This document provides an overview of airfoil theory as it relates to axial flow turbomachines. It discusses: 1) The assumptions of 1D flow analysis in axial turbomachines, including an infinite number of blades of negligible thickness and uniform flow. 2) How isolated airfoil theory is needed in practice due to a finite number of blades, which allows for blade-to-blade flow variations. 3) How isolated airfoil theory models each blade as a stationary airfoil in a stream of relative flow, and defines the angle of attack and lift and drag forces on the airfoil.

1. AIRFOIL THEORY
BY DR ARNAB SARKAR

2. LET’S BEGIN
One dimensional analysis of flow through an axial-flow turbo m/c
1) Infinite no. of blades of negligible thickness
2) Flow is assumed uniform both at inlet as well as at outlet
 CONSEQUENCES: (1) Perfect guidance of flow
(2) Only information regarding inlet and outlet velocity triangles are needed
(3) Any variation in blade-to-blade plane hub-to-tip plane is neglected.

3. AXIAL –FLOW TURBOMACHINE BLADING
ISOLATED AIRFOIL
THEORY
BLADE CASCADE
THEORY

4. CONTD…….
• AIRFOIL: A BODY WHOSE CROSS SECTION IS SUCH THAT IT HAS A WELL
ROUNDED LEADING EDGE AND A SHARP TRAILING EDGE. SUCH A BODY CAN
GENERATE A LARGE TRANSVERSE FORCE( CALLED THE LIFT) WHEN MOVING
THROUGH A FLUID.
• PLEASE NOTE DOWN THE DIAGRAMS IN THE NEXT SLIDE.

6. 𝐿 = 𝐶𝐿(
1
2
𝜌∞𝑈∞
2 )(𝑏. 𝑐)
𝐷 = 𝐶𝐷(
1
2
𝜌∞𝑈∞
2 ) 𝑏. 𝑐
𝐶𝐿=𝑓1 (𝛼, 𝑅𝑒, 𝑀)
𝐶𝐷=𝑓2 (𝛼, 𝑅𝑒, 𝑀)
CONTD…….

7. ISOLATED AIRFOIL THEORY (AXIAL FLOW
TURBO M/C)
The basic assumption of 1 D theory of flow through a turbo m/c was that the number of
blades in the rotor is infinite. This provides ‘perfect guidance’ to the flow through the
rotor and precludes any possibility blade-to-blade variation of flow.
In practice, however, the number of blades is finite, and their spacing depends on a
particular rotor design.
If the blade spacing is large, blade-to-blade variation of flow exists and each blade acts
like an isolated airfoil in an external flow.

8. CONTD..
• In the Fig. is shown an isolated airfoil moving with a uniform speed (U). Let the
fluid approach this moving airfoil with absolute velocity 𝐶1and let the flow leave
the airfoil with absolute velocity 𝐶2. The velocity relative to the moving airfoil at
inlet and outlet are denoted by 𝑤1and 𝑤2 respectively and they are obtained by
constructing the appropriate velocity triangles.
• In order to apply the airfoil theory to the moving blade it is assumed that the
blade is stationary in a stream of ‘relative flow’. The free stream velocity (w) of
the relative flow is taken as the average of the relative velocities at inlet and
outlet of the blade. This is illustrated in next Fig.

9. CONTD…
The angle 𝛾 between the average relative velocity vector (w) and the chord line
of the blade is called the angle of incidence or angle of attack.
The force exerted by the relative flow on the blade section is usually resolved in
two mutually perpendicular components namely the lift force (L) perpendicular
to w and drag force D along w as shown in Fig.
This force component may also be expressed in terms of dimensionless force
coefficients as follows.