turbine design

New York City College

Gas Turbine Design

Steam and Gas Turbine, ME I 3100

Johnaton McAdam, Fall 2016

Professor Rishi Raj

Contents1. Abstract...............................................................................................................................................2

2. Design Parameters...............................................................................................................................2

3. Introduction.........................................................................................................................................3

3.1 Ideal Brayton Cycle...........................................................................................................................3

3.2 Real Brayton Cycle............................................................................................................................4

3.3 Governing Equations.........................................................................................................................5

3.3.1 Continuity...................................................................................................................................5

3.3.2 Momentum.................................................................................................................................5

3.3.3 Energy Equations........................................................................................................................5

4. Design Calculations.............................................................................................................................5

4.1 Ideal Cycle.........................................................................................................................................5

4.2 Real Cycle.........................................................................................................................................6

4.3 Turbine Calculations..........................................................................................................................6

4.3.1 Stage 1 Design............................................................................................................................7

4.3.2 Stage 2 Design............................................................................................................................9

4.3.3 Stage 3 Design..........................................................................................................................11

4.3.4 Stage 4 Design..........................................................................................................................13

5. Acknowledgements...............................................................................................................................16

6. Reflection..............................................................................................................................................16

7. Conclusion.............................................................................................................................................16

8. Nomenclature........................................................................................................................................17

9. References.............................................................................................................................................17

10. Matlab Code........................................................................................................................................18

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1. AbstractDesign a gas turbine with given inlet turbine temperature, net shaft power and shaft rpm.

This report will feature calculation and selection of thermodynamic cycle with justification,

aerodynamic calculation of mid passage turbine stages, velocity triangles, selection of blade

profiles with number of blades and the stage efficiency.

2. Design Parameters Turbine Inlet Temperature,T3 1700F

Net Shaft Power 6000 H.P

RPM 7200

P1 1 Atm , 14.69 Psi

T1 70F

K 1.4

gc 32 lbft /lbf s232 lbft /lbf s232

ftS2

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3. IntroductionThe gas turbine is an internal combustion that converts the chemical energy that is

extracted from natural gas and other fuels into mechanical energy. The converted energy will be

used for one of two applications; producing electricity for power plants or providing thrust to

drive an aero-vehicle. The basic components of a gas turbine includes the compressor which

takes the outside air which is compacted and pressurized through a series of rotating and

stationary compressor blades. The combustor is where the pressurized air is ignited from the fuel

and the heated molecules are expanded and with high velocities enter the turbine section. The

turbine converts the energy from the high velocity gas into rotational mechanical energy over a

series of turbine rotor blades. Lastly the rotational energy is then transfer to the driven

equipment through the output shaft with a speed reduction gearbox and the spend gas is ejected

into the atmosphere.

Figure 1

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3.1 Ideal Brayton CycleThe open cycle that will be used for this project is the Brayton Cycle or the Joule Cycle

since this represents the operation of a gas turbine machine. This cycle consists of four phases as

shown in figure 1, from the Temperature vs Entropy curve from process 1 -2 there is isentropic

compression in which work is added to the compressed air at constant temperature. For process

2-3 the addition of heat at constant pressure is taking place inside the combustion chamber, for

process 3-4 isentropic expansion and the work is produced in the turbine. Lastly process 4-1

describes the heat removal at constant pressure of the system and this can be known as

population into the atmosphere.

ause of the peculiar nature of Brayton circle effectiveness for the purpose of providingmechanical shaft power, gas turbine design were centered on it. The Brayton cycle (1876),

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shown in Fig.2.0 below as a pressure-volume diagram, is a representation of the properties of afixed amount of air as it passes through a gas turbine in operation. Air is compressed from point 1 to point 2. This increases the pressure as the volume of spaceoccupied by the air is reduced. The air is then heated at constant

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pressure from 2 to 3.This heat isadded by injecting fuel into the combustor and igniting it on a continuous basis. The hotcompressed air at point 3 is then allowed to expand (from point 3 to 4) reducing the pressure andtemperature and increasing its volume. In the engine in Fig. 4b, this

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represents flow through theturbine to point 3’ and then flow through the power turbine to point 4 to turn a shaft. Braytoncircle gas turbine has an efficiency of about 25% in peak load situations, produces cheapkilowatts and turnkey operations.

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Figure 2

3.2 Real Brayton CycleThe real Brayton cycle differs from the ideal cycle due to the material properties,

pressure drop due to friction heat loss and other various factors. Therefore because of the

irreversibility of the system the work of the compressor is more than the work of the turbine.

