Three coordinates testing for centrifugal impeller

When discussing "three coordinates" for testing a centrifugal impeller, it typically refers to the different frames of reference or measurement systems used to analyze its performance, design geometry, and flow physics.

Here are the three primary coordinate systems used:

1. Cartesian Coordinates (X, Y, Z)

• Purpose: Design, Manufacturing, and Static Measurement.

• Description: The absolute, stationary reference frame. This is the language of CAD models, CNC machines, and coordinate measuring machines (CMM).

• Use in Testing:

  • Dimensional Verification: Measuring the exact blade profile, hub and shroud contours, leading and trailing edge positions.

  • Vibration Analysis: Measuring casing vibrations in X, Y, Z directions during testing.

  • Computational Fluid Dynamics (CFD) Setup: The computational domain (inlet, volute, etc.) is defined in Cartesian coordinates.

• Testing Context: "The CMM probe recorded the blade surface at 500 points defined in (X, Y, Z) to compare against the CAD nominal geometry."

2. Cylindrical Coordinates (R, θ, Z)

• Purpose: Flow Analysis and Performance Evaluation.

• Description: A rotating frame aligned with the impeller axis. R is the radius from the centerline, θ is the circumferential angle, and Z is the axial position. This is the most natural system for describing flow into and out of the impeller.

• Use in Testing:

  • Performance Mapping: Measuring total pressure, static pressure, and temperature at stations (e.g., at Impeller Inlet (R₁, Z) and Impeller Outlet (R₂, Z)).

  • Flow Angle Measurement: At the exit, the critical flow angle β is measured relative to the radial (R) direction.

  • Traverse Measurements: A radial traverse with a probe at the impeller exit collects data as a function of R.

  • Laser Doppler Velocimetry (LDV) or Particle Image Velocimetry (PIV): Data is often presented in cylindrical coordinates to show tangential (U_θ) and radial (U_r) velocity components.

• Testing Context: "The five-hole probe performed a radial traverse at the impeller exit (θ=0°, Z=mid-passage) to map the distribution of total pressure from hub to shroud as a function of radius R."

3. Relative (or Rotating) Blade Coordinates (Streamwise, Spanwise, Pitchwise)

• Purpose: Detailed Aerodynamic and Stress Analysis.

• Description: A curvilinear, non-orthogonal system fixed to the rotating blade itself. It follows the blade passage.

  • Streamwise (m): Along the mean flow direction from leading edge (LE) to trailing edge (TE).

  • Spanwise (s): Along the blade from hub to shroud (stacking axis).

  • Pitchwise (p): Perpendicular to the streamwise direction, from pressure side (PS) to suction side (SS) of the blade.

• Use in Testing:

  • Blade Loading: Measuring or calculating the pressure distribution (Cp) on the PS and SS along the streamwise direction.

  • Secondary Flow Visualization: Identifying vortices (e.g., tip leakage vortex, passage vortex) that move in the pitchwise-spanwise plane.

  • Structural Vibration Mode Shapes: Describing blade flutter modes (e.g., 1st bending in the streamwise direction).

  • High-End CFD Post-Processing: To analyze losses and flow detachment within the blade passage.

• Testing Context: "The pressure taps along the mid-span streamwise coordinate revealed a strong adverse pressure gradient on the suction side near the trailing edge."

How They Work Together in a Testing Program

A comprehensive impeller test integrates data from all three coordinate frames:

1. Manufacturing & Setup: The impeller is manufactured and inspected using Cartesian (X,Y,Z) coordinates.

2. Performance Test: The impeller is run on a test rig. Global parameters (flow rate, pressure ratio, efficiency) are recorded. Detailed flow field measurements at inlet and exit planes are taken and analyzed in Cylindrical (R, θ, Z) coordinates.

3. Internal Flow Diagnostics: Advanced techniques like PIV or blade-mounted pressure transducers provide data that is best understood in the Relative Blade Coordinates (m, s, p) to diagnose flow separation, shocks (in compressors), or secondary flows.

4. Correlation & Validation: All experimental data, tagged to its respective coordinate system, is used to validate 3D CFD simulations, which themselves compute solutions in a mesh that can be output in any of these coordinate systems.

Summary Table

In essence, moving from Cartesian → Cylindrical → Relative Coordinates represents a shift in perspective from the mechanic's bench, to the performance test engineer's station, and finally to the aerodynamicist's detailed flow analysis.