Turbomachinery Class 12

Turbine Compressor

Compressor Turbine

Radial Inflow Turbines Radial turbines largely used in power system applications Primitive design, easy to fabricate Capable of large per stage shaft work with low mass flow rate Low sensitivity to tip clearance Bulky / heavy

Low Cost Radial Compressor – Ex. 4, p. 83

Low Cost Radial Machines

Low Cost Radial Machines

Low Cost Turbine – Ex. 5 p. 85

Axial vs. Radial Machines Need to determine what type of turbine is most efficient for application - function of Ns for both compressors and turbine

Need to determine what type of turbine is most efficient for application - function of Ns for both compressors and turbine

Radial Inflow [900 IFR] Turbines Kinematic view Thermodynamic view Exit part of rotor (exducer) is curved to remove most of tangential component of velocity Advantage of IFR turbine: efficiency equal to axial turbine, greater amount of work per stage, ease of manufacture, ruggedness

Radial Flow Turbines Radial Inflow Turbine with Scroll or Distributor

Radial Flow Turbines Radial Inflow Turbine Stator/Rotor

Radial Flow Turbines Radial Inflow Turbine Stator/Rotor [No shroud]

Radial Flow Turbines Radial Inflow Turbine Scroll Scroll or distributor - streamwise decreasing cross flow area - provide nearly uniform properties at exit

Radial Flow Turbines

Radial Flow Turbines Scroll Design Principles Mass balance rVr=constant Free vortex rV=constant

Radial Flow Turbines Radial Inflow Turbine Scroll - Stator

Radial Flow Turbines Radial Inflow Turbine Impeller Note - direction of rotation - rotor rearward curvature

Radial Flow Turbine Design Nominal Stator / Rotor Design: Station 1 – Inlet to Stator Station 2 – Exit of Stator, Inlet to Rotor [Radially inward] Station 3 – Exit of Rotor [Absolute velocity is axial] Station 4 - Exit of Diffuser Rotor inlet relative velocity is radially inward - For Zero Incidence at Rotor Inlet, W2=Cr2 and Cq2=U2 Rotor exit absolute flow is axial - For Axial Flow at Rotor Exit, C3=Cx3 and Cq3=0 C2 Cm2=Cr2=W2 U2 Cm3=C3=Cx3 U3 W3  

Radial Flow Turbine Design- 900 IFR For adiabatic irreversible [friction] processes in rotating components From the Alternate Euler Equation: and

Radial Flow Turbine Design substituting: Thus from Alternate Euler’s Equation :

Specific Speed & Diameter Indicates Flowpath Shape

Specific Speed Indicates Flowpath Shape (Cordier Diagram) From Logan Ns is dimensionless From Wright and Balje

Radial Flow Turbine Design Example: Dixon 8.1 The rotor of an IFR turbine, designed to operate at nominal condition, Diameter is 23.76 cm and rotates at 38,140 rev/min. At the design point the absolute flow angle at the rotor entry is 72 deg. The rotor mean exit diameter is ½ the rotor diameter The relative velocity at the rotor exit is twice the relative velocity at the inlet.

Radial Flow Turbine Design Example: Dixon 8.1

Radial Flow Turbine Design Example: Dixon 8.1

Radial Flow Turbine Design Example: Baskharone p. 434-8 0=inlet 1=stator exit 2=rotor inlet 3=rotor exit Stator / nozzle exit Mach number M1=0.999

Radial Flow Turbine Design Example: Baskharone p. 434-8 0=inlet 1=stator exit 2=rotor inlet 3=rotor exit Stator / nozzle exit Mach number M1=0.999

Radial Flow Turbine Design Example: Baskharone p. 434-8 cont’d In constant area interstage duct, apply free-vortex condition to flow from stator exit to rotor inlet

From Centrifugal Compressor Notes Slip: flow does not leave impeller at metal angle [even for inviscid flow] If absolute flow enters impeller with no swirl, =0. If impeller has swirl (wheel speed) , relative to the impeller the flow has an angular velocity -  called the relative eddy [from Helmholtz theorem]. Effect of superimposing relative eddy and through flow at exit is one basis for concept of slip. Relative eddy Relative eddy with throughflow

Radial Flow Turbine Design Static pressure gradient across passage causes streamline to shift flow towards suction surface In reality, the incidence to the rotor varies over the pitch of the rotor as: due to Potential and wake interaction with the vane. Relative eddy effect seen at exit of compressor Effect produces a LE slip factor This variation over the pitch leads to an - optimal incidence and - optimal number of blades where the efficiency of the rotor is a maximum. P=pressure S=suction

Radial Flow Turbine Design Rotor Inlet Velocity Triangle (with incidence): Average relative velocity W and avg. relative incidence 2 If we define an incidence factor, l [like  slip factor in compressors]: C2 W2 CR2=CM2 CU2 U2

Radial Flow Turbine Design From the work of Stanitz regarding slip factors: Note: More Blades,  goes to 1 and inflow becomes radial Then from the rotor inlet velocity triangles, the inlet flow angle to the rotor is:

Radial Flow Turbine Design Criteria for the Optimal Number of Blades: Jamieson model

Radial Flow Turbine Design Criteria for the Optimal Number of Blades: Optimum blade number balances loading & friction Rohlick model uses (quantities at the inlet to rotor): Jamieson model

Radial Flow Turbine Design Other Correlations for Optimal Number of Blades (Rohlick results similar to Jamieson): from Dixon

This is to clarify some of the confusing notation in Dixon regarding blade count Stanitz correlation uses blade number and flow coefficient to calculate the relative radial turbine exit flow angle. Other correlations uses semi-empirical expressions for calculating the optimum [minimum] blade count Z for an optimum efficiency design, where For such a design the exit flow will be radial [in the absolute frame], therefore 2=0 and the correlations are in terms of the corresponding absolute frame air angles [2], e.g.

This is to clarify some of the confusing notation in Dixon regarding blade count Jamieson Rohlik