(3) ( ), ; (4) ( ), ; (5) V r,, (1), (2) (5) (1),,,, l/ t ;,, (1), (2) (3) (2), (1), (2) (3),,,,,,, ;,,,,,, (1) (4),,,, (5),,, V r 3 50, S 1 S 2,, S 1

27 3 Vol127 No13 1997 8 25 ADVANCES IN MECHAN ICS Aug125, 1997, 710048, 100084 ( ),,,,, 1,,,, ( ) [13 ],, [4 ] 1952 80,, ( ),,, ( ), 80, 2 ( ) [5,6 ] : (1) ( ), ; (2) ( ), ; 372

(3) ( ), ; (4) ( ), ; (5) V r,, (1), (2) (5) (1),,,, l/ t ;,, (1), (2) (3) (2), (1), (2) (3),,,,,,, ;,,,,,, (1) (4),,,, (5),,, V r 3 50, S 1 S 2,, S 1 / S 2 S 1 S 2, S 2m S 1, [ 7, 8 ],,,, S 2m S 1 311 S 2m 1 ( q 1, q 2, q 3 ), S 2m q 3 = ( q 1, q 2 ) (1) 373

V 3 - r = H 3 H 1 5 5 q 1 W 1 + H 3 H 2 5 5 q 2 W 2 (2) 5 ( W 1 H 2 rb f ) + 5 ( W 2 H 1 rb f ) = 0 (3) 5 q 1 5 q 2-5 ( V 3 r) H 2 5 q 2 5 + 5 ( V 3 r) 5 1 5 ( H 2 W 2 ) 5 ( H 1 W 1 ) + - H 1 5 q 1 H 1 5 q 1 H 2 5 q 2 H 1 H 2 5 q 1 5 q + 2 1 5 ( E W i - i ) = 0 (4) 1 H 2 5 q 2 ; E i i ; H 1, H 2, H 3 ; ; r, ( r,, z) ; W, V ; B f ; 1 2 3 ( q 1, q 2, q 3 ) (2) (3) (4), 4 :, W 1, W 2, W 3, ( q 1, q 2 ), ;,( q 1, q 2 ),, : r W m, S 2m V 3 V 3 r (Vr ) W m 31111 Vr, S 2m, Vr 3111111 m q 1, l, S 2m d W m d l = aw m + b + c W m (5) 1 a, b, c Vr, (2) (5), (5), (2), Vr (5) (2) Wright Novak [9 ] Vr, Jansen Kirschner [10 ], S 2m ( W s - W p ) [11, ] Jansen,, Vr 374

, S 1 [12 ],, 3111112 (1) Hirsch Warzee [13 ] S 2m,, S 2m [14, ] Vr, S 2m, [15 ], V r, V r S 1,,, (2),, Marsh [16 ] S 2m, [17 ] S 2 [18,19 ] [ 17 ] S 2m, S 1 S 2m, Vr, Vr V r, Vr = ( Vr) in + V r[ ( Vr) out - ( Vr) in ] V r S 1, S 1 / S 2,, 31112 W m q 1, S 2, : d q n = 0, = const,, q 2 d Vr - r2 = d m V m r 2 (6) V m ( V m = W m ), d= 0, = const,, d Vr d q 2 = F( q 1, q 2 ) V m r 2 Vr - r 2 (7) = const, Vr, q 2 = con2 st, V r, (6) (7) Goursat, [20 ] 3, W m,,,, W m, 375

,,, W m, Vr, V r 312 S 1, S 1, :,,, - 31211 [21 S 1 Fredholm ],,,, S 1 1973 Kashiwabara [22 ] S 1 S 2, S 1 S 2,,, 31212 1985 Cedar Stow [23 ] S 1 :,,,, Jennions Stow [24,25 ] S 1 S 2 S 1 S 2, S 2, S 1,,,,,, 31213 [26 ], ( ), ( ),,, 376

