Handbook of Hygiene Control in the Food Industry

boundary conditionsfor the controlvolume, are described by the Navier±

Stokes equations(herein incompressible form).



@ui

@t

á

@

@xj

ÖujuiÜàˇ

@p

@xi

á

@

@xj

Ö 2 sijÜ Ö 11 : 4 Ü

wheretis the time,uiandxithe velocityand position vector,pthe pressure
andsijthe strain-ratetensor.Thenumberof control volumeschosen is a
trade-off between accuracyand simulationtime.For eachparameter solved
for (u,v,wandp) the Navier±Stokesequationsare set up.
∑ Physicaland empiricalmodels for otherphenomena thanlaminar flow(heat
transfer, buoyancy, multiphase, radiation, etc.)are selected.Turbulencein the
flowis a specialsubject treated in details below.
∑ Boundaries(e.g.inlet,outletand walls)are definedon appropriatefaces of
the meshand the boundaryconditionsare specified.An inletvelocity (plug
flowor an arbitrary profile),totalmassflowthroughthe flowdomainor a
pressure difference between inlet and outlet can be used to generate
movementof the liquid. Walls can be specifiedwithdifferentroughness
parametersto influencethe pressuredrop(skin friction) throughthe flow
domain and heattransfer to and fromthe surfacecan be estimated.
∑ Physicalproperties for the liquidare selected.
∑ Theiterationprocedure is initiatedand iterations are performeduntil a
specified convergencecriterion or divergenceis reached.
Theinfluence of turbulence is includedin the Navier±Stokes equations
throughthe Reynoldsstresstensor(ij):



@Ui

@t

áUj

@Ui

@xj

àˇ

@P

@xi

á

@

@xj

Ö 2 Sijˇu^0 ju^0 iÜ Ö 11 : 5 Ü

ijàˇu^0 ju^0 iàTSij Ö 11 : 6 Ü

Tàconstk^1 =^2 l Ö 11 : 7 Ü

wherePis the average pressure,Sijthe averagestrain-ratetensor,kthe turbulent
kinetic energy,lthe turbulent length scale and the^0 denotesfluctuatingvalues.
The Reynoldsstresstensoris expressedby the average of the productof the
fluctuatingcomponent,hence, these mustbe found.Thiscan be doneby, for
example, direct numericalsimulation(DNS), largeeddysimulation(LES)or
closure models. The closuremodelssolve transportequationsfor the turbulent
kinetic energyand turbulentkineticenergy dissipation () in the core flow.In the
near-wall layer, production and dissipation of turbulent kinetic energy is
estimatedby near-walltreatments. The choice of near-walltreatment(see later)
prescribesthe recommended densityof cellsin the near-walllayer.
Descriptionsof the governingequations for finitevolumecodeshavebeen
extensivelydescribed in a number of references(for example Patankar, 1980;
Versteeg and Malalasekera, 1995;Ferzigerand Peric,1999).

198 Handbookof hygiene controlin the foodindustry