Comment calculer nombre de Dean De flux tube courbe

Calcule nombre de Dean De = Re*sqrt(d/(2R)) ratio inertie centrifuge viscosité flux tube courbe + Dean vortex. De<40 Poiseuille; 40-75 two vortex; 75-200 well-developed. Heat exchanger helical coils + microfluidique spiral. CEA + IFP Énergies + Mines Paris-PSL + TotalEnergies + Sanofi.

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Comment calculer le nombre de Dean (De) ratio adimensionnel fluidodynamique flux tubes courbes + helical coils + spiral microfluidique + bifurcations vasculaires: De = Re * sqrt(d / (2*R)). Re Reynolds; d m; R rayon courbure m. Classification: De<40 Poiseuille; 40-75 two vortex Dean; 75-200 well-developed enhanced HT 30-100%; 200-400 transition; 400-5000 turbulent. William Reginald Dean (UK 1896-1973) Cambridge Trinity College 1927-1928 Phil Mag papers classic. France recherche + universites: CEA Saclay 1945 16000 + LITEN Grenoble + DRT + ITER cooling helical; IFP Énergies Nouvelles Rueil-Malmaison Paris 1944 1700 oil + gas + heat exchanger helical; CNRS Paris 1939 32000 + INSIS; Mines Paris-PSL Paris 1783 1500 + CEMEF Sophia Antipolis + CEP; CentraleSupelec Gif Saclay 1829 4500 + LGPM; Polytechnique Palaiseau 1794 2900 + LadHyX Hydrodynamique + LMS + LULI; Telecom Paris 1878 1500; EURECOM Sophia Antipolis 1991 800; INSA Lyon 1957 5500 + LMFA + LAGEPP; 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 + GEPEA; Ecole Centrale Marseille 2006 + M2P2; Mines Saint-Etienne 1816 1900 + SPIN; ENSIC Nancy 1947 800 + LRGP. France industrie: TotalEnergies Paris La Defense 1924 105000 + Total Refining Chemicals 30000 5 raffinerie France Donges + Gonfreville + Feyzin + Grandpuits + La Mede + helical coil + cryogenic LNG; Air Liquide Paris 1902 67000 industrial gases + helium pure + cryogenic LNG + Engineering Hydrogen + medical Sante; Saint-Gobain Courbevoie 1665 170000 building materials + glass + ceramics; Arkema Colombes 2004 21000 specialty chemicals + Bostik adhesives + reactor helical; Solvay Brussels Belgium France subsidiary + BASF France + L'Oreal 87000; Sanofi Paris 1973 91000 + Pasteur Marcy + drug delivery helical; Servier Suresnes 1954 22000 cardiology + Procoralan ivabradine; Pierre Fabre Castres 1962 9000 dermatology drug delivery; BioMerieux Marcy l'Etoile Lyon 1963 13000 in-vitro diagnostics + Filmarray; LFB Les Ulis 1994 2400 plasma derivatives; Vygon Ecouen 1962 2400 medical disposable + cardiology helical; Schneider Electric Rueil-Malmaison Paris 1836 135000 energy; Veolia Aubervilliers Paris 1853 218000 water + waste + reactor;

Suez Paris 1858 90000; Engie Courbevoie Paris 1858 96000 utility + LNG + reactor helical; EDF Paris 1946 165000 utility + nuclear 56 reactors EPR + boilers + helical OTSG steam generator. France HVAC + boilers helical coil: Atlantic Group La Roche-sur-Yon 1968 5500 HVAC + heat exchanger + heat pumps + water heaters + boilers + radiators; De Dietrich Reichshoffen 1684 1000 HVAC + heat exchanger + boilers + condensing helical; Saunier Duval Pantin 1907 1100 HVAC + boilers + heat pumps Vaillant Group; Vaillant France Bois-le-Roi Paris subsidiary German parent HVAC + heat pumps; Frisquet Paris 1936 600 HVAC + boilers high-end. France automotive: Renault Boulogne-Billancourt 100000 + Stellantis 280000 + Bugatti Molsheim Alsace 1909 1000 + Alpine Renault 350 + Faurecia Forvia 110000 + Plastic Omnium. France hopitaux Dean vortex hemodynamics: AP-HP Assistance Publique Hopitaux Paris 1849 100000 39 hopitaux + Pitie-Salpetriere Paris 1656 + Necker-Enfants Malades 1778 + Hopital Bichat 1882 + Hopital Lariboisiere 1854 cardiology emergency + Hopital Henri Mondor Creteil 1969 cardiology + Hopital Beaujon Clichy + Hopital Bicetre 1633 + Avicenne Bobigny + Antoine Beclere Clamart + Charles Foix Ivry; HCL Hospices Civils Lyon 1802 22000 + Hopital Edouard Herriot + Hopital Cardiologique Louis Pradel + Hopital Femme Mere Enfant;

