2.3. Оптимизационный расчет ступеней компрессора на эвм

Возможности упрощенной математической модели по оптимизации проточной части ступеней довольно большие – оптимизируются все меридиональные размеры проточной части, диффузорности лопаточных решеток и числа лопаток. Несмотря на большое количество определяющих параметров, простота модели и маленький объем расчетов по одному варианту позволили построить циклы последовательного поиска оптимального решения направленным перебором вариантов.

В общих чертах оптимизация сводится к обеспечению диффузорности рабочего колеса (обозначение в распечатке – WT) и направляющего аппарата (Cd) в рекомендованных пределах (Wрк = (0,55) 0,6…0,75 (0,85); Сна > 0,5…0,48 (0,45)), числа лопаток (РК – Zim и НА – Zvd) – некоторое значение (12…28 (30) для рабочих колес и 10…22(24) для направляющего аппарата), при задании значений угла выхода потока (AL2) из предела чисел более (13) 14…20 градусов; нагрузки РК (DWim) в пределах 0,22…0,32 (0,35) и НА (DCvd) – 0,15…0,25; D 3 = (1,1…1,2) D 2; D 4 = (1,35…1,45) D 2.

2.3.1. Результаты оптимизационного расчета

Как уже упоминалось выше, оптимизируется вариант 15.

