{"id":118274,"date":"2023-08-24T10:03:01","date_gmt":"2023-08-24T08:03:01","guid":{"rendered":"https:\/\/www.velasolaris.com\/handbuch\/modele-dechange-de-chaleur-avec-le-terrain\/"},"modified":"2023-10-25T17:19:59","modified_gmt":"2023-10-25T15:19:59","slug":"modele-dechange-de-chaleur-avec-le-terrain","status":"publish","type":"handbuch","link":"https:\/\/www.velasolaris.com\/fr\/handbuch\/polysun-designer\/autres-composants-et-systemes\/reservoir-de-glace\/modele-dechange-de-chaleur-avec-le-terrain\/","title":{"rendered":"Mod\u00e8le d’\u00e9change de chaleur avec le terrain"},"content":{"rendered":"\n
\n\n\n\n

Param\u00e8tres<\/h4>\n\n\n\n

Le mod\u00e8le de sol n\u00e9cessite les param\u00e8tres suivants (Calc signifie qu’il est calcul\u00e9 en routine) :<\/p>\n\n\n\n

Param\u00e8tre<\/td>Description<\/td>Unit\u00e9<\/td>Valeur<\/td><\/tr>
\u00a0<\/em>\\(\\widetilde{z}\\)<\/td>Profondeur moyenne du r\u00e9servoir de glace sous la surface du sol<\/td>m<\/em><\/td>Calc<\/td><\/tr>
Gt<\/sub><\/em><\/td>Gradient g\u00e9othermique<\/td>K\/m<\/td>0.03<\/td><\/tr>
\u00a0<\/em>\\(\\rho_{grd}\\)<\/td>Densit\u00e9 du sol<\/td>kg\/m3<\/sup><\/em><\/td>2\u2019500<\/td><\/tr>
cpgrd<\/sub><\/em><\/td>Capacit\u00e9 thermique du sol<\/td>kJ\/K<\/td>800<\/td><\/tr>
grd<\/sub><\/em><\/em><\/td>Conductibilit\u00e9 thermique du sol<\/td>W\/mK<\/td>2<\/td><\/tr>
Utank<\/sub><\/em><\/td>Conductibilit\u00e9 thermique du r\u00e9servoir<\/td>W\/mK<\/td>Calc<\/td><\/tr>
Uearth<\/sub><\/em><\/td>Conductibilit\u00e9 thermique de la terre<\/td>W\/mK<\/td>Calc<\/td><\/tr>
V<\/em><\/td>Volume du r\u00e9servoir de glace<\/td>m3<\/sup><\/em><\/td>10<\/td><\/tr>
zboden<\/sub><\/em><\/td>Profondeur du fond du r\u00e9servoir de glace<\/td>m<\/em><\/td>3.2<\/td><\/tr>
htank<\/sub><\/em><\/td>Hauteur du r\u00e9servoir de glace<\/td>m<\/em><\/td>2.3<\/td><\/tr>
Dtank<\/sub><\/em><\/td>Diam\u00e8tre du r\u00e9servoir de glace<\/td>m<\/em><\/td>2.7<\/td><\/tr>
dgrd<\/sub><\/em><\/td>\u00c9paisseur de la couche de sol environnante<\/td>m<\/em><\/td>0.5<\/td><\/tr>
\u00a0<\/em>\\(\\overline{\\theta_{e}}\\)<\/td>Temp\u00e9rature ext\u00e9rieure moyenne<\/td>\u00b0C<\/em><\/td>11<\/td><\/tr>
\u00a0<\/em>\\(\\Delta\\theta_{e}\\)<\/td>Amplitude des fluctuations mensuelles de la temp\u00e9rature ext\u00e9rieure<\/td>\u00b0C<\/em><\/td>9.3<\/td><\/tr>
\u00a0<\/em>\\(\\lambda_{wall}\\)<\/td>Conductibilit\u00e9 thermique de l’enveloppe du r\u00e9servoir de glace<\/td>W\/mK<\/td>1.33<\/td><\/tr>
dwall w<\/sub><\/em><\/td>\u00c9paisseur de l’enveloppe du r\u00e9servoir de glace sur les c\u00f4t\u00e9s<\/td>m<\/em><\/td>0.1<\/td><\/tr>
dwall b<\/sub><\/em><\/td>\u00c9paisseur de l’enveloppe du r\u00e9servoir de glace vers le bas<\/td>m<\/em><\/td>0.12<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

Impl\u00e9mentation<\/h4>\n\n\n\n

La temp\u00e9rature du sol non perturb\u00e9 est calcul\u00e9e en fonction de la profondeur dans le sol et du temps.<\/p>\n\n\n\n

\\(\\ \\zeta_{grd}(t,z) = \\overline{\\theta_{e}} – \\Delta\\theta_{e}\\exp{\\left( – \\frac{z}{\\delta_{grd}} \\right)\\cos\\left\\lbrack 2\\pi\\frac{\\left( t – t_{shift} \\right)}{t_{0}} – \\frac{z}{\\delta_{grd}} \\right\\rbrack} + G_{t}z\\)<\/p>\n\n\n\n

O\u00f9 la profondeur de p\u00e9n\u00e9tration thermique \u00a0est une mesure du retard de la temp\u00e9rature en profondeur par rapport \u00e0 la temp\u00e9rature de surface. Il est calcul\u00e9 comme suit :<\/p>\n\n\n\n