AP-HM Marseille 1801 14000 + Timone + Conception + Nord; CHU Bordeaux 1905 14000 + Pellegrin + Saint-Andre + Haut-Leveque cardiology; CHU Toulouse 1858 11000 + Purpan + Rangueil cardiologie; CHU Lille 14000 + Hopital Cardiologique CHU Lille; CHU Strasbourg + Nancy + Nantes + Rennes + Montpellier + Nice + Brest + Rouen + Tours. France microfluidique: CEA + Mines Paris-PSL CEMEF + ENSIC Nancy LRGP + Pasteur 2700; BioMerieux Marcy Lyon 13000 + Filmarray respiratory; Vygon Ecouen 2400. France solar thermal CSP helical absorber: CEA + EDF + Engie + ADEME Agence Environnement Maitrise Énergie + Heliogen project France collaboration. France farmaceutico Dean vortex helical: Sanofi 91000 + Servier 22000 + Pierre Fabre 9000 + Pfizer France + Boehringer Ingelheim France + Bayer France + LFB Les Ulis 2400.

Formule Dean

De = Re*sqrt(d/(2R)).

Histoire et contexte

Dean Cambridge 1927-1928 + White 1929 + Schmidt 1967 + Berger-Talbot-Yao 1983. France CEA Saclay 16000 + LITEN Grenoble + ITER cooling; 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 LAGEPP; INSA Toulouse 5000 IMFT; Sorbonne 50000 Alembert; Paris-Saclay 35000; IMT Atlantique 800; Centrale Lyon 2000 LMFA; Centrale Nantes 1700 LHEEA GEPEA; Centrale Marseille M2P2; Mines Saint-Etienne 1900 SPIN; ENSIC Nancy 800 LRGP. Industrie: TotalEnergies 105000 + Refining 30000 5 raffinerie + helical + cryogenic LNG; Air Liquide 67000 + helium pure + cryogenic LNG + Engineering Hydrogen + medical Sante; Saint-Gobain 170000; Arkema 21000 + Bostik; Solvay + BASF France + L'Oreal 87000; Sanofi 91000 + Pasteur Marcy + drug delivery; Servier 22000 + Procoralan ivabradine; Pierre Fabre 9000; BioMerieux Marcy Lyon 13000 + Filmarray; LFB Les Ulis 2400 plasma; Vygon Ecouen 2400; Schneider Electric 135000; Veolia 218000 + Suez 90000 + Engie 96000 LNG + reactor helical; EDF 165000 + nuclear 56 EPR + boilers + helical OTSG. HVAC: Atlantic 5500 + De Dietrich 1000 + Saunier Duval 1100 + Vaillant France + Frisquet 600. Automotive: Renault 100000 + Stellantis 280000 + Bugatti Molsheim 1000 + Alpine 350 + Faurecia Forvia 110000.

