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<6165726F64796E616D6963616C6C7920> Tj 1 0 0 1 445.44 499.68 Tm <736861727020> Tj 1 0 0 1 467.04 499.68 Tm <626F6469657320> Tj 1 0 0 1 492.72 499.44 Tm <617420> Tj 1 0 0 1 501.36 499.44 Tm <7A65726F> Tj 0.48 Tc 1 0 0 1 87.84 490.32 Tm <696E636964656E63652C20> Tj 1 0 0 1 126.24 490.32 Tm <6576656E20> Tj 1 0 0 1 145.44 490.32 Tm <74686F75676820> Tj 1 0 0 1 172.56 490.32 Tm <7468657920> Tj 1 0 0 1 190.56 490.32 Tm <61726520> Tj 1 0 0 1 203.76 490.56 Tm <67656F6D6574726963616C6C7920> Tj 1 0 0 1 254.16 490.08 Tm <626C756E742E20> Tj 1 0 0 1 279.84 490.08 Tm <43616C63756C6174696F6E7320> Tj 1 0 0 1 326.16 489.84 Tm <73686F7720> Tj 1 0 0 1 346.80 489.84 Tm <7468617420> Tj 1 0 0 1 362.64 489.84 Tm <74686520> Tj 1 0 0 1 375.60 490.32 Tm <70CD65737375726520> Tj 1 0 0 1 407.76 490.08 Tm <6772616469656E7420> Tj 1 0 0 1 439.20 489.84 Tm <666F6C6C6F777320> Tj 1 0 0 1 468.00 489.60 Tm <7468617420> Tj 1 0 0 1 483.84 489.84 Tm <707265646963746564> Tj 0.48 Tc 1 0 0 1 87.36 480.00 Tm <627620> Tj 1 0 0 1 98.64 480.24 Tm <74686520> Tj 1 0 0 1 111.60 480.24 Tm <4E6577746F6E69616E20> Tj 1 0 0 1 152.40 480.00 Tm <7468656F727620> Tj 1 0 0 1 177.60 480.24 Tm <666F7220> Tj 1 0 0 1 189.84 480.00 Tm <74686520> Tj 1 0 0 1 203.04 480.24 Tm <666C6F7720> Tj 1 0 0 1 221.28 480.00 Tm <636F6E646974696F6E7320> Tj 1 0 0 1 259.92 480.00 Tm <636F6E736964657265642E> Tj 0.72 Tc /F3 11.0 Tf 1 0 0 1 255.84 443.52 Tm <494E54524F44554354494F4E> Tj 0.48 Tc /F3 9.0 Tf 1 0 0 1 86.64 420.72 Tm <54686520> Tj 1 0 0 1 105.60 420.72 Tm <7375636365737366756C20> Tj 1 0 0 1 149.04 420.48 Tm <64657369676E20> Tj 1 0 0 1 177.60 420.48 Tm <6F6620> Tj 1 0 0 1 188.88 420.72 Tm <686967682D6C6966742C20> Tj 1 0 0 1 226.80 420.48 Tm <6C6F772D6472616720> Tj 1 0 0 1 264.72 420.48 Tm <6879706572736F6E726320> Tj 1 0 0 1 310.56 420.24 Tm <636F6E66696775726174726F6E7320> Tj 1 0 0 1 369.84 420.48 Tm <7276696C6C20> Tj 1 0 0 1 388.32 420.00 Tm <646570656E6420> Tj 1 0 0 1 419.52 420.00 Tm <6F6E20> Tj 1 0 0 1 432.00 420.00 Tm <74686520> Tj 1 0 0 1 447.12 419.76 Tm <6162696C69747920> Tj 1 0 0 1 475.20 419.76 Tm <746F20> Tj 1 0 0 1 486.00 419.76 Tm <696E636F72706F72617465> Tj 0.48 Tc 1 0 0 1 73.20 409.44 Tm <72656C61746976656C7920> Tj 1 0 0 1 114.48 409.20 Tm <736861727020> Tj 1 0 0 1 139.92 409.44 Tm <6C656164696E6720> Tj 1 0 0 1 172.32 409.20 Tm <656467657320> Tj 1 0 0 1 198.24 409.20 Tm <7468617420> Tj 1 0 0 1 217.20 409.20 Tm <636F6D62696E6520> Tj 1 0 0 1 254.40 409.44 Tm <676F6F6420> Tj 1 0 0 1 277.68 408.96 Tm <6165726F6369796E616D696320> Tj 1 0 0 1 331.68 409.44 Tm <70726F7065727469657320> Tj 1 0 0 1 374.64 408.96 Tm <752C69746820> Tj 1 0 0 1 395.76 408.72 Tm <61636365707461626C6520> Tj 1 0 0 1 440.64 408.48 Tm <68656174726E6720> Tj 1 0 0 1 473.04 408.48 Tm <72617465732E20> Tj 1 0 0 1 502.32 408.24 Tm <4365727461696E> Tj 0.48 Tc 1 0 0 1 73.20 398.40 Tm <636F6E66696775726174696F6E732C20> Tj 1 0 0 1 137.04 398.16 Tm <7375636820> Tj 1 0 0 1 159.36 398.16 Tm <617320> Tj 1 0 0 1 171.84 398.16 Tm <6879706572736F6E696320> Tj 1 0 0 1 218.88 398.16 Tm <776176657269646572732C20> Tj 1 0 0 1 268.32 397.92 Tm <61726520> Tj 1 0 0 1 284.16 397.92 Tm <64657369676E656420> Tj 1 0 0 1 323.04 397.68 Tm <616E616C79746963616C6C6C2C20> Tj 1 0 0 1 372.72 397.92 Tm <2A2772746820> Tj 1 0 0 1 394.08 397.68 Tm <696E66696EEC74656C7920> Tj 1 0 0 1 433.92 397.44 Tm <736861727020> Tj 1 0 0 1 459.60 397.44 Tm <6C656164696E6720> Tj 1 0 0 1 492.72 397.20 Tm <656467657320> Tj 1 0 0 1 519.36 397.20 Tm <666F72> Tj 0.48 Tc 1 0 0 1 73.44 386.88 Tm <73686F636B20> Tj 1 0 0 1 98.88 386.88 Tm <7761766520> Tj 1 0 0 1 121.92 386.88 Tm <6174746163686D656E742E20> Tj 1 0 0 1 172.80 386.88 Tm <486F77657665722C20> Tj 1 0 0 1 213.36 386.64 Tm <7665727920> Tj 1 0 0 1 233.04 386.64 Tm <736861727020> Tj 1 0 0 1 256.80 386.64 Tm <6C656164696E6720> Tj 1 0 0 1 287.76 386.40 Tm <656467657320> Tj 1 0 0 1 312.24 386.40 Tm <61726520> Tj 1 0 0 1 326.40 386.40 Tm <6E6F7420> Tj 1 0 0 1 341.28 386.64 Tm <70726163746963616C20> Tj 1 0 0 1 377.76 386.40 Tm <666F7220> Tj 1 0 0 1 391.44 386.16 Tm <6120> Tj 1 0 0 1 397.92 386.16 Tm <6E756D62657220> Tj 1 0 0 1 430.32 386.16 Tm <6F66726561736F6E733A20> Tj 1 0 0 1 475.68 386.40 Tm <28492920> Tj 1 0 0 1 489.60 385.68 Tm <7665727920> Tj 1 0 0 1 509.28 385.68 Tm <7368617270> Tj 0.48 Tc 1 0 0 1 73.44 375.84 Tm <6C656164696E6720> Tj 1 0 0 1 106.08 375.84 Tm <656467657320> Tj 1 0 0 1 132.24 375.60 Tm <61726520> Tj 1 0 0 1 148.08 375.60 Tm <646966666963756C7420> Tj 1 0 0 1 183.12 375.60 Tm <746F20> Tj 1 0 0 1 194.64 375.60 Tm <6D616E75666163747572652C20> Tj 1 0 0 1 249.84 376.08 Tm <28322920> Tj 1 0 0 1 264.96 375.36 Tm <736F6D6520> Tj 1 0 0 1 288.96 375.36 Tm <626C756E74696E6720> Tj 1 0 0 1 325.44 375.36 Tm <697320> Tj 1 0 0 1 335.52 375.36 Tm <726571756972656420> Tj 1 0 0 1 371.76 375.12 Tm <666F7220> Tj 1 0 0 1 387.12 375.12 Tm <7374727563747572616C20> Tj 1 0 0 1 427.68 375.12 Tm <737472656E6774682C20> Tj 1 0 0 1 465.36 374.88 Tm <616E6420> Tj 1 0 0 1 483.36 375.12 Tm <28332920> Tj 1 0 0 1 498.48 374.64 Tm <74686520> Tj 1 0 0 1 514.32 374.64 Tm <6C72656174> Tj 0.48 Tc 1 0 0 1 72.96 364.56 Tm <7472616E7366657220> Tj 1 0 0 1 105.60 364.32 Tm <746F20> Tj 1 0 0 1 115.92 364.32 Tm <736861727020> Tj 1 0 0 1 139.92 364.32 Tm <6C656164696E6720> Tj 1 0 0 1 171.12 364.32 Tm <656467657320> Tj 1 0 0 1 195.84 364.32 Tm <617420> Tj 1 0 0 1 205.20 364.32 Tm <6869676820> Tj 1 0 0 1 225.12 364.32 Tm <4D61636820> Tj 1 0 0 1 249.36 364.32 Tm <6E756D6265727320> Tj 1 0 0 1 285.12 364.08 Tm <697320> Tj 1 0 0 1 294.48 364.08 Tm <7365766572652E> Tj 0.48 Tc 1 0 0 1 86.40 353.28 Tm <54686520> Tj 1 0 0 1 104.64 353.28 Tm <75736520> Tj 1 0 0 1 120.48 353.04 Tm <6F66626C756E742D6E6F736520> Tj 1 0 0 1 175.44 353.04 Tm <73686170657320> Tj 1 0 0 1 204.24 353.04 Tm <74656E647320> Tj 1 0 0 1 227.28 353.04 Tm <746F20> Tj 1 0 0 1 237.84 353.04 Tm <616C6C65766961746520> Tj 1 0 0 1 273.36 352.80 Tm <74686520> Tj 1 0 0 1 288.24 352.80 Tm <6165726F64796E616D696320> Tj 1 0 0 1 340.80 352.56 Tm <68656174696E6720> Tj 1 0 0 1 372.00 353.04 Tm <70726F626C656D20> Tj 1 0 0 1 407.52 352.32 Tm <73696E636520> Tj 1 0 0 1 430.08 352.32 Tm <74686520> Tj 1 0 0 1 444.72 352.32 Tm <6865617420> Tj 1 0 0 1 463.68 352.08 Tm <7472616E7366657220> Tj 1 0 0 1 496.80 352.08 Tm <666F7220> Tj 1 0 0 1 510.48 351.84 Tm <626C756E74> Tj 0.48 Tc 1 0 0 1 72.72 342.24 Tm <626F6469657320> Tj 1 0 0 1 102.00 342.24 Tm <697320> Tj 1 0 0 1 110.88 342.24 Tm <66617220> Tj 1 0 0 1 124.56 342.24 Tm <6C6F77657220> Tj 1 0 0 1 149.52 342.24 Tm <7468616E20> Tj 1 0 0 1 168.96 342.24 Tm <7468617420> Tj 1 0 0 1 186.48 342.24 Tm <666F7220> Tj 1 0 0 1 200.64 342.00 Tm <73686172706C7920> Tj 1 0 0 1 231.84 342.48 Tm <706F696E74656420> Tj 1 0 0 1 263.76 342.00 Tm <626F64EC65732E20> Tj 1 0 0 1 297.36 341.76 Tm <496E20> Tj 1 0 0 1 307.68 341.76 Tm <6164646974696F6E2C20> Tj 1 0 0 1 344.64 341.76 Tm <74686520> Tj 1 0 0 1 359.04 341.76 Tm <726564756374696F6E20> Tj 1 0 0 1 398.64 341.52 Tm <726E20> Tj 1 0 0 1 408.96 341.52 Tm <68656174EC6E6720> Tj 1 0 0 1 440.40 341.28 Tm <7261746520> Tj 1 0 0 1 457.92 341.28 Tm <666F7220> Tj 1 0 0 1 472.08 341.04 Tm <6120> Tj 1 0 0 1 479.04 341.04 Tm <626C756E7420> Tj 1 0 0 1 501.84 341.04 Tm <626F647920> Tj 1 0 0 1 523.92 341.04 Tm <6973> Tj 0.48 Tc 1 0 0 1 73.20 330.96 Tm <6163636F6D70616E69656420> Tj 1 0 0 1 127.68 330.96 Tm <627920> Tj 1 0 0 1 140.64 330.72 Tm <616E20> Tj 1 0 0 1 152.88 330.72 Tm <696E63726561736520> Tj 1 0 0 1 187.68 330.72 Tm <696E20> Tj 1 0 0 1 198.72 330.72 Tm <6865617420> Tj 1 0 0 1 217.92 330.72 Tm <63617061636974792C20> Tj 1 0 0 1 255.36 330.48 Tm <64756520> Tj 1 0 0 1 272.16 330.48 Tm <746F20> Tj 1 0 0 1 282.48 330.48 Tm <74686520> Tj 1 0 0 1 297.36 330.48 Tm <696E6372656173656420> Tj 1 0 0 1 337.20 330.24 Tm <766F6C756D652E20> Tj 1 0 0 1 374.64 330.24 Tm <44756520> Tj 1 0 0 1 393.36 330.24 Tm <6D61EC6E697920> Tj 1 0 0 1 423.60 330.00 Tm <746F20> Tj 1 0 0 1 433.92 330.00 Tm <6D616E75666163747572696E6720> Tj 1 0 0 1 494.16 330.00 Tm <70726F626C656D73> Tj 0.48 Tc 1 0 0 1 73.20 319.68 Tm <616E6420> Tj 1 0 0 1 92.16 319.68 Tm <74686520> Tj 1 0 0 1 109.68 319.68 Tm <65787472656D656C7920> Tj 1 0 0 1 153.60 319.68 Tm <6869676820> Tj 1 0 0 1 176.16 319.44 Tm <74656D70657261747572657320> Tj 1 0 0 1 231.84 319.44 Tm <61747461696E656420> Tj 1 0 0 1 267.60 319.44 Tm <696E20> Tj 1 0 0 1 279.84 319.20 Tm <6879706572736F6E696320> Tj 1 0 0 1 327.84 319.20 Tm <666C696768742C20> Tj 1 0 0 1 356.40 319.20 Tm <6879706572736F6E696320> Tj 1 0 0 1 404.16 318.96 Tm <76656869636C657320> Tj 1 0 0 1 441.36 318.72 Tm <77696C6C20> Tj 1 0 0 1 461.52 318.72 Tm <6861766520> Tj 1 0 0 1 484.80 318.48 Tm <626C756E7420> Tj 1 0 0 1 510.00 318.48 Tm <6E6F73652C> Tj 0.48 Tc 1 0 0 1 73.20 308.64 Tm <616C74686F75676820> Tj 1 0 0 1 111.36 308.88 Tm <70726F6261626C7920> Tj 1 0 0 1 150.96 308.40 Tm <736C656E646572696E6720> Tj 1 0 0 1 195.84 308.40 Tm <6F757420> Tj 1 0 0 1 212.64 308.40 Tm <617420> Tj 1 0 0 1 223.68 308.40 Tm <6120> Tj 1 0 0 1 232.32 308.40 Tm <73686F727420> Tj 1 0 0 1 255.84 308.16 Tm <64697374616E636520> Tj 1 0 0 1 291.84 308.16 Tm <66726F6D20> Tj 1 0 0 1 314.64 307.92 Tm <74686520> Tj 1 0 0 1 330.48 308.16 Tm <6E6F73652220> Tj 1 0 0 1 359.04 308.16 Tm <5468657265666F72652C20> Tj 1 0 0 1 404.40 307.68 Tm <64657372676E696E6720> Tj 1 0 0 1 446.40 307.44 Tm <6120> Tj 1 0 0 1 455.04 307.68 Tm <6879706572736F6E696320> Tj 1 0 0 1 502.32 307.44 Tm <76656869636C65> Tj 0.48 Tc 1 0 0 1 73.20 297.60 Tm <69656164696E6720> Tj 1 0 0 1 105.36 297.36 Tm <6564676520> Tj 1 0 0 1 126.96 297.36 Tm <726E766F6976657320> Tj 1 0 0 1 163.68 297.36 Tm <6120> Tj 1 0 0 1 170.64 297.36 Tm <74726164656F666620> Tj 1 0 0 1 204.72 297.12 Tm <6265747765656E20> Tj 1 0 0 1 240.48 297.12 Tm <6D616B696E6720> Tj 1 0 0 1 272.64 296.88 Tm <74686520> Tj 1 0 0 1 288.24 296.88 Tm <6C656164696E6720> Tj 1 0 0 1 319.68 296.64 Tm <6564676520> Tj 1 0 0 1 341.04 296.64 Tm <736861727020> Tj 1 0 0 1 365.52 296.64 Tm <656E6F75676820> Tj 1 0 0 1 397.20 296.64 Tm <746F20> Tj 1 0 0 1 408.00 296.64 Tm <6F627461696E20> Tj 1 0 0 1 435.60 296.40 Tm <61636365707461626C6520> Tj 1 0 0 1 480.24 296.16 Tm <6165726F646C6D616D6963> Tj 0.48 Tc 1 0 0 1 72.96 286.08 Tm <616E6420> Tj 1 0 0 1 89.52 286.56 Tm <70726F70756C73696F6E20> Tj 1 0 0 1 134.40 285.84 Tm <656666696369656E637920> Tj 1 0 0 1 175.92 285.84 Tm <616E6420> Tj 1 0 0 1 192.48 285.84 Tm <626C756E7420> Tj 1 0 0 1 215.28 285.84 Tm <656E6F75676820> Tj 1 0 0 1 246.00 285.84 Tm <746F20> Tj 1 0 0 1 256.08 285.84 Tm <72656475636520> Tj 1 0 0 1 284.40 285.60 Tm <74686520> Tj 1 0 0 1 299.04 285.60 Tm <6165726F64796E616D696320> Tj 1 0 0 1 351.36 285.36 Tm <68656174726E6720> Tj 1 0 0 1 382.56 285.36 Tm <696E20> Tj 1 0 0 1 392.40 285.36 Tm <74686520> Tj 1 0 0 1 406.80 285.36 Tm <737461676E6174746F6E20> Tj 1 0 0 1 449.28 285.36 Tm <706F696E742E> Tj 0.48 Tc 1 0 0 1 86.40 274.32 Tm <506F77657220> Tj 1 0 0 1 116.16 274.32 Tm <6C617720> Tj 1 0 0 1 134.40 274.08 Tm <73686170656420> Tj 1 0 0 1 166.08 274.32 Tm <6C656164696E6720> Tj 1 0 0 1 198.96 274.08 Tm <656467657320> Tj 1 0 0 1 225.36 274.56 Tm <287920> Tj 1 0 0 1 237.36 275.04 Tm <636320> Tj 1 0 0 1 247.68 273.84 Tm Tj 1 0 0 1 262.80 273.84 Tm <3020> Tj 1 0 0 1 271.68 274.80 Tm <3C20> Tj 1 0 0 1 281.28 273.84 Tm <696C20> Tj 1 0 0 1 290.40 274.80 Tm <3C20> Tj 1 0 0 1 301.20 273.84 Tm <6C2920> Tj 1 0 0 1 312.48 273.84 Tm <6D617920> Tj 1 0 0 1 333.36 274.08 Tm <70726F7669646520> Tj 1 0 0 1 367.44 273.60 Tm <74686520> Tj 1 0 0 1 383.76 273.60 Tm <726571756972656420> Tj 1 0 0 1 420.24 273.36 Tm <626C756E746E65737320> Tj 1 0 0 1 461.76 273.12 Tm <666F7220> Tj 1 0 0 1 477.12 273.12 Tm <6865617420> Tj 1 0 0 1 498.00 272.88 Tm <7472616E736665722C> Tj 0.48 Tc 1 0 0 1 72.72 263.28 Tm <6D616E75666163747572696E6720> Tj 1 0 0 1 133.68 263.04 Tm <616E6420> Tj 1 0 0 1 150.72 263.04 Tm <68616E646C696E6720> Tj 1 0 0 1 188.16 263.04 Tm <636F6E6365726E7320> Tj 1 0 0 1 226.08 263.04 Tm <7769746820> Tj 1 0 0 1 246.24 262.80 Tm <7265647563656420> Tj 1 0 0 1 280.32 262.56 Tm <6465706172747572657320> Tj 1 0 0 1 323.76 262.56 Tm <66726F6D20> Tj 1 0 0 1 345.60 262.56 Tm <696465616C20> Tj 1 0 0 1 367.92 262.32 Tm <6165726F646C2C6E616D696320> Tj 1 0 0 1 420.72 262.56 Tm <706572666F726D616E63652E20> Tj 1 0 0 1 479.28 261.84 Tm <5468EC7320> Tj 1 0 0 1 499.92 261.60 Tm <636F727263657074> Tj 0.48 Tc 1 0 0 1 72.72 252.00 Tm <697320> Tj 1 0 0 1 82.80 252.00 Tm <626173656420> Tj 1 0 0 1 109.20 252.00 Tm <6F6E20> Tj 1 0 0 1 122.16 252.00 Tm <74686520> Tj 1 0 0 1 138.24 252.00 Tm <776F726B20> Tj 1 0 0 1 162.00 251.76 Tm <6F6620> Tj 1 0 0 1 173.52 252.00 Tm <4D61736F6E20> Tj 1 0 0 1 203.76 251.76 Tm <616E6420> Tj 1 0 0 1 221.28 251.76 