{"id":118276,"date":"2023-08-24T10:10:57","date_gmt":"2023-08-24T08:10:57","guid":{"rendered":"https:\/\/www.velasolaris.com\/handbuch\/modele-dechangeur-thermique-a-serpentin\/"},"modified":"2023-08-24T10:10:57","modified_gmt":"2023-08-24T08:10:57","slug":"modele-dechangeur-thermique-a-serpentin","status":"publish","type":"handbuch","link":"https:\/\/www.velasolaris.com\/fr\/handbuch\/polysun-designer\/autres-composants-et-systemes\/reservoir-de-glace\/modele-dechangeur-thermique-a-serpentin\/","title":{"rendered":"Mod\u00e8le d&rsquo;\u00e9changeur thermique \u00e0 serpentin"},"content":{"rendered":"\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"Param\u00e8tres\" style=\"font-size:30px\">Param\u00e8tres<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">Le mod\u00e8le du r\u00e9servoir de glace pour les \u00e9changeurs thermiques \u00e0 serpentin n\u00e9cessite les param\u00e8tres suivants (Calc signifie qu&rsquo;il est calcul\u00e9 en routine) :<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td>Param\u00e8tre<\/td><td>Description<\/td><td>Unit\u00e9<\/td><td>Valeur<\/td><\/tr><tr><td><em>m<sub>ice<\/sub><\/em><\/td><td>Masse du r\u00e9servoir de glace<\/td><td><em>kg<\/em><\/td><td>Calc<\/td><\/tr><tr><td><em>m<sub>grd<\/sub><\/em><\/td><td>Masse de la terre autour du r\u00e9servoir de glace<\/td><td><em>kg<\/em><\/td><td>Calc<\/td><\/tr><tr><td><em>t<sub>shift<\/sub><\/em><\/td><td>Intervalle de temps entre l&rsquo;heure de la temp\u00e9rature annuelle la plus basse au 1er janvier<\/td><td><em>h<\/em><\/td><td>319<\/td><\/tr><tr><td><em>t<sub>0<\/sub><\/em><\/td><td>Nombre d&rsquo;heures par an pour la normalisation<\/td><td>h\/a<\/td><td>8\u2019760<\/td><\/tr><tr><td><em>T<sub>tabelle<\/sub>(H<sub>ice<\/sub>)<\/em><\/td><td>Valeur de temp\u00e9rature correspondant \u00e0 une certaine enthalpie H<\/td><td><em>\u00b0C<\/em><\/td><td>&nbsp;<\/td><\/tr><tr><td><em>V<\/em><\/td><td>Volume du r\u00e9servoir de glace<\/td><td><em>m<sup>3<\/sup><\/em><\/td><td>10<\/td><\/tr><tr><td><em>f<sub>ice<\/sub><\/em><\/td><td>Partie initiale du r\u00e9servoir de glace qui est gel\u00e9e (0..1)<\/td><td><em>&#8211;<\/em><\/td><td>0<\/td><\/tr><tr><td><em>t<sub>init<\/sub><\/em><\/td><td>Temp\u00e9rature initiale du r\u00e9servoir de glace<\/td><td><em>\u00b0C<\/em><\/td><td>15<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"Contexte\" style=\"font-size:30px\">Contexte<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">Le mod\u00e8le du r\u00e9servoir de glace est un mod\u00e8le simple pour un r\u00e9servoir d&rsquo;eau en tant qu&rsquo;\u00e9changeur thermique, qui peut absorber ou lib\u00e9rer de la chaleur latente \u00e0 des temp\u00e9ratures proches de z\u00e9ro par la transmission de phase de liquide \u00e0 solide ou de solide \u00e0 liquide.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">La temp\u00e9rature du r\u00e9servoir de glace d\u00e9pend du d\u00e9bit thermique vers la paroi et du d\u00e9bit thermique d\u00fb aux \u00e9changeurs thermiques. La formation de glace au niveau des \u00e9changeurs thermiques n&rsquo;est pas explicitement d\u00e9termin\u00e9e, mais calcul\u00e9e via l&rsquo;enthalpie.