Turbomachinery Lecture 4b Compressor / Engine Maps Radial Turbine

Total Pressure Mass Flow Parameter Defines common flow parameters. Valid for flow with one gas. Corrected flow to standard day [eliminate effect of outside ambient conditions].

Total Pressure Mass Flow Parameter Altitude Altitude Stratosphere >65,000 ft 36,089 ft 36,089 ft 3.202 psia 14.696 psia 59 F Pressure Temperature Std. Ambient Temperature Ambient Pressure B A How to compare performance of engines A & B, each at own ambient conditions? - Use corrected flow variables

Compressor Performance Map

Turbomachine Map Functional behavior of map [mc, Nc, PR] is solely dependent on machine Behavior is applicable to Compressors: axial, centrifugal Turbines: axial, centrifugal Multi-stage machines Choke limit: cannot pass more massflow Sonic flow occurs at minimum area location Surge limit: onset of instability Stall: too low mass flow, flow separates

Example: Compressor Test Assessment

Example: Compressor Test Assessment

Example: Compressor Test Assessment

Example: Compressor Test Assessment Test 1: Baseline Test 2: After modifications

Ex: Compressor Test Assessment 2 1

Flow Coefficient-Compressible

Specific Speed Ns is a non-dimensional combination of so that diameter does not appear.

Specific Speed Ns is non-dimensional when consistant units are used for N, Q & H. Inconsistent units are often used making Ns a garble of funny units. Typical: N RPM Q CFS H "Ft".......Bad! Efficiency Correlated with Specific speed for many different machines…e.g. Pumps and Compressors

Specific Speed U.S. Customary Units: H [ft], Q [gal/min], N [rpm] Europe Customary Units: H [m], Q [m3/s], N [rot/sec – Hz] Conversion ratios

Specific Speed Used to Determine Turbomachine Type

Specific Speed Used to Determine Turbomachine Type Here H (head) is in ft Q (volume flow) is in gallons per minute N (shaft speed) is in RPM Ns is dimensional  (rpm)(gpm)0.5/(ft0.75) Be careful with these strange units Low Ns High Ns

Variation of Efficiency with Ns for Various Pump Sizes Q Low Ns High Ns

Specific Speed - Compressors

Specific Speed - Turbines

Example A pump is designed to deliver 320 gpm of gasolene. The required net head is 23.5 ft. The pump shaft rotates at 1170 rpm. Pick the best type of pump. Centrifugal pump is the most apt choice [see chart 18]

Specific Speed Consider Range of Impellers If We Set: Inducer (Inlet) Diameters Inducer (Inlet) Axial Velocity, Flow Work Coefficient Backsweep (Impeller Exit Angle) RPM Pressure Rise, Inlet P & T Then: Exit Velocity Diagram, Angles & Speeds are Set

Specific Diameter Specific Diameter is another combination of the non-dimensional P’s so that N does not appear:

Specific Speed and Diameter Indicates Flowpath Shape

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

Specific Speed Indicates Flowpath Shape (Cordier Diagram) Ns is in consistent units for this plot Note that axes are switched from previous figure From Wright

Intro to Turbomachinery Analysis

Hydraulic Turbines Low flow, high head: impulse, Pelton turbine Medium flow, medium head: Francis, pump turbine High flow, low head: Kaplan, bulb turbine

Impulse Type

Francis Type

Francis Turbine

Francis Turbine Runner Velocity Triangles for Inward Flow Reaction Turbine

Blade Design Intro - Centrifugal Turbomachines Radial Turbines If no viscosity: flow off blade surface tangent to metal surface

Centrifugal Turbomachines Radial Turbines

Radial Turbine Example T0=1500 R P0=200 psia N=50,000 rpm =90% Cu1=U1, 1=0 Cu2=0 [no swirl] M2=0.25 C is absolute frame velocity vector [Cu, Cr] Cu is tangential or circumferential component

Radial Turbine Example Tip Speed Entrance Velocity Diagram [W is relative frame velocity vector]

Radial Turbine Example

Intro to Turbomachinery Analysis Uses Euler’s Equation Which Works for Axial, Radial, and Mixed Flow Turbomachinery Work done by turning Cu and by change in radius U Temperature Drops Across Turbine Rotor

Radial Turbine Example Temperature Ratio: Tr = 1.0923 = (1500)/(1500-126.8)=TT1/TT2 Rearranging the Turbine Efficiency Equation: Mass Flow: Tt2 abs = 1373.2 R = 1500 - 126.8 Pt2 abs = 141.61 psia = 200/1.4123 M2 abs = .25 = given A2 = 2.7 sq. in. =

Radial Turbine Example FP0 Equation: Power Output:

Radial Turbine Example Exit Velocity Diagram:

Radial Turbine Ex. – Dmean Velocity Triangle Circumferential Direction