diff options
Diffstat (limited to '3511/CH9')
| -rw-r--r-- | 3511/CH9/EX9.1/Ex9_1.sce | 22 | ||||
| -rw-r--r-- | 3511/CH9/EX9.10/Ex9_10.sce | 22 | ||||
| -rw-r--r-- | 3511/CH9/EX9.11/Ex9_11.sce | 34 | ||||
| -rw-r--r-- | 3511/CH9/EX9.2/Ex9_2.sce | 32 | ||||
| -rw-r--r-- | 3511/CH9/EX9.3/Ex9_3.sce | 28 | ||||
| -rw-r--r-- | 3511/CH9/EX9.4/Ex9_4.sce | 28 | ||||
| -rw-r--r-- | 3511/CH9/EX9.5/Ex9_5.sce | 31 | ||||
| -rw-r--r-- | 3511/CH9/EX9.6/Ex9_6.sce | 29 | ||||
| -rw-r--r-- | 3511/CH9/EX9.7/Ex9_7.sce | 43 | ||||
| -rw-r--r-- | 3511/CH9/EX9.8/Ex9_8.sce | 36 | ||||
| -rw-r--r-- | 3511/CH9/EX9.9/Ex9_9.sce | 17 |
11 files changed, 322 insertions, 0 deletions
diff --git a/3511/CH9/EX9.1/Ex9_1.sce b/3511/CH9/EX9.1/Ex9_1.sce new file mode 100644 index 000000000..dccc6bef8 --- /dev/null +++ b/3511/CH9/EX9.1/Ex9_1.sce @@ -0,0 +1,22 @@ +clc;
+n=10; // No of stages in the axial flow compressor
+rp=5; // Overall pressure ratio
+eff_C=0.87; // Overall isentropic efficiency
+T1=15+273; // Temperature of air at inlet in kelvin
+u=210; // Blade speed in m/s
+ca=170; // Axial velocity in m/s
+wf=1; // Work factor
+r=1.33; // Specific heat ratio
+Cp=1.005; // Specific heat in kJ/kg K
+
+Del_Tstage=(T1*(rp^((r-1)/r)-1))/(n*eff_C); // Temperature increase per stage
+// By property relations and let us assume
+// tan_beta1-tan_beta2=Del_Tstage*Cp/(wf*u*ca)
+// tan_beta1+tan_beta2=u/ca for 50% reaction
+// To solve this above equations using matrix method
+a=[1,-1;1,1]; c=[(Del_Tstage*Cp*10^3/(wf*u*ca));u/ca];
+b=a\c;
+beta1=atand(b(1));// Blade angles at inlet
+beta2=atand(b(2)); // Blade angles at outlet
+
+disp ("degree (roundoff error)",beta2,"Blade angle at outlet = ","degree (roundoff error)",beta1,"Blade angle at inlet = ");
diff --git a/3511/CH9/EX9.10/Ex9_10.sce b/3511/CH9/EX9.10/Ex9_10.sce new file mode 100644 index 000000000..0465b841b --- /dev/null +++ b/3511/CH9/EX9.10/Ex9_10.sce @@ -0,0 +1,22 @@ +clc;
+u=250; // Mean blade speed in m/s
+rp=1.3; // Pressure ratio
+ca=200; // Axial velocity in m/s
+p01=1; // Inlet pressure in bar
+T01=300; // Inlet temperature in kelvin
+R1=0.5; // Degree of reaction
+Cp=1.005; // Specific heat in KJ/kg K
+r=1.4; // Specific heat ratio
+R=287; // Characteristic gas constant in J/kg K
+
+Del_T=(rp^((r-1)/r)-1)*T01;
+//tan_beta1+tan_beta2=(R*2*u/ca);
+//tan_beta1-tan_beta2=(Del_T*Cp*10^3/(u*ca));
+A=[1 1;1 -1]; B=[(R1*2*u/ca) ;(Del_T*Cp*10^3/(u*ca))];
+tan_beta=A\B;
+beta_1=atand (tan_beta(1));
+beta_2=atand (tan_beta(2));
+alpha_1=beta_2; alpha_2=beta_1;
+
+disp ("degree",beta_2,"beta2 = ","degree",beta_1,"beta1 = ");
+disp ("degree",alpha_2,"alpha2 = ","degree",alpha_1,"alpha1 = ");
diff --git a/3511/CH9/EX9.11/Ex9_11.sce b/3511/CH9/EX9.11/Ex9_11.sce new file mode 100644 index 000000000..b8757dd54 --- /dev/null +++ b/3511/CH9/EX9.11/Ex9_11.sce @@ -0,0 +1,34 @@ +clc;
+n=4; // Number of stage
+rp=10; // Pressure ratio
+eff_p_ac=0.92; // Ploytropic efficiency of axial compressor
+eff_p_cc=0.83; // Polytropic efficiency of centrifugal compressor
+Del_Trise=30; // Axial compressor stage temperature in kelvin