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">L&rsquo;enthalpie de la glace est calcul\u00e9e selon la formule suivante&nbsp;:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(H_{ice} = \\int\\frac{1}{m_{ice}}\\left( \\sum_{i}^{}\\left( {\\dot{Q}}_{2ice} \\right)_{i} + UA_{tank}\\left( T_{wall} &#8211; T_{ice} \\right) \\right)\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>(<\/em>\\(\\dot{Q}\\) <em><sub>2ice<\/sub>)i <\/em>sont les d\u00e9bits thermiques traversant les \u00e9changeurs thermiques et <em>m<sub>ice<\/sub> <\/em>la masse du liquide dans le r\u00e9servoir de glace &#8211; volume multipli\u00e9 par la densit\u00e9 de l&rsquo;eau (1&rsquo;000 \\(kg\/m^{3}\\)).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">La temp\u00e9rature du r\u00e9servoir de glace est ensuite lue \u00e0 partir d&rsquo;une table interpol\u00e9e contenant diff\u00e9rentes valeurs de temp\u00e9rature en fonction de l&rsquo;enthalpie.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(T_{ice} = T_{tabelle}(H_{ice})\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">En acc\u00e9dant \u00e0 l&rsquo;enthalpie, la chaleur de fusion absorb\u00e9e pendant la transmission de phase ou la chaleur de solidification lib\u00e9r\u00e9e peuvent \u00eatre prises en compte.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">La temp\u00e9rature de la glace peut \u00eatre calcul\u00e9e par interpolation lin\u00e9aire en fonction de l&rsquo;enthalpie. Les paires de valeurs suivantes entre la temp\u00e9rature et l&rsquo;enthalpie (T, E) sont utilis\u00e9es comme points de support :<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td><strong>Temp\u00e9rature en <em>\u00b0C<\/em><\/strong><\/td><td><strong>Enthalpie en<\/strong> \\(\\mathbf{J\/kg}\\)<\/td><\/tr><tr><td>-10<\/td><td>-10\u00b72&rsquo;060<\/td><\/tr><tr><td>-3<\/td><td>-3\u00b72&rsquo;060<\/td><\/tr><tr><td>0<\/td><td>3.35\u00b710<sup>5<\/sup><\/td><\/tr><tr><td>10<\/td><td>10\u00b74&rsquo;182+3.35\u00b710<sup>5<\/sup><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Au d\u00e9but, l&rsquo;enthalpie doit \u00eatre initialis\u00e9e. La temp\u00e9rature initiale et la concentration initiale de glace sont utilis\u00e9es \u00e0 cet effet. Il est calcul\u00e9 selon la formule suivante :<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(H_{init} = \\left( 1 &#8211; f_{ice} \\right) \\cdot 3.35 \\cdot 10^{5} + \\Theta\\left( &#8211; f_{ice} \\right) \\cdot 4^{&lsquo;}182 \\cdot t_{init}\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Ici, <em>\u0398(x) <\/em>est la fonction de Heaviside, qui est nulle pour x n\u00e9gatif et prend la valeur un pour \\(x \\geq 0\\). <em>f<sub>ice<\/sub> <\/em>est la part du r\u00e9servoir de glace qui est initialement gel\u00e9e, et est pass\u00e9e comme param\u00e8tre.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>T<sub>wall<\/sub> <\/em>est initialis\u00e9 \u00e0 4\u00b0C, les autres param\u00e8tres sont pr\u00e9d\u00e9finis.<\/p>\n","protected":false},"author":19748,"featured_media":0,"parent":118271,"menu_order":8,"comment_status":"closed","ping_status":"closed","template":"","class_list":["post-118276","handbuch","type-handbuch","status-publish","hentry"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v28.0 (Yoast SEO v28.0) - 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