Large Eddy Simulation Using Lattice Boltzmann Method Based on Sigma Model

Large Eddy Simulation Using Lattice Boltzmann Method Based on Sigma Model

Available online at www.sciencedirect.com ScienceDirect Procedia Engineering 127 (2015) 177 – 184 ,QWHUQDWLRQDO&RQIHUHQFHRQ&RPSXWDWLRQDO+HDWDQG...

1MB Sizes 0 Downloads 54 Views

Available online at www.sciencedirect.com

ScienceDirect Procedia Engineering 127 (2015) 177 – 184

,QWHUQDWLRQDO&RQIHUHQFHRQ&RPSXWDWLRQDO+HDWDQG0DVV7UDQVIHU

/DUJH(GG\6LPXODWLRQXVLQJ/DWWLFH%ROW]PDQQ0HWKRGEDVHGRQ 6LJPD0RGHO $QLUXGGKH3UDGKDQ 6XPHGK
$EVWUDFW

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©‹7KH$XWKRUV3XEOLVKHGE\(OVHYLHU%9 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). 3HHUUHYLHZXQGHUUHVSRQVLELOLW\RIWKHRUJDQL]LQJFRPPLWWHHRI,&&+07± Peer-review under responsibility of the organizing committee of ICCHMT – 2015 .H\ZRUGV/DUJH(GG\6LPXODWLRQ/DWWLFH%ROW]PDQQ0HWKRG6LJPD0RGHO7XUEXOHQW)ORZ

,QWURGXFWLRQ 7KH/DWWLFH%ROW]PDQQ0HWKRG /%0 >@KDVJDLQHGSRSXODULW\LQWKHUHFHQW\HDUVEHFDXVHRILWVVLPSOLFLW\ 7KH PHWKRG KDV WKH DELOLW\ WR RSHUDWH RQ PXOWLSOH FRUHVWKUHDGV RU LQ D JUDSKLFV SURFHVVLQJ XQLW *38  ,Q /%0 ERXQGDU\ FRQGLWLRQV %&V  DUH DOVR HDVLO\ LPSOHPHQWHG 6FKHPHV OLNH ERXQFH EDFN DUH XVHG LQ ZKLFK WKH GHQVLW\ 



&RUUHSVRQGLQJ$XWKRUDQLUXGGKHLLWNJS#JPDLOFRP

1877-7058 © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license

(http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of ICCHMT – 2015

doi:10.1016/j.proeng.2015.11.324

178

Aniruddhe Pradhan and Sumedh Yadav / Procedia Engineering 127 (2015) 177 – 184

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±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

U

'HQVLW\ 9HORFLW\YHFWRU 3 3UHVVXUH Y .LQHPDWLFYLVFRVLW\ W LM 6*6 6XEJULGVFDOH 6*6 VWUHVVWHQVRU ¨ &KDUDFWHULVWLFOHQJWKVFDOH J LM  9HORFLW\JUDGLHQWWHQVRU WK 3DUWLFOHGLVWULEXWLRQIXQFWLRQLQ L GLUHFWLRQ I L  IL  (TXLOLEULXPSDUWLFOHGLVWULEXWLRQIXQFWLRQLQ L WK GLUHFWLRQ 6RXUFHWHUP ) W 5HOD[DWLRQSDUDPHWHUUHODWHGWRYLVFRVLW\ F 6SHHGRIVRXQG 6SHHGRIVRXQGLQPHGLXP FV  &KDQQHOKDOIZLGWK G 5HW  5H\QROGVQXPEHUEDVHGRQIULFWLRQYHORFLW\ )ULFWLRQYHORFLW\ XW 

X 

1XPHULFDO0HWKRG 7KHJRYHUQLQJHTXDWLRQVIRUIOXLGIORZDUHWKH1DYLHU6WRNHV(TXDWLRQ  

wU   U X   ’ wW

179

Aniruddhe Pradhan and Sumedh Yadav / Procedia Engineering 127 (2015) 177 – 184

wUX   UXX ’  3  ’ U Y’X  ’ wW



$SSO\LQJDILOWHULQJRSHUDWLRQDQGFRQVLGHULQJIORZWREHLQFRPSUHVVLEOHZHJHW 

wX wY wZ   w[ w\ w]



wXL wXXL wYXL wZXL    wW w[ w\ w]



