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

Feb 23, 2016

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Flow Structure In CFVNs. Ernst von Lavante University of Duisburg-Essen. Overview. 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? - PowerPoint PPT Presentation

Kein Folientitel

Flow StructureIn CFVNs

Ernst von LavanteUniversity of Duisburg-Essen

Workshop on CFVNs Poitiers 2013 International Symposium Metrologia 2008 Havanna - Cuba, 27-29. May. 2008 Page Nr.Introduction why again?Transition laminar-turbulentLow and high unchokingShock 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 anyOverview

Workshop on CFVNs Poitiers 2013 International Symposium Metrologia 2008 Havanna - Cuba, 27-29. May. 2008 Page Nr.

IntroductionThe beginning: flow in CFVNs simulated with ACHIEVEPresented at Flomeko 98Always unsteady!Next effort: premature unchoking Nakao, Takamoto, IshibashiAfter that: transition laminar-turbulentsimulation & theory (Abu Ghanam, Mayle, Schlichting, ...)Current effort: visualize transition

Workshop on CFVNs Poitiers 2013 International Symposium Metrologia 2008 Havanna - Cuba, 27-29. May. 2008 Page Nr.3

IntroductionThen came Bodo M.: Latest paper with Kramer and LiPresented at 8th ISFFM 12Definition of low and high unchokingDiscussion of flow structureDecision to carry out good flow simulation

After that: transition laminar-turbulentsimulation & theory (Abu Ghanam, Mayle, Schlichting, ...)Current effort: visualize transitionWorkshop on CFVNs Poitiers 2013 International Symposium Metrologia 2008 Havanna - Cuba, 27-29. May. 2008 Page Nr.4

Considerations in numerical simulation methods (CFD):2-D or 3-D configurationgrid generation: structured multiblock (mutigrid?)unstructured tetrahydral, hexahydral, polyhydralhybridmoving (deforming) grids (adapting to flow)overlapping grids (chimera), immersed body gridsquality of grids: smoothing, continuity, resolution in time and spaceComputation:time and space accuracy, damping Boundary conditionsMultiprozessing (parallel processing)

BasicsWorkshop on CFVNs Poitiers 2013 International Symposium Metrologia 2008 Havanna - Cuba, 27-29. May. 2008 Page Nr.7

Physics of the flow:compressible (Ma 0.3) => mixed hyperbolic-parabolic, coupledincompressible => mixed elliptic-hyperbolic-parabolic, decoupledlaminar (Re 2300 !) turbulent => turbulence model (k-, k-, RNG, realizable, SST,RSM, LES, DES, DNS)steadyunsteady periodic (deterministic) or stochastic Basicssimulation method must have low numerical dissipation, sinceTot = Phys + Num => 1/ReTot = 1/RePhys + 1/ReNum Workshop on CFVNs Poitiers 2013 International Symposium Metrologia 2008 Havanna - Cuba, 27-29. May. 2008 Page Nr.6

Choice of correct tools:hardware (minimum requirements)competence of staffSoftware: 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 !BasicsWorkshop on CFVNs Poitiers 2013 International Symposium Metrologia 2008 Havanna - Cuba, 27-29. May. 2008 Page Nr.8

CFVN 1 - ISOShape: ISO 9300, toroidal versiondifferent Reynolds numbers and pressure ratios2-D axisymmetric, 3 blocks, structured, laminar

Workshop on CFVNs Poitiers 2013 International Symposium Metrologia 2008 Havanna - Cuba, 27-29. May. 2008 Page Nr.9

CFVN 1 - ISOResulting Flow, Movies, Re=1.5 106

Workshop on CFVNs Poitiers 2013 International Symposium Metrologia 2008 Havanna - Cuba, 27-29. May. 2008 Page Nr.10

CFVN 1 - ISOResulting Flow, Movies, Re=0.1 106

Workshop on CFVNs Poitiers 2013 International Symposium Metrologia 2008 Havanna - Cuba, 27-29. May. 2008 Page Nr.11

CFVN 1 - ISOResulting Flow, Movies, Re=1.5 106

Workshop on CFVNs Poitiers 2013 International Symposium Metrologia 2008 Havanna - Cuba, 27-29. May. 2008 Page Nr.12

CFVN 1 - ISOResulting Flow, Movies, Re=0.1 106

Workshop on CFVNs Poitiers 2013 International Symposium Metrologia 2008 Havanna - Cuba, 27-29. May. 2008 Page Nr.13

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. CD (PTB)- Shock location, influence of condenzation (NRLM)

All simulations with ACHIEVE accuracy !!Workshop on CFVNs Poitiers 2013 International Symposium Metrologia 2008 Havanna - Cuba, 27-29. May. 2008 Page Nr.14

CFVN 1 - ISO

Workshop on CFVNs Poitiers 2013 International Symposium Metrologia 2008 Havanna - Cuba, 27-29. May. 2008 Page Nr.15

CFVN 1 - ISOExperimental verification by Ishibashi (NRLM)

Workshop on CFVNs Poitiers 2013 International Symposium Metrologia 2008 Havanna - Cuba, 27-29. May. 2008 Page Nr.16

CFVN 2 micro nozzleAim 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) orientationWorkshop on CFVNs Poitiers 2013 International Symposium Metrologia 2008 Havanna - Cuba, 27-29. May. 2008 Page Nr.17

Present cases: CFVN 2 micro nozzleIn our case: Kn = 1.28 0.5 Ma/Re throat diameterD in [m]Reynolds-numberRedB.L. thickness in [m] -> ratio of/dKnudsen number Kn151975,3480,35650,0153253286,9040,27620,0092354598,1690,23340,0066506569,7640,19530,004680104912,3510,15440,0029Workshop on CFVNs Poitiers 2013 International Symposium Metrologia 2008 Havanna - Cuba, 27-29. May. 2008 Page Nr.18

Simulation ParameterSimulation carried out using ACHIEVE solver developed by authorGrid generated by elliptic PDE developed in houseConfiguration: D = 15, 25, 35, 50 and 80 , P0 = 0.101325 MPa, T0 = 300 KPressure ratios pout/P0 = 0.3 and 0.4

Workshop on CFVNs Poitiers 2013 International Symposium Metrologia 2008 Havanna - Cuba, 27-29. May. 2008 Page Nr.19

Experimental Work at PTB

Results for D = 25 m:Forward nozzle: choking at p/P0 = 0.35 (ideal nozzle 0.528)Backward nozzle: no apparent chokingTask for numerical simulation: explain phenomenon !!Workshop on CFVNs Poitiers 2013 International Symposium Metrologia 2008 Havanna - Cuba, 27-29. May. 2008 Page Nr.20

Numerical Simulations - ResultsForward orientation, pout/p0 = 0,3

Workshop on CFVNs Poitiers 2013 International Symposium Metrologia 2008 Havanna - Cuba, 27-29. May. 2008 Page Nr.21

Numerical Simulations - ResultsBackward orientation, pout/p0 = 0,3

Workshop on CFVNs Poitiers 2013 International Symposium Metrologia 2008 Havanna - Cuba, 27-29. May. 2008 Page Nr.22

Numerical Simulations Boundary layer in cylindrical part

pout/p0 = 0,4

Workshop on CFVNs Poitiers 2013 International Symposium Metrologia 2008 Havanna - Cuba, 27-29. May. 2008 Page Nr.23

Numerical Simulations - ResultsDrilled nozzle, pout/p0 = 0,3

Workshop on CFVNs Poitiers 2013 International Symposium Metrologia 2008 Havanna - Cuba, 27-29. May. 2008 Page Nr.24

Numerical Simulations - ResultsDrilled nozzle, pout/p0 = 0,3

Workshop on CFVNs Poitiers 2013 International Symposium Metrologia 2008 Havanna - Cuba, 27-29. May. 2008 Page Nr.25

Summary p2/p00,40,3NozzleCd, expCd, numDeviationCd, expCd, numDeviationForward250,6620,7056,45 %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

BackWorkshop on CFVNs Poitiers 2013 International Symposium Metrologia 2008 Havanna - Cuba, 27-29. May. 2008 Page Nr.26

ConclusionsReliable 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 shinesOpenFoam 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) Workshop on CFVNs Poitiers 2013 International Symposium Metrologia 2008 Havanna - Cuba, 27-29. May. 2008 Page Nr.0,2mm

