eprintid: 752
rev_number: 10
eprint_status: archive
userid: 17
dir: disk0/00/00/07/52
datestamp: 2019-05-11 13:59:20
lastmod: 2019-05-11 13:59:20
status_changed: 2019-05-11 13:59:20
type: report
metadata_visibility: show
creators_name: Champneys, A.
creators_name: Benham, Graham
creators_name: Cowley, Stephen
creators_name: Dennison, Zoe
creators_name: Griffith, Matthew
creators_name: Kamilova, Alissa
creators_name: Kovács, Atilla
creators_name: Lacey, Andrew
creators_name: Marquis, Scott
creators_name: Morawiecki, P.
creators_name: Ockendon, John
creators_name: Sachak-Patwa, Rahil
creators_name: Please, Colin
creators_name: Wragg, Hayley
corp_creators: Adam Dixon
corp_creators: Thanya Charts
title: Optimisation of Fluid Mixing in a Hydrosacc⃝ Growing Module
ispublished: pub
subjects: Fluids
studygroups: ESGI138
companyname: Phytoponics
full_text_status: public
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.
problem_statement: Phytoponics is an ‘AgTech’ start-up based in Wales. Their vision is to innovate the food chain by facilitating the mass adoption of Hydroponic technology, so that a market sustainable agriculture can tackle this century’s food, land and water challenges. Hydroponics is the best way to grow fruit and veg, using 10 times less land and water than a traditional field and it aligns with the UN sustainable development goals. Led by the United Nations Young Champion of the Earth for Europe, Adam Dixon, Phytoponics has invented a new type of low cost and versatile growing system that could deliver a huge impact globally.
Watch video: https://www.youtube.com/watch?v=Y7ReU6dtJNM&t
Hydroponics involves growing plants in a water-based nutrient solution to induce higher growth rates. However, in a water environment, a significant constraint is the dissolved oxygen levels, as plant roots respire using this dissolved oxygen as their primary source.
Having adequate dissolved oxygen levels is essential for healthy roots due to maintaining pathogen defence systems and nutrient uptake. It is also important that nutrients are well mixed within the system and that natural fluid flow does not cause dead zones or poor concentration gradients within the growing system.
Phytoponics as a start-up has already benefited directly from taking part in two KTN agri- food mini-study-groups with industry in 2017 and 2018. The innovations developed there involved optimising the geometry of the sack to ensure its rigidity and understanding how to aerate the system to achieve desired levels of dissolved oxygen.
The bigger challenge presented here is to optimise the design of the fluid mixing within the Hydrosac⃝c growing modules, such that oxygenation is maximised in the pool of water, and that nutrients are well mixed without any dead zones or unintended concentration gradients.
The timing of the ESGI 138 is ideal because during the Study Group, Phytoponics can include analysis and experiments in an ongoing large-scale trial in Wales. There may also be scope to run experimental tests, live, on the actual apparatus, or even to arrange a day trip to visit the trial site during the study group.

Key mathematical questions to be addressed during the study group include:
1. How does the geometry of the Hydrosac⃝c growing module contribute to the spread of nutrients and oxygen?
2. How do plant roots contribute to mixing/and or stagnation?
3. Can we make a more precise model of nutrient distribution and oxygenation, backed up by data?
4. Could we run experiments with introduction of die to explain how mixing takes place?
5. Could we create an engineering model from applied mathematics for this scenario?
6. Could one design optimal baffles or make other changes to the geometry to aid mixing, and to generally enhance plant growth and cleaning?
date: 2018
citation:   Champneys, A. and Benham, Graham and Cowley, Stephen and Dennison, Zoe and Griffith, Matthew and Kamilova, Alissa and Kovács, Atilla and Lacey, Andrew and Marquis, Scott and Morawiecki, P. and Ockendon, John and Sachak-Patwa, Rahil and Please, Colin and Wragg, Hayley  (2018) Optimisation of Fluid Mixing in a Hydrosacc⃝ Growing Module.  [Study Group Report]     
document_url: http://miis.maths.ox.ac.uk/miis/752/1/Phytoponics.pdf