Comment calculer nombre de Taylor Ta flux Couette rotatif

Calcule nombre de Taylor Ta = omega^2*r_in*d^3/nu^2 ratio centrifugal visqueux flux Couette rotatif + Taylor vortex toroidal. Ta_c=1708 critique; 1708-1e4 Taylor; >1e6 turbulent. Roulements + centrifugeuses + bioreacteurs. CEA + IFP Énergies + Mines Paris-PSL + Sanofi.

Paramètres de calcul
Ce calculateur vous a-t-il été utile ?

Comment calculer le nombre de Taylor (Ta) ratio adimensionnel flux Couette rotatif cylindres concentriques centrifuge/visqueux: Ta = (omega^2 * r_in * d^3) / nu^2.

Ta_c=1707.76 critique.

Classification: Ta1e6 featureless.

Sir Geoffrey Ingram Taylor (UK 1886-1975) Cambridge Trinity College 1923 + Manhattan Project Los Alamos 1944.

France recherche + universites: CEA Saclay 1945 16000 + LITEN Grenoble + DRT; IFP Énergies Nouvelles Rueil-Malmaison Paris 1944 1700; CNRS Paris 1939 32000 + INSIS; Mines Paris-PSL Paris 1783 1500 + CEMEF + CEP Sophia; CentraleSupelec Gif Saclay 1829 4500 + LGPM; Polytechnique Palaiseau 1794 2900 + LadHyX + LMS + LULI; Telecom Paris 1878 1500; EURECOM Sophia 1991 800; INSA Lyon 1957 5500 + LMFA; INSA Toulouse 1963 5000 + IMFT; Sorbonne Universite Paris 1257 50000 + Alembert; Universite Paris-Saclay 2020 35000; Telecom Bretagne IMT Atlantique Brest 1977 800; Ecole Centrale Lyon 1857 2000 + LMFA; Ecole Centrale Nantes 1919 1700 + LHEEA; Ecole Centrale Marseille 2006 + M2P2; Mines Saint-Etienne 1816 1900 + SPIN; ENSIC Nancy 1947 800 + LRGP; Mines Albi-Carmaux 1993 + RAPSODEE. France industria bearings: SKF France subsidiary Swedish parent + bearings; FAG Schaeffler France Calais subsidiary German parent; NSK France subsidiary; NTN France Annecy subsidiary Japanese; Timken France subsidiary US. France industria centrifuge + olive oil + biotech: Alfa Laval France Nevers Bourgogne subsidiary Swedish + decanter centrifuges; GEA Group France subsidiary German + centrifugal separators + dairy + brewery; Westfalia France subsidiary GEA; Andritz France subsidiary Austrian decanter; FIMA + Mori-Tem subsidiary Italia; Pieralisi France subsidiary Italian + olive oil decanter; Eppendorf France subsidiary German laboratory centrifuges;

Beckman Coulter France subsidiary US analytical ultracentrifuges; Thermo Fisher France subsidiary US. France industria bioreactor + pharma: Sanofi Paris 1973 91000 + drug delivery + bioreactor; Servier Suresnes 1954 22000 cardiology + bioreactor; Pierre Fabre Castres 1962 9000 dermatology + bioreactor; BioMerieux Marcy l'Etoile Lyon 1963 13000 IVD + bioreactor; LFB Les Ulis 1994 2400 plasma derivatives + bioreactor; Stallergenes 1500 allergy. France industria chemical reactor petrochimie rotating: TotalEnergies Paris La Defense 1924 105000 + Total Refining Chemicals 30000 5 raffinerie France Donges Gonfreville Feyzin Grandpuits La Mede + Renewable Energy + Hydrogen; Air Liquide Paris 1902 67000 industrial gases + helium pure + Engineering Hydrogen + cryogenic LNG; Saint-Gobain Courbevoie 1665 170000 + ceramics; Arkema Colombes 2004 21000 specialty chemicals + Bostik adhesives; Solvay Brussels Belgium France subsidiary; BASF France Levallois-Perret; L'Oreal Clichy Paris 1909 87000 cosmetics; EDF Paris 1946 165000 nuclear 56 reactors EPR + boilers; Engie Courbevoie Paris 1858 96000 utility + LNG; Veolia Aubervilliers 1853 218000 water + waste + reactor; Suez Paris 1858 90000; Schneider Electric Rueil-Malmaison Paris 135000 energy + automation.

