A steam engine having swept volume 0.034 m³ and clearance volume 20% of the piston displacement, consumes 2725 kg of steam per hour at 250 r.p.m. The engine is double acting and the pressure of steam near cut-off is 8.8 bar, when piston has traversed 30% of working stroke. If the compression

Question

A steam engine having swept volume 0.034 m³ and clearance volume 20% of the piston displacement, consumes 2725 kg of steam per hour at 250 r.p.m. The engine is double acting and the pressure of steam near cut-off is 8.8 bar, when piston has traversed 30% of working stroke. If the compression commences at 65% of the return stroke when the steam remaining in the cylinder is dry at 0.14 bar, estimate the mass of cushion steam at this point. Also find the dryness fraction of the steam at cut-off.

Accepted Answer

Swept volume, [latex] V_{s} [/latex] = 0.034 m³
Clearance volume, [latex] V_{c} = 0.2 V_{s} [/latex]
Steam consumption = 2725 kg/h
Engine speed, N = 250 r.p.m.
Pressure of steam near cut-off, [latex] p_{1} [/latex] = 8.8 bar
Exhaust or back pressure, [latex] p_{b} [/latex] = 0.14 bar.

(i) Mass of cushion steam :

[latex] V_{c} = 0.2V_{s} [/latex] = 0.2 × 0.034 = 0.0068 m³
Total volume, [latex] V_{2 } = V_{c} + V_{s} [/latex] = 0.0068 + 0.034 = 0.0408 m³
[latex] V_{4 } = V_{c} + 0.35V_{s} [/latex]
= 0.0068 + 0.35 × 0.034 = 0.0187 m³
[latex] V_{1} = V_{c} + 0.3V_{s} [/latex] = 0.0068 + 0.3 × 0.034
= 0.017 m³

Cylinder feed/stroke = [latex] \frac{2725}{60 × 250 × 2} = 0.09083 kg [/latex]

Now, mass of cushion steam at point 4 is the mass of 0.0187 m³ dry steam at 0.14 bar.

= [latex] \frac{0.0187}{ 10.69} = [/latex] 0.001749 kg. [From steam tables : Specific volume, [latex] v_{g} [/latex] of steam at 0.14 bar = 10.69 m³ / kg]

(ii) Dryness fraction of steam at cut-off :
The mass of steam present in the cylinder during expansion
= 0.09083 + 0.001749 = 0.09258 kg
Now, the indicated dry mass at a point of cut-off (point 1)

= [latex] \frac{0.017}{ 0.219} = 0.07762 kg [/latex] [Specific volume, [latex] v_{g} [/latex] of steam at 8.8 bar = 0.219 m³ / kg ]

∴ Dryness fraction of steam at cut-off

= [latex] \frac{0.07762}{0.09258} =[/latex] 0.838.

Question 3.5: A steam engine having swept volume 0.034 m³ and clearance vo...

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