Tm <4C656520> Tj 1 0 0 1 239.76 249.84 Tm <5B315D2C20> Tj 1 0 0 1 256.80 251.76 Tm <77686F20> Tj 1 0 0 1 276.96 251.52 Tm <6861766520> Tj 1 0 0 1 298.32 251.76 Tm <706F696E74656420> Tj 1 0 0 1 331.44 251.28 Tm <6F757420> Tj 1 0 0 1 347.28 251.28 Tm <746861742C20> Tj 1 0 0 1 367.92 251.28 Tm <666F7220> Tj 1 0 0 1 382.80 251.04 Tm <6365727461696E20> Tj 1 0 0 1 412.80 251.04 Tm <6578706F6E656E74732E20> Tj 1 0 0 1 458.40 251.28 Tm <706F77657220> Tj 1 0 0 1 486.72 250.80 Tm <6C617720> Tj 1 0 0 1 504.24 250.56 Tm <736861706573> Tj 0.48 Tc 1 0 0 1 72.96 240.72 Tm <6578686962697420> Tj 1 0 0 1 102.96 240.48 Tm <6165726F64796E616D696320> Tj 1 0 0 1 156.24 240.96 Tm <70726F7065727469657320> Tj 1 0 0 1 198.24 240.48 Tm <73696D696C617220> Tj 1 0 0 1 227.76 240.48 Tm <746F20> Tj 1 0 0 1 237.84 240.72 Tm <67656F6D6574726963616C6C7920> Tj 1 0 0 1 294.00 240.00 Tm <736861727020> Tj 1 0 0 1 317.76 240.00 Tm <7368617065732E20> Tj 1 0 0 1 351.12 240.00 Tm <5468657920> Tj 1 0 0 1 373.92 239.76 Tm <73756767657374656420> Tj 1 0 0 1 414.72 239.76 Tm <74686520> Tj 1 0 0 1 429.12 240.00 Tm <706F73736962696C69747920> Tj 1 0 0 1 472.80 239.28 Tm <6F6620> Tj 1 0 0 1 483.60 239.28 Tm <6120> Tj 1 0 0 1 490.56 239.28 Tm <646966666572656E6365> Tj 0.48 Tc 1 0 0 1 72.72 229.44 Tm <6265747765656E20> Tj 1 0 0 1 108.72 229.44 Tm <73686170657320> Tj 1 0 0 1 137.76 229.20 Tm <7468617420> Tj 1 0 0 1 155.76 229.20 Tm <61726520> Tj 1 0 0 1 170.40 229.68 Tm <67656F6D6574726963616C6C7920> Tj 1 0 0 1 226.80 229.20 Tm <736861727020> Tj 1 0 0 1 251.04 228.96 Tm <616E6420> Tj 1 0 0 1 268.08 228.96 Tm <73686170657320> Tj 1 0 0 1 296.64 228.72 Tm <7468617420> Tj 1 0 0 1 313.92 228.72 Tm <62656861766520> Tj 1 0 0 1 344.64 228.72 Tm <6165726F64796E616D6963616C6C7920> Tj 1 0 0 1 412.32 228.48 Tm <617320> Tj 1 0 0 1 423.36 228.48 Tm <696620> Tj 1 0 0 1 432.24 228.24 Tm <7468657920> Tj 1 0 0 1 451.92 228.24 Tm <7765726520> Tj 1 0 0 1 474.00 228.00 Tm <73686172702E20> Tj 1 0 0 1 503.76 228.00 Tm <4D61736F6E> Tj 0.72 Tc 1 0 0 1 72.96 218.40 Tm <616E6420> Tj 1 0 0 1 90.48 218.40 Tm <4C656520> Tj 1 0 0 1 107.76 216.48 Tm <5B315D20> Tj 1 0 0 1 121.44 218.16 Tm <73686F77656420> Tj 1 0 0 1 154.08 218.16 Tm <7468617420> Tj 1 0 0 1 171.60 218.16 Tm <666F7220> Tj 1 0 0 1 185.52 218.16 Tm <76616C75657320> Tj 1 0 0 1 213.36 218.16 Tm <6F663020> Tj 1 0 0 1 231.36 219.12 Tm <3C20> Tj 1 0 0 1 239.76 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Rarefed Hypersonic Flow over Power Law Shaped Leading Edges Wilson F. N. Santos. and Mark J. Lewis'Combustion and Propulsion Laboratory, INPE, Cachoeira Paulsta, SP 12630-000, BrazilrDepartmen of Aerospace Engineering, Universig, of Maryland, Coltege Park, MD 20742, USAAbstract. This paper deals with a numerical study of the aerodynamic surface quantities on power law shaped leadingedgessituatedinararefiedhlpersonicflow. Thesensitivityoftheheatfluxto,andpressuregradientonthebodysurfacedue to changes in the angle of attack is investigated by using a Direct Simulation Monte Carlo method. A method thathas demonstrated to yield excellent comparisons with fight- and ground-test data, and that properly accounts fornonequilibrium aspects of the flow that arise near the nose of the leading edges. The work is motivated by the Newtonianflow theory that predicts that certain classes ofpower-law leading edges behave as aerodynamically sharp bodies at zeroincidence, even though they are geometrically blunt. Calculations show that the pessure gradient follows that predictedbv the Newtonian theorv for the flow conditions considered. INTRODUCTIONThe successful design of high-lift, low-drag hypersonrc configuratrons rvill depend on the ability to incorporaterelatively sharp leading edges that combine good aerociynamic properties u,ith acceptable heatrng rates. Certainconfigurations, such as hypersonic waveriders, are designed analyticalll, *'rth infintely sharp leading edges forshock wave attachment. However, very sharp leading edges are not practical for a number ofreasons: (I) very sharpleading edges are difficult to manufacture, (2) some blunting is required for structural strength, and (3) the lreattransfer to sharp leading edges at high Mach numbers is severe.The use ofblunt-nose shapes tends to alleviate the aerodynamic heating problem since the heat transfer for bluntbodies is far lower than that for sharply pointed bodes. In addition, the reduction rn heatng rate for a blunt body isaccompanied by an increase in heat capacity, due to the increased volume. Due maniy to manufacturing problemsand the extremely high temperatures attained in hypersonic flight, hypersonic vehicles will have blunt nose,although probably slendering out at a short distance from the nose" Therefore, desrgning a hypersonic vehicleieading edge rnvoives a tradeoff between making the leading edge sharp enough to obtain acceptable aerodlmamicand propulsion efficiency and blunt enough to reduce the aerodynamic heatrng in the stagnatton point.Power law shaped leading edges (y cc ', 0 < il < l) may provide the required bluntness for heat transfer,manufacturing and handling concerns with reduced departures from ideal aerodl,namic performance. Ths corrceptis based on the work of Mason and Lee [1], who have pointed out that, for certain exponents. power law shapesexhibit aerodynamic properties similar to geometrically sharp shapes. They suggested the possibility of a differencebetween shapes that are geometrically sharp and shapes that behave aerodynamically as if they were sharp. Masonand Lee [1] showed that for values of0 < n< 112, the leading-edge radius ofcurvature goes to infinite atthe nose, aeharacteristc of a blunt shape. For values of 112 < n < 1 the leading-edge radius of curvature approaches zero at thenose, a charactenstic of a sharp shape. Furthernore, for 213 < n < 7 . their computational investigation predicts thatthe derivatrve of the pressure coefficient with respect to the body coordinate dC,/ds approaches -o at x : 0. acharacteristic of a sharp body. 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23960 endobj 16 0 obj << /Length 17 0 R >> stream The sensitivity ofboth the pressure gradient and the stagnation point heating to shape variations ofsuch leadingedges was investigated by Santos and Lewis [2] for the idealized situation of two-dimensional rarefied hypersonicflow at zero angle of incidence. Through the use of Direct Simulation Monte Carlo (DSMC) method, they showedthat the pressure gradent on the power law shapes in a rarefied environment is in surprising agreement with thatobtained by Mason and Lee [ ] by emplolng Newtonian analysis. It was found that the pressure gradient along thebodysurfacegoestozeroatthenoseoftheleadingedgeforn<2l3,acharacteristicsofbluntbody. Itisfiniteforn: 213 and goes to minus infinite for n > 213, a characteristic of sharp body. Santos and Lewis [2] also found that thestagnation point heating behavior for power iaw leading edges with finite radius of curvature (n : 1 /2), followed thatpredicted for lassial blunt body, i.e., the heating rate on blunt bodies scales inversely wth the square root ofstagnation point radius. For those power lav/ leading edges with zero radii of curvature fu> 112). the stagnationpoint heating is not a function of the curvature radius in the vicinity of the leading edges, but agrees witlr thelassical blunt body behavior predicted by the continuum far from the stagnation pont.The purpose of this work is to investigate the impact of the angle of attack on the behavior of the pressuregradient and the stagnaton point heating. For positive angle of attack, important clranges occur in the flowfieldstructure and in the aerodynamic surface quantities on blunt leading edges. This involves the modification of theflowfield properties and shock strength and, consequently, some effects on aerodynamic forces acting on, and onheat transfer to the body surface. Moreover, the knowledge of these properties at zero angle of attack is notsufficient to predict with certainty the flow characteristics over these shapes with incidence. ln this context, theessential characteristics ofthe angle ofattack effect on both pressure gradient and stagnation point heating will beexamined for power law bodies defined by exponents of 112, 213 and 314. and posrtrve angle of attack witlr 5, 8 and12 degree of incidence. In the current study, DSMC method will be employed to calculate the rarefied hypersonictwo-dimensional flow. LEADING EDGE GEOMETRY DEFINITIONThe power-law shapes, y = ax", are modeled by assuming a sharp leading edge of half angle with a circularcylinder of radius R inscribed tangent to this wedge. The power law shapes, inscribed between the wedge and thecylinder, are also tangent to the wedge and the cylinder at the same common point where they have tlre same slopeangle. It was assumed that the leading edge half angle is 10o, a circuiar cylinder diameter of l0-2m and power lawexponents of | 12,2/3, and 3/4. Figure I illustrates schematically this construction for this set of power law leadingedees. FIGURE 1, Drawing illustrating the leading edge geometry.From geometric considerations, the power law constant rz is obtained by matching slope on the wedge, circularcylinder and power law body at the tangency point. The common bociy herght ff at the tangency point is equal to2RcosA and the body length I from the nose to the tangency point rn the axrs of symmetry rs given by nHl2tan0. 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<6C696E65617220> Tj 1 0 0 1 217.44 621.36 Tm <64696D656E73696F6E7320> Tj 1 0 0 1 264.48 621.36 Tm <6F6620> Tj 1 0 0 1 275.28 621.36 Tm <74686520> Tj 1 0 0 1 290.16 621.36 Tm <63656C6C7320> Tj 1 0 0 1 310.80 621.36 Tm <73686F756C6420> Tj 1 0 0 1 339.12 621.36 Tm <626520> Tj 1 0 0 1 351.60 621.36 Tm <736D616C6C20> Tj 1 0 0 1 375.36 621.36 Tm <696E20> Tj 1 0 0 1 385.92 621.36 Tm <636F6D70617269736F6E20> Tj 1 0 0 1 434.16 621.36 Tm <7769746820> Tj 1 0 0 1 454.56 621.36 Tm <74686520> Tj 1 0 0 1 469.44 621.36 Tm <7363616C6520> Tj 1 0 0 1 492.00 621.36 Tm <6C656E67746C7220> Tj 1 0 0 1 519.36 621.36 Tm <6F66> Tj 0.48 Tc 1 0 0 1 69.84 609.84 Tm <74686520> Tj 1 0 0 1 84.72 609.84 Tm <6D6163726F73636F70696320> Tj 1 0 0 1 137.52 610.08 Tm <666C6F7720> Tj 1 0 0 1 158.16 610.56 Tm <6772616469656E747320> Tj 1 0 0 1 197.04 610.08 Tm <696E20> Tj 1 0 0 1 207.36 610.08 Tm <74686520> Tj 1 0 0 1 222.24 610.08 Tm <73747265616D7769736520> Tj 1 0 0 1 269.04 610.08 Tm <646972656374696F6E732C20> Tj 1 0 0 1 312.48 610.32 Tm <776869636820> Tj 1 0 0 1 338.88 610.32 Tm <6D65616E7320> Tj 1 0 0 1 366.72 610.32 Tm <7468617420> Tj 1 0 0 1 384.24 610.32 Tm <74686520> Tj 1 0 0 1 398.88 610.32 Tm <63656C6C20> Tj 1 0 0 1 415.92 610.32 Tm <64696D656E73696F6E7320> Tj 1 0 0 1 463.44 610.08 Tm <73686F756C6420> Tj 1 0 0 1 492.24 610.08 Tm <626520> Tj 1 0 0 1 504.72 610.08 Tm <6F6620> Tj 1 0 0 1 515.52 610.32 Tm <746865> Tj 0.48 Tc 1 0 0 1 69.84 598.56 Tm <6F7264657220> Tj 1 0 0 1 93.60 598.80 Tm <6F6620> Tj 1 0 0 1 104.88 598.80 Tm <74686520> Tj 1 0 0 1 120.00 598.80 Tm <6C6F63616C20> Tj 1 0 0 1 142.08 598.80 Tm <6D65616E20> Tj 1 0 0 1 166.56 599.04 Tm <6672656520> Tj 1 0 0 1 184.32 599.52 Tm <7061746820> Tj 1 0 0 1 204.48 599.04 Tm <6F7220> Tj 1 0 0 1 215.52 599.04 Tm <6576656E20> Tj 1 0 0 1 236.88 599.04 Tm <736D616C6C657220> Tj 1 0 0 1 268.80 597.12 Tm <5B335D2E20> Tj 1 0 0 1 288.24 599.04 Tm <54686520> Tj 1 0 0 1 306.48 599.04 Tm <736D616C6C65737420> Tj 1 0 0 1 341.28 599.04 Tm <756E697420> Tj 1 0 0 1 359.52 599.04 Tm <6F6620> Tj 1 0 0 1 370.32 599.52 Tm <706879736963616C20> Tj 1 0 0 1 406.08 599.04 Tm <737061636520> Tj 1 0 0 1 430.56 599.28 Tm <697320> Tj 1 0 0 1 439.92 599.04 Tm <746C726520> Tj 1 0 0 1 455.28 599.04 Tm <73756263656C6C2C20> Tj 1 0 0 1 488.40 599.04 Tm <776865726520> Tj 1 0 0 1 515.28 599.04 Tm <746865> Tj 0.48 Tc 1 0 0 1 69.84 587.52 Tm <636F6C6C6973696F6E20> Tj 1 0 0 1 107.76 588.00 Tm <706172746E65727320> Tj 1 0 0 1 143.52 587.76 Tm <61726520> Tj 1 0 0 1 159.60 587.76 Tm <73656C656374656420> Tj 1 0 0 1 194.88 587.76 Tm <666F7220> Tj 1 0 0 1 210.00 587.76 Tm <74686520> Tj 1 0 0 1 225.84 587.76 Tm <65737461626C6973686D656E7420> Tj 1 0 0 1 283.20 587.76 Tm <6F6620> Tj 1 0 0 1 294.96 587.76 Tm <74686520> Tj 1 0 0 1 311.04 587.76 Tm <636F6C6C6973696F6E20> Tj 1 0 0 1 348.24 588.00 Tm <726174652E20> Tj 1 0 0 1 373.20 588.00 Tm <496E20> Tj 1 0 0 1 385.44 588.00 Tm <6164646974696F6E2C20> Tj 1 0 0 1 423.36 588.00 Tm <74686520> Tj 1 0 0 1 439.20 588.00 Tm <74696D6520> Tj 1 0 0 1 460.80 587.76 Tm <7374657020> Tj 1 0 0 1 480.48 587.76 Tm <6F7567687420> Tj 1 0 0 1 506.64 587.76 Tm <746F20> Tj 1 0 0 1 518.16 588.00 Tm <6265> Tj 