+R=0.5; // Reaction stage
+beta_2=20; // Outlet stator angle in degree
+D=0.25; // Mean diameter of each stage in m
+wf=0.8; // Work done factor
+ca=150; // Axial velocity in m/s
+Di=0.33; //Impeller diameter in m
+mu=0.9; // Slip factor
+p01=1.01; // Ambient pressure in bar
+T01=288; // Ambient temperature in kelvin
+pif=1.04; // Power input factor
+Cp=1.005; // Specific heat in KJ/kg K
+r=1.4; // Specific heat ratio
+R=287; // Characteristic gas constant in J/kg K
+
+beta_1=atand (sqrt ((Cp*10^3*Del_Trise/(wf*ca^2))+(tand(beta_2)^2)));
+u=ca*(tand (beta_1)+tand(beta_2));
+Nac=(u/(3.14*D));
+r1=(1+n*Del_Trise/T01)^(eff_p_ac*r/(r-1)); // Total pressure ratio across the axial compressor
+
+r2=rp/r1; // Pressure ratio across centrifugal compressor
+T02=T01*r1^((r-1)/(eff_p_ac*r));
+T03=T02*r2^((r-1)/(eff_p_cc*r));
+Del_Tsc=T03-T02;
+u=sqrt ((Del_Tsc*Cp*10^3)/(pif*mu));
+Ncc=u/(3.14*Di);
+
+disp ("rps (roundoff error)",Nac,"Speed of the axial compressor = ");
+disp ("rps (roundoff error)",Ncc,"Speed of the centrifugal compressor = ");
diff --git a/3511/CH9/EX9.2/Ex9_2.sce b/3511/CH9/EX9.2/Ex9_2.sce new file mode 100644 index 000000000..16ee79351 --- /dev/null +++ b/3511/CH9/EX9.2/Ex9_2.sce @@ -0,0 +1,32 @@ +clc;
+P1=1.0132; // Inlet air pressure in bar
+T01=288; // Inlet air temperature in kelvin
+ca=150; // axial velocity in m/s
+dtip=60; // Tip diameter of rotor in cm
+dhub=50; // Hub diameter of rotor in cm
+N=100; // Speed of rotor in rps
+t_angle=30; // Deflected angle of air in degree (in question it is 30.2 but in solution it is 30)
+P2_P1=1.2; // Stage pressure ratio
+Cp=1005; // Specific heat in J/kg K
+r=1.4; // Specific heat ratio
+R=287; // Characteristic gas constant in J/kg K
+
+u=(3.142857*(dhub+dtip)*10^-2*N)/2; // Mean blade velocity
+beta_1=atand(u/ca); // Blade angle at inlet
+beta_2=beta_1-t_angle; // As air is deflected by 30
+// from velocity triangle
+x=ca*tand(beta_2);
+alpha_2=atand ((u-x)/ca);
+C1=ca;
+T1=T01-(C1^2/(2*Cp)); // Static temperature at inlet
+P2=P1*P2_P1; // Pressure at outlet
+T2=T1*(P2/P1)^((r-1)/r); // Static temperature at outlet
+row_2=(P2*10^5)/(R*T2); // Density at outlet
+m=3.14*(dtip^2-dhub^2)*ca*row_2*10^-4/4; // Mass flow rate
+wf=1; // Work factor
+P=wf*u*ca*m*(tand(beta_1)-tand(beta_2))/1000; // Power developed
+R=ca*(tand(beta_1)+tand(beta_2))/(2*u); // Degree of reaction
+
+disp ("kg/s",m,"Mass flow rate = ");
+disp("kW (Error due to more decimal values in expression)",P,"Power developed = ");
+disp (R,"Degree of Reaction = ");
diff --git a/3511/CH9/EX9.3/Ex9_3.sce b/3511/CH9/EX9.3/Ex9_3.sce new file mode 100644 index 000000000..f6fc103fe --- /dev/null +++ b/3511/CH9/EX9.3/Ex9_3.sce @@ -0,0 +1,28 @@ +clc;
+beta_1=45; // Inlet blade angle in degree
+beta_2=10; // Outlet blade angle in degree
+rp=6; // Compressor pressure ratio
+eff_C=0.85;// Overall isentropic efficiency
+T1=37+273; // Inet static temperature in kelvin
+u=200; // Blade speed in m/s
+Cp=1005; // Specific heat in J/kg K
+r=1.4; // Specific heat ratio
