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Heat Mass Transfer

DOI 10.1007/s00231-015-1570-y

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

W. Qian1 · B. Rosic2 · Q. Zhang3 · B. Khanal4

Received: 7 April 2014 / Accepted: 12 April 2015 © Springer-Verlag Berlin Heidelberg 2015

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.

List of symbols

H Annulus gap height (m) h Average heat transfer coefficient in the inner cylinder surface [W/(m2K)] λ Axial wavelength s Azimuthal wave speed

Tac Critical Taylor number f Fundamental frequency of the azimuthal waves (Hz) d Gap width = R2 − R1(m)

Z Height from the end of the annulus gap (m)

TH Highest temperature (K)

Vin Inlet velocity (m/s) ν Kinematic viscosity (m2/s) keq Local mean equivalent conductivity

TL Lowest temperature (K) m Number of azimuthal waves τ Period time (s) r Radial coordinate (m)

R1 Radius of inner cylinder (m)

R2 Radius of outer cylinder (m)

Abstract In nuclear power plants the primary-loop recirculation (PLR) pump circulates the high temperature/highpressure 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 * Q. Zhang

Qiang.Zhang@city.ac.uk

W. Qian 399300@163.com

B. Rosic budimir.rosic@eng.ox.ac.uk

B. Khanal b.khanal@cranfield.ac.uk 1

University of Michigan-Shanghai Jiao Tong University Joint

Institute, Shanghai Jiao Tong University, Shanghai, China 2

Osney Thermo-Fluids Laboratory, Department of Engineering Science, University of Oxford, Oxford, UK 3

Department of Mechanical Engineering and Aeronautics,

School of Mathematics, Computer Science & Engineering (MCSE), City University London, London, UK 4

Cranfield University, Shrivenham SN6 8LA, UK

Heat Mass Transfer 1 3 η Radius ratio = R1/R2 Ω1 Rotating speed of the inner cylinder (rad/s) Ω2 Rotating speed of the outer cylinder (rad/s)

Re Reynolds number

Ta Taylor number which is defined as ΩdR1 ν k Thermal conductivity

Vz Z-direction velocity (m/s) 1 Introduction 1.1 Taylor–Couette flow phenomena

Different forms of Taylor–Couette flow instabilities that can develop within the narrow gap of two concentric rotating cylinders, have been extensively investigated by many researchers. At low Reynolds numbers (Re) the laminar

Couette flow regime is established [1]. As the rotational speed of cylinders increases a family of different flow instabilities, Taylor–Couette flows is developed [2].

Andereck et al. [3] presented a detailed map showing different types of Taylor vortices that can form under different rotating speed of cylinders. The critical angular velocity (or Taylor number) for the onset of Taylor vortices is strongly dependent upon the cylindrical gap radius ratio (η). By applying linear stability theory, Sparow et al. [4] and Roberts [5] showed that the critical Taylor number would increase with smaller radius ratio (wider gap).

The experimental work of Cognet [6] also confirmed these trend. Burkhalter and Koschmieder [7] found that the perturbation caused by the imperfection in their experiment did not have any effect on the stability of the toroidal vortices as long as Taylor vortices were present.

With the further increase in rotational speed, wavy Taylor–Couette flow is established, characterized by wavy vortices azimuthally travelling around the annular gap and fluctuating along the axis direction. The rotational speed for forming wavy Taylor vortices is approximately 20 % higher than the critical value for onset of Taylor vortices. Kingt [8] reported that the wave speed is strongly linked to the radius ratio of the two cylinders, and is not significantly affected by Taylor number. With even higher rotational speed, wavy

Taylor–Couette flow becomes chaotic and finally becomes fully turbulent.

Adding axial flow to the Taylor–Couette flows results in formation of another flow family—Taylore–Couette–Poiseuille flows. These flow stabilities caused by superposition of rotational and axial flows were experimentally demonstrated by Wereley and Lueptow [9]. The experimental investigation by Becker and Kaye [10] showed that addition of axial flow delays the transition process that leads to formation of Taylor vortices. The study of Martin and

Hasoon [11] indicates the same gap radius ratio η effect on critical Taylor number as in the cases without axial flow. 1.2 PLR pump application

In boiling water nuclear reactor 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-casing gap where the Taylor flow instabilities develop. Due to the temperature difference between the hot recirculating water and the cold purge water (in the order of two hundred degrees Celsius), the temperature fluctuations could potentially lead to shaft or casing thermal fatigue cracks. Figure 1 shows a schematic of a PLR pump shaft detail given by Narabayashi et al. [12]. The purge coolant water enters the gap from the top of the shaft and eventually mixes with the hot water in the casing impeller cavity. This important engineering problem was originally experimentally investigated by Narabayashi et al. [12] and