MINISTRY OF EDUCATION AND SCIENCE OF UKRAINEAviation University
The gas-dynamic calculation of THE axial turbine stage
Methodical guide for performing the course paper for students specialty 8.100106 Manufacturing, maintenance and repair of aircraft and engines
by I.I. Gvozdetsky, V.V. Kharyton, S.I.Tkachenko
KYIV 2007
Contents
Introductiongeneral law of circulation change across blade heightof the turbine stage geometrical dimensionsstage calculation on the middle radiusparameters determination on different turbine stage radiuses1 The example of gas-dynamic calculation of the axial turbine stage
Introduction
turbine serves to provide the power to drive the compressor and accessories. in a case of turboprop or turboshaft engine the turbine, in addition, provides the power to rotate propeller or rotor. It does this by extracting energy from the hot gases released from the combustion system and expanding them to a lower pressure and temperature. These processes take place when hot gases flow along specially shaped passages created by two rows of airfoils: stator vanes and rotor blades. These two rows of airfoils form a turbine stage. To produce the driving torque, the turbine unit may consist of one or several stages. The useful torque, created by turbine is transmitted to compressor by turbine shaft. Three stage turbine unite assembly is shown in fig.1. br/>В
this turbine unit can be divided into two main parts (fig.2): all rotating components (three bladed disks joined with shaft) are named turbine rotor, and all unmovable components (three turbine nozzle diaphragms and turbine casing) create the turbine stator.
The main objectives of turbine stage gas-dynamic calculation are determination of stage geometrical dimensions, gas cinematic parameters and speed plans construction. In course paper cinematic parameters are determined in three sections: sleeve, middle and peripheral. <В
Stage scheme, sections designation and diametrical dimensions are shown in figure 3.
. 3. Main geometrical dimensions of the turbine stage
initial data for turbine stage calculation are taken from gas-dynamic calculation of the designed engine. They are:
В· full gas pressure and stagnated gas temperature at the entry to the turbine stage;
В· mass gas flow rate;
В· turbine stage work;
В· circumferential velocity on the middle radius of the working wheel;
В· jet velocity of gas at the exit from the nozzle diaphragm;
В· reduced velocity at the nozzle diaphragm exit;
В· angle of the stream output from the nozzle diaphragm;
В· pressure recovery coefficient in the nozzle diaphragm;
В· external, middle and sleeve diameters at the entry to the working wheel;;.
All of these parameters are chosen for the first turbine stage of the designed engine.
The general law of circulation change across blade height
gas work, the reactivity rate, the gas velocity, Mach numbers, efficiency, blade incidence angles and other parameters depend on law of circulation change across stage working wheel radius. Different laws of circulation change across radius are expressed by general equation
, (1); m - index rate.
If m = 1 law of circulation constancy is implemented. This law of profiling is used for comparatively short blades (), because in this case reactivity rate across blade height is changed very essentially. And using long blades the reactivity rate can be negative near sleeve.longer blades profiling with index rate m <1 is applied. Particularly, for law of profiling with constant angle of the stream output from nozzle diaphragm is realized.obtain small m angle is increased. It causes increase of the axial gas velocity, which can reach local sonic speed at exit from working wheel. It will mean choking of the turbine stage. As a result, it is no point in increasing of angle more then on 20-25 ° at first stages. At these values ​​negative reactivity rate can occur near blade root, especially at high values ​​of loading coefficient.a result of this, profiling on the base of equation (1) is common, because it gives possibility to avoid negative values ​​of the reactivity rate near the blade root by matching of rate index m at the all values.
Determination of the turbine stage geometrical dimensions
