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Related Experiment Video

Updated: May 14, 2026

A Modeling and Simulation Method for Preliminary Design of an Electro-Variable Displacement Pump
09:04

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Published on: June 1, 2022

3D Simulation Study for a Pneumatic Nozzle-Cylindrical Flapper System.

Peimin Xu1, Kazuaki Inaba1, Toshiharu Kagawa2

  • 1Department of Transdisciplinary Science and Engineering, Institute of Science Tokyo, Tokyo 152-8550, Japan.

Sensors (Basel, Switzerland)
|May 13, 2026
PubMed
Summary

This study clarifies the complex 3D flow in pneumatic nozzle-cylindrical flappers used for high-speed rotating body displacement measurement. Findings reveal curvature

Keywords:
high-speed rotation spindle with aerostatic bearingsmachiningnozzle flapperpneumatic

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Area of Science:

  • Fluid dynamics
  • Mechanical engineering
  • Semiconductor manufacturing

Background:

  • Air spindles with compensation systems are crucial for efficient semiconductor machining.
  • Pneumatic nozzle-cylindrical flappers offer high precision for measuring high-speed rotating bodies.
  • Existing models fail to capture the complex 3D flow in nozzle-cylindrical flappers, limiting their application.

Purpose of the Study:

  • To elucidate the flow mechanisms within nozzle-cylindrical flapper systems.
  • To develop a predictive framework for the static characteristics of these systems.
  • To address the limitations of conventional models in describing the unique flow behavior.

Main Methods:

  • Development of a computational fluid dynamics (CFD) model to simulate gas flow in micron-scale clearances.
  • Analysis of flow behavior under varying gap sizes and angular orientations.
  • Validation of CFD results against experimental measurements.

Main Results:

  • Flow behavior is dominated by surface curvature, enhancing inertia and weakening viscous effects.
  • Strong recirculation occurs due to flow wrapping around the cylindrical surface.
  • Two-dimensional approaches cannot accurately represent these complex 3D flow phenomena.

Conclusions:

  • The study establishes a reliable framework for predicting static characteristics of nozzle-cylindrical flappers.
  • A quadratic relationship between mass flow rate and momentum compensation coefficients was identified, linked to recirculation.
  • Findings support prior assumptions and reduce the need for extensive experimental calibration.