76 resultados para Fluid Flow Modeling

em Doria (National Library of Finland DSpace Services) - National Library of Finland, Finland


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Diplomityön tavoitteena oli tarkastella numeerisen virtauslaskennan avulla virtaukseen liittyviä ilmiöitä ja kaasun dispersiota. Diplomityön sisältö on jaettu viiteen osaan; johdantoon, teoriaan, katsaukseen virtauksen mallinnukseen huokoisessa materiaalissa liittyviin tutkimusselvityksiin, numeeriseen mallinnukseen sekä tulosten esittämiseen ja johtopäätöksiin. Diplomityön alussa kiinnitettiin huomiota erilaisiin kokeellisiin, numeerisiin ja teoreettisiin mallinnusmenetelmiin, joilla voidaan mallintaa virtausta huokoisessa materiaalissa. Kirjallisuusosassa tehtiin katsaus aikaisemmin julkaistuihin puoliempiirisiin ja empiirisiin tutkimusselvityksiin, jotka liittyvät huokoisen materiaalin aiheuttamaan painehäviöön. Numeerisessa virtauslaskenta osassa rakennettiin ja esitettiin huokoista materiaalia kuvaavat numeeriset mallit käyttäen kaupallista FLUENT -ohjelmistoa. Työn lopussa arvioitiin teorian, numeerisen virtauslaskennan ja kokeellisten tutkimusselvitysten tuloksia. Kolmiulotteisen huokoisen materiaalinnumeerisessa mallinnuksesta saadut tulokset vaikuttivat lupaavilta. Näiden tulosten perusteella tehtiin suosituksia ajatellen tulevaa virtauksen mallinnusta huokoisessa materiaalissa. Osa tässä diplomityössä esitetyistä tuloksista tullaan esittämään 55. Kanadan Kemiantekniikan konferenssissa Torontossa 1619 Lokakuussa 2005. ASME :n kansainvälisessä tekniikan alan julkaisussa. Työ on hyväksytty esitettäväksi esitettäväksi laskennallisen virtausmekaniikan (CFD) aihealueessa 'Peruskäsitteet'. Lisäksi työn yksityiskohtaiset tulokset tullaan lähettämään myös CES:n julkaisuun.

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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.

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The objective of the work is to study fluid flow behavior through a pinch valve and to estimate the flow coefficient (KV ) at different opening positions of the valve. The flow inside a compressed valve is more complex than in a straight pipe, and it is one of main topics of interest for engineers in process industry. In the present work, we have numerically simulated compressed valve flow at different opening positions. In order to simulate the flow through pinch valve, several models of the elastomeric valve tube (pinch valve tube) at different opening positions were constructed in 2D-axisymmetric and 3D geometries. The numerical simulations were performed with the CFD packages; ANSYS FLUENT and ANSYS CFX by using parallel computing. The distributions of static pressure, velocity and turbulent kinetic energy have been studied at different opening positions of the valve in both 2D-axisymmetric and 3D experiments. The flow coefficient (KV ) values have been measured at different valve openings and are compared between 2D-axisymmetric and 3D simulation results.

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Hydraulic head is distributed through a medium with porous aspect. The analysis of hydraulic head from one point to another is used by the Richard's equation. This equation is equivalent to the groundwater ow equation that predicts the volumetric water contents. COMSOL 3.5 is used for computation applying Richard's equation. A rectangle of 100 meters of length and 10 meters of large (depth) with 0,1 m/s fl ux of inlet as source of our fl uid is simulated. The domain have Richards' equation model in two dimension (2D). Hydraulic head increases proportional with moisture content.