,,, [27,28 ] A B, Liu Yan [29 ] A,, 31214 -, (,),, Bonataki [30 ] W (,) A 1 (ln W ) + A 2 ( l nw) + 2 A 3 ( l nw) + A 4 ( l nw) + A 5 ( l nw) + 2 A 6 ( l nw) + A 7 ( l nw) + A 8 ( l nw) ( l nw) + A 9 = 0 (8) 5 5 = F 1 (W,,R,h) (9) 5 5 = F 2 (W,,R,h) (10) A 1 2 A 9, h W, (8) (9) (10), S 1 Bonataki,,,, Chaviaropoulos [31,32 ] 31215 [33,34 ], S 1,,, S 1 [35, ] [36 ],, S 1 31216 [37 ] S 2m / S 1, S 1 : gvr, S 1 gvr gvr, gvr gvr f ( n +1) = f ( n) + f ( n +1) d ( f ( n +1) ) d m = - ( gvr) + ( gvr) W m r 2 377

f, n, m,, gvr [ 23 ] 4,,,,,, ;,,,, :,, 411 Okuroumu McCune [38 ] 1974,,, r,,,, d / d r ( ), Falco [39 ],,,,, 412 1983 Tan [40 ], Clebsch, s ( r,, z) = - f ( r, z) (11) = ( g gvr g s ) p ( s) (12) gv gv V = gv + gv (13) gv = g + rgvg s (14) 378

gv = g ~- T ( s) g gvr (15) j = + ; T ( s) = ; g e ijb / ijb, B ; j = - j 0, ( ) 5 2 5 r 2-1 r 5 5 r + 52 5 z 2 = - r (16) g 2 g= g [ T ( s) g gv r ] (17) 5 f gv z 5 z + gv 5 f r 5 r = gv - gv r bl g s (18) gv bl,, Tan [40 ],, Besel, f Chebyshev, f gvr 5 f / 5 n = 0 5 gvr/ 5 n = 0 Borges [6 ], Tan,,,,,, :,,,,, Ghaly [41 ], Zangeneh [42 ], Borges,,, Ghaly Borges,, Euler, gvr, Dang [43 ] Zangeneh [44 ], Dawes [45 ], Eckardts 30 o,, Bando [46 ] Tan, ( P ) 379

g 2 = Q (19) g 2 = q (20), q = 2 Q Re exp ( ijb ) (21) j = 1 Q = B 2r 5 5 r ( gw 3 r t ) + 5 5 z ( W 3 z r) (22), r, z r, z [47 ] Borges [48 ], 8 5 5 r 1 r 5 + 5 5 r 5 z 1 5 5 = F( r, z) + R ( r, z) (23) r 5 z F( r, z), R ( r, z), [37 ] (21) (22), [37 ], 413 1952 Wu [4 ] S 2m q ( ) S 2m m q ( ) = q ( m ) + (- m ) q ( m ) + (- m) 2 2 q ( m ) + (24) Zhao [49 ], S 2m, S 2m gvr, S 2m S 2m, 5 r = m + ( 2-2m ) + 5 1 2 m 2 ( 2-2m ) 2 5 2 n 5 2 2 m + (25) = m +, ( 2-2m ) B m + 1 2 ( 2-2m ) 2 5B an 5 2 m + 1 6 ( 2-2m ) 3 5 2 B 5 2 2 m + (26) 380

gvr,,, 414 [50 ], V = - g + g (27),, V = g (28) [51 ], gw 1 gw 2 gw 3 = - = 5 5 x 3 (29) = 5 5 x 3 (30) 5 5 x 1 + 5 5 x 2 (31), W j 1 5 R g5 x 3 x j + W j W i 1 ij + 2 i W j ij1 - ( ) 2 r 1 = - R T 5ln 5 x 1 g k1 - R 5 T 5 x 1 g k1 (32) W j 1 5 g5 x 3 x j + W j W i 2 ij + 2 i W j ij2 - ( ) 2 r 2 = - R T 5ln 5 x 2 g k2 - R 5 T 5 x 2 g k2 (33) W j ( j = 1,3) x j ( j = 1,3), k ij, R, T, (29) - (33) [51 ] Xu [52,53 ] - - x 1 M x 1 = - M 0 + M 0-2 ( M 0 - M ) M 0 2 ( M 0 - M ) (34), 381

415 22, 5 U 5 t + 5 F 5 x + 5 G 5 y + 5 H 5 z = 0 (35) t, 1982 Tong [54 ] Euler Meauze [55 ] 5 f 5 t - ( W g ) f + 5 F 5 x + 5 G 5 y + f u h d h d x 0 (36), h, Singh [56 ] Leonard [57 ] Zannetti [58 ] Zannetti [59 ] 22, Tong, Leonard, n n( T ) i - 1 + s ( n) i +( n + i - 1 2 = n( ) i (37) Zannetti, P, 5,,,, 511 [35 ] S 1,,, :,,,,,, [50 ],, [36 ],,,,,, 382

,, 512 Zangeneh [44 ] : gvr,,,,, B aero = gv aera m gv m mass (38) gv mass m = 2 s P V m V m rd 2 s V m rd P, gv mass m = 2 s V m rd P 2 s rd P bl v = bl + v (39) v, [ 44 ] Dawes [45 ], Eckardts 30 o, 6,,, 50,,,,, 60 70, [60,, ] 80, [6164 ] [65 ], ( S 1 ), S 2m, 80 [66 ( S 1 ), ], 383

, : 2 611, : 1 ; 2 Papailou [60 ], [67,68 ],,, ( ) [67,68 ],,, [69 ],, [70 ],,, [71 ] Vr 612,, F( X), min F( X) X E n (40) h j ( X) g j ( X) = 0 j = 1,2,, m (41) Φ 0 j = m + 1,, p (42) X n,, [61 ],,,,, Massardo [62,63 ],, 384

F( X) = G(1 - T T ) + G A (1 - ga SP ) + G c (1 - C h ) (43) G G A G c, 1,, X x n R x n = a n1 + a n2 R + a n3 R 2 (44), [72 ],,,,,,, [37 ],, :, gvr, F = G+ G (45) GG 1,,,,,, [74 ] 613 22, 2 2 : X,,, [73 ] G i ( X) Φ 0 ( i = 1,2,, n) (46) 22, X, G i ( X), G i ( X) Φ 0 X, [75 ], 2,, IB,,,,, 7 385

, : (1) S 2m,, [15,18,19 ], gv r S 1,,,, [11,12 S 2m ] S 1 / S 2m (2) S 1,,,,,,,, S 1, S 2m, [24, 25 ],,, S 1, gv r, (3),,,,,, S 2m,, 3,, ( ), Euler, 22, 3,,,,, (4),,,,,,, gv r, gvr,, 386

, (5), 1 Lakshminarayana B A S M E J Fl ui ds Engi neeri ng, 1991, 113 : 315 352 2 Vu T C Heon K, Shyy W Beijing : Proceeding of 17th IAHR symposium, 1994 329 340 3, 1989, 8 : 22 32 4 Wu C H NACA, TN2604 1952 5, 1985, 3 : 24 33 6 Borges J E Ph D Dissertation, Department of Engineering, Cambridge University, 1986 7 Wang Q H, Zhu G X, Wu C H A S M E J Engng f or Gas Turbi nes and Power, 1985, 107 : 277 285 8,,, 1988 29 183 9 Wright L C, Novak R A ASME Paper 602WA2270 1960 10 Jansen W, Kirschner A M NASA SP304 1975 537 563 11,, 1981, 2 (2) : 157 159 12, 1991 191 296 13 Hirsch C, Warzee G A S M E J Fl ui ds Engng, 1976, 98 : 403 421 14, 1992, 4 : 63 69 15 Wu J C Beijing : Proceeding of International Conference on Pumps and Systems, 1992 456 461 16 Marsh H ARC R & M 3509 1966 17, 1980, 1 (1) : 28 35 18,,,, 1985, 6 (1) : 27 32 19,,, 1985, 6 (3) : 125 129 20,,,, 1990, 29 (5) : 77 82 21,, 1995, 2 : 34 41 22 Kashiwabara Y B ulleti n of JS M E, 1973, 16 (92) : 765 772 23 Cedar R D, Stow P Int J N umer Methods Fl ui ds, 1985, 5 : 331 307 24 Jennious I K, Stow P A S M E J Eng f or Gas Turbi nes and Power, 1985, 107 (2) : 301 307 25 Jennious I K, Stow P A S M E J Eng f or Gas Turbi nes and Power, 1985, 107 (2) : 308 316 26 Liu G L, Yan S ASME Paper 912GT2169 1991 27,,, 1995, 16 (2) : 161 164 28 :, 1991 15 20 29 Yan S, Liu G L Beijing : Proceeding of First International Symposium on Experimental and Computational Aerothermody2 namics of Internal Flow, 1990 449 463 30 Bonataki E, Chaviarpoulos P, Papailiou K D A S M E J Fl ui ds Engng, 1993, 115 : 121 127 31 Chaviarpoulos P, Dedoussis V, Papailiou K D J Fl ui d Mech, 1995, 282 : 131 146 32 Dedoussis V, Chaviarpoulos P, Papailiou K D J Fl ui d Mech, 1995, 282 : 147 162 33, 1985, 6 (4) : 336 341 34,,, 1986, 7 (1) : 31 38 35,,, 1987, 8 (3) : 242 245 36, 1989, 10 (4) : 390 392 37, 1995 38 Okurounm O, McCune J E A IA A J 1974, 12 (10) : 1023 1030 39 Falcao A F Int J Mechanical Science, 1976, 18 : 313 320 40 Tan C S, Hawthrone W R A S M E J Engng f or Gas Turbi nes and Power, 1984, 106 : 346 365 41 Ghaly W S Int J N umer Methods i n Fl ui ds, 1990, 10 : 179 197 42 Zangeneh, M Int J N umer Methods i n Fl ui ds, 1991, 13 : 599 624 43 Dang T Q A S M E J Turbomachi nery, 1993, 115 : 354 361 44 Zangeneh M A S M E J Turbomachi nery, 1994, 116 : 281 290 45 Dawes W N ASME Paper No 882GT270 387

