PROBLEMS
1. Experimental compressor cascade results suggest that the stalling lift coefficient of a low-speed cascade blade may be expressed as
where c1 and c2 are the entry and exit velocities, respectively. Find the stalling inlet angle for a compressor cascade of space-chord ratio unity if the outlet air angle is 30o.
2. Show, for a low-speed turbine cascade, using the angle notation of Figure 3.28, that the lift coefficient is
where tan αm 5 ð1=2Þðtan αm 2 tan α1Þ and CD 5 drag=ðð1=2Þρc2 lÞ: A cascade of turbine nozzle vanes has a blade inlet angle α0 of 0o, a blade outlet angle α0 of 65.5o, a chord length l of 45 mm and an axial chord b of 32 mm. The flow entering the blades is to have zero incidence and an estimate of the deviation angle based upon similar cascades is that δ will be about 1.5o at low outlet Mach number. If the blade load ratio Z defined by Eq. (3.55) is to be 0.85, estimate a suitable space-chord ratio for the cascade. Determine the drag and lift coefficients for the cascade given that the profile loss coefficient is
c. The stagnation pressure loss derived from flow measurements on this cascade is 149 Pa when the inlet velocity c1 is 100 m/s at an air density ρ of 1.2 kg/m3. Determine the values of
i. pressure rise and
ii. drag and lift coefficients.
4. A low-speed compressor has stator vanes that are to have an inlet flow angle of 45o and an exit flow angle of 25o.
a. Calculate the pitch-chord ratio of the stators assuming a Lieblein diffusion factor of 0.45.
Using Lieblein’s diffusion factor reaching 0.6 as a criterion, and assuming that the exit flow angle remains constant, determine the incidence that corresponds to the blade stalling.
b. Use Carter’s deviation correlation to estimate the required metal exit angle given that a parabolic arc camber line is employed with maximum camber at 40% chord. (Note that some iteration is needed.)
5. Use γ 5 1.4, R 5 287 J/kg/K1 and cp 5 1005 J/kg/K in this question.
a. A two-dimensional compressor cascade operates in air. The inlet metal angle of the blades is 55o and the exit metal angle is 37o. When the flow is at zero incidence with an inlet Mach number of 0.65, the exit Mach number is 0.44, and the stagnation pressure loss coefficient is given by
Determine the exit flow angle and give two reasons why this is greater than the exit metal angle.
b. Find the blade pitch-to-chord ratio needed such that DF 5 0.45 when the cascade is at the operating point described in part (a).
c. Assuming that the exit flow angle and loss remain constant, estimate the new value of DF when the incidence of the flow is increased to 5o while maintaining an inlet Mach number of 0.65. Use the pitch-to-chord ratio found in part (b).
d. If the cascade throat width to pitch ratio o/s is 0.6, determine the incidence of the flow onto the blades at which the cascade will choke with an inlet Mach number of 0.65. Assume that there is no loss upstream of the cascade throat.
6. A high-speed air turbine cascade is estimated to have an AVDR of 0.97. At inlet the Mach number is 0.22 and the flow angle is 30o. The blades turn the flow through 100o and at exit the flow is just sonic. Take γ to be 1.4.
a. Determine the stagnation pressure loss coefficient based on exit conditions and the energy loss coefficient, ζ.
b. Estimate ζ using the Soderberg correlation for this cascade, Eq. (3.46), assuming an aspect ratio of 3. Compare with the value found in (a) and explain why the correlation might be expected to underestimate the loss in this case.
c. Neglecting streamtube contraction and the stagnation pressure loss downstream of the throat, estimate the opening-to-pitch ratio of the cascade.
7. A two-dimensional compressor cascade is tested in air with an inlet stagnation pressure of 1 bar and an inlet stagnation temperature of 300 K. For an inlet Mach number of 0.75 and an inlet flow angle of 50o, the exit flow angle is measured as 15.8o. Determine the mass flow rate per unit frontal area. Assuming the flow is isentropic, calculate the exit Mach number and the static pressure ratio across the cascade.
8. A compressor blade design tested in a cascade is found to choke with an inlet Mach number of 0.9 when the inlet flow angle is 52o. If the ratio of the throat area to the frontal area, A*/H1 s,for the cascade is 0.625, calculate the loss of stagnation pressure between the far upstream and the throat and express this as a loss coefficient. Comment on what could cause this loss.
9. A turbine cascade operates in air with an inlet angle of 45o from the axial direction. The ratio of inlet stagnation pressure to exit static pressure is 2.6 and the inlet Mach number is 0.3.
a. If the stagnation pressure loss coefficient, Yp, is measured to be 0.098, calculate the exit Mach number and show that the exit angle is 67.7o. It can be assumed that the blade height is constant through the cascade and that the growth of sidewall boundary layers is negligible.
b. The opening-to-pitch ratio of the cascade is 0.354. For the operating point described in part (a), show that approximately two-thirds of the total loss in stagnation pressure occurs downstream of the throat.
c. The exit static pressure from the cascade is lowered until limit load is achieved. The exit Mach number at this condition is measured to be 1.77. Given that the stagnation pressure loss upstream of the throat is unchanged, determine the new overall stagnation pressure loss coefficient for the cascade.
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- inlet stagnation air compressor of a two dimentional compressor cascade determine the flow rate per unit frontal area exit mach numbe and the static pressure ratio
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- calculate exit mach number and the static pressure ratio across the cacade
- experiment compressor cascade result suggest that the stalling lift coefficient of a cascade blade may be expressed at
- if the ratio of the throat area to the frontal area
- solution experimental compressor cascade result suggest that the staling lift coefficient of a cascade blade may be expressed as
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