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The bedrock of old crystalline cratons is characteristically saturated with brittle structures formed during successive superimposed episodes of deformation and under varying stress regimes. As a result, the crust effectively deforms through the reactivation of pre-existing structures rather than by through the activation, or generation, of new ones, and is said to be in a state of 'structural maturity'. By combining data from Olkiluoto Island, southwestern Finland, which has been investigated as the potential site of a deep geological repository for high-level nuclear waste, with observations from southern Sweden, it can be concluded that the southern part of the Svecofennian shield had already attained structural maturity during the Mesoproterozoic era. This indicates that the phase of activation of the crust, i.e. the time interval during which new fractures were generated, was brief in comparison to the subsequent reactivation phase. Structural maturity of the bedrock was also attained relatively rapidly in Namaqualand, western South Africa, after the formation of first brittle structures during Neoproterozoic time. Subsequent brittle deformation in Namaqualand was controlled by the reactivation of pre-existing strike-slip faults.In such settings, seismic events are likely to occur through reactivation of pre-existing zones that are favourably oriented with respect to prevailing stresses. In Namaqualand, this is shown for present day seismicity by slip tendency analysis, and at Olkiluoto, for a Neoproterozoic earthquake reactivating a Mesoproterozoic fault. By combining detailed field observations with the results of paleostress inversions and relative and absolute time constraints, seven distinctm superimposed paleostress regimes have been recognized in the Olkiluoto region. From oldest to youngest these are: (1) NW-SE to NNW-SSE transpression, which prevailed soon after 1.75 Ga, when the crust had sufficiently cooled down to allow brittle deformation to occur. During this phase conjugate NNW-SSE and NE-SW striking strike-slip faults were active simultaneous with reactivation of SE-dipping low-angle shear zones and foliation planes. This was followed by (2) N-S to NE-SW transpression, which caused partial reactivation of structures formed in the first event; (3) NW-SE extension during the Gothian orogeny and at the time of rapakivi magmatism and intrusion of diabase dikes; (4) NE-SW transtension that occurred between 1.60 and 1.30 Ga and which also formed the NW-SE-trending Satakunta graben located some 20 km north of Olkiluoto. Greisen-type veins also formed during this phase. (5) NE-SW compression that postdates both the formation of the 1.56 Ga rapakivi granites and 1.27 Ga olivine diabases of the region; (6) E-W transpression during the early stages of the Mesoproterozoic Sveconorwegian orogeny and which also predated (7) almost coaxial E-W extension attributed to the collapse of the Sveconorwegian orogeny. The kinematic analysis of fracture systems in crystalline bedrock also provides a robust framework for evaluating fluid-rock interaction in the brittle regime; this is essential in assessment of bedrock integrity for numerous geo-engineering applications, including groundwater management, transient or permanent CO2 storage and site investigations for permanent waste disposal. Investigations at Olkiluoto revealed that fluid flow along fractures is coupled with low normal tractions due to in-situ stresses and thus deviates from the generally accepted critically stressed fracture concept, where fluid flow is concentrated on fractures on the verge of failure. The difference is linked to the shallow conditions of Olkiluoto - due to the low differential stresses inherent at shallow depths, fracture activation and fluid flow is controlled by dilation due to low normal tractions. At deeper settings, however, fluid flow is controlled by fracture criticality caused by large differential stress, which drives shear deformation instead of dilation.

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This thesis work deals with a mathematical description of flow in polymeric pipe and in a specific peristaltic pump. This study involves fluid-structure interaction analysis in presence of complex-turbulent flows treated in an arbitrary Lagrangian-Eulerian (ALE) framework. The flow simulations are performed in COMSOL 4.4, as 2D axial symmetric model, and ABAQUS 6.14.1, as 3D model with symmetric boundary conditions. In COMSOL, the fluid and structure problems are coupled by monolithic algorithm, while ABAQUS code links ABAQUS CFD and ABAQUS Standard solvers with single block-iterative partitioned algorithm. For the turbulent features of the flow, the fluid model in both codes is described by RNG k-ϵ. The structural model is described, on the basis of the pipe material, by Elastic models or Hyperelastic Neo-Hookean models with Rayleigh damping properties. In order to describe the pulsatile fluid flow after the pumping process, the available data are often defective for the fluid problem. Engineering measurements are normally able to provide average pressure or velocity at a cross-section. This problem has been analyzed by McDonald's and Womersley's work for average pressure at fixed cross section by Fourier analysis since '50, while nowadays sophisticated techniques including Finite Elements and Finite Volumes exist to study the flow. Finally, we set up peristaltic pipe simulations in ABAQUS code, by using the same model previously tested for the fl uid and the structure.

