Helical groove seal is designed in reactor coolant pump to control the leakage along the front surface of the impeller face due to its higher resistance than the circumferentially grooved seal. The flow and the friction factors in helical groove seals are predicted by employing a commercial CFD code, FLUENT. The friction factors of the helical groove seals with helix angles varying from 20 deg to 50 deg, at a range of rotational speed and axial Reynolds number, were, respectively, calculated. For the helically grooved stator with the helix angle greater than 20 deg, the leakage shows an upward trend with the helix angle. The circumferentially grooved stator has a lower resistance to leakage than the 20 deg and 30 deg stators. It can be predicated that, for a bigger helix angle, the friction factor increases slightly with an increase in high axial Reynolds number, which arises from the high-pressure operation condition, and the friction factor is generally sensitive to changes in the helix angle in this operation condition. The study lays the theoretical foundation for liquid seal design of reactor coolant pump and future experimental study to account for the high-pressure condition affecting the leakage characteristic.
Recently, it has been recognized that the leakage flow of highly effective seal is the key point of nuclear plant safety. Leakage flow characteristics of the seal in the nuclear equipment were investigated by several researchers.
In high temperature gas-cooled reactor (HTGR) core, the prevention of leakage flows of coolant gas is important for a thermal hydraulic design; the seal mechanism for the core was researched by Kaburaki and Takizuka [
The improvements in the leakage along the front surface of the impeller face are the key point of reactor coolant pump (RCP) reliability. Leakage control in the clearance is the most important problem to be solved, which can increase the reliability and efficiency of RCP and, thus, assure the satisfactory operation. If the leakage is out of control, the leakage flow will disturb the main flow at the inlet of the impeller, and then the circulation area will decrease. It will lead to a decrease of the hydraulic efficiency of RCP. Once the pump operates on a low head due to the larger leakage, there will be a serious danger of water coolant undersupply, which leads to excess reactor core temperature.
To gain a better leakage control, circumferentially grooved seal is commonly used in the pump. But its performance in the high-pressure condition is unsatisfied. To fit in the extreme condition, helical groove seal is designed in reactor coolant pump to obtain a higher resistance to leakage than the circumferentially grooved seal. High rotational speed yields backflow along the groove-forward inlet and reduction in the average axial and circumferential fluid velocity. Beyond that, the helically grooved stator application is to remove any impurities through the groove path.
However, helically grooved seals have not been investigated thoroughly because of their complex characteristics. Bootsma [
Kim and Childs [
Some studies were presented to determine the leakage characteristics of helical groove seals, which were just operated in the low-pressure condition. Kanki and Kawakami [
Gowda and Prabhu [
Before this paper, the leakage characteristic of the helical groove seal in the pressure higher than 17 MPa condition has not been researched. To fit in the extreme condition, helical groove seal is designed to control the leakage in reactor coolant pump. To obtain helical groove seal with high-resistance, this paper is initiated to predict a high friction factor for a proper choice of the helix angle
A three-dimensional CFD model is used in this study to calculate the steady incompressible flow within the seal. Water is employed as the sealing medium, and the temperature is treated as a constant value. The leakage characteristics are determined by employing the standard
The turbulence kinetic energy,
A second order discretization scheme is used for the pressure, density, and momentum terms. First-order upwind scheme is used for turbulent dissipation rate terms. Resolving boundary layers, standard wall function is used to model the viscous effects in the near-wall regions. The convergence criterion for continuity, velocity,
A typical helically grooved stator annular seal is illustrated in Figure
Helically grooved stator.
The helix angle
The five seal configurations were computed to evaluate the influence of helix angle
Groove dimension.
Groove cross section (not scaled)
Helix angle
The 3D mesh applying the structured hexagonal cells for the land and groove is created using the commercial mesh generator Gambit. The 2D view for the inlet section of the helical groove seal mesh is defined as shown in Figure
2D view for the inlet section mesh.
Mesh density study.
