Consider again the example of subsurface contamination but now with a source of thermal energy. This could for example be a so-called heat well which is an enhanced subsurface remediation technique as displayed in Figure 2.9, top. At the spot where thermal energy is brought into the system, the soil and the fluid phases are heated and heat is also transported to the surrounding area by convection and conduction. In some cases, the source of thermal energy may even be that strong that a liquid phase reaches its boiling point. To capture these effects, a rather expensive, non- isothermal compositional multiphaseflow model has to be set up. This is, however, not necessary in all parts of the model domain since a significant change in temperature only takes place near the heat source. It is therefore proposed to incorporate non- isothermal models in this subdomain of special interest. A possible model domain setup for this approach is sketched in Figure 2.9, bottom, where the subdomain for the non-isothermal models is marked by the dashed rectangle (green). Inside this subdomain, non-isothermal isoenergetic phase equilibrium calculations as presented in Section 3.3.4 and the non-isothermal pressure equation (2.76) are applied. For the case of non-isothermal one-phase flow, equation (2.76) can be simplified in a similar way as presented in Section 2.8.1, where the term containing the derivative of total specific volume subject to internal energy will remain to get
The purpose of this report is to give students that are already familiar with the physics and numerical computation of single phase flow a compact introduction into the computational modeling of multiphase flows. The report is restricted to the hydrodynamics of multiphaseflow and does not consider heat transfer, mass transfer and phase change. The report gives first an insight in the fundamental hydrodynamical phenomena of multiphase flows. It then presents the most popular modeling concepts for multiphase flows and points out their achievements and limitations. It details the continuous or interpenetrating field formulation of two-phase flow based on a volume averaging procedure and presents the related models as there are the homoge- neous model, the diffusion model and drift flux model, and the two-fluid model. The report also discusses the Euler-Lagrange approach for disperse flow as well as interface resolving simulation methods such as the volume-of-fluid method, the level-set method and the front-tracking method.
An extension of the Turbulent Flame Speed Closure model rendering the model applicable to multiphaseflow and ignition is presented. As formerly no coupling between reaction progress variable and enthalpy was existent, except through the temperature dependency of the laminar flame speed, an adaptation is proposed which offers an interface to initiate the combustion process. The modification to incorporate multiphase conditions is achieved by substituting the mixture fraction variable as representation of the composition in the original implementation of the Turbulent Flame Speed Closure model with independent species. Source terms to correlate the species progress to the reaction progress variable are derived in this work. The additional transport equations serve a higher generality of the model and enable the proper treatment of vaporizing fuel droplets. It is demonstrated that limitations which arise in the standard formulation of the model, stemming from differences in the transport equation for the reaction progress variable and the mixture fraction, are addressed and resolved by the new approach. Regarding the initiation of the flame, an additional source term for the reaction progress variable is introduced, which relates the reaction progress to the auto-ignition time. This allows the development of the flame without imposing artificial boundary conditions. The correct model behavior is established by means of a series of widely used test cases. The results of these simulations show that the model’s potential to predict flame growth and more generally the flame evolution as a function of time and space is preserved. At the same time more sophisticated test case boundary conditions involving multiphase conditions and variable inflows in terms of composition can be incorporated. As a thorough assessment of the extended model capabilities, a multiphase lab scale set-up, which provides a comprehensive data set, is presented. The good agreement of the obtained results underline the range of applicability of the extended model and its accuracy, albeit its simplicity, for multiphase conditions.
for implementation and discuss some implementation details in the first section. In the second section we will describe the three different test cases that were used for this work and their numerical realization for the calculation of the primal solutions. In particular this means that the flow fields governed by the incompressible single-phase and multi- phase Navier-Stokes equations are calculated and validated. Following these simulations of flow problems with static objects we will take a look at dynamic calculations for the determination of running attitudes of ships in multiphaseflow in the third section. After the realization and validation of these dynamic simulations using the equations of motion the aim is to accelerate the solution process of this flow problem. The first approach to achieve this is by the application of damping forces to the equations of motion as de- scribed in Section 2.7.4. This will be presented in the same section and compared to the results computed before, which serve as reference solutions. Afterwards the flow prob- lem is solved with the mathematical approach developed throughout the Chapters 3-5 that deploys gradient-based optimization. Hence, in the fourth section the calculation of gradients is realized with the newly developed adjoint method, and the results are com- pared and validated. Finally the gradient-based optimization process for the calculation of optimal body positions is carried out and validated.
