De transport- en overdrachtsprocessen van warmte, massa en impuls worden naar hun analogie behandeld. De processen worden beschreven met behulp van macro- en microbalansen die in veel gevallen leiden tot differentiaalvergelijkingen. Ook veel aspecten van stromingsleer komen op deze manier aan de orde en zo bereidt het boek ook voor op moderne Computational Fluid Dynamics technieken. Het doel van het boek is ook studenten te trainen in het oplossen van problemen waarbij transportverschijnselen centraal staan. Daartoe bevat het boek bijna 100 uitgewerkte vraagstukken.

Classical mechanics is the starting point of physics. Over the centuries, via Newton’s three fundamental laws formulated around 1687, we have built a solid framework describing the material world around us. This textbook includes animations, demos and exercises for studying introductory classical mechanics. Moreover, we will consider the first steps of Einstein’s Special Theory of Relativity published 1905.

This book starts from the three laws of Newton and builds up classical mechanics from scratch. Its content carefully constructs the classical mechanics from Newtons laws, providing a rigorous, fundamental framework. Emphasis is placed on working with the basic concepts of momentum, energy and angular momentum. Special attention is paid to oscillations, collisions including non-ideal ones and the Kepler problem. Rigid body dynamics is extensively discussed. The use of polar coordinates is extensively discussed.

Non-inertial frames of reference are treated starting from linearly accelerating ones and moving to the rotating frames of reference. The centrifugal and Coriolis forces are introduced and explained.

In the second part, the switch to special relativity is made. The problems coming out of Maxwells equations for electro-magnetic waves are used as the step towards modern mechanics. The Lorentz Transformation, where events in 4-dimensional space, time dilation and length contraction are discussed. Furthermore, the book introduces the world of four-vectors, deriving the four-velocity and four-momentum. Velocity transformation, Doppler shift and relativistic collision form the final parts of the book.

A treatment of the transport and transfer processes of heat, mass and momentum in terms of their analogy. The processes are described with the help of macro and micro balances which in many cases lead to differential equations. This way, the textbook also prepares for Computational Fluid Dynamics techniques. The topics of the five chapters of the textbook are: • Balances: shape and recipe, mass balance, residence time distribution, energy and heat balances, Bernoulli equation, momentum balances • Molecular transport, dimensional analysis, forces on immersed objects • Heat transport: steady-state and unsteady conduction, the general heat transport equation, forced and free convective heat transport, radiant heat transport • Mass transport: steady-state and unsteady diffusion, the general mass transport equation, mass transfer across a phase interface, convective mass transport, wet bulb temperature • Fluid mechanics: flow meters, pressure drop, packed beds, laminar flow of Newtonian and non-Newtonian fluids, Navier-Stokes equations The leading idea behind this textbook is to train students in solving problems where transport phenomena are key. To this end, the textbook comprises almost 80 problems with solutions. • Retaining the analogy between mass, heat and momentum transport • Using the technique of drawing up balances throughout the book • Suitable for a single term course.

In this work, the rise characteristics of a single H₂ bubble, in the ellipsoidal regime, in (i) water, (ii) single electrolyte (2 M, 4.5 M NaCl) solution and (iii) various concentrations of electrolyte mixture (up to 6.4 M of 1:5 weight fraction NaCl-NaClO₃), have been studied, at temperatures up to 80°C. Our results show that both individual and collective effects of the temperature and the electrolyte concentration on the rise velocity and the bubble shape are purely dependent on the changes in liquid properties (density, viscosity, and surface tension); the bubble motion can be described by known non-dimensional correlations for clean bubble rise in pure fluids.

Deze vraagstukkenbundel is bedoeld als oefenmateriaal bij het bestuderen van de basiscolleges Fysische Transportverschijnselen, zoals die aan de TU Delft worden gegeven. De vraagstukken zijn afkomstig uit oude vraagstukkenbundels en uit recente tentamens. Wij hebben de formulering van veel van deze vraagstukken herzien.

Vooral door de vraagstukken in meerdere onderdelen te splitsen, hopen we aan te geven dat een stapsgewijze aanpak, veelal gebaseerd op één of meer balansen, een bruikbaar recept voor het oplossen van de opgaven is. Overigens is deze splitsing bij lang niet alle opgaven doorgevoerd om aan studenten de gelegenheid te geven juist dit moeilijke facet zelf te oefenen.

