Optimization of Injectors Location in a Water Reservoirs Aeration Problem

<table class="table-group" width="800px"><tr class="fig-image" id="a"><td><img alt="875979.fig.0011a" src="https://static.hindawi.com/articles/mpe/volume-2013/875979/figures/875979.fig.0011a.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(a) </b> <svg height="18.987499" id="M262" style="vertical-align:-5.76988pt" version="1.1" viewbox="0 0 21.825001 18.987499" width="21.825001" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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q-83 0 -145 -50q-61 -49 -61 -128q0 -37 20 -60.5t53 -23.5q98 0 139 119h20q-12 -57 -55 -103t-103 -46q-51 0 -83 31.5t-32 82.5q0 90 78 151q80 62 178 62q74 0 126 -39q53 -38 53 -107q0 -65 -38 -124l-186 -287q-39 -62 -39 -87q0 -28 29 -28q38 0 93 47q55 48 106 118
q98 133 153 235z" id="x1D4B0"></path></g>
<g transform="matrix(.012,-0,0,-.012,14.375,15.825)"><path d="M546 430q-14 -33 -37.5 -140t-38.5 -209q-29 -195 -156 -289q-29 -21 -70 -37t-78 -16q-62 0 -102.5 37t-40.5 69q0 27 26 48q19 15 25 -3q13 -43 46.5 -69t87.5 -26q55 0 83 21q29 22 50 65t43 140q14 64 29 163h-2q-55 -81 -149 -152q-59 -44 -102 -44q-23 0 -43.5 30
t-20.5 85q0 74 32.5 145.5t84.5 117.5q40 35 100 58.5t117 23.5q21 0 65 -8q30 -6 44 -6zM456 386q-40 16 -81 16q-29 0 -64 -13q-42 -17 -85 -97q-19 -36 -31.5 -86t-12.5 -86q0 -64 30 -64q20 0 52.5 21t60.5 52q74 81 95 123q26 62 36 134z" id="x1D454"></path></g>
</svg></td></tr></table></td></tr><tr class="fig-image" id="b"><td><img alt="875979.fig.0011b" src="https://static.hindawi.com/articles/mpe/volume-2013/875979/figures/875979.fig.0011b.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(b) </b><svg height="11.9625" id="M263" style="vertical-align:-3.3907pt" version="1.1" viewbox="0 0 14.775 11.9625" width="14.775" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,7.675)"><path d="M515 96q-37 -44 -84.5 -76t-71.5 -32q-12 0 -18 7t-6 34t10 75l19 89h-2q-87 -113 -181 -176q-43 -29 -83 -29q-46 0 -46 63q0 31 9 67l52 222q7 36 -1 36q-10 0 -76 -50l-13 24q47 45 92 71.5t67 26.5q18 0 21 -16.5t-8 -65.5l-56 -242q-16 -67 13 -67q41 0 114 74
t114 146l32 145l74 26h11q-52 -199 -80 -347q-8 -39 6 -39q7 0 32 17.5t47 39.5z" id="x1D462"></path></g>
<g transform="matrix(.012,-0,0,-.012,9.213,11.762)"><path d="M387 375q0 -16 -17 -31t-29 -15q-9 0 -12 13q-13 74 -80 74q-36 0 -61 -24.5t-25 -56.5t24 -51.5t68 -19.5q33 0 47 2l2 -7l-32 -42q-20 2 -54 2q-45 0 -74 -21.5t-29 -60.5q0 -41 28 -65.5t73 -24.5q78 0 145 67l17 -23q-33 -47 -84.5 -75t-111.5 -28q-70 0 -114.5 35.5
t-44.5 92.5q0 46 38 78t95 45v2q-35 10 -54.5 33t-19.5 52q0 55 53 88.5t122 33.5q67 0 98.5 -23.5t31.5 -49.5z" id="x1D700"></path></g>
</svg> after 3 iterations.</td></tr></table></td></tr></table>

<table>The wanted and obtained fluid flow on the measurement domain <svg height="15.65" id="M261" style="vertical-align:-3.3907pt" version="1.1" viewbox="0 0 23 15.65" width="23" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.362)"><path d="M719 146l-18 -146h-243l-5 18q2 4 17 25t24 36l25 42t26.5 52.5t21 56.5t16 65t5.5 68q0 121 -55.5 194.5t-149.5 73.5q-95 0 -150 -72t-55 -199q0 -54 18.5 -114t36.5 -94t48.5 -82.5t32.5 -51.5l-7 -18h-244l-17 146l27 1q17 -49 31.5 -62t45.5 -13h89l-21 21t-26 26.5
l-26 29t-28 35.5l-23 37.5t-20.5 43t-12 45.5t-5.5 51q0 133 88 218.5t219 85.5q132 0 218 -83t86 -218q0 -40 -11.5 -78t-33 -71.5t-39 -56t-44 -51t-32.5 -35.5h84q35 0 48 12t31 63z" id="x3A9"></path></g>
<g transform="matrix(.012,-0,0,-.012,12.925,15.45)"><path d="M766 88q-40 -45 -83.5 -72.5t-63.5 -27.5q-39 0 -16 103l49 224q15 68 -10 68q-36 0 -112.5 -78.5t-105.5 -133.5q-27 -101 -38 -165q-35 -4 -77 -18l-6 6q42 153 70 288q12 55 10 78t-19 23q-38 0 -114 -80.5t-101 -131.5q-24 -68 -41 -165q-36 -3 -76 -18l-8 6
q56 202 87 347q7 33 -3 33q-8 0 -31.5 -17.5t-41.5 -35.5l-12 28q42 45 84 72t63 27q44 0 10 -124l-20 -75h2q92 121 193 178q36 21 64 21q62 0 28 -159l-8 -37h2q50 67 103.5 112t94.5 65q39 19 62 19q60 0 23 -156l-45 -189q-9 -39 2 -39q17 0 71 49z" id="x1D45A"></path></g>
</svg>.</table>

Mathematical Problems in Engineering

fig11

Figure 11

Figure 11: Optimization of Injectors Location in a Water Reservoirs Aeration Problem 