Decoupling tests on axial heat-transfer in highly turbulent Taylor-Couette flow using thermal waves

Highlights

• We experimentally study the axial heat-transfer in Taylor-Couette flow.

• The axial heat-transfer and viscous-heating are decoupled using thermal waves.

• The effects of boundary heat-loss on measured Nusselt number are modeled.

• The measured Nusselt number is insensitive to oscillating period of thermal waves.

• The correlations between axial Nusselt number and Taylor number, radius ratio are established.

Abstract

This study experimentally investigates the axial heat transfer of the secondary flow in the cylindrical annular gap around a flywheel within a canned reactor coolant pump, belonging to the Taylor-Couette (TC) flow. A dynamic method based on the transient temperature responses of the TC flow to the input thermal waves, where the axial heat transfer coefficient is determined by the amplitude decay and phase lag of axially propagating temperature waves, is proposed. The influences of viscous heating are distinguished using the mean temperature distribution, allowing for the performance of decoupling tests of axial heat transfer and viscous heating in TC flow. The modification of the boundary heat loss on the axial propagation of temperature waves in a rotor-fluid-stator TC system was modeled. The measured axial heat-transfer coefficient was insensitive to the oscillating periods of the input thermal waves within the maximum permitted period. The axial heat transfer coefficients with different Taylor numbers and radius ratios were measured based on the proposed method. The correlations between the axial heat-transfer coefficient and Taylor number satisfied the scaling law with an effective exponent of 0.5, but they change non-monotonically with respect to the radius ratio in highly turbulent TC flow. This study provides insight into the axial heat transfer characteristics of TC flow.

Introduction

The flow confined in the cylindrical annular gap between the rotor and stator is common in rotating machinery. In a canned reactor coolant pump [1], the annular gap flow around the flywheel is a transition from a high-temperature primary coolant loop to a low-temperature slide-bearing region. Owing to the lack of a net axial flow rate in the cylindrical gap around the flywheel, the heat conducted from the primary loop and the viscous dissipation is axially transported to the slide-bearing region through the secondary flow in the annular gap. Therefore, the study of the axial heat transfer behavior in cylindrical annular gap flow is crucial to preventing slide-bearing overheating.

The flow in a closed annular gap with a rotating inner cylinder and a stationary outer cylinder belongs to the Taylor-Couette (TC) flow. The rotating speed of the inner cylinder is commonly characterized using the Taylor number, $\mathit{Ta}$. Once the $\mathit{Ta}$ exceeds a critical number determined by Taylor [2], the annular flow becomes unstable and forms counter-rotating Taylor vortex pairs. Following an increase in $\mathit{Ta}$, a sequence of flow states appears, that is, unidirectional azimuthal flow transitions to wavy vortex flow, subsequently to modulated wavy vortex flow, and eventually to turbulent Taylor vortex flow (the so-called ultimate flow regime) [3], [4], [5]. Hence, the TC flow exhibits various flow regimes following the enhancement of the rotating effects.

The cylindrical gap width and axial length play an essential role in the transitions of the TC flow. Ostilla-Mónico et al. [6] numerically explored the transition of the TC flow to the ultimate flow regime with various gap widths. They found that the transition is delayed in the wide gap owing to the combined effects of the stabilizing curvature of the inner cylinder and the reduced shear. Cole [7] observed that the transitions of TC flow are considerably delayed owing to the increase in end effects as the axial length of the cylindrical gap decreases. When the ratio of axial length to gap width exceeds 40, the end effects are negligible in the TC flow.

The secondary flow in the TC system mainly consists of large-scale Taylor vortices and small-scale turbulent fluctuations. In the ultimate regime TC flow, the axial size of the Taylor vortex pair is approximately twice the gap width [8], [9]. Moreover, the Taylor vortices are in a residual state [10] whose coherency increases as the gap width decreases [6], [11], [12]. The strength of the large-scale Taylor vortices and small-scale turbulent fluctuations were rescaled to the wind Reynolds numbers ${\mathit{Re}}_w$ and ${\mathit{Re}}_{\lambda }$, respectively, enhanced with rotating effects, exhibiting the scaling laws ${\mathit{Re}}_w\propto {\mathit{Ta}}^{0.5}$ [13], [14] and ${\mathit{Re}}_{\lambda }\propto {\mathit{Ta}}^{0.18}$ [15] with respect to the $\mathit{Ta}$.

Radial convective heat transfer in TC flow has been widely researched [16]. Based on the Reynolds analogy between heat and momentum transfer, Taylor [2] proposed an experimental correlation of the Nusselt (${\mathit{Nu}}_r$) number: ${\mathit{Nu}}_r\propto {\mathit{Ta}}^{1/4}$. The scaling of ${\mathit{Nu}}_r$ measured by Tzeng [17], Viazzo, and Poncet [18] yielded an effective exponent of 1/3, resulting from the high natural convection effects [19], [20]. Following an increase in the gap width, the convective heat-transfer coefficient rapidly decreases because of the thickened boundary layers developed on the rotor and stator [21]. In addition, the effects of radiation from the hot surface [22] and small-scale G$\ddot{\mathrm{o}}$rtle vortices [23] on the radial convective heat transfer were investigated numerically. Current studies on convective heat transfer have mainly focused on the radial advection of heat by Taylor vortices in TC flow.

This study considers the axial heat transfer through the Taylor vortices in a TC flow, which has rarely been studied. Because the intense shear in the TC flow results in the coupling of axial heat transfer and viscous heating, measuring the axial heat-transfer coefficient in highly turbulent TC flow is significantly challenging. A dynamic method is proposed and used in this study to decouple the axial heat transfer of the secondary flow from viscous heating in the TC system.