De transport- en overdrachtsprocessen van warmte, massa en impuls worden naar hun analogie behandeld. De processen worden beschreven met behulp van macro- en microbalansen die in veel gevallen leiden tot differentiaalvergelijkingen. Ook veel aspecten van stromingsleer komen op deze manier aan de orde en zo bereidt het boek ook voor op moderne Computational Fluid Dynamics technieken. Het doel van het boek is ook studenten te trainen in het oplossen van problemen waarbij transportverschijnselen centraal staan. Daartoe bevat het boek bijna 100 uitgewerkte vraagstukken.

Het permanent najagen van kennis en vaardigheden voor onze persoonlijke en professionele ontwikkeling zal ons steeds meer veranderen in levenslang lerenden. Maar wat houdt 'een leven lang ontwikkelen' precies in, en welke rol kunnen universiteiten daarin spelen?

Emulsion formation is a major concern when dealing with multiphasic fermentations. Flocculants can be used together with other demulsification techniques to improve oil recovery in multiphasic fermentations. In this paper, the impact of adding flocculants during a multiphasic fermentation with 10 wt% dodecane, to destabilize the broth emulsion, improve creaming formation and enhance oil recovery is studied. Flocculants, CaCl₂ and (NH₄)₂SO₄ were shown to be the most promising flocculants. Flocculant addition, their time of addition, and its impact on multiphasic fermentations has been evaluated by comparing fermentation performance against reference fermentations and three oil recovery methods: gravity settling, gas enhanced oil recovery and centrifugation. When adding 75 mM of (NH₄)₂SO₄ during fermentation, the creaming rate during gravity settling increased 3-fold and the oil recovery by gas enhanced oil recovery was 35%, without altering fermentation performance. Addition of CaCl₂ during fermentation resulted in 88% and 67% oil recovery for early and late addition, which is a 4 and 3-fold increase in comparison with the reference. Yet, CaCl₂ deviated from standard fermentation performance when added immediately after second phase addition. In conclusion, flocculant addition during multiphasic fermentation can be used to destabilize microbial emulsions and potentially improve in situ oil recovery.

In this work, the effect of an electrolyte (up to 2 M of NaCl dissolved in water) on a homogeneous dense bubbly flow, in an airlift bubble column, is studied using nonintrusive techniques. X-ray and high-speed imaging are used to investigate the bubble size distribution, the local and the global gas-fraction profiles. The major effect of the electrolyte is the bubble size distribution at the fine-pore sparger, which is a consequence of the bubble coalescence inhibition promoted by the electrolyte. The bubble plume widening, the increase in overall gas fraction, and the onset of bubble recirculation in the column can all be explained by the bubble size reduction at the fine-pore spargers. As a result of the bubble size reduction, the overall role of the electrolyte is in a reduction of the driving force for the liquid recirculation. Furthermore, an accumulation of the small bubbles causes a layer of foam at the free surface, which is dynamic in nature and induces additional bubble recirculation.

Cavitation is a complicated multiphase phenomenon, where the production of vapor cavities leads to an opaque flow. Exploring the internal structures of the cavitating flows is one of the most significant challenges in this field of study. While it is not possible to visualize the interior of the cavity with visible light, we use X-ray computed tomography to obtain the time-averaged void fraction distribution in an axisymmetric converging-diverging nozzle (’venturi’). This technique is based on the amount of energy absorbed by the material, which in turn depends on its density and thickness. Using this technique, two different partial cavitation mechanisms are examined: the re-entrant jet mechanism and the bubbly shock mechanism. 3D reconstruction of the X-ray images is used (i) to differentiate between vapor and liquid phase, (ii) to obtain radial geometric features of the flow, and (iii) to quantify the local void fraction. The void fraction downstream of the venturi in the bubbly shock mechanism is found to be more than twice compared to the re-entrant jet mechanism. The results show the presence of intense cavitation at the walls of the venturi. Moreover, the vapor phase mixes with the liquid phase downstream of the venturi, resulting in cloud-like cavitation.

Multiphasic fermentations where an organic phase is spontaneously formed or when it is added for product removal are commonly used for production of valuable compounds. The turbulent conditions and the presence of surface-active compounds (SACs) during fermentation create a stable emulsion difficult to separate. A gas bubble/oil droplet separation method has been proposed to break such emulsion. In this paper, we propose a mathematical model to describe oil/bubble interaction in a region of high oil droplet concentration. Model validation was performed using a synthetic emulsion and an emulsion from a fermentation broth. By applying the optimal parameters predicted by the model, a 6- and 3-times oil recovery improvement was reached for the synthetic emulsion and the fermentation broth, respectively. In conclusion, the proposed mechanistic model allowed to improve oil recovery in the existing laboratory set-up, and can be used to optimize the separation and recovery method at large scale.