0.48 Tc 1 0 0 1 70.08 576.24 Tm <73756666696369656E746C7920> Tj 1 0 0 1 117.36 576.24 Tm <736D616C6C20> Tj 1 0 0 1 140.88 576.48 Tm <696E20> Tj 1 0 0 1 151.44 576.24 Tm <636F6D70617269736F6E20> Tj 1 0 0 1 199.20 576.48 Tm <7769746820> Tj 1 0 0 1 219.12 576.48 Tm <74686520> Tj 1 0 0 1 233.52 576.48 Tm <6C6F63616C20> Tj 1 0 0 1 254.40 576.48 Tm <6D65616E20> Tj 1 0 0 1 278.16 576.48 Tm <636F6C6C6973696F6E20> Tj 1 0 0 1 314.16 576.48 Tm <74696D6520> Tj 1 0 0 1 334.32 574.56 Tm <5B335D2E> Tj 0.48 Tc 1 0 0 1 83.52 564.96 Tm <496E20> Tj 1 0 0 1 94.80 564.96 Tm <7468697320> Tj 1 0 0 1 112.56 564.96 Tm <73747564792C20> Tj 1 0 0 1 139.44 565.20 Tm <74686520> Tj 1 0 0 1 154.80 565.20 Tm <6D6F6C6563756C617220> Tj 1 0 0 1 197.52 565.20 Tm <636F6C6C6973696F6E7320> Tj 1 0 0 1 238.08 565.20 Tm <61726520> Tj 1 0 0 1 253.20 565.20 Tm <6D6F64656C656420> Tj 1 0 0 1 290.16 565.20 Tm <7573696E6720> Tj 1 0 0 1 314.40 565.20 Tm <74686520> Tj 1 0 0 1 329.52 565.20 Tm <7661726961626C6520> Tj 1 0 0 1 364.32 565.44 Tm <6861726420> Tj 1 0 0 1 385.20 565.20 Tm <73706865726520> Tj 1 0 0 1 413.76 565.92 Tm <285648532920> Tj 1 0 0 1 442.80 565.44 Tm <6D6F6C6563756C617220> Tj 1 0 0 1 485.76 565.20 Tm <6D6F64656C20> Tj 1 0 0 1 513.84 563.28 Tm <5B345D2E> Tj 0.48 Tc 1 0 0 1 69.84 553.68 Tm <5468697320> Tj 1 0 0 1 90.00 553.92 Tm <6D6F64656C20> Tj 1 0 0 1 117.12 553.92 Tm <656D706C6F797320> Tj 1 0 0 1 152.88 553.92 Tm <74686520> Tj 1 0 0 1 167.52 553.92 Tm <73696D706C6520> Tj 1 0 0 1 195.84 554.16 Tm <6861726420> Tj 1 0 0 1 216.00 553.92 Tm <73706865726520> Tj 1 0 0 1 243.84 554.16 Tm <616E67756C617220> Tj 1 0 0 1 275.52 554.16 Tm <73636174746572696E6720> Tj 1 0 0 1 315.84 554.16 Tm <6C617720> Tj 1 0 0 1 332.16 554.16 Tm <736F20> Tj 1 0 0 1 342.96 554.16 Tm <7468617420> Tj 1 0 0 1 360.48 554.16 Tm <616C6920> Tj 1 0 0 1 372.72 554.16 Tm <646972656374696F6E7320> Tj 1 0 0 1 413.52 554.16 Tm <61726520> Tj 1 0 0 1 427.92 554.16 Tm <657175616C6C7920> Tj 1 0 0 1 458.88 554.40 Tm <706F737369626C6520> Tj 1 0 0 1 494.16 554.16 Tm <666F7220> Tj 1 0 0 1 507.84 554.40 Tm <706F73742D> Tj 0.48 Tc 1 0 0 1 69.84 542.40 Tm <636F6C6C6973696F6E20> Tj 1 0 0 1 107.76 542.64 Tm <76656C6F6369747920> Tj 1 0 0 1 143.04 542.64 Tm <696E20> Tj 1 0 0 1 154.32 542.64 Tm <74686520> Tj 1 0 0 1 170.40 542.64 Tm <63656E7465722D6FCA6D61737320> Tj 1 0 0 1 232.08 542.88 Tm <6672616D6520> Tj 1 0 0 1 258.48 542.88 Tm <6F6620> Tj 1 0 0 1 270.00 542.88 Tm <7265666572656E63652E20> Tj 1 0 0 1 316.08 542.88 Tm <486F77657665722C20> Tj 1 0 0 1 357.60 542.88 Tm <74686520> Tj 1 0 0 1 373.68 542.88 Tm <636F6C6C6973696F6E20> Tj 1 0 0 1 410.88 542.88 Tm <63726F737320> Tj 1 0 0 1 434.64 542.88 Tm <73656374696F6E20> Tj 1 0 0 1 466.08 542.88 Tm <646570656E647320> Tj 1 0 0 1 502.08 542.64 Tm <6F6E20> Tj 1 0 0 1 515.28 542.88 Tm <746865> Tj 0.48 Tc 1 0 0 1 69.60 531.36 Tm <72656C617469766520> Tj 1 0 0 1 102.24 531.12 Tm <737065656420> Tj 1 0 0 1 127.20 531.36 Tm <6F6620> Tj 1 0 0 1 138.48 531.36 Tm <636F6C6C6964696E6720> Tj 1 0 0 1 175.44 531.36 Tm <6D6F6C6563756C65732E20> Tj 1 0 0 1 223.20 531.60 Tm <54686520> Tj 1 0 0 1 241.20 531.60 Tm <656E6572677920> Tj 1 0 0 1 270.00 531.36 Tm <65786368616E676520> Tj 1 0 0 1 309.36 531.36 Tm <6265747765656E20> Tj 1 0 0 1 344.64 531.60 Tm <6B696E6574EC6320> Tj 1 0 0 1 373.92 531.36 Tm <616E6420> Tj 1 0 0 1 390.72 531.60 Tm <696E7465726E616C20> Tj 1 0 0 1 422.88 531.60 Tm <6D6F64657320> Tj 1 0 0 1 451.44 531.36 Tm <697320> Tj 1 0 0 1 460.56 531.36 Tm <636F6E74726F6C6C656420> Tj 1 0 0 1 503.28 531.36 Tm <627920> Tj 1 0 0 1 515.28 531.36 Tm <746865> Tj 0.48 Tc 1 0 0 1 69.84 519.84 Tm <426F72676E616B6B652D4C617273656E20> Tj 1 0 0 1 147.12 519.84 Tm <737461746973746963616C20> Tj 1 0 0 1 187.44 520.08 Tm <6D6F64656C20> Tj 1 0 0 1 216.24 518.16 Tm <5B355D2E20> Tj 1 0 0 1 236.88 520.08 Tm <54686520> Tj 1 0 0 1 255.84 520.08 Tm <657373656E7469616C20> Tj 1 0 0 1 293.04 520.08 Tm <6665617475726520> Tj 1 0 0 1 323.76 520.08 Tm <6F6620> Tj 1 0 0 1 335.28 520.08 Tm <7468697320> Tj 1 0 0 1 353.04 520.08 Tm <6D6F64656C20> Tj 1 0 0 1 381.36 520.08 Tm <697320> Tj 1 0 0 1 391.20 520.08 Tm <7468617420> Tj 1 0 0 1 409.92 520.08 Tm <6120> Tj 1 0 0 1 417.84 520.08 Tm <6672616374696F6E20> Tj 1 0 0 1 451.92 520.08 Tm <6F6620> Tj 1 0 0 1 463.68 520.08 Tm <74686520> Tj 1 0 0 1 479.52 520.08 Tm <636F6C6C6973696F6E7320> Tj 1 0 0 1 520.80 520.08 Tm <6973> Tj 0.48 Tc 1 0 0 1 69.84 508.56 Tm <7472656174656420> Tj 1 0 0 1 99.60 508.80 Tm <617320> Tj 1 0 0 1 110.40 508.56 Tm <636F6D706C6574656C7920> Tj 1 0 0 1 156.96 508.80 Tm <696E656C61737469632C20> Tj 1 0 0 1 194.88 508.80 Tm <616E6420> Tj 1 0 0 1 211.68 508.80 Tm <74686520> Tj 1 0 0 1 226.32 509.04 Tm <72656D61696E64657220> Tj 1 0 0 1 268.56 508.80 Tm <6F6620> Tj 1 0 0 1 279.12 508.80 Tm <74686520> Tj 1 0 0 1 293.76 508.80 Tm <6D6F6C6563756C617220> Tj 1 0 0 1 335.76 508.80 Tm <636F6C6C6973696F6E7320> Tj 1 0 0 1 375.60 508.80 Tm Tj 1 0 0 1 384.96 509.04 Tm <726567617264656420> Tj 1 0 0 1 421.92 508.80 Tm <617320> Tj 1 0 0 1 432.96 508.80 Tm <656C61737469632E20> Tj 1 0 0 1 466.08 508.80 Tm <53EC6D756C6174696F6E7320> Tj 1 0 0 1 515.76 508.80 Tm <617265> Tj 0.48 Tc 1 0 0 1 69.60 497.52 Tm <706572666F726D656420> Tj 1 0 0 1 115.68 497.28 Tm <7573696E6720> Tj 1 0 0 1 141.60 497.28 Tm <6120> Tj 1 0 0 1 150.24 497.52 Tm <6E6F6E7265616374696E6720> Tj 1 0 0 1 201.36 498.00 Tm <67617320> Tj 1 0 0 1 218.88 497.52 Tm <6D6F64656C20> Tj 1 0 0 1 247.92 497.52 Tm <636F6E73697374696E6720> Tj 1 0 0 1 291.84 497.52 Tm <6F6620> Tj 1 0 0 1 304.32 497.52 Tm <74776F20> Tj 1 0 0 1 323.52 497.52 Tm <6368656D6963616C20> Tj 1 0 0 1 363.36 497.52 Tm <737065636965732C20> Tj 1 0 0 1 398.40 497.52 Tm <4E3220> Tj 1 0 0 1 413.28 497.52 Tm <616E6420> Tj 1 0 0 1 431.76 497.52 Tm <30322E20> Tj 1 0 0 1 453.60 497.52 Tm <456E6572677920> Tj 1 0 0 1 486.48 497.28 Tm <65786368616E676573> Tj 0.48 Tc 1 0 0 1 69.60 486.00 Tm <6265747765656E20> Tj 1 0 0 1 107.04 486.00 Tm <74686520> Tj 1 0 0 1 123.36 486.00 Tm <7472616E736C6174696F6E616C20> Tj 1 0 0 1 176.88 486.24 Tm <616E6420> Tj 1 0 0 1 195.36 486.24 Tm <696E74656D616C20> Tj 1 0 0 1 229.20 486.48 Tm <6D6F64657320> Tj 1 0 0 1 259.44 486.24 Tm <61726520> Tj 1 0 0 1 275.52 486.24 Tm <636F6E736964657265642E20> Tj 1 0 0 1 328.80 486.24 Tm <54686520> Tj 1 0 0 1 348.48 486.48 Tm <766962726174696F6E616C20> Tj 1 0 0 1 394.80 486.24 Tm <74656D706572617475726520> Tj 1 0 0 1 445.92 486.24 Tm <697320> Tj 1 0 0 1 457.20 486.24 Tm <636F6E74726F6C6C656420> Tj 1 0 0 1 501.12 486.00 Tm <627920> Tj 1 0 0 1 515.28 486.24 Tm <746865> Tj 0.48 Tc 1 0 0 1 69.84 474.72 Tm <646973747269627574696F6E20> Tj 1 0 0 1 118.08 474.72 Tm <6F6620> Tj 1 0 0 1 129.36 474.96 Tm <656E6572677920> Tj 1 0 0 1 158.64 474.96 Tm <6265747765656E20> Tj 1 0 0 1 194.16 474.96 Tm <74686520> Tj 1 0 0 1 209.04 474.96 Tm <7472616E736C6174696F6E616C20> Tj 1 0 0 1 260.16 474.96 Tm <616E6420> Tj 1 0 0 1 276.96 475.20 Tm <726F746174696F6E616C20> Tj 1 0 0 1 317.04 474.96 Tm <6D6F64657320> Tj 1 0 0 1 345.36 474.96 Tm <616674657220> Tj 1 0 0 1 366.24 474.96 Tm <616E20> Tj 1 0 0 1 378.24 474.96 Tm <696E656C617374696320> Tj 1 0 0 1 413.28 474.96 Tm <636F6C6C6973696F6E2220> Tj 1 0 0 1 455.04 474.96 Tm <54686520> Tj 1 0 0 1 473.28 475.44 Tm <70726F626162696C69747920> Tj 1 0 0 1 519.12 474.96 Tm <6F66> Tj 0.48 Tc 1 0 0 1 69.84 463.44 Tm <616E20> Tj 1 0 0 1 81.84 463.68 Tm <696E656C617374696320> Tj 1 0 0 1 117.60 463.44 Tm <636F6C6C6973696F6E20> Tj 1 0 0 1 154.32 463.68 Tm <64657465726D726E657320> Tj 1 0 0 1 199.92 463.68 Tm <74686520> Tj 1 0 0 1 214.80 463.92 Tm <7261746520> Tj 1 0 0 1 232.08 463.68 Tm <617420> Tj 1 0 0 1 241.44 463.92 Tm <776869636820> Tj 1 0 0 1 268.08 463.68 Tm <656E6572677920> Tj 1 0 0 1 297.36 463.68 Tm <697320> Tj 1 0 0 1 306.48 463.68 Tm <7472616E7366657272656420> Tj 1 0 0 1 351.12 463.68 Tm <6265747765656E20> Tj 1 0 0 1 386.40 463.68 Tm <74686520> Tj 1 0 0 1 401.04 463.68 Tm <7472616E736C6174696F6E616C20> Tj 1 0 0 1 452.40 463.44 Tm <616E6420> Tj 1 0 0 1 469.20 463.68 Tm <696E74656D616C20> Tj 1 0 0 1 501.84 463.44 Tm <6D6F646573> Tj 0.48 Tc 1 0 0 1 69.84 452.16 Tm <616674657220> Tj 1 0 0 1 91.44 452.40 Tm <616E20> Tj 1 0 0 1 104.16 452.40 Tm <696E656C617374696320> Tj 1 0 0 1 140.40 452.40 Tm <636F6C6C6973696F6E2E20> Tj 1 0 0 1 183.84 452.40 Tm <466F7220> Tj 1 0 0 1 200.88 452.40 Tm <6120> Tj 1 0 0 1 208.56 452.88 Tm <676976656E20> Tj 1 0 0 1 233.52 452.64 Tm <636F6C6C6973696F6E2C20> Tj 1 0 0 1 273.12 452.40 Tm <74686520> Tj 1 0 0 1 288.24 452.88 Tm <70726F626162696C697469657320> Tj 1 0 0 1 340.32 452.40 Tm <61726520> Tj 1 0 0 1 355.68 452.40 Tm <64657369676E6174656420> Tj 1 0 0 1 400.80 452.40 Tm <627920> Tj 1 0 0 1 413.76 452.40 Tm <74686520> Tj 1 0 0 1 429.12 452.40 Tm <696E766572736520> Tj 1 0 0 1 461.04 452.16 Tm <6F6620> Tj 1 0 0 1 472.56 452.16 Tm <74686520> Tj 1 0 0 1 487.92 452.40 Tm <72656C61786174696F6E> Tj 0.48 Tc 1 0 0 1 69.60 440.88 Tm <6E756D626572732E20> Tj 1 0 0 1 110.16 441.12 Tm <7768EC636820> Tj 1 0 0 1 138.00 440.88 Tm <636F72726573706F6E6420> Tj 1 0 0 1 185.04 441.12 Tm <746F20> Tj 1 0 0 1 196.32 441.12 Tm <74686520> Tj 1 0 0 1 212.16 441.12 Tm <6E756D62657220> Tj 1 0 0 1 245.76 441.12 Tm <6F6620> Tj 1 0 0 1 257.52 441.12 Tm <636F6C6C6973696F6E7320> Tj 1 0 0 1 298.32 441.12 Tm <6E65636573736172792C20> Tj 1 0 0 1 342.24 441.12 Tm <6F6E20> Tj 1 0 0 1 355.92 441.12 Tm <617665726167652C20> Tj 1 0 0 1 392.16 441.12 Tm Tj 1 0 0 1 407.52 441.12 Tm <6120> Tj 1 0 0 1 415.20 441.12 Tm <6D6F6C6563756C6520> Tj 1 0 0 1 454.80 441.12 Tm <746F20> Tj 1 0 0 1 466.32 440.88 Tm <72656C61782E20> Tj 1 0 0 1 496.08 440.88 Tm <466F7220> Tj 1 0 0 1 513.12 440.88 Tm <74686973> Tj 0.48 Tc 1 0 0 1 69.84 429.84 Tm <73747564792C20> Tj 1 0 0 1 97.44 429.84 Tm <74686520> Tj 1 0 0 1 113.28 430.08 Tm <72656C61786174696F6E20> Tj 1 0 0 1 156.72 430.08 Tm <6E756D6265727320> Tj 1 0 0 1 194.40 430.08 Tm <6F6620> Tj 1 0 0 1 206.88 430.08 Tm <3520> Tj 1 0 0 1 215.52 430.08 Tm <616E6420> Tj 1 0 0 1 233.52 430.08 Tm <353020> Tj 1 0 0 1 247.20 430.08 Tm <7765726520> Tj 1 0 0 1 270.00 430.08 Tm <7573656420> Tj 1 0 0 1 291.84 430.08 Tm <666F7220> Tj 1 0 0 1 306.72 430.08 Tm <74686520> Tj 1 0 0 1 322.56 430.08 Tm <726F746174696F6E20> Tj 1 0 0 1 356.88 430.08 Tm <616E6420> Tj 1 0 0 1 374.88 430.08 Tm <766962726174726F6E2C20> Tj 1 0 0 1 416.16 430.08 Tm <726573706563746976656C792E20> Tj 1 0 0 1 473.76 429.84 Tm <54686520> Tj 1 0 0 1 492.96 429.84 Tm <656666656374697665> Tj 0.48 Tc 1 0 0 1 69.60 418.80 Tm <6E756D62657220> Tj 1 0 0 1 103.44 418.80 Tm <6F6620> Tj 1 0 0 1 114.96 418.80 Tm <6465677265657320> Tj 1 0 0 1 148.56 418.80 Tm <6F6620> Tj 1 0 0 1 160.08 418.80 Tm <66726565646F6D20> Tj 1 0 0 1 196.08 418.80 Tm <696E20> Tj 1 0 0 1 206.88 418.80 Tm <74686520> Tj 1 0 0 1 222.24 419.28 Tm <7061727469616C6C7920> Tj 1 0 0 1 258.00 418.80 Tm <6578636974656420> Tj 1 0 0 1 289.68 418.80 Tm <766962726174696F6E616C20> Tj 1 0 0 1 335.28 418.80 Tm <73746174657320> Tj 1 0 0 1 360.24 418.80 Tm <697320> Tj 1 0 0 1 370.08 418.80 Tm <63616C63756C6174656420> Tj 1 0 0 1 413.04 418.80 Tm <66726F6D20> Tj 1 0 0 1 435.12 418.80 Tm <74686520> Tj 1 0 0 1 450.72 418.80 Tm <6861726D6F6E696320> Tj 1 0 0 1 491.28 418.56 Tm <6F7363696C6C61746F72> Tj 0.24 Tc 1 0 0 1 69.60 407.52 Tm <7468656F72792E> Tj 0.48 Tc 1 0 0 1 83.04 396.48 Tm <54686520> Tj 1 0 0 1 101.28 396.48 Tm <6672656573747265616D20> Tj 1 0 0 1 145.68 396.48 Tm <616E6420> Tj 1 0 0 1 162.72 396.72 Tm <666C6F7720> Tj 1 0 0 1 183.12 396.48 Tm <636F6E646974696F6E7320> Tj 1 0 0 1 226.56 396.72 Tm <7573656420> Tj 1 0 0 1 246.96 396.72 Tm <696E20> Tj 1 0 0 1 257.28 396.48 Tm <74686520> Tj 1 0 0 1 271.92 396.96 Tm <70726573656E7420> Tj 1 0 0 1 302.64 396.48 Tm <63616C63756C6174696F6E7320> Tj 1 0 0 1 352.08 396.48 Tm <61726520> Tj 1 0 0 1 366.48 396.48 Tm <74686F736520> Tj 1 0 0 1 390.00 396.96 Tm <676976656E20> Tj 1 0 0 1 414.24 396.48 Tm <627920> Tj 1 0 0 1 426.72 396.48 Tm <53616E746F7320> Tj 1 0 0 1 455.52 396.24 Tm <616E6420> Tj 1 0 0 1 472.32 396.48 Tm <4C6577697320> Tj 1 0 0 1 499.68 394.32 Tm <5B325D20> Tj 1 0 0 1 513.60 396.24 Tm <616E64> Tj 0.48 Tc 1 0 0 1 69.84 384.24 Tm <73756D6D6172697A656420> Tj 1 0 0 1 121.20 384.24 Tm <696E20> Tj 1 0 0 1 132.00 384.24 Tm <5461626C6520> Tj 1 0 0 1 158.88 384.48 Tm <4C20> Tj 1 0 0 1 171.60 384.48 Tm <54686520> Tj 1 0 0 1 190.32 384.48 Tm <6672656573747265616D20> Tj 1 0 0 1 234.48 384.48 Tm <76656C6F6369747920> Tj 1 0 0 1 269.76 384.24 Tm <552D20> Tj 1 0 0 1 283.92 384.24 Tm <697320> Tj 1 0 0 1 293.76 384.24 Tm <617373756D656420> Tj 1 0 0 1 330.24 384.24 Tm <746F20> Tj 1 0 0 1 341.04 384.24 Tm <626520> Tj 1 0 0 1 353.76 384.24 Tm <636F6E7374616E7420> Tj 1 0 0 1 389.52 384.24 Tm <617420> Tj 1 0 0 1 399.60 384.24 Tm <332E3520> Tj 1 0 0 