Comment calculer nombre de Bejan Be perte charge adimensionnelle

Calcule nombre de Bejan Be = dP*L^2/(mu*alpha) perte charge adimensionnelle convection forcee. Be<<1 visqueux lent; Be>>1 turbomachinery jet. Adrian Bejan Romania-USA Duke 1948 + constructal theory 1996 + EGM. CEA + EDF + Sanofi + Total + Atlantic + IFPEN applications.

Paramètres de calcul
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Nombre de Bejan Be perte charge adimensionnelle convection forcee Bhattacharjee-Grosshandler 1988 + Adrian Bejan: Be = dP*L^2/(mu*alpha).

Alternative entropy: Paoletti-Rispoli-Sciubba Sapienza Roma 1989.

Regimes: Be<1e6; 1e6-1e9 HVAC; Be>1e12 turbomachinery.

Constructal theory Bejan 1996.

EGM. Histoire: Adrian Bejan (Galati Romania 1948 - Duke USA) MIT 1971-1975 + Berkeley + Colorado + Duke 1984-2014; 1982 'Entropy Gen' Wiley + 1995 'Convection HT' + 1996 constructal Int J HMT 40:799. Bhattacharjee-Grosshandler 1988. Paoletti-Rispoli-Sciubba Sapienza 1989.

France recherche Bejan: CEA Saclay + Cadarache + Grenoble + Marcoule 16000; CNRS 11000 + LIMSI + LEMTA + 1100 laboratoires; Mines Paris PSL CES Sophia 2000; IFPEN Rueil-Malmaison 1700 + EGM optimization + heat exchangers; EDF R&D Saclay 158000 + Code Saturne; IRSN 1740; ONERA Palaiseau 2200; ANDRA 660.

France universites: Sorbonne Paris 55000 LIMSI; PSL 17000 ENS ESPCI Mines; X Polytechnique 3500 LadHyX; Centrale Supelec 7000 EM2C; INSA Lyon 6000 LMFA + CETHIL; Centrale Lyon 1700; Toulouse III 35000 IMFT; Aix-Marseille 80000 IRPHE; UGA Grenoble 60000 LEGI + LITEN; ENSAM 6000; Bordeaux 50000 I2M Sebastian Perre.

France industrie HVAC: Daikin France 600; Mitsubishi 400; Carrier 300; Atlantic Group La Roche-sur-Yon 9000; Saunier Duval Vaillant 500; De Dietrich Mertzwiller 1500; Frisquet 200; Chappee Saint-Gobain 1500; Viessmann 600; Bosch Thermo 800.

France industrie petrochimica: Total Énergies 102000 + raffinerie Donges Gonfreville Lavera + heat exchangers; Petroineos 1500; Esso France 1500; BP France 800; Veolia 220000; Suez 90000; Air Liquide 67000.

France industrie turbomachinery + jet engines + pumps: Safran Group Paris 92000 + jet engines LEAP CFM + Rafale + A320neo; Airbus Toulouse 134000; Dassault Saint-Cloud 12000 Rafale Falcon; Thales 81000; ArianeGroup 9000; MBDA 11000; Snecma Safran; Turbomeca Safran; SDMS Saint-Romain-de-Jalionas 200; KSB France 600; Wilo France 200; Grundfos France 300; Pompes Salmson France 200.

France microchannel + microelettronica: STMicroelectronics Crolles 6500; Soitec Bernin 2200; X-FAB Corbeil-Essonnes 700; Schneider Electric 135000; HP France 1500.

France cogeneracion EGM: EDF 158000; Engie 100000; Total Énergies 102000; Veolia 220000; Suez 90000.

Formule Bejan

Définition: Be = dP*L^2/(mu*alpha).

Histoire

Adrian Bejan (Galati Romania 1948 - Duke USA) MIT 1971-1975 + Berkeley + Colorado + Duke 1984-2014 + 30 doctorates + 1982 'Entropy Gen' Wiley + 1995 'Convection HT' + 1996 constructal + ASME Award 1994. Bhattacharjee-Grosshandler 1988. Paoletti-Rispoli-Sciubba Sapienza 1989.

France recherche: CEA 16000; CNRS 11000 LIMSI LEMTA; Mines Paris PSL 2000; IFPEN 1700 EGM heat exchangers; EDF R&D 158000; IRSN 1740; ONERA 2200; ANDRA 660.

France universites: Sorbonne 55000 LIMSI; PSL 17000; X 3500 LadHyX; Centrale Supelec 7000; INSA Lyon 6000 LMFA CETHIL; Centrale Lyon 1700; Toulouse III 35000 IMFT; Aix-Marseille 80000 IRPHE; UGA Grenoble 60000 LEGI LITEN; ENSAM 6000; Bordeaux 50000 I2M.

France HVAC: Daikin 600; Atlantic 9000; De Dietrich 1500; Saunier Duval 500; Frisquet 200; Chappee 1500; Viessmann 600; Bosch Thermo 800.

France petrochimica: Total Énergies 102000; Petroineos 1500; Esso France 1500; BP 800; Veolia 220000; Suez 90000; Air Liquide 67000.

France turbomachinery: Safran 92000 LEAP CFM Rafale; Airbus Toulouse 134000; Dassault 12000 Rafale Falcon; Thales 81000; ArianeGroup 9000; MBDA 11000; SDMS 200.

France pumps: KSB France 600; Wilo France 200; Grundfos France 300; Salmson 200.

France microchannel: STM Crolles 6500; Soitec Bernin 2200; X-FAB 700; Schneider Electric 135000; HP France 1500.

France cogeneracion: EDF 158000; Engie 100000; Total Énergies 102000; Veolia 220000; Suez 90000.

