The gas-dynamic calcualation of the axial turbine stage
Методическое пособие - Разное
Другие методички по предмету Разное
erential component are determined by the formulas:
; .
temperature and critical gas velocity in the relative direction are computed from the equations:
velocities at the entry to the working wheel and behind turbine stage are calculated by the formulas:
; .
reactivity rate is determined from the equation
,
is airtwist in the working wheel.of on the middle radius must be within limits of 0,2-0,35.verify calculations accuracy it is necessary to compute turbine stage work by the formula
.
obtained value differs more than on 3% from accepted at the beginning it is necessary to look for mistake in previous calculations.
Cinematic parameters determination on different turbine stage radiuses
plan calculation and construction (see pic. X.x) is done for chosen law of blade profiling across radius.
. X.x
approximate turbine stage calculations we can accept design sections diameters as average between diameters of inlet and output edge, i.e.
flow parameters calculation first of all law of blade profiling across radius are chosen. For that reactivity rate are determined at rate index value m=1,0 () from the equation
.
, the law of circulation constancy is accepted, which provide high stage efficiency. In this case angle of nozzle diaphragm blade incidence is changed across blade height., blades can be profiled by the law of , which allows to obtain same profiles across the blade height and simplifies blade manufacturing technology. Disadvantage of these blades is non-constant axial component of the jet velocity at the exit from the nozzle diaphragm. If value is obtained at index value m=1,0, then assigning , index value m can be found by the formulas:
, if ;
, if .
and on different radiuses in common case are calculated from the equations:
;
.
the law of profiling is accepted, then:
; .
the law of profiling is accepted, velocities and
are calculated from the equations (x.x) and (x.x) with index value .components of the jet velocity are determined by the formulas:
;
.
the law of profiling is accepted, then:
;.
the law of profiling is accepted, velocities and
are calculated from the equations (x.x) and (x.x) with index value .
Table 1cinematic parameters on different radiuses
Parameter and formulaSectionNotesleevemiddleperipheral, m, m/s, m/s,m/s, m/s, deg, m/s, m/s, deg, m/s, m/s, m/s, deg, deg, m/s, m/s, K,J/kg, %
Appendix 1
THE EXAMPLE OF gas-dynamic CALCULATION OF THE axial turbine stage
The initial data for the axial turbine stage gas-dynamic calculation are gas parameters and geometrical dimensions at the entry to the turbine obtained during gas-dynamic calculation of the designed engine.main goals of the turbine stage gas-dynamic calculation are geometrical dimensions determinationof the turbine stage, speed plans construction in three sections across the blade height.the engine gas-dynamic calculation following parameters are known:
gas pressure at the entry to the high-pressure turbine ;
gas temperature at the entry to the high-pressure turbine ;
mass gas flow rate ;
HPT stage work ;
circumferential velocity on the middle radius ;
angle of the stream output from nozzle diaphragm ;
external, middle and sleeve diameters at the entry to the working wheel , , ;
jet velocity of gas at the exit from the nozzle diaphragm ;
reduced velocity at the nozzle diaphragm exit ;
pressure recovery coefficient in the nozzle diaphragm .
Section area at the entry to the HPT first stage working wheel was determined in the engine gas-dynamic calculation:
.
relative density and then;
.dimensions before the working wheel will be found on the basis of the next formulas:
blade height
;
external diameter
;
sleeve diameter
;
relative sleeve diameter
;
determine geometrical dimensions at the exit from the working wheel, first of all, it is necessary to compute flow parameters in this section.temperature at the exit from the turbine stage is calculated from the equation
; .
pressure at the exit from the turbine stage is calculated by the formula
; ,
.component of the jet velocity is assigned at the exit from the working wheel:
;
;;.
velocity is calculated by the formula
; ,.
area at the exit from the working wheel is calculated from the equation
;
.
, we assume.dimensions at the working wheel exit:
;
;
;
stage flow duct are drown in scale x:x (see pic x.x)
. X.x Turbine stage flow duct
is necessary to determine stage loading coefficient for turbine stage calculation on the middle radius:
;
velocity and reduced velocity at the exit from the nozzle diaphragm is computed supposing axial flow output, i.e. :
; ;
; .
component of the jet velocity and parameter at the entry to the working wheel are calculated by the formulas:
; ;
; .
components of the jet velocity at the entry to the working wheel and behind turbine stage, and parameters , and are calculated by the formulas:
; ;
; ;
; ;
; ;
; .
gas velocity and its circumferential component can be found from the expressions:
;;
; .
of the stream inlet into the working wheel in the relative direction is computed by formula
; .
velocity and reduced velocity at the exit from the working wheel are calculated by the formulas:
; ;
; .
output angle at the exit from the working wheel in the relative direction can be found by the formula
; .
velocity at the exit from the working wheel and its circumferential component are determined by the formulas:
; ;
; .
temperature and critical gas velocity in the relative direction are computed from the equations:
;
;
; .
is calculated by the formula
; .
velocities at the entry to the working wheel and behind turbine stage are calculated by the formulas:
;
;
Cinematic reactivity rate is determined from the equation
; .
velocities at the entry to the working wheel and behind it are accepted the same (). Turbine stage work is verified by the equation
;
;
; .
, all calculations are correct.calculate flow parameters on different radiuses, first of all, it is necessary to choose law of profiling across blade height. To do it, calculate reactivity rate an rate index value m=1:
;
.
,we choose law of circulation constancy across the radius .parameters calculations on different radiuses are summarized in the table x.x.
Table X.x
Parameter and formulaSectionsleevemiddleperipheral, m0,6860,7180,75, m/s382400417,81,681,531,4, m/s222,9222,9222,9,m/s641,1612,5586,4, m/s678,7651,8627,3
,966
,927
0,892, deg
.3
.3
22.3, m/s259,1212,5168,6, m/s341,8308279,5, deg
,7
,4
52,9, m/s263,6263,6263,6, m/s000, m/s263,6263,6263,6, deg
90
,4
,4
0,4, deg
,6
,4
32,2, m/s
,2
494,7, m/s382,1400418,6, K
1364
,51
,46
0,42
,696
,716
0,738
,16
,234
0,3,J/kg
245314, %
,04
,013
0,13the basis of foregoing calculation we plot speed plans for three sections on blade height (see pic. X).
)
)
). X.x. Axial turbine stage speed plans:- sleeve section; b - middle section; c- peripheral section.