1 415.20 384.24 Tm <4B6D2F732C20> Tj 1 0 0 1 442.08 384.24 Tm <776869636820> Tj 1 0 0 1 469.20 384.00 Tm <636F72726573706F6E647320> Tj 1 0 0 1 519.84 384.00 Tm <746F> Tj 0.48 Tc 1 0 0 1 69.84 372.24 Tm <6672656573747265616D20> Tj 1 0 0 1 114.00 372.48 Tm <4D61636820> Tj 1 0 0 1 138.96 372.48 Tm <6E756D62657220> Tj 1 0 0 1 171.36 372.48 Tm <4D2A6F6620> Tj 1 0 0 1 199.20 372.48 Tm <31322E20> Tj 1 0 0 1 215.52 372.48 Tm <54686520> Tj 1 0 0 1 233.28 372.48 Tm <77616C6C20> Tj 1 0 0 1 252.48 372.48 Tm <74656D706572617475726520> Tj 1 0 0 1 302.64 372.48 Tm <5A2C7520> Tj 1 0 0 1 313.92 372.48 Tm <697320> Tj 1 0 0 1 323.52 372.24 Tm <617373756D656420> Tj 1 0 0 1 359.52 372.24 Tm <636F6E7374616E7420> Tj 1 0 0 1 394.80 372.24 Tm <617420> Tj 1 0 0 1 404.64 372.24 Tm <38383020> Tj 1 0 0 1 421.44 372.48 Tm <4B2E20> Tj 1 0 0 1 436.56 372.24 Tm <416C736F2C20> Tj 1 0 0 1 460.08 372.24 Tm <6469666675736520> Tj 1 0 0 1 490.08 372.24 Tm <7265666C656374696F6E> Tj 0.48 Tc 1 0 0 1 69.84 360.96 Tm <7769746820> Tj 1 0 0 1 90.24 361.20 Tm <66756C6C20> Tj 1 0 0 1 106.32 361.20 Tm <746865726D616C20> Tj 1 0 0 1 139.20 361.20 Tm <6163636F6D6D6F646174696F6E20> Tj 1 0 0 1 204.24 361.20 Tm <697320> Tj 1 0 0 1 213.60 361.20 Tm <617373756D656420> Tj 1 0 0 1 249.60 361.20 Tm <666F7220> Tj 1 0 0 1 263.28 361.20 Tm <74686520> Tj 1 0 0 1 277.92 361.44 Tm <6761732D7375726661636520> Tj 1 0 0 1 324.72 361.20 Tm <696E746572616374696F6E732E20> Tj 1 0 0 1 378.00 360.96 Tm <54686520> Tj 1 0 0 1 395.76 360.96 Tm <6F766572616C6C20> Tj 1 0 0 1 425.28 361.20 Tm <4B6E756473656E20> Tj 1 0 0 1 462.48 360.96 Tm <6E756D6265722C20> Tj 1 0 0 1 498.00 360.72 Tm <646566696E6564> Tj 0.48 Tc 1 0 0 1 69.84 349.68 Tm <617320> Tj 1 0 0 1 83.04 349.92 Tm <74686520> Tj 1 0 0 1 100.08 349.92 Tm <726174696F20> Tj 1 0 0 1 123.36 349.92 Tm <6F6620> Tj 1 0 0 1 136.32 349.92 Tm <74686520> Tj 1 0 0 1 153.60 349.92 Tm <6D6F6C6563756C617220> Tj 1 0 0 1 197.52 349.92 Tm <6D65616E20> Tj 1 0 0 1 223.92 349.92 Tm <6672656520> Tj 1 0 0 1 243.60 350.40 Tm <7061746820> Tj 1 0 0 1 265.68 349.92 Tm <696E20> Tj 1 0 0 1 278.16 349.92 Tm <74686520> Tj 1 0 0 1 295.20 349.92 Tm <6672656573747265616D20> Tj 1 0 0 1 341.28 350.16 Tm <67617320> Tj 1 0 0 1 359.04 349.92 Tm <746F20> Tj 1 0 0 1 371.76 349.68 Tm <74686520> Tj 1 0 0 1 388.80 349.92 Tm <6469616D6574657220> Tj 1 0 0 1 427.68 349.68 Tm <6F6620> Tj 1 0 0 1 440.88 349.68 Tm <74686520> Tj 1 0 0 1 457.92 349.68 Tm <63EC7263756C617220> Tj 1 0 0 1 492.96 349.68 Tm <63796C696E6465722C> Tj 0.72 Tc 1 0 0 1 69.84 337.92 Tm <636F72726573706F6E647320> Tj 1 0 0 1 119.76 337.92 Tm <746F20> Tj 1 0 0 1 129.84 338.16 Tm <4B6E2A3A302E303930332E20> Tj 1 0 0 1 190.80 338.16 Tm <46696E616C6C792C20> Tj 1 0 0 1 223.20 337.92 Tm <74686520> Tj 1 0 0 1 237.84 338.16 Tm <6672656573747265616D20> Tj 1 0 0 1 281.28 337.92 Tm <5265796E6F6C647320> Tj 1 0 0 1 320.16 337.92 Tm <6E756D626572627920> Tj 1 0 0 1 364.56 337.92 Tm <756E697420> Tj 1 0 0 1 382.32 337.92 Tm <6C656E67746820> Tj 1 0 0 1 410.40 337.92 Tm <52652A697332313435352E> Tj 0.48 Tc 1 0 0 1 83.04 326.64 Tm <54686520> Tj 1 0 0 1 101.28 326.64 Tm <636F6D7075746174696F6E616920> Tj 1 0 0 1 160.08 326.64 Tm <646F6D61696E20> Tj 1 0 0 1 192.00 326.88 Tm <7573656420> Tj 1 0 0 1 212.64 326.88 Tm <666F7220> Tj 1 0 0 1 226.32 326.88 Tm <74686520> Tj 1 0 0 1 241.20 326.64 Tm <63616C63756C6174696F6E732C20> Tj 1 0 0 1 292.32 326.64 Tm <74686520> Tj 1 0 0 1 306.96 327.12 Tm <6772696420> Tj 1 0 0 1 324.96 327.12 Tm <67656E65726174696F6E20> Tj 1 0 0 1 368.88 326.64 Tm <736368656D652C20> Tj 1 0 0 1 402.72 326.64 Tm <74686520> Tj 1 0 0 1 417.60 326.64 Tm <65666665637420> Tj 1 0 0 1 442.56 326.40 Tm <6F6620> Tj 1 0 0 1 453.12 326.88 Tm <6772696420> Tj 1 0 0 1 471.60 326.40 Tm <7265736F6C7574696F6E20> Tj 1 0 0 1 513.60 326.40 Tm <616E64> Tj 0.48 Tc 1 0 0 1 69.60 315.60 Tm <74686520> Tj 1 0 0 1 84.48 315.60 Tm <636F6D706C65746520> Tj 1 0 0 1 122.88 315.60 Tm <76616C69646174696F6E20> Tj 1 0 0 1 164.64 316.08 Tm <70726F6365737320> Tj 1 0 0 1 196.56 315.60 Tm <656D706C6F79656420> Tj 1 0 0 1 237.12 315.84 Tm <696E20> Tj 1 0 0 1 247.44 315.60 Tm <7468697320> Tj 1 0 0 1 264.00 315.60 Tm <737475647920> Tj 1 0 0 1 287.28 315.60 Tm <61726520> Tj 1 0 0 1 301.68 315.60 Tm <64657363726962656420> Tj 1 0 0 1 341.28 315.60 Tm <696E20> Tj 1 0 0 1 351.36 315.60 Tm <64657461696C7320> Tj 1 0 0 1 379.20 315.60 Tm Tj 1 0 0 1 389.52 315.60 Tm <5265662E20> Tj 1 0 0 1 408.48 313.68 Tm <5B365D2E> Tj 0.48 Tc 1 0 0 1 69.84 293.76 Tm <5441424C4520> Tj 1 0 0 1 102.48 294.00 Tm <6C2E20> Tj 1 0 0 1 111.12 294.00 Tm <4672656573747265616D20> Tj 1 0 0 1 156.48 294.00 Tm <436F6E646974696F6E7320> Tj 1 0 0 1 199.68 294.00 Tm <616E6420> Tj 1 0 0 1 216.00 294.00 Tm <466C6F7720> Tj 1 0 0 1 236.88 294.00 Tm <506172616D65746572732E> Tj 0.72 Tc 1 0 0 1 69.60 282.00 Tm <416C746974756465> Tj 0.24 Tc 1 0 0 1 69.84 269.76 Tm <54656D706572617475726520> Tj 1 0 0 1 122.64 270.24 Tm <2820> Tj 1 0 0 1 126.96 270.00 Tm <492DEC> Tj 0.48 Tc 1 0 0 1 70.08 258.00 Tm <507265737375726520> Tj 1 0 0 1 105.84 258.48 Tm <28702D29> Tj 0.48 Tc 1 0 0 1 69.84 246.00 Tm <44656E7369747920> Tj 1 0 0 1 102.96 246.24 Tm <28702D29> Tj 0.48 Tc 1 0 0 1 69.60 234.00 Tm <4E756D62657220> Tj 1 0 0 1 104.64 233.76 Tm <64656E7369747920> Tj 1 0 0 1 135.60 234.48 Tm <286E2D29> Tj 0.72 Tc 1 0 0 1 69.84 222.00 Tm <566973636F7369747920> Tj 1 0 0 1 109.44 222.48 Tm <28702D29> Tj 0.72 Tc 1 0 0 1 69.60 210.00 Tm <56656C6F6369747920> Tj 1 0 0 1 106.08 210.72 Tm <28552D29> Tj 0.48 Tc 1 0 0 1 69.84 198.00 Tm <4D65616E20> Tj 1 0 0 1 94.80 198.00 Tm <6672656520> Tj 1 0 0 1 112.56 198.48 Tm <7061746820> Tj 1 0 0 1 132.00 198.48 Tm <28322D29> Tj 0.72 Tc 1 0 0 1 69.84 186.96 Tm <4D6F6C6563756C617220> Tj 1 0 0 1 112.80 186.96 Tm <776569676874> Tj 0.48 Tc 1 0 0 1 69.84 175.68 Tm <4D6F6C6520> Tj 1 0 0 1 93.36 175.68 Tm <6669616374696F6E> Tj 0.48 Tc 1 0 0 1 69.84 164.64 Tm <4D6F6C6520> Tj 1 0 0 1 93.36 164.64 Tm <6672616374696F6E> Tj 0.72 Tc 1 0 0 1 70.08 153.12 Tm <4D6F6C6563756C617220> Tj 1 0 0 1 112.80 153.12 Tm <6D617373> Tj 0.72 Tc 1 0 0 1 69.84 142.08 Tm <4D6F6C6563756C617220> Tj 1 0 0 1 112.80 141.84 Tm <6D617373> Tj 0.48 Tc 1 0 0 1 69.84 130.80 Tm <4D6F6C6563756C617220> Tj 1 0 0 1 112.80 130.56 Tm <6469616D65746572> Tj 0.48 Tc 1 0 0 1 69.84 119.52 Tm <4D6F6C6563756C617220> Tj 1 0 0 1 112.80 119.52 Tm <6469616D65746572> Tj 0.72 Tc /F3 10.0 Tf 1 0 0 1 246.48 282.00 Tm <3730> Tj 0.24 Tc 1 0 0 1 246.48 270.00 Tm <3232302E30> Tj 0.96 Tc 1 0 0 1 246.48 258.00 Tm <352E353832> Tj 0.96 Tc 1 0 0 1 246.48 246.00 Tm <382E37353320> Tj 1 0 0 1 270.72 246.00 Tm <7820> Tj 1 0 0 1 278.88 246.00 Tm <6C302D35> Tj 0.96 Tc 1 0 0 1 247.20 234.00 Tm <312E3832303920> Tj 1 0 0 1 275.52 233.76 Tm <7820> Tj 1 0 0 1 283.92 233.76 Tm <31303231> Tj 0.96 Tc 1 0 0 1 247.20 222.00 Tm <312E34353520> Tj 1 0 0 1 270.72 222.00 Tm <7820> Tj 1 0 0 1 278.88 222.00 Tm <6C302D35> Tj 1.20 Tc 1 0 0 1 246.24 210.00 Tm <332E3536> Tj 0.72 Tc 1 0 0 1 246.24 198.00 Tm <392E303320> Tj 1 0 0 1 265.92 198.00 Tm <7820> Tj 1 0 0 1 274.32 198.00 Tm <31302D61> Tj 0.48 Tc 1 0 0 1 246.48 186.72 Tm <32382E3936> Tj 0.96 Tc 1 0 0 1 246.24 175.68 Tm <302E323331> Tj 0.96 Tc 1 0 0 1 246.24 164.40 Tm <3022373633> Tj 1.20 Tc 1 0 0 1 246.48 153.12 Tm <352E33313220> Tj 1 0 0 1 270.72 153.12 Tm <7820> Tj 1 0 0 1 279.12 153.12 Tm <6C302D3236> Tj 0.96 Tc 1 0 0 1 246.00 141.84 Tm <342E363520> Tj 1 0 0 1 265.92 141.84 Tm <7820> Tj 1 0 0 1 274.32 141.84 Tm <31302D32F3> Tj 1.20 Tc 1 0 0 1 246.24 130.80 Tm <342E303120> Tj 1 0 0 1 265.92 130.56 Tm <7820> Tj 1 0 0 1 274.32 130.56 Tm <31302D726F> Tj 1.20 Tc 1 0 0 1 246.24 119.52 Tm <342E3120> Tj 1 0 0 1 259.68 119.52 Tm <747220> Tj 1 0 0 1 265.92 119.28 Tm <7820> Tj 1 0 0 1 274.32 119.52 Tm <31302D726F> Tj 0.48 Tc 1 0 0 1 351.60 281.76 Tm <4B6D> Tj 0.00 Tc 1 0 0 1 351.84 269.76 Tm <4B> Tj 0.48 Tc /F3 9.0 Tf 1 0 0 1 351.60 258.24 Tm <4E2F6D32> Tj 0.48 Tc 1 0 0 1 351.60 245.76 Tm <4B672F6D33> Tj 0.72 Tc /F3 4.0 Tf 1 0 0 1 358.80 239.28 Tm <2D6C> Tj 0.00 Tc /F3 8.0 Tf 1 0 0 1 351.60 234.00 Tm <6D> Tj 0.72 Tc 1 0 0 1 351.60 221.76 Tm <4E732F6D32> Tj 0.48 Tc /F3 10.0 Tf 1 0 0 1 351.60 209.76 Tm <4B6D2F73> Tj 0.48 Tc 1 0 0 1 351.60 186.72 Tm <4B67694B674D6F6C65> Tj 0.72 Tc 1 0 0 1 351.60 152.88 Tm <4B67> Tj 0.96 Tc 1 0 0 1 351.60 141.60 Tm <4B67> Tj 0.00 Tc /F3 8.0 Tf 1 0 0 1 351.60 130.56 Tm <6D> Tj 0.00 Tc 1 0 0 1 351.60 119.28 Tm <6D> Tj 0.72 Tc /F3 10.0 Tf 1 0 0 1 175.92 175.68 Tm <6F32> Tj 0.00 Tc /F3 8.0 Tf 1 0 0 1 175.92 164.88 Tm <4E32> Tj 0.72 Tc /F3 10.0 Tf 1 0 0 1 175.92 153.12 Tm <6F32> Tj 0.00 Tc /F3 8.0 Tf 1 0 0 1 175.92 142.08 Tm <4E32> Tj 0.72 Tc /F3 10.0 Tf 1 0 0 1 175.92 130.56 Tm <6F32> Tj 0.00 Tc /F3 8.0 Tf 1 0 0 1 175.92 119.52 Tm <4E32> Tj ET endstream endobj 23 0 obj 31246 endobj 24 0 obj << /Length 25 0 R >> stream COMPUTATIONAL METHOD AND PROCEDUREA number of significant problems in fluid mechanics involve flows in the transitional regime, i.e., flows forwhich the Knudsen number is larger than 0.01 and less than 10. The most successful numerical technique formodeling complex flows in the transitional regime has been the Direct Simulation Monte Carlo (DSMC) method [3].DSMC models the flow as being a collection of discrete particles, each one with a position, velocity and intemalenergy. The state of the particles is stored and modified with time as the particles move, collide, and undergoboundary interactions in simulated physical space. The physical space is represented by a computational cellnetwork. The cell provides a convenient reference for the choice ofthe potential collision pairs and for the samplngof the macroscopic gas properties. The dimensions of the cells must be such that the change in flow propedesacross each cell is small. The linear dimensions of the cells should be small in comparison with the scale lengtlr ofthe macroscopic flow gradients in the streamwise directions, which means that the cell dimensions should be of theorder of the local mean free path or even smaller [3]. The smallest unit of physical space is tlre subcell, where thecollision partners are selected for the establishment of the collision rate. In addition, the time step ought to besufficiently small in comparison with the local mean collision time [3].In this study, the molecular collisions are modeled using the variable hard sphere (VHS) molecular model [4].This model employs the simple hard sphere angular scattering law so that ali directions are equally possible for post-collision velocity in the center-omass frame of reference. However, the collision cross section depends on therelative speed of colliding molecules. The energy exchange between kinetc and internal modes is controlled by theBorgnakke-Larsen statistical model [5]. The essential feature of this model is that a fraction of the collisions istreated as completely inelastic, and the remainder of the molecular collisions s regarded as elastic. Smulations areperformed using a nonreacting gas model consisting of two chemical species, N2 and 02. Energy exchangesbetween the translational and intemal modes are considered. The vibrational temperature is controlled by thedistribution of energy between the translational and rotational modes after an inelastic collision" The probability ofan inelastic collision determrnes the rate at which energy is transferred between the translational and intemal modesafter an inelastic collision. For a given collision, the probabilities are designated by the inverse of the relaxationnumbers. whch correspond to the number of collisions necessary, on average, br a molecule to relax. For thisstudy, the relaxation numbers of 5 and 50 were used for the rotation and vibratron, respectively. The effectivenumber of degrees of freedom in the partially excited vibrational states is calculated from the harmonic oscillatortheory.The freestream and flow conditions used in the present calculations are those given by Santos and Lewis [2] andsummarized in Table L The freestream velocity U- is assumed to be constant at 3.5 Km/s, which corresponds tofreestream Mach number M*of 12. The wall temperature Z,u is assumed constant at 880 K. Also, diffuse reflectionwith full thermal accommodation is assumed for the gas-surface interactions. The overall Knudsen number, definedas the ratio of the molecular mean free path in the freestream gas to the diameter of the crcular cylinder,corresponds to Kn*:0.0903. Finally, the freestream Reynolds numberby unit length Re*is21455.The computationai domain used for the calculations, the grid generation scheme, the effect of grid resolution andthe complete validation process employed in this study are described in details n Ref. [6].TABLE l. Freestream Conditions and Flow Parameters. AltitudeTemperature ( I-Pressure (p-)Density (p-)Number density (n-)Viscosity (p-)Velocity (U-)Mean free path (2-)Molecular weightMole fiactionMole fractionMolecular massMolecular massMolecular diameterMolecular diameter 70220.05.5828.753 x l0-51.8209 x 10211.455 x l0-53.569.03 x 10-a28.960.2310"7635.312 x l0-264.65 x 10-24.01 x 10-ro4.1 tr x 10-ro KmKN/m2Kg/m3-lmNs/m2Km/sKgiKgMoleKgKgmm o2N2o2N2o2N2 endstream endobj 25 0 obj 4349 endobj 26 0 obj << /Length 27 >> stream % CANON_PFINF_TYPE0_TEXTON endstream endobj 27 0 obj << /Length 45 >> stream q 595.20 0 0 841.68 0.00 0.00 cm /Obj21 Do Q endstream endobj 28 0 obj << /Type /Page /MediaBox [ 0 0 595.20 841.68 ] /Parent 11 0 R /Resources << /Font << /F3 5 0 R >> /XObject << /Obj21 21 0 R >> /Subtype 24 0 R /ProcSet [ /PDF /Text /ImageB /ImageC /ImageI ] >> /Contents [ 26 0 R 27 0 R 22 0 R ] >> endobj 29 0 obj << /Type /XObject /Subtype /Image /Width 2480 /Height 3507 /BitsPerComponent 1 /ColorSpace /DeviceGray /Filter /CCITTFaxDecode /DecodeParms << /K -1 /Columns 2480 >> /Length 98966 >> stream 2z":eF0sX! 8f )Np3HdTȪ; aA@A; AIHA q mX8!BCBB* ȘUd & hCCg*n"8m%d$CHlX0@`0J d6!PBa mXm@h> ":NNDL'%?Dh"]aDhZ ݮu{B>|:Aݤtmꓤ_o[{[mzM 7oIշ]n}}&V;w׺N7}'_߷ޗ~u7?f~-޿c{}?]