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Workshop on CFVNs – Poitiers 2013 Flow Structure In CFVNs Ernst von Lavante University of Duisburg-Essen

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Workshop on CFVNs – Poitiers 2013 Introduction – why again? Transition laminar-turbulent Low and high unchoking Shock at the exit? Steady or unsteady? 2-D, 2-D axisymmetric, 3-D or what? Is there a hope to predict the flow? Conclusions – if any Overview

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Workshop on CFVNs – Poitiers 2013 Introduction The beginning: flow in CFVNs simulated with ACHIEVE Presented at Flomeko ’98 Always unsteady! Next effort: “premature unchoking” – Nakao, Takamoto, Ishibashi After that: transition laminar-turbulent simulation & theory (Abu Ghanam, Mayle, Schlichting,...) Current effort: visualize transition

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Workshop on CFVNs – Poitiers 2013 Introduction Then came Bodo M.: Latest paper with Kramer and Li Presented at 8 th ISFFM ’12 Definition of “low” and “high” unchoking Discussion of flow structure Decision to carry out “good” flow simulation After that: transition laminar-turbulent simulation & theory (Abu Ghanam, Mayle, Schlichting,...) Current effort: visualize transition

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Workshop on CFVNs – Poitiers 2013 Main goal: numerical simulation of flow fields in flow metering configurations In all cases, scale sufficiently large to give Kn = λ/L < 0.01 with λ 10 -8 – 10 -9 m => continuum Notice: Kn M/Re a) flows with M/Re > 1 called rarefied b) incompressible gas (M 0) can not be rarefied c) small Re flow could mean rarefied fluid d) large Re flows are always continuum Basics

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Workshop on CFVNs – Poitiers 2013 Physics of the flow: compressible (Ma ≥ 0.3) => mixed hyperbolic-parabolic, coupled incompressible => mixed elliptic-hyperbolic-parabolic, decoupled laminar (Re ≤ 2300 !) turbulent => turbulence model (k-ε, k-ω, RNG, realizable, SST, RSM, LES, DES, DNS) steady unsteady – periodic (deterministic) or stochastic Basics simulation method must have low numerical dissipation, since μ Tot = μ Phys + μ Num => 1/Re Tot = 1/Re Phys + 1/Re Num

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Workshop on CFVNs – Poitiers 2013 Considerations in numerical simulation methods (CFD): 2-D or 3-D configuration grid generation: structured multiblock (mutigrid?) unstructured tetrahydral, hexahydral, polyhydral hybrid moving (deforming) grids (adapting to flow) overlapping grids (chimera), immersed body grids quality of grids: smoothing, continuity, resolution in time and space Computation:time and space accuracy, damping Boundary conditions Multiprozessing (parallel processing) Basics

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Workshop on CFVNs – Poitiers 2013 Choice of correct tools: hardware (minimum requirements) competence of staff Software: system preprocessing (grid generation) simulation system (CFX, Fluent, adapco Star CCM+, my own programs ACHIEVE, trace, Flower, ….) postprocessing (included, Tecplot, …) The correct choice will „make you or break you“ ! Basics

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Workshop on CFVNs – Poitiers 2013 CFVN 1 - ISO Shape: ISO 9300, toroidal version different Reynolds numbers and pressure ratios 2-D axisymmetric, 3 blocks, structured, laminar

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Workshop on CFVNs – Poitiers 2013 CFVN 1 - ISO Resulting Flow, Movies, Re=1.5 10 6

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Workshop on CFVNs – Poitiers 2013 CFVN 1 - ISO Resulting Flow, Movies, Re=0.1 10 6

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Workshop on CFVNs – Poitiers 2013 CFVN 1 - ISO Resulting Flow, Movies, Re=1.5 10 6

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Workshop on CFVNs – Poitiers 2013 CFVN 1 - ISO Resulting Flow, Movies, Re=0.1 10 6

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Workshop on CFVNs – Poitiers 2013 CFVN 1 - ISO - Unsteady effects (Elster, eon) - Premature unchocking - National Calibration Standard at Pigsar (Pigsar, Elster, PTB, eon) - Real gas effects in CFVN (eon) - Influencing of flow fields in CFVN (steps, suction) - Micro nozzles (PTB) - Reynolds number effects in CFVN (transition laminar-turbulent) - Geometric factors (PTB) - Theoretical determination discharge coeff. C D (PTB) - Shock location, influence of condenzation (NRLM) All simulations with ACHIEVE – accuracy !!

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Workshop on CFVNs – Poitiers 2013 CFVN 1 - ISO

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Workshop on CFVNs – Poitiers 2013 CFVN 1 - ISO Experimental verification by Ishibashi (NRLM)

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Workshop on CFVNs – Poitiers 2013 CFVN 2 – micro nozzle Aim of present study: comparison of high resolution CFD simulations with experimental results (PTB) Two basic shapes: punched and drilled Utilized in forward (L to R) and backward (R to L) orientation

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Workshop on CFVNs – Poitiers 2013 Present cases: CFVN 2 – micro nozzle In our case: Kn = 1.28 κ 0.5 Ma/Re throat diameter D in [µm] Reynolds -number Re d B.L. thickness δ in [µm] -> ratio of δ/d Knudsen number Kn 151975,3480,35650,0153 253286,9040,27620,0092 354598,1690,23340,0066 506569,7640,19530,0046 80104912,3510,15440,0029

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Workshop on CFVNs – Poitiers 2013 Simulation Parameter Simulation carried out using ACHIEVE solver developed by author Grid generated by elliptic PDE developed in house Configuration: D = 15, 25, 35, 50 and 80 μ, P 0 = 0.101325 MPa, T 0 = 300 K Pressure ratios p out /P 0 = 0.3 and 0.4

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Workshop on CFVNs – Poitiers 2013 Experimental Work at PTB Results for D = 25 µm: 1.Forward nozzle: choking at p/P 0 = 0.35 (ideal nozzle 0.528…) 2.Backward nozzle: no apparent choking Task for numerical simulation: explain phenomenon !!

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Workshop on CFVNs – Poitiers 2013 Numerical Simulations - Results Forward orientation, p out /p 0 = 0,3

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Workshop on CFVNs – Poitiers 2013 Numerical Simulations - Results Backward orientation, p out /p 0 = 0,3

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Workshop on CFVNs – Poitiers 2013 Numerical Simulations Boundary layer in cylindrical part p out /p 0 = 0,4

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Workshop on CFVNs – Poitiers 2013 Numerical Simulations - Results Drilled nozzle, p out /p 0 = 0,3

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Workshop on CFVNs – Poitiers 2013 Numerical Simulations - Results Drilled nozzle, p out /p 0 = 0,3

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Workshop on CFVNs – Poitiers 2013 Summary p 2 /p 0 0,40,3 NozzleC d, exp C d, num DeviationC d, exp C d, num Deviation Forward250,6620,7056,45 %0,6640,7117,07 % Backward250,6700,7075,47 %0,6760,7439,97 % Forward Drilled250,6600,6924,90 %0,6620,7229,12 % Backward Drilled250,6630,6974,96 %0,6670,7248,57

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Workshop on CFVNs – Poitiers 2013 Conclusions Reliable numerical simulation of komplex flows in flow metering configurations possible using low numerical dissipation schemes Commercial codes should be used with care – it is not all gold that shines OpenFoam looks promising in many cases Present simulations were able to provide an explanation of many flow behaviour questions Much higher resolution simulations in future – there is never enough computer power (CPU and RAM)

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