Reference no: EM131029527

QUESTION 1

A. What is the significance of Mach number? Define and write the mathematical expression for Mach number and explain each term in the expression along with their units.

B. What is a compressible flow? When do you say that the flow is compressible and what is the Mach number beyond which the flow is said to be compressible?

C. Write an expression for Reheat Factor. What is the range of reheat factor?

D. Define flow capacity. Express in terms of a mathematical equation. Explain each term in the equation along with their units.

E. Define stagnation pressure, stagnation temperature and stagnation enthalpy. Write the mathematical expression with explanation of each term.

QUESTION 2

Making suitable assumptions, derive specific equations for 1) a compressor and 2) a turbine starting form a general steady flow energy equation

QUESTION 3

In an isentropic process a perfect gas expands from 140kPa to 110kPa. If the initial temperature is of the gas is 150 deg C, determine the temperature of the gas at the end of expansion.

QUESTION 4

The total-to-total pressure ratio of an Axial flow compressor is 7 to 1. The stagnation temperatures are 325 and 565 K, at the inlet and outlet respectively. Determine the overall total- to-total efficiency and the polytropic efficiency of the compressor. Assume y=1.4.

QUESTION 5

The diameter of an axil flow fan is 1.75 m and runs at 1350 rpm. The average axial air velocity is 13 m/s. A quarter scale model has been built to obtain a check on the design and the rotational speed of the model fan is 3900 rev/min. Determine the axial air velocity of the model so that dynamical similarity with the full-scale fan is preserved. Neglect the effect of Reynolds number change.

At what pressure must the model be tested, If a sufficiently large pressure vessel becomes available in which the complete model can be placed and tested under conditions of complete similarity? The viscosity of the air is independent of pressure and the temperature and is maintained constant.

QUESTION 6

Dry saturated steam at 1.2 atm. flows through a tube with 265 m/s velocity. Calculate the stagnation (total) pressure and the stagnation temperature of the steam using the following two methods (i) using steam tables, (ii) assuming steam to behave as a perfect gas.

QUESTION 7

The static pressure, the static temperature and the flow velocity, in a steam turbine are 55 bar, 535°C and 200 m/s respectively. The measurements at the turbine exit for the static pressure, static temperature and velocity are 1.1 bar, 130°C and 250 m/s respectively.

Calculate:

(a) the total-to-total efficiency

(b) total-to-static-efficiency

QUESTION 8

In an axial flow turbine stage, the axial velocity cx is constant. The absolute velocities entering and leaving the stage are in the axial direction. If the flow coefficient cx/U is 0.65 and the gas leaves the stator blades at 69 deg from the axial direction, calculate the following.

(i) the stage loading factor, AW/U2 ;

(ii) the flow angle relative to the rotor blades;

(iii) the degree of reaction;

QUESTION 9 (Two-dimensional cascades: Dixon and Hall)

i) A 2D cascade of a compressor is tested in air with inlet stagnation pressure of 1.1 bar and inlet stagnation temperature of 313K. When inlet Mach number is 0.8 and inlet flow angle is 48 deg, the exit flow angle is measured as 16 deg. For these conditions determine the mass flow rate per unit frontal area. Assume isentropic flow and calculate the exit Mach number and the static pressure ration across the cascade.

ii) In a cascade of a compressor, choking takes place at the inlet Mach number of 0.88 and with the inlet flow angle 15 deg. If the ratio of the throat area to the frontal area, A*/H1s, 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 the cause for this loss.

QUESTION 10 (Axial-flow turbines: Mean-line analysis and design: Dixon and Hall)

The mass flow rate is 28kg/s in an axial flow gas turbine that develops 3.5 MW. The stagnation conditions are 780kPa and 730 deg. C. at the entry. At the exit of the nozzle, the static pressure is measured as 479kPa and the corresponding absolute flow direction is 70 deg. to the axial direction. Assuming that the axial velocity is constant across the stage and that the gas enters and leaves the stage without any absolute swirl, determine (i) the nozzle exit velocity, (ii) the blade speed (iii) the total-to-total efficiency (iv) the stage reaction. The Soderburg correlation for estimating blade losses should be used in this problem. For the gas assume that Cp = 1.148 kJ(kg K) and R = 0.287 kJ(kg K).

QUESTION 11 (Axial flow compressors: Dixon and Hall)

In a jet engine, high-pressure axial flow compressor rotates at 14,500 rpm. The overall stagnation pressure ratio is 9.0. The mass flow rate of air through the compressor is 17 kg/s and the stagnation conditions at inlet are 205 kPa and 460 K. The polytropic efficiency is 91%.

(a) If the mean radius is 0.25 m and this is constant throughout the compressor, calculate the total-to-total isentropic efficiency of the compressor and if the stage loading to be less than 0.4 in all stages, how many stages are required?

(b) The compressor is designed with repeating stages and zero inlet swirl. If the inlet axial Mach number is 0.55, calculate the mean flow coefficient and sketch the velocity triangles for one stage. Calculate the blade height at exit from the compressor.

QUESTION 12 (Three-dimensional flow in axial turbomachines: Dixon and Hall)

In a gas turbine, initial absolute pressure and temperature of the gas are 360 kPa and 565°C with negligible initial velocity. The conditions at the mean radius, 0.35 m, are as follows:

Nozzle exit flow angle 68°
Nozzle exit absolute pressure 195 kPa
Stage reaction 0.2

At the design speed of 130 rev/s, determine, the flow coefficient and stage loading factor at the mean radius and the reaction at the hub, radius 0.30 m. Assume that stage is to have a free- vortex swirl at this speed. You may also assume that losses are absent. Take Cp =1.147 kJ(kg K) and y =1.33.

QUESTION 13 (Centrifugal compressors: Dixon and Hall)

a) Derive the expression for the diffuser efficiency:

b) In an axial diffuser air enters with a velocity of 415 m/s, the stagnation pressure is 310 kPa and the stagnation temperature is 625 K. The stagnation pressure is 290kPa and the static pressure is 265 kPa at the exit of the diffuser. Use compressible flow analysis to determine (i) the static temperature, static pressure, and Mach number at inlet and the diffuser efficiency; (ii) the Mach number at exit and entry. For air take y = 1.376 and R =287 J/(kg K).

c) In a diffuser air enters with an averaged velocity of 350 m/s at a stagnation pressure and temperature of 335 kPa and 415 K and leaves at a stagnation pressure of 295 kPa with an averaged velocity of 125 m/s and a static pressure of 290 kPa. Determine,

(i) the static pressure and Mach number of the air at inlet;

(ii) the diffuser efficiency;

(iv)the Mach number at exit and the overall entropy increase.