Effect of Turbulence Intensity on Cross-Injection Film Cooling at a Stepped or Smooth Endwall of a Gas Turbine Vane Passage

<table>Effect of stepped endwall on averaged effectiveness at low turbulence intensity (<svg height="11.375" id="M87" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 89.112503 11.375" width="89.112503" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.112)"><path d="M631 18l-4 -26q-24 0 -35 1q-57 3 -92.5 23t-69.5 68q-21 30 -101 160q-13 22 -30.5 31t-54.5 9h-32v-159q0 -63 14 -77.5t74 -19.5v-28h-262v28q62 5 76 19.5t14 77.5v402q0 62 -13 76t-73 19v28h248q109 0 159 -34q67 -42 67 -131q0 -115 -127 -172q27 -52 89 -144
q49 -71 81 -104q31 -36 72 -47zM212 316h48q73 0 108 29q55 42 55 124q0 76 -42 112t-104 36q-41 0 -54 -10q-11 -7 -11 -44v-247z" id="x52"></path></g><g transform="matrix(.017,-0,0,-.017,10.619,11.112)"><path d="M380 106l15 -22q-42 -52 -87 -74t-76 -22q-89 0 -142 62t-53 151q0 103 66 175q67 73 146 73h1q61 0 105.5 -46.5t44.5 -105.5q0 -16 -4.5 -22.5t-18.5 -9.5q-54 -10 -262 -17q1 -95 46 -143.5t104 -48.5q61 0 115 50zM225 412q-35 0 -64.5 -32.5t-40.5 -90.5q83 0 170 3
q14 0 19 4.5t5 15.5q1 41 -23.5 70.5t-65.5 29.5z" id="x65"></path></g><g transform="matrix(.017,-0,0,-.017,25.391,11.112)"><path d="M535 323h-483v50h483v-50zM535 138h-483v50h483v-50z" id="x3D"></path></g><g transform="matrix(.017,-0,0,-.017,40.095,11.112)"><path d="M384 0h-275v27q67 5 81.5 18.5t14.5 68.5v385q0 38 -7.5 47.5t-40.5 10.5l-48 2v24q85 15 178 52v-521q0 -55 14.5 -68.5t82.5 -18.5v-27z" id="x31"></path></g><g transform="matrix(.017,-0,0,-.017,48.254,11.112)"><path d="M412 140l28 -9q0 -2 -35 -131h-373v23q112 112 161 170q59 70 92 127t33 115q0 63 -31 98t-86 35q-75 0 -137 -93l-22 20l57 81q55 59 135 59q69 0 118.5 -46.5t49.5 -122.5q0 -62 -29.5 -114t-102.5 -130l-141 -149h186q42 0 58.5 10.5t38.5 56.5z" id="x32"></path></g><g transform="matrix(.017,-0,0,-.017,56.413,11.112)"><path d="M456 178h-96v-72q0 -51 12.5 -62.5t72.5 -16.5v-27h-256v27q65 5 78 17t13 62v72h-260v28q182 271 300 426h40v-407h96v-47zM280 225v295h-2q-107 -148 -196 -295h198z" id="x34"></path></g><g transform="matrix(.017,-0,0,-.017,64.573,11.112)"><path d="M241 635q53 0 94 -28.5t63.5 -76t33.5 -102.5t11 -116q0 -58 -11 -112.5t-34 -103.5t-63.5 -78.5t-94.5 -29.5t-95 28t-64.5 75t-34.5 102.5t-11 118.5q0 58 11.5 112.5t34.5 103t64.5 78t95.5 29.5zM238 602q-32 0 -55.5 -25t-35.5 -68t-17.5 -91t-5.5 -105
q0 -76 10 -138.5t37 -107.5t69 -45q32 0 55.5 25t35.5 68.5t17.5 91.5t5.5 105t-5.5 105.5t-18 92t-36 68t-56.5 24.5z" id="x30"></path></g><g transform="matrix(.017,-0,0,-.017,72.732,11.112)"><path d="M241 635q53 0 94 -28.5t63.5 -76t33.5 -102.5t11 -116q0 -58 -11 -112.5t-34 -103.5t-63.5 -78.5t-94.5 -29.5t-95 28t-64.5 75t-34.5 102.5t-11 118.5q0 58 11.5 112.5t34.5 103t64.5 78t95.5 29.5zM238 602q-32 0 -55.5 -25t-35.5 -68t-17.5 -91t-5.5 -105
q0 -76 10 -138.5t37 -107.5t69 -45q32 0 55.5 25t35.5 68.5t17.5 91.5t5.5 105t-5.5 105.5t-18 92t-36 68t-56.5 24.5z" id="x30"></path></g><g transform="matrix(.017,-0,0,-.017,80.892,11.112)"><path d="M241 635q53 0 94 -28.5t63.5 -76t33.5 -102.5t11 -116q0 -58 -11 -112.5t-34 -103.5t-63.5 -78.5t-94.5 -29.5t-95 28t-64.5 75t-34.5 102.5t-11 118.5q0 58 11.5 112.5t34.5 103t64.5 78t95.5 29.5zM238 602q-32 0 -55.5 -25t-35.5 -68t-17.5 -91t-5.5 -105
q0 -76 10 -138.5t37 -107.5t69 -45q32 0 55.5 25t35.5 68.5t17.5 91.5t5.5 105t-5.5 105.5t-18 92t-36 68t-56.5 24.5z" id="x30"></path></g>