France automotive engines bearings: Renault Boulogne-Billancourt 100000 + Stellantis 280000 worldwide ex-PSA ex-FCA + Bugatti Molsheim Alsace 1909 1000 + Alpine Renault 350 + Faurecia Forvia 110000 + Plastic Omnium + Safran Paris Saint-Cloud 80000 + CFM56 LEAP-1A LEAP-1B + Dassault Aviation Saint-Cloud 12000 Rafale; Liebherr Aerospace Toulouse aircraft systems; Airbus Defence Space France Toulouse 35000 satelliti. France astrofisica + accretion disk: Observatoire Paris-Meudon 1667 200; CNRS LERMA + IRAM Grenoble 30 m + NOEMA Plateau de Bure 12 antennes; Nancay 200 m radioheliograph; CEA AIM Saclay; CNES Toulouse 2400 + Solar Orbiter ESA + Parker Solar Probe NASA contribution. France geomagnetic: BCMT Bureau Central Magnetisme Terrestre Saint-Maur-des-Fosses Paris 1883 + Chambon-la-Foret + Antarctica + INTERMAGNET network; CNRS LPP Laboratoire Physique Plasmas Palaiseau 200; IPGP Institut Physique Globe Paris 1921 350 geomagnetic + Mahgreb partner.

Formule Taylor

Ta=(omega^2*r_in*d^3)/nu^2. Ta_c=1707.76.

Histoire et contexte

Sir G.I. Taylor Cambridge 1923. France CEA Saclay 16000 + LITEN Grenoble; IFP Énergies 1700; CNRS 32000 INSIS; Mines Paris-PSL 1500 + CEMEF; CentraleSupelec 4500 LGPM; Polytechnique 2900 + LadHyX + LMS + LULI; Telecom Paris 1500; EURECOM 800; INSA Lyon 5500 LMFA; INSA Toulouse 5000 IMFT; Sorbonne 50000 + Alembert; Paris-Saclay 35000; Centrale Lyon 2000 LMFA; Centrale Nantes 1700 LHEEA; Centrale Marseille; Mines Saint-Etienne 1900 SPIN; ENSIC Nancy 800 LRGP. Industria bearings: SKF + FAG Schaeffler Calais + NSK + NTN Annecy + Timken. Centrifughe: Alfa Laval Nevers + GEA + Westfalia + Andritz + Pieralisi subsidiary + Eppendorf + Beckman + Thermo Fisher. Pharma: Sanofi 91000 + Servier 22000 + Pierre Fabre 9000 + BioMerieux Marcy 13000 + LFB Les Ulis 2400. Chemical: TotalEnergies 105000 + Refining 30000 5 raffinerie + Air Liquide 67000 + Saint-Gobain 170000 + Arkema 21000 + L'Oreal 87000 + EDF 165000 + Engie 96000 + Veolia 218000 + Suez 90000 + Schneider 135000. Automotive: Renault 100000 + Stellantis 280000 + Bugatti Molsheim 1000 + Alpine 350 + Faurecia Forvia 110000 + Safran 80000 CFM56 LEAP + Dassault 12000 Rafale + Airbus DS Toulouse 35000. Astrofisica: Observatoire Paris-Meudon 1667 200 + Nancay 200 m + IRAM 30 m + NOEMA + CEA AIM Saclay + CNES Toulouse 2400. Geomagnetic: BCMT Saint-Maur 1883 + Chambon-la-Foret + Antarctica + INTERMAGNET; CNRS LPP Palaiseau 200; IPGP Paris 1921 350.

