of Compressors and Turbines (AE 651) Autumn Semester 2009 - PowerPoint PPT Presentation

Aerodynamics of Compressors and Turbines (AE 651) Autumn Semester 2009 Instructor : Bhaskar Roy Professor, Aerospace Engineering Department I.I.T., Bombay e-mail : aeroyia@aero.iitb.ac.in 1

CFD of Turbomachinery Blades Fundamental of Fluid mechanics are often expressed mathematically as Partial Differential Equations (PDEs), mostly of second order PDEs. Generally the governing equations are a set of coupled, non-linear PDEs valid within an arbitrary (or irregular) domain and are subject to various initial and boundary conditions. Analytical solutions of various fluid mechanic equations are limited. This is mainly due to imposition of various boundary conditions of typical fluid flow problems. Experimental fluid mechanics provides some fluid flow information. Hard ware and instruments often limit the extent and details of information available. Expts are often used for validation of CFD solutions. Together they (data produced) are used for design purposes. 2 2 AE 651 - Prof Bhaskar Roy, IITB Lecture-20

CFD of Turbomachinery Blades Linear and Non-linear PDEs ∂u ∂u = -a Linear : ∂t ∂x (Wave Equation) ∂u ∂u Non- = -u (Inviscid Flow – Burgess eqn) Linear ∂t ∂x 2 nd Order equation  2   2   2   2     A B C D    2  2  2 x y . x x y        0 E F G  y 3 3 AE 651 - Prof Bhaskar Roy, IITB Lecture-20

CFD of Turbomachinery Blades Assume that    (x,y ) is a solution of the diffl eqn This solution, typically is a surface in space, and the solutions produce space curves, called charateristics. 2 nd order derivatives along the characteristics are often indeterminate and may be discontinuous across the characteristics. The 1 st order derivatives are continuous. A simpler version of the 2 nd order equation may be written as: 2     dy dy A   - B   +C = 0     dx dx 4 4 AE 651 - Prof Bhaskar Roy, IITB Lecture-20

CFD of Turbomachinery Blades Solution of this yields the equations of the characteristics in physical space : 2   dy B± B - 4AC   =   dx 2A These characteristic curves can be real or imaginary depending on the values of (B 2 – 4AC). A 2 nd order PDE is classified according to the sign of : (a) (B 2 – 4AC) < 0 ----- Elliptic - M<1.0 – Subsonic flow (b) (B 2 – 4AC) = 0 ----- Parabolic M =1.0 – Sonic flow (c) (B 2 – 4AC) > 0 ----- Hyperbolic M>1.0 – Supersonic flow 5 5 AE 651 - Prof Bhaskar Roy, IITB Lecture-20

CFD of Turbomachinery Blades When a real solution exists the zone of influence (downstream) is finite. Similarly, the zone of dependence (upstream) is also finite. Zone of Influence (horizontal shades) Zone of Dependence (vertical shades) 6 6 AE 651 - Prof Bhaskar Roy, IITB Lecture-20

CFD of Turbomachinery Blades Elliptic equations  2   2    0 or,  2  2 x y = ( , ) f x y The domain of solution for elliptic PDE is a closed region. BCs The domain of solution for provide the solution an elliptic PDE within the domain 7 7 AE 651 - Prof Bhaskar Roy, IITB Lecture-20

CFD of Turbomachinery Blades Parabolic equation 2   T T    2  t x The solution domain is normally an open region. Parabolic PDE has one characteristic line. One IC and two The Domain of Solution of a BCs are rqeuired for Parabolic PDE complete solution. 8 8 AE 651 - Prof Bhaskar Roy, IITB Lecture-20

CFD of Turbomachinery Blades Hyperbolic Equations        1 st Order HE – One IC is required   t x  2   2    2 2 nd Order HE – 2 ICs and 2 BCs Reqd.  2  2 t x Solution of HEs for supersonic flow have often been done with Method of Characteristics with two independent variables. Along the Characteristic line PDE reduces to ODE 9 AE 651 - Prof Bhaskar Roy, IITB Lecture-20