D 4mm

d

l=d

= 34

a

D 4mm

0,2mm

d

l=d

5d

= 34

b

x/d

x/d

x/d

large vertical velocity

x/d

x/d

x/d

Diagramm50.071247050.65715707290.071247050.68912746690.70513163250.70662415970.7114628730.74340045520.73410050910.73819381250.75125051610.76957467560.7482473830.79246079390.77508637510.80609835230.76573529830.81897933590.79710337870.844434244

FW 0,4BW 0,4FW 0,3BW 0,31/Re^0,5Discharge CoefficientDischarge Coefficient vs. 1/Re^0,5

Kolmogorov_Knudsen_ZahlL0.0000150.0000250.0000350.000050.00008kb00000T293.15293.15293.15293.15293.15P100000100000100000100000100000Sauerstoff0.02812154030.01687292420.01205208870.00843646210.0052727888Stickstoff0.03149415160.0188964910.01349749350.00944824550.0059051534Luft0.03070321450.01842192870.01315852050.00921096430.0057568527mittlere freie Weglnge421.82 nm421.82 nm421.82 nm421.82 nm421.82 nmmittlere freie Weglnge472.41 nm472.41 nm472.41 nm472.41 nm472.41 nmmittlere freie Weglnge460.55 nm460.55 nm460.55 nm460.55 nm460.55 nmb m^3/moln Teilchen/molV=b/4NAr=((3/4)*V/PI)^(1/3)Sauerstoff0.00003260219999999999996000000000.0000000001146.92Stickstoff0.00002760219999999999996000000000.0000000001138.83Luft0.0000280560219999999999996000000000.0000000001140.61prop Ma/Re>=9Ma/Re Molekulare Gasdynamik: Einfhrung in die kinetische Theorie der Gase und ... Dieter HnelKolmogorovvisc0.00001823kappa1.4Macharakteristische LngeRe10500.00336262663.3626 mm1.310.00188953950.00008151.16316312846560.00236300452.3630 mm1.310.00302441540.00005151.22077104124590.00180778251.8078 mm1.310.00432247610.000035151.28666244473280.00140505091.4051 mm1.310.00604883080.000025151.22077104121970.00095859760.9586 mm1.310.01007114980.000015151.0672474158