Several important combustion systems involve particles or liquid droplets flowing within a turbu- lent flow resulting in multiphaseflow systems. This is the case of IC engines or aircraft combustion chambers in which the liquid fuel used undergoes breakup, atomization, dispersion, evaporation and subsequent combustion. Other systems use solid particles or bubbles under reacting or isother- mal conditions (e.g. firing of wastes, coals; fluidized bed combustion; Cryogenic engine, chemical looping etc.). The overall common feature is the multi-scale and multi-physical character of the systems whereby various physical and chemical processes may occur and interact. In particular, the multiphase flows involve movements of many individual particles and their interaction with the carrier flow turbulence, mass transfer between fluid and particulate phase, heat transfer between the phases and their surrounding phase and interaction between the individual particles themselves. It is even more complicated when the particles/droplets change their physical state and experience combustion after appropriate mixture formation at both micro- and meso-scale levels.
1.4 TAYLOR (SLUG) FLOW IN THE CAPILLARY MICROREACTORS
Taylor flow is a flow pattern observed in microchannels, in which a series of plugs of one phase are separated by a series of plugs of another phase (Kashid et al., 2014). The small diameter of the microchannels allows formation of highly ordered laminar flow and enhances the interactions between the walls of the capillary and the fluid as well as between the phases, what enables the formation of this flow pattern (Aoki et al., 2011). The phases can be described as either a continuous phase (the fluid that forms a thin film on the inner walls of the capillary) or a dispersed phase (the fluid that forms the uniform plugs surrounded by the continuous phase) (Čech et al., 2013). Slug flow microreactors are widely used in chemical processing, since they offer numerous advantages over other multiphaseflow settings. The main advantages are enhanced mixing and mass transfer rates between the two phases as well as improved heat transfer (Antony et al., 2014).
The paper presents the implementation of non-Newtonian fluid properties for compressible multiphase solver in the open source framework Open- FOAM. The transport models for Power Law, Cross Power Law, Casson, Bird-Carreau and Herschel-Bulkley fluids were included in the thermophysi- cal model library. Appropriate non-Newtonian liquids have been chosen from literature, and pressure driven test simulations are carried out. There- fore, the solver compressibleInterFoam is used to compute air-liquid mixture flows over a backward facing step. A validation of the novel models has been performed by means of a sample-based comparison of the strain rate viscosity relation. The theoretical rheological properties of the selected liquids agree well with the results of the simulated data.
6.3.3. Experimental procedure
In a typical kinetic reaction run, the catalyst is placed in the baskets attached to a rotating shaft located into the water phase. Given that in our experimental set up the effect of the adsorption and chemical reaction cannot be separated; the cumulated effect of these steps will be studied together; therefore three 2-butanol concentration levels were used in these experiments: 5, 8 and 20 wt%. At the beginning, the reactor was filled with water- SBA mixtures and the operating pressure was set. The reactor was heated to the desired reaction temperature, between 117-130°C. After the desired temperature was achieved, the butene starts to be fed into the reactor, until the separation line between the phases reaches the middle of the reactor. After the volumetric butene:water ratio was set and corresponding to this the volumetric flow was adjusted, the stirrer was started. The operating parameters are given in table 6.2.
An independent estimation of the model parameters has been discussed by Qian and Cai ( 2001 ) in order to find a best set of constants for the k − model. The corresponding optimization problem was solved in this case applying the Newton- Raphson scheme, investigating three configurations: channel flow with Reynolds number 388 000, backward facing step (BFS) with expansion rate 1.5 and Reynolds number 44 000 and BFS with expansion rate 1.125 and Reynolds number 36 000. This differs from the present work, as the parameter estimation has been performed separately for each cases. The authors finally do not come up with a single, best set of model parameters. Moreover, some of the optimal values differ strongly from the conventional values (see Table 4.1 ), which might be surprising for such a well- established model.
