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Similarity Laws for Turbo-machinery

Similarity Laws for Turbo-machinery. P M V Subbarao Professor Mechanical Engineering Department. From Inception to Utilization…. Buckingham, E. The principle of similitude. Nature 96 , 396-397 (1915). The purpose of Dimensional Analysis. Want to determine which variables to study.

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Similarity Laws for Turbo-machinery

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  1. Similarity Laws for Turbo-machinery P M V Subbarao Professor Mechanical Engineering Department From Inception to Utilization….

  2. Buckingham, E. The principle of similitude. Nature 96, 396-397 (1915).

  3. The purpose of Dimensional Analysis • Want to determine which variables to study. • Want to determine the parameters that significantly affect the system. • Reduce the cost/effort of experimental analysis by studying the most important groups of variables. • The ideas can be used for any physical system. • This will help in the design of scale test models

  4. Similitude & Dimensional Analysis • Scale model to prototype design and analysis. • Used to select proper turbo-machine (axial, radial or mixed flow,…) • Used to define performance parameters

  5. Similarity Laws • GEOMETRIC • Linear dimension ratios are the same everywhere. • Photographic enlargement • KINEMATIC (ϕm = ϕp) • Same flow coefficients • Same fluid velocity ratios (triangles) are the same • DYNAMIC (ψm = ψp) • Same loading coefficient • Same force ratios (and force triangles) • Energetic (Pm = Pp) • Same power coefficient • Same energy ratios.

  6. Euler’s GENERIC TURBOMACHINE (turbine, compressor, pump, ….) • List the n physical quantities (Qn) with dimensions and the k fundamental dimensions. • There will be (n-k) π-terms. • Select k of these quantities, none dimensionless and no two having the same dimensions. • All fundamental dimensions must be included collectively in the quantities selected.

  7. Fundamental Quantities for Turbo-machines

  8. The First Non-dimensional Parameter Flow Coefficient or Capacity Coefficient (f) “the dimensionless ‘swallowing’ capacity of the machine”

  9. Flow Velocity Vs Blade Speed Volumetric flow rate (Q) can be related to the fluid velocity : A particular value of f implies a specific relationship between fluid velocity and blade/impeller speed.

  10. Efficiency (η) vs Flow coefficient (ϕ)

  11. Design Innovations for Better Performance

  12. Strategies to Capture More Power from Wind

  13. Pitch-Controlled Variable-Speed Wind Turbine Generation

  14. Grid Acceptable Power

  15. The second Non-dimensional Parameter • Dp corresponds to the energy per unit volume of the fluid. • rN2D2 relates to the rotor or impeller dynamic pressure (K.E. per unit volume). • Loading Coefficient

  16. Load Coefficient or Head Coefficient For compressible fluid machines : For incompressible fluid machines :

  17. Selection of Load Coefficient for an Axial Flow Compressor

  18. Accepted Technology for Hydro Power generation

  19. Universal Design Chart for Power Consuming Turbo-machines

  20. The Third non-dimensional Parameter

  21. Role of Power Coefficient : Wind Turbines

  22. Size Vs Capacity of A Wind TUrbine

  23. Design Upgradation

  24. Similarity of Model & Prototype

  25. Design for Best Efficiency for Pumps & Fans

  26. Dimensions for Performance

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