What Is the Taylor-Couette Flow Instability & Ta Number Calculator?
In 1923, G.I. Taylor solved the stability of viscous flow between rotating cylinders, providing the first exact quantitative match between hydrodynamic stability theory and experiment.
Centrifugal forces drive fluid from the rapidly spinning inner cylinder outward, while viscous shear resists the radial motion.
How Does the Taylor-Couette Flow Instability & Ta Number Calculator Work?
At low speeds, flow is pure azimuthal circular Couette flow with velocity u_theta(r).
Exceeding Tac = 1708 creates alternating pairs of counter-rotating toroidal vortex rings stacked along the cylinder axis.
Taylor-Couette Flow Instability & Ta Number Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
Taylor number for centrifugal instability in narrow concentric annular gaps.
How to Use the Taylor-Couette Flow Instability & Ta Number Calculator
- Input inner and outer cylinder radii, inner rotational speed, and fluid viscosity.
- Review Taylor number, critical speed for vortex onset, and hydrodynamic stability status.
Step-by-Step Example Calculation
Viscometer Concentric Cup Flow
Input Values:
Understanding Your Result
Higher rotational speeds trigger further secondary transitions into wavy vortex flow and turbulent Couette flow.
Factors That Affect the Result
- Narrower annular gap widths d stabilize the flow, requiring significantly higher rotational speeds to trigger vortex onset.
When Should You Use This Calculator?
- Rotational viscometer design, journal bearing oil film stability, and vortex bioreactor engineering.
Assumptions & Limitations
- Applies to narrow gap approximation (d << R1) with stationary outer cylinder.
Frequently Asked Questions
Calculation Accuracy & Reference Note
Classical hydrodynamic stability benchmark derived by G.I. Taylor.