinen sind Untersuchungen der Turbinenwirkungsgrade und Durchsatzkennzahlen in diesen Betriebspunkten essentiell. Zur Untersuchung von Wechselwirkungen zwischen aufgeladenen Verbrennungsmotoren und Aufladesystemen stellt die Motorprozessrechnung eine wichtige Technologie dar. Die numerische Beschreibung des Turboladerverhaltens im Motorbetrieb erfolgt ebenfalls auf Basis von gemessenen Turboladerkennfeldern. Aufgrund des eingeschränkten Messbereichs der Turbinenkennfelder werden diese stark extrapoliert und beschreiben das thermodynamische Verhalten der Turboladerturbine fragwürdig. Die vorliegende Arbeit stellt ein neues Verfahren an einem erweiterten Heißgasprüfstand zur Vermessung und Untersuchung von Turboladerturbinen in motorrelevanten Betriebszuständen vor. Parallel wird ein Berechnungsmodell entwickelt, um Messergebnisse zu plausibilisieren und die numerische Beschreibung instationärer Turbinenströmungen zu untersuchen. Die Methode basiert auf der Ausnutzung zusätzlicher Beschleunigungsleistung zur Erhöhung der Aufnahme der Turbinenleistung, um niedrigere Schnelllaufzahlen unter motorrealistischen Randbedingungen untersuchen zu können. Mit Hilfe eines geeigneten Druckverlaufes werden temporär stationäre Strömungszustände erzeugt, sodass thermodynamische Zustände in der Turbine zuverlässig beschrieben werden können. Ferner werden Betriebsbedingungen der Turbinenuntersuchung denen der Turboladerturbine im Motorbetrieb angepasst. Kurzzeitig stellen sich quasi-stationäre Zustände ein, woraufhin phasenkorrigierte Messgrößen die Strömung in den Schaufelkanälen der Turbine belastbar beschreiben. Durch Variation der pulsierenden Strömung können Wirkungsgrad- und Massendurchsatzkennfelder mit hoher Abtastrate erweitert werden, wodurch verlässliche Interpolationen der Turbinenkennfelder bei niedrigen Laufzahlen möglich sind. Am Heißgasprüfstand lassen sich Turbineneintrittstemperatur, Druckamplitude und mittleres Druckverhältnis mit speziellen Impulsgeneratoren einstellen. Auch eine instationäre Massenstrommessung und Temperaturmessung ist möglich. Die instationäre Messmethode bildet eine Synthese mit stationären Turbinenvermessungen und deckt einen Großteil des Turbinenbetriebes aufgeladener Hubkolbenverbrennungsmotoren ab. Damit hat dieses Verfahren das Potential Turboladerkennfelder die am stationären Heißgasprüfstand ermittelt wurden sinnvoll zu ergänzen. Ergebnisse der neuen Messmethode werden mit Resultaten äquivalenter Simulationsrechnungen auf Grundlage stationär und instationär ermittelter Kennfelder verglichen. Auf Basis erweiterter Turbinenkennfelder können Wechselwirkungen zwischen dem Verbrennungsmotor und dem Aufladeaggregat mit Hilfe der Motorprozessrechnung genauer untersucht werden. Dies ermöglicht eine ideale Anpassung des Abgasturboladers an den Motor, wodurch Effizienz und Dynamik verbessert sowie Abgasemissionswerte des Antriebes reduziert werden können.