+R=287; // Characteristic gas constant in J/kg K
+
+// (i). wf=1
+wf=1; // Work factor
+ca=u/(tand(beta_1)+tand(beta_2)); // Axial velocity
+Del_Tstage=wf*u*ca*(tand(beta_1)-tand(beta_2))/Cp; // Stage temperature drop
+Del_Toverall=(T1*(rp^((r-1)/r)-1))/eff_C; // Overall temperature drop
+n=Del_Toverall/Del_Tstage; // No of stages
+
+disp (n,"Number of stages required = ","(i).wf = 1");
+
+// (ii).wf = 0.87
+wf =0.87; // Work factor
+ca=u/(tand(beta_1)+tand(beta_2)); // Axial velocity
+Del_Tstage=wf*u*ca*(tand(beta_1)-tand(beta_2))/Cp; // Stage temperature drop
+Del_Toverall=T1*(rp^((r-1)/r)-1)/eff_C; // Overall temperature drop
+n=Del_Toverall/Del_Tstage; // No of stages
+
+disp (n,"Number of stages required = ","(ii).wf = 0.87");
diff --git a/3511/CH9/EX9.4/Ex9_4.sce b/3511/CH9/EX9.4/Ex9_4.sce new file mode 100644 index 000000000..e37bf1934 --- /dev/null +++ b/3511/CH9/EX9.4/Ex9_4.sce @@ -0,0 +1,28 @@ +clc;
+rp=4; // Total head pressure ratio
+eff_O=0.85; // Overall total head isentropic efficiency
+T01=290; // Total head inlet temperature in kelvin
+alpha_1=10; // Inlet air angle in degree
+alpha_2=45; // Outlet air angle in degree
+u=220; // Blade velocity in m/s
+wf=0.86; // Wok done factor
+R=284.6; // Characteristic gas constant in kJ/kg K
+Cp=1005; // Specific heat in J/kg K
+r=1.4; // Specific heat ratio
+
+eff_P=1/(log10(((rp^((r-1)/r)-1)/eff_O)+1)/(log10(rp)*((r-1)/r)));;
+// From velocity triangle
+ca=u/(tand(alpha_1)+tand(alpha_2)); // Axial velocity
+Del_Tstage=wf*u*ca*(tand(alpha_2)-tand(alpha_1))/Cp; // Stage temperature rise
+T02=T01*(rp)^((r-1)/(r*eff_P)); // Total head temperature
+T02_T01=T02-T01; // Total temperature rise
+n=T02_T01/Del_Tstage; // Total number of stages
+// from velocty traingles
+w1=ca/cosd(alpha_2);
+c1=ca/cosd(alpha_1);
+T1=T01-c1^2/(2*Cp); // Static temperature
+M=w1/sqrt(r*R*T1); // Mach number at inlet
+
+disp (eff_P*100,"Polytropic efficiency of the compressor = ");
+disp (n,"Total number of stages = ");
+disp (M,"Mach number at inlet = ");
diff --git a/3511/CH9/EX9.5/Ex9_5.sce b/3511/CH9/EX9.5/Ex9_5.sce new file mode 100644 index 000000000..b44bb889c --- /dev/null +++ b/3511/CH9/EX9.5/Ex9_5.sce @@ -0,0 +1,31 @@ +clc;
+Q=1000; // Flow rate of free air in m^3/min
+P1=0.98; // Inlet pressure in bar
+T1=15+273; // Inlet temperature in kelvin
+Dm=0.6; // Mean diameter in m
+h=6.75; // blade length in cm
+CL=0.6; CD=0.05; // At zero angle of incidence
+Cp=1.005; // Specific heat in kJ/kg K
+r=1.4; // Specific heat ratio
+R=287; // Characteristic gas constant in J/kg K
+k=1-0.1; //Blade occupys 10% of axial area
+N=6000; // speed in rpm
+Ac=19.25*10^-4; // Projected area in m^2
+n=50;
+eff_C=1; // Efficiency of compressor
+
+row=(P1*10^5)/(R*T1); // Density
+A=k*3.14*Dm*h*10^-2; // Area of axial
+ca=Q/(60*A); // Axial velocity
+u=3.14*Dm*N/60; // Blade velocity
+beta_1=atand(u/ca); // Blade angle at inlet
+w=sqrt (ca^2+u^2); // From velocity triangle
+L=CL*row*w^2*Ac/2;
+D=CD*row*w^2*Ac/2;
+P=(L*cosd(beta_1)+D*sind (beta_1))*u*n*10^-3; // Power input / stage