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A rigorous unit operation model is developed for vapor membrane separation. The new model is able to describe temperature, pressure, and concentration dependent permeation as wellreal fluid effects in vapor and gas separation with hydrocarbon selective rubbery polymeric membranes. The permeation through the membrane is described by a separate treatment of sorption and diffusion within the membrane. The chemical engineering thermodynamics is used to describe the equilibrium sorption of vapors and gases in rubbery membranes with equation of state models for polymeric systems. Also a new modification of the UNIFAC model is proposed for this purpose. Various thermodynamic models are extensively compared in order to verify the models' ability to predict and correlate experimental vapor-liquid equilibrium data. The penetrant transport through the selective layer of the membrane is described with the generalized Maxwell-Stefan equations, which are able to account for thebulk flux contribution as well as the diffusive coupling effect. A method is described to compute and correlate binary penetrant¿membrane diffusion coefficients from the experimental permeability coefficients at different temperatures and pressures. A fluid flow model for spiral-wound modules is derived from the conservation equation of mass, momentum, and energy. The conservation equations are presented in a discretized form by using the control volume approach. A combination of the permeation model and the fluid flow model yields the desired rigorous model for vapor membrane separation. The model is implemented into an inhouse process simulator and so vapor membrane separation may be evaluated as an integralpart of a process flowsheet.

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The transport of macromolecules, such as low-density lipoprotein (LDL), and their accumulation in the layers of the arterial wall play a critical role in the creation and development of atherosclerosis. Atherosclerosis is a disease of large arteries e.g., the aorta, coronary, carotid, and other proximal arteries that involves a distinctive accumulation of LDL and other lipid-bearing materials in the arterial wall. Over time, plaque hardens and narrows the arteries. The flow of oxygen-rich blood to organs and other parts of the body is reduced. This can lead to serious problems, including heart attack, stroke, or even death. It has been proven that the accumulation of macromolecules in the arterial wall depends not only on the ease with which materials enter the wall, but also on the hindrance to the passage of materials out of the wall posed by underlying layers. Therefore, attention was drawn to the fact that the wall structure of large arteries is different than other vessels which are disease-resistant. Atherosclerosis tends to be localized in regions of curvature and branching in arteries where fluid shear stress (shear rate) and other fluid mechanical characteristics deviate from their normal spatial and temporal distribution patterns in straight vessels. On the other hand, the smooth muscle cells (SMCs) residing in the media layer of the arterial wall respond to mechanical stimuli, such as shear stress. Shear stress may affect SMC proliferation and migration from the media layer to intima. This occurs in atherosclerosis and intimal hyperplasia. The study of blood flow and other body fluids and of heat transport through the arterial wall is one of the advanced applications of porous media in recent years. The arterial wall may be modeled in both macroscopic (as a continuous porous medium) and microscopic scales (as a heterogeneous porous medium). In the present study, the governing equations of mass, heat and momentum transport have been solved for different species and interstitial fluid within the arterial wall by means of computational fluid dynamics (CFD). Simulation models are based on the finite element (FE) and finite volume (FV) methods. The wall structure has been modeled by assuming the wall layers as porous media with different properties. In order to study the heat transport through human tissues, the simulations have been carried out for a non-homogeneous model of porous media. The tissue is composed of blood vessels, cells, and an interstitium. The interstitium consists of interstitial fluid and extracellular fibers. Numerical simulations are performed in a two-dimensional (2D) model to realize the effect of the shape and configuration of the discrete phase on the convective and conductive features of heat transfer, e.g. the interstitium of biological tissues. On the other hand, the governing equations of momentum and mass transport have been solved in the heterogeneous porous media model of the media layer, which has a major role in the transport and accumulation of solutes across the arterial wall. The transport of Adenosine 5´-triphosphate (ATP) is simulated across the media layer as a benchmark to observe how SMCs affect on the species mass transport. In addition, the transport of interstitial fluid has been simulated while the deformation of the media layer (due to high blood pressure) and its constituents such as SMCs are also involved in the model. In this context, the effect of pressure variation on shear stress is investigated over SMCs induced by the interstitial flow both in 2D and three-dimensional (3D) geometries for the media layer. The influence of hypertension (high pressure) on the transport of lowdensity lipoprotein (LDL) through deformable arterial wall layers is also studied. This is due to the pressure-driven convective flow across the arterial wall. The intima and media layers are assumed as homogeneous porous media. The results of the present study reveal that ATP concentration over the surface of SMCs and within the bulk of the media layer is significantly dependent on the distribution of cells. Moreover, the shear stress magnitude and distribution over the SMC surface are affected by transmural pressure and the deformation of the media layer of the aorta wall. This work reflects the fact that the second or even subsequent layers of SMCs may bear shear stresses of the same order of magnitude as the first layer does if cells are arranged in an arbitrary manner. This study has brought new insights into the simulation of the arterial wall, as the previous simplifications have been ignored. The configurations of SMCs used here with elliptic cross sections of SMCs closely resemble the physiological conditions of cells. Moreover, the deformation of SMCs with high transmural pressure which follows the media layer compaction has been studied for the first time. On the other hand, results demonstrate that LDL concentration through the intima and media layers changes significantly as wall layers compress with transmural pressure. It was also noticed that the fraction of leaky junctions across the endothelial cells and the area fraction of fenestral pores over the internal elastic lamina affect the LDL distribution dramatically through the thoracic aorta wall. The simulation techniques introduced in this work can also trigger new ideas for simulating porous media involved in any biomedical, biomechanical, chemical, and environmental engineering applications.

