On the Study of Packed Catalyst Bed Stresses for Outward Radial Flow Reactors

Pressure drop in a radial flow reactor occurs when process flow crosses the packed catalyst bed installed between the two concentric perforated screens during operation. This pressure drop generates the lateral bed stress against the reactor’s perforated screens to shift. The pressure drop will further grow as catalyst attrition increases in production. For an outward radial flow, the pressure drop may exert higher stresses to the outer screen as the packed bed is pushed toward it. An extreme case is when the entire catalyst bed could be pinned to the outer screen of the reactor by enough pressure drop. This could cause the internal components to be overly stressed on the excessive bed load, for which the components might not have been designed adequately. Predicting how radial pressure drop impacts the bed stress and shifts the load distribution is important in preventing mechanical failure during operation. In this study, an analytical model is derived based on Janssen’s theory, a classical semi-empirical granular solid material model, to examine a generic packed catalyst bed in an outward radical flow reactor. A modification to Janssen’s theory is introduced to include pressure drop in order to explore its effects on bed stress and load. The critical condition is derived.

A 3D Hydrodynamic Model for Shallow Water Flow Through a Circular Patch of Emergent Cylinders

3D numerical computations are performed to simulate the shallow water flow through an array of non-submerged cylinders occupying a circular area in the middle of the domain. A hydrodynamic model capable of capturing the free surface positions is developed with the SST (shear strain transport) k-ω turbulence closure. The model is first verified and validated against experimental data available in the literature. It is demonstrated that the present model can predict both the average velocity and turbulence structure well. In addition, both cylinder-scale flow as well as patch-scale flow can be well reproduced. The velocity field and distribution of bed stress are then analyzed to study the flow patterns and sediment deposition with different solid volume fractions and water depths.

The role of velocity, pressure, and bed stress fluctuations in bed load transport over bed forms: numerical simulation downstream of a backward-facing step

Bed load transport over ripples and dunes in rivers exhibits strong spatial and temporal variability due to the complex turbulence field caused by flow separation at bedform crests. A turbulence-resolving flow model downstream of a backward-facing step, coupled with a model integrating the equations of motion of individual sand grains, is used to investigate the physical interaction between bed load motion and turbulence downstream of separated flow. Large bed load transport events are found to correspond to low-frequency positive pressure fluctuations. Episodic penetration of fluid into the bed increases the bed stress and moves grains. Fluid penetration events are larger in magnitude near the point of reattachment than farther downstream. Models of bed load transport over ripples and dunes must incorporate the effects of these penetration events of high stress and sediment flux.

Prediction of Packed Catalyst Bed Stress and Load for Radial Flow Reactors

For the radial flow reactor with a packed catalyst bed, the pressure drop in radial direction will affect bed support stress and load condition significantly. Increased fines due to catalyst attrition during operation will increase the radial pressure drop. For an extreme case, the entire catalyst bed could be pushed inward and pinned to the reactor’s perforated center screen, potentially causing the internal components to be overly stressed by the excessive load. Understanding the impact of radial pressure drop to bed stress and load distribution is very important for reactor internals design and operation. In this study, a generic packed catalyst bed for a radial flow reactor is analytically modeled and examined for stress and load by a classical granular solid material model, i.e., Janssen’s theory, which is further modified to include the pressure drop effects for a radial flow reactor. Interactions between bed stress, load, and radial pressure drop are explored. The critical condition is derived.

The role of velocity, pressure, and bed stress fluctuations in bed load transport over bed forms: numerical simulation downstream of a backward-facing step

Bed load transport over ripples and dunes in rivers exhibits strong spatial and temporal variability due to the complex turbulence field caused by flow separation at bedform crests. A turbulence-resolving flow model downstream of a backward-facing step, coupled with a model integrating the equations of motion of individual sand grains, is used to investigate the physical interaction between bed load motion and turbulence downstream of separated flow. Large bed load transport events are found to correspond to low-frequency, positive pressure fluctuations. Episodic penetration of fluid into the bed increases the bed stress and moves grains. Fluid penetration events are larger in magnitude near the point of reattachment than further downstream. Models of bed load transport over ripples and dunes must incorporate the effects of these penetration events of high stress and sediment flux.