+m=Q*row/60;// mass flow rate
+rp=((P*eff_C/(m*Cp*T1))+1)^(r/(r-1)); // pressure ratio
+P2=rp*P1; // Pressure
+
+disp ("kW (Roundoff error )",P,"Power input/stage = ");
+disp ("bar",P2,"Pressure at outlet = ");
diff --git a/3511/CH9/EX9.6/Ex9_6.sce b/3511/CH9/EX9.6/Ex9_6.sce new file mode 100644 index 000000000..dfbb9325d --- /dev/null +++ b/3511/CH9/EX9.6/Ex9_6.sce @@ -0,0 +1,29 @@ +clc;
+T1=290; // Temperature at inlet in kelvin
+n=10; // Number of stages
+rp=6.5; // Pressure ratio
+m=3; // mass flow rate in kg/s
+eff_C=0.9; // isentropic efficiency of the compression
+ca=110; // Axial velocity in m/s
+u=180; // Mean blade velocity in m/s
+Cp=1.005; // Specific heat in kJ/kg K
+r=1.4; // Specific heat ratio
+R=287; // Characteristic gas constant in J/kg K
+
+T_2=(rp)^((r-1)/r)*T1; // temperature after isentropic compression
+T2=((T_2-T1)/eff_C)+T1; // Temperature after actual compression
+P=m*Cp*(T2-T1); // Power given to the air
+Del_Tstage=(T2-T1)/n; // Temperature rise per stage
+Del_ct=Cp*10^3*Del_Tstage/u; // For work done per kg of air per second
+// To find blade angles let solve the following equations
+// Del_ct=ca(tan beta_1-tan beta_2) for symmetrical stages
+// u=ca(tan beta_1=tan beta_2) for degree of reaction = 0.5
+// Solving by matrix method
+A=[1,-1;1,1]; C=[Del_ct/ca;u/ca];
+B=A\C;
+// Blade angles at entry and exit
+beta_1=atand(B(1));
+beta_2=atand(B(2));
+
+disp ("kW (roundoff error)",P,"Power given to the air = ");
+disp ("degree",beta_2,"Blade angle at exit = ","degree",beta_1,"Blade angle at inlet = ");
diff --git a/3511/CH9/EX9.7/Ex9_7.sce b/3511/CH9/EX9.7/Ex9_7.sce new file mode 100644 index 000000000..ba05eed7a --- /dev/null +++ b/3511/CH9/EX9.7/Ex9_7.sce @@ -0,0 +1,43 @@ +clc;
+rp=4; // Overall pressure ratio
+m=3; // mass flow rate in kg/s
+eff_pc=0.88; // Polytropic efficiency
+Del_Tstage=25; // The stagnation temperature pressure rise in kelvin
+c1=165; // Absolute velocity in m/s
+alpha_1=20; // air angle from axial direction in degree
+wf=0.83; // Workdone factor
+D=18; // Mean diameter of the last stage rotor in cm
+P01=1.01; // Ambient pressure in bar
+T01=288; // Ambient temperature in kelvin
+Cp=1005; // Specific heat in J/kg K
+r=1.4; // Specific heat ratio
+R=287; // Characteristic gas constant in J/kg K
+
+n=1/(1-(r-1)/(r*eff_pc));
+T02=T01*(rp)^((n-1)/n); // Total pressure at stage 2
+Del_Toverall= T02-T01; // Overall temperature difference
+Ns=Del_Toverall/Del_Tstage; // Number of stages
+eff_C=((rp^((r-1)/r)-1)/(rp^((r-1)/(r*eff_pc))-1));// Efficiency of compressor
+rp1=(1+(eff_C*Del_Tstage/T01))^(r/(r-1)); // Pressure ratio acrocc first stage
+Del_Tstage1=Del_Toverall/Ns; // Temperature rise across stage 1
+T0ls=T02-Del_Tstage1; // Temperature at inlet to last stage
+rpls=(1+(eff_C*Del_Tstage1/T0ls))^(r/(r-1)); // Pressure ratio acrocc last stage
+// For symmetrical blade, R=0.5
+beta_2=alpha_1;
+ca=c1*cosd (alpha_1); // Axial velocity
+beta_1=atand(sqrt(((Cp*Del_Tstage1/(wf*ca))/ca)+(tand(beta_2))^2)); // blade angle
+u=ca*(tand(beta_1)+tand(beta_2)); // mean velocity of blade
