Pulsed Disc Research Articles

Extraction of Caprolactam with Toluene in a Pulsed Disc and Doughnut Column–Part III: Mass Transfer Characteristics

The mass transfer characteristics of a pulsed disc and doughnut column with a 0.04 m internal diameter and 4.24 m active column length are investigated in order to evaluate its contacting efficiency for caprolactam extraction with toluene. Pilot plant experiments for both the forward and back‐extraction process were performed in order to determine the concentration profile along the column length in both the extract and raffinate phase as a function of the operating conditions. The experimental conditions covered the industrial operating range. Furthermore the dispersed phase hold‐up, average droplet diameter and operating regime were determined and compared with the results obtained for the equilibrium situation, as discussed in Part II. In the forward extraction process a significant influence of operating conditions was observed, where an increase in the flux decreased the separation efficiency, but an increase in pulsation intensity, temperature, or the addition of ammonium sulphate increased the separation efficiency. In the back‐extraction all concentration profiles were comparable and all caprolactam was extracted after a column length of L/m=2. Compared to the equilibrium situation the drop diameter and pulsation intensity required for the transition of the mixer‐settler to the dispersion operating regime were found to increase under mass transfer conditions, while the hold‐up decreased. HETS values were determined for both the forward and back‐extraction. For the latter HETS=0.28 to 0.41, whereas in the forward extraction HETS=0.32 to 0.67. The concentration profiles were described with the backflow model, using a constant backflow parameter for the continuous phase and a constant overall mass transfer coefficient. The interfacial area was correlated using drop diameter and hold‐up expressions derived for the equilibrium situation, taking into account the relative effect of mass transfer. Using these expressions the measured data could be correlated and described well.

Extraction of Caprolactam with Toluene in a Pulsed Disc and Doughnut Column—Part I: Recommendation of a Model for Hydraulic Characteristics

Caprolactam, the monomer for Nylon‐6, is industrially recovered from an aqueous feed containing ammonium sulphate by extraction with organic solvents like benzene, toluene, or chlorinated hydrocarbons followed by back‐extraction with water. Extraction columns like the Rotating Disk Contactor and Pulsed Packed Column are industrially applied. In this paper a model is recommended for the description of the hydraulic characteristics of a pulsed disc and doughnut column for caprolactam extraction with toluene. In Part II and III the hydraulic and mass transfer characteristics, respectively, are determined and described with the developed models. The hydraulic characteristics are correlated as a function of the operating conditions for the experimental conditions covering the industrial operating range. The model is derived for equilibrium conditions in order to avoid the influence of mass transfer. The final model describes the operational window via equations describing flooding due to insufficient pulsation, and flooding due to a too small relative velocity between both phases and phase inversion. In the operational window several operational regimes can be distinguished, being mixer‐settler, dispersion, and emulsion type operation. Finally, two equations are presented for the description of the Sauter drop diameter and hold‐up at each operational point. The hydraulic characteristics are correlated using physical properties, operational parameters, and geometrical characteristics of the column.

Comparison of the Performance of a Pulsed Disc and Doughnut Column with a Pulsed Sieve Plate Liquid Extraction Column

The hydrodynamic and mass‐transfer performance of a 75 mm diameter pulsed disc and doughnut column (PDD) and a pulsed sieve‐plate column (PSP) are presented and compared for a toluene–acetone–water system under similar operating conditions. It was found that the pulsed disc and doughnut column flooded earlier than the pulsed sieve‐plate column, indicating that the total throughput per unit cross‐sectional area through the pulsed disc and doughnut column was less. At similar operating conditions (i.e., flowrates, pulse frequency, and amplitude), the mass‐transfer performance of the pulsed disc and doughnut column was higher, and its holdup higher. The mass‐transfer performance of the PSP column, when compared at similar holdup to the PDD, was found to be higher, and so it is concluded that it is a more efficient column for this system.

Numerical simulation of the dispersion phenomenon in a pulsed column

The numerical solutions of the unsteady Navier-Stokes equations are used to study the longitudinal dispersion of a contaninant in a pulsed disc and doughnut column used in liquid-liquid extraction processes. The velocity fields of the oscillatory continuous phase flow have been computed in a previous work for a wide range of frequencies while keeping the amplitude the same. A transition from an unstable to a stable recirculation regime was pointed out. The results of the present study shed new light on the vortex mixing cycle and reveal the effect of the stability of the recirculations and their kinetic energy in the longitudinal dispersion phenomenon. A quantitative analysis of the dispersion process is obtained from the time variation of spatial moments.

The aerodynamics of hovering insect flight. V. A vortex theory

A full derivation is presented for the vortex theory of hovering flight outlined in preliminary reports. The theory relates the lift produced by flapping wings to the induced velocity and power of the wake. Suitable forms of the momentum theory are combined with the vortex approach to reduce the mathematical complexity as much as possible. Vorticity is continuously shed from the wings in sympathy with changes in wing circulation. The vortex sheet shed during a half-stroke convects downwards with the induced velocity field, and should be approximately planar at the end of a half-stroke. Vorticity within the sheet will roll up into complicated vortex rings, but the rate of this process is unknown. The exact state of the sheet is not crucial to the theory, however, since the impulse and energy of the vortex sheet do not change as it rolls up, and the theory is derived on the assumption that the extent of roll-up is negligible. The force impulse required to generate the sheet is derived from the vorticity of the sheet, and the mean wing lift is equal to that impulse divided by the period of generation. This method of calculating the mean lift is suitable for unsteady aerodynamic lift mechanisms as well as the quasi-steady mechanism. The relation between the mean lift and the impulse of the resulting vortex sheet is used to develop a conceptual artifice - a pulsed actuator disc - that approximates closely the net effect of the complicated lift forces produced in hovering. T he disc periodically applies a pressure impulse over some defined area, and is a generalized form of the Froude actuator disc from propeller theory. The pulsed disc provides a convenient link between circulatory lift and the powerful momentum and vortex analyses of the wake. The induced velocity and power of the wake are derived in stages, starting with the simple Rankine-Froude theory for the wake produced by a Froude disc applying a uniform, continuous pressure to the air. The wake model is then improved by considering a ‘modified’ Froude disc exerting a continuous, but non-uniform pressure. This step provides a spatial correction factor for the Rankine-Froude theory, by taking into account variations in pressure and circulation over the disc area. Finally, the wake produced by a pulsed Froude disc is analysed, and a temporal correction factor is derived for the periodic application of spatially uniform pressures. Both correction factors are generally small, and can be treated as independent perturbations of the Rankine-Froude model. Thus the corrections can be added linearly to obtain the total correction for the general case of a pulsed actuator disc with spatial and temporal pressure variations. The theory is compared with Rayner’s vortex theory for hovering flight. Under identical test conditions, numerical results from the two theories agree to within 3%. Rayner presented approximations from his results to be used when applying his theory to hovering animals. These approximations are not consistent with my theory or with classical propeller theory, and reasons for the discrepancy are suggested.