/~c_cc{ۭFM᭶_jaÝ7 /_^l5_𖞕~>ao?V׿S]O?6K o厶m"mtR+k}iu"÷xn{ュ  {p_ut:~ ޷楷Du~7_OCujZq?~(wFGK?Աv+}N}v_{[._bo:_mziwMW[imi6Kw_Vzm/Ҧ׽[Ji&K ݫa%~SmVm,/z P] $W+a-G RtA@AN/v (a+ 0woa+ 'a[ ZPҰi[A0M0Ah mLP.qLPBa'M6! 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524.88 Tm <616E6420> Tj 1 0 0 1 432.96 524.64 Tm <302E31392C20> Tj 1 0 0 1 456.24 524.64 Tm <726573706563746976656C792E20> Tj 1 0 0 1 513.36 524.40 Tm <546865> Tj 0.48 Tc 1 0 0 1 71.04 514.08 Tm <6C6F636174696F6E7320> Tj 1 0 0 1 109.68 514.08 Tm <6F6620> Tj 1 0 0 1 120.24 514.08 Tm <74686520> Tj 1 0 0 1 135.60 514.08 Tm <73746174726F6E7320> Tj 1 0 0 1 168.24 514.08 Tm <776869636820> Tj 1 0 0 1 194.88 514.08 Tm <61726520> Tj 1 0 0 1 209.76 514.08 Tm <6964656E74696669656420> Tj 1 0 0 1 250.08 514.08 Tm <7769746820> Tj 1 0 0 1 269.76 513.84 Tm <74686520> Tj 1 0 0 1 284.64 514.32 Tm <706F696E747320> Tj 1 0 0 1 311.28 513.84 Tm <6F6620> Tj 1 0 0 1 321.84 513.84 Tm <74616E67656E637920> Tj 1 0 0 1 360.00 513.84 Tm <6F6620> Tj 1 0 0 1 370.80 513.60 Tm <74686520> Tj 1 0 0 1 385.68 513.84 Tm <6E6F726D616C20> Tj 1 0 0 1 415.92 513.60 Tm <746F20> Tj 1 0 0 1 426.24 513.60 Tm <746C726520> Tj 1 0 0 1 441.60 513.60 Tm <666C6F7720> Tj 1 0 0 1 462.00 513.36 Tm <646972656374696F6E20> Tj 1 0 0 1 500.16 513.36 Tm <616E6420> Tj 1 0 0 1 516.72 513.36 Tm <746865> Tj 0.72 Tc 1 0 0 1 70.80 501.84 Tm <626F647920> Tj 1 0 0 1 93.84 502.08 Tm <7375726661636520> Tj 1 0 0 1 126.24 501.84 Tm <61726520> Tj 1 0 0 1 140.64 503.76 Tm <2D732F29222E2C3A20> Tj 1 0 0 1 172.08 502.08 Tm <302E30382C302E313420> Tj 1 0 0 1 215.04 502.08 Tm <616E6420> Tj 1 0 0 1 232.08 501.84 Tm <302E323120> Tj 1 0 0 1 252.24 502.08 Tm <666F7220> Tj 1 0 0 1 266.64 501.84 Tm <352C20> Tj 1 0 0 1 277.20 501.84 Tm <3820> Tj 1 0 0 1 284.88 501.84 Tm <616E6420> Tj 1 0 0 1 302.88 501.84 Tm <6C3220> Tj 1 0 0 1 314.64 501.60 Tm <6465677265657320> Tj 1 0 0 1 347.28 501.60 Tm <6F66696E636964656E63652C20> Tj 1 0 0 1 401.04 501.60 Tm <726573706563746976656C792E20> Tj 1 0 0 1 457.20 501.36 Tm <436F6E73657175656E746C792C20> Tj 1 0 0 1 516.24 501.36 Tm <746865> Tj 0.48 Tc 1 0 0 1 70.80 491.04 Tm <67656F6D657472696320> Tj 1 0 0 1 113.04 490.80 Tm <737461676E6174696F6E20> Tj 1 0 0 1 156.00 491.04 Tm <706F696E7420> Tj 1 0 0 1 179.04 490.80 Tm <646F657320> Tj 1 0 0 1 199.20 490.80 Tm <6E6F7420> Tj 1 0 0 1 214.80 490.80 Tm <636F72726573706F6E6420> Tj 1 0 0 1 260.16 490.80 Tm <746F20> Tj 1 0 0 1 270.48 490.56 Tm <74686520> Tj 1 0 0 1 285.12 490.56 Tm <6165726F64796E616D696320> Tj 1 0 0 1 337.92 490.32 Tm <737461676E6174696F6E20> Tj 1 0 0 1 380.40 490.80 Tm <706F696E742E20> Tj 1 0 0 1 408.24 490.32 Tm <466F7220> Tj 1 0 0 1 424.32 490.32 Tm <74686520> Tj 1 0 0 1 438.96 490.32 Tm <6F7468657220> Tj 1 0 0 1 461.52 490.56 Tm <706F77657220> Tj 1 0 0 1 489.12 490.08 Tm <6C617720> Tj 1 0 0 1 505.68 490.08 Tm <63617365732E> Tj 0.48 Tc 1 0 0 1 70.80 479.52 Tm <74686520> Tj 1 0 0 1 85.68 479.52 Tm <73616D6520> Tj 1 0 0 1 108.00 479.52 Tm <6265686176696F7220> Tj 1 0 0 1 145.20 479.52 Tm <317320> Tj 1 0 0 1 154.32 479.52 Tm <6F627365727665642C20> Tj 1 0 0 1 194.64 479.52 Tm <686F77657665722C20> Tj 1 0 0 1 233.04 479.52 Tm <697420> Tj 1 0 0 1 240.72 479.52 Tm <74616B657320> Tj 1 0 0 1 263.04 479.76 Tm <706C61636520> Tj 1 0 0 1 286.08 479.28 Tm <636C6F73657220> Tj 1 0 0 1 311.76 479.28 Tm <746F20> Tj 1 0 0 1 321.36 479.28 Tm <74686520> Tj 1 0 0 1 336.00 479.04 Tm <6178697320> Tj 1 0 0 1 354.24 479.04 Tm <6F6620> Tj 1 0 0 1 364.80 479.04 Tm <73796D6D657472792E> Tj 0.48 Tc 1 0 0 1 84.24 468.24 Tm <4E6577746F6E69616E20> Tj 1 0 0 1 131.52 468.00 Tm <666C6F7720> Tj 1 0 0 1 153.36 466.08 Tm <5B315D20> Tj 1 0 0 1 167.76 468.48 Tm <707265646963747320> Tj 1 0 0 1 202.56 468.24 Tm <7468617420> Tj 1 0 0 1 220.56 468.24 Tm <74686520> Tj 1 0 0 1 236.16 468.00 Tm <6465726976617469766520> Tj 1 0 0 1 278.64 468.00 Tm <6F6620> Tj 1 0 0 1 290.16 468.48 Tm <707265737375726520> Tj 1 0 0 1 326.16 467.76 Tm <636F656666696369656E7420> Tj 1 0 0 1 371.28 468.00 Tm <7769746C7220> Tj 1 0 0 1 391.92 467.76 Tm <7265737065637420> Tj 1 0 0 1 423.12 467.76 Tm <746F20> Tj 1 0 0 1 434.40 467.76 Tm <626F647920> Tj 1 0 0 1 457.44 467.52 Tm <636F6F7264696E61746520> Tj 1 0 0 1 502.80 467.52 Tm <64432C2F6473> Tj 0.48 Tc 1 0 0 1 70.80 456.00 Tm <617070726F616368657320> Tj 1 0 0 1 118.80 457.92 Tm <2DFA20> Tj 1 0 0 1 132.72 456.00 Tm <617420> Tj 1 0 0 1 142.56 456.00 Tm <7820> Tj 1 0 0 1 150.96 458.40 Tm <3A20> Tj 1 0 0 1 160.32 456.00 Tm <3020> Tj 1 0 0 1 168.48 456.24 Tm <666F7220> Tj 1 0 0 1 183.36 456.00 Tm <61786973292C726E6D657472696320> Tj 1 0 0 1 240.00 456.48 Tm <706F77657220> Tj 1 0 0 1 268.08 456.00 Tm <6C617720> Tj 1 0 0 1 285.36 456.00 Tm <73686170657320> Tj 1 0 0 1 314.64 456.00 Tm <696E20> Tj 1 0 0 1 325.44 455.76 Tm <74686520> Tj 1 0 0 1 340.80 456.00 Tm <72616E676520> Tj 1 0 0 1 366.24 456.00 Tm <32313320> Tj 1 0 0 1 382.08 456.96 Tm <3C20> Tj 1 0 0 1 390.96 455.76 Tm <6E20> Tj 1 0 0 1 399.12 456.72 Tm <3C20> Tj 1 0 0 1 409.44 455.76 Tm <6C2E20> Tj 1 0 0 1 422.40 455.76 Tm <486F77657665722C20> Tj 1 0 0 1 464.16 455.52 Tm <4E6577746F6E69616E20> Tj 1 0 0 1 510.96 455.52 Tm <666C6F77> Tj 0.48 Tc 1 0 0 1 70.80 444.72 Tm <617373756D657320> Tj 1 0 0 1 107.52 444.72 Tm <616E20> Tj 1 0 0 1 120.48 444.72 Tm <696E66696E69746520> Tj 1 0 0 1 152.64 444.72 Tm <4D61636820> Tj 1 0 0 1 178.32 444.72 Tm <6E756D6265722C20> Tj 1 0 0 1 214.56 444.72 Tm <726174696F20> Tj 1 0 0 1 236.16 444.72 Tm <6F6620> Tj 1 0 0 1 247.92 444.72 Tm <737065636966696320> Tj 1 0 0 1 281.76 444.72 Tm <686561747320> Tj 1 0 0 1 305.28 444.48 Tm <657175616C20> Tj 1 0 0 1 330.00 444.48 Tm <746F20> Tj 1 0 0 1 341.28 444.48 Tm <6F6E652E20> Tj 1 0 0 1 361.44 444.48 Tm <616E6420> Tj 1 0 0 1 379.20 444.48 Tm <6120> Tj 1 0 0 1 387.12 444.48 Tm <73686F636B20> Tj 1 0 0 1 413.52 444.24 Tm <736861706520> Tj 1 0 0 1 439.20 444.24 Tm <7468617420> Tj 1 0 0 1 457.44 444.24 Tm <6D61746368657320> Tj 1 0 0 1 493.44 444.00 Tm <74686520> Tj 1 0 0 1 509.28 444.00 Tm <626F6479> Tj 0.48 Tc 1 0 0 1 71.04 433.44 Tm <736861706522> Tj 0.48 Tc 1 0 0 1 84.96 422.40 Tm <496E20> Tj 1 0 0 1 95.76 422.40 Tm <6F7264657220> Tj 1 0 0 1 119.52 422.16 Tm <746F20> Tj 1 0 0 1 130.80 422.16 Tm <636F6D7061726520> Tj 1 0 0 1 167.52 422.16 Tm <74686520> Tj 1 0 0 1 182.88 422.40 Tm <76616C696469747920> Tj 1 0 0 1 216.00 422.16 Tm <6F6620> Tj 1 0 0 1 227.04 422.16 Tm <74686520> Tj 1 0 0 1 242.16 422.16 Tm <4E6577746F6E72616E20> Tj 1 0 0 1 288.48 422.16 Tm <617070726F78696D6174726F6E7320> Tj 1 0 0 1 352.32 422.16 Tm <696E20> Tj 1 0 0 1 362.88 422.40 Tm <7072656369696374696E6720> Tj 1 0 0 1 405.60 421.92 Tm <74686520> Tj 1 0 0 1 420.72 422.16 Tm <707265737375726520> Tj 1 0 0 1 456.72 422.16 Tm <6772616469656E7420> Tj 1 0 0 1 492.00 421.44 Tm <62656C726176696F722E> Tj 0.48 Tc 1 0 0 1 70.56 411.12 Tm <64436C647320> Tj 1 0 0 1 101.04 411.12 Tm <77617320> Tj 1 0 0 1 120.48 411.12 Tm <657374696D6174656420> Tj 1 0 0 1 162.48 411.12 Tm <666F7220> Tj 1 0 0 1 177.36 411.12 Tm <74686520> Tj 1 0 0 1 193.44 411.12 Tm <6E20> Tj 1 0 0 1 202.32 414.96 Tm <2D2D20> Tj 1 0 0 1 212.40 410.88 Tm <33313420> Tj 1 0 0 1 228.72 411.12 Tm <6361736520> Tj 1 0 0 1 249.36 410.88 Tm <66726F6D20> Tj 1 0 0 1 272.16 410.88 Tm <74686520> Tj 1 0 0 1 288.24 410.88 Tm <44534D4320> Tj 1 0 0 1 319.68 410.88 Tm <736F6C7574696F6E732E20> Tj 1 0 0 1 365.04 410.88 Tm <54686520> Tj 1 0 0 1 384.48 411.12 Tm <7175616C6974617469766520> Tj 1 0 0 1 429.36 410.64 Tm <6265686176696F7220> Tj 1 0 0 1 467.76 410.40 Tm <6F6620> Tj 1 0 0 1 479.76 410.40 Tm <74686520> Tj 1 0 0 1 496.08 410.88 Tm <7072657373757265> Tj 0.48 Tc 1 0 0 1 70.80 399.60 Tm <6772616469656E7420> Tj 1 0 0 1 106.32 399.12 Tm <697320> Tj 1 0 0 1 116.16 399.12 Tm <646570696374656420> Tj 1 0 0 1 152.88 399.12 Tm <696E20> Tj 1 0 0 1 163.92 399.12 Tm <46696775726520> Tj 1 0 0 1 192.72 398.88 Tm <352C20> Tj 1 0 0 1 203.04 399.36 Tm <706172616D65746572697A6564627920> Tj 1 0 0 1 274.32 398.88 Tm <74686520> Tj 1 0 0 1 289.92 398.88 Tm <616E676C6520> Tj 1 0 0 1 314.16 398.64 Tm <6F6620> Tj 1 0 0 1 325.44 398.64 Tm <61747461636B20> Tj 1 0 0 1 351.60 398.64 Tm <63722E20> Tj 1 0 0 1 366.96 398.88 Tm <466F7220> Tj 1 0 0 1 383.76 399.12 Tm <707572706F736520> Tj 1 0 0 1 417.84 398.64 Tm <6F6620> Tj 1 0 0 1 429.36 398.64 Tm <636F6D70617269736F6E2C20> Tj 1 0 0 1 480.48 398.40 Tm <74686520> Tj 1 0 0 1 496.32 398.64 Tm <7072657373757265> Tj 0.48 Tc 1 0 0 1 70.80 388.32 Tm <6772616469656E7420> Tj 1 0 0 1 107.04 387.84 Tm <666F7220> Tj 1 0 0 1 121.92 387.84 Tm <74686520> Tj 1 0 0 1 138.00 387.84 Tm <6361736520> Tj 1 0 0 1 158.88 387.84 Tm <6F6620> Tj 1 0 0 1 170.40 387.84 Tm <7A65726F20> Tj 1 0 0 1 191.04 387.84 Tm <64656772656520> Tj 1 0 0 1 220.80 387.84 Tm <6F6620> Tj 1 0 0 1 232.56 387.84 Tm <696E636964656E636520> Tj 1 0 0 1 273.60 387.84 Tm <697320> Tj 1 0 0 1 283.92 387.60 Tm <616C736F20> Tj 1 0 0 1 303.36 387.60 Tm <696C6C757374726174656420> Tj 1 0 0 1 345.84 387.60 Tm <696E20> Tj 1 0 0 1 357.12 387.60 Tm <7468697320> Tj 1 0 0 1 375.12 387.36 Tm <4669677572652E20> Tj 1 0 0 1 410.40 387.60 Tm <4163636F7264EC6E6720> Tj 1 0 0 1 455.28 387.12 Tm <746F20> Tj 1 0 0 1 466.56 387.12 Tm <7468697320> Tj 1 0 0 1 485.04 387.12 Tm <4669677572652C20> Tj 1 0 0 1 516.48 387.12 Tm <746865> Tj 0.48 Tc 1 0 0 1 70.56 376.32 Tm <707265737375726520> Tj 1 0 0 1 106.32 376.56 Tm <6772616469656E7420> Tj 1 0 0 1 141.12 376.56 Tm <70726573656E747320> Tj 1 0 0 1 175.92 375.84 Tm <74686520> Tj 1 0 0 1 190.56 375.84 Tm <657870656374656420> Tj 1 0 0 1 228.00 375.84 Tm <6265686176696F7220> Tj 1 0 0 1 264.72 375.84 Tm <696E20> Tj 1 0 0 1 274.80 375.84 Tm <7468617420> Tj 1 0 0 1 292.08 375.84 Tm <697420> Tj 1 0 0 1 300.24 375.60 Tm <617070726F616368657320> Tj 1 0 0 1 346.80 377.52 Tm <2D6F6F20> Tj 1 0 0 1 359.76 375.60 Tm <617320> Tj 1 0 0 1 370.08 375.60 Tm <74686520> Tj 1 0 0 1 384.96 375.60 Tm <61726320> Tj 1 0 0 1 399.84 375.60 Tm <6C656E67746820> Tj 1 0 0 1 426.48 375.84 Tm <676F657320> Tj 1 0 0 1 447.12 375.36 Tm <746F20> Tj 1 0 0 1 457.44 375.36 Tm <7A65726F5E20> Tj 1 0 0 1 482.40 375.12 Tm <496E20> Tj 1 0 0 1 492.96 375.12 Tm <7468697320> Tj 1 0 0 1 510.24 375.36 Tm <7761792C> Tj 0.48 Tc 1 0 0 1 70.56 364.80 Tm <74686520> Tj 1 0 0 1 85.44 365.28 Tm <707265737375726520> Tj 1 0 0 1 121.68 365.28 Tm <6772616469656E7420> Tj 1 0 0 1 156.48 364.80 Tm <6265686176657320> Tj 1 0 0 1 191.28 364.80 Tm <617320> Tj 1 0 0 1 202.08 365.04 Tm <696674686520> Tj 1 0 0 1 226.08 365.04 Tm <6C656164696E6720> Tj 1 0 0 1 257.52 364.80 Tm <6564676520> Tj 1 0 0 1 278.64 364.80 Tm <7765726520> Tj 1 0 0 1 300.48 364.56 Tm <6120> Tj 1 0 0 1 307.68 364.56 Tm <626C756E7420> Tj 1 0 0 1 330.72 364.56 Tm <6F6E6520> Tj 1 0 0 1 347.28 364.56 Tm <696E20> Tj 1 0 0 1 358.08 364.56 Tm <737069746520> Tj 1 0 0 1 379.20 364.56 Tm <6F6674686520> Tj 1 0 0 1 405.12 364.56 Tm <6661637420> Tj 1 0 0 1 422.40 364.32 Tm <7468617420> Tj 1 0 0 1 440.16 364.32 Tm <74686520> Tj 1 0 0 1 455.28 364.32 Tm <6C656164696E6720> Tj 1 0 0 1 487.20 364.08 Tm <6564676520> Tj 1 0 0 1 508.56 364.08 Tm <68617320> Tj 1 0 0 1 524.40 364.08 Tm <61> Tj 0.24 Tc 1 0 0 1 70.56 353.52 Tm <7A65726F20> Tj 1 0 0 1 90.00 353.76 Tm <72616469757320> Tj 1 0 0 1 116.64 353.52 Tm <6F6620> Tj 1 0 0 1 127.68 353.52 Tm <6375727661747572652E> Tj 0.48 Tc 1 0 0 1 84.24 342.72 Tm <54686520> Tj 1 0 0 1 103.20 342.72 Tm <6865617420> Tj 1 0 0 1 123.12 342.72 Tm <666C757820> Tj 1 0 0 1 142.08 342.96 Tm <712C20> Tj 1 0 0 1 154.56 342.48 Tm <746F20> Tj 1 0 0 1 165.84 