*** Variant # 15 ***

Amount of rotors, nr=1

Amount of stages on rotor #1, nst=3

+---+------+------+------+------+----------+------+------+------+------+------+

| # | Type | F | Mu | PSIt | Reu | U2 | D2 | ETA | Tin | Tout |

+---+------+------+------+------+----------+------+------+------+------+------+

|Rotor # 1 n=60000. Dhb=0.25 |

| 1 |3D+VD |0.0306|0.5382|0.7500| 6.140E+06|555.36|0.1768|0.8288|308.00|354.36|

| 2 |3D+VD |0.0263|0.5018|0.7400| 7.140E+06|555.36|0.1768|0.8303|354.36|400.40|

| 3 |3D+VD |0.0231|0.4720|0.7300| 8.140E+06|555.36|0.1768|0.8312|400.40|446.12|

+---+------+------+------+------+----------+------+------+------+------+------+

Polytropic Efficiency, ETAp=0.830

Power consumption, Nc=281.03 kW

Stage # 1

**** Input data ****

F = .306E-01

PSIt = .750E+00

Mu = .538E+00

K = .166E+01

Reu = .614E+07

Dhb = .250E+00

DELim = .120E-01

DELvd = .150E-01

DELrch = .200E-01

Kp = .450E+00

Stage exit - RCh

Impeller - 3D

Diffuser - VD

**** Optimization parameters *****

Ad = .100E+01-

AL2 = .180E+02-

DWim = .350E+00-

DCvd = .207E+00-

DCrch = .400E+00-

DAL34 = .100E+02-

B3/B2 = .100E+01-

D3 = .115E+01-

D4 = .145E+01-

B5/B6 = .700E+00-

B66 = .100E+01-

I5 = .000E+00-

******* Calculation rezults ********

+------------------+------------------+------------------+

| Impeller | Diffuser | Return channel |

+------------------+------------------+------------------+

| Stage's geometry parameters |

| D1= .453E+00 | D3= .115E+01 | D5= .145E+01 |

| D0= .453E+00 | D4= .145E+01 | D6= .453E+00 |

| B1= .101E+00 | B3= .286E-01 | B5= .789E-01 |

| B2= .286E-01 | B4= .286E-01 | B6= .113E+00 |

| BT1'= .303E+02 | AL3'= .199E+02 | AL5'= .220E+02 |

| BT2'= .457E+02 | AL4'= .299E+02 | AL6'= .900E+02 |

| Zim= .170E+02 | Zvd= .190E+02 | Zrch= .130E+02 |

| WT= .682E+00 | Cd= .476E+00 | Crch= .545E+00 |

| BTbl1= .323E+02 | ALbl3= .189E+02 | ALbl5= .182E+02 |

| BTbl2= .755E+02 | ALbl4= .329E+02 | ALbl6= .900E+02 |

| Rblim=---------- | Rblvd= .151E+01 | Rbrch= .344E+00 |

| flow rates in control planes |

| F0= .215E+00 | F2= .244E+00 | F4= .159E+00 |

| F1= .215E+00 | F3= .212E+00 | F5= .846E-01 |

| F1'= .265E+00 | F3'= .236E+00 | F5'= .968E-01 |

| F2'= .256E+00 | F4'= .165E+00 | F6'= .141E+00 |

| efficiency losses in elements |

| dETim= .253E-01 | dETvd= .351E-01 | dETrc= .131E-01 |

| dETin= .000E+00 | dETvl= .324E-01 | dETbt= .565E-02 |

| loss coefficients of elements |

| Sim= .138E+00 | Svd= .107E+00 | Src= .281E+00 |

| Sin= .000E+00 | Svl= .781E-01 | Sbt= .791E-01 |

+------------------+------------------+------------------+

Disk friction coefficient, BETfr= .248E-01

Disk leakage coefficient, BETlk= .105E-01

Disk leakage-friction coefficient, BETim= .353E-01

Polytropic efficiency 2-2, ETA(0-2)= .942

Polytropic efficiency 4-4, ETA(0-4)= .876

Polytropic efficiency, ETA= .858

*** Stage performances ***

+---+--------+--------+--------+--------+--------+--------+--------+

| N | F | ETA | PSIi | PSIp | Pi | KN | Kn |

+---+--------+--------+--------+--------+--------+--------+--------+

| 1| .0263| .8284| .8038| .6659| 1.3478| .0212| .2201|

| 2| .0278| .8440| .7938| .6700| 1.3506| .0221| .2253|

| 3| .0294| .8554| .7841| .6707| 1.3514| .0230| .2313|

| 4| .0306| .8610| .7764| .6685| 1.3504| .0238| .2366|

| 5| .0321| .8633| .7670| .6622| 1.3468| .0246| .2442|

| 6| .0337| .8596| .7577| .6513| 1.3406| .0255| .2531|

| 7| .0352| .8532| .7486| .6387| 1.3333| .0263| .2626|

| 8| .0367| .8454| .7395| .6252| 1.3255| .0272| .2725|

| 9| .0382| .8366| .7305| .6112| 1.3174| .0279| .2829|

| 10| .0398| .8266| .7216| .5965| 1.3090| .0287| .2938|

| 11| .0413| .8152| .7128| .5811| 1.3002| .0294| .3054|

| 12| .0428| .8019| .7041| .5646| 1.2908| .0302| .3178|

| 13| .0444| .7867| .6954| .5471| 1.2808| .0309| .3311|

| 14| .0459| .7687| .6867| .5279| 1.2700| .0315| .3459|

| 15| .0474| .7473| .6781| .5068| 1.2581| .0322| .3626|

| 16| .0490| .7207| .6696| .4825| 1.2446| .0328| .3822|

| 17| .0505| .6887| .6611| .4552| 1.2295| .0334| .4054|

| 18| .0520| .6489| .6526| .4235| 1.2121| .0339| .4345|

| 19| .0536| .5970| .6441| .3846| 1.1910| .0345| .4739|

+---+--------+--------+--------+--------+--------+--------+--------+

Рис. 5. Треугольники скоростей первой ступени.