Ergebnisse_DuesenWerte im Dsenhals --> ACHTUNG: Verdrngungsdicke und Impulsverlustdicke basieren auf u99p2/p0=0,4dRe-ZahlMidealMreal expMreal, numStd Dev.VarianceCd expCd, numDeviationa Annahmeb berechnetMit gemitteltem Cd-Wert berechneter MassenflussAbweichungStatusxminxmaxxmin/dxmax/ddelta mindelta maxZusatzinfodelta* mindelta* maxdelta** mindelta** maxshape H minshape H maxshape H meandelta*/ddelta**/dFrequenzFrequenzcharakteristikAeff/A0 minAeff/A0 maxDiff max-minAeff/A0 meanAbweichungcdAeff/AeffcdAbweichung Amin/cdFW1519742.2691380.000 1^-3 mgNANANANANA1NA1.392 1^-3 mgNANANANA0NA25328117.414 1^-3 mg78.589 1^-3 mg82.793 1^-3 mg0.7530 1^-3 mg0.0010 1^-3 mg0.6690.7055.35%15.34029326541.303 1^-3 mg1.57%premature unchoked-21.000 ^-3 mmNAN0.845.738 ^-3 mm6.592 ^-3 mm1.5130 ^-3 mm1.7450 ^-3 mm0.7010 ^-3 mm0.7730 ^-3 mm2.1592232.2570292.20812613.03%5.90%782 kHzregelmig0.730.780.050.7551.89%0.70517.1%3.53%35459230.132 1^-3 mg0.000 1^-3 mg168.940 1^-3 mg1.4540 1^-3 mg0.0020 1^-3 mg0.7340.00%15.69670655111.256 1^-3 mg0.74%premature unchoked25.500 ^-3 mm0.000.737.174 ^-3 mm7.647 ^-3 mm2.0980 ^-3 mm2.4100 ^-3 mm0.9380 ^-3 mm1.0170 ^-3 mm2.2364352.3690662.302750512.88%5.59%478 kHznahezu regelmig0.7580.7820.0240.770.92%0.73414.9%3.26%50656469.657 1^-3 mg0.000 1^-3 mg351.420 1^-3 mg0.0410 1^-3 mg0.0002 1^-3 mg0.7480.00%16.44801313481.215 1^-3 mg0.35%premature unchoked0.000.007.336 ^-3 mm7.920 ^-3 mm2.5800 ^-3 mm2.6300 ^-3 mm1.0300 ^-3 mm1.0800 ^-3 mm2.2977762.2564192.277097510.42%4.22%4553 kHzunregelmig aber serh geringe Schwankungen0.770.780.010.7750.39%0.74823.6%2.91%8010491202.322 1^-3 mg0.000 1^-3 mg920.661 1^-3 mg28.1660 1^-3 mg0.7930 1^-3 mg0.7660.00%17.5874282891.170 1^-3 mg0.13%premature unchoked-60.000 ^-3 mmNAN0.7510.000 ^-3 mm30.000 ^-3 mmwandernd von mitte nach auen3.3830 ^-3 mm6.0390 ^-3 mm1.5230 ^-3 mm2.4570 ^-3 mm2.2219532.457552.339751511.78%4.98%777 kHzgleichmig0.720.840.120.784.68%0.76571.9%-5.97%BW1519742.269 1^-3 mg0.000 1^-3 mg27.777 1^-3 mg0.1150 1^-3 mg0.0000 1^-3 mg0.6570.00%14.81202979221.392 1^-3 mg5.01%not critical--NANNAN4.836 ^-3 mm4.904 ^-3 mm1.2420 ^-3 mm1.3000 ^-3 mm0.5740 ^-3 mm0.5890 ^-3 mm2.1628192.1953782.179098516.95%7.75%1383 kHzregelmig0.690.70.010.6950.35%0.65725.8%5.00%25328117.414 1^-3 mg78.668 1^-3 mg82.968 1^-3 mg2.3300 1^-3 mg0.0050 1^-3 mg0.6700.7075.47%15.31326244761.303 1^-3 mg1.57%premature unchoked-21.500 ^-3 mmNAN0.865.150 ^-3 mm7.483 ^-3 mm1.2030 ^-3 mm1.8200 ^-3 mm0.5970 ^-3 mm0.8010 ^-3 mm2.0148552.2724442.143649512.09%5.59%877 kHzregelmig0.720.820.10.773.85%0.70669.0%1.89%35459230.132 1^-3 mg0.000 1^-3 mg169.882 1^-3 mg5.1060 1^-3 mg0.0260 1^-3 mg0.7380.00%15.60901045091.256 1^-3 mg0.74%premature unchoked-30.000 ^-3 mmNAN0.866.276 ^-3 mm10.356 ^-3 mm1.5090 ^-3 mm2.2640 ^-3 mm0.7340 ^-3 mm1.0000 ^-3 mm2.0575272.2632062.160366510.78%4.95%409 kHzsehr regelmig0.760.840.080.83.20%0.73828.4%2.95%50656469.657 1^-3 mg0.000 1^-3 mg372.185 1^-3 mg2.4830 1^-3 mg0.0060 1^-3 mg0.7920.00%15.31559728251.215 1^-3 mg0.33%unchoked-49.000 ^-3 mmNAN0.988.584 ^-3 mm8.711 ^-3 mm2.2450 ^-3 mm2.5870 ^-3 mm1.0290 ^-3 mm1.0880 ^-3 mm2.1813352.3786392.2799879.66%4.23%294 kHzregelmig0.80.820.020.810.81%0.79252.2%0.95%8010491202.322 1^-3 mg0.000 1^-3 mg984.677 1^-3 mg17.5250 1^-3 mg0.3070 1^-3 mg0.8190.00%15.86294605161.170 1^-3 mg0.12%unchoked--NANNAN10.331 ^-3 mm30.331 ^-3 mm2.5830 ^-3 mm4.3180 ^-3 mm1.2680 ^-3 mm1.8160 ^-3 mm2.0370992.377022.20705958.63%3.86%900 kHzsehr regelmig0.80.880.080.843.36%0.81902.6%-2.32%0.00%FW drilled25328117.414 1^-3 mg0.000 1^-3 mg81.290 1^-3 mg1.0850 1^-3 mg0.0010 1^-3 mg0.6920.00%15.57205178711.303 1^-3 mg1.60%short time choked0.000.006.199 ^-3 mm6.420 ^-3 mm1.8940 ^-3 mm2.0010 ^-3 mm0.8250 ^-3 mm0.8350 ^-3 mm2.2676192.39640718562.332013092815.58%6.64%390 kHzsehr unregelmig0.70.750.050.7251.81%0.69234.7%1.11%BW drilled25328117.414 1^-3 mg0.000 1^-3 mg75.461 1^-3 mg9.6390 1^-3 mg0.0930 1^-3 mg0.6430.00%16.47108623211.303 1^-3 mg1.73%premature unchoked-16.000 ^-3 mmNAN0.645.114 ^-3 mm6.330 ^-3 mm1.5870 ^-3 mm2.7740 ^-3 mm0.6770 ^-3 mm0.7820 ^-3 mm2.312693.5477882.93023917.44%5.84%426 kHzregelmig0.6410.7720.1310.70654.63%0.64279.9%-0.26%0.00%0.0000p2/p0=0,3dRe-ZahlMidealMreal expMreal, numStd Dev.VarianceCd expCd, numDeviationa Annahmeb berechnetMit gemitteltem Cd-Wert berechneter MassenflussAbweichungStatusxminxmaxxmin/dxmax/ddelta mindelta maxZusatzinfodelta* mindelta* maxdelta** mindelta** maxshape H minshape H maxshape H meandelta*/ddelta**/dFrequenzFrequenzcharakteristikAeff/A0 minAeff/A0 maxDiff max-minCd, numFW1519742.269 1^-3 mg0.000 1^-3 mgNANANANANA1NA1.392 1^-3 mgNANANANA0.00%0.00%0NA25328117.414 1^-3 mg77.963 1^-3 mg83.536 1^-3 mg0.3530 1^-3 mg0.0000 1^-3 mg0.6640.7117.15%15.22562962321.303 1^-3 mg1.56%choked15.000 ^-3 mm18.000 ^-3 mm0.600.725.056 ^-3 mm5.479 ^-3 mm1.1860 ^-3 mm1.3590 ^-3 mm0.5910 ^-3 mm0.6570 ^-3 mm2.0055722.0667882.0361810.18%4.99%749 kHzregelmig0.760.820.060.792.37%0.711511.0%6.82%35459230.132 1^-3 mg0.000 1^-3 mg172.887 1^-3 mg0.4570 1^-3 mg0.0001 1^-3 mg0.7510.00%15.32927990681.256 1^-3 mg0.73%choked20.000 ^-3 mm28.000 ^-3 mm0.570.805.645 ^-3 mm5.834 ^-3 mm1.5400 ^-3 mm1.6230 ^-3 mm0.7370 ^-3 mm0.7630 ^-3 mm2.0889382.1123662.1006529.04%4.29%509 kHzregelmig0.780.830.050.8052.01%0.75137.2%3.83%50656469.657 1^-3 mg0.000 1^-3 mg364.025 1^-3 mg0.7620 1^-3 mg0.0011 1^-3 mg0.7750.00%15.76059953051.215 1^-3 mg0.33%choked20.000 ^-3 mm25.000 ^-3 mm0.400.507.525 ^-3 mm8.715 ^-3 mmvon mitte bis austritt stabiler anstieg1.9300 ^-3 mm2.6150 ^-3 mm0.9430 ^-3 mm1.1250 ^-3 mm2.0464472.323482.18496359.09%4.14%536 kHzunregelmig0.820.860.040.841.68%0.77518.4%5.79%8010491202.322 1^-3 mg0.000 1^-3 mg958.375 1^-3 mg1.7090 1^-3 mg0.0030 1^-3 mg0.7970.00%16.57147044851.170 1^-3 mg0.12%choked23.000 ^-3 mm25.000 ^-3 mm0.290.319.820 ^-3 mm10.638 ^-3 mmortsstabil maximum in mitte 302.5850 ^-3 mm3.2010 ^-3 mm1.2630 ^-3 mm1.4500 ^-3 mm2.0458062.2071212.12646357.23%3.39%715 kHzunregelmig0.850.870.020.860.86%0.79717.9%6.64%BW1519742.269 1^-3 mg0.000 1^-3 mg29.129 1^-3 mg0.0120 1^-3 mg0.0000 1^-3 mg0.6890.00%14.36330392771.392 1^-3 mg4.78%choked12.000 ^-3 mm12.000 ^-3 mm0.800.804.061 ^-3 mm4.298 ^-3 mm0.9980 ^-3 mm1.1370 ^-3 mm0.4800 ^-3 mm0.5120 ^-3 mm2.2772972.0791732.17823514.23%6.61%1310 kHzeinigermaen