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Diffstat (limited to '1358/CH7/EX7.11/Example711.sce')
-rwxr-xr-x | 1358/CH7/EX7.11/Example711.sce | 35 |
1 files changed, 35 insertions, 0 deletions
diff --git a/1358/CH7/EX7.11/Example711.sce b/1358/CH7/EX7.11/Example711.sce new file mode 100755 index 000000000..15eb5cbeb --- /dev/null +++ b/1358/CH7/EX7.11/Example711.sce @@ -0,0 +1,35 @@ +// Display mode
+mode(0);
+// Display warning for floating point exception
+ieee(1);
+clear;
+clc;
+disp("Turbomachinery Design and Theory,Rama S. R. Gorla and Aijaz A. Khan, Chapter 7, Example 11")
+disp("The overall efficiency of turbine from nozzle inlet to diffuser outlet is given by")
+disp("etatt = (T01 - T03)/(T01 - T03ss)")
+disp("Turbine work per unit mass flow")
+disp("W = U2^2 = Cp(T01 - T03); (Cw3 = 0)")
+disp("Now using isentropic p–T relation")
+disp("T01 (1 - T03ss/T01) = T01(1 - (P03/P01)((gamma-1)/gamma)")
+disp("Therefore")
+disp("U2^2 = etatt*Cp*T01(1 - (P03/P01)^((gamma-1)/gamma)")
+etatt = 0.9;
+Cp = 1147;
+T01 = 1145;
+P03 = 100;
+P01 = 310;
+U2 = (etatt*Cp*T01*(1 - (P03/P01)^0.2498))^0.5
+disp("Impeller tip speed, U2 = 539.45 m/s")
+disp("The Mach number of the absolute flow velocity at nozzle exit is given by")
+disp("M = C1/a1 = U1/alpha1*sin(alpha1)")
+disp("Since the flow is adiabatic across the nozzle, we have")
+disp("T01 = T02 = T2 + C2^2/2Cp = T2 + U2^2/2Cp(sin(alpha2))^2")
+disp("or T2/T01 = 1 - U2^2/2CpT01(sin(alpha2))^2; but Cp = gamma*R/(gamma - 1)")
+disp("Therefore; T2/T01 = 1 - U2^2*(gamma - 1)/(2gammaRT01(sin(alpha2))^2")
+disp(" = 1- U2^2*(gammaa-1)/(2*a01^2 * (sin(alpha2))^2)")
+disp("But (T2/T01)^2 = a2/a01 = a2/a02; since T01 = T02")
+disp("and a2/a02 = U2/M2*a02*sin(alpha2)")
+disp(" Therefore (U2/M2*a02*sin(alpha2))^2 = 1 - U2^2*(gammaa-1)/(2*a01^2 * (sin(alpha2))^2)")
+disp("and 1 = (U2/a02*sin(alpha2))^2 *((gamma - 1)/2 + 1/M2^2)")
+disp("or (sin(alpha2))^2 = (U2/a02)^2 * ((gamma - 1)/2 + 1/M2^2)")
+disp("Therefore nozzle angle alpha2 = 75 degrees")
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