CFD Prediction of Airfoil Drag in Viscous Flow Using the Entropy Generation Method

<table class="fixed-width table-group" id="tab2"><tr><td><table class="table"><colgroup><col style="width:7.96em"/><col style="width:6.85em"/><col style="width:10.19em"/><col style="width:9.08em"/><col style="width:5.00em"/><col style="width:5.00em"/><col style="width:5.00em"/><col style="width:5.00em"/><col style="width:9.08em"/></colgroup><tr><td class="thead-hr" colspan="9"><hr/></td></tr><tr class="thead"><td class="align_left" rowspan="2">Angle-of-attack</td><td class="align_center" rowspan="2"><span style="width: 58.0918ptpx;"><svg height="14.7762pt" id="M169" style="vertical-align:-5.48787pt" version="1.1" viewbox="-0.0498162 -9.28833 58.0918 14.7762" width="58.0918pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M449 634C442 637 425 643 405 650C376 660 341 666 307 666C181 666 98 590 98 485C98 400 170 343 215 310L246 288C307 243 343 204 343 147C343 67 291 18 219 18C104 18 61 124 51 202L23 199C28 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id="g121-73"></path></g><g transform="matrix(.013,0,0,-0.013,53.359,.183)"><path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z" id="g113-42"></path></g></svg></span></td><td class="align_center" rowspan="2">Drag from experiment</td><td class="align_center" rowspan="2">Drag from surface integration</td><td class="align_center" colspan="4">Drag from wake integration</td><td class="align_center" rowspan="2">Drag from entropy generation</td></tr><tr class="thead"><td class="align_center"><span style="width: 48.493ptpx;"><svg height="11.439pt" id="M170" style="vertical-align:-2.15067pt" version="1.1" viewbox="-0.0498162 -9.28833 48.493 11.439" width="48.493pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M536 404C536 423 520 448 491 448C445 448 398 404 308 283L286 338C255 416 242 448 217 448C182 448 138 402 92 341L111 321C149 368 169 378 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transform="matrix(.013,0,0,-0.013,32.805,0)"><path d="M456 178V225H360V632H320C217 496 115 347 20 206V178H280V106C280 40 276 34 189 27V0H445V27C364 34 360 39 360 106V178H456ZM280 225H82C149 335 214 431 278 520H280V225Z" id="g113-53"></path></g><g transform="matrix(.013,0,0,-0.013,39.046,0)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z" id="g113-47"></path></g><g transform="matrix(.013,0,0,-0.013,42.01,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z" id="g113-49"></path></g></svg></span></td></tr><tr><td class="thead-hr" colspan="9"><hr/></td></tr><tr><td class="align_left"><span style="width: 10.3778ptpx;"><svg height="11.0031pt" id="M174" style="vertical-align:-0.2064009pt" version="1.1" viewbox="-0.0498162 -10.7967 10.3778 11.0031" width="10.3778pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z" id="g113-49"></path></g><g transform="matrix(.0091,0,0,-0.0091,6.24,-5.741)"><path d="M339 262C339 340 273 403 193 403S48 340 48 262S113 121 193 121S339 184 339 262ZM283 262C283 210 242 168 193 168S104 210 104 262S144 356 193 356S283 314 283 262Z" id="g54-73"></path></g></svg></span></td><td class="align_center">1.35</td><td class="align_center">80.0</td><td class="align_center">94.2</td><td class="align_center">95.3</td><td class="align_center">93.4</td><td class="align_center">92.4</td><td class="align_center">92.1</td><td class="align_center">89.1</td></tr><tr><td class="align_left"><span style="width: 10.3778ptpx;"><svg height="11.0031pt" id="M175" style="vertical-align:-0.2064009pt" version="1.1" viewbox="-0.0498162 -10.7967 10.3778 11.0031" width="10.3778pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M153 