Calculating Gas Turbine Shaft Power

[Pud]

Homework Statement

I have been asked to calculate a range of values relating to a Gas Turbine engine, and while I have been able to find the majority of the values I am almost certain that the Thermal Efficiency value of 1.64% I have come up with is incorrect.

This relies on Shaft power, fuel mass flow rate, and the Lower Calorific Value in the formula shown below.

LCV = 42,000 kJ/kg (Given value)
Fuel mass flow rate = 0.00821256 kg/sec (Calculated)
Shaft power = 5.66 kW (Calculated, but not confident of this result)

N = 3040 rpm (Given value)
F (brake load)= 50 N (Given Value)

Homework Equations

The formula for Thermal Efficiency that I have is: $$\eta$$_thermal = $$\dot{W}$$_Shaft/($$\dot{m}$$_fuel $$\times$$ Lower Calorific Value)

The formula for Shaft Power (in kW) I have is: $$\dot{W}$$_Shaft = (F * N) / 26850

(Not sure where 26850 comes from, I was given this equation. If someone can explain where that number comes from I would be very grateful.)


The mass flow rate of fuel I worked out as follows:

2 litres of fuel used in 207 seconds (Given values) = 9.6618E^-3 l/sec

0.0096618 $$\div$$ 1000 = 9.6618E^-6 m³/sec

Relative density of fuel = 0.85 (Given value)

Mass flow rate = 9.6618E^-6 $$\times$$ 850 = 0.00821256 kg/sec



There are a whole range of other values (Temps/Pressures/C_p(g)/C_p(a)/Gamma_a/Gamma_g etc) which I haven't included as I don't believe them to be relevant.

If necessary I will add these as requests.

Thanks

 

[nucleus]

Pud
Your turbine speed is in RPM and your fuel flow is in kg/sec, so you have to get Wf in kg/min.
I have an example of this but it isn’t in metric but your formulas appear to be correct. The number 26850 probably comes from correcting for units.

 

[Mene]

I appreciate your thoroughness in calculating the values for the gas turbine engine. However, I agree that the Thermal Efficiency value of 1.64% does seem low and may be incorrect. One possibility could be that there was an error in your calculation for Shaft power. I suggest double-checking the equation and values used to ensure accuracy.

Regarding the number 26850 in the formula for Shaft Power, it is most likely a conversion factor used to convert from units of Nm (Newton-meters) to kW (kilowatts). This factor is commonly used in engineering calculations.

In addition, it would be helpful to include the other values (Temps/Pressures/Cp(g)/Cp(a)/Gammaa/Gammag) in your calculation as they could potentially affect the accuracy of your results. it is important to consider all relevant variables and factors in your calculations.

Overall, it is important to carefully review and verify all calculations to ensure accurate results. If you are still unsure about the Thermal Efficiency value, I suggest seeking guidance from a colleague or conducting further research to confirm your findings.