Figure 3

3.3 Governing Equations

3.3.1 Continuity m ¿ ρVA

∇ .u=0

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3.3.2 Momentum

U ∂U∂ X

=−1ρ

∂ P∂ X (Incompressible Steady Non-viscous Naiver Stokes Equation)

3.3.3 Energy Equations∆ U=Q−W (First Law of Thermodynamics)

ds≥ 0 (Second Law of Thermodynamics)

4. Design Calculations

4.1 Ideal CycleTemperature

T 2=(T 1∗T 3)12 →¿¿

T 4=T 3 ¿

Pressure Ratio

P2

P1=¿

Enthalpy Calculation

h1=Cp 1T 1 →0.241 ×530=127.48 Btu /lbm

h2=C p2 T2 →0.242 ×1068.7=258.73 Btu / lbm

h3=C p 3 T3 → 0.25× 2160=539.75 Btu/ lbm

h4=C p4 T 4→ 0.242 ×1068.7=257.57 Btu /lbm

Process 1-2 (Work of compressor)

wC=h2−h1→(258.73−127.48)=130.24 Btu/ lbm

Process 2-3 (Heat addition)

qH=h3−h2 → (539.75−258.73 )=281.12 Btu/ lbm

Process 3-4 (Work of Turbine)

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wT=h3−h4 → (541.90−257.57 )=282.98 Btu/ lbm

Process 4-1 (Heat ejection)

qL=h4−h1 → (257.57−127.48 )=130.06 Btu /lbm

Cycle Thermal Efficiency

ηth=W N

q¿→

wT−w c

q¿=262.76−130.24

130.06=50 %

4.2 Real CycleAssume: ηth(w ¿¿T , real)=93%→ ηWtr¿

ηth(w ¿¿c ,real )=87 %→ ηWcr¿

T 2=T 1+¿

h '2=C p4 T 4 → 0.242×1149.38=278.2 Btu / lbm

T 4=T 3−¿

h ' 4=C p 4 T 4→ 0.242 ×1145.08=277.57 Btu / lbm

4.3 Turbine CalculationsMass Flow Rate

P=6000HP →4474.2 Kwt

P= m× Δh3412

P=m [(h3−h4 ' )−(h2 '−h1)¿ ¿3142

→ m= 6000 ×34123600 [(539.75−277.57)−(278.2−127.48)¿

¿→37.35 lbms

4.3.1 Stage 1 Design Reaction stage design

Δ hstage=(h 3−h 4 ' )

4→ (539.2−277.57)

4=65.95 Btu/ lbm

10

R=0.4

ψ=2 (1−R )→ 1.2

R=Δhr 1

Δ hstage⟹0.4=

Δ hr 1

70.54⟹ Δhr 1=26.38 Btu /lbm

Δ hstage=Δ hr1+ Δhs1 Δ hs 1=39.57 Btu/ lbm

Adiabatic velocity

V o=√2 × gc × Δhstage

V o=√2 ×32 ×65.95 ×778=1817.8( ft /s )

n=.89

UV o

=√ n2ψ

→√ .892 x 1.2

=0.6021

Blade velocity

U=V o× .6021=1932.45 ×0.6021=1094.4 ft / s

Mean radius

N=7200 rpm

U=2× π × N × rm⟹ r m=U × 60

2× π × N→ 1094.4 × 60

2× 3.142× 7200=1.451 ft

Absolute velocity V 2=√¿¿

V 2=√¿¿

Relative velocity

∝2=80

W 2=V 2−U →1480.8−1094.4=313.59 ft /s Vx = V2 cos∝2→ 1480 cos (75 )=244.50 ft /s

cosβ2 = Vx/W2β2 = 38.21

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tanβ 3=2URVx

+tanβ2

β 3=77.15

W3 =Vx

cosβ 3 = 1095.4

Work

w= Ugc × 778

¿

w= 1094.432.2× 778

¿

Stage Efficiency

ηstage=WV o

2

2× gc × 778

ηstage=55.41

1817.82

2× 32× 778

=84 %

Length of Rotor and Stator Blades

m=ρ V x A=ρ V x 2π rm l

l= 37.350.0748 ×244.50 ×2 ×3.142 ×1.451

=0.2197 ft

Number of Blades

Assumptions:

b ≈ c=0.50 ft

∅=0.85

∅=2 Sb

¿

Nb S=2 π rm

S=∅× b2¿¿

12

N b=2 π r m

s=2×3.142 ×1.45

0.24=36.53 ≈ 37 blades

4.3.2 Stage 2 DesignReaction stage design

Δ hstage=70Btu / lbm

R=0.35

ψ=2 (1−R )→ 1.3

R=Δhr 1

Δ hstage→ Δhr 1=24.5 Btu /lbm

Δ hstage=Δ hr1+ Δhs1 Δ hs 1=45.5 Btu /lbm

Adiabatic velocity


V o=1872.8( ft /s)

n=.89

UV o

=√ n2ψ

→=0.5785

Blade velocity

U=V o× .5785=1872.8 × 0.5785=1083.3 ft / s

Mean radius

N=7200 rpm

U=2× π × N × rm⟹ r m=U × 60

2× π × N=1.4368 ft


V 2=√¿¿

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Relative velocity

∝2=78

W 2=V 2−U=426.55 ft / s Vx = V2 cos∝2=313.91 ft / s

cosβ2 = Vx/W2β2 = 42.61tanβ 3=2UR

Vx+tanβ2

β 3=73.31

W3 =Vx

cosβ 3 = 1093.2

Work

w= Ugc × 778

¿

w=57.76 Btu/ lbm

Stage Efficiency

ηstage=WV o

2

2× gc × 778

ηstage=82.52%


m=ρ V x A=ρ V x 2π rm l l=0.1729 ft

Number of Blades

Assumptions:

b ≈ c=0.50 ft

∅=0.85

14

∅=2 Sb

¿

Nb S=2 π rm

S=∅× b2¿¿

N b=2 π r m

s=42.43 ≈ 43blades


Δ hstage=73 Btu / lbm

R=0.41

ψ=2 (1−R )→ 1.18

R=Δhr 1

Δ hstage→ Δhr1=29.93 Btu /lbm

Δ hstage=Δ hr 1+ Δhs 1 Δ hs 1=43.07 Btu /lbm

Adiabatic velocity


V o=1912.5(ft /s)

n=.89

UV o

=√ n2ψ

→=0.6072

Blade velocity

U=V o× .6072=1872.8 ×0.5785=1161.2 ft / s

Mean radius

N=7200 rpm

U=2× π × N × rm⟹ r m=U × 60

2× π × N=1.5401 ft

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V 2=√¿¿

Relative velocity

∝2=80

W 2=V 2−U=307.81 ft /s Vx = V2 cos∝2=255.08 ft /s


Vx+tanβ2

β 3=77.21

W3 =Vx

cosβ 3 = 1153

Work

w= Ugc × 778

¿

w=60.10 Btu/ lbm

Stage Efficiency

ηstage=WV o

2

2× gc × 778

ηstage=82.34 %


m=ρ V x A=ρ V x 2π rm l

16

l=0.1985 ft

Number of Blades

Assumptions:

b ≈ c=0.50 ft

∅=0.85

∅=2 Sb

¿

Nb S=2 π rm

S=∅× b2¿¿

Nb=2 πr m

s=32.9287 ≈33 blades


Δ hstage=75 Btu / lbm

R=0.45

ψ=2 (1−R )→ 1.10

R=Δhr 1

Δ hstage→ Δhr 1=33.75 Btu /lbm

Δ hstage=Δ hr 1+ Δhs 1 Δ hs 1=41.25 Btu /lbm

Adiabatic velocity


V o=1938.5(ft /s)

n=.89

UV o

=√ n2ψ

→=0.6289

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Blade velocity

U=V o× .6072=1872.8 ×0.5785=1219 ft / s

Mean radius

N=7200 rpm

U=2× π × N × rm⟹ r m=U × 60

2× π × N=1.6168 ft


V 2=√¿¿

Relative velocity

∝2=80

W 2=V 2−U=218.59 ft /s Vx = V2 cos∝2=274.31 ft / s


Vx+tanβ2

β 3=76.24

W3 =Vx

cosβ 3 = 1130.2

Work

w= Ugc × 778

¿

w=54.75Btu / lbm

Stage Efficiency

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ηstage=WV o

2

2× gc × 778

ηstage=73.00 %


m=ρ V x A=ρ V x 2π rm l l=0.1932 ft

Number of Blades

Assumptions:

b ≈ c=0.50 ft

∅=0.85

∅=2 Sb

¿

Nb S=2 π rm

S=∅× b2¿¿

N b=2 π r m

s=25.93 ≈26 blades

5. AcknowledgementsI would like to thank my Professor, Rishi Raj for assigning such an interesting and

practical design project because it has allowed me to apply my classroom knowledge into real

world applications. I would also like to thank him for helping me with this project with

questions or uncertainty I may have come across. Lastly I thank all of the engineers who have

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made their information regarding this topic available so it may help me to complete this

assignment.