A multiphase composite with periodic distributed in- clusions with a smooth boundary is considered in this contribution. The composite component materials are supposed to be linear viscoelastic and aging (of the nonconvolution integral type, for which the Laplace transform with respect to time is not effectively ap- plicable) and are subjected to isotropic shrinkage. The free shrinkage deformation can be considered as a ficti- tious temperature deformation in the behavior law. The procedure presented in this paper proposes a way to determine average (effective homogenized) viscoelastic and shrinkage (temperature) composite properties and the homogenized stressfield from known properties of the components. This is done by the extension of the asymptotic homogenization technique known for pure elastic nonhomogeneous bodies to the nonhomo- geneous thermoviscoelasticity of the integral noncon- volution type. Up to now, the homogenization theory has not covered viscoelasticity of the integral type. SanchezPalencia (1980), Francfort & Suquet (1987) (see , ) have considered homogenization for viscoelas- ticity of the differential form and only up to the first derivative order. The integralmodeled viscoelasticity is more general then the differential one and includes almost all known differential models. The homogeni- zation procedure is based on the construction of an asymptotic solution with respect to a period of the composite structure. This reduces the original problem to some auxiliary boundary value problems of elastic- ity and viscoelasticity on the unit periodic cell, of the same type as the original non-homogeneous problem. The existence and uniqueness results for such problems were obtained for kernels satisfying some constrain conditions. This is done by the extension of the Volterra integral operator theory to the Volterra operators with respect to the time, whose 1 kernels are space linear operators for any fixed time variables. Some ideas of such approach were proposed in  and , where the Volterra operators with kernels depending addi- tionally on parameter were considered. This manuscript delivers results of the same nature for the case of the spaceoperator kernels.
In the standard toolbox of OpenFOAM, the available generic boundary conditions are often not practical for hydraulic engineering investigations. Only with some workarounds it is possible to set a fixed water level or a specific water inflow condition, when simulating with the VoF-solver interFoam. This was the motivation to develop a set of boundary conditions for hydraulic engineering purposes. In particular, a boundary condition for a fixed water level (to be used primarily at the downstream side of a model) and one for a fixed flow rate of water independent from the water level (to be used at the upstream side) were developed amongst others at the Federal Institute for Waterway Engineering and Research. A more de- tailed description of this code extension can be found in Thorenz und Strybny (2012). A release of the code to the public is planned in the near future.
the tool. Developing single-phase coatings, which provide a high hardness, low adhesion to molten metals, high toughness, thermal stability, oxida- tion resistance, and corrosive resistance is chal- lenging . Based on this spectrum of properties, multiphase hardcoatings with a nanocomposite structure ensure an enhanced overall performance and attracted much attention in recent years [1- 10]. Nanocomposite coatings contain nanocrys- talline (nc-) grains that are embedded in an amor- phous (a-) matrix material (see Fig. 1) [2,3].
Steel is still the most important construction material for private and utility vehicles. The saving of fuel based on crude oil is therefore always associated with a reduction in weight of the components made of steel. The dimensioning of these components plays an important role for the weight reduction of modern vehicles. If components are particularly efficient, they are able to withstand the loads occurring with minimum material usage throughout the entire product life. For efficient components, considering the toughness of modern multiphase steels is a main factor. So far, there is no suitable method to investigate sheets with small thicknesses in an experiment that is comparable to the Charpy impact test. Therefore, a new test procedure for steels with sheet thicknesses below 2 mm has been developed in recent years at the Steel Institute of RWTH-Aachen. This procedure can be used to avoid over-dimensioning with unnecessary reserves, which lead to inefficient vehicles with high fuel consumption. The method proposed in this article for the investigation of these materials is the tensile impact test. This enables the toughness examination of thin sheets and provides information about their behavior in relevant stress situations.