Stage # 2

**** Input data ****

F = .263E-01

PSIt = .740E+00

Mu = .502E+00

K = .166E+01

Reu = .714E+07

Dhb = .250E+00

DELim = .120E-01

DELvd = .150E-01

DELrch = .200E-01

Kp = .450E+00

Stage exit - RCh

Impeller - 3D

Diffuser - VD

**** Optimization parameters *****

Ad = .100E+01-

AL2 = .180E+02-

DWim = .303E+00-

DCvd = .196E+00-

DCrch = .384E+00-

DAL34 = .800E+01-

B3/B2 = .100E+01-

D3 = .115E+01-

D4 = .145E+01-

B5/B6 = .700E+00-

B66 = .100E+01-

I5 = .000E+00-

******* Calculation rezults ********

+------------------+------------------+------------------+

| Impeller | Diffuser | Return channel |

+------------------+------------------+------------------+

| Stage's geometry parameters |

| D1= .441E+00 | D3= .115E+01 | D5= .145E+01 |

| D0= .441E+00 | D4= .145E+01 | D6= .441E+00 |

| B1= .955E-01 | B3= .253E-01 | B5= .761E-01 |

| B2= .253E-01 | B4= .253E-01 | B6= .109E+00 |

| BT1'= .301E+02 | AL3'= .197E+02 | AL5'= .194E+02 |

| BT2'= .444E+02 | AL4'= .277E+02 | AL6'= .900E+02 |

| Zim= .190E+02 | Zvd= .170E+02 | Zrch= .130E+02 |

| WT= .714E+00 | Cd= .515E+00 | Crch= .478E+00 |

| BTbl1= .321E+02 | ALbl3= .188E+02 | ALbl5= .161E+02 |

| BTbl2= .686E+02 | ALbl4= .307E+02 | ALbl6= .900E+02 |

| Rblim=---------- | Rblvd= .124E+01 | Rbrch= .342E+00 |

| flow rates in control planes |

| F0= .200E+00 | F2= .240E+00 | F4= .158E+00 |

| F1= .200E+00 | F3= .209E+00 | F5= .790E-01 |

| F1'= .255E+00 | F3'= .231E+00 | F5'= .922E-01 |

| F2'= .255E+00 | F4'= .164E+00 | F6'= .133E+00 |

| efficiency losses in elements |

| dETim= .258E-01 | dETvd= .357E-01 | dETrc= .183E-01 |

| dETin= .000E+00 | dETvl= .355E-01 | dETbt= .684E-02 |

| loss coefficients of elements |

| Sim= .147E+00 | Svd= .111E+00 | Src= .338E+00 |

| Sin= .000E+00 | Svl= .868E-01 | Sbt= .828E-01 |

+------------------+------------------+------------------+

Disk friction coefficient, BETfr= .280E-01

Disk leakage coefficient, BETlk= .119E-01

Disk leakage-friction coefficient, BETim= .398E-01

Polytropic efficiency 2-2, ETA(0-2)= .937

Polytropic efficiency 4-4, ETA(0-4)= .868

Polytropic efficiency, ETA= .844

*** Stage performances ***

+---+--------+--------+--------+--------+--------+--------+--------+

| N | F | ETA | PSIi | PSIp | Pi | KN | Kn |

+---+--------+--------+--------+--------+--------+--------+--------+

| 1| .0224| .8105| .8029| .6508| 1.2916| .0179| .2064|

| 2| .0237| .8272| .7915| .6547| 1.2939| .0187| .2114|

| 3| .0250| .8395| .7804| .6551| 1.2944| .0195| .2171|

| 4| .0263| .8468| .7695| .6516| 1.2929| .0202| .2236|

| 5| .0276| .8479| .7587| .6433| 1.2890| .0210| .2313|

| 6| .0289| .8428| .7482| .6305| 1.2827| .0216| .2404|

| 7| .0302| .8353| .7377| .6162| 1.2757| .0223| .2501|

| 8| .0316| .8262| .7274| .6010| 1.2683| .0230| .2603|

| 9| .0329| .8158| .7172| .5851| 1.2606| .0236| .2710|

| 10| .0342| .8040| .7071| .5685| 1.2525| .0242| .2824|

| 11| .0355| .7908| .6970| .5512| 1.2442| .0247| .2945|

| 12| .0368| .7753| .6871| .5327| 1.2353| .0253| .3077|

| 13| .0381| .7569| .6772| .5126| 1.2257| .0258| .3224|

| 14| .0395| .7349| .6674| .4904| 1.2151| .0263| .3389|

| 15| .0408| .7066| .6576| .4646| 1.2029| .0268| .3588|

| 16| .0421| .6715| .6479| .4350| 1.1890| .0273| .3830|

| 17| .0434| .6268| .6382| .4000| 1.1727| .0277| .4142|

| 18| .0447| .5670| .6285| .3564| 1.1526| .0281| .4584|

| 19| .0460| .4933| .6189| .3053| 1.1295| .0285| .5223|

+---+--------+--------+--------+--------+--------+--------+--------+

Рис. 6. Треугольники скоростей второй ступени.