W LM6*6





6*6 w3 w § wX · w § wX · w § wX · wW LM  ¨Q L ¸  ¨Q L ¸  ¨Q L ¸  Uw[L w[ © w[ ¹ w\ © w\ ¹ w] © w] ¹ w[ M 



XLX M  XL X M LVWKHHIIHFWRIVPDOOVFDOHVRQODUJHVFDOHV

 7KLVWHUPLVPRGHOOHGXVLQJWKH%RXVVLQHVTDSSUR[LPDWLRQDV W LM

Y7 6LM ZKHUH 6LM LVWKHILOWHUHGVWUDLQ

6*6

UDWHWHQVRU 5HIHUULQJWRWKHVLJPDPRGHO>@ 

Y7



'&V



'V 

' LVWKHFKDUDFWHULVWLFOHQJWKVFDOHZKLFKLVWDNHQWREHWKHFXEHURRWRIWKHYROXPHRIWKHFHOODQG &V LVWKHPRGHO FRQVWDQWDQG 'V LVGHILQHGDVIROORZV

'V



V  V  V  V   V   V 



V   V   V  DUHWKHVTXDUHURRWVRI(LJHQYDOXHVRIWKHPDWUL[ * J 7 J ZKHUHHOHPHQWVRIWKH J PDWUL[DUH wXL JLYHQE\ JLM  w[ M 7KHQHZIRUPXODWLRQIRUVLJPDPRGHOXVLQJ/%0FDQEHZULWWHQDV 

IL [ FLG W  W  G W





ĭL

§ IL  [  W   IL [  W · §  ¨ ¸  ¨  ¨ ¸ W © ¹ © W

IL [  W  ĭL 

FL  X FL º ) · ZLG W ª »  ¸  « FL  X   FV  ¼ ¹ FV ¬

) LVWKHVRXUFHWHUPDQG W LVWKHUHOD[DWLRQSDUDPHWHUDQGWKHWRWDOYLVFRVLW\LVUHODWHGWRWKHUHOD[DWLRQSDUDPHWHU E\WKLVUHODWLRQ  

Y7  Y FV  W   G W 

180

Aniruddhe Pradhan and Sumedh Yadav / Procedia Engineering 127 (2015) 177 – 184

 ,QRXUVLPXODWLRQZHKDYHXVHGWKH'4ODWWLFHPRGHOIRUVLPXODWLRQ7KHYHORFLW\GLUHFWLRQVDUH 

FL

ª                   º «                  »  » « «¬                  ¼»

 $QGWKHFRUUHVSRQGLQJZHLJKWVDUH 

ZL

ª       ¬«       

 

 

 

 

 

 

 

 

 7KHFRUUHVSRQGLQJPDFURSDUDPHWHUVDUHFDOFXODWHGE\

U



¦I  

L

L

X



 · §  ¨ ¦ L IL FL   ) ¸  ¹ © 

U

7RILQGWKHYHORFLW\GHULYDWLYHVZHXVHWKHIROORZLQJVFKHPH 



’XL

­ Ö  ½ Ö ° L ¦ZL FL L ª¬XL U  FG W  XL U  FG W º¼ ° °  ° °  ° Ö  ® M ¦ZL FL  ÖM ª¬XL U  FG W  XL U  FG W º¼ ¾  FG W °  ° °  ° °NÖ¦ZL FL NÖ ª¬XL U  FG W  XL U  FG W º¼ ° ¯  ¿

:KHUH F LVHTXDOWRDQG G W LVWKHWLPHVWHS  IL  LVWKHHTXLOLEULXPGLVWULEXWLRQIXQFWLRQJLYHQE\ 

 

 

 

º  »¼

181

Aniruddhe Pradhan and Sumedh Yadav / Procedia Engineering 127 (2015) 177 – 184

IL





­ Xº ª  XX ZL U «  ZKHQ K L °  » ¬  F ¼ ° ®  X º ° Z U ª   FL X   FL X   XX L « »   °  F  F ¼ F ¬ ¯

 

