Aerodynamics of Compressors and Turbines (AE 651) Autumn Semester - - PowerPoint PPT Presentation

Aerodynamics

• f

Compressors and Turbines

(AE 651)

Autumn Semester 2009

Instructor : Bhaskar Roy Professor, Aerospace Engineering Departm ent I .I .T., Bom bay e-m ail : aeroyia@aero.iitb.ac.in

Fundamentals of Compression

1

2 1

V 1 1 2 2 V

W = p v - p v + p.dv ∂

∫

x

W F dx ∂ =

AE 651 - Prof Bhaskar Roy, IITB Lect -3

WORK DONE Volumetric Compression Linear Compression

Fundamental Thermodynamics of Compression

Open System

2

2 2 2 1 1 1

. dp W v dp ρ ∂ = − = −

∫ ∫ ∫

AE 651 - Prof Bhaskar Roy, IITB Lect -3

Basic Thermodynamic Processes of Compression

3

i) Adiabatic (process 1-2/) //) (iv) polytropic (1-2)

Ae 651 - Prof Bhaskar Roy, IITB Lect -3

Basic Thermodynamic Processes of Compression

i) Adiabatic (process 1-2/) (ii) Isothermal process (1-2//), (iii) isochoric (Process 1-2///),

2 2 2 2 1 c R 1

C

• C

H = v.dp + L + 2

∫

Flowing Fluid Enthalpy change

LR = Losses

4

Ae 651 - Prof Bhaskar Roy, IITB Lect -3

Thermodynamic Definition of Parameters of State in a Compression Process

1) T, T0- Static, Total - temp. 2) p, p0 - Static, Total - pr.

5

3) H = h + C2/2 = cp.T + ½ (Ca

2 + CW 2),

H and h are Total and Static enthalpies

AE 651 - Prof Bhaskar Roy, IITB Lect -3

Thermodynamic Definition of Parameters of State in a Compression Process

p p

Q γ 1 - c .d T

• v .d p

k = = d Q p .d v 1 - γ . c .d T ⎛ ⎞ ∂ ⎜ ⎟ ⎜ ⎟ ⎝ ⎠

The polytropic index, k, is

6

γ is the ratio of the specific heats at constant pressure, cp

to specific heat at constant volume, cv - for an isentropic process

AE 651 - Prof Bhaskar Roy, IITB Lect -3

7

Thermodynamic T-s diagram of Compressors

i) Isentropic process (1-2/) ii) polytropic process (1-2) iii) Isothermal process (1-2//), (iv) isochoric Process (1-2///),

AE 651 - Prof Bhaskar Roy, IITB Lect -3

Compressor in engine thermodynamic cycle

Ideal cycle

Lect -3

Real Cycle

AE 651 - Prof Bhaskar Roy, IITB

8

9

Thermodynamics of compressor

AE 651 - Prof Bhaskar Roy, IITB Lect -3

10

Thermodynamic representation

• f Compression

AE 651 - Prof Bhaskar Roy, IITB Lect -3

11

Efficiency Definition of Compressor Stages- Static

• Stage Static Efficiency, based on static-to-static changes

where, x = T3 – T3

// = Static Loss

=T3-T3

/ + T3 / - T3 // = T2- T2 /+ T3 / - T3 //

= x1+x2 ,

assuming that the pressure lines are linear and parallel to each other.

1 s 1

3 3

• =

=

• s

1

x x T T η ∆ T T T

1 1

/ 3 s 3

• =
• T

T η T T

AE 651 - Prof Bhaskar Roy, IITB Lect -3

12

Thermodynamic representation

• f Compression

process

AE 651 - Prof Bhaskar Roy, IITB Lect -3

Efficiency Definition of Compressor Stages - Total

13

• A Total efficiency based on total-to-total

temperature variations is given as

• where, y = T03 – T03// = Aerodyn. Loss in Total frame
• If , C1 = C3 then, ∆Tos = ∆Ts i.e. the dynamic heads

are assumed same at inlet and outlet. If the pressure lines are assumed to be straight and parallel to each

• ther, then y = x, and ηs = ηos.

/ / 03 01

• s

03 01

• =

=

• s

1

y T T η ∆ T T T

AE 651 - Prof Bhaskar Roy, IITB Lect -3

14

Axial Compressor Stage Thermodynamics

AE 651 - Prof Bhaskar Roy, IITB Lect -3

Constancy of Enthalpy and Rothalpy

15

• Across the rotor a Relative Total Enthalpy, in the

rotational frame of reference, called Rothalpy may be written down as H0rel = cp .T + ½ V2 is constant across the rotor from station 1 to 2 in the relative frame of reference. The corresponding relative total temperatures are : T01rel = T02 rel Similarly, H = h + C2/2 = cp T + ½ (Ca2 + Ct2), is the absolute total enthaply constant across the stator. Whereby, absolute total temp.s are : T02 = T03

AE 651 - Prof Bhaskar Roy, IITB Lect -3

Static and Total Polytropic Index

16

• Introducing cor = specific heat for total changes
• for a multistage compressor with polytropic

compression if, for example, static, k = 1.5

πoc

1.5 2 3 6 10 k0 1.575 1.53 1.519 1.51 1.507

1

3

• r

r 03 01

C = C =

T ln T T ln T

⎡ ⎤ ⎢ ⎥ ⎣ ⎦ ⎡ ⎤ ⎢ ⎥ ⎣ ⎦

AE 651 - Prof Bhaskar Roy, IITB Lect -3

17

Compressor Performance Parameters

• stage pressure rise on the basis of Total

parameter changes in

• total head based polytropic efficiency - for small

values of ∆T0 & ∆P0 , (assuming C1 = C3),

• c

01

• 1
• k

k

• s

=

• s

η

∆T 1 T

π

+ . ⎡ ⎤ ⎢ ⎥ ⎣ ⎦

Total Head Losses 1- Static or Total Work Done

• 0poly

(

• 1)

= = γ (γ - 1)

k k

η

AE 651 - Prof Bhaskar Roy, IIT Lect -3

a polytropic process

18

Compressor – Polytropic process with heat transfer

AE 651 - Prof Bhaskar Roy, IIT Lect -3

Heating Cooling

2 poly 1 poly

H = v.dp ⎛ ⎞ ⎜ ⎟ ⎝ ⎠

∫

k

pv = Const

2 2 a2 a1 c poly R

C

• C

H = H + L + 2

19

Compressor Polytropes – with heat transfer

AE 651 - Prof Bhaskar Roy, IIT Lect -3

Compression with negative heat transfer i.e. at 2// -- with cooling provides compression with lesser work input

20

Compressor Polytropes – Multi-stage

AE 651 - Prof Bhaskar Roy, IIT Lect -3

Thermodynamics

• f multi-stage

compressor