Tableau Taylor

  • Ta=(omega^2*r_in*d^3)/nu^2
  • Ta_c=1707.76
  • Ta<1708 stable Couette
  • 1708-1e4 Taylor vortex
  • >1e6 turbulent featureless
  • Taylor 1923 Phil Trans Roy Soc 223:289
  • France CEA Saclay 1945: 16000
  • France IFP Énergies 1944: 1700
  • France Mines Paris-PSL 1783: 1500 CEP Sophia
  • France SKF + FAG Calais + NSK + NTN Annecy + Timken: bearings
  • France Alfa Laval Nevers + GEA + Pieralisi: centrifuges
  • France Sanofi 1973: 91000 bioreactor
  • France BioMerieux 1963: 13000 IVD bioreactor
  • France TotalEnergies 1924: 105000 5 raffinerie
  • France EDF 1946: 165000 nuclear 56 EPR
  • France Renault 100000: + Stellantis 280000
  • France Safran 80000: CFM56 LEAP
  • France Observatoire Paris-Meudon 1667: 200 oldest
  • France Nancay 1956: 200 m radioheliograph
  • France BCMT 1883: magnetic obs Saint-Maur

Exemples numériques

Exemple 1 - Lab classic. Ta=1.25e6. France: Polytechnique LadHyX + INSA Lyon LMFA research.

Exemple 2 - Roulement huile. Ta=868. France: SKF + FAG Schaeffler Calais + NSK + NTN Annecy bearings.

Exemple 3 - Bioreacteur. Ta=625. France: Sanofi + Servier + Pierre Fabre + BioMerieux Marcy + LFB Les Ulis.

Exemple 4 - Centrifugeuse industrielle. Ta=1.125e9. France: Alfa Laval Nevers + GEA + Westfalia + Andritz + Pieralisi subsidiary olive oil decanter + Eppendorf + Beckman + Thermo Fisher.

Exemple 5 - Low Re demo. Ta=3125. France: Polytechnique LadHyX + Mines Paris-PSL CEP + INSA Lyon LMFA research.

Limites

  1. Inner cylinder rotation only.
  2. Small gap d/r_in.
  3. Newtonien.
  4. Aspect ratio L/d.
  5. Wavy modulated turbulent Andereck.
  6. Ekman pumping.
  7. Magnetique MRI Balbus-Hawley.
  8. Stratification.
  9. Compressibilite Mach.
  10. CFD numérique.

Erreurs communes

Ta définition variants.

r_in vs r_avg.

Critical Ta_c inner only.

Couette azimuthal vs plane.

Wavy régime visualization.

Applications

  1. Roulements rotating: France SKF + FAG Schaeffler Calais + NSK + NTN Annecy + Timken.
  2. Centrifugeuses industrielles: Alfa Laval Nevers + GEA + Westfalia + Andritz + Pieralisi subsidiary olive oil decanter + Eppendorf France + Beckman France + Thermo Fisher France.
  3. Bioreacteur biopharma: Sanofi 91000 + Servier 22000 + Pierre Fabre 9000 + BioMerieux Marcy 13000 + LFB Les Ulis 2400 + Stallergenes 1500.
  4. Reactor petrochimie: TotalEnergies 105000 + 5 raffinerie + Air Liquide 67000 + Saint-Gobain 170000 + Arkema 21000 + L'Oreal 87000.
  5. Astrofisica MRI: Observatoire Paris-Meudon 1667 200 + Nancay 200 m radioheliograph + IRAM 30 m + NOEMA Plateau Bure 12 antennes + CEA AIM Saclay.
  6. Plasma fusion dynamo: CEA IRFM Cadarache + ITER 1500 + WEST tokamak.
  7. Earth dynamo: BCMT Saint-Maur 1883 + Chambon-la-Foret + Antarctica + INTERMAGNET + IPGP Paris 350.
  8. Automotive engines bearings: Renault 100000 + Stellantis 280000 + Bugatti Molsheim 1000 + Alpine + Faurecia Forvia 110000 + Safran 80000 + Dassault 12000 Rafale + Airbus DS Toulouse 35000.
  9. HVAC scroll compressor: Atlantic 5500 + De Dietrich 1000 + Saunier Duval 1100 + Vaillant + Frisquet 600.
  10. Universites recherche: Mines Paris-PSL 1500 + CentraleSupelec 4500 + Polytechnique 2900 LadHyX + INSA Lyon 5500 LMFA + INSA Toulouse 5000 IMFT + Centrale Lyon Nantes Marseille + Mines Saint-Etienne SPIN + ENSIC LRGP.

Mis à jour en juillet 2026

Questions fréquentes

Qu est-ce que le nombre de Taylor?