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The reduction of greenhouse gas emissions in the European Union promotes the combustion of biomass rather than fossil fuels in energy production. Circulating fluidized bed (CFB) combustion offers a simple, flexible and efficient way to utilize untreated biomass in a large scale. CFB furnaces are modeled in order to understand their operation better and to help in the design of new furnaces. Therefore, physically accurate models are needed to describe the heavily coupled multiphase flow, reactions and heat transfer inside the furnace. This thesis presents a new model for the fuel flow inside the CFB furnace, which acknowledges the physical properties of the fuel and the multiphase flow phenomena inside the furnace. This model is applied with special interest in the firing of untreated biomass. An experimental method is utilized to characterize gas-fuel drag force relations. This characteristic drag force approach is developed into a gas-fuel drag force model suitable for irregular, non-spherical biomass particles and applied together with the new fuel flow model in the modeling of a large-scale CFB furnace. The model results are physically valid and achieve very good correspondence with the measurement results from large-scale CFB furnace firing biomass. With the methods and models presented in this work, the fuel flow field inside a circulating fluidized bed furnace can be modeled with better accuracy and more efficiently than in previous studies with a three-dimensional holistic model frame.

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This thesis is focused on process intensification. Several significant problems and applications of this theme are covered. Process intensification is nowadays one of the most popular trends in chemical engineering and attempts have been made to develop a general, systematic methodology for intensification. This seems, however, to be very difficult, because intensified processes are often based on creativity and novel ideas. Monolith reactors and microreactors are successful examples of process intensification. They are usually multichannel devices in which a proper feed technique is important for creating even fluid distribution into the channels. Two different feed techniques were tested for monoliths. In the first technique a shower method was implemented by means of perforated plates. The second technique was a dispersion method using static mixers. Both techniques offered stable operation and uniform fluid distribution. The dispersion method enabled a wider operational range in terms of liquid superficial velocity. Using dispersion method, a volumetric gas-liquid mass transfer coefficient of 2 s-1 was reached. Flow patterns play a significant role in terms of the mixing performance of micromixers. Although the geometry of a T-mixer is simple, channel configurations and dimensions had a clear effect on mixing efficiency. The flow in the microchannel was laminar, but the formation of vortices promoted mixing in micro T-mixers. The generation of vortices was dependent on the channel dimensions, configurations and flow rate. Microreactors offer a high ratio of surface area to volume. Surface forces and interactions between fluids and surfaces are, therefore, often dominant factors. In certain cases, the interactions can be effectively utilised. Different wetting properties of solid materials (PTFE and stainless steel) were applied in the separation of immiscible liquid phases. A micro-scale plate coalescer with hydrophilic and hydrophobic surfaces was used for the continuous separation of organic and aqueous phases. Complete phase separation occurred in less than 20 seconds, whereas the separation time by settling exceeded 30 min. Fluid flows can be also intensified in suitable conditions. By adding certain additives into turbulent fluid flow, it was possible to reduce friction (drag) by 40 %. Drag reduction decreases frictional pressure drop in pipelines which leads to remarkable energy savings and decreases the size or number of pumping facilities required, e.g., in oil transport pipes. Process intensification enables operation often under more optimal conditions. The consequent cost savings from reduced use of raw materials and reduced waste lead to greater economic benefits in processing.