Hopitaux: AP-HP 100000 39 hopitaux + Pitie-Salpetriere 1656 + Necker 1778 + Bichat + Lariboisiere + Henri Mondor + Bicetre 1633 + Avicenne + Antoine Beclere + Charles Foix; HCL Lyon 22000 + Louis Pradel cardiologique; AP-HM Marseille 14000 + Timone; CHU Bordeaux 14000 + Haut-Leveque; CHU Toulouse 11000 + Rangueil; CHU Lille 14000; CHU Strasbourg Nancy Nantes Rennes Montpellier Nice Brest Rouen Tours. Microfluidique: CEA + Mines Paris-PSL CEMEF + ENSIC Nancy LRGP + Pasteur; BioMerieux Marcy 13000 + Vygon Ecouen 2400. Solar CSP: CEA + EDF + Engie + ADEME. Farmaceutico: Sanofi + Servier + Pierre Fabre + LFB.

Tableau Dean

  • De = Re*sqrt(d/(2R))
  • De<40 Poiseuille
  • 75-200 well-developed +30-100% HT
  • Dean Cambridge 1927-1928
  • France CEA Saclay 1945: 16000 + ITER cooling
  • France IFP Énergies 1944: 1700
  • France Mines Paris-PSL 1783: 1500 CEP CEMEF
  • France ENSIC Nancy: 800 LRGP
  • France TotalEnergies 1924: 105000 5 raffinerie helical
  • France Air Liquide 1902: 67000 He cryogenic Engineering H2
  • France EDF 1946: 165000 nuclear 56 EPR boilers helical OTSG
  • France Sanofi 91000: drug delivery
  • France BioMerieux 1963: 13000 IVD Filmarray
  • France Atlantic 5500: HVAC heat pumps
  • France Vygon Ecouen 2400: medical helical
  • France AP-HP Paris: 100000 39 hopitaux Pitie-Salpetriere

Exemples numériques

Exemple 1 - Helical coil lab. De=316. France: TotalEnergies + IFP Énergies + Mines Paris-PSL CEP.

Exemple 2 - Aorta arch. De=1500. France: AP-HP Pitie-Salpetriere + HCL Lyon Louis Pradel + AP-HM Timone Marseille + CHU Bordeaux Haut-Leveque.

Exemple 3 - Microfluidique spiral. De=11.2. France: CEA + Pasteur + BioMerieux Marcy Lyon 13000.

Exemple 4 - Heat exchanger industrial. De=1443. France: TotalEnergies 5 raffinerie + Air Liquide cryogenic LNG.

Exemple 5 - Solar thermal helical. De=54.8. France: CEA + EDF + Engie + ADEME.

Limites

  1. Curvature ratio d/(2R)<1.
  2. Steady-state.
  3. Constant cross-section.
  4. Newtonien.
  5. Schmidt 1967.
  6. Pressure drop Mishra-Gupta.
  7. Critical Re curved.
  8. Helical pitch.
  9. CFD numérique.
  10. Microfluidique Dean sorting.

Erreurs communes

Curvature ratio d/(2R) vs d/R.

Re définition diamètre.

Critical Re curved vs straight.

Heat transfer Schmidt range.

Dean vortex régimes.

Applications

  1. Helical coil heat exchanger industriel: France TotalEnergies 105000 5 raffinerie + Air Liquide 67000 + Saint-Gobain 170000 + Arkema 21000 + Vallourec.
  2. Nuclear OTSG helical steam generators: EDF 165000 nuclear 56 EPR + Areva Framatome + Hinkley UK.
  3. Cardiovascular hemodynamics aortic arch: AP-HP Paris 100000 + Pitie-Salpetriere 1656 + HCL Lyon Louis Pradel cardiologique + AP-HM Timone + CHU Bordeaux Haut-Leveque + CHU Toulouse Rangueil.
  4. Microfluidic Dean cell sorting: CEA Saclay LITEN + Pasteur 2700 + BioMerieux Marcy Lyon 13000 + Vygon Ecouen 2400 + Mines Paris-PSL CEMEF.
  5. HVAC helical coil: Atlantic 5500 + De Dietrich 1000 + Saunier Duval 1100 + Vaillant France + Frisquet 600.
  6. Solar thermal CSP helical: CEA + EDF + Engie + ADEME + Heliogen France collaboration.
  7. Cryogenic LNG spiral wound: TotalEnergies + Air Liquide + Engie LNG.
  8. Automotive cooling EV thermal: Renault 100000 + Stellantis 280000 + Bugatti Molsheim + Alpine + Faurecia Forvia 110000.
  9. Drug delivery helical: Sanofi 91000 + Servier 22000 + Pierre Fabre 9000 + LFB Les Ulis 2400 + Vygon Ecouen 2400.
  10. Universites recherche: Mines Paris-PSL 1500 + CentraleSupelec 4500 LGPM + 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 Dean?