CFD of Turbomachinery Blades Initial and Boundary conditions ( supplementary condns ) ICs : A dependant variable is specified at some initial condn BCs : A dependent variable or its derivative must satisfy on the boundary of the domain of the PDE 1) Dirichlet BC : Dependent variable prescribed at boundary 2) Neumann BC: Normal gradient of the d.v. is specified 3) Robin BC : A linear combination of Dirichlet & Neumann 4) Mixed BC : Some part of the boundary has Dirichlet bc and some other part has Neumann bc BCs Body Surface Far Field Symmetry In / Outflow 10 10 AE 651 - Prof Bhaskar Roy, IITB Lecture-20

CFD of Turbomachinery Blades Grid generation PDEs Algebraic equations : Finite Difference Equations Various Finite Difference Techniques Computational space 11 11 AE 651 - Prof Bhaskar Roy, IITB Lecture-20

CFD of Turbomachinery Blades Structured Grid generation Orthogonal Grid Grid without Orthogonality Domain Transformation 12 12 AE 651 - Prof Bhaskar Roy, IITB Lecture-20

CFD of Turbomachinery Blades Unstructured Grid generation Domain Nodalization => Triangulation 13 13 AE 651 - Prof Bhaskar Roy, IITB Lecture-20

CFD of Turbomachinery Blades Blade design system Through Flow Blade-to-Blade design Blade Section Design Blade-to-Blade Analysis Blade section stacking Three-Dimensional Flow Analysis Full Blade Structural and Aero-elastic analysis Blade Construction 14 14 AE 651 - Prof Bhaskar Roy, IITB Lecture-20

CFD of Turbomachinery Blades Through Flow Program Input : a) annulus Information Blade row exit information Inlet profiles of Pr, Temp,  1 Inlet Mass flow Rotational speeds of rotors Blade geometry, Loss distributions Passage averaged perturbation terms Output : b) Blade row inlet and exit conditions Streamline definition and streamtube height 15 15 AE 651 - Prof Bhaskar Roy, IITB Lecture-20

CFD of Turbomachinery Blades Through Flow Program 16 16 AE 651 - Prof Bhaskar Roy, IITB Lecture-20

CFD of Turbomachinery Blades Through Flow Program 17 17 AE 651 - Prof Bhaskar Roy, IITB Lecture-20

CFD of Turbomachinery Blades Blade-to-Blade program Input : Blade geometry Inlet and Exit Velocity distribution Streamline Definition Output : Surface velocity distribution Profile and loss distribution Section Stacking Program Input : Blade section geometry Stacking points and stacking line Axial and Tangential leans (sweep and Dihedral) Output : Three-Dimensional blade geometry 18 18 AE 651 - Prof Bhaskar Roy, IITB Lecture-20

CFD of Turbomachinery Blades Blade-to-Blade program 2D MISES code for Cascade Analysis 19 19 AE 651 - Prof Bhaskar Roy, IITB Lecture-20

CFD of Turbomachinery Blades Blade-to-Blade program 2D MISES code for Cascade Analysis 20 20 AE 651 - Prof Bhaskar Roy, IITB Lecture-20

CFD of Turbomachinery Blades Fluent 21 21 AE 651 - Prof Bhaskar Roy, IITB Lecture-20

CFD of Turbomachinery Blades Fluent 22 22 AE 651 - Prof Bhaskar Roy, IITB Lecture-20

CFD of Turbomachinery Blades CFX-Ansys 23 23 AE 651 - Prof Bhaskar Roy, IITB Lecture-20

CFD of Turbomachinery Blades CFX-Ansys 24 24 AE 651 - Prof Bhaskar Roy, IITB Lecture-20

CFD of Turbomachinery Blades CFX-Ansys 25 25 AE 651 - Prof Bhaskar Roy, IITB Lecture-20

CFD of Turbomachinery Blades CFX-Ansys 26 26 AE 651 - Prof Bhaskar Roy, IITB Lecture-20

CFD of Turbomachinery Blades CFX-Ansys Vector diagram of tip flows with (a) Rotating Frame 27 27 AE 651 - Prof Bhaskar Roy, IITB Lecture-20

CFD of Turbomachinery Blades CFX-Ansys Vector diagram of tip flows with (b) Stationary frame, 28 28 AE 651 - Prof Bhaskar Roy, IITB Lecture-20

Thank you very much for participating in this course AE 651 AE 651 - Prof Bhaskar Roy, Aerospace Engg. Dept., IIT,Bombay