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Degree of reaction : ウィキペディア英語版
Degree of reaction

Degree of reaction or reaction ratio (R) is defined as the ratio of static pressure drop in the rotor to the static pressure drop in the stage or as the ratio of static enthalpy drop in the rotor to the static enthalpy drop in the stage.
Degree of reaction (R) is an important factor in designing the blades of a turbine, compressors, pumps and other turbo-machinery. It also
tells about the efficiency of machine and is used proper selection of machine for the required purpose.
Various definitions exist in terms of enthalpies, pressures or flow geometry of the device.
In case of turbines, both impulse and reaction machines, Degree of reaction (R) is defined as the ratio of energy transfer by the change in static head to the total energy transfer in the rotor i.e.
:R = \frac } .〔Peng, William W., Fundamentals of turbomachinery, John Wiley, 2008〕
For a gas turbine or compressor it is defined as the ratio of isentropic heat drop in the moving blades (i.e. the rotor) to the sum of the isentropic heat drops in the fixed blades(i.e. the stator) and the moving blades i.e.
:R = \frac } .
In pumps, degree of reaction deals in static and dynamic head. Degree of reaction is defined as the fraction of energy transfer by change in static head to the total energy transfer in the rotor i.e.
: R = \frac } .
==Relation==
Most turbo machines are efficient to a certain degree and can be approximated to undergo isentropic process in the stage.
Hence from Tds = dh - (\frac)dp,
it is easy to see that for isentropic process ∆H ≃ ∆P. Hence it can be implied
:R = \frac}
The same can be expressed mathematically as:〔S.M,Yahya, Turbines, Compressors and Fans, 4th ed. McGraw,2011〕
:\ R = \frac \textrm}} \,\ \textrm \,\ \frac \textrm }}
Where 1 to 3ss in Figure 1 represents the isentropic process beginning from stator inlet at 1 to rotor outlet at 3. And 2 to 3ss is the isentropic process from rotor inlet at 2 to rotor outlet at 3. The velocity triangle〔 (Figure 2.) for the flow process within the stage represents the change in fluid velocity as it flows first in the stator or the fixed blades and then through the rotor or the moving blades. Due to the change in velocities there is a corresponding pressure change.
Another useful definition used commonly uses stage velocities as:〔
:\, h_2 - h_3 = ^2 - V_^2) + -h_ = h_ - h_ = ( U_2\,V_- U_1\,V_)
is the total enthalpy drop. The degree of reaction is then expressed as〔Dixon, S. L., Fluid Mechanics and Thermodynamics of Turbo-machinery, 5th ed. Elsevier,2011.〕
: R =\frac^2 - V_^2) + )}
For axial machines U2 =U1= U, then〔
: R=\frac^2)})}
The degree of reaction can also be written in terms of the geometry of the turbomachine as obtained by〔
: R= (\frac)(\tan - \tan)
where \beta_3 is the vane angle of rotor outlet and \beta_2 is the vane angle of stator outlet. In practice (\frac) is substituted as ϕ and (\tan - \tan)〔 as \tan giving R= \phi \tan. The degree of reaction now depends only on ϕ and \tan which again depend on geometrical parameters β3 and β2 i.e. the vane angles of stator outlet and rotor outlet. Using the velocity triangles degree of reaction can be derived as:〔
: R=\frac+\frac(\tan - \tan)
This relation is again very useful when the rotor blade angle and rotor vane angle are defined for the given geometry.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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