Starting with the one node away from the wall, the mesh points are redistributed as the double-sided ratio 1.15 in the radial direction and 1.2 in the circumferential direction of the groove width. The near-wall mesh points are disturbed so as to maintain a smaller value
Law-of-the-wall formulations model the sharp pressure gradients near the wall and are used with standard
Consider that
The laws of the wall for mean velocity and pressure are based on the wall unit,
Two faces are located about the midplane of the seal at 0.23 and 0.5 of the seal length. The pressure differential is defined as the pressure computed upstream and immediately inside the seal. The axial pressure gradient is defined by the two average pressure faces at 0.23
The friction factor definition reference of Childs et al. [
Friction factor for five helix angles.
0 deg
20 deg
30 deg
40 deg
50 deg
There are comparable representative resistance characteristics among the five models. As can be observed from Figure
As can be observed from Figure
Friction factor for helically grooved stators at 1750 rpm versus Re.
Figure
Friction factor for helically grooved stators at 4000 rpm versus Re.
Figure
Pressure contour of circumferential grooved stator.
Pressure contour of 20 deg stator.
Pressure contour of 0.2
20 deg
30 deg
40 deg
50 deg
Contours of turbulent kinetic energy of 0.2
20 deg
30 deg
40 deg
50 deg
The turbulent kinetic energy value is related to the energy dissipation. It is seen that the turbulent kinetic energy of 20 deg stator is higher than any other stator, and the highly turbulent kinetic energy region existing on the left of the groove is the largest, which is in favour of energy dissipation. The highly turbulent kinetic energy region shrinks in area and moves to leeward as the helix angle increases. The highly turbulent kinetic energy region of the 50 deg stator is the smallest, and the peak value is the lowest. It is speculated that the difference in friction factor among helically grooved stators is related to the relative location of the highly turbulent kinetic energy region in the groove and the turbulent kinetic energy value range.
The friction factor shows an upward trend with the helix angle reduction, because the seal with a smaller helix angle has less axial component flow and longer groove in favour of energy dissipation. Helically grooved stators with helix angles greater than 20 deg leak increasingly more as the helix angle increases. The circumferentially grooved stator has a lower resistance to leakage than the 20 deg and 30 deg stators, thereby helical groove seal is designed better than the circumferentially grooved seal in reactor coolant pump. For all helically grooved stators, the friction factor generally increases with increasing the running speed. The friction factor is more sensitive to the rotational speed especially for the smaller helix angle stator. The friction factor generally decreases with axial Reynolds number. At Re lower than 160000, the friction factor drops monotonically with axial Reynolds number. At high Re, for At 1750 rpm, 20 deg stator has much higher resistance to leakage than the circumferentially grooved stator; therefore, in reactor coolant pump, the helically-grooved stator with significantly higher power consumption can be used as the axial seal to control backflow leakage along the front surface of the impeller face and reduce the leakage flow rate, while keeping the clearance comparable to that of a plain seal. Because a helical groove yields a backflow along the groove forward inlet, the other object of the application is to remove impurities through the groove path.
Besides, numerical studies are conducted to determine the basic characteristics of the helically grooved stator in high-pressure condition. The conclusions will be summarized for effective application in helical groove seals of RCP and contribute future experimental studies on this type of seal.
Axial Reynolds number
Helix angle (deg)
Friction factor
Static pressure (Pa)
Seal length (m)
Axial seal coordinate (m)
Hydraulic diameter (m)
Density (
Average axial velocity (m/s)
Dynamic viscosity (Pa·s)
Turbulent kinetic energy (
Turbulent dissipation rate (
Turbulent viscosity constant
Von Kármán constant
Empirical constant
Mean velocity of the fluid at the near-wall node
Turbulence kinetic energy at the near-wall node
Distance from point
Generation of turbulence kinetic energy due to the mean velocity gradients
Generation of turbulence kinetic energy due to buoyancy
Contribution of the fluctuating dilatation in compressible turbulence to the overall dissipation rate
Model constants for
Turbulent Prandtl number for
Turbulent Prandtl number for
User-defined source term for
User-defined source term for
The authors appreciate the financial support from the National Basic Research Program of China (973 Program).