Tomographic Particle-Image Velocimetry Measurement in a Turbulent Wavy Channel Flow

section,� the� flow� reaches� the� test� section. � Upon� entering� the� test� section,� a� steady� and� fully� turbulent� velocity� profile� matching� direct� numerical� simulation� (DNS)� results� by� Niederschulte� (2)� has� developed. The� test� section� itself� measures� 2.5� m� in� length. � One� wall� possesses� a� sinusoidal� wall� contour. � Its� wavelength� measures� 100� mm� with� an� amplitude� of� 2.5� mm. � While� the� contour� crests� reach� 5� mm� into� the� channel,� the� trough� maintains� the� original� flat� wall� position. � The� sinusoidal� wall� contour� covers� 1.5� m� of� the� test� section� with� 15� individual� crests. � The� wave� between� the� 13th� and� 14th� crest� is� equipped� with� pressure� taps� leading� to� a� micro�manometer� to� record� steady� pressure� differences� with� respect� to� the� ambient� pressure. � The� final� part� of� the� test� section� maintains� the� flat� walls� on� find� a� closure� model� for� fluctuating� quantities� and� their� higher� moments� use� some� kind� of� local� statistic� assumption. � While� there� are� many� different� models� that� have� proved� reasonably� successful� in� many� applications,� limits� of� each� modelling� approach� exist� leaving� room� for� improvement. One� attempt� to� address� this� and� better� represent� geometric� structures� was� proposed� by� Wang� and� Peters� (3). � The� method� is� based� on� a� fluctuating� scalar� such� as� absolute� velocity,� turbulent� energy,� or� individual� velocity� components� and� decomposes� the� scalar� field� into� individual� monotonic� structures� which� are� called� "dissipation� elements". � Each� element� consists� of� all� possible� gradient� trajectories� connecting� a� particular� pair� of� local� maximum� and� minimum� points. � Since� the� local� gradient� is� unambiguously� defined� for� each� point,� the� resulting� gradient� trajectories� cannot� overlap. � Consequently,� the� dissipation� elements� method� can� be� viewed� as� a� way� to� partition� an� instantaneous� flow� field� yielding� a� room� filling� ensemble� of� monotonic� structures. To� expand� this� approach� beyond� generic� shear� cases� and� standard� channel� flows� that� have� been� investigated� in� previous� experiments� towards� more� complex� flows,� tomographic� particle�image� velocimetry� measurements� in� a� channel� flow� with� modified� geometry� were� conducted. � To� impose� a� streamwise� pressure� gradient,� a� sinusoidal� surface� profile� was� introduced� as� one� channel� wall. � The� absolute� velocity� is� chosen� as� the� underlying� scalar� of� the� dissipation� element� method� to� provide� data� comparable� to� streamline� segment� analyses. � This� analysis� focuses� on� statistical� quantities� such� as� element� length,� scalar� difference� along� such� elements,� and� their� directionality� in� flows� driven� by� a� local� pressure� gradients. � It� is� attempted� to� predict� local� statistical� properties� based� on� larger� scale� mean� flow� properties� such� as� local� mean� acceleration. All� experiments� were� performed� in� the� Eiffel�type� wind� tunnel� at� the� Institute� of� Aerodynamics� at� RWTH� Aachen� University. � Its� cross� section� measures� 100� mm� x� 2000� mm� (height� x� width). � Transition� is� forced� by� two� strips� of� sandpaper� on� the� channel� walls� directly� downstream� of� the� wind� tunnel� nozzle. � After� passing� a� 9� m� long� inlet� section,� the� flow� reaches� the� test� section. � Upon� entering� the� test� section,� a� steady� and� fully� turbulent� velocity� profile� matching� direct� numerical� simulation� (DNS)� results� by� Niederschulte� (2)� has� developed. The� test� section� itself� measures� 2.5� m� in� length. � One� wall� possesses� a� sinusoidal� wall� contour. � Its� wavelength� measures� 100� mm� with� an� amplitude� of� 2.5� mm. � While� the� contour� crests� reach� 5� mm� into� the� channel,� the� trough� maintains� the� original� flat� wall� position. � The� sinusoidal� wall� contour� covers� 1.5� m� of� the� test� section� with� 15� individual� crests. � The� wave� between� the� 13th� and� 14th� crest� is� equipped� with� pressure� taps� leading� to� a� micro�manometer� to� record� steady� pressure� differences� with� respect� to� the� ambient� pressure. � The� final� part� of� the� test� section� maintains� the� flat� walls� on� both� sides. Based� on� the� 2D� reference� data,� four� measurement� volumes� spanning� 15� x� 15� x� 8� mm 3 � representative� for� the� crest� (C),� expansion