Tableau valeurs

  • Be = dP*L^2/(mu*alpha)
  • Be<1e6
  • Be>1e12 turbomachinery
  • Constructal Bejan 1996
  • EGM
  • Bejan Duke 1948
  • Bhattacharjee-Grosshandler 1988
  • Paoletti-Rispoli-Sciubba 1989
  • France CEA 16000
  • France IFPEN 1700
  • France EDF R&D 158000
  • France Total Énergies 102000
  • France Atlantic 9000
  • France Safran 92000
  • France Airbus 134000
  • France ArianeGroup 9000
  • France STM Crolles 6500
  • France Soitec 2200
  • France EDF 158000: 56 reactors
  • France Veolia 220000

Exemples numériques

Exemple 1 - Microchannel. Be=7e6. France: STM Crolles + HP France + ESPCI microfluidique.

Exemple 2 - HVAC. Be=9e8. France: Daikin France + Atlantic + De Dietrich.

Exemple 3 - Industrial HX. Be=9e14. France: Total Énergies + Petroineos + Esso France.

Exemple 4 - Jet engine. Be=2e14. France: Safran 92000 LEAP CFM + Airbus + Dassault Rafale + ArianeGroup.

Exemple 5 - Pipeline. Be=3e17. France: Total Énergies + Engie pipelines.

Limites

  1. Two definitions.
  2. Reynolds vs Bejan.
  3. Constructal paradigm.
  4. EGM.
  5. Microchannel surface.
  6. Compressibility.
  7. Buoyancy.
  8. Variable properties.
  9. Multi-component.
  10. Turbulence.

Erreurs courantes

Confondre Be definitions.

Constructal.

EGM.

Microchannel.

Italian heritage Sapienza.

Applications

  1. HVAC France: Daikin 600 + Atlantic 9000 + De Dietrich 1500 + Saunier Duval Frisquet Chappee Viessmann.
  2. Petrochimica France: Total Énergies 102000 Donges Gonfreville Lavera + Petroineos + Esso + BP France + Air Liquide 67000.
  3. Turbomachinery France: Safran 92000 LEAP CFM + Airbus Toulouse 134000 + Dassault Rafale + ArianeGroup 9000 + MBDA + Thales.
  4. Pumps France: KSB France 600 + Wilo + Grundfos + Salmson.
  5. Microchannel France: STM Crolles 6500 + Soitec Bernin 2200 + X-FAB + Schneider Electric + HP France.
  6. Cogeneration France: EDF 158000 + Engie + Total Énergies + Veolia 220000 + Suez 90000.
  7. EGM optimization France: IFPEN + CEA + ENPC.
  8. Constructal France: X LadHyX + Centrale Supelec.
  9. Solar thermique France: CNIM Themis + EDF Renouvelables + Total Eren CSP.
  10. Universites: Sorbonne LIMSI + X LadHyX + Centrale Supelec EM2C + INSA Lyon LMFA CETHIL + Toulouse IMFT + Aix-Marseille IRPHE + UGA LEGI LITEN.

Mis à jour en juillet 2026

Questions fréquentes

Qu est-ce que le nombre de Bejan?

Be = dP*L^2/(mu*alpha) perte charge adimensionnelle convection forcee Bhattacharjee-Grosshandler 1988. Alternative entropy Paoletti-Rispoli-Sciubba Sapienza 1989 Italian heritage. Be<1e6; Be>1e12 turbomachinery. Adrian Bejan Romania-USA Duke 1948 + constructal 1996 + EGM. France: CEA 16000 + IFPEN 1700 + EDF R&D 158000 + Atlantic 9000 + Safran 92000.

Comment calculer Bejan?

Procedure: (1) Be = dP*L^2/(mu*alpha); (2) dP Pa; (3) L m; (4) mu Pa*s; (5) alpha m^2/s; (6) régime. Microchannel: Be=7e6. Industrial: Be=9e14. France: X LadHyX + Centrale Supelec EM2C + INSA Lyon LMFA CETHIL.

Qu est-ce que la constructal theory?

Constructal theory Adrian Bejan Duke 1996 paper Int J HMT 40:799 + flow architecture optimization access-time + tree-shaped + nature inspired. France: X LadHyX + Centrale Supelec.

Quels régimes classifie Be?

Be<1e6 low microchannel; 1e6-1e9 medium HVAC; 1e9-1e12 high industrial; Be>1e12 very high turbomachinery. France: STM Crolles microchannel + Atlantic HVAC + Total Énergies industrial + Safran jet engines.

Qui est Adrian Bejan?

Adrian Bejan (Galati Romania 1948 - Duke USA emeritus) MIT BSc 1971 + MS 1972 + ScD 1975 + Berkeley 1975-1976 + Colorado 1976-1984 + Duke 1984-2014 J A Jones Professor + 30 honorary doctorates; 1982 'Entropy Gen' Wiley + 1995 'Convection HT' + 1996 constructal Int J HMT 40:799 + ASME Award 1994.

Qu est-ce que entropy génération minimization?

EGM Bejan Duke + 1982 textbook + 1996 'Entropy Gen Min' CRC + S_gen = Q*dT/T^2 + dP*v/T thermodynamic optimization heat exchanger sizing. Paoletti-Rispoli-Sciubba Sapienza 1989 alternative Italian heritage. France: IFPEN + CEA + Mines Paris CES.

Quelles applications de Bejan?

Applications: HVAC Atlantic 9000 + Daikin France 600 + De Dietrich 1500; petrochimica Total Énergies 102000 + Petroineos + Esso France + Air Liquide; turbomachinery Safran 92000 LEAP CFM + Airbus 134000 + Dassault Rafale + ArianeGroup; microchannel STM Crolles 6500 + Soitec Bernin 2200 + Schneider Electric; cogeneration EDF 158000 + Engie + Veolia 220000.

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