This thesis was aimed developing a fundamental understanding of the boundary layer response
to arbitrary motion. In this context arbitrary motion was defined as the unsteady translation and
rotation of an object.
Research objectives were developed from the gaps in knowledge as defined during the literature survey.
The objectives were divided into three main activities; mathematical formulations for non-inertial
bulk flow and boundary layer equations, implementation of said formulations in a numerical solver and
simulations for various applications in arbitrary motion.
Mathematical formulations were developed for the bulk flow and boundary layer equations in arbitrary
motion. It was shown that the conservation of momentum and energy equations remains invariant
in the non-inertial forms. The conservations of momentum equation can at most have six fictitious terms
for unsteady arbitrary motion. The origin of the terms were found to be from transformation of the material
derivative to the non-inertial frame. All fictitious terms were found to be present in the boundary
layer equations, none could be eliminated during an order of magnitude analysis.
The vector form of the non-inertial equations were implemented in a novel OpenFOAM solver. The
non-inertial solver requires prescribed motion input and operate on a stationary mesh. Validation of the
solver was done using analytical solutions of a steady, laminar flat plate and rotating disk respectively.
Numerical simulation were done for laminar flow on a translating plate, rotating disk and rotating
cone in axial flow. A test matrix was executed to investigated various cases of acceleration and deceleration
over a range of 70 g to 700 000g. The boundary layer profiles, boundary layer parameters and
skin friction coefficients were reported.
Three types of boundary layer responses to arbitrary motion were defined. Response Type I is viscous
dominant and mimics the steady state velocity profile. In Response Type II certain regions of the
boundary layer are dominated by viscosity and others by momentum. Response Type III is dominated
by momentum. In acceleration the near-wall velocity gradient increases with increasing acceleration. In
deceleration separation occurs at a result of momentum changes in the flow.
The mechanism that causes these responses have been identified using the developed boundary layer
equations. In acceleration the relative frame fictitious terms become a momentum source which results
in an increase in velocity gradient at the wall. In deceleration the relative frame fictitious terms become
a momentum sink that induced an adverse pressure gradient and subsequently laminar separation.
Hierdie tesis is gerig op die ontwikkeling van 'n fundamentele begrip aangaande die grenslaag
reaksie op arbitrêre beweging. In hierdie konteks word arbitrêre beweging gedefinieer as die
ongestadigde translasie en rotasie van 'n voorwerp.
Navorsingsdoelwitte is ontwikkel uit die gapings soos omskryf in die literatuuroorsig. Die doelwitte
is verdeel in drie hoof aktiwiteite; wiskundige formulerings vir ongestadigde vloei en grenslaag
vergelykings, implementering van hierdie formulerings in 'n numeriese kode en simulasies vir verskeie
gevalle van arbitrêre beweging.
Wiskundige formulerings is ontwikkel vir die vloei en grenslaag vergelykings in arbitrêre beweging.
Daar is bewys dat die behoud van massa en energie vergelykings onveranderd in die nie-inertiële
vorms bly. Die behoud van momentum vergelyking kan hoogstens ses fiktiewe terme vir ongestadigde,
arbitrêre beweging hê. Die oorsprong van die terme is vanuit die transformasie van die ongestadigde
en adveksie terme (aan die linker kant van die momentum vergelyking) na die nie-inertiële raam. Alle
fiktiewe terme is teenwoordig in die grenslaag vergelykings.
Die vektor vorm van die nie-inertiële vergelykings is in 'n nuwe OpenFOAM oplosser geïmplementeer.
Die nie-inertiële oplosser vereis voorgeskrewe beweging insette en werk op 'n stilstaande
rooster. Die oplosser is getoets teen analitiese oplossings van 'n gestadigde, laminêre plaat plaat en
'n roterende skyf, onderskeidelik.
Numeriese simulasies is gedoen vir laminêre vloei op 'n translerende plaat, roterende skyf en roterende
konus in aksiale vloei. 'n Toets matriks is gebruik om ondersoek in te stel na gevalle van versnelling en
vertraging oor 'n verskeidenheid van 70 g tot 700 000 g. Die grenslaag profiele, grenslaag parameters
en oppervlak wrywingskoëffisiënte is aangemeld nie.
Drie tipes grenslaag reaksies op arbitrêre beweging is gedefinieer. Reaksie Tipe I is viskeus dominant
en boots die bestendige snelheidsprofiel na. In reaksie Tipe II sekere dele van die grenslaag is
oorheers deur viskositeit en ander deur momentum. Reaksie Tipe III word in totaliteit oorheers deur
momentum. In versnelling die snelheid helling teen die objek neem toe met toenemende versnelling. In
vertraging is 'n negatiewe snelheidsprofiel waargeneem as gevolg van momentum veranderinge in die
vloei.
Die meganisme wat hierdie reaksies veroorsaak is geïdentifiseer deur die grenslaag vergelykings. In
versnelling word die fiktiewe terme 'n bron van momentum. Dit lei tot 'n toename in snelheid helling op
die objek. In vertraging word die fiktiewe terme 'n momentum gebruiker wat 'n negatiewe drukgradiënt
veroorsaak en gevolglik laminêre vloei wegbreking veroorsaak.
