In a single stage steam turbine saturated steam at 10 bar abs. is supplied through a convergent-divergent steam nozzle. The nozzle angle is 20° and the mean blade speed is 400 m/s. The steam pressure leaving the nozzle is 1 bar abs. Find : (i) The best blade angles if blades are equiangular. (ii)

Question

In a single stage steam turbine saturated steam at 10 bar abs. is supplied through a convergent-divergent steam nozzle. The nozzle angle is 20° and the mean blade speed is 400 m/s. The steam pressure leaving the nozzle is 1 bar abs. Find :
(i) The best blade angles if blades are equiangular.
(ii) The maximum power developed by the turbine if a number of nozzles used are 5 and area at the throat of each nozzle is 0.6 cm².
Assume nozzle efficiency 88% and blade friction co-efficient of 0.87.

Accepted Answer

Supply steam pressure (to nozzles) = 10 bar abs.
Nozzle angle, α = 20°
Mean blade speed, [latex] C _{bl} [/latex] = 400 m/s
Steam pressure leaving the nozzle= 1 bar abs.
Number of nozzles used = 5
Area of throat at each nozzle = 0.6 cm²
Nozzle efficiency, [latex] η _{nozzle} [/latex] = 88%
Blade friction co-efficient, K = [latex] \frac{ C _{r_0}}{ C _{r_1}} [/latex] = 0.87.

The velocity of steam at the outlet of nozzle is found representing the expansion through nozzle on h-s chart as shown in Fig. 27.

From h-s chart,
[latex]h_{1} – h_{3} \simeq [/latex]402 kJ/kg

[latex]η_{nozzle} = \frac{ h_{1} – h_{3} ^{′}}{ h_{1} – h_{3} } [/latex] = 0.88

∴ [latex] h_{1} – h_{3} ^{′} [/latex] = 0.88 × 402 = 353.76 kJ/kg

Also [latex] \frac{C_{3} ^{′}²}{2} = h_{1} – h_{3} ^{′} [/latex]

or [latex]C_{3} ^{′} = \sqrt{2 ( h_{1} – h_{3} ^{′} )} = \sqrt{2 × 353.76 × 1000} [/latex] = 841.14 m/s

(i) Blade angles :
Construct the velocity triangles as per data given as shown in Fig. 27.
By measurement, θ (= Φ) = 35.5°.

(ii) Maximum power developed, P :
For finding out the maximum power developed by the turbine let us first find out the maximum mass of steam passing through the nozzle.
The required condition for the maximum mass flow through the nozzle is given by

[latex] \frac{p_{2}}{p_{1}} = (\frac{2}{n + 1})^{\frac{n}{n - 1}} [/latex]
where, [latex] p_{1}[/latex] = Pressure of steam at inlet of the nozzle,
[latex] p_{2}[/latex] = Pressure of steam at the throat of the nozzle, and
n (index of expansion) = 1.135 as steam is saturated.

∴ [latex] \frac{p_{2}}{p_{1}} = (\frac{2}{1.135 + 1})^{\frac{1.135}{0.135 }} [/latex] = 0.58

∴ [latex] p_{2}[/latex] = 10 × 0.58 = 5.8 bar

From h-s chart (Fig. 27)

[latex]h_{1} – h_{2} \simeq [/latex] 105 kJ/kg

and [latex]h_{1} – h_{2} ^{′} [/latex] = 0.88 × 105 = 92.5 kJ/kg
[latex]v_{2} ^{′} (specific volume at point 2 ^{′} ) \simeq [/latex] 0.32 m³/kg
The maximum velocity of steam at the throat of the nozzle is given by

[latex]C = \sqrt{2 ( h_{1} – h_{2} ^{′} )} = \sqrt{2 × 92.4 × 1000} [/latex] = 429.88 m/s

Using the continuity equation at the throat of the nozzle, we can write
m . [latex]v_{2} ^{′} [/latex] = A × C where A is the area of the nozzle.
∴ m × 0.32 = 0.6 × [latex]10^{–4} [/latex]× 429.88

∴ m = [latex] \frac{0.6 × 10^{–4} × 429.88}{0.32} [/latex] = 0.0806 kg/s.

Total mass of steam passing through 5 nozzles per second is given by
[latex]m_{t} [/latex] = 0.0806 × 5 = 0.403 kg/s

∴ Power developed by the turbine = [latex] \frac{m_{t} × C_{w} C_{bl}}{1000} [/latex] kW

From velocity diagram, [latex]C_{w}[/latex] = 750 m/s (by measurement)

∴ Power developed = [latex] \frac{0.403 × 750 × 400}{1000} [/latex] = 120.9 kW.

Question 6.18: In a single stage steam turbine saturated steam at 10 bar ab...

Related Answered Questions

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:

Verified Answer: