H.E.A. van den Akker

An experimental and numerical study of turbulent swirling flow in gas cyclones

Experimental results on the turbulent, strongly swirling flow field in a reverse flow gas cyclone separator are presented, and used to evaluate the performance of three turbulence closure models. Mean and fluctuating velocity components were measured for gas cyclones with different geometric swirl numbers by means of laser-Doppler velocimetry. The experimental data show the strong effect of the geometric swirl number on mean flow characteristics, in particular with respect to vortex core size and the magnitude of the maximum tangential velocity. It is shown that the forced vortex region of the flow is dominated by the so-called precessing vortex core. Numerical calculation of the cyclonic flow shows that turbulence models based on the eddy-viscosity approach fail to predict the combined vortex observed experimentally. Predictions with the Reynolds stress transport model are in reasonable agreement with measured profiles for all three swirl numbers, though the turbulent normal stresses are generally overpredicted.

Particle imaging velocimetry experiments and lattice-Boltzmann simulations on a single sphere settling under gravity

A comparison is made between experiments and simulations on a single sphere settling in silicon oil in a box. Cross-correlation particle imaging velocimetry measurements were carried out at particle Reynolds numbers ranging from 1.5 to 31.9. The particle Stokes number varied from 0.2 to 4 and at bottom impact no rebound was observed. Detailed data of the flow field induced by the settling sphere were obtained, along with time series of the sphere’s trajectory and velocity during acceleration, steady fall and deceleration at bottom approach. Lattice–Boltzmann simulations prove to capture the full transient behavior of both the sphere motion and the fluid motion. The experimental data were used to assess the effect of spatial resolution in the simulations over a range of 2–8 grid nodes per sphere radius. The quality of the flow field predictions depends on the Reynolds number. When the sphere is very close to the bottom of the container, lubrication theory has been applied to compensate for the lack of spatial resolution in the simulations.

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.

Fully resolved simulations of colliding monodisperse spheres in forced isotropic turbulence

Fully resolved simulations of particles suspended in a sustained turbulent flow field are presented. To solve the Navier–Stokes equations a lattice-Boltzmann scheme was used. A spectral forcing scheme is applied to maintain turbulent conditions at a Taylor microscale Reynolds number of 61. The simulations contained between 2 and 10 vol % particles with a solid to fluid density ratio between 1.15 and 1.73. A lubrication force is used to account for subgrid hydrodynamic interaction between approaching particles. Results are presented on the influence of the particle phase on the turbulence spectrum and on particle collisions. Energy spectra of the simulations show that the particles generate fluid motion at length scales of the order of the particle size. This results in a strong increase in the rate of energy dissipation at these length scales and a decrease of kinetic energy at larger length scales. Collisions due to uncorrelated particle motion are observed (primary collisions), and collision frequencies are in agreement with theory on inertial particle collisions. In addition to this, a large number of collisions at high frequencies is encountered. These secondary collisions are due to the correlated motion of particles resulting from shortrange hydrodynamic interactions and spatial correlation of the turbulent velocity field at short distances. This view is supported by the distribution of relative particle velocities, the particle velocity correlation functions and the particle radial distribution

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.

A COMPUTATIONAL SNAPSHOT OF GAS-LIQUID FLOW IN BAFFLED STIRRED REACTORS

Abstract In a stirred reactor, flow around the rotating impeller blades interacts with the stationary baffles and generates a complex, three-dimensional, recirculating turbulent flow. When gas is sparged in such a reactor, gas tends to accumulate in the low pressure region behind the impeller blades forming so-called gas cavities, which significantly alter the flow and turbulence in the reactor. In this paper, a computational technique is developed to predict the turbulent gas—liquid flow in a stirred reactor. The technique is also able to predict the flow around the impeller blades and the accumulation of gas behind these blades. Unlike the past efforts, no empirical (in the form of impeller boundary conditions) is required. A computational snapshot approach has been used to model the gas—liquid flow in a stirred reactor with a disc turbine. This approach essentially boils down to capturing the flow characteristics of a stirred vessel at one time instant from the solution of steady-state equations with boundary conditions corresponding to that particular time instant. A mathematical model is developed for turbulent, dispersed gas—liquid flow. The time-averaged two-phase momentum equations are solved by using a finite volume algorithm. The turbulent stresses are simulated using ak—ɛ model. The distribution of gas around the impeller blades is predicted for the first time. The model also enables an a priori prediction of the drop in the power dissipated by the impeller in the presence of gas. Predicted flow characteristics of the gas—liquid reactor show good agreement with the experimental data.

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.

Measurements on wave propagation and bubble and slug velocities in cocurrent upward two-phase flow

Abstract Experiments on two-phase flow characteristics have been performed in vertical upward air-water flow through a transparent pipe system 17 m in height under atmospheric pressure. This system has been designed such that, in the first 7 m, both bubbly flow and slug flow can exist, depending on the air- and water-flow rates at the inlet, but that, owing to a decrease in pipe diameter, the flow will shift to slug flow quite easily in the upper 10 m. Experimental techniques used comprise pressure measurements with pressure transducers mounted flush to the pipe wall, light attenuation measurements with the use of two parallel laser beams 1 cm apart, and high-speed photography at 200 frames/s. With this setup, we measured both semi-steady flow parameters, such as slug frequencies and Taylor bubble rise velocities, and wave-propagation phenomena, such as the velocity of sound and of voidage waves in the two-phase medium. The results of these experiments have been compared with correlations from the literature and with simulations using the two-phase flow code SOPHY-2 (software package for hyperbolic equations) developed in house.