?url_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.relation=http%3A%2F%2Fmiis.maths.ox.ac.uk%2Fmiis%2F752%2F&rft.title=Optimisation+of+Fluid+Mixing+in+a+Hydrosacc%E2%83%9D+Growing+Module&rft.creator=Champneys%2C+A.&rft.creator=Benham%2C+Graham&rft.creator=Cowley%2C+Stephen&rft.creator=Dennison%2C+Zoe&rft.creator=Griffith%2C+Matthew&rft.creator=Kamilova%2C+Alissa&rft.creator=Kov%C3%A1cs%2C+Atilla&rft.creator=Lacey%2C+Andrew&rft.creator=Marquis%2C+Scott&rft.creator=Morawiecki%2C+P.&rft.creator=Ockendon%2C+John&rft.creator=Sachak-Patwa%2C+Rahil&rft.creator=Please%2C+Colin&rft.creator=Wragg%2C+Hayley&rft.subject=Fluids&rft.description=A+mathematical+model+is+sought+for+the+flow+of+nutrients+in+the+Hydrosac%E2%83%9Dc+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%3A+partial+drainage+and+refilling+of+each+bag+with+nutrient+infused+water%2C+with+inlet+and+outlet+at+opposite+ends+of+the+bag%3B+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.%0D%0AThe+aim+of+the+modelling+is+to+determine+the+key+parameters+and+fluid+regimes+underlying+the+nutrient+mixing+process%2C+to+ensure+that+required+nutrient+levels+are+maintained+through-+out+the+root+zones%2C+and+to+enable+optimal+scheduling+of+the+nutrient+and+bubble+flow.%0D%0ASimple+experiments+were+performed+via+the+injection+of+dye+into+an+operating+Hydrosac%E2%83%9Dc+that+contained+semi-mature+plants.+This+enabled+a+basic+understanding+of+the+time+and+lengthscales+of+nutrient+flow%2C+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%2C+a+Stokes-flow+approximation+may+be+used.+At+the+scale+of+the+individual+plant%2C+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.%0D%0AA+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%2C+which+is+also+found+to+be+consistent+with+previous+literature.%0D%0AThe+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+Hydrosac%E2%83%9Dc+.+Wave+effects+can+be+ignored%2C+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%2C+while+the+recirculation+from+the+bubble+flow+enables+enables+nutrients+to+spread+within+the+plant+roots.+Nevertheless%2C+regions+of+stagnation+can+occur+via+this+process+near+any+sharp+corners+of+the+bag.%0D%0AIt+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+Hydrosac%E2%83%9Dc+%2C+which+can+also+be+adaptable+to+other+geometries+and+growing+conditions.&rft.date=2018&rft.type=Study+Group+Report&rft.type=NonPeerReviewed&rft.format=application%2Fpdf&rft.language=en&rft.identifier=http%3A%2F%2Fmiis.maths.ox.ac.uk%2Fmiis%2F752%2F1%2FPhytoponics.pdf&rft.identifier=++Champneys%2C+A.+and+Benham%2C+Graham+and+Cowley%2C+Stephen+and+Dennison%2C+Zoe+and+Griffith%2C+Matthew+and+Kamilova%2C+Alissa+and+Kov%C3%A1cs%2C+Atilla+and+Lacey%2C+Andrew+and+Marquis%2C+Scott+and+Morawiecki%2C+P.+and+Ockendon%2C+John+and+Sachak-Patwa%2C+Rahil+and+Please%2C+Colin+and+Wragg%2C+Hayley++(2018)+Optimisation+of+Fluid+Mixing+in+a+Hydrosacc%E2%83%9D+Growing+Module.++%5BStudy+Group+Report%5D+++++