{"id":45215,"date":"2019-10-17T18:57:08","date_gmt":"2019-10-17T17:57:08","guid":{"rendered":"https:\/\/www.thermal-engineering.org\/exemple-efficacite-des-turbines-isentropiques-definition\/"},"modified":"2020-02-23T15:51:42","modified_gmt":"2020-02-23T14:51:42","slug":"exemple-efficacite-des-turbines-isentropiques-definition","status":"publish","type":"post","link":"https:\/\/www.thermal-engineering.org\/fr\/exemple-efficacite-des-turbines-isentropiques-definition\/","title":{"rendered":"Exemple: efficacit\u00e9 des turbines isentropiques – d\u00e9finition"},"content":{"rendered":"
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Calculez le travail effectu\u00e9 par cette turbine et calculez la temp\u00e9rature r\u00e9elle \u00e0 la sortie de la turbine, lorsque le rendement de la turbine isentropique est \u03b7T = 0,91 (91%).\u00a0G\u00e9nie thermique<\/div>\n<\/div>\n
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Exemple: efficacit\u00e9 de la turbine isentropique<\/h2>\n
\"Expansion<\/a>
Le processus isentropique est un cas particulier de processus adiabatiques.\u00a0C’est un processus adiabatique r\u00e9versible.\u00a0Un processus isentropique peut \u00e9galement \u00eatre appel\u00e9 processus \u00e0 entropie constante.<\/figcaption><\/figure>\n

Supposons une\u00a0expansion isentropique<\/strong>\u00a0de l’h\u00e9lium (3 \u2192 4) dans une turbine \u00e0 gaz.\u00a0Dans cette turbine, l’\u00e9tage haute pression re\u00e7oit du gaz (point 3 sur la figure; p\u00a03<\/sub>\u00a0=\u00a06,7 MPa<\/strong>\u00a0; T\u00a03<\/sub>\u00a0= 1190 K (917 \u00b0 C)) d’un \u00e9changeur de chaleur et l’\u00e9vacue vers un autre \u00e9changeur de chaleur, o\u00f9 la pression de sortie est p\u00a04<\/sub>\u00a0=\u00a02,78 MPa<\/strong>\u00a0(point 4)\u00a0.\u00a0<\/strong>La temp\u00e9rature (pour le processus isentropique) du gaz \u00e0 la sortie de la turbine est T\u00a04s<\/sub>\u00a0= 839 K (566 \u00b0 C).<\/p>\n

Calculez<\/strong>\u00a0le travail effectu\u00e9 par cette turbine et calculez la temp\u00e9rature r\u00e9elle \u00e0 la sortie de la turbine, lorsque le\u00a0rendement de la turbine isentropique<\/strong>\u00a0est\u00a0\u03b7\u00a0<\/strong>T<\/sub><\/strong>\u00a0= 0,91 (91%)<\/strong>\u00a0.<\/p>\n

Solution:<\/strong><\/p>\n

A partir du premier principe de la thermodynamique, le travail effectu\u00e9 par turbine dans un processus isentropique peut \u00eatre calcul\u00e9 \u00e0 partir de:<\/p>\n

W\u00a0<\/strong>T<\/sub><\/strong>\u00a0= h\u00a0<\/strong>3<\/sub><\/strong>\u00a0– h\u00a0<\/strong>4s<\/sub><\/strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u2192 W\u00a0<\/strong>Ts<\/sub><\/strong>\u00a0=\u00a0c\u00a0<\/em><\/strong>p<\/sub><\/em><\/strong>\u00a0(T\u00a0<\/em><\/strong>3<\/sub><\/em><\/strong>\u00a0– T\u00a0<\/em><\/strong>4s<\/sub><\/em><\/strong>\u00a0)<\/em><\/strong><\/p>\n

D’apr\u00e8s la loi des gaz parfaits, nous savons que la chaleur sp\u00e9cifique molaire d’un gaz parfait monoatomique est:<\/p>\n