The increase of inter-particle cohesive force greatly changes the fluidization dynamics, finally leading to the partial or complete failure of fluidization. However, few studies concern such transition process. This paper investigates the fluidization dynamics of Geldart B particles with a wide-range of cohesive force by analyzing the in-bed pressure fluctuation signals. Combining the bubble information reported in Part I, the local and global fluidization dynamics under different cohesive forces were discussed. The results show that bulk bubble dynamics is weaken with the presence of inter-particle cohesive force. As the force increases, fluidization changes from multi-bubbling regime to single-bubble regime and the factor governing the pressure fluctuation changes from bubble formation to bubble eruption. When the cohesive force is strong, slugging appears near the bed surface, then gradually extends toward the bottom bed by capturing freely fluidizing particles, and finally develops into the whole-bed slugging. At this time, regular fluidization turns into an alternative process between whole-bed slugging and regular status, corresponding to two distinct peaks in power spectral density of pressure signals at 0.1 Hz and 1 Hz respectively. The size of gas slug decreases with the elevation of measurement height. Basically, any operations that promote bubble growth will also facilitate the appearance of whole-bed slugging under strong cohesive force. Reducing the static bed height is a preferable approach to weaken, or even avoid the defluidization of whole-bed slugging, without changing other operational parameters.

This study aimed to characterise the gas-liquid flow and mixing behaviour in a gas-mixed anaerobic digester by improving phase interaction modelling using Computational Fluid Dynamics (CFD). A 2D axisymmetric model validated with experimental data was set up using an Eulerian-Eulerian method. Uncertainty factors, including bubble size, phase interaction forces and liquid rheology were found to significantly influence the flow field. A more reliable and complete validation was obtained by critical comparison and assessment of the referred experimental data, compared to the models reported in other studies. Additionally, justifiable corrections and predictions in detail were obtained. Mixing was evaluated by trajectory tracking of a large number of particles based on an Euler-Lagrange method. The mixing performance approximated to a laminar-flow reactor (LFR) that distinctly deviated from expected continuous stirred tank reactor (CSTR) design, indicating limited enhancement from the applied gas-sparging strategy in the studied digester. The study shows the importance of a proper phase-interaction description for a reliable hydrodynamic characterisation and mixing evaluation in gas-mixed digesters. Validations, bend to experimental data without a critical assessment, may lead to an inaccurate model for further scaled-up applications.

Due to the presence of inter-particle cohesive force, cohesive particles reveal totally different fluidization behaviors as compared to the non-cohesive system. This paper studies the fluidization dynamics of Geldart B particles with varying thermal-induced cohesive forces. Multi-source X-ray tomography was applied to reconstruct 3D temporal images of bubbles, based on which, various bubble properties were extracted. The results show that increasing cohesive force will decrease bubble number while increase bubble size, implying that the presence of cohesive force facilitates bubble coalescence. By examining the bubble size distribution, cohesive force is found to have no effect on the number of median bubbles but greatly influence small and large bubbles. When the cohesive force is strong, the bubbles grow to a considerable size similar with bed dimension, giving rise to slugging near bed surface. With the action of inter-particle cohesive force, particle slug gradually grows by capturing other freely fluidizing particles, finally inducing “whole-bed” slugging. The particle slug may rupture in the rising process, and the bed turns back to normal fluidization. In comparison to normal bubbles, the gas slug has much larger size but far smaller frequency. The rise velocity of gas slug is also very low due to the particle-wall friction and gas-solid momentum dissipation. Therefore, the averaged values of bubble properties dramatically changed as bed temperature exceeds 35 °C. When the temperature attains 45 °C, the cohesive force is so strong that the fluidization completely fails in terms of stable whole-bed slugging.

The performance of fluidized bed reactors strongly depends on the bubble behavior, for which reason knowledge concerning the bubble properties is important for modeling and reactor optimization. X-ray measurements can be used to characterize bubbles within the cross-section of a fluidized bed on a laboratory scale, but cannot easily be extended to hot, pressurized large scale plants. For future measurements at hot conditions in a fluidized bed methanation reactor, we have developed an optical probing system that can be employed under these conditions. However, optical sensors are only able to investigate the local fluidization patterns at a defined position in the bed. The objective of this study is to characterize differences in bubble properties between local optical measurements and an X-ray tomography method that is able to detect bubbles over the entire cross-section. Therefore, an artificial optical signal is created out of existing hydrodynamic X-ray measurement data obtained at a cold flow model of a pilot scale methanation reactor. The determined bubble properties of both methods (i.e. evaluation of the derived artificial optical probe signal and image reconstruction based on the evaluation of original X-ray tomographic data) are compared with regard to the bubble rise velocity and the bubble size (for the X-ray method) or pierced chord length (for the optical evaluation method), respectively. The comparison shows that for the evaluation of the optical probe data, statistical effects have to be considered carefully. The detected mean chord length of the optical method does not immediately correspond to the mean bubble size determined by the X-ray method. Moreover, also differences regarding the bubble rise velocity were detected for some fluidization states. The reason for the discrepancies between both methods could be identified and corrected, amongst others by means of a Monte Carlo simulation in which rising bubbles in a fluidized bed were simulated and characterized by a local virtual optical sensor.

