Thermoacoustic Stability Boundaries in the Model Combustion Chamber with a Gas-Centered Swirl Coaxial Injector

<div>Damping factors plotted on coordinate planes of (a) <svg height="11.9087pt" id="M61" style="vertical-align:-3.2728pt" version="1.1" viewbox="-0.0498162 -8.6359 56.2028 11.9087" width="56.2028pt" 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="M861 0V28C774 35 771 41 768 147L759 509C756 612 762 614 851 622V650H681L449 149L221 650H57V622C148 613 153 609 144 479L130 271C123 166 117 123 111 88C104 46 85 34 26 28V0H259V28C192 35 169 42 167 90C166 130 166 173 170 256L185 541H187L411 7H431L675 555H679L683 147C683 41 680 35 598 28V0H861Z"></path></g><g transform="matrix(.013,0,0,-0.013,11.583,0)"><path d="M493 503C489 551 484 614 483 650H43V622C120 616 128 611 128 525V126C128 40 120 34 40 28V0H312V28C221 34 213 40 213 126V307H316C407 307 412 296 424 227H453V420H424C412 355 407 346 316 346H213V584C213 613 216 616 246 616H322C398 616 419 607 436 579C449 559 455 539 464 499L493 503Z"></path></g><g transform="matrix(.013,0,0,-0.013,18.46,0)"><path d="M631 18C609 24 585 35 559 65C534 91 514 117 478 169C448 214 406 281 389 313C462 346 516 399 516 485C516 545 490 590 449 616C412 641 363 650 290 650H42V622C120 615 128 612 128 527V125C128 40 120 34 38 28V0H300V28C221 34 212 40 212 125V284H244C295 284 312 272 329 244C359 195 395 133 430 84C475 19 516 -3 592 -7C603 -8 615 -8 627 -8L631 18ZM212 316V563C212 591 215 602 223 607C231 613 248 617 277 617C352 617 423 577 423 469C423 415 407 375 368 345C343 324 310 316 260 316H212Z"></path></g><g transform="matrix(.013,0,0,-0.013,29.538,0)"><path d="M535 230V280H52V230H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,40.074,0)"><path d="M671 0V28C608 36 593 47 562 130C495 309 432 486 368 665L336 656C270 481 202 311 134 139C98 47 84 39 20 28V0H241V28C167 38 156 47 178 115C217 236 276 383 327 530H329C375 398 437 223 484 92C499 47 489 37 424 28V0H671Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,50.878,3.132)"><path d="M257 449C165 449 37 374 37 209C37 98 119 -12 256 -12C355 -12 473 65 473 226C473 349 381 449 257 449ZM244 416C333 416 380 320 380 204C380 67 329 21 267 21C184 21 130 115 130 241C130 354 184 416 244 416Z"></path></g></svg> and (b) <svg height="11.9087pt" id="M62" style="vertical-align:-3.2728pt" version="1.1" viewbox="-0.0498162 -8.6359 53.9975 11.9087" width="53.9975pt" 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="M861 0V28C774 35 771 41 768 147L759 509C756 612 762 614 851 622V650H681L449 149L221 650H57V622C148 613 153 609 144 479L130 271C123 166 117 123 111 88C104 46 85 34 26 28V0H259V28C192 35 169 42 167 90C166 130 166 173 170 256L185 541H187L411 7H431L675 555H679L683 147C683 41 680 35 598 28V0H861Z"></path></g><g transform="matrix(.013,0,0,-0.013,11.583,0)"><path d="M493 503C489 551 484 614 483 650H43V622C120 616 128 611 128 525V126C128 40 120 34 40 28V0H312V28C221 34 213 40 213 126V307H316C407 307 412 296 424 227H453V420H424C412 355 407 346 316 346H213V584C213 613 216 616 246 616H322C398 616 419 607 436 579C449 559 455 539 464 499L493 503Z"></path></g><g transform="matrix(.013,0,0,-0.013,18.46,0)"><path d="M631 18C609 24 585 35 559 65C534 91 514 117 478 169C448 214 406 281 389 313C462 346 516 399 516 485C516 545 490 590 449 616C412 641 363 650 290 650H42V622C120 615 128 612 128 527V125C128 40 120 34 38 28V0H300V28C221 34 212 40 212 125V284H244C295 284 312 272 329 244C359 195 395 133 430 84C475 19 516 -3 592 -7C603 -8 615 -8 627 -8L631 18ZM212 316V563C212 591 215 602 223 607C231 613 248 617 277 617C352 617 423 577 423 469C423 415 407 375 368 345C343 324 310 316 260 316H212Z"></path></g><g transform="matrix(.013,0,0,-0.013,29.538,0)"><path d="M535 230V280H52V230H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,40.074,0)"><path d="M715 650H476L470 622C550 619 562 610 562 570C562 536 553 481 535 384L523 321C485 121 408 37 283 37C178 37 99 109 134 297L178 532C193 612 199 616 278 622L284 650H29L23 622C105 616 109 609 94 532L48 291C23 160 51 83 98 40C143 -1 202 -16 260 -16C321 -16 387 3 439 49C509 111 542 204 563 312L577 384C595 479 608 533 619 569C629 603 637 620 709 622L715 650Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,48.68,3.132)"><path d="M257 449C165 449 37 374 37 209C37 98 119 -12 256 -12C355 -12 473 65 473 226C473 349 381 449 257 449ZM244 416C333 416 380 320 380 204C380 67 329 21 267 21C184 21 130 115 130 241C130 354 184 416 244 416Z"></path></g></svg> under <i>self-excited</i> instability.</div>

International Journal of Aerospace Engineering

fig10

Figure 10

Figure 10: Thermoacoustic Stability Boundaries in the Model Combustion Chamber with a Gas-Centered Swirl Coaxial Injector 