Stage # 3

**** Input data ****

F = .231E-01

PSIt = .730E+00

Mu = .472E+00

K = .166E+01

Reu = .814E+07

Dhb = .250E+00

DELim = .120E-01

DELvd = .150E-01

NUscr = .270E+03

Kp = .450E+00

Stage exit - Scroll

Impeller - 3D

Diffuser - VD

**** Optimization parameters *****

Ad = .100E+01-

AL2 = .180E+02-

DWim = .325E+00-

DCvd = .186E+00-

DAL34 = .750E+01-

B3/B2 = .100E+01-

D3 = .115E+01-

D4 = .145E+01-

******* Calculation rezults ********

+------------------+------------------+------------------+

| Impeller | Diffuser | Scroll |

+------------------+------------------+------------------+

| Stage's geometry parameters |

| D1= .428E+00 | D3= .115E+01 | D180= .153E+01 |

| D0= .428E+00 | D4= .145E+01 | D360= .153E+01 |

| B1= .889E-01 | B3= .228E-01 | Ds180= .257E+00 |

| B2= .228E-01 | B4= .228E-01 | Ds360= .364E+00 |

| BT1'= .298E+02 | AL3'= .198E+02 | AL4= .273E+02 |

| BT2'= .428E+02 | AL4'= .273E+02 | NUscr= .270E+03 |

| Zim= .180E+02 | Zvd= .170E+02 |------------------|

| WT= .747E+00 | Cd= .528E+00 |------------------|

| BTbl1= .318E+02 | ALbl3= .188E+02 | ALscr= .265E+02 |

| BTbl2= .674E+02 | ALbl4= .303E+02 |------------------|

| Rblim=---------- | Rblvd= .119E+01 |------------------|

| flow rates in control planes |

| F0= .193E+00 | F2= .237E+00 | F4= .158E+00 |

| F1= .193E+00 | F3= .206E+00 | F180= .316E+00 |

| F1'= .245E+00 | F3'= .228E+00 | F360= .158E+00 |

| F2'= .250E+00 | F4'= .163E+00 |------------------|

| efficiency losses in elements |

| dETim= .256E-01 | dETvd= .371E-01 | dETsc= .541E-01 |

| dETin= .000E+00 | dETvl= .383E-01 |------------------|

| loss coefficients of elements |

| Sim= .154E+00 | Svd= .117E+00 | Sscr= .631E+00 |

| Sin= .000E+00 | Svl= .950E-01 |------------------|

+------------------+------------------+------------------+

Disk friction coefficient, BETfr= .310E-01

Disk leakage coefficient, BETlk= .131E-01

Disk leakage-friction coefficient, BETim= .441E-01

Polytropic efficiency 2-2, ETA(0-2)= .933

Polytropic efficiency 4-4, ETA(0-4)= .861

Polytropic efficiency, ETA= .809

*** Stage performances ***

+---+--------+--------+--------+--------+--------+--------+--------+

| N | F | ETA | PSIi | PSIp | Pi | KN | Kn |

+---+--------+--------+--------+--------+--------+--------+--------+

| 1| .0189| .7733| .8048| .6223| 1.2436| .0152| .1964|

| 2| .0201| .7903| .7926| .6264| 1.2456| .0159| .2013|

| 3| .0213| .8030| .7807| .6269| 1.2460| .0166| .2069|

| 4| .0224| .8105| .7690| .6233| 1.2447| .0172| .2134|

| 5| .0231| .8122| .7622| .6191| 1.2430| .0176| .2178|

| 6| .0243| .8096| .7509| .6080| 1.2383| .0182| .2262|

| 7| .0254| .8005| .7398| .5922| 1.2317| .0188| .2361|

| 8| .0266| .7892| .7288| .5752| 1.2245| .0194| .2468|

| 9| .0277| .7758| .7180| .5571| 1.2169| .0199| .2582|

| 10| .0289| .7609| .7073| .5382| 1.2090| .0204| .2704|

| 11| .0300| .7431| .6967| .5177| 1.2004| .0209| .2839|

| 12| .0312| .7239| .6862| .4967| 1.1917| .0214| .2985|

| 13| .0323| .7012| .6757| .4738| 1.1823| .0219| .3149|

| 14| .0335| .6754| .6654| .4494| 1.1723| .0223| .3334|

| 15| .0346| .6449| .6551| .4224| 1.1613| .0227| .3552|

| 16| .0358| .6107| .6449| .3938| 1.1497| .0231| .3806|

| 17| .0370| .5659| .6347| .3592| 1.1357| .0235| .4144|

| 18| .0381| .5076| .6246| .3170| 1.1190| .0238| .4621|

| 19| .0393| .4320| .6145| .2654| 1.0988| .0241| .5359|

| 20| .0404| .3244| .6044| .1961| 1.0721| .0244| .6823|

+---+--------+--------+--------+--------+--------+--------+--------+

Рис. 7. Треугольники скоростей третьей ступени.

**** New stages Diameters and rotation Speeds ****

Rotor # 1

D2( 1)= .1768 m U2( 1)=555.4 m/s

D2( 2)= .1768 m U2( 2)=555.4 m/s

D2( 3)= .1768 m U2( 3)=555.4 m/s

**** Design Point Parameters ****

Efficiency, ETC= .8392

Pressure ratio, Pi= 2.1730

Power consumption, N= 279.06 kW

Проверка отклонения отношения давлений от заданного:

Отклонение невелико и находится в допустимых пределах и в пределах точности расчета.

Рис. 8. Рассчитанная в программе zzz1 характеристика компрессора .

Рис. 9. Рассчитанная в программе zzz1 характеристика компрессора .

Рис. 10. Полученный в программе zzz1 меридиональный разрез компрессора.

.