550H386L412 615L406 623H120L82 318C104 327 142 338 184 338C294 338 347 275 347 187C347 112 305 39 221 39C160 39 119 71 97 89C88 97 80 96 71 90C59 80 50 67 49 57C48 45 52 36 66 23C80 9 123 -12 169 -12C221 -11 288 15 342 59C403 109 431 165 431 225C431 308 366 395 238 395C212 395 165 379 127 364L153 550Z" id="g113-54"></path></g><g transform="matrix(.0091,0,0,-0.0091,6.24,-5.741)"><path d="M339 262C339 340 273 403 193 403S48 340 48 262S113 121 193 121S339 184 339 262ZM283 262C283 210 242 168 193 168S104 210 104 262S144 356 193 356S283 314 283 262Z" id="g54-73"></path></g></svg></span></td><td class="align_center">1.53</td><td class="align_center">90.0</td><td class="align_center">112.7</td><td class="align_center">110.5</td><td class="align_center">109.2</td><td class="align_center">107.6</td><td class="align_center">107.1</td><td class="align_center">101.0</td></tr><tr><td class="align_left"><span style="width: 16.6412ptpx;"><svg height="11.0031pt" id="M176" style="vertical-align:-0.2064009pt" version="1.1" viewbox="-0.0498162 -10.7967 16.6412 11.0031" width="16.6412pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M384 0V27C293 34 287 42 287 114V635C232 613 172 594 109 583V559L157 557C201 555 205 550 205 499V114C205 42 199 34 109 27V0H384Z" id="g113-50"></path></g><g transform="matrix(.013,0,0,-0.013,6.24,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z" id="g113-49"></path></g><g transform="matrix(.0091,0,0,-0.0091,12.48,-5.741)"><path d="M339 262C339 340 273 403 193 403S48 340 48 262S113 121 193 121S339 184 339 262ZM283 262C283 210 242 168 193 168S104 210 104 262S144 356 193 356S283 314 283 262Z" id="g54-73"></path></g></svg></span></td><td class="align_center">2.23</td><td class="align_center">120.0</td><td class="align_center">177.8</td><td class="align_center">166.3</td><td class="align_center">164.5</td><td class="align_center">163.0</td><td class="align_center">162.4</td><td class="align_center">147.2</td></tr><tr><td class="align_left"><span style="width: 16.6412ptpx;"><svg height="11.0031pt" id="M177" style="vertical-align:-0.2064009pt" version="1.1" viewbox="-0.0498162 -10.7967 16.6412 11.0031" width="16.6412pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M384 0V27C293 34 287 42 287 114V635C232 613 172 594 109 583V559L157 557C201 555 205 550 205 499V114C205 42 199 34 109 27V0H384Z" id="g113-50"></path></g><g transform="matrix(.013,0,0,-0.013,6.24,0)"><path d="M153 550H386L412 615L406 623H120L82 318C104 327 142 338 184 338C294 338 347 275 347 187C347 112 305 39 221 39C160 39 119 71 97 89C88 97 80 96 71 90C59 80 50 67 49 57C48 45 52 36 66 23C80 9 123 -12 169 -12C221 -11 288 15 342 59C403 109 431 165 431 225C431 308 366 395 238 395C212 395 165 379 127 364L153 550Z" id="g113-54"></path></g><g transform="matrix(.0091,0,0,-0.0091,12.48,-5.741)"><path d="M339 262C339 340 273 403 193 403S48 340 48 262S113 121 193 121S339 184 339 262ZM283 262C283 210 242 168 193 168S104 210 104 262S144 356 193 356S283 314 283 262Z" id="g54-73"></path></g></svg></span></td><td class="align_center">4.15</td><td class="align_center">190.0</td><td class="align_center">346.3</td><td class="align_center">312.2</td><td class="align_center">311.5</td><td class="align_center">310.3</td><td class="align_center">309.6</td><td class="align_center">273.9</td></tr><tr class="table-tr"><td colspan="9"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

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Mathematical Problems in Engineering

tab2

Table 2

Table 2: CFD Prediction of Airfoil Drag in Viscous Flow Using the Entropy Generation Method 