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

Aerodynamics of 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 Volumetric Compression Linear Compression WORK DONE V ∂ = 2 W F dx ∫ ∂ W = p v - p v + p.dv x 1 1 2 2 V 1 1 AE 651 - Prof Bhaskar Roy, IITB Lect -3

Fundamental Thermodynamics of Compression Open System 2 2 2 dp ∫ ∫ ∫ ∂ = − = − W v dp . ρ 1 1 1 2 AE 651 - Prof Bhaskar Roy, IITB Lect -3

Basic Thermodynamic Processes of Compression i) Adiabatic (process 1-2 / ) // ) (iv) polytropic (1-2) 3 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 C - C Flowing Fluid ∫ L R = Losses H = v.dp + L + 2 1 Enthalpy change c R 2 1 4 Ae 651 - Prof Bhaskar Roy, IITB Lect -3

Thermodynamic Definition of Parameters of State in a Compression Process 1) T, T 0 - Static, Total - temp. 2) p, p 0 - Static, Total - pr. 3) H = h + C 2 /2 2 + C W = c p . T + ½ (C a 2 ), H and h are Total and Static enthalpies 5 AE 651 - Prof Bhaskar Roy, IITB Lect -3

Thermodynamic Definition of Parameters of State in a Compression Process The polytropic index, k , is ⎛ ⎞ ∂ Q γ ⎜ 1 - c ⎟ ⎜ ⎟ .d T -v .d p ⎝ ⎠ p k = = d Q p .d v 1 - γ . c .d T p γ is the ratio of the specific heats at constant pressure, c p to specific heat at constant volume, c v - for an isentropic process 6 AE 651 - Prof Bhaskar Roy, IITB Lect -3

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 7 Lect -3

Compressor in engine thermodynamic cycle Ideal cycle Real Cycle AE 651 - Prof Bhaskar Roy, IITB 8 Lect -3

Thermodynamics of compressor 9 AE 651 - Prof Bhaskar Roy, IITB Lect -3

Thermodynamic representation of Compression 10 AE 651 - Prof Bhaskar Roy, IITB Lect -3

Efficiency Definition of Compressor Stages- Static Stage Static Efficiency, based on static-to-static changes • / T T - η 3 = 1 T T s - 3 1 // = Static Loss where, x = T 3 – T 3 / + T 3 / - T 3 // = T 2 - T 2 / - T 3 =T 3 -T 3 / + T 3 // = x 1 +x 2 , T T x x - - η 3 = 1 = - 1 ∆ T T - T s 3 s 1 assuming that the pressure lines are linear and parallel to each other. 11 AE 651 - Prof Bhaskar Roy, IITB Lect -3

Thermodynamic representation of Compression process 12 AE 651 - Prof Bhaskar Roy, IITB Lect -3

Efficiency Definition of Compressor Stages - Total • A Total efficiency based on total-to-total temperature variations is given as / / y T T - η 03 01 = = - 1 ∆ T T os - T 03 01 os • where, y = T 03 – T 03// = Aerodyn. Loss in Total frame • If , C 1 = C 3 then, ∆ T os = ∆ T s 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 other, then y = x, and η s = η os . 13 AE 651 - Prof Bhaskar Roy, IITB Lect -3

Axial Compressor Stage Thermodynamics 14 AE 651 - Prof Bhaskar Roy, IITB Lect -3

Constancy of Enthalpy and Rothalpy • Across the rotor a Relative Total Enthalpy , in the rotational frame of reference, called Rothalpy may be written down as H 0rel = c p .T + ½ V 2 is constant across the rotor from station 1 to 2 in the relative frame of reference. The corresponding relative total temperatures are : T 01rel = T 02 rel Similarly, H = h + C 2 /2 = c p T + ½ (C a2 + C t2 ), is the absolute total enthaply constant across the stator . Whereby, absolute total temp.s are : T 02 = T 03 Lect -3 15 AE 651 - Prof Bhaskar Roy, IITB

Static and Total Polytropic Index • Introducing c or = specific heat for total changes ⎡ ⎤ T ln 3 ⎢ ⎥ T ⎣ ⎦ 1 C = C = or r ⎡ ⎤ T ln 03 ⎢ ⎥ T ⎣ ⎦ 01 • for a multistage compressor with polytropic compression if, for example, static , k = 1.5 π oc 1.5 2 3 6 10 1.575 1.53 1.519 1.51 1.507 k 0 16 AE 651 - Prof Bhaskar Roy, IITB Lect -3

Compressor Performance Parameters • stage pressure rise on the basis of Total k o parameter changes in ⎡ ⎤ 1 k - o ∆ T os + . 1 π = ⎢ η ⎥ a polytropic process os ⎣ ⎦ oc T 01 • total head based polytropic efficiency - for small values of ∆ T 0 & ∆ P 0 , ( assuming C 1 = C 3 ), k o ( - 1) Total Head Losses k η o = = 1- Static or Total Work Done γ 0poly ( γ - 1) 17 AE 651 - Prof Bhaskar Roy, IIT Lect -3

Compressor – Polytropic process with heat transfer k pv = Const Heating Cooling ⎛ ⎞ 2 2 C - C 2 ∫ H = H + L + a2 a1 H = v.dp ⎜ ⎟ poly c poly R 2 ⎝ ⎠ 1 poly 18 AE 651 - Prof Bhaskar Roy, IIT Lect -3

Compressor Polytropes – with heat transfer Compression with negative heat transfer i.e . at 2 // -- with cooling provides compression with lesser work input 19 AE 651 - Prof Bhaskar Roy, IIT Lect -3

Compressor Polytropes – Multi-stage Thermodynamics of multi-stage compressor 20 AE 651 - Prof Bhaskar Roy, IIT Lect -3