Unified modeling of bubbly flows in pipes, bubble columns, and airlift columns

The purpose of computer-aided process engineering (CAPE) is to assist the development and operation of complex processes involving chemical or physical change. Computational fluid dynamics (CFD) simulations are a means to study in detail unit operations, such as mixing, reaction, separation or combinations thereof, performed in a specific type of equipment. In particular scale-up studies and the evaluation of concepts for process intensification in an early design phase promise high benefits in terms of identifying energy- and resource-efficient solutions that are expensive to assess by conventional semi-empirical methods.
CFD simulations of dispersed bubbly flow on the scale of technical equipment are feasible within the Eulerian two-fluid framework of interpenetrating continua. However, accurate numerical predictions rely on suitable closure models describing the physics on the scale of individual bubbles or groups thereof. A large number of works exists, in each of which largely a different set of closure relations is compared to a different set of experimental data. For the limited range of conditions to which each model variant is applied, reasonable agreement with the data is mostly obtained, but due to a lack of comparability between the individual works no complete, reliable, and robust formulation has emerged so far. Moreover, the models usually contain a number of empirical parameters that have been adjusted to match the particular data that were used in the comparison. Predictive simulation, however, requires a model that works without any adjustments within the targeted domain of applicability.
As a step towards this goal, an attempt has been made to collect the best available description for all aspects known to be relevant for adiabatic bubbly flows where only momentum is exchanged between liquid and gas phases. Apart from interest in its own right, results obtained for this restricted problem also provide a good starting point for the investigation of more complex situations including heat and mass transport and possibly phase change or chemical reactions.
Aspects requiring closure for the case under consideration are: (i) the exchange of momentum between liquid and gas phases, (ii) the effects of the dispersed bubbles on the turbulence of the liquid carrier phase, and (iii) processes of bubble coalescence and breakup that determine the distribution of bubble sizes. All of these aspects are coupled and therefore in principle have to be considered as a whole.
At the same time it is highly desirable to separately validate the individual sub-models of this complex coupled problem. To this end we use a step-by-step procedure where we first consider situations where a fixed distribution of bubble sizes may be imposed. In this way the sub-models for bubble forces (i) and bubble-induced turbulence (ii) can be validated independently of bubble coalescence and breakup processes (iii). The latter will be added later on in a second step building on the already established sub-models for the former.
In the present contribution the baseline model referred to above is applied to several different configurations commonly encountered in chemical engineering applications, namely bubbly flows in pipes, bubble columns, and airlift columns. Since in all of these systems the small scales are governed by the same physics it is expected that they can be treated in a unified manner using the same set of closure relations. By comparison of simulation results to experimental data taken from the literature this is shown to be the case within a certain accuracy and the model is validated for all of these configurations.
In this way a starting point for the prediction of flow phenomena is obtained. Expanding the range of applicability as well as the achieved accuracy is a continuously ongoing development effort. From the observed level of agreement between simulation and experiment issues requiring further investigation can be identified. This includes both the need for further model development and the need for CFD-grade experimental investigations.