6. ReflectionWorking on this design project has truly been a wonderful experience, I was able to

incorporate some basic thermodynamics knowledge I have learn for years into a real world

project. I was able to apply the theory I have learn for so long in to a practical approach.

Although this project is simple compare to the real implications for gas turbines, I plan on

improving my topic by trying different methods to improve my overall efficiency of my system.

The first idea I would like to implement in my future studies is refrigeration. I will also

experiment with other close system for turbines to minimize the pollution that will be created

from an open system.

7. ConclusionThe design of gas turbine system is a very interesting process due to its complexity to

achieve the desired results. There is no not a one calculation that is used rather a series of

calculations are preform based on the desired efficiency of the system. There are two main types

of gas turbines, open and close system and each has their uses for example the close system is

use for aircraft and the close system is for consumer utilizes and submarines. The gas turbine

that was design for this project is an open model and due to its nature of being open it will create

pollution which will be a design aspect I will tackle in future research of this topic.

8. Nomenclaturep Pressure in psi units

T Temperature, ºR

ηth Efficiency

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h Specific enthalpy, Btu/lbm

S Specific entropy, Btu/lbm . R

ν Specific volume, ft3/lbm

m Mass flow rate, lbm/s

P Power, Kw

Qh Heat in, Btu/lbm

ql Heat out, Btu/lbm

l blade length, ft

N b Number of blades

rm Mean radius, ft

Ψ Loading Factor

R Reaction

w Work Btu/lbm

V 2 Absolute Velocity, ft/s

U Blade velocity, ft/s

V o Adiabatic Velocity, ft/s

9. References [1] Thermo-fluid system analysis and design- Prof. R.S Raj

[2] http://web.mit.edu/16.unified/www/SPRING/propulsion/notes/node51.html

10. Matlab Code%Steam and Gas Turbine %Turbine Projectclear allclc

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r= 459; % RankineT1=70+r; %inlet temp (R)T3= 1700+r; %Max temp (R)k=1.4;P1= 14.69; %Psicp1 = .241; %BTU/ F lbcp2 = 0.242;cp3 = 0.25;cp4 = 0.241;P = 6000; %HPN= 7200;rho = 0.0765; %Ideal Cycle%Pressure Ratio P2/P1P21 = (T3/T1) ^ (k / (2*(k-1))); %Temperature at 2nd stepT2 = (T1) * ((P21) ^ ( (k-1)/k)); %Pressure P2P2 = P1*(T2/T1)^(k/((k-1)));P3 = P2;P4 = P1; %Outet Temperature T4 = (T1)* (T3/T2); %h at each stageh1 = cp1*T1; h2 = cp2*T2; h3 = cp3*T3; h4 = cp4*T4; %work of compressorwc = h2 - h1; %Heat additionqh = h3-h2; %Work of turbinewt = h3-h4; %heat lossql = h4-h1; %total workwnet = wt-wc; %thermal efficency nt = (wnet/qh) * 100; %For real' ntr = .93; ncr= .87;%work for turbinewtr = wt*ntr ;T4p = T3 - ((T3 - T4)* ntr);

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h4p = cp4*T4p; %work for compressorwcr = wc*ncr;T2p = T1+ ((T2 - T1)/ ncr);h2p = cp2*T2p; %mass flow ratePkw = P*(0.7457); %convert HP to Kwhnet = (h3-h4p)-(h2p-h1); %delta hmh= (Pkw*3412) /hnet; %mass flow rate in hoursms = mh/3600; %mass flow rate in seconds %reaction stage 1dstage1 = (h3-h4p)/4;R = 0.4;Lf = 2*(1-R);dr1 = R*dstage1;ds1 = dstage1 - dr1; %adiabatic velocitygc = 32.2;Vo1 = sqrt( 2* gc* dstage1 * 778);UVo1 = sqrt( ncr / (2* Lf)); %Blade velocityU1 = UVo1*Vo1; %Mean Radiusrm1 = U1*60 / ( 2* pi * N); %Absolute velocity V21 = sqrt(2*gc*(1-R)*dstage1*778); %Relative velocitya21 = 80;Vx1 = V21*cosd(a21);w21 = (V21 - U1);b21= acosd(Vx1/w21);b31= atand((2*U1*R/Vx1) + tand(b21));w31 = Vx1 / (cosd(b31)); %workWork1 = (U1 / (gc * 778)) *(w21*sind(b21) + w31*sind(b31)); %stage efficiencynstage1 = Work1/ ( Vo1^2 / (2*gc*778)) * 100; %lenght of rotor and stator bladesL1 = ms/(rho*Vx1*2*pi*rm1); %Number of bladesPhi = 0.85;

