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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