The preliminary design of an axial flow compressor is to be based upon a simplified consideration of the mean diameter conditions. Suppose that the characteristics of a repeating stage of such a design are as follows: Stagnation temperature rise (ΔTst) 30 K Degree of reaction (Λ) 0.6 Flow

Question

The preliminary design of an axial flow compressor is to be based upon a simplified consideration of the mean diameter conditions. Suppose that the characteristics of a repeating stage of such a design are as follows:

Stagnation temperature rise ([latex] \Delta T_{s t} [/latex] )	30 K
Degree of reaction ( [latex] \Lambda [/latex] )	0.6
Flow coefficienty ([latex] V_{f} / U [/latex] )	0.5
Blade speed ([latex] U [/latex] )	300 m/s

Assuming constant axial velocity across the stage and equal absolute velocities at inlet and outlet, determine the blade angles of the rotor for a shock free flow. ([latex] c_{p} [/latex] for air = 1005 J/kg K).

Accepted Answer

Specific work input [latex] w=1005 imes 30 \mathrm{~J} / \mathrm{kg} [/latex]

From Eq. (16.17)

[latex] \Delta T_{s t}=\Delta T_{s}=\frac{U V_{f}}{c_{p}}\left( an \beta_{1}- an \beta_{2} ight) [/latex] (16.17)

[latex] 1005 imes 30=(300)^{2} imes(0.5)\left( an \beta_{1}- an \beta_{2} ight) [/latex]

Or [latex] an \beta_{1}- an \beta_{2}=0.67 [/latex]

Again from Eq. (16.24),

[latex] \Lambda=\frac{V_{f}}{2 U}\left( an \beta_{1}+ an \beta_{2} ight) [/latex] (16.24)

[latex] 0.6=\frac{0.5}{2}\left( an \beta_{1}+ an \beta_{2} ight) [/latex]

[latex] an \beta_{1}+ an \beta_{2}=2.4 [/latex]

The above two equations give

[latex] \beta_{1}=56.92^{\circ}, \quad \beta_{2}=40.86^{\circ} [/latex]

Question 16.7: The preliminary design of an axial flow compressor is to be ...

Related Answered Questions

A centrifugal fan running at 1500 rpm has inner and outer diameter of the impeller as 0.2 m and 0.24 m. The absolute and relative velocities of air at entry are 21 m/s and 20 m/s respectively and those at exit are 25 m/s and 18 m/s respectively. The flow rate is 0.6 kg/s and the motor efficiency ...

Verified Answer:

The conditions of air at the entry of an axial flow compressor stage are p1 = 100kN/m^2 and Tl = 300 K. The air angles are β1 = 51º, β2 = 10º, a1 = a 3 = 8º. The mean diameter and peripheral speed are 0.5 m and 150 m/s respectively. Mass flow rate through the stage is 30 kg/s; the work done ...

Verified Answer:

At the mean diameter, U = 200 m/s, V f = 180 m/s, β1 = 43.9° and β2 = 13.5°. The factor λ = 0.86 and ηs = 0.85 and inlet temperature T1t is 288 K. Calculate the pressure ratio. ...

Verified Answer:

Air at a temperature of 27°C flows into a centrifugal compressor running at 20,000 rpm. The following data are given: Slip factor 0.80 Power input factor 1 Isentropic efficiency 80% Outer diameter of blade tip 0.5 m Assuming the absolute velocities of air entering and leaving the compressor are ...

Verified Answer:

A centrifugal compressor has an impeller tip speed of 360 m/s. Determine (i) the absolute Mach number of flow leaving the radial vanes of the impeller and (ii) the mass flow rate. The following data are given: Impeller Tip speed 360 m/s Radial component of flow velocity at impeller exit 30 m/s ...

Verified Answer:

Determine the pressure ratio developed and the specific work input to drive a centrifugal air compressor of an impeller diameter of 0.5 m and running at 7000 rpm. Assume zero whirl at the entry and T1t = 290 K. The slip factor and power input factor to be unity, the process of compression is ...

Verified Answer:

Air at a stagnation temperature of 27º C enters the impeller of a centrifugal compressor in the axial direction. The rotor which has 15 radial vanes, rotates at 20000 rpm. The stagnation pressure ratio between the diffuser outlet and the impeller inlet is 4 and the isentropic efficiency is 85%. ...

Verified Answer: