Experimental validation of convection-diffusion discretisation scheme employed for computational modelling of biological mass transport

Abstract

Background: The finite volume solver Fluent (Lebanon, NH, USA) is a computational fluid dynamics software employed to analyse biological mass-transport in the vasculature. A principal consideration for computational modelling of blood-side mass-transport is convection-diffusion discretisation scheme selection. Due to numerous discretisation schemes available when developing a mass-transport numerical model, the results obtained should either be validated against benchmark theoretical solutions or experimentally obtained results.

Methods: An idealised aneurysm model was selected for the experimental and computational mass-transport analysis of species concentration due to its well-defined recirculation region within the aneurysmal sac, allowing species concentration to vary slowly with time. The experimental results were obtained from fluid samples extracted from a glass aneurysm model, using the direct spectrophometric concentration measurement technique. The computational analysis was conducted using the four convection-diffusion discretisation schemes available to the Fluent user, including the First-Order Upwind, the Power Law, the Second-Order Upwind and the Quadratic Upstream Interpolation for Convective Kinetics (QUICK) schemes. The fluid has a diffusivity of 3.125 x 10-10 m2/s in water, resulting in a Peclet number of 2,560,000, indicating strongly convection-dominated flow.

Results: The discretisation scheme applied to the solution of the convection-diffusion equation, for blood-side mass-transport within the vasculature, has a significant influence on the resultant species concentration field. The First-Order Upwind and the Power Law schemes produce similar results. The Second-Order Upwind and QUICK schemes also correlate well but differ considerably from the concentration contour plots of the First-Order Upwind and Power Law schemes. The computational results were then compared to the experimental findings. An average error of 140% and 116% was demonstrated between the experimental results and those obtained from the First-Order Upwind and Power Law schemes, respectively. However, both the Second-Order upwind and QUICK schemes accurately predict species concentration under high Peclet number, convection-dominated flow conditions.

Conclusion: Convection-diffusion discretisation scheme selection has a strong influence on resultant species concentration fields, as determined by CFD. Furthermore, either the Second-Order or QUICK discretisation schemes should be implemented when numerically modelling convection-dominated mass-transport conditions. Finally, care should be taken not to utilize computationally inexpensive discretisation schemes at the cost of accuracy in resultant species concentration.

Figure 1

Idealised axisymmetric aneurysm model utilised for both computational and experimental analysis. Maximum aneurysm diameter is twice inlet/outlet diameter of 25.1 mm.

Figure 2

Schematic of experimental flow system. Test section refers to idealised aneurysm model.

Figure 3

Idealised axisymmetric aneurysm model utilised for both computational and experimental analysis. Volume fluid extraction was conducted using syringe pump.

Figure 4

Variation of ϕ between x = 0 and x = L [Developed from Fluent, [19]].

Figure 5

One-Dimensional control volume [Developed from Fluent, [19]].

Figure 6

(A) Illustration of experimental hemispherical cap of fluid extracted from idealised aneurysm. (B) Sub-division of the idealised hemisphere for concentration quantification of computational models.

Figure 7

Typical contours and vectors of velocity within the idealised aneurysmal sac. (A) Velocity contours in computational aneurysm model (ms^-1). (B) Velocity vectors within the recirculation region (ms^-1).

Figure 8

Contours of normalised species concentration as determined by the four different convection-diffusion upwinding techniques, T = 4 mins: First-Order Upwind Scheme, Power Law scheme, Second-Order Upwind Scheme and Quadratic Upstream Interpolation for Convective Kinetics (QUICK) Scheme.

Figure 9

Comparison between computational and experimental normalised species concentration results. The experimental data presented is the average values of eight sets of experimental results.