</svg>, <svg height="11.175" id="M88" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 45.0625 11.175" width="45.0625" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.113)"><path d="M998 650l-8 -28q-71 -4 -86 -16t-22 -69l-50 -397q-3 -28 -4.5 -44t2 -29t6.5 -18.5t17 -10.5t24.5 -6.5t37.5 -3.5l-8 -28h-271l7 28q63 6 78 22t25 90l60 415h-2l-353 -552h-23l-130 536h-2l-70 -254q-44 -158 -47 -188q-5 -38 9 -51t71 -18l-6 -28h-241l8 28
q45 4 67 18.5t35 45.5q16 38 74 233l52 173q24 79 11.5 98t-89.5 26l6 28h177l136 -508l337 508h172z" id="x1D440"></path></g><g transform="matrix(.017,-0,0,-.017,22.127,11.113)"><path d="M535 323h-483v50h483v-50zM535 138h-483v50h483v-50z" id="x3D"></path></g><g transform="matrix(.017,-0,0,-.017,36.831,11.113)"><path d="M384 0h-275v27q67 5 81.5 18.5t14.5 68.5v385q0 38 -7.5 47.5t-40.5 10.5l-48 2v24q85 15 178 52v-521q0 -55 14.5 -68.5t82.5 -18.5v-27z" id="x31"></path></g>
</svg>, and <svg height="12.1375" id="M89" style="vertical-align:-0.4368pt" version="1.1" viewbox="0 0 76.625 12.1375" width="76.625" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.537)"><path d="M592 498l-30 -3q-13 63 -31 89q-13 19 -33.5 25.5t-75.5 6.5h-70v-493q0 -60 16 -75.5t86 -19.5v-28h-286v28q68 4 83.5 19.5t15.5 75.5v493h-62q-60 0 -83 -7t-33 -24q-12 -17 -32 -90h-29q10 116 12 180h20q10 -16 21 -20.5t34 -4.5h395q19 0 28.5 5t21.5 20h21
q2 -89 11 -177z" id="x54"></path></g><g transform="matrix(.017,-0,0,-.017,10.551,11.537)"><path d="M113 -12q-24 0 -39.5 16t-15.5 42q0 24 16 40.5t40 16.5t40 -16.5t16 -40.5q0 -26 -16 -42t-41 -16z" id="x2E"></path></g><g transform="matrix(.017,-0,0,-.017,14.426,11.537)"><path d="M303 0h-265v28q62 5 76 19.5t14 77.5v400q0 63 -14 77.5t-76 19.5v28h265v-28q-62 -5 -76 -19.5t-14 -77.5v-400q0 -64 14 -78t76 -19v-28z" id="x49"></path></g><g transform="matrix(.017,-0,0,-.017,20.223,11.537)"><path d="M113 -12q-24 0 -39.5 16t-15.5 42q0 24 16 40.5t40 16.5t40 -16.5t16 -40.5q0 -26 -16 -42t-41 -16z" id="x2E"></path></g><g transform="matrix(.017,-0,0,-.017,28.807,11.537)"><path d="M535 323h-483v50h483v-50zM535 138h-483v50h483v-50z" id="x3D"></path></g><g transform="matrix(.017,-0,0,-.017,43.511,11.537)"><path d="M384 0h-275v27q67 5 81.5 18.5t14.5 68.5v385q0 38 -7.5 47.5t-40.5 10.5l-48 2v24q85 15 178 52v-521q0 -55 14.5 -68.5t82.5 -18.5v-27z" id="x31"></path></g><g transform="matrix(.017,-0,0,-.017,51.671,11.537)"><path d="M113 -12q-24 0 -39.5 16t-15.5 42q0 24 16 40.5t40 16.5t40 -16.5t16 -40.5q0 -26 -16 -42t-41 -16z" id="x2E"></path></g><g transform="matrix(.017,-0,0,-.017,55.546,11.537)"><path d="M249 635q70 0 116 -43t46 -105q0 -46 -28 -80q-22 -25 -80 -64q62 -35 97 -75t35 -99q0 -81 -63 -131t-135 -50q-83 0 -137.5 45.5t-54.5 123.5q0 52 45 95q29 28 89 64q-109 62 -109 155q0 66 50.5 115t128.5 49zM238 603q-42 0 -67.5 -31t-25.5 -72q0 -50 32.5 -79.5
t98.5 -62.5q61 48 61 124q0 59 -29.5 90t-69.5 31zM248 20q46 0 76.5 33.5t30.5 89.5q0 50 -39 85.5t-110 71.5q-81 -54 -81 -137q0 -67 35.5 -105t87.5 -38z" id="x38"></path></g><g transform="matrix(.017,-0,0,-.017,63.706,11.537)"><path d="M594 629l-404 -661l-31 23l402 661zM194 635q70 0 107 -56t37 -125t-37.5 -125.5t-107.5 -56.5t-107 56.5t-37 124.5q0 70 37.5 126t107.5 56zM193 605q-28 0 -45 -29t-21.5 -59.5t-4.5 -62.5t4.5 -63t22 -60t45.5 -29q22 0 37.5 16t22 42t9 48t2.5 45q0 152 -72 152z
M567 351q69 0 106 -56t37 -125t-37 -125.5t-107 -56.5t-107.5 56.5t-37.5 124.5q0 43 14.5 83t49 69.5t82.5 29.5zM566 322q-28 0 -45 -28.5t-22 -59.5t-5 -64q0 -23 3 -46t10.5 -48.5t23 -41.5t36.5 -16q28 0 45 29.5t21 59.5t4 62q0 24 -2.5 46.5t-9.5 48.5t-22 42t-37 16
z" id="x25"></path></g>
</svg>).</table>

The Scientific World Journal

fig17

Figure 17

Figure 17: Effect of Turbulence Intensity on Cross-Injection Film Cooling at a Stepped or Smooth Endwall of a Gas Turbine Vane Passage 