C\u00a0<\/em><\/strong>v<\/sub><\/em><\/strong>\u00a0= 3 \/ 2R = 12,5 J \/ mol K<\/em><\/strong>\u00a0et\u00a0C\u00a0<\/em><\/strong>p<\/sub><\/em><\/strong>\u00a0= C\u00a0<\/em><\/strong>v<\/sub><\/em><\/strong>\u00a0+ R = 5 \/ 2R = 20,8 J \/ mol K<\/em><\/strong><\/p>\n

Nous transf\u00e9rons les capacit\u00e9s thermiques sp\u00e9cifiques en unit\u00e9s de\u00a0J \/ kg K via:<\/strong><\/p>\n

c\u00a0<\/em><\/strong>p<\/sub><\/em><\/strong>\u00a0= C\u00a0<\/em><\/strong>p<\/sub><\/em><\/strong>\u00a0.\u00a01 \/ M (poids molaire d’h\u00e9lium) = 20,8 x 4,10\u00a0<\/em><\/strong>-3<\/sup><\/em><\/strong>\u00a0= 5200 J \/ kg K<\/em><\/strong><\/p>\n

Le travail effectu\u00e9 par turbine \u00e0 gaz dans le processus isentropique est alors:<\/p>\n

W\u00a0<\/em><\/strong>T, S<\/sub><\/em><\/strong>\u00a0= C\u00a0<\/em><\/strong>p<\/sub><\/em><\/strong>\u00a0(T\u00a0<\/em><\/strong>3<\/sub><\/em><\/strong>\u00a0– T\u00a0<\/em><\/strong>4s<\/sub><\/em><\/strong>\u00a0) = 5200 x (1190-839) = 1.825 MJ \/ kg<\/em><\/strong><\/p>\n

Le travail r\u00e9el effectu\u00e9 par la turbine \u00e0 gaz en processus adiabatique est alors:<\/span>
\nW\u00a0<\/span><\/em><\/strong>T, r\u00e9el<\/span><\/sub><\/em><\/strong>\u00a0= c\u00a0<\/span><\/em><\/strong>p<\/span><\/sub><\/em><\/strong>\u00a0(T\u00a0<\/span><\/em><\/strong>3<\/span><\/sub><\/em><\/strong>\u00a0– T\u00a0<\/span><\/em><\/strong>4s<\/span><\/sub><\/em><\/strong>\u00a0).\u00a0<\/span><\/em><\/strong>\u03b7\u00a0<\/span><\/em><\/strong>T<\/span><\/sub><\/em><\/strong>\u00a0= 5200 x (1190 – 839) x 0,91 = 1,661 MJ \/ kg<\/span><\/em><\/strong><\/p>\n<\/div>\n<\/div>\n

……………………………………………………………………………………………………………………………….<\/p>\n

Cet article est bas\u00e9 sur la traduction automatique de l’article original en anglais. Pour plus d’informations, voir l’article en anglais. Pouvez vous nous aider Si vous souhaitez corriger la traduction, envoyez-la \u00e0 l’adresse: translations@nuclear-power.com ou remplissez le formulaire de traduction en ligne. Nous appr\u00e9cions votre aide, nous mettrons \u00e0 jour la traduction le plus rapidement possible. Merci<\/p>\n","protected":false},"excerpt":{"rendered":"

Calculez le travail effectu\u00e9 par cette turbine et calculez la temp\u00e9rature r\u00e9elle \u00e0 la sortie de la turbine, lorsque le rendement de la turbine isentropique est \u03b7T = 0,91 (91%).\u00a0G\u00e9nie thermique Exemple: efficacit\u00e9 de la turbine isentropique Le processus isentropique est un cas particulier de processus adiabatiques.\u00a0C’est un processus adiabatique r\u00e9versible.\u00a0Un processus isentropique peut \u00e9galement … Lire la suite<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[8],"tags":[],"yoast_head":"\nExemple: efficacit\u00e9 des turbines isentropiques - d\u00e9finition<\/title>\n<meta name=\"description\" content=\"Calculez le travail effectu\u00e9 par cette turbine et calculez la temp\u00e9rature r\u00e9elle \u00e0 la sortie de la turbine, lorsque le rendement de la turbine isentropique est \u03b7T = 0,91 (91%). 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