Download - Similarity Laws for Turbo-machinery
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Similarity Laws for Turbo-machinery
P M V SubbaraoProfessor
Mechanical Engineering Department
From Inception to Utilization….
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Buckingham, E. The principle of similitude. Nature 96, 396-397 (1915).
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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
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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
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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 (m = p)– Same power coefficient– Same energy ratios.
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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.
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Fundamental Quantities for Turbo-machines
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The First Non-dimensional Parameter
dcba QDN 1
31 DNQ
Flow Coefficient or Capacity Coefficient ()
3DNQ
“the dimensionless ‘swallowing’ capacity of the machine”
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Flow Velocity Vs Blade Speed
Volumetric flow rate (Q) can be related to the fluid velocity :
A particular value of implies a specific relationship betweenfluid velocity and blade/impeller speed.
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Efficiency (η) vs Flow coefficient (ϕ)
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Design Innovations for Better Performance
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Strategies to Capture More Power from Wind
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Pitch-Controlled Variable-Speed Wind Turbine Generation
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Grid Acceptable Power
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The second Non-dimensional Parameter
dcba pDN 2
222 DNp
•p corresponds to the energy per unit volume of the fluid.
• N2D2 relates to the rotor or impeller dynamic pressure (K.E. per unit volume).
•Loading Coefficient
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Load Coefficient or Head Coefficient
For compressible fluid machines :
2 :t Coefficien LoadU
h
For incompressible fluid machines :
22 :t Coefficien HeadDN
gH
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Selection of Load Coefficient for an Axial Flow Compressor
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Accepted Technology for Hydro Power generation
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Universal Design Chart for Power Consuming Turbo-machines
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The Third non-dimensional Parameter
dcba PDN 3
52 DNP
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Role of Power Coefficient : Wind Turbines
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Size Vs Capacity of A Wind TUrbine
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Design Upgradation
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Similarity of Model & Prototype
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Design for Best Efficiency for Pumps & Fans
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Dimensions for Performance
2/1
4/1
QgHDDs