K Lz ZKHQ

/ŶŝƚŝĂůŝnjĂƚŝŽŶŽĨ ǀĂƌŝĂďůĞƐ͕ƚсϬ

ŽůůŝƐŝŽŶ

^ƚƌĞĂŵŝŶŐ

ĂůĐƵůĂƚŝŽŶŽĨ DĂĐƌŽͲ sĂƌŝĂďůĞƐĂŶĚ ĞƌŝǀĂƚŝǀĞƐ

ŽƵŶĚĂƌLJ ŽŶĚŝƚŝŽŶƐ  )LJ)ORZ&KDUWRIWKH$OJRULWKP  5HVXOWV 7RWHVWWKLVQHZ/DWWLFH%ROW]PDQQ0HWKRGIRUPXODWLRQZHWU\WRVHWXSWKHFKDQQHOIORZZLWK 5HW  7KH

5HW LVGHILQHGDV

5HW

XW G X Y W

WZ U



G LVWKHFKDQQHOKDOIZLGWKDQGZHGHILQHDSSURSULDWHVFDOLQJIDFWRUIRU\DQGXEDVHGRQIULFWLRQYHORFLW\DQG YLVFRXVOHQJWKVFDOH \

XW \  8 Y

8  XW

)RU RXU VLPXODWLRQ ZH FRQVLGHU D JULG VL]H RI  [  [  ZLWK  JULG SRLQWV DORQJ VWUHDPZLVH GLUHFWLRQ 3HULRGLFFRQGLWLRQKDVEHHQDSSOLHGRQWZRIDFHVQRUPDOWRWKHVWUHDPZLVHGLUHFWLRQ7KHIORZLVIRUFHGE\DGGLQJ DSUHVVXUHJUDGLHQWWHUPDVDERG\IRUFHDORQJWKHVWUHDPZLVHGLUHFWLRQZKLFKGHFLGHVWKHILQDO5H\QROGVQXPEHU 7RDGMXVWWKHSUHVVXUHJUDGLHQWWHUPDXWRPDWLFDOO\ZHGHILQHWKHSUHVVXUHJUDGLHQWWHUPLQWKHIROORZLQJPDQQHUIRU

182

Aniruddhe Pradhan and Sumedh Yadav / Procedia Engineering 127 (2015) 177 – 184

DQHZWLPHVWHS

)



§ 5H SUHVHQW § GS · ¨ ¸  D ¨¨  5H ILQDO © G[ ¹ROG ©

S· § GS ¨ ¸ © G[ ¹QHZ

· ¸¸  ¹

+HUHµD¶LVWKHFRQVWDQWZKLFKFDQEHDSSURSULDWHO\DGMXVWHG ,Q WKH QH[W VHFWLRQ FRQWRXUV RI WKH YHORFLW\ ILHOG DQG WXUEXOHQW ILHOG KDV EHHQ SORWWHG IRU WKH VLPXODWLRQ VKRZLQJ WXUEXOHQW YHORFLW\ IOXFWXDWLRQV LQ D SODQH $ TXDQWLWDWLYH YDOLGDWLRQ RI WKH QHZ /DWWLFH %ROW]PDQQ IRUPXODWLRQ RI 6LJPD0RGHOKDVEHHQGRQHLQWKHQH[WVHFWLRQVWRVHHZKHWKHUWKH/%0GLVFUHWLVDWLRQRIWKHILOWHUHG1DYLHU6WRNHV (TXDWLRQSUHVHUYHVDOOWKHIHDWXUHVRIWKH6LJPD0RGHO

  

        E 

D 

)LJ D &RQWRXURIYHORFLW\LQ[GLUHFWLRQ E &RQWRXURIYHORFLW\LQ\GLUHFWLRQ

         

        

D 

E 

 )LJ D &RQWRXURIYHORFLW\LQ]GLUHFWLRQ E &RQWRXURIWXUEXOHQWYLVFRVLW\ 

  D 



E 





VLJPD/(6 '16 

VLJPD/(6 '16

8

8506



 

 



 \



 















\

 )LJ D &RPSDULVRQRIPHDQYHORFLW\SURILOHIURPWKHZDOOWRZDUGVWKHFKDQQHOKDOIZLGWKZLWK'16>@ E &RPSDULVRQRI506YHORFLW\ SURILOHIURPWKHZDOOWRZDUGVWKHFKDQQHOKDOIZLGWKZLWK'16>@