The internal deformation history of high-grade marble bod- ies in the migmatitic centre of the Naxos metamorphic dome is recorded by multiphase boudinage and folding of amphi- bolite layers. We identified five generations of boudins with age relationships and orientations consistent across different marble bodies in the migmatite complex. The boudin gener- ations are from oldest to youngest: two generations of pinch- and-swell boudins, the first with a longer and the second with a shorter wavelength. These are followed by domino boudins, torn boudins and hairline veins reflecting embrit- tlement of the amphibolite layers. Outcrop-scale asymmet- ric folds predate torn boudins and hairline veins. Folds and domino boudins occur in both chiralities and indicate lo- cally deviating shear sense. The long-wavelength pinch-and- swell boudins are consistent with synmigmatic flow in the surrounding rocks. The timing and nature of static recrystal- lization in the amphibolite therefore remains elusive: if static recrystallization coincided with peak M2 b , both pinch-and-
The temperature distribution in the vapor region is of even more importance. The difference between isothermal and adiabatic expansion is tremendous due to the very high Joule- Thomson coefficient. This is demonstrated by various expansion scenarios, as depicted in Figure 5. To end up at low pressure and minus 40°C, one may start at high pressure, 60barg/-40°C and expand isothermally, A → C, or start from 60barg/+40°C and expand adiabatically, B → C. Starting from 60barg/+40°C, expanding to low pressure and +40°C is again an isothermal process. Whether expanding adiabatically or isothermally, or at least close to the ideal thermodynamic changes of state, respectively, is solely depending on the amount of leakage. Low leakage allows sufficient heat to be transferred from seat and seal face into the fluid, thus keeping the fluid temperature virtually unchanged. In the opposite extreme, if the amount of flow is high, the rate of heat transferred from the rings is not sufficient to compensate the temperature drop in the CO 2 . Starting from
The aim of the present intercomparison is to figure out the effect of different microphysical approaches and numerical schemes on cloud chemistry and, at last, on changes in particle composition and size distribution by microphysical processes. Moreover, these changes feed back on cloud microphysics. From the numerical point of view, the participating models differ in the manner of coupling between micro- physics and multiphase chemistry, the discretization of the particle/droplet spectrum and the time integration schemes, see chapter 2. Two principal approaches for cou- pling microphysics and multiphase chemistry are considered. In the ”fully-coupled” approach (Knoth, 2005), the model equations for the microphysical variables (tem- perature, water vapor, liquid water content) as well as for all chemical species are considered as one system which is integrated in a coupled manner by an implicit- explicit time integration scheme. Therefore, the splitting error between microphysics and multiphase is avoided. The second approach is the coupled model (spaccim ) presented in chapter 4. This approach allows the coupling of a complex multi- phase chemistry model with microphysical codes of various types. In this study, the multiphase chemistry is coupled to three microphysical models which use different discretization techniques of the particle/droplet spectrum.
A toroidal core is also alternative approach to produce a symmetrical coupled inductor, for a 3-phase coupled inductor via theory analysis a perfect symmetrical coupled inductor is obtained. Each phase has almost same leakage inductance and mutual inductance base on the model analysis of magnetic circuit. Therefore, it is recommended for multiphase interleaved converter with coupled inductor. However, one of main disadvantage of this core structure is concerning air-gap. For a storage inductor, an air-gap is quite important for the consideration in case of magnetic sat- uration under high current condition. Therefore, with increasing of output current, the practical inductance of using toroidal is possible to be decreased, and in a result output ripple current is also enlarged due to decreasing inductance. Following, related power losses such as conduction losses, copper losses, core loses and switching losses is possible to be increased. Based on this reason, in order to overcome this shortcoming, required winding turns have to be increased in order to avoid magnetic saturation or sloping of inductances. This approach will directly lead to high copper losses of each coupled inductor. Hereby for the large current application, it should be considered carefully due to above mentioned issues.
In dem hier vorgestellten Forschungsprojekt sollten Flow-Zustände bei Lesern empirisch nachgewiesen, Zusammenhänge zwischen Flow und anderen Konzepten zum Leseerleben modelliert und das Potenzial der Flow-Theorie für die experimentelle und psychophysiolo- gische Leseforschung aufgezeigt werden. Anhand einer speziell an den Lesekontext adaptier- ten Flow-Kurzskala und eines neuentwickelten, alle Flow-Komponenten umfassenden lese- spezifischen Fragebogens konnte stichhaltige Evidenz für Flow-Zustände beim Lesen er- bracht werden. Es zeigte sich zudem, dass Flow als zentraler Prädiktor für Lesefreude, Text- verständnis und vielschichtige Leseerlebnisse eine Schlüsselrolle im Leseprozess einnehmen kann, nicht zuletzt durch die Vermittlung anderer Erlebnisformen wie Presence. Auch unter kontrollierten Laborbedingungen war es möglich, Flow bei Lesern zu beobachten. Das Zu- sammenspiel von Faktoren auf Seiten von Text und Leser konnte hierbei insofern demons- triert werden, als kardiale Vagotonie, ein psychophysiologischer Indikator für innere Ent- spannung beim Leser, und der stilistische Anspruchsgrad des Textes in Interaktion mitein- ander Flow vorhersagten. Jedoch fanden sich keine Hinweise auf eine Veränderung der Herz- aktivität durch Flow-Erleben beim Lesen oder auf ein über Lesesituationen hinweg mit Flow assoziiertes kardiovaskuläres Muster, das als objektiver Flow-Indikator dienen könnte. Psychometrische Erfassung von Flow beim Lesen