342.48 Tm <74686520> Tj 1 0 0 1 180.96 342.48 Tm <626F647920> Tj 1 0 0 1 204.48 342.48 Tm <7375726661636520> Tj 1 0 0 1 235.92 342.48 Tm <697320> Tj 1 0 0 1 245.76 342.48 Tm <63616C63756C6174656420> Tj 1 0 0 1 288.72 342.24 Tm <627920> Tj 1 0 0 1 301.44 342.24 Tm <74686520> Tj 1 0 0 1 316.80 342.24 Tm <6E657420> Tj 1 0 0 1 332.64 342.24 Tm <656E6572677920> Tj 1 0 0 1 362.16 342.24 Tm <666C7578657320> Tj 1 0 0 1 389.52 342.00 Tm <6F6620> Tj 1 0 0 1 401.04 342.00 Tm <74686520> Tj 1 0 0 1 416.40 342.24 Tm <6D6F6C6563756C657320> Tj 1 0 0 1 459.60 342.00 Tm <696D70696E67696E6720> Tj 1 0 0 1 503.28 341.76 Tm <6F6E20> Tj 1 0 0 1 516.48 341.76 Tm <746865> Tj 0.48 Tc 1 0 0 1 70.80 331.20 Tm <737572666163652E20> Tj 1 0 0 1 109.68 331.44 Tm <54686520> Tj 1 0 0 1 128.88 331.44 Tm <6E657420> Tj 1 0 0 1 145.20 331.44 Tm <6865617420> Tj 1 0 0 1 165.84 331.44 Tm <666C757820> Tj 1 0 0 1 185.04 331.44 Tm <697320> Tj 1 0 0 1 195.60 331.44 Tm <72656C6174656420> Tj 1 0 0 1 226.08 331.20 Tm <746F20> Tj 1 0 0 1 237.84 331.20 Tm <74686520> Tj 1 0 0 1 253.92 331.20 Tm <73756D20> Tj 1 0 0 1 274.08 331.20 Tm <6F6620> Tj 1 0 0 1 285.84 330.96 Tm <74686520> Tj 1 0 0 1 301.92 330.96 Tm <7472616E736C6174696F6E616C2C20> Tj 1 0 0 1 356.16 330.96 Tm <726F746174696F6E616C20> Tj 1 0 0 1 397.92 330.72 Tm <616E6420> Tj 1 0 0 1 415.92 330.72 Tm <766962726174696F6E616C20> Tj 1 0 0 1 462.24 330.48 Tm <656E65726769657320> Tj 1 0 0 1 499.20 330.48 Tm <6F6620> Tj 1 0 0 1 511.44 330.48 Tm <626F7468> Tj 0.48 Tc 1 0 0 1 70.56 319.20 Tm <696E636964656E7420> Tj 1 0 0 1 106.08 319.20 Tm <616E6420> Tj 1 0 0 1 123.36 319.20 Tm <7265666C656374656420> Tj 1 0 0 1 161.28 319.20 Tm <6D6F6C6563756C65732E20> Tj 1 0 0 1 210.48 319.20 Tm <54686520> Tj 1 0 0 1 228.72 319.20 Tm <6865617420> Tj 1 0 0 1 248.64 319.20 Tm <666C757820> 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R >> stream COMPUTATIONAL RESUI,TS AND DISCUSSIONThe impact of the angle of attack on the pressure acting on and the heat transfer to the body surface resultngfrom DSMC simulations are highlighted in this section.The pressurep," on the body surface is calculated by the sum of the normal momentum fluxes of both incidentand reflected molecules at each time step. A flux s regarded as positive if it is directed toward the sudace^ Resultsare normalized by the freestream dynamic pressure t/zp-L) i and presented in terms of the pressure coefficient ,.The dependence ofthe pressure coefficient due to variations in the angle ofattack is demonstrated in Figures 2, 3and 4 forpower law exponents of 112,2/3 and 3/4, respectively. In this set of Figures, the plots in the left siderepresent the pressure coeficients along the windward sides of the leading edges, while the plots in the right sidetirose in the leeward sides. Also, the dimensionless arc lengh is measured lom the stagnation point along the bodysurface for the case of zero degree of incidence. For purpose of comparison, the pressure coefficients for thesepower law shapes by considering zero degree angle ofattack [2] are also presented in this set ofFigures.According to these Figures, by increasing the incidence causes the expected aslmmetry in the pressurecoefficient as the stagnation point moves from the axis to the lower windward side. The pressure coefficientpresents the expected behavior in that it increases in the windward side and decreases in the leeward side witlrincreasing the angle ofattack.Refening to Figure 2, the maximum values for the pressure coefficient in the wrndward side. which correspondto angles of attack of 5, 8 and 12 degrees are located at stations -siL-:0.06" 0.i7 and 0.19, respectively. Thelocations of the statrons which are identified with the points of tangency of the normal to tlre flow direction and thebody surface are -s/)".,: 0.08,0.14 and 0.21 for 5, 8 and l2 degrees ofincidence, respectively. Consequently, thegeometric stagnation point does not correspond to the aerodynamic stagnation point. For the other power law cases.the same behavior 1s observed, however, it takes place closer to the axis of symmetry.Newtonian flow [1] predicts that the derivative of pressure coefficient witlr respect to body coordinate dC,/dsapproaches - at x : 0 for axis),rnmetric power law shapes in the range 213 < n < l. However, Newtonian flowassumes an infinite Mach number, ratio of specific heats equal to one. and a shock shape that matches the bodyshape"In order to compare the validity of the Newtonran approximatrons in preciicting the pressure gradient belravior.dClds was estimated for the n -- 314 case from the DSMC solutions. The qualitative behavior of the pressuregradient is depicted in Figure 5, parameterizedby the angle of attack cr. For purpose of comparison, the pressuregradient for the case of zero degree of incidence is also illustrated in this Figure. Accordng to this Figure, thepressure gradient presents the expected behavior in that it approaches -oo as the arc length goes to zero^ In this way,the pressure gradient behaves as ifthe leading edge were a blunt one in spite ofthe fact that the leading edge has azero radius of curvature.The heat flux q, to the body surface is calculated by the net energy fluxes of the molecules impinging on thesurface. The net heat flux is related to the sum of the translational, rotational and vibrational energies of bothincident and reflected molecules. The heat flux is normalized by %p-(J-3 and presented in terms of heat transfercoefficient C,"The impact on heat transfer oeffiient due to changes in the angle ofattack is illustrated in Figures 6, 7 and 8 forpower law exponents of l12,2l3 and 3l4, respectively. According to this set of Figures, the heat transfer coefficientfollows the same trend observed for pressure coefficient in that it increases in the windward side and decreases inthe leeward side with increasing the incidence. The heat transfer coefficient presents the maximum value in thestagnation region and drops offa short distance away ofthe leading edge nose as the po'ier law exponent lncreases.Also, it is seen that the blunter the leading edge the lower the heat transfer eoefficient in the viinity of thestagnatlon pornt.A number of theoretical and numerial predictions of stagnation point heat transfer on blunt bodies have beenreported in the literature [7-13]. Theoretical formulations, experimental data, and semi-empirical formulas all agreein the fact that stagnation point heat transfer for blunt bodies is inversely proportional to the square root oftlre noseradius (,, . 1l",lR). ln this context, it seems to be interesting to investigate this behavior for the power law shapedleading edges, that are blunt by definition (dyldx -+ co at x : 0), even though the radius of curvature at the nose goesto zero for n> l12.In order to verify the dependence ofthe heat transfer coefficient C1, on tire leading edge radius ofcurvature, tlreproduct Ch\1R./-), named here by functron K(n,a), was obtained from the DSMC results" Figr-rres 9 and l0 displaythe function K(n,o) along the body surface for power law exponents of i/2 and3l4, respectively. 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<73696465> Tj ET endstream endobj 39 0 obj 8727 endobj 40 0 obj << /Length 41 0 R >> stream 2.0 i.r 1.20.80.40.0 2.42.0,o.a 1.20.8o.40.0 n:l/2W indw ard side ---O._ n m ++ 1ao 30 l0 l-S"* 0.1 l0 IO 0l 00 0.40.0l0 0.40"00 s/ l"- S".. 0.is/."*, FIGURE 2, Effect of the angle of attack on pressure coefficient along the windward side (left) and leeward side (right) of bodysurface forpower law exponentof l12. 1 0.01 _-_!_ , ^ o+.O---El- - g o!- o: Iz i{) l0 30 l0 I 0.t-S"* FIGURE 3. Effect of the angle of attack on pressure coefficient along the windward side (left) and leeward side (right) of bodysurface for power law exponent af 213 " 2.4 2.4 ---o- a---{i- 0c50go120 0.0 30 i0 I cl 001 0 001 -sitr- 0 00i 0.01 30 l0 FIGURE 4. Effect of the angle of attack on pressure coefficient along the windward side (left) and leeward side (right) of bodysurface for power law exponent of 314. n = I/2i-eew d W indw ard n=213Leew ard s ide n=3/4Leeward side endstream endobj 41 0 obj 868 endobj 42 0 obj << /Length 27 >> stream % CANON_PFINF_TYPE0_TEXTON endstream endobj 43 0 obj << /Length 45 >> stream q 595.20 0 0 841.68 0.00 0.00 cm /Obj37 Do Q endstream endobj 44 0 obj << /Type /Page /MediaBox [ 0 0 595.20 841.68 ] /Parent 11 0 R /Resources << /Font << /F3 5 0 R >> /XObject << /Obj37 37 0 R >> /Subtype 40 0 R /ProcSet [ /PDF /Text /ImageB /ImageC /ImageI ] >> /Contents [ 42 0 R 43 0 R 38 0 R ] >> endobj 45 0 obj << /Type /XObject /Subtype /Image /Width 2480 /Height 3507 /BitsPerComponent 1 /ColorSpace /DeviceGray /Filter /CCITTFaxDecode /DecodeParms << /K -1 /Columns 2480 >> /Length 35902 >> stream &?*-*__ ^?@L(9-D$Y# Ba\7;Þ9C`qRe%m&8L Vrᎏm<&&塴`2AaN q#l tH+>ZgZYe(qGdvGEÑD AODDDDC sw%C8㟊*= !'Du]r `#adpG##sؽuq5aQcy|":iB ad6w)ل\8{\Z[xbYf9N$2C]ur@/i%:oj _CHi]HdXT"nrq @Z!8CDUmgکVH UT@]!͞nH0E%@B@]pجL<$qD2gH<_P [xGDp< qC<oh-GvUf*=:X< sp/ PM'\_AͤT[)uw ?V9Ur8jw[yvb"Nw#`ޞnPݿ%/E: ?˅Ɠq ֶO#!xvAp~GLa0E0E[R1?9 (ŭRoGF4>ؐh6Gh>alk#ױ!_׬5?Ai^y }+?1ӿ}G_ !)ki6ib_U({Tɶ?¯Cz۲ zŵ]v֟{/[[+k hê#e_񏱧oHX](bњ29+F~{W/84$ݓ7;G #)e~"?קOKVG_VhU/$Az|Hgʚ]]{iai"M0Zt)n[0qI:~Ast~z+LOVú_<+_XPA@u0eB="ղ?Ψj#I^5eu5GB8Dte.BIq2,sP?YXXI -ꃋ1oe.OJ`$;Ne.}A^E].h#pŕCوXDudvz\h[lVE 1#L"W b6W¹h& ":>-}.>tK+-].(1{W F~_SΏ[&WY_^UL GI,i ":~GDs#`?ƃ#I}!xP눲͉M5hT(DtG]e=&V*1oӤn6!eC_FBW&NDu|?h^au_#;|":D#^*|iDIS#$ !.k4[N0=#q;.>]GB?FI,r1Z_n{tV w҄ UƮF<,Q:2%޾rtM4A}~Go״~[E6{_^z](_; kkr~Sjҙr+_?"A?_qaڮzn%K4_F@d(A##p*iiWK_-]v?J/.J[V]U2ҵ|R߽i?]6ivd ?{LzBMڶ:M-a0!EǶ>s1q3dx>qJ"DDG!>(L#}xF<6zؔ-&1NKIHnj~ߥhIKIZ}v:O*ZK|W݇[o_;(v/b}~<_tOk5cP}ޗ-X]cu\FiHuRmӽ?""!κdHAMЧJ뼧k_۷$DuZoK뺿nT>^G_#5_f>])K鍑ܱvdΧ|AiׯO6zaɽ_oOt~(pE_?~wOTSS%_ߏ5tqۛ?^Q,Wk? __wjyuoayձh/I_g/ǘ]Eb?GK#a,{Luk}w()k5ςtۂ{/La|x_#{_;A=h'}C_qA@xDuDt]^;-k߯?KɎ X>+ֻ¶]Ԅdo$euB(z[9kf!?JTy4~GHx_t;^j(ˌMߝ eD*" >hѝ\*e ev]A7MjB^ѝh̦[A~ںW,ntv?~NǶJʅMS'߯tt8}/Ay&߯!E-_0__]q?_髥O| t?_.W]iiy6G|߽յo.a5q]zo &_[&!4xtoDG_h4 a.~"#=":_wҢul"Y@@DIh>^zH#]+#״HJJ}0+$Zh%̊]UM}Zv(Y ?zK ]kT 6oKvzxk]WK$R8i(د?G9}2:m+0V]{UDcqJm tuCK* V\"9~Zw#kDpw_Д/"+cI}[Du":/. 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<2D2D2D806C2D20> Tj 1 0 0 1 282.72 189.84 Tm <6F20> Tj 1 0 0 1 289.44 190.32 Tm <6F> Tj 1.50 Tc /F3 7.0 Tf 1 0 0 1 450.24 286.32 Tm <6E3D323133> Tj 0.96 Tc 1 0 0 1 450.48 269.76 Tm <4C65657720> Tj 1 0 0 1 470.16 269.52 Tm <61726420> Tj 1 0 0 1 484.08 269.52 Tm <73696465> Tj ET endstream endobj 47 0 obj 8010 endobj 48 0 obj << /Length 49 0 R >> stream 0.0-2 0 00.0-4000.0oL y'as -000.0-8000.0 0.80.6(-. 0.44.20.0 0.0-2000.0-4000.0-6000.0-8000.00 30 l0 0.1 0l Leeward side su,- s/2* IO s/1* 30 l0 I 0.1-s/),- 0.01 00 0.20.0l0 0.20.0i0 FIGURE 5. Pressure gradient behavior along the windward side (left) and leeward side (right) of body surface for power lawexponent of 3/4. 0.8 ____a_ n n o---I- = g o____<_ _-lao 30 l0 i-s/A* 0l l0 l0 FIGURE 6. Effect of the angle of attack on heat transfer coefficient along the windward side (left) and leeward side (right) ofbody surface for power law exponent of 3/4. 0.80.60,4Lp0.20.0 0.8 30 t0 | 0.i-s/* 30 0 0.0 FIGURE 7. Effect of the angle of attack on heat transfer coefficient along the windward side (left) and leeward side (right) ofbody surface for power law exponent of 3/4. n: I12Leew ard side Wrndward side ___a_ _ ^o---l- o o n=213Leew ard side endstream endobj 49 0 obj 853 endobj 50 0 obj << /Length 27 >> stream % CANON_PFINF_TYPE0_TEXTON endstream endobj 51 0 obj << /Length 45 >> stream q 595.20 0 0 841.68 0.00 0.00 cm /Obj45 Do Q endstream endobj 52 0 obj << /Type /Page /MediaBox [ 0 0 595.20 841.68 ] /Parent 11 0 R /Resources << /Font << /F3 5 0 R >> /XObject << /Obj45 45 0 R >> /Subtype 48 0 R /ProcSet [ /PDF /Text /ImageB /ImageC /ImageI ] >> /Contents [ 50 0 R 51 0 R 46 0 R ] >> endobj 53 0 obj << /Type /XObject /Subtype /Image /Width 2480 /Height 3507 /BitsPerComponent 1 /ColorSpace /DeviceGray /Filter /CCITTFaxDecode /DecodeParms << /K -1 /Columns 2480 >> /Length 42280 >> stream &x*kQN% BUk_Z׏[BQBiI7aWܴ "9dv`B>Gˁ।f]ˁ2"! &B#8T n"Q;#F2:._ټ9 A PU_B"""?o_.__/?wYA>WKh~D{M ޿Du y|}ThX9}m֛""ݶ_IWJ{ 4a= j"ƒG_IژC4xG0B7]~^}64?h"9F`ak?O*GOcq̊FEg,KzA ::ݮ&DDsBB*.eRaq^Mց4A0x?48-ȠJ_&(pcb!2?z_JB9DI@Gwwب W#3)ba7 $rN>貨A,:[a h#z@'fZ .߿̦/T< X4B?j_O5ֿ2,N[@So粇1( M1Zի_iv"#O)$ 0GM1UI&&J0n|G;JpJ=ߠͥhDT &i=:<*M q>FK!1A15`Ћ8Oy:"t ٹ5tG!YO&23EA{LALDmI8E[J h5Je_.L/d젎MA|2! m[PJ>ak_"<2DàDC]LR~ %}_aБAG!'F&WQ?f &$栗4i{$[+">4YI$2M_c D!ݷ kkiBRC@":$ 8 n\*M5av&(3"J m=$_d0"?o%] #;CMiQ#N .AvNFpo $N"Z":a v i4D}(xcagti6G6GI-"@zA!oIKlA L,1wT[ O#=˿ RҋIan;= kzM.AiSiazME$]. _,rc7LBҨXK(Dv"8k{ e !Q^ \D8A#10a%6 }#fB0h _@&Ch0h 7M,8rϨaO &I0` 6#k_bhPAy ,C (6_a;a$wXVڭ(!nF!*pPn߶ذiРBF;h.;m-yJ?C;"BH[qlZ}zk 4I":K_gƖTkI8#nm&Ehzw޺kI6cI(]m;1#2:. 