Robert F. Mudde

Two- and three-dimensional simulations of a bubble plume using a two-fluid model

Numerical simulations of a meandering bubble plume in a rectangular flat geometry are presented using the ASTRID code. The simulations are based on a full two-fluid model including turbulence modelling using a k–e model on 2 two-dimensional and 2 three-dimensional grids. For the interfacial forces between the two phases the drag force and virtual mass have been taken into account. The simulations are time dependent and a time step of 50 ms is used. In the 2D case a steady solution is obtained with one large liquid circulation cell. The turbulent viscosity is high, damping all oscillations. In case of 3D simulations the flow becomes transient. If only the drag force is used for the mutual interaction between the phases both the amplitude and the oscillation period are much smaller than observed experimentally. The turbulent viscosity is smaller in the 3D case, consequently the diffusion of the bubble plume is less than in the 2D case. Changing the standard k–e model to a low Reynolds k–e one does not alter the flow behavior significantly. If, however, also the virtual mass is taken into account the oscillations have a period of 34 s and an amplitude for the vertical component of the liquid velocity of about 20 cm/s. This is quite comparable with the experimental finding reported in literature.

Liquid velocity field in a bubble column: LDA experiments

Abstract This paper reports on LDA experiments in bubble columns 15.2, 23.4, and 38.4 cm in diameter. The gas fraction ranges up to 25%, but the columns are still in the bubbly regime, i.e. coalescence of bubbles is minor. It is shown that both the axial and tangential liquid velocity components can be measured with confidence, especially close to the wall. In that domain the data rates are sufficiently high to obtain time series that can be studied at high frequencies, i.e. above 1000 Hz. It is reported that the fluctuations in the velocity field are of the same order as the mean velocity. Furthermore, results on the Reynolds stresses are presented. The axial normal stress is higher than the tangential one indicating anisotropic turbulence. Furthermore, the axial normal stress shows a minimum at a radial position of 0.8 of the column radius which has not been reported before. This minimum becomes more pronounced with increasing gas fraction. The axial-tangential Reynolds shear stress is zero. A frequency analysis shows that for the higher frequencies the − 5/3 power law is obeyed. At low frequencies the presence of vortical structures is found. Short-time frequency analysis indicates that these structures are well separated in space and arrive at irregular intervals.

On the accuracy of the void fraction measurements using optical probes in bubbly flows

The accuracy of the measurement of the void fraction in bubbly flows using an optical probe is investigated. Experiments were performed in tap water with ellipsoidal-shaped air bubbles with equivalent diameters and velocities in the range of 2.8–5.2 mm and 0.22–0.28 m∕s. Comparison of charge coupled devices (CCD) images of dynamic bubble piercing events with optical probe signals shows that for piercing in the area around the bubble side, the so-called low-level criterion gives the best agreement with the actual gas-liquid transition for the undisturbed bubble. In addition, residence time underestimation due to a partial blinding effect is observed in the outer regions of the bubble. Residence times of the probe inside the bubble are obtained from the probe signal and from CCD images of the undisturbed bubble. These are compared to study the relevance of various probe-bubble interaction effects. The crawling effect is found to play an important role. For perpendicular piercing, the experiment shows that i...

Coherent structures and axial dispersion in bubble column reactors

In this paper results of measurements of the local and time-dependent behaviour of the two-phase flow in a bubble column are presented. Measurements with Laser Doppler Anemometry (LDA) and with glass fibre probes were performed in two homogeneously aerated air/water bubble columns, of 15 and of 23 cm dia. These measurements show that considering the flow field as stationary considerably underestimates the velocities present. Although the time averaged liquid velocity profiles resemble textbook data, these averaged values are a result of the passage of coherent structures. LDA measurements showed that these swarms have typical velocities and that at different radial positions, different typical velocities are dominant. The measurements performed with sets of glass fibre probes show that these swarms are typically of the order of the column diameter, indicating that dispersive transport in the axial direction is limited to a distance of approximately the column diameter. Axial dispersion in a bubble column is thus regarded as transport with a typical velocity over a typical distance. A simple model is proposed, defining the axial dispersion coefficient as the product of the typical velocities with the column diameter. Agreement of results obtained with this model with existing literature data is good, especially at lower superficial gas velocity conditions.

2D and 3D simulations of an internal airlift loop reactor on the basis of a two-fluid model

Two- and three-dimensional (2D and 3D) simulations of an airlift reactor under steady state conditions at low gas flow rates are presented. The simulations are based on a two-fluid model with a k–e model for the turbulence and as little as possible ad hoc closure terms. The results are compared with an one-dimensional mechanical energy balance and are found to be in good agreement. The 2D results show sensitivity to the gas inlet geometry: whether or not the gas is partially sparged into the liquid directly next to a wall affects the liquid velocity distribution and thereby the gas disengagement at the top of the airlift. The three-dimensional calculations make a more realistic geometry possible. The friction in the system is found to be about a factor of two larger in the 3D case at the same gas inlet conditions. For a given gas flow rate, the mean gas fraction in the riser is the same for the 2D and 3D simulations, the liquid circulation rate is about 30% higher in the 2D case than in the 3D one. A comparison is made with experimental data obtained in an airlift of the same dimensions. The simulated overall gas fraction is in agreement with the experimental findings. The simulated superficial velocity in the riser is compared to LDA data. For the lowest superficial velocities the LDA data coincide with the results from the 2D simulations, for higher gas flow rates the LDA results switch over towards the 3D results.