Ta = (omega^2 * r_in * d^3) / nu^2 ratio adimensionnel flux Couette rotatif cylindres concentriques centrifuge/visqueux. omega rad/s; r_in m; d gap; nu m^2/s. Ta_c=1708 critique onset Taylor vortex; 1708-1e4 Taylor toroidal; >1e6 turbulent featureless. Sir Geoffrey Ingram Taylor Cambridge UK 1923. France: CEA Saclay 16000 + IFP Énergies 1700 + Mines Paris-PSL 1500 + Polytechnique LadHyX + SKF France + Sanofi 91000.

Comment calculer Taylor?

Procedure: (1) Ta = (omega^2 * r_in * d^3) / nu^2; (2) omega rad/s = 2*pi*RPM/60; (3) r_in intérieur m; (4) d=r_out-r_in m; (5) nu m^2/s. Exemple roulement omega=500 + r_in=0.025 + d=5e-5 + huile nu=3e-5: Ta=868 stable Couette. France: SKF + FAG Schaeffler Calais + NSK + NTN Annecy bearings + Pieralisi subsidiary olive oil decanter.

Quels régimes classe Ta?

Ta<1708 stable Couette: laminaire; 1708-1e4 Taylor vortex: toroidal stationnaire; 1e4-1.6e4 wavy: ondes traveling; 1.6e4-1e5 modulated: quasi-periodique; 1e5-1e6 turbulent Taylor; Ta>1e6 featureless turbulence. France: recherche Polytechnique LadHyX + Mines Paris-PSL CEP + INSA Lyon LMFA + Centrale Lyon LMFA + Centrale Nantes LHEEA.

Qu est-ce que Critical Taylor?

Ta_c = 1707.76 précision linear stability theory G.I. Taylor 1923 Phil Trans Roy Soc 223:289 Cambridge classique + onset premier Taylor vortex pair counter-rotating axisymetrique. Verification experimentale Taylor 1923 + Coles 1965 + Andereck-Liu-Swinney 1986 PRL. Pionnier première fois agreement théorie-expérience + naissance moderne fluid stability theory. France: recherche CEA + Polytechnique + Mines Paris-PSL + INSA Lyon.

Qui etait Sir Geoffrey Taylor?

Sir Geoffrey Ingram Taylor (UK Londres 1886 - Cambridge 1975) Trinity College Cambridge fellow 1910-1975 + Cavendish Lab mathematicien physicien anglais pionnier fluid dynamics + meteorology + plasticity + atomic energy + Manhattan Project Los Alamos 1944 + Trinity test 1945; 1923 Phil Trans Roy Soc A 223:289 classique linear stability + Taylor vortices + Ta_c=1707.76 + first agreement théorie-expérience + naissance moderne fluid stability theory. France: recherche CEA + Polytechnique + Mines Paris-PSL.

Difference Ta vs Re rotating?

Re_rotating = omega*r_in*d/nu Reynolds rotating Couette; Ta = (omega^2*r_in*d^3)/nu^2 Taylor centrifuge/visqueux. Relation Ta = Re^2 * (d/r_in) pour gap petit d<<r_in. Re_critique Couette 1708 (gap petit Re_c = sqrt(Ta_c * r_in/d) ~ 130 r_in/d=10). France: recherche Polytechnique LadHyX + INSA Lyon LMFA + Centrale Lyon LMFA + Mines Paris-PSL CEP.

Applications du Ta?

Applications: roulements rotating France SKF + FAG Schaeffler Calais + NSK + NTN Annecy + Timken; centrifugeuses industrielles Alfa Laval Nevers + GEA + Westfalia + Andritz + Pieralisi subsidiary olive oil decanter + Eppendorf France + Beckman France + Thermo Fisher; bioreacteur Sanofi 91000 + Servier 22000 + Pierre Fabre 9000 + BioMerieux Marcy 13000 + LFB Les Ulis 2400; reactor TotalEnergies 105000 + Air Liquide 67000 + Saint-Gobain 170000 + Arkema 21000; astrofisica Observatoire Paris-Meudon 1667 + Nancay 200 m + IRAM 30 m + NOEMA + CEA AIM Saclay.

Commentaires (0)

Pas encore de commentaire. Soyez le premier !