+N=60*u/(3.14*D*10^-2*60); // Speed in rps
+Po=rp/rpls; // Total pressure at inlet to the last stage
+T0=T0ls; // Total temperature to the last stage
+Tst=T0-c1^2/(2*Cp); // Static temperature
+Pst=Po/(T0/Tst)^((r-1)/r); // Static pressure
+row=(Pst*10^5)/(R*Tst); // Density
+h=m/(ca*row*3.14*D*10^-2);// Length of last stage
+
+disp (Ns,"Number of stages = ");
+disp (rp1,"Pressure ratio across first stage = ");
+disp (" (roundoff error)",rpls,"Temperature at inlet to last stage = ");
+disp ("degree (roundoff error)",beta_1,"beta1=" );
+disp ("rps (roundoff error)",N,"Speed = ");
+disp ("cm (roundoff error)",h*100,"Length of last stage = ");
diff --git a/3511/CH9/EX9.8/Ex9_8.sce b/3511/CH9/EX9.8/Ex9_8.sce new file mode 100644 index 000000000..c5d15553c --- /dev/null +++ b/3511/CH9/EX9.8/Ex9_8.sce @@ -0,0 +1,36 @@ +clc;
+N=6000; // Speed in rpm
+Del_rise=20; // Stagnation temperature rise in kelvin
+wf=0.93; // Work done factor eff_c=0.89; // Isentropic efficiency of the state
+c1=140; // Inlet velocity in m/s
+p01=1.01; // Ambient pressure in bar
+T01=288; // Ambient temperature in kelvin
+M1=0.95; // Mach number
+Cp=1.005; // Specific heat in J/kg K
+r=1.4; // Specific heat ratio
+R=287; // Characteristic gas constant in J/kg K
+H_T_ratio=0.6; // Hub tip ratio in
+eff_s=0.89; // Stage efficiency
+T1=T01-c1^2/(2*Cp*10^3);
+w1=M1*sqrt (r*R*T1);
+beta_1=acosd (c1/w1);
+u=w1*sind (beta_1);
+beta_2=atand (tand(beta_1)-((Cp*10^3*Del_rise)/(u*wf*c1)));
+p1=p01/(T01/T1)^(r/(r-1));
+row_1=(p1*10^5)/(R*T1);
+Rtip=60*u/(2*3.14*N);
+Rroot=H_T_ratio*Rtip;
+Rm=(Rtip+Rroot)/2;
+h=Rtip-Rroot;
+m=row_1*2*3.14*Rm*h*c1;
+rp=(1+(eff_s*Del_rise)/(T01))^(r/(r-1));
+P=m*Cp*Del_rise;
+uroot=2*3.14*Rroot*N/60;
+beta_1root=atand (uroot/c1);
+beta_2root=atand (tand (beta_1root)-((Cp*10^3*Del_rise)/(wf*uroot*c1)));
+
+disp ("degree",beta_2,"beta 2 = ","degree",beta_1,"beta 1 = ","Rotor air angles at tip:","m",Rtip,"Tip Radius = ","(i). ");
+disp ("kg/s (Roundoff error)",m,"Mass flow rate = ","(ii).");
+disp ("kW",P,"Power input = ",rp,"Stagnation pressure ratio = ","(iii).");
+disp ("degree",beta_2root,"beta 2 = ","degree",beta_1root,"beta 1 = ","Rotor air angles at root sections","(iv).");
+
diff --git a/3511/CH9/EX9.9/Ex9_9.sce b/3511/CH9/EX9.9/Ex9_9.sce new file mode 100644 index 000000000..eaf44d850 --- /dev/null +++ b/3511/CH9/EX9.9/Ex9_9.sce @@ -0,0 +1,17 @@ +clc;
+rp=1.35; // Actual pressure ratio
+DelT_rise=30; // Actual temperature rise in K
+beta_1=47; // Inlet blade angle in degree
+beta_2=15; // Outlet blade angle in degree
+u=225; // Peripheral velocity in m/s
+ca=180; // Axial velocity in m/s
+T01=27+273; // Ambient temperature in kelvin
+Cp=1.005; // Specific heat in KJ/kg K
+r=1.4; // Specific heat ratio
+R=287; // Characteristic gas constant in J/kg K
+
+eff_s=(rp^((r-1)/r)-1)*T01/DelT_rise;
+wf=(DelT_rise*Cp*10^3)/(u*ca*(tand(beta_1)-tand(beta_2)));
+
+disp ("%",eff_s*100,"Stage Efficiency = ");
+disp (wf,"Work done factor = ");
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