# Influence of fluid temperature gradient on the flow within the shaft gap of a PLR pump

## Abstract

In nuclear power plants the primary-loop recirculation (PLR) pump circulates the high temperature/high-pressure coolant in order to remove the thermal energy generated within the reactor. The pump is sealed using the cold purge flow in the shaft seal gap between the rotating shaft and stationary casing, where different forms of Taylor–Couette flow instabilities develop. Due to the temperature difference between the hot recirculating water and the cold purge water (of order of 200 °C), the flow instabilities in the gap cause temperature fluctuations, which can lead to shaft or casing thermal fatigue cracks. The present work numerically investigated the influence of temperature difference and rotating speed on the structure and dynamics of the Taylor–Couette flow instabilities. The CFD solver used in this study was extensively validated against the experimental data published in the open literature. Influence of temperature difference on the fluid dynamics of Taylor vortices was investigated in this study. With large temperature difference, the structure of the Taylor vortices is greatly stretched at the interface region between the annulus gap and the lower recirculating cavity. Higher temperature difference and rotating speed induce lower fluctuating frequency and smaller circumferential wave number of Taylor vortices. However, the azimuthal wave speed remains unchanged with all the cases tested. The predicted axial location of the maximum temperature fluctuation on the shaft is in a good agreement with the experimental data, identifying the region potentially affected by the thermal fatigue. The physical understandings of such flow instabilities presented in this paper would be useful for future PLR pump design optimization.

## Keywords

Couette Flow Thermal Fatigue Axial Flow Radius Ratio Taylor Number## List of symbols

*H*Annulus gap height (m)

*h*Average heat transfer coefficient in the inner cylinder surface [W/(m

^{2}K)]*λ*Axial wavelength

*s*Azimuthal wave speed

*Ta*_{c}Critical Taylor number

*f*Fundamental frequency of the azimuthal waves (Hz)

*d*Gap width = R

_{2}− R_{1}(m)*Z*Height from the end of the annulus gap (m)

*T*_{H}Highest temperature (K)

*V*_{in}Inlet velocity (m/s)

*ν*Kinematic viscosity (m

^{2}/s)*k*_{eq}Local mean equivalent conductivity

*T*_{L}Lowest temperature (K)

*m*Number of azimuthal waves

*τ*Period time (s)

*r*Radial coordinate (m)

*R*_{1}Radius of inner cylinder (m)

*R*_{2}Radius of outer cylinder (m)

*η*Radius ratio = R

_{1}/R_{2}*Ω*_{1}Rotating speed of the inner cylinder (rad/s)

*Ω*_{2}Rotating speed of the outer cylinder (rad/s)

*Re*Reynolds number

*Ta*Taylor number which is defined as \(\frac{{\varOmega dR_{1} }}{\nu }\)

*k*Thermal conductivity

*V*_{z}Z-direction velocity (m/s)

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