Euler–Lagrange computational fluid dynamics simulations offer great potential for the integration of transport dynamics and metabolic dynamics in fermentation systems. Since the seminal work of Lapin et al. [1,2], progress has been made, mainly in the analysis of CFD data and translation to laboratory setup designs. Different large-scale processes require different analysis methods; in this paper we discuss which analysis methods are best suited for given reactor types, by reviewing prior simulation cases as well as introducing new test cases. Furthermore, we address challenges in the translation from Euler–Lagrange simulations to laboratory scale systems, and propose methods to work around these shortcomings. Based on the current state of the art, we propose guidelines for the selection of data analysis methods, and we discuss the design of rational scale-down simulators. We conclude with a brief discussion regarding the requirements and possibilities of next-generation scale-down simulators, such as microfluidic single-cell analysis, and possible ways to approximate cellular lifelines from invasive intra-cellular measurements.

CFD simulations of mixing in single-phase multi-Rushton stirred tanks based on the RANS methodology frequently show an over-prediction of the mixing time. This hints at an under-prediction of the mass exchange between the compartments formed around the individual impellers. Some studies recommend tuning the turbulent Schmidt number to address this issue, but this appears to be an ad-hoc correction rather than physical adjustment, thereby compromising the predictive value of the method. In this work, we study the flow profile in between two Rushton impellers in stirred tank. The data hints at the presence of macro-instabilities, and a peak in turbulent kinetic energy in the region of convergent flow, which both may promote inter-compartment mass exchange. CFD studies using the steady-state multiple reference frame model (unsteady simulations are treated in part II) inherently fail to include the macro-instability, and underestimate the turbulent kinetic energy, thereby strongly over-estimating mixing time. Furthermore, the results are highly mesh-sensitive, with increasing mesh density leading to a poorer prediction of the mixing time. Despite proper results for 1-impeller studies, we do not deem MRF-RANS models suitable for mixing studies in multi-impeller geometries.

Cavitation is a complex multiphase phenomenon, where the production of vapor bubbles leads to opaqueness of the flow. While it is nearly impossible to visualize the interior of the cavitation region with visible light, we show that with X-ray computed tomography it is possible to obtain the time-averaged void fraction distribution in an axisymmetric converging-diverging nozzle (venturi). This technique is based on the amount of energy absorbed by the material, based on its density and thickness. Time-averaged 3D reconstruction of the X-ray images is used (i) to distinguish between vapor and liquid phase, (ii) to get radial geometric features of the flow, and (iii) to quantify the local void fraction. The results show the presence of intense cavitation at the walls of the venturi, and the vapor fraction decreases downstream of the venturi with the vapor cloud.

Steady state multiple reference frame-RANS (MRF-RANS) simulations frequently show strong over-predictions of the mixing time in single-phase, multi-impeller mixing tanks, which is sometimes patched by ad hoc tuning of the turbulent Schmidt-number. In Part I of this work, we experimentally revealed the presence of macro-instabilities in the region between the impellers, as well as a peak in the turbulent kinetic energy in the region where the flow from the individual impellers converges. The MRF-RANS method was found unable to capture both. In this second paper, we show that the sliding-mesh RANS (SM-RANS) approach does capture the effect of macro-instabilities, while still underestimating the turbulent kinetic energy. Consequently, the SM-RANS method mildly over-estimates the mixing time, while being less sensitive to the exact mesh geometry. Large eddy simulations with the dynamic Smagorinsky model reasonably capture the kinetic energy contained in macro-instabilities, and properly assess the turbulent kinetic energy in the region between the impellers, even for crude meshes. Consequently, the mixing time is reasonably assessed, and even under-predicted at the crudest meshes. However, the turbulent kinetic energy and energy dissipation in the impeller discharge stream are poorly assessed by the dynamic Smagorinsky model.