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There is an increasing reliance on computers to solve complex engineering problems. This is because computers, in addition to supporting the development and implementation of adequate and clear models, can especially minimize the financial support required. The ability of computers to perform complex calculations at high speed has enabled the creation of highly complex systems to model real-world phenomena. The complexity of the fluid dynamics problem makes it difficult or impossible to solve equations of an object in a flow exactly. Approximate solutions can be obtained by construction and measurement of prototypes placed in a flow, or by use of a numerical simulation. Since usage of prototypes can be prohibitively time-consuming and expensive, many have turned to simulations to provide insight during the engineering process. In this case the simulation setup and parameters can be altered much more easily than one could with a real-world experiment. The objective of this research work is to develop numerical models for different suspensions (fiber suspensions, blood flow through microvessels and branching geometries, and magnetic fluids), and also fluid flow through porous media. The models will have merit as a scientific tool and will also have practical application in industries. Most of the numerical simulations were done by the commercial software, Fluent, and user defined functions were added to apply a multiscale method and magnetic field. The results from simulation of fiber suspension can elucidate the physics behind the break up of a fiber floc, opening the possibility for developing a meaningful numerical model of the fiber flow. The simulation of blood movement from an arteriole through a venule via a capillary showed that the model based on VOF can successfully predict the deformation and flow of RBCs in an arteriole. Furthermore, the result corresponds to the experimental observation illustrates that the RBC is deformed during the movement. The concluding remarks presented, provide a correct methodology and a mathematical and numerical framework for the simulation of blood flows in branching. Analysis of ferrofluids simulations indicate that the magnetic Soret effect can be even higher than the conventional one and its strength depends on the strength of magnetic field, confirmed experimentally by Völker and Odenbach. It was also shown that when a magnetic field is perpendicular to the temperature gradient, there will be additional increase in the heat transfer compared to the cases where the magnetic field is parallel to the temperature gradient. In addition, the statistical evaluation (Taguchi technique) on magnetic fluids showed that the temperature and initial concentration of the magnetic phase exert the maximum and minimum contribution to the thermodiffusion, respectively. In the simulation of flow through porous media, dimensionless pressure drop was studied at different Reynolds numbers, based on pore permeability and interstitial fluid velocity. The obtained results agreed well with the correlation of Macdonald et al. (1979) for the range of actual flow Reynolds studied. Furthermore, calculated results for the dispersion coefficients in the cylinder geometry were found to be in agreement with those of Seymour and Callaghan.

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The purpose of this work is to obtain a better understanding of behaviour of possible ultrasound appliance on fluid media mixing. The research is done in the regard to Newtonian and non-Newtonian fluids. The process of ultrasound appliance on liquids is modelled in COMSOL Multiphysics software. The influence of ultrasound using is introduced as waveform equation. Turbulence modelling is fulfilled by the k-ε model in Newtonian fluid. The modeling of ultrasound assisted mixing in non-Newtonian fluids is based on the power law. To verify modelling results two practical methods are used: Particle Image Velocimetry and measurements of mixing time. Particle Image Velocimetry allows capturing of velocity flow field continuously and presents detailed depiction of liquid dynamics. The second way of verification is the comparison of mixing time of homogeneity. Experimentally achievement of mixing time is done by conductivity measurements. In modelling part mixing time is achieved by special module of COMSOL Multiphysics – the transport of diluted species. Both practical and modelling parts show similar radial mechanism of fluid flow under ultrasound appliance – from the horn tip fluid moves to the bottom and along the walls goes back. Velocity profiles are similar in modelling and experimental part in the case of Newtonian fluid. In the case of non-Newtonian fluid velocity profiles do not agree. The development track of ultrasound-assisted mixing modelling is presented in the thesis.