\\(\\delta_{grd} = \\sqrt{\\frac{t_{0} \\cdot 3600\\left\\lbrack \\frac{s}{h} \\right\\rbrack \\cdot \\lambda_{grd}}{\\pi \\cdot \\rho_{grd} \\cdot cp_{grd}}}\\)<\/p>\n\n\n\n

Pour z, on choisit la profondeur moyenne du r\u00e9servoir de glace z\u0303 <\/em>(\\(\\widetilde{z} = z_{boden} – 0.5 \\cdot h_{tank}\\)) et on suppose que la temp\u00e9rature du sol autour du r\u00e9servoir est homog\u00e8ne.<\/p>\n\n\n\n

Si le sol a une temp\u00e9rature diff\u00e9rente de celle du r\u00e9servoir de glace, un flux thermique se produit. Ainsi, la temp\u00e9rature de la paroi du r\u00e9servoir de glace est calcul\u00e9e selon la formule :<\/p>\n\n\n\n

\\(T_{Wall} = \\int\\frac{1}{m_{grd}cp_{grd}}\\left( UA_{earth}\\left( \\zeta_{grd} – T_{wall} \\right) – UA_{tank}\\left( T_{wall} – T_{ice} \\right) \\right)\\mathbb{d}t\\)<\/p>\n\n\n\n

O\u00f9 UAearth<\/sub><\/em> est le coefficient de transmission thermique de la strate de terre entre le sol non perturb\u00e9 et la paroi du r\u00e9servoir de glace. Il est calcul\u00e9 selon la formule :<\/p>\n\n\n\n

\\(UA_{earth} = \\frac{\\lambda_{grd}}{d_{grd}} \\times \\left\\lbrack \\pi\\left( \\frac{D_{tank} + 2d_{grd}}{2} \\right)^{2} + \\pi\\left( D_{tank} + 2d_{grd} \\right)\\left( h_{tank} + d_{grd} \\right) \\right\\rbrack\\)<\/p>\n\n\n\n

UAtank<\/sub> <\/em>est le coefficient de transmission thermique de l’envoloppe du r\u00e9servoir de glace et est calcul\u00e9 \u00e0 partir de la surface du paroi ou du sol divis\u00e9e par la r\u00e9sistance de transmission thermique respective. Dans ce mod\u00e8le, l’\u00e9change thermique entre le r\u00e9servoir de glace et le sol est limit\u00e9 \u00e0 la partie inf\u00e9rieure et cylindrique du r\u00e9servoir de glace. Les rendements\/pertes thermiques via le couvercle conique ne sont pas pris en compte.<\/p>\n\n\n\n

\\(UA_{tank} = \\frac{\\left( \\frac{D_{tank}}{2} \\right)^{2}\\pi}{\\frac{d_{wall\\ b}}{\\lambda_{wall}}} + \\frac{D_{tank\\ }\\pi\\ h_{tank}}{\\frac{\\mathbb{d}_{wall\\ w}}{\\lambda_{wall}}}\\)<\/p>\n\n\n\n

mgrd<\/sub> <\/em>est calcul\u00e9 \u00e0 partir du volume de la strate de terre multipli\u00e9 par sa densit\u00e9 – le volume est calcul\u00e9 \u00e0 partir de la surface ext\u00e9rieure du r\u00e9servoir de glace et de l’\u00e9paisseur de la strate de terre.<\/p>\n\n\n\n

\n
\"\"
Figure: Repr\u00e9sentation sch\u00e9matique du mod\u00e8le de sol<\/figcaption><\/figure>\n<\/div>\n","protected":false},"author":19748,"featured_media":0,"parent":118271,"menu_order":14,"comment_status":"closed","ping_status":"closed","template":"","class_list":["post-118274","handbuch","type-handbuch","status-publish","hentry"],"acf":[],"yoast_head":"\nMod\u00e8le d'\u00e9change de chaleur avec le terrain - POLYSUN<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.velasolaris.com\/fr\/handbuch\/polysun-designer\/autres-composants-et-systemes\/reservoir-de-glace\/modele-dechange-de-chaleur-avec-le-terrain\/\" \/>\n<meta property=\"og:locale\" content=\"fr_FR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Mod\u00e8le d'\u00e9change de chaleur avec le terrain\" \/>\n<meta property=\"og:description\" content=\"Param\u00e8tres Le mod\u00e8le de sol n\u00e9cessite les param\u00e8tres suivants (Calc signifie qu’il est calcul\u00e9...\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.velasolaris.com\/fr\/handbuch\/polysun-designer\/autres-composants-et-systemes\/reservoir-de-glace\/modele-dechange-de-chaleur-avec-le-terrain\/\" \/>\n<meta property=\"og:site_name\" content=\"POLYSUN\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/polysun.switzerland\/\" \/>\n<meta property=\"article:modified_time\" content=\"2023-10-25T15:19:59+00:00\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/www.velasolaris.com\\\/fr\\\/handbuch\\\/polysun-designer\\\/autres-composants-et-systemes\\\/reservoir-de-glace\\\/modele-dechange-de-chaleur-avec-le-terrain\\\/\",\"url\":\"https:\\\/\\\/www.velasolaris.com\\\/fr\\\/handbuch\\\/polysun-designer\\\/autres-composants-et-systemes\\\/reservoir-de-glace\\\/modele-dechange-de-chaleur-avec-le-terrain\\\/\",\"name\":\"Mod\u00e8le d'\u00e9change de chaleur avec le terrain - 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