De = Re * sqrt(d / (2*R)) ratio adimensionnel fluidodynamique flux tubes courbes + helical coils + spiral microfluidique + bifurcations vasculaires. Re Reynolds; d diamètre; R rayon courbure. De<40 Poiseuille; 40-75 two vortex Dean; 75-200 well-developed heat transfer +30-100%; 200-400 transition; 400-5000 turbulent. William Reginald Dean Cambridge UK 1927-1928. France: CEA Saclay 16000 + Mines Paris-PSL 1500 + ENSIC Nancy 800 LRGP + TotalEnergies 105000 + EDF 165000 nuclear 56 EPR helical OTSG.

Comment calculer Dean?

Procedure: (1) De = Re * sqrt(d/(2R)); (2) Re Reynolds; (3) d diamètre tube m; (4) R rayon courbure centerline m; (5) curvature ratio d/(2R) <1. Exemple helical coil Re=1000 + d=0.01 + R=0.05: De=316 transition four vortex pairs unstable. France: TotalEnergies Refining 30000 5 raffinerie + IFP Énergies 1700 + Air Liquide 67000 cryogenic LNG.

Qu est-ce que Dean vortex?

Dean vortex: deux paires symetriques counter-rotating helical motion in cross-section tube courbe. Causees par forces centrifuges desequilibre fluide rapide noyau interne + lent paroi externe. Velocite secondary u_s/u_max ~ 0.05-0.2 De increasing. France: research Polytechnique LadHyX + INSA Lyon LMFA + Mines Paris-PSL CEMEF microfluidique.

Quels régimes classe De?

De<40 stable Poiseuille: tube droit-like; 40-75 two vortex Dean: weak secondary; 75-200 well-developed: complete Dean vortices + heat transfer +30-100% Schmidt 1967; 200-400 transition; 400-5000 turbulent. France: industrie TotalEnergies + Air Liquide + Saint-Gobain + EDF nuclear OTSG + Atlantic HVAC.

Qui etait William Reginald Dean?

William Reginald Dean (UK Sheffield 1896 - Wells 1973) Cambridge University Trinity College mathematicien anglais applied mathematics + fluid dynamics + plasticity + elasticity; 1927 Phil Mag 4:208 + 1928 Phil Mag 5:673 classique two-paper analysis Stokes équations curved pipe + secondary flow vortex; pioneer fluid dynamics Cambridge Mathematics tradition. France: research CEA + Mines Paris-PSL + Polytechnique LadHyX + INSA Lyon LMFA.

Qu est-ce que Re critique tube courbe?

Re_c curved = 2100 * (1 + 12*sqrt(d/(2R))) > Re_c = 2100 tube droit. Curved pipe transition turbulent retardee parce que Dean vortices stabilisent laminar flow. Exemple d/(2R)=0.1 Re_c=10000; d/(2R)=0.05 Re_c=7740. France: research Polytechnique LadHyX + INSA Lyon LMFA + ENSIC Nancy LRGP + TotalEnergies.

Applications du De?

Applications: helical coil heat exchanger industriel France TotalEnergies 105000 5 raffinerie + Air Liquide 67000 + Saint-Gobain 170000; nuclear OTSG EDF 165000 nuclear 56 EPR + Areva Framatome; cardiovascular hemodynamics AP-HP Pitie-Salpetriere 1656 + HCL Lyon Louis Pradel + AP-HM Timone; microfluidique Dean sorting CEA + Pasteur 2700 + BioMerieux Marcy Lyon 13000 + Vygon Ecouen; HVAC helical Atlantic 5500 + De Dietrich + Saunier Duval; drug delivery Sanofi 91000 + Servier 22000 + Pierre Fabre 9000.

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