46 Bando K, Miyake Y, Tsujimoto K Osaka : Proc the 3rd Japan2China Joint Conference on Fluid Machinery, 1990 275 282 47, 1992 48,,, 1995, : 30 36 49 Zhao X L, Sun C L, Wu C H A S M E J Engng f or Gas Turbi nes and Power, 1985, 107 : 293 300 50 Sherif A M Int J N umer Methods i n Fl ui ds, 1988, 8 : 17 29 51,, 1992, 13 (2) : 150 155 52 Xu J Z, Gu C W, Trans A S M E J Turbomachi nery, 1992, 114 : 548 552 53,, 1993, 14 (10) : 785 791 54 Thompkins W T, Tong S S A S M E J Engng f or Power, 1982, 104 : 281 285 55 Meauze G M Trans A S M E J Engng f or Power, 1982, 104 : 650 656 56 Singh U K ASME Paper 862GT2167 57 Leonard O, et al Trans A S M E J Turbomachi nery, 1992, 114 : 553 560 58 Zannetti L, Pandolfi M, NASA CR3836 1984 59 Zannetti I, Larocca F, Marsilio R ASME, FED266 1988 71 79 60 Papailiou K D, A S M E J Engng f or Power, 1971, 93 : 79 84 61, 1987 62 Massardo A, Hafez A, Satta A A S M E J Turbomachi nery, 1990, 112 : 399 404 63 Massardo A, Satta A, Marine M A S M E J Turbomachi nery, 1990, 112 : 405 410 64 :, 1993 65 73 65,, 1984, 14 (2) : 161 174 66,, 1989, 9 (4) : 10 13 67, 1980, 4 : 337 346 68, 1982, 2 : 122 128 69,, 1983, 3 : 248 254 70, 1980, 4 : 341 347 71, 1989, 4 : 393 395 72, 1993 263 316 73, 1994, 2 : 1 6 74, 1986 151 170 75, : 92, 1992 284 290 THE RESEARCH AND D EVELOPMENT OF D ESIGN METHODS FOR TURBOMACHINERY Luo Xingqi Liao Weili Xian University of Technology, Xian 710048 Chen Naixiang Lin Ruchang Tsinghua University, Beijing 100084 Abstract The research and development of design methods for turbomachinery is reviewed and assessed in detail in t his paper Some recommendations for f ut ure researches are suggested Keywords t urbomachinery, impeller, inverse problem, optimization design 388