{"id":3146,"date":"2017-02-10T07:45:09","date_gmt":"2017-02-10T07:45:09","guid":{"rendered":"http:\/\/www.vtei.cz\/?p=3146"},"modified":"2024-07-16T11:58:34","modified_gmt":"2024-07-16T10:58:34","slug":"flow-of-the-curve-of-the-podkrusnohorsky-canal","status":"publish","type":"post","link":"https:\/\/www.vtei.cz\/en\/2017\/02\/flow-of-the-curve-of-the-podkrusnohorsky-canal\/","title":{"rendered":"Flow of the curve of the Podkru\u0161nohorsk\u00fd canal"},"content":{"rendered":"

<\/i> This article is available in Czech only. For translation or more information on this topic, please contact author.<\/h4>\n

 <\/p>\n

Souhrn<\/h2>\n

\u010cl\u00e1nek se zab\u00fdv\u00e1 hydraulick\u00fdm v\u00fdzkumem proud\u011bn\u00ed v\u00a0oblasti oblouku v\u00a0lokalit\u011b Podkru\u0161nohorsk\u00e9ho p\u0159ivad\u011b\u010de (PKP IV\u00a0\u2013 \u0159. km 2,812\u20132,736). Koryto p\u0159ivad\u011b\u010de v\u00a0oblouku je lichob\u011b\u017en\u00edkov\u00e9ho pr\u016f\u0159ezu se sklonem st\u011bn 9 : 1. Proud\u011bn\u00ed je p\u0159ev\u00e1\u017en\u011b byst\u0159inn\u00e9ho charakteru.<\/p>\n\"\"<\/a>\n

Obr.\u00a01. Podkru\u0161nohorsk\u00fd p\u0159ivad\u011b\u010d
\nFig. 1. Podkru\u0161nohorsk\u00fd canal<\/h6>\n

M\u011b\u0159en\u00ed prob\u00edhala na fyzik\u00e1ln\u00edm modelu v\u00a0m\u011b\u0159\u00edtku 1 : 15, kter\u00fd byl postaven \u010dleny katedry hydrotechniky ve vodohospod\u00e1\u0159sk\u00e9 laborato\u0159i Fakulty stavebn\u00ed, \u010cVUT. Na fyzik\u00e1ln\u00edm modelu byly m\u011b\u0159eny rychlosti a\u00a0hladiny v\u00a0celkem dev\u00edti profilech. D\u00e1le byl sestaven 3D matematick\u00fd model v\u00a0programu Ansys CFX, na kter\u00e9m je mo\u017en\u00e9 krom\u011b rychlost\u00ed a\u00a0hladin pozorovat tvar proudov\u00e9ho pole. C\u00edlem v\u00fdzkumu je vyhodnocen\u00ed proud\u011bn\u00ed v\u00a0oblasti oblouku v\u00a0re\u017eimu byst\u0159inn\u00e9ho proud\u011bn\u00ed pomoc\u00ed metod hybridn\u00edho modelov\u00e1n\u00ed a\u00a0tak\u00e9 verifikace matematick\u00e9ho modelu pomoc\u00ed hodnot nam\u011b\u0159en\u00fdch na modelu.<\/p>\n

\u00davod<\/h2>\n

P\u0159ivad\u011b\u010d je soustava vodn\u00edch kan\u00e1l\u016f, podzemn\u00edch potrub\u00ed, n\u00e1dr\u017e\u00ed a\u00a0akvaduktu na Mostecku. Jeho v\u00fdstavba prob\u00edhala v\u00a0letech 1957\u20131982. Soustava se skl\u00e1d\u00e1 z\u00a0P\u0159ivad\u011b\u010de pr\u016fmyslov\u00e9 vody a\u00a0z\u00a0Podkru\u0161nohorsk\u00e9ho p\u0159ivad\u011b\u010de. \u00da\u010delem t\u00e9to 33,8\u2008km dlouh\u00e9 soustavy kan\u00e1lu je ochrana p\u0159ed pr\u016fnikem povrchov\u00fdch vod do hn\u011bdouheln\u00fdch lom\u016f Libou\u0161, \u0160verma, Obr\u00e1nc\u016f m\u00edru a\u00a0\u010cSA. Dal\u0161\u00ed funkc\u00ed je p\u0159iv\u00e1d\u011bt vodu z\u00a0povod\u00ed \u0159eky Oh\u0159e pro pr\u016fmysl na Chomutovsku a\u00a0Mostecku.<\/p>\n

Zkouman\u00fd oblouk se nach\u00e1z\u00ed v\u00a0\u00faseku PKP IV\u00a0\u2013 \u0159. km 2,812\u20132,736, kter\u00fd se nach\u00e1z\u00ed u\u00a0obce Vysok\u00e1 Pec (obr.\u00a01, 2<\/em>). \u00dasek m\u00e1 lichob\u011b\u017en\u00edkov\u00fd profil se sklony st\u011bn 9 : 1 a\u00a0\u0161\u00ed\u0159ky ve dn\u011b 3,6\u2008m, pod\u00e9ln\u00fd sklon je 4,7\u00a0%, polom\u011br oblouku je 60\u2008m. Jeho celkov\u00e1 d\u00e9lka je necel\u00fdch 80\u2008m [1].<\/p>\n\"\"<\/a>\n

Obr.\u00a02. Mapa PKP
\nFig. 2. Map of PKP<\/h6>\n

Fyzik\u00e1ln\u00ed model<\/h2>\n

Modelov\u00e9 podm\u00ednky<\/h3>\n

Model byl sestaven \u010dleny katedry hydrotechniky ve vodohospod\u00e1\u0159sk\u00e9 laborato\u0159i Fakulty stavebn\u00ed, \u010cVUT v\u00a0r\u00e1mci v\u00fdzkumn\u00e9ho projektu PPV a\u00a0PKP\u00a0\u2013 dopln\u011bn\u00ed bezpe\u010dnostn\u00edch prvk\u016f v\u00a0koryt\u011b toku.<\/p>\n

Pro fyzik\u00e1ln\u00ed model bylo zvoleno m\u011b\u0159\u00edtko 1 : 15 a\u00a0p\u0159\u00edstup podle Froudova z\u00e1kona podobnosti. U\u00a0tohoto typu modelov\u00e9 podobnosti jsou vyj\u00e1d\u0159eny podm\u00ednky dynamick\u00e9 podobnosti hydrodynamick\u00fdch jev\u016f za v\u00fdhradn\u00edho p\u016fsoben\u00ed gravita\u010dn\u00edch sil.<\/p>\n\"\"<\/a>\n

Obr.\u00a03. Fyzik\u00e1ln\u00ed model PKP
\nFig. 3. Physical Model of PKP<\/h6>\n

Krom\u011b gravita\u010dn\u00edch sil v\u0161ak mohou zkouman\u00e9 proud\u011bn\u00ed ovliv\u0148ovat i\u00a0dal\u0161\u00ed s\u00edly\u00a0\u2013 odpor t\u0159en\u00edm vazk\u00e9 kapaliny, s\u00edly kapil\u00e1rn\u00ed, s\u00edly objemov\u00e9\u00a0apod. Podle Froudova z\u00e1kona podobnosti m\u016f\u017eeme ur\u010dit\u00fd hydrodynamick\u00fd jev zkoumat tehdy, jestli\u017ee \u00fa\u010dinky t\u011bchto sil jsou zanedbateln\u00e9 v\u00a0porovn\u00e1n\u00ed s\u00a0gravita\u010dn\u00edmi silami. Mezn\u00ed podm\u00ednky vymezuj\u00ed oblasti a\u00a0m\u011b\u0159\u00edtka, v\u00a0nich\u017e lze hydrodynamick\u00fd jev modelovat.<\/p>\n

Kinematicky podobn\u00e9 jevy, kter\u00e9 ovliv\u0148uje v\u00fdhradn\u011b gravita\u010dn\u00ed s\u00edla, jsou dynamicky podobn\u00e9, jestli\u017ee ve vz\u00e1jemn\u011b p\u0159\u00edslu\u0161n\u00fdch pr\u016f\u0159ezech budou stejn\u00e1 Froudova \u010d\u00edsla. Fyzik\u00e1ln\u00ed model v\u00a0m\u011b\u0159\u00edtku 1 : 15 odpov\u00edd\u00e1 v\u0161em podm\u00ednk\u00e1m [2, 3].<\/p>\n

Na z\u00e1klad\u011b modelov\u00fdch podobnost\u00ed vypl\u00fdvaj\u00ed pro pou\u017eit\u00e9 geometrick\u00e9 m\u011b\u0159\u00edtko 1 : 15 n\u00e1sleduj\u00edc\u00ed podm\u00ednky:<\/p>\n

Geometrick\u00e9 m\u011b\u0159\u00edtko: \u00a0 \u00a0 \u00a0Mh<\/sub> = Ml<\/sub> = Mb<\/sub> = 15 \u00a0 \u00a0<\/em><\/p>\n

M\u011b\u0159\u00edtko rychlost\u00ed:<\/em>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Mv<\/sub> = M1\/2<\/sup> l<\/sub> = 3,87<\/em><\/p>\n

M\u011b\u0159\u00edtko pr\u016ftok\u016f: \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 MQ<\/sub> = M 5\/2<\/sup> l<\/sub> = 871,42<\/em><\/p>\n

M\u011b\u0159\u00edtko \u010das\u016f: \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Mt<\/sub> = M1\/2<\/sup> l<\/sub> = 3,87<\/em><\/p>\n

Popis modelu<\/h3>\n

Model, viz\u00a0obr.\u00a03<\/em>, je tvo\u0159en uklid\u0148ovac\u00ed a\u00a0n\u00e1tokovou n\u00e1dr\u017e\u00ed, celkem 21 p\u0159\u00ed\u010dn\u00fdmi profily vymezuj\u00edc\u00edmi tvar modelu (10 profil\u016f p\u0159ed objektem (v\u00fdvarem) tvo\u0159\u00edc\u00ed zat\u00e1\u010dku, 6 profil\u016f objektov\u00fdch a\u00a05 profil\u016f za objektem). V\u00a0r\u00e1mci t\u00e9to pr\u00e1ce je pozornost zam\u011b\u0159ena pouze na prvn\u00edch 10 profil\u016f p\u0159ed objektem v\u00fdvaru.<\/p>\n

M\u011b\u0159en\u00e9 veli\u010diny<\/h3>\n

Rychlostn\u00ed pole bylo m\u011b\u0159eno pomoc\u00ed dvou hydrometrick\u00fdch vrtulek typu STS 005 firmy Erfisinger electronic GmbH a\u00a0dataloggeru. Z\u00edskan\u00e1 hodnota rychlosti je pr\u016fm\u011brn\u00e1 hodnota z\u00a030\u00a0sekund m\u011b\u0159en\u00ed. M\u011b\u0159en\u00ed prob\u00edhalo v\u00a0ka\u017ed\u00e9m profilu v\u00a05 bodech v\u00a0jednotliv\u00fdch hloubk\u00e1ch. Rastr m\u011b\u0159en\u00ed je vid\u011bt v\u00a0tabulce 1<\/em>. Celkem bylo m\u011b\u0159eno 8 profil\u016f, a\u00a0to profil \u010d.\u00a03 a\u017e profil \u010d.\u00a010.<\/p>\n

Tabulka 1. M\u011b\u0159en\u00e9 rychlosti \u2013\u00a0profil 6
\nTable 1. Measured velocity\u00a0\u2013 profile 6<\/h5>\n\"\"<\/a>\n

M\u011b\u0159en\u00e9 hloubky (obr.\u00a04<\/em>) byly p\u0159evzaty z\u00a0p\u0159ede\u0161l\u00fdch m\u011b\u0159en\u00ed v\u00a0r\u00e1mci v\u00fdzkumn\u00e9ho projektu PPV a\u00a0PKP\u00a0\u2013 dopln\u011bn\u00ed bezpe\u010dnostn\u00edch prvk\u016f v\u00a0koryt\u011b toku. Polohy hladin byly m\u011b\u0159eny v\u00a0ka\u017ed\u00e9m profilu ve \u010dty\u0159ech bodech. Jako m\u011b\u0159ic\u00ed za\u0159\u00edzen\u00ed slou\u017eily ultrazvukov\u00e9 sondy. Frekvence ode\u010dtu sond je 10\u2008Hz a\u00a0hodnoty hladin jsou n\u00e1sledn\u011b z\u00edsk\u00e1ny jako pr\u016fm\u011br p\u0159es 10sekundov\u00fd interval na ka\u017ed\u00e9m profilu.<\/p>\n\"\"<\/a>\n

Obr.\u00a04. Pod\u00e9ln\u00fd profil
\nFig. 4. Longitudinal profile<\/h6>\n

M\u011b\u0159en\u00ed prob\u00edhala v\u00a0ust\u00e1len\u00e9m re\u017eimu, kdy byla horn\u00ed okrajov\u00e1 podm\u00ednka nastavena pr\u016ftokem. Doln\u00ed okrajov\u00e1 podm\u00ednka byla tvo\u0159ena nezatopen\u00fdm v\u00fdtokem. Rychlostn\u00ed pole na modelu bylo m\u011b\u0159eno celkem na \u0161esti pr\u016ftoc\u00edch, a\u00a0to 5, 10, 20, 30, 40 a\u00a050\u2008m3<\/sup>.s-1<\/sup>.<\/p>\n

Matematick\u00fd model<\/h2>\n

V\u00a0r\u00e1mci v\u00fdzkumu byl sestaven matematick\u00fd model, kter\u00fd se skl\u00e1d\u00e1 z\u00a0n\u00e1tokov\u00e9 n\u00e1dr\u017ee a\u00a0zkouman\u00e9 \u010d\u00e1sti oblouku ukon\u010den\u00e9 p\u0159ed v\u00fdvarem (obr.\u00a05<\/em>).<\/p>\n

V\u00fdpo\u010detn\u00ed s\u00ed\u0165 byla vytvo\u0159ena v\u00a0programu ICEM CFD<\/em>, kter\u00fd je sou\u010d\u00e1st\u00ed platformy ANSYS Workbench.<\/em> Byla vytvo\u0159ena strukturovan\u00e1 s\u00ed\u0165 (mesh) o\u00a0maxim\u00e1ln\u00ed velikosti elementu 1\u2008m. V\u00a0m\u00edst\u011b oblouku byla s\u00ed\u0165 zahu\u0161t\u011bna na maxim\u00e1ln\u00ed velikost elementu 30\u2008cm, aby nedoch\u00e1zelo ke zkreslen\u00ed proud\u011bn\u00ed v\u00a0oblouku. Celkov\u00fd po\u010det element\u016f tak dos\u00e1hl 1\u2009126\u2009315.<\/p>\n\"\"<\/a>\n

Obr.\u00a05. Geometrie matematick\u00e9ho modelu
\nFig. 5. Geometry of the numerical model<\/h6>\n

Pro samotn\u00fd v\u00fdpo\u010det byl pou\u017eit program CFX<\/em>, kter\u00fd je tak\u00e9 sou\u010d\u00e1st\u00ed platformy ANSYS Workbench.<\/em> Horn\u00ed i\u00a0doln\u00ed okrajov\u00e1 podm\u00ednka byla nastavena pomoc\u00ed hladiny, kter\u00e9 na fyzik\u00e1ln\u00edm modelu odpov\u00eddaly pr\u016ftoku 50\u2008m3<\/sup>.s-1<\/sup>. Tento pr\u016ftok pak slou\u017eil pro kalibraci modelu. Kalibrace prob\u00edhala pomoc\u00ed drsnosti st\u011bn, kde po\u010d\u00e1te\u010dn\u00ed hodnota drsnosti 0,014 byla m\u011bn\u011bna a\u017e na tzv.\u00a0hladkou st\u011bnu (no slip wall) [4, 5]. Model byl nastaven tak, aby umo\u017e\u0148oval proud\u011bn\u00ed s\u00a0volnou hladinou (dvouf\u00e1zov\u00e9 proud\u011bn\u00ed voda\u00ad\u2011vzduch). Samotn\u00fd v\u00fdpo\u010det je nastaven\u00fd jako ust\u00e1len\u00e9 proud\u011bn\u00ed.<\/p>\n\"\"<\/a>\n

Obr.\u00a06. Tvar hladiny z\u00a0matematick\u00e9ho modelu
\nFig. 6. The shape of water level of the numerical model<\/h6>\n

Vyhodnocen\u00ed<\/h2>\n

Rychlostn\u00ed pole byla vyhodnocena pro n\u00e1vrhov\u00fd maxim\u00e1ln\u00ed pr\u016ftok 50\u2008m3<\/sup>.s-1<\/sup>. Rychlosti byly vykresleny pomoc\u00ed plo\u0161n\u00e9 interpolace do jednotliv\u00fdch profil\u016f (obr.\u00a06 <\/em>a\u00a07<\/em>). Maxim\u00e1ln\u00ed rychlosti dosahovaly t\u00e9m\u011b\u0159 9 ms-1<\/sup>. Rozlo\u017een\u00ed rychlost\u00ed v\u00a0jednotliv\u00fdch profilech je plynul\u00e9, z\u00a0toho lze vyvodit, \u017ee v\u00a0cel\u00e9m oblouku nedoch\u00e1z\u00ed k\u00a0velk\u00fdm turbulenc\u00edm.<\/p>\n\"\"<\/a>\n

Obr.\u00a07. Rychlosti profil 3
\nFig. 7. The velocity profile 3<\/h6>\n

\u00a0\"\"<\/a><\/em><\/p>\n

Obr.\u00a08. Rychlosti profil 6
\nFig. 8. The velocity profile 6<\/h6>\n\"\"<\/a>\n
Obr.\u00a09. Rychlosti profil 9
\nFig. 9. The velocity profile 9<\/h6>\n

Matematick\u00fd model umo\u017enil popsat proudov\u00e1 pole. Na z\u00e1klad\u011b pozorov\u00e1n\u00ed hladiny se o\u010dek\u00e1valo zna\u010dn\u011b turbulentn\u00ed proud\u011bn\u00ed a\u00a0\u0161roubovit\u00fd tvar proudnic v\u00a0druh\u00e9 polovin\u011b oblouku. Oproti tomuto p\u0159edpokladu se uk\u00e1zalo, \u017ee proudnice jsou t\u00e9m\u011b\u0159 plynul\u00e9 a\u00a0jsou plynul\u00e9 v\u00a0cel\u00e9 d\u00e9lce oblouku, viz\u00a0obr.\u00a08, 9 <\/em>a\u00a010<\/em>.<\/p>\n\"\"<\/a>\n

Obr.\u00a010. Proudnice
\nFig. 10. Streamline<\/h6>\n

Z\u00e1v\u011br<\/h2>\n

V\u00a0r\u00e1mci v\u00fdzkumu bylo zkoum\u00e1no proud\u011bn\u00ed v\u00a0oblouku s\u00a0velk\u00fdm sklonem dna a\u00a0byst\u0159inn\u00fdm charakterem proud\u011bn\u00ed. Metodou hybridn\u00edho modelov\u00e1n\u00ed bylo mo\u017en\u00e9 vyhodnotit nejen rychlosti v\u00a0jednotliv\u00fdch profilech, ale tak\u00e9 proudov\u00e1 pole v\u00a0tomto \u00faseku, kter\u00e9 bylo mo\u017eno ur\u010dit po \u00fasp\u011b\u0161n\u00e9 verifikaci matematick\u00e9ho modelu z\u00a0nam\u011b\u0159en\u00e9ho pr\u016fb\u011bhu hladin na fyzik\u00e1ln\u00edm modelu. V\u00fdzkum uk\u00e1zal, \u017ee p\u0159i vysok\u00e9m sklonu dna i\u00a0p\u0159i velk\u00fdch pr\u016ftoc\u00edch nedoch\u00e1z\u00ed k\u00a0turbulentn\u00edmu proud\u011bn\u00ed v\u00a0oblouc\u00edch.<\/p>\n

Pod\u011bkov\u00e1n\u00ed<\/h3>\n

Tento p\u0159\u00edsp\u011bvek vznikl za podpory grantu SGS16\/059\/OHK1\/1T\/11 V\u00fdzkum hydraulicky komplikovan\u00e9ho proud\u011bn\u00ed vody na hydrotechnick\u00fdch stavb\u00e1ch.<\/em><\/p>\n","protected":false},"excerpt":{"rendered":"

This article pursues the hydraulic research of flow of the curve in the Podkru\u0161nohorsk\u00fd canal (PKP). Measurements were conducted on a physical model.<\/p>\n","protected":false},"author":8,"featured_media":3087,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[86],"tags":[741,743,742,739,740,738],"coauthors":[695,696,697],"class_list":["post-3146","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-hydraulics-hydrology-and-hydrogeology","tag-canal","tag-flow-field","tag-flow-of-the-curve","tag-mathematical-modelling","tag-model-similarity","tag-physical-modelling"],"acf":[],"_links":{"self":[{"href":"https:\/\/www.vtei.cz\/en\/wp-json\/wp\/v2\/posts\/3146","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.vtei.cz\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.vtei.cz\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.vtei.cz\/en\/wp-json\/wp\/v2\/users\/8"}],"replies":[{"embeddable":true,"href":"https:\/\/www.vtei.cz\/en\/wp-json\/wp\/v2\/comments?post=3146"}],"version-history":[{"count":2,"href":"https:\/\/www.vtei.cz\/en\/wp-json\/wp\/v2\/posts\/3146\/revisions"}],"predecessor-version":[{"id":30378,"href":"https:\/\/www.vtei.cz\/en\/wp-json\/wp\/v2\/posts\/3146\/revisions\/30378"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.vtei.cz\/en\/wp-json\/wp\/v2\/media\/3087"}],"wp:attachment":[{"href":"https:\/\/www.vtei.cz\/en\/wp-json\/wp\/v2\/media?parent=3146"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.vtei.cz\/en\/wp-json\/wp\/v2\/categories?post=3146"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.vtei.cz\/en\/wp-json\/wp\/v2\/tags?post=3146"},{"taxonomy":"author","embeddable":true,"href":"https:\/\/www.vtei.cz\/en\/wp-json\/wp\/v2\/coauthors?post=3146"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}