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Fluid Mechanics,Thermodynamics ofTurbomachineryCONTENT Turbomachines Dimensional analysis and performance laws Incompressible fluid analysis Performance characteristics Variable geometry turbomachines Specific speed Cavitation Compressible gas flow relations Compressible fluid analysisThe equation of continuity The first law of thermodynamics internal The momentum equation Newtons second law of motion

CONTENT Moment of momentum Eulers pump and turbine equations Defining rothalpy The second law of thermodynamics entropy Definitions of efficiency Diffusers

Introduction: DimensionalAnalysis: SimilitudeCHAPTER 1

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TURBOMACHINES

TURBOMACHINES

TURBOMACHINES

TURBOMACHINES

TURBOMACHINESDIMENSIONAL ANALYSIS AND PERFORMANCE LAWS

DIMENSIONAL ANALYSIS AND PERFORMANCE LAWS

INCOMPRESSIBLE FLUID ANALYSIS

INCOMPRESSIBLE FLUID ANALYSIS

PERFORMANCE CHARACTERISTICS

VARIABLE GEOMETRY TURBOMACHINES

VARIABLE GEOMETRY TURBOMACHINES

SPECIFIC SPEED

CAVITATION

COMPRESSIBLE GAS FLOW RELATIONS

Where the Match number is:

COMPRESSIBLE GAS FLOW RELATIONSSo that the stagnation temperature can be defined asThe Gibbs relation, derived from the second law of thermodynamics

con

COMPRESSIBLE GAS FLOW RELATIONSCOMPRESSIBLE FLUID ANALYSIS

Power coefficient may be wren

The flow coefficient can now be more conveniently expressed as

COMPRESSIBLE FLUID ANALYSIS

COMPRESSIBLE FLUID ANALYSISBasic Thermodynamics,Fluid Mechanics:Definitions of EfficiencyCHAPTER 2The equation of continuity

(1)(2)

The first law of thermodynamics internal energyThe steady flow energy equation

(3)(4)(5)(6)(7)The momentum equation Newtons second law of motion

Bernoullis equation

Eulers equation of motion

(8)(9)(10)(11)Moment of momentum

(12)29

Eulers pump and turbine equationsEulers pump equation.Eulers turbine equation

(13)(14)Defining rothalpyFrom first law

From Eulers pump equation.

(15)The second law of thermodynamics entropy

(16)Definitions of efficiencyEfficiency of turbines

(17)Efficiency of compressors and pumps

(18)

Small stage or polytropic efficiencyCompression process

(19)(20)

Small stage efficiency for a perfect gas

(21)(22)Turbine polytropic efficiency

Reheat factor

(23)(24)(25)(26)Nozzle efficiency

(27)(29)(30)(28)Diffusers

two-dimensionalconicalannularDiffuser performance parameters

Alternative expressions for diffuser performance(32)(36)(31)(34)(33)(35)

(37)Diffuser design calculation

EXAMPLE. Design a conical diffuser to give maximum pressure recovery in a non-dimensional length N/R1 = 4,66 using the data given in Figure 2.17.

Two-dimensional CascadesCHAPTER 3Two-dimensional Cascades

Two-dimensional Cascades

Cascade nomenclature

Cascade nomenclature

Analysis of cascade forces

Analysis of cascade forces

Energy losses

Lift and drag

Lift and drag

Lift and drag coefficients

Lift and drag

Circulation and lift

Efficiency of a compressor cascade

Efficiency of a compressor cascade

Performance of two-dimensional cascades

The cascade wind tunnel

The cascade wind tunnel

COMPRESSOR CASCADE PERFORMANCE

TURBINE CASCADE PERFORMANCE

Reaction: flows accelerated through the blade row and experiences a pressure drop

Impulse: theres no pressure drop on the blade row

COMPRESSOR CASCADE CORRELATIONS

Liebleins correlation (valid only in mid point of working range)

NACA 65-(A10) y British C.4 circular-arc blade

k = 0.0117 NACA 65-(A10) k=0.007 British C.4

Valid for non-stalling subsonic axial compressors

COMPRESSOR CASCADE CORRELATIONSFLUID DEVIATION

Compressor cascades

Compressor inlet guide vaneHowells empirical ruleNominal DesviationMACH NUMBER EFECTS

FAN BLADE DESIGN (MCKENZIE)

Outlet flow deflection

Static pressure rise ideal coeficientStaggler AngleBritish C.5 or C.4 or similar profile must be assumed Maximun efficience lineTURBINE CASCADE CORRELATIONS (AINLEY)Total pressure loss correlationsProfile loss coefficient

Profile loss ratio is assumed only as a function of the incidence ratioStalling incidence is is defined as the incidence when the profile loss ratio is 2

For impulse blades

For nozzle blades

Secondary losses

Z = blade aerodynamic loading coefficient

= Flow acceleration parameterTip clearance losses

k = clearance gap coefficient

FLUID DEVIATION FOR TURBINES

Approximation used in outlet Mach number near unity

0 < Ma < 0.5OPTIMUM SPACE-CHORD RATIO OF TUBINE BLADE

Actual unitary tangencial load

Ideal unitary tangencial loadIncompressible fluid and ignored losses only

Actual load-ideal load ratePrecise only for outlet flow angles between 60-70, actual load-ideal load rate is 0.8BibliographyFluid Mechanics, Thermodynamics of TurbomachineryS.L. Dixon, B.Eng., PH.D.FOURTH EDITION in SI/METRIC UNITS