In order to simulate the results of practical cleaning tests on closed processing equipment, based on wall shear stress predicted by computational fluid dynamics, a critical wall shear stress is required for that particular cleaning method. This work presents investigations that provide a critical wall shear stress of 3 Pa for the standardised EHEDG cleaning test method. The cleaning tests were performed on a test disc placed in a radial flowcell assay. Turbulent flow conditions were generated and the corresponding wall shear stresses were predicted from CFD simulations. Combining wall shear stress predictions from a simulation using the low Re k-e and one using the two-layer model of Norris and Reynolds were found to produce reliable predictions compared to empirical solutions for the ideal flow case. The comparison of wall shear stress curves predicted for the real RFC with the empirical solution showed that the empirical solution gives a good prediction even in the real RFC from a radius of 15 mm and outwards.

Critical wall shear stress for the EHEDG test method

The radial Navier-Stokes flow in a fracture bounded by impermeable corrugated rock surfaces is significantly different from the commonly used creeping flow model between two parallel surfaces, described by Darcy's law on the macroscale. Continuous variations in the Reynolds number along the radial coordinate determine the important role of the nonlinear inertial effects, which are reinforced by local oscillations of the velocity field caused by wall corrugation. The system behaviour is studied both analytically and numerically. A solution for the full system of Navier-Stokes equations in a thin cylindrical domain with oscillating walls is developed as a biparametric and two-scale asymptotic expansion with respect to fracture aperture and corrugation period. The numerical solution is derived based on the finite volume method. A new macroscale flow equation is obtained, which explicitly displays the relative roles of viscous dissipation caused by corrugation, local and global inertia, and cross inertia-viscous effects. The effective flow parameters are defined using analytical relationships.

Macroscale model and viscous inertia effects for Navier Stokes flow in a radial fracture with corrugated walls

This paper deals with the power series solutions of the steady, laminar, radial flows either purely accelerating, or purely decelerating, that develop in the gap formed by two flat disks. The results include velocity profiles and static pressure distributions. These are compared with previously reported approximate solutions or the experimental data for the pressure obtained by others. The development of the two types of flows is shown to be entirely different except for λ (parameter that combines the non-dimensional radial distance and Reynolds number) close to zero where both behave as Poiseuille's flows between two infinite plates. For the inflow, the radial velocity flattens near the mid-plane diffusing towards the walls as the parameter λ increases. In contrast to the inflow, the magnitude of the maximum velocity of the outflow is shown to increase with λ, indicating that most of the fluid motion is taking place near the central channel region. For the outflow, two critical values of λ are used to indicate notable flow field transformations. The first marks the point where the pressure difference changes sign, while the second denotes when the derivative of the velocity (in the axial direction) on the wall becomes zero. Beyond the second value, purely decelerating flow cannot exist. The sign change of the pressure is attributed to the interaction between the inertia, viscous, and pressure forces.

Purely accelerating and decelerating flows within two flat disks

The flow driven by a rapidly expanding and collapsing cavitation bubble in a narrow cylindrical gap is studied with the volume of fluid method. The simulations reveal a developing plug flow during the early expansion followed by flow reversal at later stages. An adverse pressure gradient leads to boundary layer separation and flow reversal, causing large shear stress near the boundaries. Analytical solution to a planar pulsating flow shows qualitative agreement with the CFD results. The shear stress close to boundaries has implications to deformable objects located near the bubble: experiments reveal that thin, flat biological cells entrained in the boundary layer become stretched, while cells with a larger cross-section are mainly transported with the flow.

Flow field from transient bubble oscillation in a narrow gap: numerical simulations and effect on biological cells

This paper deals with sink and source flows developed in cones with small apex angles and in narrow gaps formed by two concentric cones. Numerical and approximate analytical solutions to these flows are presented. An exact solution for the creeping flow in conical gaps in terms of Legendre polynomials is derived. The analytical solutions to the flow in cones, includes the linearized inertia terms in the momentum equations, and are given using Gauss' hypergeometric series. For low Reynolds numbers, both converging and diverging flows are shown to coincide and are similar to Poiseuille's flow. However, when inertia effects are included, these are found to be radically different. For a sink flow, the radial velocity flattens in the neighborhood of the mid-angle and, as Re increases, the plateau expands out towards the conical walls, tending to the inviscid flat profile throughout the entire flow field. Contrary to the accelerating flow, the maximum velocity of the decelerating flow is shown to increase with Re. As a first critical Reynolds number is approached, the shear stress reduces to zero on the cone walls or, for a conical gap, on the outer cone walls. A further increase in Re above this first critical value, is found to produce a flow reversal either near the wall or, for the case of a conical gap, in the proximity of the outer cone. Thus, when Re exceeds this second value, purely decelerating flow cannot exist. The results for accelerating (sink) flow indicate that the approximate analytic solution is an excellent representation of this flow, whereas, for decelerating (source) flows particularly near separation, the results indicate that the numerical approach is needed to properly capture all flow features.

Converging and diverging flow in narrow conical passages

A numerical solution to the radial inflow between two flat disks is presented. The pressure and the radial velocity distribution are shown to be functions of solely one non-dimensional parameter that combines the Reynolds number and the radial distance. The numerically predicted pressure correlates well with the experiment. By comparison to the results of the linearized theory, the radial velocity profile is seen to be lower at the mid-plane and larger near the disk surface.

G. Zitouni

Papers

Purely accelerating and decelerating flows within two flat disks

Radial inflow between two flat disks