A 50% reaction turbine (with symmetrical velocity triangles) running at 400 r.p.m. has the exit angle of the blades as 20° and the velocity of steam relative to the blades at the exit is 1.35 times the mean blade speed. The steam flow rate is 8.33 kg/s and at a particular stage the specific volume is 1.381 m³/kg. Calculate for this stage :
(i) A suitable blade height, assuming the rotor mean diameter 12 times the blade height, and
(ii) The diagram work. (N.U.)

Question

Accepted Answer

Speed, N = 400 r.p.m. ; α = 20°
[latex]C_{r_0} = C_{1} = 1.35 C_{bl} ; \dot{m}_{s} [/latex] = 8.33 kg/s
v = 1.381 m³/kg ; D = 12 h

(i) Blade height, h :
Refer Fig. 49.

Axial flow velocity, [latex]C_{f_1} = C_{f_0} = C_{f} = C_{1} \sin α[/latex]

[latex] = 1.35 C_{bl} \sin 20°[/latex]
[latex]= 0.4617 C_{bl} [/latex]

Area of flow, A = πDh = πD × [latex] \frac{D}{12} = \frac{πD²}{12} [/latex]

Mass flow rate, [latex]\dot{m} = \frac{A C_{f}}{v}[/latex] or 8.33 = [latex] \frac{A × 0.4617 C_{bl}}{1.381} [/latex]

or [latex] \frac{8.33 × 1.381 }{0.4917} = A × C_{bl} = \frac{πD²}{12} × \frac{πDN}{60}[/latex]

or 24.916 = [latex] \frac{π²D³ × 400}{720} or D³ = \frac{24.919 × 720}{π² × 400 } or D = 1.656 m [/latex]

∴ Blade height, h = [latex] \frac{D}{12} = \frac{1.656}{12} [/latex] = 0.138 m or 138 mm.

(ii) The diagram work :

Diagram work = [latex]\dot{m} × C_{bl} (C_{w_1} + C_{w_0})[/latex]

= [latex]\dot{m} × C_{bl} (2 C_{1} \cos α – C_{bl})[/latex]

= [latex]8.33 × C_{bl} (2 × 1.35 C_{bl} \cos 20° - C_{bl}) [/latex]

= [latex]8.33 × C_{bl}² (2 × 1.35 \cos 20° - 1 )[/latex]

= 8.33 × ([latex] \frac{πDN}{60} [/latex])² × 1.537 = 8.33 × ([latex] \frac{π × 1.656 × 400}{60} [/latex])² × 1.537

= 15401.2 W or 15.4 kW.

Question 6.34: A 50% reaction turbine (with symmetrical velocity triangles)...

Related Answered Questions

Verified Answer:

In a three-stage steam turbine steam enters at 35 bar and 400°C and exhausts at 0.05 bar, 0.9 dry. If the work developed per stage is equal, determine : (i) Condition of steam at entry to each stage. (ii) The stage efficiencies. (iii) The reheat factor.( iv) Internal turbine efficiency. Assume ...

Verified Answer:

Verified Answer:

The following data relate to a stage of reaction turbine : Mean rotor diameter = 1.5 m ; speed ratio = 0.72 ; blade outlet angle = 20° ; rotor speed = 3000 r.p.m. (i) Determine the diagram efficiency. (ii) Determine the percentage increase in diagram efficiency and rotor speed if the rotor is ...

Verified Answer:

Verified Answer:

Verified Answer:

Verified Answer:

Verified Answer:

Verified Answer:

Verified Answer: