 Research
 Open access
 Published:
CFD analysis in effects of spacervane on thermal–hydraulic performance of twophase flow in annular channel
Journal of Engineering and Applied Science volume 71, Article number: 127 (2024)
Abstract
Spacer performs a key function in the construction of nuclear rod assembly. It is utilized to ensure the appropriate spacing and firmness of the rods in assembly. In rod bundle structures, spacers are typically incorporated with vanes to promote turbulence and improve heat transfer. The aim of this work is to analyze the impacts of spacervane on the thermal–hydraulic performance of twophase flow in an annular channel. CFD model of an upward flow annular channel with spacervane has been developed. In addition, an annular channel model with a spacer but without vane has been generated and modeled in order to examine the impact of the spacervane in a twophase flow. Transient simulations were performed with flow considerations of mass flux 714.4 kg/m^{2}s, liquid temperature 330 K, volume fraction 0.35, heat flux 197.2 kW/m^{2}, and atmospheric pressure conditions. CFD results have been validated with experimental data. Results show that the core zone of the annulus gap exhibits the highest level of turbulent intensity, and the outer pipe wall temperature is lower for spacervane relative to spacer alone. It is observed that the majority of water vapor is concentrated at the center of the channel in the farthest downstream location.
Introduction
Numerous systems that rely on the phenomenon of twophase flow are prevalent across various industrial sectors, including chemical, petrochemical, and nuclear engineering. Rod bundles, annular channels, and pipes are frequently employed as flow domains in these industrial sectors. In reactor rod bundles, the phenomenon of twophase flow is extremely complicated due to intricate flow patterns, interface distortion, relative motion between fluids, and strong secondary flow. The precise forecast of thermal–hydraulic characteristics in a twophase flow within reactor fuel channels relies on a thorough analysis of several factors. These factors include the impacts of grid spacer vanes on the mechanisms of phase interactions (specifically the interfacial area concentration analysis), flow phenomena, and the distribution of flow characteristics for the twophase fluids (including the analysis for distributions of velocity, volume fraction, and bubble size). Therefore, the examination of thermal–hydraulic performance in twophase flow plays an essential part in the effective design of rod bundles equipped with grid spacervane and in the safe functioning of the reactor core.
Many researchers have used numerical and experimental methods to predict twophase thermal–hydraulic performance in nuclear rod applications. Serizawa et al. [1] investigated experimentally the turbulent phenomena of water–air bubbly flow in a vertical pipe. A tracer technique with a concentration of helium gas was used for the analysis of heat and transport of bubbles in twophase flow. Numerical and experimental analyses of the flow behavior of subcooled boiling in vertical annulus were conducted by Lee et al. [2]. Water and vapor were considered as fluid of twophase flow, and analyses were performed for different mass fluxes range 476–1061 kg/m^{2}s. Ustinenko et al. [3] developed the methodology using CFD (computational fluid dynamics) to validate the various experimental work performed in twophase flow by past researchers. Thermal–hydraulic performance was analyzed with constant heat flux in annular channels and pipes.
Ala et al. [4] studied the impacts of partial and complete blockage of the flow passage of the subchannels in nuclear fuel rod bundle for twophase fluid flow. The authors investigated the blockage effects on void fraction, turbulent intensity, pressure drop, and velocity distributions inside the subchannels at different locations downstream. Chalgeri and Jeong [5] studied the flow regimes transition of twophase fluid flow in rectangular channels with narrow gaps. Air and water were employed as twophase fluids inside the domain. They proposed a model for transition criteria and showed good agreement against measurement data. Sadatomi et al. [6, 7] performed experiments on rod bundles having triangular and square arrays for twophase (air–water) flow. The fluctuation in differences in static pressure between the subchannels of the rod bundle was measured. Turbulent mixing rates were compared for the different arrays used in the experiments and concluded that array configurations of subchannels play an important part in examining the turbulent mixing rate.
Kawahara et al. [8,9,10] conducted experiments on the rectangularshaped subchannels for twophase fluid flow. Water and air flow characteristics visualization was accomplished with the help of acrylic glass. Authors reported that large bubbles have a significant effect on turbulent mixing rate as compared to that of small bubbles, and also, they developed a model for slug flow to predict the effect on turbulent mixing rate.
Dhurandhar et al. [11] presented a thorough review of mixing vane impacts on thermal–hydraulic characteristics for different channel geometries. A detailed review was provided by considering supercritical fluids (as single phase) and different twophase fluids. Dhurandhar et al. [12,13,14,15] performed computer simulations to examine the impacts of spacers and vanes on thermal–hydraulic characteristics of various fluids in a vertical flow annular channel and concluded that spacers and the vanes are significant channel structures for improving heat transfer.
Arai et al. [16] executed an experimental analysis of void fraction in a boiling water reactor for nonheated provisions of the rods. Pressure drop and density distributions along the bundle length were disused. Williams et al. [17] examined twophase flow patterns experimentally. Bubbly, annular, and slug flow were analyzed at constant pressure in a vertical flow rod bundle. Ren et al. [18] studied the impact of grid spacer and mixing vane on the phase distribution within rod bundle assembly. Air and water were employed as twophase fluids. Also, experimental results explained the void fraction distributions in the subchannels.
Drucker et al. [19] explained the heat transfer mechanism in twophase fluid flow in a tube and fuel rod assembly. Analyses of heat transfer were performed for different ranges of Reynolds numbers. Air and water were employed as twophase fluids inside the domain, and void fraction distributions were discussed in detail. Li et al. [20] conducted experiments to analyze the heat transfer performance of twophase fluid flow in a vertical rod bundle assembly. They found that for their test conditions, increasing the system pressure or mass flux will reduce the wall surface superheating degree. Mixing vane effects were studied numerically on the fuel rod assembly for twophase fluid flow by Xiao et al. [21]. CFD results validation against experimental data was performed. They analyzed the flow and thermal characteristics within the subchannels of the rod bundle. The authors found that the crossflow plays an important role in the accumulation of vapor on the fuel rod in the domain.
Yang et al. [22] investigated the impacts of spacer grids, including plastic protrusions, on air–water (twophase) flow within assembly of an 8 × 8 array. The downstream turbulence behavior is stronger, and the lowpressure zone is visible behind the grid spacer. Tian et al. [23] conducted tests to measure the pressure drop within rod bundle assembly for a twophase (air–water) flow. They discussed the turbulent intensity and velocity distributions in the domain. Also, they developed a correlation for a twophase friction multiplier and tested it successfully.
Hosokawa et al. [24] examined flow behaviors of two phases like liquid velocity, void fraction, and bubble velocity in rod bundle subchannels. The work was done on a lattice with a square shape assembly of 4 × 4 array having 10mm rod diameter, 9.1mm hydraulic diameter, and 1.25 pitchtorod diameter ratio, and the authors reported that the acting lift force across bubbles in rod bundle subchannels affects void fraction distributions significantly. Inoue et al. [25] experimentally analyzed the distributions of void fraction within rod bundle. Measurements were performed for normal operating conditions of boiling water reactor rod bundles. An Xray CT scanner was used to measure the void fractions in the domain.
Based on the aforementioned study of literature, it is inferred that the inclusion of a spacer or grid spacer with vanes has a positive impact on the rate of turbulence mixing and heat transfer improvement. This effect is particularly notable at the spacer location and in the downstream zone of the spacer. Despite the existence of several studies on spacer analysis, the precise forecast of thermal–hydraulic characteristics using computational analysis remains an ongoing area of research for twophase. This is mainly significant for the design of spacers with varying vane shapes. Moreover, the detailed comparative analysis for the impacts of spacervane and spacer alone on thermal–hydraulic performance of twophase flow in annular channel has received little attention in the literature. Most investigations have been conducted in adiabatic flow conditions. This study presents a novel approach to predicting the thermal–hydraulic performance of twophase annulus flow with a spacervane. The present study examines the impacts of spacervane on thermal–hydraulic performance of twophase flow in annular channels using computational CFD analysis. The Eulerian model was employed to solve the twophase fluid flow within a threedimensional annular channel model. The SST k\(\omega\) mixture turbulence model was utilized for twophase turbulent flow simulations. Simulations were achieved in ANSYS Fluent for the flow considerations of mass flux 714.4 kg/m^{2}s, liquid temperature 330 K, volume fraction 0.35, heat flux 197.2 kW/m^{2}, and atmospheric pressure condition. A detailed investigation was conducted to examine the impacts of spacervane on thermal–hydraulic performance of twophase annulus flow.
Numerical modeling approach
Mathematical equations
The ANSYS Fluent multiphase Eulerian model was used to solve twophase fluid flow in threedimensional models of annular channels. Water (liquid) and water vapor were considered as primary and secondary phases, respectively. The governing equations [26] were solved for the twophase fluid flow during the simulations, which are given as follows:
Continuity equation of phase q
where \({\overrightarrow{V}}_{q}\) = velocity of \({q}^{th}\) phase
\({\dot{m}}_{pq}\) = mass transfer from \(p^{th}\;to\;q^{th}\) phase
\({\dot{m}}_{qp}\) = mass transfer from \(q^{th\;}to\;p^{th}\) phase
\({\alpha }_{q}\) = volume fraction of \({q}^{th}\) phase
\({S}_{q}\) = source term
Momentum equation of phase q
where \({\overline{\tau }}_{q}\) = stress–strain tensor of \({q}^{th}\) phase
where \({\mu }_{q}\) = shear viscosity of phase q
\({\lambda }_{q}\) = bulk viscosity of phase q
Energy equation of phase q
where \({h}_{q}\) = specific enthalpy of \({q}^{th}\) phase
\({\overrightarrow{q}}_{q}\) = heat flux
\({Q}_{pq}\) = heat exchange intensity between \(p^{th}\;and\;q^{th}\) phases
\({h}_{pq}\) = interphase enthalpy
Turbulence model
The equations of SST k\(\omega\) mixture turbulence model [26] are given as follows:
where mixture density, \({\rho }_{m}= \sum_{i=1}^{N}{\alpha }_{i}{\rho }_{i}\)
Mixture molecular viscosity, \({\mu }_{m}= \sum_{i=1}^{N}{\alpha }_{i}{\mu }_{i}\)
Mixture velocity, \({\overrightarrow{V}}_{m}=\frac{\sum_{i=1}^{N}{\alpha }_{i}{\rho }_{i{\overrightarrow{V}}_{i}}}{\sum_{i=1}^{N}{\alpha }_{i}{\rho }_{i}}\)
Mixture turbulent viscosity, \(\mu_{t,m}=\rho_mC_\mu\frac k\omega,\;where\;C_\mu=0.024\;(constant)\)
The production of turbulence kinetic energy; \({G}_{k,m}\)
Interfacial forces modeling
Drag force
The interphase momentum transfer between two phases due to the drag force can be obtained via the drag model of Schiller and Naumann model [27]. The drag function \(\text{f}\) is given as follows:
where coefficient of drag \({(C}_{D})\) is given as follows:
The relative Reynolds number for primary phase q and secondary phase p is obtained as follows:
where \({d}_{p}\) is the bubble diameter of phase p.
Lift force
The lift force acting on a secondary phase p in a primary phase q can be calculated as follows:
where \({\rho }_{q}=\) primary phase density
\({\alpha }_{p}=\) secondary phase volume fraction
\({\overrightarrow V}_q\;and\;{\overrightarrow V}_p=\) velocity of primary and secondary phase respectively
\({C}_{l}=\) lift coefficient
Tomiyama lift force model [28] has been used in the simulations to solve the lift coefficient \({(C}_{l})\), which is given as follows:
where
\({Eo}{\prime}\) is a modified Eotvos number based on the long axis of the deformable bubble, \({d}_{h}\)
where \(\sigma =\) surface tension
g = gravity
\({d}_{p}=\) bubble diameter
Wall lubrication force
Wall lubrication force proposed by Antal et al. [29] is given as follows:
where \(\left{\overrightarrow{V}}_{q}{\overrightarrow{V}}_{p}\right=\) relative velocity between phases
\({\overrightarrow{n}}_{w}\) = unit normal from wall
\({C}_{wl}=\) wall lubrication coefficient
Wall lubrication coefficient \({(C}_{wl})\) proposed by Antal et al. [29] is given as follows:
where \({C}_{w1}=0.01\) and \({C}_{w2}=0.05\) are dimensionless coefficients.
\({y}_{w}=\) nearest wall distance
Turbulent dispersion force
The turbulenceinduced dispersion force proposed by Lopez de Bertodano model [30] is given as follows:
where \({k}_{q}=\) primary phase turbulent kinetic energy
\(\nabla {\alpha }_{p}=\) secondary phase volume fraction gradient
\({C}_{TD}=1\), turbulent dispersion constant
Virtual mass force:
The equation for virtual or added mass force [26] is given as follows:
where \(\frac{{d}_{q}}{dt}=\) time derivative of phase material
Geometry development and boundary details
CFD model of an upward flow annular channel with spacervane has been developed. Additionally, an annular channel model with a spacer but without vane has been generated and modeled to study the impacts of spacervane in a twophase flow. Figure 1 a, b, c, and d shows the geometry details of a threedimensional annular channel with spacervane. The blockage ratio of spacer located at the center of the annular channel is assumed to be 0.4. Vanes have been positioned on the spacer tip in the flow direction, and the vane dimensions are shown in Fig. 2. The vane angle is taken as 7° with the flow direction. Table 1 represents the dimensions of simulation geometry.
In the present work, an Eulerian model was used for twophase fluid (water and water vapor mixture) formulation. Transient simulations were performed with time step size of 0.005 s and total number of time steps of 600. Temperature, hydraulic diameter, volume fraction, mass flux, and turbulent intensity were applied at the domain inlet. The saturation temperature of water has been set as 373.15 K at atmospheric pressure. Constant pressure was employed at the domain outlet. Adiabatic and constant heat flux criteria were employed on the inner and outer pipes, respectively. Smooth wall with noslip criteria was employed on the walls for momentum equation. Table 2 provides the details of boundary condition.
Mesh model and mesh independence
Mesh independence analysis was executed employing three distinct mesh models. Meshes 1, 2, and 3 possess element counts of 1.9, 1.6, and 1.3 million, respectively. The unstructured tetrahedron mesh models were generated employing ICEM CFD. Mesh was generated by specifying the size of global element with a fixed scaling factor. Mesh refinement was accomplished by retaining distinct sizes of elements on the vane, spacer, and innerouter pipe surfaces. In order to effectively represent the heat transfer phenomenon, prismatic layers of elements were built close to pipe walls. The initial layer’s height on the pipe surface was kept low enough; thus, y + is smaller than 1. An expansion ratio of 1.2 was employed among layers. Figure 3 represents a mesh model for the geometry used in the present analysis. Figures 3 a and b represents the surface and volume mesh over the inner pipe with spacervane and at the annulus gap, respectively.
Mesh independence analysis was executed in an annular channel with spacervane. The dimensions of the annular channel and flow parameters for mesh independence analysis are given in Tables 1 and 2, respectively. Eulerian model was used to solve the twophase fluid (water and water vapor) flow. The simulation was accomplished using SST kω mixture turbulence model. The tangential velocity distributions of liquid in radial coordinates for three mesh models are displayed in Fig. 4. The tangential velocities were taken at 460 mm from channel inlet, which is over 40 times of the hydraulic diameter to avoid entrance effect [31]. Hydraulic diameter of the annular channel is 6 mm. Based on the comparison made for the tangential velocity distributions (Fig. 4), mesh 2 was adopted for further numerical analysis as the variation of tangential velocities is less than 0.3% compared to the other two mesh models, i.e., meshes 1 and 3 (it is per the authors consideration). Table 3 shows the numerical percentage deviation of meshes 1 and 3 with respect to mesh 2.
Methods
The multiphase Eulerian model was applied to solve twophase (water — primary phase and vapor — secondary phase) fluid flow in a threedimensional model of annular channel. The time step size was taken as 0.005 s for the present transient simulations. The phasecoupled SIMPLE algorithm was employed to couple the velocity and pressure. The finite volume method is the basis of this algorithm. The value of the residuals was specified as \({10}^{6}\) to get converged results for the turbulence model and governing equations. The residuals were achieved using a firstorder upwind discretization scheme. The equation for volume fraction was solved by the QUICK scheme. The precision of the results is confirmed by these algorithms and the criteria for residuals to determine the convergence of the solution. During simulation, the values for underrelaxation were reduced for better convergence of solutions. The convergence was verified with the flux report of net mass flow rate from inlet and outlet boundaries of the domain. Also, the gravity influence was specified for the accuracy of numerical results.
CFD results validation and adoption of turbulence model
The simulation was accomplished in ANSYS Fluent for CFD results validation. Data from an experiment executed by Serizawa et al. [1] was used for CFD results validation. Model dimensions and boundary parameters for CFD validation are identical to an experiment executed by Serizawa et al. [1]. The CFD model used for the validation is shown in Fig. 5. It is a vertical pipe, and the model dimensions are as follows: the diameter and length are 0.06 m and 2.15 m, respectively. The simulation was performed for twophase fluid (water–air) flow with flow parameters of liquid superficial velocity as 1.03 m/s, gas velocity as 0.151 m/s, bubble diameter as 4 mm, and atmospheric pressure condition. The turbulence models, such as standard kε and SST kω, were examined to analyze flow performance of this CFD model. Figure 6a and b shows the comparative results for radial distributions of void fraction and liquid velocity obtained from CFD and the experiment, respectively. The radial distributions of void fraction and liquid velocity were taken on line L1, which is at 1.8 m from pipe inlet (Fig. 5). Figure 6a shows that the peak of void fraction is close to the pipe wall because of the lift force acting on gaseous phase and the higher bubble diameter. Figure 6b shows that the liquid velocity is maximum at the center of the pipe and zero at the pipe wall. Tables 4 and 5 represent the uncertainty in CFD results for void fraction and liquid velocity distributions compared with experiment, respectively. It is obvious from Fig. 6a and b that the CFD results of void fraction and liquid velocity determined by turbulence model of SST kω were a better match to experimental data than the standard kε. Thus, the impacts of spacervane were analyzed by adopting the SST kω for subsequent simulations of CFD in the annular channel. Moreover; several researchers have found that the SST kω is more appropriate for thermal–hydraulic analysis within nuclear rod bundle assemblies compared to other turbulence models [32,33,34,35,36,37,38]. Based on the previous research works conducted by several researchers [32,33,34,35,36,37,38] for flow thermal characteristics analysis in nuclear fuel channels, the authors examined the SST kω and the standard kε in the present work. The SST kω turbulence model predicted more accurately than the standard kε model.
Results and discussion
In this section, the thermal–hydraulic performance of twophase flow in annular channels with spacervane was discussed. Simulation results were produced for the flow considerations of mass flux 714.4 kg/m^{2}.s, liquid temperature 330 K, volume fraction 0.35, heat flux 197.2 kW/m^{2}, and at atmospheric pressure condition. The parametric plot for convergence of the present simulation in an annular channel with spacervane is shown in Fig. 7.
Effect of spacervane on velocity and pressure distributions
The tangential and radial velocity distributions of liquid in radial coordinates have been presented in Figs. 8 and 9, respectively. The velocity distributions and distance in radial coordinates are shown on the ordinate and abscissa, respectively. The velocity distributions have been taken at different sites (X/D = 1, 2, 5, 20, 30, 40, and 50) in downstream from the spacer tip. X and D represent the downstream distance from spacer tip and a hydraulic diameter, respectively. Figure 8 represents that the tangential velocity magnitude is significantly improved near the wall of outer pipe in the downstream area near the spacer tip (at X/D = 1). This improved tangential velocity is because of the spacer influence as it decreases the area of flow. The tangential velocity gradually reduces adjacent to the outer pipe wall further downstream from the spacer tip (i.e., X/D = 2 and 5) due to the recovery of flow area [36]. It is obvious from Fig. 8 that from X/D = 20 onwards downstream, the flow has become fully developed since the variations in the flow velocity profiles are negligible along the flow direction and the spacer effects are negligible. Also, the turbulence induced by the spacervane in the flow greatly dies down from X/D = 20 onwards due to the axial decay of vortexes, which appeared due to the presence of the spacervane in the flow domain.
Similarly, Fig. 9 shows that the radial velocity magnitude is maximum near the wall of outer pipe which is around 0.8 m/s for location of X/D = 1. Further downstream up to X/D = 5, the radial velocity reduces gradually near the outer pipe wall due to the recovery of flow area, and X/D = 20 onwards in downstream of the spacer effects disappear [36].
Figure 10 a and b represents the axial velocity contour of liquid for spacer only (without vane) and spacervane in annular channel, respectively. The velocity contour has been taken on the midplane of the channel annulus gap. The spacer serves the purpose of decreasing domain flow area by acting as a flow blockage. Decreased domain flow area increases flow velocity. The spacer’s vane further increases flow velocity considerably in the downstream area near the spacer. Figure 10 clearly shows that the maximum velocity magnitude exceeds 1.3 m/s with spacervane, which is higher than that of spacer alone in the annular channel. Enhanced flow velocity contributes significantly to reducing the channel wall temperature, which enhances heat transfer performance.
Figure 11 shows the axial velocity distribution of liquid in radial coordinates of the annular channel with spacervane. Figure 11 shows that the axial velocity magnitude is maximum near the wall of outer pipe which is around 1.1 m/s for location of X/D = 1. This enhanced velocity (for X/D = 1) is because of the spacer influence as it decreases the area of flow. Due to the recovery of flow area, the velocity gradually reduces near the wall of outer pipe in downstream from spacer tip (i.e., X/D = 2 and 5). Further downstream, the flow has become fully developed [36].
Figure 12 shows the dynamic pressure distribution of liquid. The dynamic pressure magnitude is maximum near the outer pipe wall which is about 650 Pa for location of X/D = 1. The dynamic pressure increased near the wall of outer pipe due to the augmented flow velocity near spacer downstream. The difference in dynamic pressure between the locations X/D = 1 and 2 is observed as 250 Pa at radial distance of 12 mm (near the wall of outer pipe). Further downstream, up to X/D = 5, the dynamic pressure reduces gradually near the outer pipe wall, and then the spacer effects are observed to be negligible (X/D = 20 onwards).
Effect of spacervane on turbulent intensity
Figure 13 a and b shows the turbulent intensity contour of the mixture for spacer only (without vane) and spacervane in annular channel, respectively. The contour of turbulent intensity has been taken on the midplane of the channel which is symmetry from the concentric axis of annular channel. The midplane has been created in annulus gap along the channel length. The maximum turbulent intensity is observed in the core zone of the annulus gap, which is over 16%. This enhanced turbulent intensity in the annulus gap is about 11% higher than the turbulent intensity specified at the inlet of channel. The magnitude of turbulent intensity is observed to be greater using spacervane compared to spacer alone in downstream of the channel. Additionally, the effect of vane on turbulent intensity is noticed up to the farthest downstream from the spacer tip compared to spacer alone. This prolonged effect of turbulent intensity in the annulus gap enhances the heat transfer rate in the channel.
Figure 14 shows the turbulent intensity distribution of the mixture in radial coordinates. The distribution has been taken at different sites (X/D = 1, 2, 5, 20, 30, 40, and 50) in downstream from the spacer tip. Figure 14 clearly shows that near the spacer tip (X/D = 1, 2, and 5) downstream, the turbulent intensity magnitudes are higher at the core zone [39] (at radial distance = 11 mm) of the annulus gap, and the turbulent intensities are again improved significantly near the wall of outer pipe due to spacer influence. The spacer provides a flow blockage and yields vortexes behind the spacer downstream. These vortexes increase the turbulent mixing in the core zone of the annulus gap, and thus, the turbulent intensity magnitudes are higher at the core zone of the annulus. Maximum turbulent intensity is observed about 14% at the core zone for location of X/D = 2. Also, Fig. 13b clearly shows that the turbulent intensity magnitude exceeds 16% in the core zone of the annulus gap for location of X/D = 3. Further, from X/D = 20 onwards downstream, the turbulent intensity variations are noticed as negligible.
Effect of spacervane on temperature distributions
Figure 15 a and b shows the temperature contour of liquid for spacer only (without vane) and spacervane in annular channel, respectively. The contour has been taken on the midplane which is created in annulus gap along the channel length. Figure 15 a and b clearly shows that near the spacer tip downstream, the temperature magnitude is less near the wall of outer pipe using spacervane compared to spacer alone in the channel. The spacer’s vane further enhances the turbulent mixing in the downstream area near spacer; thus, the drop in temperature is observed to be greater using spacervane compared to spacer alone [12]. In the downstream area near the spacer tip, the temperature magnitude is observed in the range of 365 to 373 K near the wall of outer pipe using spacervane. Hence, it is obvious that the spacer’s vane further reduces the wall temperature significantly near the spacer downstream.
Figure 16 shows the temperature distribution of liquid in annular channel with spacervane. The temperature magnitude is minimum near the wall of outer pipe, which is about 365 K for location of X/D = 1. Due to the formation of vortexes, the turbulent mixing is predominant in the downstream area near the spacer. Turbulent mixing of fluid enhances the turbulence kinetic energy, which causes a reduction in temperature near the spacer downstream [12]. Further downstream, a gradual increase in temperature is observed due to the axial decay of vortexes [40]. In downstream, the temperature magnitude increases gradually near the wall of outer pipe and is observed as 375 K for X/D = 5 and about 395 K for X/D = 50.
Effect of spacervane on volume fraction
Figure 17 represents the volume fraction distribution of water vapor in radial coordinates of the annular channel with spacervane. Figure 17 shows that the maximum volume fraction of vapor is about 0.44 (near the spacer tip, i.e., at X/D = 1 to 5) at a radial distance 11.7 mm from inner pipe wall and then gradually decreases to a minimum at the outer pipe wall. When the flow has fully developed, i.e., X/D = 20 onwards, the maximum volume fraction (about 0.45 at X/D = 50) is noticed at the center zone of the annulus gap (i.e., at a radial distance of 11 mm). It is observed that in the farthest downstream, most of the water vapor is present at the core of the annulus gap. The peak of the volume fraction is observed at the core of the annulus gap due to the higher water vapor input (0.35) at the inlet [1] and the small size (diameter 0.01 mm) of the water vapor bubbles used in the flow field. The minimum volume fraction of water vapor at the outer pipe wall is favorable to enhance the heat transfer rate from the channel wall.
Conclusions
A detailed investigation was conducted to examine the impacts of spacervane on thermal–hydraulic performance of twophase annulus flow. Additionally, an annular channel model with a spacer but without vane was generated and modeled in order to examine the impact of the spacervane in a twophase flow. The multiphase Eulerian model was applied to solve twophase (water — primary phase and vapor — secondary phase) fluid flow in a threedimensional model of annular channel. Simulation results were produced for the flow considerations of mass flux 714.4 kg/m^{2}.s, liquid temperature 330 K, volume fraction 0.35, heat flux 197.2 kW/m^{2}, and at atmospheric pressure condition. The simulation was accomplished using SST kω mixture turbulence model. The impacts of spacervane on thermal–hydraulic performance of twophase annulus flow were studied, and the conclusions are as follows:

Maximum turbulent intensity is observed in the core zone of annulus gap, which is over 16%. The augmented turbulent intensity in the annulus gap is approximately 11% higher than the turbulent intensity indicated at the channel’s inlet.

The velocity magnitude near the wall of outer pipe is significantly improved in the downstream area near the spacer tip. This improved velocity is because of the spacer influence as it decreases the area of flow.

Enhanced flow velocity plays a significant role in reducing the wall temperature of channel, and hence, it enhances the heat transfer performance.

X/D = 20 onwards in downstream, the flow has become fully developed, and the variations in flow parameters are negligible.

Near the spacer tip downstream, the temperature magnitude is observed to be less near the wall of outer pipe using spacervane compared to spacer alone in the channel.

Due to the small size of water vapor used in the flow field, most of the water vapor is present at the core of the annulus gap in farthest downstream of the channel. The volume fraction of water vapor is observed as minimum at the outer pipe wall, which is favorable to increase the heat transfer rate from the channel wall.
Availability of data and materials
The datasets used and analyzed during the current study are available from the corresponding author upon reasonable request.
Abbreviations
 CFD:

Computational fluid dynamics
 CT:

Computed tomography
 SST:

Shear stress transport
 SIMPLE:

Semiimplicit method for pressurelinked equations
 QUICK:

Quadratic upstream interpolation for convective kinematics
References
Serizawa A, Kataoka I, Michiyoshi I (1975) Turbulent structure of airwater bubbly flowII. Local Properties. Int J Multiphase Flow 2:235–246. https://doi.org/10.1016/03019322(75)900129
Lee TH, Park GC, Lee DJ (2002) Local flow characteristics of subcooled boiling flow of water in a vertical concentric annulus. Int J Multiphase Flow 28:1351–1368. https://doi.org/10.1016/S03019322(02)000265
Ustinenko V, Samigulin M, Ioilev A, Lo S, Tentner A, Lychagin A, Razin A, Girin V, Ye V (2008) Validation of CFDBWR, a new twophase computational fluid dynamics model for boiling water reactor analysis. Nucl Eng Des 238:660–670. https://doi.org/10.1016/j.nucengdes.2007.02.046
Ala AA, Tan S, Qiao S, Shiru GA (2023) Simulation of the effect of partial and total blockage of a subchannel on twophase flow through a 5 x 5 square rod bundle. Prog Nucl Energy 155:104514. https://doi.org/10.1016/j.pnucene.2022.104514
Chalgeri VS, Jeong JH (2022) Flow regime transition criteria for vertical downward twophase flow in rectangular channel. Nucl Eng Technol 54(2):546–553. https://doi.org/10.1016/j.net.2021.08.014
Sadatomi M, Kawahara A, Kano K, Sumi Y (2004) Single and two phase turbulent mixing rate between adjacent subchannels in a vertical 2x3 rod array channel. Int J Multiph Flow 30(5):481–498. https://doi.org/10.1016/j.ijmultiphaseflow.2004.03.001
Sadatomi M, Kawahara A, Kano K, Tanoue S (2004) Flow characteristics in hydraulic equilibrium twophase flows in a vertical 2x3 rod bundle channel. Int J Multiph Flow 30(9):1093–1119. https://doi.org/10.1016/j.ijmultiphaseflow.2004.05.012
Kawahara A, Sato Y, Sadatomi M (1997) The turbulent mixing rate and the fluctuations of static pressure difference between adjacent subchannels in a twophase subchannel flow. Nucl Eng Des 175(1–2):97–106. https://doi.org/10.1016/S00295493(97)001660
Kawahara A, Sadatomi M, Tomino T, Sato Y (2000) Prediction of turbulent mixing rates of both gas and liquid phases between adjacent subchannels in a twophase slugchurn flow. Nucl Eng Des 202(1):27–38. https://doi.org/10.1016/S00295493(00)003009
Kawahara A, Sadatomi M, Kudo H, Kano K (2006) Single and two phase turbulent mixing rate between subchannels in triangle tight lattice rod bundle. JSME Int J, Ser B 49(2):287–295. https://doi.org/10.1299/jsmeb.49.287
Dhurandhar SK, Sinha SL, Verma SK (2020) Effects of mixing vane spacer on flow and thermal behavior of fluid in fuel channels of nuclear reactors  a review. Nucl Technol 206:663–696. https://doi.org/10.1080/00295450.2019.1698257
Dhurandhar SK, Sinha SL, Verma SK (2022) Numerical evaluation for spacer vane effects on flow and heat transfer of water at supercritical pressure in annular channel. Nucl Sci Eng 196(5):600–613. https://doi.org/10.1080/00295639.2021.2003650
Dhurandhar SK, Sinha SL, Verma SK (2022) Spacer effects on thermalhydraulic performance of fluid flow at supercritical pressure in annular channelCFD methodology. J Mech Eng Sci. 16(1):8770–8787. https://doi.org/10.15282/jmes.16.1.2022.10.0693
Dhurandhar SK, Sinha SL, Verma SK (2019) Investigation of ring type spacer effects on performance of heat transfer and flow behaviour of supercritical r134a flow using CFD in an annular channel. Int J Adv Trends Comp Appl 1(1):7–13
Dhurandhar SK, Sinha SL, Verma SK (2023) Numerical simulation to study mixing vane spacer effects on heat transfer performance of supercritical pressure fluid in an annular channel. J Therm Eng 9(6):1428–1441. https://doi.org/10.18186/thermal.1395460
Arai T, Ui A, Furuya M, Okawa R, Iiyama T, Ueda S, Shirakawa K (2023) Effect of nonheated rod arrangements on void fraction distribution in a rod bundle in highpressure boiling flow. Nucl Eng Des 402:112101. https://doi.org/10.1016/j.nucengdes.2022.112101
Williams CL, Peterson AC Jr (2017) Twophase flow patterns with highpressure water in a heated fourrod bundle. Nucl Sci Eng 68:155–169. https://doi.org/10.13182/NSE78A27286
Ren QY, Pan LM, Pu Z, Zhu F, He H (2021) Twogroup phase distribution characteristics for airwater flow in 5 × 5 vertical rod bundle channel with mixing vane spacer grids. Int J Heat Mass Transf 176:121444. https://doi.org/10.1016/j.ijheatmasstransfer.2021.121444
Drucker MI, Dhir VK, Duffey RB (1984) Twophase heat transfer for flow in tubes and over rod bundles with blockages. J Heat Transfer 106(4):856–864. https://doi.org/10.1115/1.3246764
Li J, Zhang C, Zhang Q, Yang P, Gan F, Chen S, Xiong Z, Xiao Y, Gu H (2022) Experimental investigation on onset of nucleate boiling and flow boiling heat transfer in a 5 × 5 rod bundle. Appl Therm Eng 208:118263. https://doi.org/10.1016/j.applthermaleng.2022.118263
Xiao Y, Duan TC, Ren QY, Zheng XY, Zheng M, He R (2022) Modeling and simulation analysis on mixing characteristics of twophase flow around spacer grid. Front Energy Res 10:891074. https://doi.org/10.3389/fenrg.2022.891074
Yang X, Schlegel JP, Liu Y, Paranjape S, Hibiki T, Ishii M (2013) Experimental study of interfacial area transport in airwater two phase flow in a scaled 8 x 8 BWR rod bundle. Int J Multiphase Flow 50:16–32. https://doi.org/10.1016/j.ijmultiphaseflow.2012.10.006
Tian XW, Kui Z, Hou Y, Zhang Y (2016) Hydrodynamics of twophase flow in a rod bundle under crossflow condition. Ann Nucl Energy 91:206–214. https://doi.org/10.1016/j.anucene.2016.01.025
Hosokawa S, Hayashi K, Tomiyama A (2014) Void distribution and bubble motion in bubbly flows in a 4 x 4 rod bundl. Part I: Experiments. J Nucl Sci Technol 51:220–230. https://doi.org/10.1080/00223131.2013.862189
Inoue A, Kurosu T, Aoki T, Yagi M, Mitsutake T, Morooka S (1995) Void fraction distribution in BWR fuel assembly and evaluation of subchannel code. J Nucl Sci Technol 32(7):629–640. https://doi.org/10.1080/18811248.1995.9731754
ANSYS Inc (2013) Fluent R15 User’s Theory Guide Release
Schiller L, Naumann Z (1935) A drag coefficient correlation. Z Ver Deutsch Ing 77:318–320
Tomiyama A (1998) Struggle with computational bubble dynamics. Multiph Sci Technol 10(4):369–405. https://doi.org/10.1615/MultScienTechn.v10.i4.40
Antal SP, Lahey RT, Flaherty JE (1991) Analysis of phase distribution in fully developed laminar bubbly twophase flow. Int J Multiph Flow 17(5):635–652. https://doi.org/10.1016/03019322(91)900293
Lopez de Bertodano M (1991) Turbulent bubbly flow in a triangular duct. Rensselaer Polytechnic Institute, Troy, New York.
Nikuradse J (1966) Laws of turbulent flow in smooth pipes. NASA TT F10, 359. (English Translation)
Podila K, Rao Y (2016) CFD modelling of turbulent flows through 5 × 5 fuel rod bundles with spacergrids. Ann Nucl Energ 97:86–95. https://doi.org/10.1016/j.anucene.2016.07.003
Liu CC, Ferng YM, Shih CK (2012) CFD evaluation of turbulence models for flow simulation of the fuel rod bundle with a spacer assembly. Appl Therm Eng 40:389–396. https://doi.org/10.1016/j.applthermaleng.2012.02.027
Cheng S, Chen H, Zhang X (2017) CFD analysis of flow field in a 5 × 5 rod bundle with multigrid”. Ann Nucl Energ 99:464–470. https://doi.org/10.1016/j.anucene.2016.09.053
Sohag FA, Mohanta L, Cheung FB (2017) CFD analyses of mixed and forced convection in a heated vertical rod bundle. Appl Therm Eng 117:85–93. https://doi.org/10.1016/j.applthermaleng.2012.02.027
Xiao Y, Li J, Deng J, Gao X, Pan GuH, J, (2020) Study of spacer effects on deteriorated heat transfer of supercritical fluid flow in an annulus. Prog Nucl Energy 123:103306. https://doi.org/10.1016/j.pnucene.2020.103306
Jaromin M, Anglart H (2013) A numerical study of heat transfer to supercritical water flowing upward in vertical tubes under normal and deteriorated conditions. Nucl Eng Des 264(11):61–70. https://doi.org/10.1016/j.nucengdes.2012.10.028
Cheng H, Zhao J, Rowinski MK (2017) Study on two wall temperature peaks of supercritical fluid mixed convective heat transfer in circular tubes. Int J Heat Mass Transf 113:257–267. https://doi.org/10.1016/j.ijheatmasstransfer.2017.05.078
Wang Y, Ferng YM, Sun LX (2019) CFD assist in design of spacergrid with mixingvane for a rod bundle. Appl Therm Eng 149:565–577. https://doi.org/10.1016/j.applthermaleng.2018.12.090
Dhurandhar SK, Sinha SL, Verma SK (2024) Numerical analysis for effects of grid spacer vane on flowthermal characteristics of two phase flow in a 5 x 5 rod bundle. Multiph Sci Technol 36(3):19–44. https://doi.org/10.1615/MultScienTechn.2024051035
Acknowledgements
The authors acknowledge the cooperation and support extended by the authorities of the National Institute of Technology Raipur for the present work.
Funding
The authors declare that they receive no funding.
Author information
Authors and Affiliations
Contributions
SKD, SLS, and SKV worked on the conceptualization, methodology, and software implementation for the CFD simulation of the present work. SKD and SKV performed the validation of the work with previous experimental work. SKD compiled graphs and contour related to the CFD simulation results. SKD prepared the original draft and wrote the manuscript. SLS and SKV supervised the study and helped in the reviewing and editing of the manuscript. All authors have read and approved the manuscript.
Corresponding author
Ethics declarations
Competing interests
The authors declare that they have no competing interests.
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated in a credit line to the data.
About this article
Cite this article
Dhurandhar, S.K., Sinha, S.L. & Verma, S.K. CFD analysis in effects of spacervane on thermal–hydraulic performance of twophase flow in annular channel. J. Eng. Appl. Sci. 71, 127 (2024). https://doi.org/10.1186/s44147024004622
Received:
Accepted:
Published:
DOI: https://doi.org/10.1186/s44147024004622