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578.88 Tm <302E31> Tj 0.24 Tc 1 0 0 1 417.36 566.16 Tm <732F20> Tj 1 0 0 1 424.56 565.92 Tm Tj 0.24 Tc /F3 9.0 Tf 1 0 0 1 418.08 137.28 Tm <736CC32A> Tj 0.24 Tc 1 0 0 1 209.76 353.28 Tm <2D732FC32D> Tj 0.24 Tc 1 0 0 1 77.28 337.68 Tm <46494755524520> Tj 1 0 0 1 114.72 337.68 Tm <392E20> Tj 1 0 0 1 127.20 337.68 Tm <45666665637420> Tj 1 0 0 1 151.68 337.68 Tm <6F6620> Tj 1 0 0 1 162.00 337.92 Tm <74686520> Tj 1 0 0 1 175.68 337.92 Tm <616E676C6520> Tj 1 0 0 1 197.76 337.92 Tm <6F6620> Tj 1 0 0 1 208.08 337.92 Tm <61747461636B20> Tj 1 0 0 1 231.60 337.92 Tm <6F6E20> Tj 1 0 0 1 243.36 337.92 Tm <74686520> Tj 1 0 0 1 256.80 338.40 Tm <70726F6475637420> Tj 1 0 0 1 287.04 337.92 Tm <43686C2F2852284129> Tj 0.48 Tc 1 0 0 1 77.28 327.84 Tm <2872696768742920> Tj 1 0 0 1 102.24 327.36 Tm <6F66626F647920> Tj 1 0 0 1 131.76 327.36 Tm <7375726661636520> Tj 1 0 0 1 159.84 327.60 Tm <666F7220> Tj 1 0 0 1 171.60 327.84 Tm <706F77657220> Tj 1 0 0 1 196.32 327.60 Tm <6C617720> Tj 1 0 0 1 211.20 327.60 Tm <6578706F6E656E746F6620> Tj 1 0 0 1 255.84 327.60 Tm <312C31322E> Tj 0.48 Tc /F3 8.0 Tf 1 0 0 1 77.76 123.60 Tm <46494755524520> Tj 1 0 0 1 115.20 123.60 Tm <31302E20> Tj 1 0 0 1 131.28 123.60 Tm <45666665637420> Tj 1 0 0 1 155.76 123.60 Tm <6F6620> Tj 1 0 0 1 165.60 123.60 Tm <74686520> Tj 1 0 0 1 179.28 123.60 Tm <616E676C6520> Tj 1 0 0 1 200.88 123.60 Tm <6F6620> Tj 1 0 0 1 211.20 123.60 Tm <61747461636B20> Tj 1 0 0 1 234.48 123.84 Tm <6F6E20> Tj 1 0 0 1 246.00 123.60 Tm <74686520> Tj 1 0 0 1 259.20 124.08 Tm <70726F6475637420> Tj 1 0 0 1 289.20 123.60 Tm <436879272852696CE020> Tj 1 0 0 1 330.48 124.32 Tm <3D20> Tj 1 0 0 1 337.68 123.60 Tm <4B282E6E2C612920> Tj 1 0 0 1 364.32 123.60 Tm <616C6F6E6720> Tj 1 0 0 1 386.16 123.60 Tm <74686520> Tj 1 0 0 1 399.60 123.60 Tm <77696E6477617264> Tj 0.48 Tc 1 0 0 1 77.76 114.00 Tm <2872696768742920> Tj 1 0 0 1 102.48 113.28 Tm <6F6620> Tj 1 0 0 1 112.08 113.28 Tm <626F647920> Tj 1 0 0 1 132.24 113.28 Tm <7375726661636520> Tj 1 0 0 1 160.08 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338.16 Tm <6C656577617264> Tj 1.50 Tc /F3 7.0 Tf 1 0 0 1 452.40 292.08 Tm <6E3A332F34> Tj 0.96 Tc 1 0 0 1 452.88 275.52 Tm <4C65657720> Tj 1 0 0 1 471.84 275.52 Tm <61726420> Tj 1 0 0 1 485.76 275.28 Tm <73696465> Tj 1.50 Tc 1 0 0 1 146.88 203.28 Tm <6E3A332F34> Tj 0.96 Tc 1 0 0 1 147.12 186.48 Tm <5720> Tj 1 0 0 1 155.04 186.48 Tm <696E647720> Tj 1 0 0 1 172.56 186.48 Tm <617264> Tj ET endstream endobj 55 0 obj 8263 endobj 56 0 obj << /Length 57 0 R >> stream 30 l0 I 0.1_s/7* 0.0| 0.001 0001 001 I l0 l0 FIGURE 8. Effect of the angle of attack on heat transfer coefficient along the windward side (left) and leeward side (right) ofbodv surface for power law exponent of 3/4" 1.00.80.6ch0"40.20.0 t.00.80.6K(n,a)0.40.20.0 K(n,a) t.61.20.80.40.0 I .0 12.0 8.0 4.0 ___a_ - ^ o____ o o+ '^O: |z 20.0 16.0 l2.0 8.0 4.0-s/)"* 1.00.80.60.40.20.0 1.00.806 0.20.0 00 00 00 00 +0 80 12.0 16.0 20.0side (left) and leeward side 0.1s/ n sl* -s/-FIGURE 9. Effect of the angle of attack on the product Chl/(R(A)(right) ofbody surface for power law exponentof 1,12. FIGURE 10. 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199.92 501.60 Tm <6E6F7420> Tj 1 0 0 1 215.76 501.60 Tm <6578686962697420> Tj 1 0 0 1 245.76 501.36 Tm <63696173737263616C20> Tj 1 0 0 1 281.28 501.12 Tm <626C756E7420> Tj 1 0 0 1 304.32 501.12 Tm <626F647920> Tj 1 0 0 1 326.16 500.88 Tm <6265686176696F722C20> Tj 1 0 0 1 366.00 500.64 Tm <616E6420> Tj 1 0 0 1 382.80 500.64 Tm <63616E20> Tj 1 0 0 1 398.88 500.40 Tm <626520> Tj 1 0 0 1 411.12 500.40 Tm <636F6E7369646572656420> Tj 1 0 0 1 456.24 500.16 Tm <617320> Tj 1 0 0 1 467.28 500.16 Tm <69667468657920> Tj 1 0 0 1 495.60 499.92 Tm <7765726520> Tj 1 0 0 1 517.68 499.68 Tm <7368617270> Tj 0.48 Tc 1 0 0 1 81.36 491.04 Tm <666F7220> Tj 1 0 0 1 95.04 490.80 Tm <74686520> Tj 1 0 0 1 109.92 490.80 Tm <63616C63756C6174696F6E20> Tj 1 0 0 1 155.52 490.56 Tm <6F66707265737375726520> Tj 1 0 0 1 201.12 490.32 Tm <646973747269627574696F6E2E> Tj 0.48 Tc 1 0 0 1 94.32 479.76 Tm <416E6F7468657220> Tj 1 0 0 1 129.60 479.52 Tm Tj 1 0 0 1 152.40 479.52 Tm <7468617420> Tj 1 0 0 1 170.16 479.52 Tm <7374696D756C6174656420> Tj 1 0 0 1 213.60 479.04 Tm <7468697320> Tj 1 0 0 1 230.88 479.04 Tm <737475647920> Tj 1 0 0 1 254.64 479.04 Tm <77617320> Tj 1 0 0 1 272.88 478.80 Tm <74686520> Tj 1 0 0 1 287.76 478.80 Tm <6865617420> Tj 1 0 0 1 306.72 478.56 Tm <7472616E7366657220> Tj 1 0 0 1 339.12 478.32 Tm <726174652E20> Tj 1 0 0 1 362.40 478.32 Tm <497420> Tj 1 0 0 1 371.04 478.56 Tm <77617320> Tj 1 0 0 1 389.04 478.08 Tm <616C736F20> Tj 1 0 0 1 407.76 478.08 Tm <666F756E6420> Tj 1 0 0 1 433.20 477.84 Tm <7468617420> Tj 1 0 0 1 450.48 477.60 Tm <74686520> Tj 1 0 0 1 465.84 477.60 Tm <6865617420> Tj 1 0 0 1 485.04 477.60 Tm <666C757820> Tj 1 0 0 1 503.52 477.36 Tm <746F20> Tj 1 0 0 1 514.08 477.60 Tm <706F776572> Tj 0.48 Tc 1 0 0 1 81.36 468.72 Tm <6C617720> Tj 1 0 0 1 98.16 468.48 Tm <73686170656420> Tj 1 0 0 1 128.40 468.48 Tm <6C656164696E6720> Tj 1 0 0 1 159.60 468.24 Tm <656467657320> Tj 1 0 0 1 184.56 468.24 Tm <666F6C6C6F777320> Tj 1 0 0 1 216.48 468.00 Tm <7468617420> Tj 1 0 0 1 234.00 468.00 Tm <666F7220> Tj 1 0 0 1 247.92 467.76 Tm <636C6173736963616C20> Tj 1 0 0 1 283.20 467.52 Tm <626C756E7420> Tj 1 0 0 1 306.00 467.52 Tm <626F647920> Tj 1 0 0 1 328.08 467.52 Tm <66617220> Tj 1 0 0 1 341.28 467.28 Tm <66726F6D20> Tj 1 0 0 1 362.64 467.28 Tm <74686520> Tj 1 0 0 1 377.52 467.04 Tm <6E6F736520> Tj 1 0 0 1 397.92 467.04 Tm <6F6674686520> Tj 1 0 0 1 423.84 467.04 Tm <6C656164696E6720> Tj 1 0 0 1 454.56 466.56 Tm <656467657320> Tj 1 0 0 1 479.52 466.56 Tm <696E20> Tj 1 0 0 1 489.84 466.32 Tm <7468617420> Tj 1 0 0 1 507.12 466.32 Tm <697420> Tj 1 0 0 1 515.52 466.08 Tm <7363616C6573> Tj 0.48 Tc 1 0 0 1 80.88 457.44 Tm <696E76657273656C7920> Tj 1 0 0 1 120.96 457.20 Tm <7769746820> Tj 1 0 0 1 142.56 456.96 Tm <74686520> Tj 1 0 0 1 158.88 456.96 Tm <72616469757320> Tj 1 0 0 1 186.72 456.72 Tm <6F6620> Tj 1 0 0 1 198.96 456.72 Tm <6375727661747572652E20> Tj 1 0 0 1 246.24 456.72 Tm <5468697320> Tj 1 0 0 1 267.60 456.48 Tm <646570656E64656E636520> Tj 1 0 0 1 317.52 456.24 Tm <7769746820> Tj 1 0 0 1 338.40 456.00 Tm <74686520> Tj 1 0 0 1 354.48 456.00 Tm <72616469757320> Tj 1 0 0 1 382.32 455.76 Tm <6F6620> Tj 1 0 0 1 394.32 455.76 Tm <63757276617475726520> Tj 1 0 0 1 435.12 455.52 Tm <697320> Tj 1 0 0 1 445.68 455.28 Tm <6D6F726520> Tj 1 0 0 1 469.92 455.04 Tm <7369676E69666963616E7420> Tj 1 0 0 1 515.28 454.80 Tm <696E20> Tj 1 0 0 1 526.80 454.80 Tm <746865> Tj 0.48 Tc 1 0 0 1 81.12 445.92 Tm <6C65657761726420> Tj 1 0 0 1 115.44 445.68 Tm <7369646520> Tj 1 0 0 1 134.16 445.68 Tm <7468616E20> Tj 1 0 0 1 154.32 445.44 Tm <7468617420> Tj 1 0 0 1 172.08 445.68 Tm <696E20> Tj 1 0 0 1 182.88 445.44 Tm <74686520> Tj 1 0 0 1 198.00 445.44 Tm <77696E647761726420> Tj 1 0 0 1 240.24 445.20 Tm <7369646520> Tj 1 0 0 1 258.96 445.20 Tm <7769746820> Tj 1 0 0 1 279.12 444.96 Tm <696E6372656173696E6720> Tj 1 0 0 1 322.08 444.72 Tm <74686520> Tj 1 0 0 1 337.44 444.48 Tm <616E676C6520> Tj 1 0 0 1 361.68 444.48 Tm <6F6620> Tj 1 0 0 1 372.72 444.48 Tm <61747461636B2C20> Tj 1 0 0 1 401.52 444.24 Tm <616E6420> Tj 1 0 0 1 418.80 444.24 Tm <697420> Tj 1 0 0 1 427.20 444.00 Tm <6469736170706561727320> Tj 1 0 0 1 471.84 443.76 Tm <696E20> Tj 1 0 0 1 482.16 443.76 Tm <74686520> Tj 1 0 0 1 497.52 443.52 Tm <766963696E69747920> Tj 1 0 0 1 530.40 443.28 Tm <6F66> Tj 0.48 Tc 1 0 0 1 80.88 434.64 Tm <74686520> Tj 1 0 0 1 95.52 434.64 Tm <737461676E6174696F6E20> Tj 1 0 0 1 138.24 434.88 Tm <706F696E742E> Tj 0.24 Tc /F3 12.0 Tf 1 0 0 1 244.80 397.20 Tm <41434B4E4F5C7279492C4544474D454E5453> Tj 0.48 Tc /F3 9.0 Tf 1 0 0 1 94.08 374.88 Tm <54686520> Tj 1 0 0 1 113.04 374.88 Tm <666972737420> Tj 1 0 0 1 132.24 374.64 Tm <617574686F7220> Tj 1 0 0 1 160.80 374.64 Tm <697320> Tj 1 0 0 1 170.88 374.88 Tm <677261746566756C20> Tj 1 0 0 1 204.72 374.40 Tm <746F20> Tj 1 0 0 1 215.76 374.40 Tm <74686520> Tj 1 0 0 1 231.12 374.40 Tm <4869676820> Tj 1 0 0 1 254.16 374.16 Tm <506572666F726D616E636520> Tj 1 0 0 1 307.20 373.68 Tm <436F6D707574657220> Tj 1 0 0 1 349.68 373.44 Tm <43656E74657220> Tj 1 0 0 1 378.96 373.68 Tm <284E414341442D434F5050452F5546524A2920> Tj 1 0 0 1 483.12 372.48 Tm <617420> Tj 1 0 0 1 493.44 372.48 Tm <74686520> Tj 1 0 0 1 509.04 372.48 Tm <4665646572616C> Tj 0.48 Tc 1 0 0 1 80.88 363.60 Tm <556EEC7665727369747920> Tj 1 0 0 1 124.80 363.36 Tm <6F6620> Tj 1 0 0 1 135.84 363.36 Tm <52696F20> Tj 1 0 0 1 152.88 363.12 Tm <646520> Tj 1 0 0 1 164.88 363.12 Tm <4A616E6569726F20> Tj 1 0 0 1 195.84 363.12 Tm <616E6420> Tj 1 0 0 1 212.64 362.88 Tm <74686520> Tj 1 0 0 1 227.28 362.88 Tm <5765617468657220> Tj 1 0 0 1 263.04 362.64 Tm <50726564696374696F6E20> Tj 1 0 0 1 305.76 362.16 Tm <43656E74657220> Tj 1 0 0 1 334.32 362.16 Tm <616E6420> Tj 1 0 0 1 351.12 362.16 Tm <436C696D61746520> Tj 1 0 0 1 384.72 361.92 Tm <5374756469657320> Tj 1 0 0 1 415.92 362.64 Tm <2843505445432F494E50452920> Tj 1 0 0 1 480.00 361.20 Tm <617420> Tj 1 0 0 1 489.84 361.20 Tm <74686520> Tj 1 0 0 1 504.72 360.96 Tm <4E6174696F6E616C> Tj 0.48 Tc 1 0 0 1 80.88 352.32 Tm <496E7374697475746520> Tj 1 0 0 1 115.44 352.32 Tm <666F7220> Tj 1 0 0 1 129.36 352.08 Tm <537061636520> Tj 1 0 0 1 155.28 352.08 Tm <526573656172636820> Tj 1 0 0 1 193.68 351.84 Tm <666F7220> Tj 1 0 0 1 207.60 351.60 Tm <75736520> Tj 1 0 0 1 222.96 351.60 Tm <6F6620> Tj 1 0 0 1 233.52 351.60 Tm <74686520> Tj 1 0 0 1 247.92 351.60 Tm <776F726B73746174696F6E732E> Tj 0.48 Tc /F3 11.0 Tf 1 0 0 1 270.24 314.64 Tm <5245464552454E434553> Tj 0.72 Tc /F3 8.0 Tf 1 0 0 1 81.12 293.28 Tm <312E20> Tj 1 0 0 1 93.60 293.28 Tm <4D61736F6E2C482E572E2C616E644C65652C4A2E2C4A6F75726E616C6F6653706163656372616674616E64526F636B657473336C2833292C3337382D3338322C2831393934292E> Tj 0.48 Tc 1 0 0 1 80.16 283.20 Tm <322E20> Tj 1 0 0 1 93.84 283.20 Tm <53616E746F732E20> Tj 1 0 0 1 123.60 283.20 Tm <572E20> Tj 1 0 0 1 138.48 282.96 Tm <462E20> Tj 1 0 0 1 149.52 282.96 Tm <4E2E2C20> Tj 1 0 0 1 164.40 282.96 Tm <616E6420> Tj 1 0 0 1 180.96 282.96 Tm <4C657769732C20> Tj 1 0 0 1 209.04 282.72 Tm <4D2E20> Tj 1 0 0 1 222.96 282.48 Tm <4A2E2C20> Tj 1 0 0 1 234.96 282.48 Tm <22506F77657220> Tj 1 0 0 1 264.72 282.24 Tm <4C617720> Tj 1 0 0 1 284.64 282.24 Tm <53686170656420> Tj 1 0 0 1 314.40 282.00 Tm <4C656164696E6720> Tj 1 0 0 1 347.04 281.76 Tm <456467657320> Tj 1 0 0 1 372.72 281.76 Tm <696E20> Tj 1 0 0 1 383.52 281.52 Tm <526172656669656420> Tj 1 0 0 1 417.60 281.52 Tm <4879706572736F6E696320> Tj 1 0 0 1 462.48 281.04 Tm <466C6F772C20> Tj 1 0 0 1 483.60 280.56 Tm <2220> Tj 1 0 0 1 490.32 280.80 Tm <6C6E20> Tj 1 0 0 1 501.60 280.80 Tm <34646820> Tj 1 0 0 1 518.40 280.80 Tm <41494141> Tj 0.24 Tc 1 0 0 1 93.12 273.12 Tm <4165726F737061636520> Tj 1 0 0 1 132.96 272.88 Tm <536369656E63657320> Tj 1 0 0 1 165.60 272.88 Tm <4D656574696E6720> Tj 1 0 0 1 196.56 272.64 Tm <616E6420> Tj 1 0 0 1 212.16 272.64 Tm <45786869F3696C2C20> Tj 1 0 0 1 242.16 272.40 Tm <4149414120> Tj 1 0 0 1 265.68 272.64 Tm <706170657220> Tj 1 0 0 1 288.00 272.16 Tm <323030322D303634352C20> Tj 1 0 0 1 330.24 271.92 Tm <52656E6F2C20> Tj 1 0 0 1 352.56 271.68 Tm <4E562E20> Tj 1 0 0 1 371.04 271.68 Tm <31342D313720> Tj 1 0 0 1 393.84 271.44 Tm <4A616E7561727920> Tj 1 0 0 1 422.88 271.44 Tm <323030322E> Tj 0.48 Tc 1 0 0 1 80.16 263.04 Tm <332E20> Tj 1 0 0 1 93.60 263.04 Tm <427272642C20> Tj 1 0 0 1 114.48 262.80 Tm <472E20> Tj 1 0 0 1 126.00 262.80 Tm <412E2C20> Tj 1 0 0 1 139.20 262.80 Tm <4D6F6C6563756C617220> Tj 1 0 0 1 179.76 262.56 Tm <47617320> Tj 1 0 0 1 196.08 262.56 Tm <44796E616D69637320> Tj 1 0 0 1 234.48 262.32 Tm <616E6420> Tj 1 0 0 1 250.80 262.32 Tm <74686520> Tj 1 0 0 1 264.24 262.08 Tm <44697265637420> Tj 1 0 0 1 289.20 261.84 Tm <53696D756C6174696F6E20> Tj 1 0 0 1 330.24 261.60 Tm <6F6620> Tj 1 0 0 1 340.08 261.60 Tm <47617320> Tj 1 0 0 1 356.40 261.60 Tm <2D74726C6F77732C20> Tj 1 0 0 1 383.52 261.36 Tm <4F78666F726420> Tj 1 0 0 1 411.84 261.12 Tm <556E697665727369747920> Tj 1 0 0 1 451.68 260.88 Tm <50726573732C20> Tj 1 0 0 1 475.44 260.64 Tm <4F78666F72642C20> Tj 1 0 0 1 506.16 260.40 Tm <456E6769616E642E> Tj 0.96 Tc 1 0 0 1 93.36 252.96 Tm <754B2E20> Tj 1 0 0 1 111.60 252.96 Tm <3139393422> Tj 0.48 Tc 1 0 0 1 79.92 243.12 Tm <342E20> Tj 1 0 0 1 93.36 243.12 Tm <426972642C20> Tj 1 0 0 1 113.76 242.64 Tm <472E20> Tj 1 0 0 1 124.56 242.88 Tm <342E2C20> Tj 1 0 0 1 138.00 242.64 Tm <224D6F6E746520> Tj 1 0 0 1 166.80 242.40 Tm <4361726C6F20> Tj 1 0 0 1 188.88 242.40 Tm <53696D756C6174696F6E20> Tj 1 0 0 1 229.92 