Aniruddhe Pradhan and Sumedh Yadav / Procedia Engineering 127 (2015) 177 – 184

183

 7KH YLVFRVLW\ RI WKH IOXLG LV VHW WR EH  LQ ODWWLFH XQLWV FKDQQHO KDOI ZLGWK LV  ODWWLFH OHQJWK XQLWV DQG WKH PRGHO FRHIILFLHQW  &V LV VHW WR EH  'RLQJ DSSURSULDWH FDOFXODWLRQV ZH JHW

8



XW

 \ 

 \ 



8   1H[WZHSORWWKH 8 0HDQ YV \ DQGFRPSDUHLWZLWK'16VLPXODWLRQE\>@

 7KH SURILOH RI PHDQ YHORFLW\ IRXQG E\ HQVHPEOH DYHUDJH RI WKH YHORFLW\ GDWD SRLQWV XVLQJ WKH QHZ VLJPD /%0 PRGHOZDVIRXQGWREHPDWFKLQJZLWKWKH'16GDWD,QWKLVVLPXODWLRQZHKDYHFRQVLGHUHGDXQLIRUPJULGIRUWKH VDNH RI LPSOHPHQWDWLRQ DQG YDOLGDWLRQ RI WKH PRGHO +RZHYHU ZH H[SHFW EHWWHU UHVXOWV LI QXPEHU RI ODWWLFHV DUH LQFUHDVHGQHDUWKHZDOOVE\FRQVLGHULQJODWWLFHVRIGLIIHUHQWVL]HV7KLVLVWKHPDLQUHDVRQWKH506SURILOHIURPWKH VLPXODWLRQGLGQ¶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

$FNQRZOHGJHPHQWV  :HDUHYHU\JUDWHIXOWR3URIHVVRU3.'DVIRUSURYLGLQJXVJXLGDQFHWKURXJKRXWWKHSURMHFW:HDOVRZLVK WRWKDQNKLPIRUSURYLGLQJXVZLWKQHFHVVDU\FRPSXWDWLRQDOUHVRXUFHVIRUWKLVSURMHFW

184

Aniruddhe Pradhan and Sumedh Yadav / Procedia Engineering 127 (2015) 177 – 184

5HIHUHQFHV  >@6&KHQ*''RROHQ/DWWLFHEROW]PDQQPHWKRGIRUIOXLGIORZV$QQX5HY)OXLG0HFKSS >@;+H/6/XR/DWWLFHEROW]PDQQPRGHOIRUWKHLQFRPSUHVVLEOHQDYLHUVWRNHVHTXDWLRQ-6WDW3K\V9ROSS >@;+H/6/XR7KHRU\RIWKHODWWLFH%ROW]PDQQPHWKRG)URPWKHEROW]PDQQHTXDWLRQWRWKHODWWLFHEROW]PDQQHTXDWLRQ3+<6,&$/ 5(9,(:(YROQRSS >@8)ULVFK%+DVVODFKHU<3RPHDX/DWWLFHJDVDXWRPDWDIRUWKH1DYLHU±6WRNHVHTXDWLRQ3K\V5HY/HWWHUVSS >@+:=KHQJ&6KX<7&KHZ$ODWWLFHEROW]PDQQPRGHOIRUPXOWLSKDVHIORZVZLWKODUJHGHQVLW\UDWLR-RXUQDORI&RPSXWDWLRQDO3K\VLFV SS± >@+%D\DWRGDHWDO$VXEJULGVFDOHPRGHOEDVHGRQVLQJXODUYDOXHVIRU/(6LQFRPSOH[JHRPHWULHV&HQWHUIRU7XUEXOHQFH5HVHDUFK 3URFHHGLQJVRIWKH6XPPHU3URJUDPSS >@)1LFRXG+%D\DWRGD2&DEULW6%RVH-/HH8VLQJVLQJXODUYDOXHVWREXLOGDVXEJULGVFDOHPRGHOIRUODUJHHGG\VLPXODWLRQV3K\V )OXLGV  SS >@5'0RVHU-.LP110DQVRXU'LUHFWQXPHULFDOVLPXODWLRQRIWXUEXOHQWFKDQQHOIORZXSWR5H 3K\V)OXLGV9ROXPH SS