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b=0.5;c=b;S1 = (Phi*b *.5) / (tand(b21) + tand(b31) * cosd(b31)^3);Nb1 = (2*pi*rm1) / (S1); %Stage 2% dstage2 = 70;R2 = 0.35;Lf2 = 2*(1-R2);dr2 = R2*dstage2;ds2 = dstage2 - dr2; %adiabatic velocity gc = 32.2;Vo2 = sqrt( 2* gc* dstage2 * 778);UVo2 = sqrt( ncr / (2* Lf2)); %Blade velocityU2 = UVo2*Vo2; %Mean Radiusrm2 = U2*60 / ( 2* pi * N); %Absolute velocity V22 = sqrt(2*gc*(1-R2)*dstage2*778); % %Relative velocity a22 = 78;Vx2 = V22*cosd(a22);w22 = (V22 - U2);b22= acosd(Vx2/w22);b32= atand((2*U2*R2/Vx2) + tand(b22));w32 = Vx2 / (cosd(b32)); %workWork2 = (U2 / (gc * 778)) *(w22*sind(b22) + w32*sind(b32)); %stage efficiencynstage2 = Work2/ ( Vo2^2 / (2*gc*778)) * 100; %lenght of rotor and stator bladesL2 = ms/(rho*Vx2*2*pi*rm2); %Number of bladesPhi = 0.85;b=0.5;c=b;S2 = (Phi*b *.5) / (tand(b22) + tand(b32) * cosd(b32)^3);Nb2 = (2*pi*rm2) / (S2); %Stage 3dstage3 = 73;R3 = 0.41;Lf3 = 2*(1-R3);dr3 = R3*dstage3;

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ds3 = dstage3 - dr3; %adiabatic velocitygc = 32.2;Vo3 = sqrt( 2* gc* dstage3 * 778);UVo3 = sqrt( ncr / (2* Lf3)); %Blade velocityU3 = UVo3*Vo3; %Mean Radiusrm3 = U3*60 / ( 2* pi * N); %Absolute velocity V23 = sqrt(2*gc*(1-R3)*dstage3*778); %Relative velocitya23 = 80;Vx3 = V23*cosd(a23);w23 = (V23 - U3);b23= acosd(Vx3/w23);b33= atand((2*U3*R3/Vx3) + tand(b23));w33 = Vx3 / (cosd(b33)); %workWork3 = (U3 / (gc * 778)) *(w23*sind(b23) + w33*sind(b33)); %stage efficiencynstage3 = Work3/ ( Vo3^2 / (2*gc*778)) * 100; %lenght of rotor and stator bladesL3 = ms/(rho*Vx3*2*pi*rm3); %Number of bladesPhi = 0.85;b=0.5;c=b;S3 = (Phi*b *.5) / (tand(b23) + tand(b33) * cosd(b33)^3);Nb3 = (2*pi*rm3) / (S3); %Stage 4dstage4 = 75;R4 = 0.45;Lf4 = 2*(1-R4);dr4 = R4*dstage4;ds4 = dstage4 - dr4; %adiabatic velocitygc = 32.2;Vo4 = sqrt( 2* gc* dstage4 * 778);UVo4 = sqrt( ncr / (2* Lf4)); % %Blade velocityU4 = UVo4*Vo4;

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%Mean Radiusrm4 = U4*60 / ( 2* pi * N); %Absolute velocity V24 = sqrt(2*gc*(1-R4)*dstage4*778); %Relative velocitya24 = 80;Vx4 = V24*cosd(a24);w24 = (V24 - U4);b24= acosd(Vx4/w24);b34= atand((2*U4*R4/Vx4) + tand(b24));w34 = Vx4 / (cosd(b34)); %workWork4 = (U4 / (gc * 778)) *(w24*sind(b24) + w33*sind(b34)); %stage efficiencynstage3 = Work4/ ( Vo4^2 / (2*gc*778)) * 100; %lenght of rotor and stator bladesL4 = ms/(rho*Vx4*2*pi*rm4); %Number of bladesPhi = 0.85;b=0.5;c=b;S4 = (Phi*b *.5) / (tand(b24) + tand(b34) * cosd(b34)^3);Nb4 = (2*pi*rm4) / (S4);

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turbine design

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