Application of LDA to bubbly flows

Abstract The fluctuating velocity field in an air–water bubble column (i.d. 15.2 cm) at a gas fraction of 25% is investigated using backscatter LDA. Since the interpretation of LDA signals in bubbly flows is not straight forward also experiments on a single bubble train are reported. It is discussed that in the latter case when using seeding the backscatter LDA measures predominantly the liquid velocity. No improvement from thresholding on the discrimination between gas and liquid was found. The bubble column experiments show that the radial averaged liquid velocity profile represents the well known gross scale circulation present in the column. More interesting, it is also seen that the fluctuating velocity field can be studied in great detail. The velocity probability density functions directly indicate high turbulence intensity. Low frequency fluctuations are observed in agreement with visual observations. The data rate is an exponential function of the distance from the column wall. This limits the possibilities of spectral analysis in the central part of the flow. However, close to the wall the mean data rate is sufficient to study the frequency contents of the signal. It is shown that the power spectral density function obeys a −5/3 power law and that the autocorrelation function is of similar shape as reported in literature on bubbly flows.

Simulation of a slurry airlift using a two-fluid model

A two-fluid approach is used to simulate the flow of a three-phase mixture in an internal-loop airlift reactor. The loop consists of a riser, in which gas is injected and two downcomers on both sides. The airlift loop is at first treated as a two-phase system (gas-liquid). A full two-fluid formulation is used to describe the dynamics of the two-phase flow. Subsequently, the distribution of the third, solid phase is considered by solving a mass balance in which the solids velocity is the superposition of the liquid velocity, a gravitational settling and turbulent dispersion. An extended version of Tchens theory is applied for the dispersed phases; turbulence in the carrier-phase is modelled by a modified k-e equation. The model is implemented in the in-house finite-volume code DISSIM (Lathouwers, D. (1999). Modelling and simulation of turbulent bubbly flow. Ph.D. Thesis), a 2-D pressure-based code. Variation of the gas flow rate revealed the existence of different flow regime with respect to the gas fraction in the downcomer, in agreement with literature. In case the gas separation at the top is complete, the circulation velocity simulated agreed well with a simple mechanical energy balance. The solid phase is found to accumulate in the dead corners if the turbulent dispersion is ignored. The settling process is very slow and part of the solids are trapped in the circulation of the liquid. When the turbulent dispersion is taken into account a smooth solids distribution is found with a higher volume fraction of solids in the lower part of the downcomers, where the liquid velocity is minimal.

Subchannel void-fraction measurements in a 6 × 6 rod bundle using a simple gamma-transmission method

A relatively simple subchannel void-fraction measurement system was developed and applied to a scaled model of a BWR fuel assembly. The measurement system is based upon the gamma-transmission technique and uses a tomographic reconstruction procedure to calculate the void-fractions in the subchannels. Data pre-processing is used to remove positioning errors of the gamma source and detector. Measurements are performed under different operating conditions and radial power profiles. The measurements are compared with the drift-flux two-phase flow model. The void-fraction in the wall and corner subchannels is lower than average. By applying the drift-flux model to each subchannel separately and comparing this calculation with measurements the presence of lateral void-drift should be detectable. However, the data do not show evidence for lateral void-drift. By comparing two chordal void-fractions, one through the fuel rods and one in between the fuel rods, a flow pattern transition could clearly be seen between a void-fraction of 30% and 40%.

Analysis of a bubbling 2-D gas-fluidized bed using image processing

Experiments on the behaviour of bubbles in a two-dimensional gas fluidized bed have been recorded on video and analyzed using image analysis techniques. It is shown that these techniques offer the possibility to quantify local hold-up and all kind of bubble properties, such as size, shape and velocity, as a function of the bubble height in the bed. The accuracy of the technique is good and the results are in agreement with those reported in the literature. Special attention is paid to determining shape properties of spherical-cap bubbles. The contour of these bubbles is decomposed into two circles, so that determination of the wake angle and wake area is possible. Both parameters are investigated as function of the bubble height in the bed.

Feasibility study of a time-resolving x-ray tomographic system

This paper discusses the possibilities for developing a tomographic scanner for studying the phase distribution of fluidized beds. The system is based on a medical x-ray source equipped with 30 CdWO4 detectors. We mimic a five-source system via simulation and in experiments of voids in a 23 fluidized bed filled with polystyrene particles. Both static voids and moving ones are studied. The reconstruction uses the simultaneous algebraic reconstruction technique with regularization. We find that it is possible to reconstruct objects with a spatial resolution of about 5 mm at a frame rate of 200 Hz. It is concluded that noise levels should be kept below 2%.