regelmig0.720.750.030.7351.10%0.68916.7%4.48%25328117.414 1^-3 mg79.372 1^-3 mg87.286 1^-3 mg0.3970 1^-3 mg0.0003 1^-3 mg0.6760.7439.97%14.64721540811.303 1^-3 mg1.49%choked18.000 ^-3 mm22.500 ^-3 mm0.720.904.296 ^-3 mm5.707 ^-3 mm1.0630 ^-3 mm1.4930 ^-3 mm0.5280 ^-3 mm0.6940 ^-3 mm2.0143692.1510612.08271510.22%4.89%807 kHzregelmig0.770.840.070.8052.82%0.74348.3%3.58%35459230.132 1^-3 mg0.000 1^-3 mg177.104 1^-3 mg2.8310 1^-3 mg0.0080 1^-3 mg0.7700.00%14.93669788751.256 1^-3 mg0.71%short time unchoked-25.000 ^-3 mmNAN0.715.543 ^-3 mm9.449 ^-3 mm1.1910 ^-3 mm2.2240 ^-3 mm0.6230 ^-3 mm1.0080 ^-3 mm1.9125412.2066592.05969.76%4.66%374 kHzregelmig0.760.870.110.8154.48%0.76965.9%-1.24%50656469.657 1^-3 mg0.000 1^-3 mg378.590 1^-3 mg1.8990 1^-3 mg0.0040 1^-3 mg0.8060.00%14.96630536071.215 1^-3 mg0.32%choked40.000 ^-3 mm48.000 ^-3 mm0.800.967.201 ^-3 mm10.519 ^-3 mm1.6460 ^-3 mm2.4020 ^-3 mm0.8400 ^-3 mm1.0880 ^-3 mm1.9595712.207862.08371558.10%3.86%282 kHzstreut, regelmig0.810.880.070.8452.96%0.80614.8%0.48%8010491202.322 1^-3 mg0.000 1^-3 mg1015.282 1^-3 mg1.6240 1^-3 mg0.0030 1^-3 mg0.8440.00%15.03850562751.170 1^-3 mg0.12%choked60.000 ^-3 mm70.000 ^-3 mm0.750.888.352 ^-3 mm19.933 ^-3 mm1.8340 ^-3 mm3.4960 ^-3 mm0.9530 ^-3 mm1.5990 ^-3 mm1.9242012.1859742.05508756.66%3.19%641 kHzsehr unregelmig0.830.910.080.873.48%0.84443.0%-1.71%FW drilled25328117.414 1^-3 mg0.000 1^-3 mg84.817 1^-3 mg0.5150 1^-3 mg0.0002 1^-3 mg0.7220.00%15.027986011.303 1^-3 mg1.54%choked17.500 ^-3 mm22.000 ^-3 mm0.700.885.171 ^-3 mm5.728 ^-3 mm1.2360 ^-3 mm1.5250 ^-3 mm0.6150 ^-3 mm0.7130 ^-3 mm2.0101922.1383192.074255511.04%5.31%459 kHzunregelmig0.750.820.070.7852.75%0.72248.7%3.82%BW drilled25328117.414 1^-3 mg0.000 1^-3 mg85.029 1^-3 mg0.4050 1^-3 mg0.0000 1^-3 mg0.7240.00%14.99531361720.00%choked17.500 ^-3 mm20.000 ^-3 mm0.700.805.006 ^-3 mm6.080 ^-3 mm1.3060 ^-3 mm1.7450 ^-3 mm0.6340 ^-3 mm0.7790 ^-3 mm2.0589722.2394942.14923312.20%5.65%460 kHzunregelmig0.740.760.020.750.75%0.72423.6%2.18%24Avg5.495033301574.42%25.58%Vergleich der Grenzschichtdicken fr die vorwrts und rckwrts Orientierungp2/p1=0,4dFW/BW150.00%0.00%0.00%0.00%0.00%0.00%0.00%0.00%0.00%0.00%2510.25%-13.52%0.00%20.49%-4.30%14.84%-3.62%6.69%-0.68%-12.15%3512.52%-35.43%0.00%28.07%6.06%21.75%1.67%8.00%4.47%14.44%50-17.01%-9.99%0.00%12.98%1.63%0.10%-0.74%5.07%-5.42%93.54%80-3.31%-1.10%0.00%23.65%28.50%16.74%26.09%8.32%3.28%-15.83%Drilled2517.50%1.40%0.00%16.21%-38.63%17.94%6.35%-1.99%-48.05%-9.23%p2/p1=0,3dFW/BW150.00%0.00%0.00%0.00%0.00%0.00%0.00%0.00%0.00%0.00%2515.03%-4.16%0.00%10.37%-9.86%10.66%-5.63%-0.44%-4.08%-7.74%351.81%-61.96%0.00%22.66%-37.03%15.47%-32.11%8.44%-4.46%26.52%504.31%-20.70%0.00%14.72%8.15%10.92%3.29%4.25%4.98%47.39%8014.95%-87.38%0.00%29.05%-9.22%24.54%-10.28%5.94%0.96%10.35%Drilled253.19%-6.15%0.00%-5.66%-14.43%-3.09%-9.26%-2.43%-4.73%-0.22%1/Re^0,5FW 0,4BW 0,4FW 0,3BW 0,30.0710.657 1^-3 mg0.68913 1^-3 mg0.0550.705 1^-3 mg0.707 1^-3 mg0.711 1^-3 mg0.74340 1^-3 mg0.0470.734 1^-3 mg0.738 1^-3 mg0.751 1^-3 mg0.76957 1^-3 mg0.0390.748 1^-3 mg0.792 1^-3 mg0.775 1^-3 mg0.80610 1^-3 mg0.0310.766 1^-3 mg0.819 1^-3 mg0.797 1^-3 mg0.84443 1^-3 mg

