Slip factor in turbines and compressors
Slip factor is the ratio of actual whirl velocity (tangential component of fluid velocity) of the fluid to the theoretical whirl velocity (theoretical tangential velocity component) in a compressor or a pump. Slip occurs at the outlet of impeller in a turbo machine. When the fluid leaves the impeller consisting of guide vanes, then in a real situation the fluid outlet angle is lesser than vane angle because of slip. This slip results in reduction of tangential velocity component of the fluid. Slip factor plays a very important role in manufacturing of the pumps and compressors to the correct specification and to supply the required power. Even for ideal fluids slip occurs.
Formulae
The mathematical expression is given by \({\sigma}\,\) = \(\frac{V'_{w2}}{V_{w2}}\,\)
\({\sigma}\,\) - Slip factor
\(V'_{w2}\,\) - Actual whirl velocity
\(V_{w2}\,\) - Theoretical whirl velocity
Usually the value of slip factor lies between 0.8 to 0.9.
The fluid head at outlet is reduced due to the slip. The reduced Euler pump expression -
\(\frac{W}{m}\,\) = \({\sigma}\,\) \({V'_{w2} U_2}\,\) - \({V_{w1} U_1}\,\)
Here,
\(V_{w1}\,\) - Theoretical whirl velocity
\(U_1\,\) - Blade speed at inlet
\(U_w2\,\) - Blade speed at outlet
In the figure, \({\beta'_2}\,\) is the angle at which the fluid leaves the impeller and \({\beta_2}\,\) is the actual blade angle and \(V'_{w2}\,\) and \(V_{w2}\,\) are the tangential components of the absolute velocity corresponding to the angles \({\beta'_2}\,\) and \({\beta_2}\,\) respectively.
Figure shows the leading side of a blade, where there is a high-pressure region while on the trailing side of the blade there is a low-pressure region. Due to the lower pressure on the trailing face, there will be a higher velocity and a velocity gradient across the passage. This pressure distribution is associated with the existence of circulation around the blade, so that low velocity on the high pressure side and high velocity on the low-pressure side and velocity distribution is not uniform at any radius. Due to this fact, the flow may separate from the suction surface of the blade.Thus, \(V'_{w2}\,\) is less than \(V_{w2}\,\) and their difference is defined as slip velocity.
- Slip factor correlations
For purely radial blades, which are often used in centrifugal compressors, \({\beta_2}\,\) will be 90° and slip factor given by Stodola for such compressor is
\({\sigma}\,\) = 1 - \({\frac{\pi}{n}}\,\)
Here n is number of vanes.
The Sanitz slip factor for pumps and compressors is given by,
\({\sigma}\,\) = 1 - \({\frac{0.63\pi}{n}}\,\)
References
- S.L.Dixon, Fluid mechanics and thermodynamics of turbo machinery (fifth edition), Elsevier Butterworth–Heinemann, ISBN 0-7506-7870-4
- S.M. Yahya,(4th edition), Turbines,compressors and fans , Tata McGraw-Hill Education
