Turbulence dispersion force

Effects similar to those of the lift force are observed when implementing the turbulent dispersion force using the gradient diffusion model. This dispersion force closure smoothes out sharp velocity gradients in the domain. If the model overestimates the diffusive effect, the velocity profiles may become completely flat over the column cross section. 

Nevertheless, the turbulent dispersion force acting on bubbles in turbulent liquid flow is commonly modeled using the gradient hypothesis (e.g., [20]) ... 

Lucas D, Krepper E, Prasser HM Use of models for lift, wall and turbulent dispersion forces acting on bubbles for poly-disperse flows, Chem Eng Sci 62 4146-4157,2007. http //dx. doi.org/10.1016/j.ces. 2007.04.035. 

Atomization. A gas or Hquid may be dispersed into another Hquid by the action of shearing or turbulent impact forces that are present in the flow field. The steady-state drop si2e represents a balance between the fluid forces tending to dismpt the drop and the forces of interfacial tension tending to oppose distortion and breakup. When the flow field is laminar the abiHty to disperse is strongly affected by the ratio of viscosities of the two phases. Dispersion, in the sense of droplet formation, does not occur when the viscosity of the dispersed phase significantly exceeds that of the dispersing medium (13). 

Wilson, K. C. and Puoh, F. ]. Can. Ji. Chem. Eng. 66 (1988) 721. Dispersive-force modelling of turbulent suspensions in heterogeneous slurry flow. 

Dynamic Powder Disperser Lactose 12 Cartridge Gas assist Turbulence, shear force... 

When a gas stream is introduced into a turbulent liquid flow in a motionless mixer, the gas is broken up into bubbles. The breakup is due mainly due to the turbulent shear force of the liquid but, for motionless mixers, also partly to the collision between the gas and the leading edge of an element. Gas dispersion is a physical process and involves bubble breakup and coalescence, which can both take place in the same mixer/reactor. 

Kuboi et al. [303] used a self-derived calculation method for determining v in turbulent dispersions on the basis of a force balance instead and evaluated their mass transfer measurements in terms of expression (5.54c). They could be reproduced to an accuracy of 17% with the relationship... 

In a recent study Jakobsen et al [66] examined the capabilities and limitations of a dynamic 2D axi-symmetric two-fluid model for simulating cylindrical bubble column reactor flows. In their in-house code all the relevant force terms consisting of the steady drag, bulk lift, added mass, turbulence dispersion and wall lift were considered. Sensitivity studies disregarding one of the secondary forces like lift, added mass and turbulent dispersion at the time in otherwise... 

The steady-drag, virtual mass, turbulent dispersion, and wall lift forces were approximated using a semi-implicit time discretization scheme ... 

In particular, the loose packing of particles promotes an open powder structure that is less adhesive and flows and disperses more readily. There is a strong correlation between the interaction parameters derived by IGC and the in vitro data that play an important role in the prediction of aerosol performance of dry powder inhalation formulations. Enhanced dispersibility is particularly important for DPI devices, where performance strongly depends on powder deaggregation at relatively low dispersion forces. Clearly, high turbulence is preferable for dispersion, but it inevitably leads to high pressure differentials, which may prevent many devices from functioning correctly. In addition, low dispersion forces for supercritically produced... 

Neglecting the gravitational force and particle inertia leads to the zero-order approximation that V u that is, the aerosol follows the streamlines of the airflow. This approximation is often sufficient for most atmospheric applications, such as turbulent dispersion. However, it is often necessary to quantify the deviation of the aerosol trajectories from the fluid streamlines (Figure 8.13). 

Oil droplets entrained in the exhaust vapor are usually separated by cyclones. Water spray is mixed with the hot gases as they enter the centrifugal blower, where violent turbulence disperses the water and throws the oil and water droplets to the blower walls by centrifugal force. Separation is completed in a tangential entry centrifugal separator that follows the blowers. Volatile organic compounds are directed to the burner used to heat the oil, as already mentioned, or to a combustion chamber if such a burner is not used. 

Turbulent action forces the gas to break away from the cavity and exit the impeller zone. This breakage is the source of gas dispersion in STRs. The large cavity deserves special attention because it induces gas breaking away less violently than the other cavity types. Large cavities also have an advantage in that they hold more gas and have more surface area from which gas can break away. 

In a recent study Jakobsen et al. [71] examined the capabilities and limitations of a dynamic 2D axi-symmetric two-fluid model for simulating cylindrical bubble column reactor flows. In their in-house code all the relevant force terms consisting of the steady drag, bulk lift, added mass, turbulence dispersion and wall lift were considered. Sensitivity studies disregarding one of the secondary forces like lift, added mass and turbulent dispersion at the time in otherwise equivalent simulations were performed. Additional simulations were run with three different turbulence closures for the liquid phase, and no shear stress terms for the gas phase. A standard k — e model [95] was used to examine the effect of shear induced turbulence, case (a). In an alternative case (b), both shear- and bubble induced turbulence were accounted for by linearly superposing the turbulent viscosities obtained from the A — e model and the model of Sato and Sekoguchi [138]. A third approach, case (c), is similar to case (b) in that both shear and bubble induce turbulence contributions are considered. However, in this model formulation, case (c), the bubble induced turbulence contribution was included through an extra source term in the turbulence model equations [64, 67, 71]. The relevant theory is summarized in Sect. 8.4.4. 

Several papers on Euler—Euler simulations (both RANS based and of the above EELES type) report about the need to include a separate turbulent dispersion term (or force) for reproducing a correct spatial distribution of suspended particle clouds or bubble swarms. Various models for this turbulent dispersion have been suggested, all of them modeling this effect in terms of the gradient of the particle or bubble volume fraction. Sometimes, this additional term is in the continuity equations (Bakker and Van den Akker, 1994 Sardeshpande and Ranade, 2012 Tamburini et al, 2014) with the justification that is due to fluctuations in the volume fractions however, as the volume fraction which anyhow is an averaged variable does not vary... 

In addition, it was concluded that the liquid-phase diffusion coefficient is the major factor influencing the value of the mass-transfer coefficient per unit area. Inasmuch as agitators operate poorly in gas-liquid dispersions, it is impractical to induce turbulence by mechanical means that exceeds gravitational forces. They conclude, therefore, that heat- and mass-transfer coefficients per unit area in gas dispersions are almost completely unaffected by the mechanical power dissipated in the system. Consequently, the total mass-transfer rate in agitated gas-liquid contacting is changed almost entirely in accordance with the interfacial area—a function of the power input. 

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