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Fluid handling systems such as pump and fan systems are found to have a significant potential for energy efficiency improvements. To deliver the energy saving potential, there is a need for easily implementable methods to monitor the system output. This is because information is needed to identify inefficient operation of the fluid handling system and to control the output of the pumping system according to process needs. Model-based pump or fan monitoring methods implemented in variable speed drives have proven to be able to give information on the system output without additional metering; however, the current model-based methods may not be usable or sufficiently accurate in the whole operation range of the fluid handling device. To apply model-based system monitoring in a wider selection of systems and to improve the accuracy of the monitoring, this paper proposes a new method for pump and fan output monitoring with variable-speed drives. The method uses a combination of already known operating point estimation methods. Laboratory measurements are used to verify the benefits and applicability of the improved estimation method, and the new method is compared with five previously introduced model-based estimation methods. According to the laboratory measurements, the new estimation method is the most accurate and reliable of the model-based estimation methods.

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Fluid flow behaviour in porous media is a conundrum. Therefore, this research is focused on filtration-volumetric characterisation of fractured-carbonate sediments, coupled with their proper simulation. For this reason, at laboratory rock properties such as pore volume, permeability and porosity are measured, later phase permeabilities and oil recovery in function of flow rate are assessed. Furthermore, the rheological properties of three oils are measured and analysed. Finally based on rock and fluid properties, a model using COMSOL Multiphysics is built in order to compare the experimental and simulated results. The rock analyses show linear relation between flow rate and differential pressure, from which phase permeabilities and pressure gradient are determined, eventually the oil recovery under low and high flow rate is established. In addition, the oils reveal thixotropic properties as well as non-Newtonian behaviour described by Bingham model, consequently Carreau viscosity model for the used oil is given. Given these points, the model for oil and water is built in COMSOL Multiphysics, whereupon successfully the reciprocity between experimental and simulated results is analysed and compared. Finally, a two-phase displacement model is elaborated.

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This thesis addresses the coolability of porous debris beds in the context of severe accident management of nuclear power reactors. In a hypothetical severe accident at a Nordic-type boiling water reactor, the lower drywell of the containment is flooded, for the purpose of cooling the core melt discharged from the reactor pressure vessel in a water pool. The melt is fragmented and solidified in the pool, ultimately forming a porous debris bed that generates decay heat. The properties of the bed determine the limiting value for the heat flux that can be removed from the debris to the surrounding water without the risk of re-melting. The coolability of porous debris beds has been investigated experimentally by measuring the dryout power in electrically heated test beds that have different geometries. The geometries represent the debris bed shapes that may form in an accident scenario. The focus is especially on heap-like, realistic geometries which facilitate the multi-dimensional infiltration (flooding) of coolant into the bed. Spherical and irregular particles have been used to simulate the debris. The experiments have been modeled using 2D and 3D simulation codes applicable to fluid flow and heat transfer in porous media. Based on the experimental and simulation results, an interpretation of the dryout behavior in complex debris bed geometries is presented, and the validity of the codes and models for dryout predictions is evaluated. According to the experimental and simulation results, the coolability of the debris bed depends on both the flooding mode and the height of the bed. In the experiments, it was found that multi-dimensional flooding increases the dryout heat flux and coolability in a heap-shaped debris bed by 47–58% compared to the dryout heat flux of a classical, top-flooded bed of the same height. However, heap-like beds are higher than flat, top-flooded beds, which results in the formation of larger steam flux at the top of the bed. This counteracts the effect of the multi-dimensional flooding. Based on the measured dryout heat fluxes, the maximum height of a heap-like bed can only be about 1.5 times the height of a top-flooded, cylindrical bed in order to preserve the direct benefit from the multi-dimensional flooding. In addition, studies were conducted to evaluate the hydrodynamically representative effective particle diameter, which is applied in simulation models to describe debris beds that consist of irregular particles with considerable size variation. The results suggest that the effective diameter is small, closest to the mean diameter based on the number or length of particles.