Optimisation of Fluid Mixing in a Hydrosacc⃝ Growing Module

Abstract

A mathematical model is sought for the flow of nutrients in the Hydrosac⃝c growing module being developed by Phytoponics. The basic operation involves long fluid-filled bags with periodic growing zones from which root systems emerge into the bulk fluid. The system is periodically perturbed via two main processes: partial drainage and refilling of each bag with nutrient infused water, with inlet and outlet at opposite ends of the bag; and a more violent oxygenation of the water through bubbles that rise from the pores of an aeration tube that runs underneath the central long axis of the bag.
The aim of the modelling is to determine the key parameters and fluid regimes underlying the nutrient mixing process, to ensure that required nutrient levels are maintained through- out the root zones, and to enable optimal scheduling of the nutrient and bubble flow.
Simple experiments were performed via the injection of dye into an operating Hydrosac⃝c that contained semi-mature plants. This enabled a basic understanding of the time and lengthscales of nutrient flow, and also the extent to which mixing occurs in different zones within the bag. Four different flow regimes are identified. At the scale of a single root, a Stokes-flow approximation may be used. At the scale of the individual plant, a so-called Brinkman flow regime may be employed which is describes a transition between slow porous- medium flow and fast channel flow. These equations may be homogenised into a 1D model that can be used to estimate the macro-scale flow of nutrients along the length of the bag.
A shear flow model is used to predict the extent to which this flow permeates into regions dominated by plant roots. This leads to the requirement to model the bubble-driven flow within a bag cross-section containing a plant. Simplified two-phase flow equations are de- rived and solved within the software COMSOL. The results suggest that the bubble flow is sufficient to drive recirculating flow, which is also found to be consistent with previous literature.
The overall conclusion is that both the periodic flow of nutrients and the aeration are re- quired in order to enable even nutrient spread in the Hydrosac⃝c . Wave effects can be ignored, as can the effect of stagnated nutrient diffusion. The longitudinal nutrient flow enables the whole sack to be reached on the time scale of several cycles of the main inlet flow, while the recirculation from the bubble flow enables enables nutrients to spread within the plant roots. Nevertheless, regions of stagnation can occur via this process near any sharp corners of the bag.
It is recommend that the various analyses are combined into a a reduced-order mathemat- ical model that can be used to optimise the dynamic operation of the Hydrosac⃝c , which can also be adaptable to other geometries and growing conditions.