Experimental Study of a Low-Specific Speed Francis Model Runner during Resonance

<div>Two examples of the histogram, the distribution and the cumulative probability of the coefficients <svg height="14.4219pt" id="M63" style="vertical-align:-4.3506pt" version="1.1" viewbox="-0.0498162 -10.0713 29.8307 14.4219" width="29.8307pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,1.781,-1.044)"><path d="M470 619L451 641C422 610 391 595 348 595C316 595 288 601 248 612C197 628 172 633 138 633C97 633 43 615 0 555L19 532C54 562 86 578 130 578C166 578 189 571 222 562C267 549 301 540 337 540C381 540 434 557 470 619Z"></path></g><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M570 304C570 398 525 448 414 448C385 448 343 445 312 434L329 511L321 518C297 504 262 482 244 460L233 411C195 397 159 381 128 358L135 332C160 347 189 360 224 373L111 -147C97 -210 84 -218 17 -231L13 -257L254 -247L259 -218L233 -216C183 -212 177 -202 189 -142L218 -1C238 -10 266 -12 283 -12C351 3 429 48 483 105C543 168 570 242 570 304ZM482 289C482 161 380 33 304 33C278 33 248 51 233 69L303 396C326 400 352 403 369 403C428 403 482 380 482 289Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.384,3.132)"><path d="M390 111C344 68 312 56 269 56C212 56 118 102 118 241C118 346 175 401 241 401C277 401 312 388 342 360C350 352 355 349 361 349C372 349 394 371 394 392C394 403 391 411 378 422C362 436 329 449 288 449H287C250 449 190 432 138 392C71 341 37 274 37 197C37 90 112 -12 238 -12C297 -12 363 32 407 90L390 111Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,12.791,3.132)"><path d="M639 21C616 28 593 39 566 68C542 92 523 117 486 170C457 215 415 282 397 314C472 346 524 398 524 485C524 545 497 590 456 617C417 641 369 650 296 650H43V617C122 612 130 608 130 523V129C130 45 122 38 38 33V0H306V33C225 38 216 45 216 129V282H249C302 282 319 270 336 243C365 195 401 132 436 84C483 18 525 -5 597 -8C610 -9 622 -9 635 -9L639 21ZM216 319V559C216 586 219 596 227 603S250 613 281 613C356 613 429 576 429 469C429 416 413 379 374 348C349 327 316 319 265 319H216Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,18.606,3.132)"><path d="M384 109C349 76 310 59 268 59C197 59 123 113 120 245C240 248 367 259 384 262C403 266 407 275 407 296C407 376 338 451 254 451H253C201 451 148 425 105 378C65 334 39 272 39 203C39 88 112 -12 235 -12C266 -12 339 5 402 84L384 109ZM230 411C285 411 319 365 319 313C319 298 313 293 294 293C236 291 180 290 125 290C141 370 185 411 230 411Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,22.592,3.132)"><path d="M98 134C72 134 46 117 46 90C46 73 55 65 60 64C95 55 124 32 124 -4C124 -42 95 -68 44 -89L57 -123C122 -104 194 -60 194 22C194 94 136 134 98 134Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,24.749,3.132)"><path d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z"></path></g></svg> and <span class="nowrap"><svg height="9.25202pt" id="M64" style="vertical-align:-3.29111pt" version="1.1" viewbox="-0.0498162 -5.96091 17.7216 9.25202" width="17.7216pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M615 290C615 392 563 448 529 448C511 448 491 441 484 434L483 425C518 400 546 349 546 273C546 158 504 46 417 46C381 46 356 77 356 142C356 184 380 293 392 334L387 340L307 323C305 288 296 228 287 188C265 94 221 52 180 52C144 52 112 89 112 171C112 278 164 372 241 430L226 454C106 394 23 288 23 155C23 40 79 -12 139 -12C184 -12 245 32 285 85C292 31 322 -12 376 -12C423 -12 470 18 501 45C570 104 615 184 615 290Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.969,3.132)"><path d="M504 89L488 119C453 85 428 69 416 69C408 69 405 75 412 102L462 304C492 438 460 451 436 451S388 441 356 423C311 397 229 336 170 256H168L189 340C208 418 200 451 177 451C144 451 82 413 24 352L40 322C65 345 98 369 108 369C114 369 119 363 112 335L28 -3L36 -12C54 -3 83 4 112 10C125 73 138 122 153 174C205 258 328 382 376 382C395 382 399 369 384 305L330 93C312 25 323 -12 351 -12C378 -12 439 21 504 89Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,12.628,3.132)"><path d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z"></path></g></svg>.</span>Mean and 95% confidence interval are indicated.</div>

Shock and Vibration

fig13

Figure 13

Figure 13: Experimental Study of a Low-Specific Speed Francis Model Runner during Resonance 