242.40 Tm <696E20> Tj 1 0 0 1 238.80 242.16 Tm <616E20> Tj 1 0 0 1 249.60 242.16 Tm <456E67696E656572696E6720> Tj 1 0 0 1 294.48 241.68 Tm <436F6E746578742C20> Tj 1 0 0 1 325.44 240.72 Tm <2220> Tj 1 0 0 1 330.48 241.44 Tm <696E20> Tj 1 0 0 1 339.12 241.44 Tm <50726F677265737320> Tj 1 0 0 1 373.68 241.20 Tm Tj 1 0 0 1 382.32 241.20 Tm <417374726F6E61757469637320> Tj 1 0 0 1 429.12 240.96 Tm <616E6420> Tj 1 0 0 1 444.48 240.72 Tm <4165722E6F6E6175FC6373> Tj 0.24 Tc 1 0 0 1 492.72 240.48 Tm <526172656669656420> Tj 1 0 0 1 526.32 240.72 Tm <676173> Tj 0.48 Tc 1 0 0 1 93.36 232.80 Tm <44796E616E6963732C20> Tj 1 0 0 1 133.20 232.56 Tm <65646974656420> Tj 1 0 0 1 156.72 232.56 Tm <627920> Tj 1 0 0 1 168.00 232.32 Tm <53616D20> Tj 1 0 0 1 186.00 232.32 Tm <532E20> Tj 1 0 0 1 195.60 232.32 Tm <4669736865722C20> Tj 1 0 0 1 221.76 232.32 Tm <566F6C2E37342C7061727420> Tj 1 0 0 1 268.56 231.84 Tm <492C20> Tj 1 0 0 1 275.52 231.84 Tm <414941412C20> Tj 1 0 0 1 301.44 231.60 Tm <4E657720> Tj 1 0 0 1 320.64 233.76 Tm <796F726B2C20> Tj 1 0 0 1 343.68 236.40 Tm <2C6C3938382C20> Tj 1 0 0 1 364.56 231.60 Tm <70702E20> Tj 1 0 0 1 378.72 231.12 Tm <3233392D3235352E> Tj 0.48 Tc 1 0 0 1 93.36 222.96 Tm <426F72676E616B6B652C20> Tj 1 0 0 1 136.56 222.48 Tm <432E20> Tj 1 0 0 1 146.88 222.72 Tm <616E6420> Tj 1 0 0 1 162.00 222.48 Tm <4C617273656E2C20> Tj 1 0 0 1 190.32 222.48 Tm <502E20> Tj 1 0 0 1 199.68 222.24 Tm <352E2C20> Tj 1 0 0 1 210.72 222.24 Tm <4A6F75726E616C20> Tj 1 0 0 1 240.48 222.00 Tm <6F6620> Tj 1 0 0 1 249.60 222.00 Tm <636F6D70757461ED696F6E616C20> Tj 1 0 0 1 302.16 221.76 Tm <5068797369637320> Tj 1 0 0 1 332.16 221.52 Tm <31382C3430352D3432302C20> Tj 1 0 0 1 378.00 221.76 Tm <2831393735292E> Tj 0.48 Tc 1 0 0 1 93.36 212.88 Tm <53616E746F732C20> Tj 1 0 0 1 122.64 212.64 Tm <572E20> Tj 1 0 0 1 136.56 212.64 Tm <462E20> Tj 1 0 0 1 146.88 212.64 Tm <4E2E2C20> Tj 1 0 0 1 161.28 212.64 Tm <2244697265637420> Tj 1 0 0 1 190.80 212.40 Tm <53696D756C6174696F6E20> Tj 1 0 0 1 232.80 212.16 Tm <4D6F6E746520> Tj 1 0 0 1 258.96 211.92 Tm <4361726C6F20> Tj 1 0 0 1 281.52 211.68 Tm <6F6620> Tj 1 0 0 1 292.32 211.68 Tm <526172656669656420> Tj 1 0 0 1 326.16 211.44 Tm <4879706572736F6E696320> Tj 1 0 0 1 369.84 211.20 Tm <466C6F7720> Tj 1 0 0 1 391.20 210.96 Tm <6F6E20> Tj 1 0 0 1 403.44 210.96 Tm <506F77657220> Tj 1 0 0 1 429.12 210.72 Tm <4C617720> Tj 1 0 0 1 448.56 210.48 Tm <53686170656420> Tj 1 0 0 1 477.84 210.24 Tm <4C656164696E6720> Tj 1 0 0 1 510.24 210.24 Tm <45646765732C22> Tj 0.48 Tc 1 0 0 1 93.36 202.80 Tm <50682E442E20> Tj 1 0 0 1 115.68 202.56 Tm <446973736572746174696F6E2C20> Tj 1 0 0 1 162.96 202.32 Tm <446570742E20> Tj 1 0 0 1 184.08 202.08 Tm <6F6620> Tj 1 0 0 1 193.68 202.08 Tm <4165726F737061636520> Tj 1 0 0 1 233.04 202.08 Tm <456E67696E656572696E672C20> Tj 1 0 0 1 280.08 201.36 Tm <556E697665727369747920> Tj 1 0 0 1 319.44 201.12 Tm <6F6620> Tj 1 0 0 1 329.04 201.12 Tm <4D6172796C616E642C20> Tj 1 0 0 1 367.44 200.88 Tm <436F6C6C65676520> Tj 1 0 0 1 396.72 200.88 Tm <5061726B2C20> Tj 1 0 0 1 417.60 200.64 Tm <4D442220> Tj 1 0 0 1 435.84 200.40 Tm <4465632E2E20> Tj 1 0 0 1 456.72 200.40 Tm <323030312E> Tj 0.48 Tc 1 0 0 1 79.68 192.72 Tm <372E20> Tj 1 0 0 1 93.36 192.48 Tm <536962756C6B726E2C20> Tj 1 0 0 1 127.68 192.24 Tm <4D2E2C20> Tj 1 0 0 1 141.60 192.24 Tm <4A6F7520> Tj 1 0 0 1 154.80 192.24 Tm <726E20> Tj 1 0 0 1 162.96 192.24 Tm <6120> Tj 1 0 0 1 167.28 192.24 Tm <4920> Tj 1 0 0 1 171.84 192.24 Tm <6F6620> Tj 1 0 0 1 180.24 192.00 Tm <4120> Tj 1 0 0 1 186.24 192.00 Tm <65726F6E20> Tj 1 0 0 1 202.56 192.00 Tm <6175746963616C20> Tj 1 0 0 1 228.72 191.76 Tm <536369656E63657320> Tj 1 0 0 1 261.60 191.76 Tm <313920> Tj 1 0 0 1 270.24 192.00 Tm <2838292C20> Tj 1 0 0 1 284.64 191.52 Tm <353720> Tj 1 0 0 1 293.52 191.28 Tm <3020> Tj 1 0 0 1 299.28 192.96 Tm <2D353720> Tj 1 0 0 1 310.56 191.28 Tm <312C20> Tj 1 0 0 1 318.24 192.24 Tm <2820> Tj 1 0 0 1 322.32 191.28 Tm <6C6720> Tj 1 0 0 1 331.20 191.04 Tm <3532292E> Tj 0.48 Tc 1 0 0 1 79.68 182.40 Tm <382E20> Tj 1 0 0 1 93.12 182.40 Tm <4C6565732E20> Tj 1 0 0 1 114.24 182.16 Tm <4C2E2C20> Tj 1 0 0 1 125.52 182.16 Tm <6920> Tj 1 0 0 1 130.08 182.16 Tm <6520> Tj 1 0 0 1 134.16 182.16 Tm <7420> Tj 1 0 0 1 138.24 182.16 Tm <5020> Tj 1 0 0 1 144.24 182.16 Tm <726F20> Tj 1 0 0 1 151.68 182.88 Tm <707520> Tj 1 0 0 1 161.28 181.92 Tm <4920> Tj 1 0 0 1 163.20 181.92 Tm <7320> Tj 1 0 0 1 167.04 181.92 Tm <6920> Tj 1 0 0 1 169.20 181.92 Tm <6F20> Tj 1 0 0 1 173.76 181.92 Tm <6E20> Tj 1 0 0 1 180.96 181.92 Tm <32362834292C20> Tj 1 0 0 1 204.24 181.68 Tm <32353920> Tj 1 0 0 1 217.20 183.36 Tm <2D3236392C20> Tj 1 0 0 1 237.36 182.16 Tm <283120> Tj 1 0 0 1 244.80 181.44 Tm <3920> Tj 1 0 0 1 250.08 181.44 Tm <35362920> Tj 1 0 0 1 261.36 179.76 Tm <22> Tj 0.72 Tc 1 0 0 1 79.44 172.32 Tm <392E20> Tj 1 0 0 1 93.12 172.32 Tm <526F6D72672C20> Tj 1 0 0 1 121.68 172.08 Tm <4D2E2C20> Tj 1 0 0 1 135.60 172.08 Tm <4A657420> Tj 1 0 0 1 148.32 172.08 Tm <50726F70756C73696F6E20> Tj 1 0 0 1 190.56 171.84 Tm <3236283132292C313039382D3120> Tj 1 0 0 1 243.84 171.60 Tm <6930312E20> Tj 1 0 0 1 260.40 172.08 Tm <2831393536292E> Tj 0.48 Tc 1 0 0 1 80.40 162.24 Tm <4920> Tj 1 0 0 1 84.00 162.24 Tm <302E20> Tj 1 0 0 1 92.88 162.24 Tm <4661792C20> Tj 1 0 0 1 110.40 162.00 Tm <4A2E20> Tj 1 0 0 1 118.56 162.00 Tm <342E2C20> Tj 1 0 0 1 131.52 161.76 Tm <616E6420> Tj 1 0 0 1 146.64 161.76 Tm <52696464656C6C2C20> Tj 1 0 0 1 177.12 161.76 Tm <4620> Tj 1 0 0 1 182.16 160.08 Tm <2220> Tj 1 0 0 1 186.24 161.76 Tm <522E2E20> Tj 1 0 0 1 198.24 161.52 Tm <4A6F75726E616C20> Tj 1 0 0 1 228.48 161.52 Tm <6F6620> Tj 1 0 0 1 236.88 161.52 Tm <4165726F6E6175746963616C20> Tj 1 0 0 1 285.12 161.04 Tm <536369656E63657320> Tj 1 0 0 1 317.52 160.80 Tm <32352832292C20> Tj 1 0 0 1 341.04 160.56 Tm <37332D38352C20> Tj 1 0 0 1 365.76 161.28 Tm <2820> Tj 1 0 0 1 369.84 160.56 Tm <4920> Tj 1 0 0 1 373.20 160.32 Tm <39353820> Tj 1 0 0 1 387.12 159.36 Tm <29> Tj 0.72 Tc 1 0 0 1 80.40 152.16 Tm <31312E20> Tj 1 0 0 1 92.88 152.16 Tm <5A6F62792C382E2C20> Tj 1 0 0 1 127.92 151.92 Tm <4D6F73732C20> Tj 1 0 0 1 151.44 151.68 Tm <4E2E20> Tj 1 0 0 1 162.72 151.68 Tm <4A2E20> Tj 1 0 0 1 170.40 151.68 Tm <616E6420> Tj 1 0 0 1 185.52 151.68 Tm <537574746F6E2C20> Tj 1 0 0 1 212.88 151.44 Tm <4B2E2C20> Tj 1 0 0 1 225.12 151.44 Tm <4A6F75726E616C20> Tj 1 0 0 1 255.12 151.20 Tm <6F6620> Tj 1 0 0 1 264.00 151.20 Tm <5370616365637261667420> Tj 1 0 0 1 303.84 150.72 Tm <616E6420> Tj 1 0 0 1 319.20 150.72 Tm <526F63C0656C7320> Tj 1 0 0 1 348.96 150.48 Tm <6C38286C292E20> Tj 1 0 0 1 372.00 150.24 Tm <36342D37302C20> Tj 1 0 0 1 396.72 151.20 Tm <2820> Tj 1 0 0 1 401.04 150.24 Tm <31393831292E> Tj 0.48 Tc 1 0 0 1 80.40 142.08 Tm <31322E20> Tj 1 0 0 1 92.88 142.08 Tm <44654A61726E657474652C20> Tj 1 0 0 1 135.36 141.84 Tm <462E20> Tj 1 0 0 1 144.96 141.60 Tm <522E2C20> Tj 1 0 0 1 157.68 141.60 Tm <48616D696C746F6E2C20> Tj 1 0 0 1 195.36 141.36 Tm <482E20> Tj 1 0 0 1 206.40 141.36 Tm <482E2C20> Tj 1 0 0 1 219.60 141.36 Tm <5765696C6D75656E737465722C20> Tj 1 0 0 1 273.12 140.88 Tm <4B2E20> Tj 1 0 0 1 283.68 140.88 Tm <4A2E2C20> Tj 1 0 0 1 294.00 140.64 Tm <616E6420> Tj 1 0 0 1 308.88 140.64 Tm <4368656174776F6F642C20> Tj 1 0 0 1 353.28 140.40 Tm <462E4D2E2C4A6F75726E616920> Tj 1 0 0 1 406.80 139.92 Tm <6F6620> Tj 1 0 0 1 416.64 140.16 Tm <546865726D6F70686C2C7369637320> Tj 1 0 0 1 471.60 139.44 Tm <616E6420> Tj 1 0 0 1 486.96 139.44 Tm <4865617420> Tj 1 0 0 1 507.36 139.20 Tm <5472616E73666572> Tj 1.44 Tc /F3 10.0 Tf 1 0 0 1 93.60 132.00 Tm <722872292E352D72322E20> Tj 1 0 0 1 132.72 132.24 Tm <2872393837292E> Tj 0.48 Tc /F3 8.0 Tf 1 0 0 1 80.40 121.92 Tm <31332E20> Tj 1 0 0 1 93.12 121.92 Tm <5A757070617264692C20> Tj 1 0 0 1 129.84 121.44 Tm <472E2E20> Tj 1 0 0 1 142.80 121.44 Tm <616E6420> Tj 1 0 0 1 157.68 121.68 Tm <56657264652C20> Tj 1 0 0 1 183.60 121.20 Tm <472E2C20> Tj 1 0 0 1 196.08 121.20 Tm <4A6F7474726E736C20> Tj 1 0 0 1 226.32 120.96 Tm <6F6620> Tj 1 0 0 1 235.20 120.96 Tm <5370616365637261667420> Tj 1 0 0 1 275.04 120.72 Tm <616E6420> Tj 1 0 0 1 289.92 120.48 Tm <526F636B65747320> Tj 1 0 0 1 319.44 120.24 Tm <33352833292C20> Tj 1 0 0 1 342.72 120.24 Tm <3430332D3430352E20> Tj 1 0 0 1 376.56 120.72 Tm <2820> Tj 1 0 0 1 380.64 120.00 Tm <4920> Tj 1 0 0 1 384.00 120.00 Tm <39393829> Tj 1.20 Tc /F3 9.0 Tf 1 0 0 1 79.92 222.96 Tm <352E> Tj 0.96 Tc 1 0 0 1 79.68 212.88 Tm <362E> Tj ET endstream endobj 63 0 obj 29941 endobj 64 0 obj << /Length 65 0 R >> stream Interesttng features can be drawn from Figures 9 and 10. In the vicinity ofthe stagnation point, the dependenceof the heat transfer coefficient on the radius of curvature follows that predicted by the continuum flow for power lawshapes wrth finite radius, n: 112 case, and zero angle of attack. Furthermore, it fails for tlte n > l/2 cases for wlrichthe radii of curvature approach zero at x : 0. Moreover, the function K(n,a) tends to a constant value downstreamthe stagnation region for the range of incidence investigated. The constant value, which is a function of the powerlaw exponent and angle ofattack, is reached faster in the leeward side than that in the windward side. CONCLUDING REMARKSThis study applies the Direct Simulation Monte Carlo method to assess the angle of attack effect on aerodynamicsurface quantities ofpower law shaped leading edges. The calculations provided information concerning the natureof, the pressure coefficient and heat transfer coefficient at the vicinity of the nose resulting from variations in theleading edge thickness at incidence for the idealized situation oftwo-dimensional hypersonic rarefied flow at 70 kmof altitude. Performance results for 5, 8 and i2 degrees of incidence for power law exponents of l/2. 213 and3l4were compared to those cases for zero degree angle ofattack.The simuiations confirmed the quaiitative behavior of the pressure coefficient predicted by the Newtoniantheory. It was found that. even though at incidence, the pressure gradient along the both windward and leewardsides of the power law leading edges goes to minus infinite for n > 2/3 cases. Thus, leading edges with n > 2/3produce a flowfield that does not exhibit ciassrcal blunt body behavior, and can be considered as ifthey were sharpfor the calculation ofpressure distribution.Another ssue that stimulated this study was the heat transfer rate. It was also found that the heat flux to powerlaw shaped leading edges follows that for classical blunt body far from the nose ofthe leading edges in that it scalesinversely with the radius of curvature. This dependence with the radius of curvature is more significant in theleeward side than that in the windward side with increasing the angle of attack, and it disappears in the vicinity ofthe stagnation point. ACKNO\ryI,EDGMENTSThe first author is grateful to the High Performance Computer Center (NACAD-COPPE/UFRJ) at the FederalUnversity of Rio de Janeiro and the Weather Prediction Center and Climate Studies (CPTEC/INPE) at the NationalInstitute for Space Research for use of the workstations. REFERENCES1. Mason,H.W.,andLee,J.,JournalofSpacecraftandRockets3l(3),378-382,(1994).2. Santos. W. F. N., and Lewis, M. J., "Power Law Shaped Leading Edges in Rarefied Hypersonic Flow, " ln 4dh AIAAAerospace Sciences Meeting and Exhiil, AIAA paper 2002-0645, Reno, NV. 14-17 January 2002.3. Brrd, G. A., Molecular Gas Dynamics and the Direct Simulation of Gas -trlows, Oxford University Press, Oxford, Engiand.uK. 1994" 4. Bird, G. 4., "Monte Carlo Simulation in an Engineering Context, " in Progress t Astronautics and Aer.onaucs Rarefied gas Dynanics, edited by Sam S. Fisher, Vol.74,part I, AIAA, New york, ,l988, pp. 239-255.Borgnakke, C. and Larsen, P. 5., Journal of computaional Physics 18,405-420, (1975). Santos, W. F. N., "Direct Simulation Monte Carlo of Rarefied Hypersonic Flow on Power Law Shaped Leading Edges,"Ph.D. Dissertation, Dept. of Aerospace Engineering, University of Maryland, College Park, MD" Dec.. 2001. 7. Sibulkrn, M., Jou rn a I of A eron autical Sciences 19 (8), 57 0 -57 1, ( lg 52).8. Lees. L., i e t P ro pu I s i o n 26(4), 259 -269, (1 9 56) "9. Romrg, M., Jet Propulsion 26(12),1098-1 i01. (1956).I 0. Fay, J. 4., and Riddell, F " R.. Journal of Aeronautical Sciences 25(2), 73-85, ( I 958 )11. Zoby,8., Moss, N. J. and Sutton, K., Journal of Spacecraft and Rocels l8(l). 64-70, ( 1981).12. DeJarnette, F. R., Hamilton, H. H., Weilmuenster, K. J., and Cheatwood, F.M.,Journai of Thermophl,sics and Heat Transferr(r).5-r2. (r987).13. Zuppardi, G.. and Verde, G., Jottrnsl of Spacecraft and Rockets 35(3), 403-405. 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