Ergebnisse_Duesen0.7550.6950.790.7350.0188750.0188750.0034750.0034750.0110250.0110250.02370.02370.770.770.8050.8050.009240.009240.03850.03850.0281750.0281750.0201250.0201250.7750.80.840.8150.0038750.0038750.0320.0320.0448250.0448250.01680.01680.780.810.860.8450.04680.04680.00810.00810.0295750.0295750.00860.00860.840.870.03360.03360.03480.0348

forward - p2/p0=0,4backward - p2/p0=0,4forward - p2/p0=0,3backward - p2/p0=0,3Throat diameter [m]Aeff/A*Effective Area Ratio vs. Throat Diameter

Tabelle30.7550.6950.790.7350.770.770.8050.8050.7750.80.840.8150.780.810.860.8450.840.87

forward - p2/p0=0,4backward - p2/p0=0,4forward - p2/p0=0,3backward - p2/p0=0,3Throat diameter [m]Aeff/A*Effective Area Ratio vs. Throat Diameter

00000000000000000000000

forward p2/p0=0,4backward p2/p0=0,4forward p2/p0=0,3backward p2/p0=0,3idealThroat Diameter [m]Flow Rate [g]Flow Rate vs. Throat Diameter

000000000000000000

forward p2/p0=0,4backward p2/p0=0,4forward p2/p0=0,3backward p2/p0=0,3Throat Diameter [m]Discharge CoefficientDischarge coefficient vs. Throat Diameter

00000000000000000000

FW 0,4BW 0,4FW 0,3BW 0,31/Re^0,5Discharge CoefficientDischarge Coefficient vs. 1/Re^0,5

Piston Proverd0.014Revolution0.0001A0.000153938Steps/s2000Volumenstrom0.2m=rho*V*Arho*0.763336a*313.159d0.00008Athroat0.000000005m0.0000012016

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