Numerical investigation of pump performance and internal characteristics in ALIP with different winding schemes

Abstract

Annular linear induction pump (ALIP) is considered as an ideal type of coolant pump in liquid metal cooled reactors. However, the low pump efficiency and the flow instability have yet been solved, especially for large-scale pump design. In this work, a two-dimensionally symmetrical ALIP model is developed and both single-sided (SS) and double-sided (DS) windings in stators are simulated in the designed ALIP model. The pump performance characteristics (H-Q curve) are obtained by calculating the differential pressure between inlet and outlet at varying flow rate conditions. The simulated results are validated with the previously published experiment. The results show that the differential pressure of the DS-type pumps is slightly lower than that of SS pump with the same input energy while the radial velocity profile in the channel of the DS pumps with the winding number of outer stator twice that of inner stator shows the best uniform velocity distribution. By peeking into the Lorentz force and induced magnetic field, the DS pump with equal winding numbers at inner and outer stators actually deteriorates the induced magnetic field, resulting in a highly non-uniform Lorentz force in the channel radial direction, particularly at high flow rate. The results demonstrate the importance of finding an appropriate ratio of winding numbers in the DS-type pump design in order to improve the pump performance.

Keywords

ALIP CFD MHD winding scheme pump performance

1. Introduction

Annular linear induction pump (ALIP) has been receiving increasing attention in the last decade since the sodium-cooled faster reactor (SFR) is a promising alternative for the new generation nuclear reactor and ALIP can be applied to transport the liquid sodium in the main and secondary circulating loops [1]. ALIP possesses of several advantages against with conventionally mechanical pumps which usually suffer from the problems, such as vibration of the impeller, leakage and lubrication [2]. However, the state of the art ALIP can only reach the maximum flow rate of 160 m ${}^{3}$ /min while the commercial reactor requires 500 m ${}^{3}$ /min [3]. In large flow rate design, the flow in the pump channel could induce strong unsteady flows, resulting in large fluctuations of flow rate and pressure at the outlet. In worse case, large-scale vortex or reverse flow will appear in the channel [4].

The early ALIPs were developed under low flow rate. Since 1980s, large ALIP was developed in Russian, France and Germany [5] and the flow instability became a challenge for building larger prototype. Much work has been focused on understanding the mechanism of the unstable flow in ALIP under certain conditions. Gailitis and Lielausis [6] found the critical condition for unsteady flow appearance was Rm $\cdot$ s>1, where Rm is the magnetic Reynolds number and s, the slip. Kirillov and Ostapenki [7] proved the criteria for occurring unsteady flow in a real ALIP. They found low frequency fluctuations in the pumping flow rate and pressure at outlet and non-uniform azimuthal velocity and magnetic field distributions. Meanwhile, Araseki et al. [8] studied the double-supply-frequency (DSF) pressure fluctuation of ALIP when applying a low frequency current. The unstable pressure was attributed to the cutting off of the induced magnetic field at both ends of the pump channel. To suppress the fluctuation, they proposed to arrange grading windings (gradually decreasing windings) at both ends in order to reduce the end effect [9]. Araseki et al. [10] further studied the low frequency pressure pulsation and the reason for this phenomenon, according to the simulation, was due to large scale vortex occurring in the azimuthal plane of the pump channel. They proposed to change the phase order in the windings to reduce the Lorentz force and to have a better control of the flow pattern in the channel [11].

Although the experiment can yield the most reliable result of the performance of ALIP, it has the difficulty in obtaining the details, such as flow pattern, velocity and pressure inside the pump. Numerical modeling provides a tool of studying the detailed fluid flow in the pump. In fact, in Araseki et al’s work [10], a very simple 2D model was presented by simultaneously solving the Navier-Stokes equation and the derivative magnetic induction equation. The simulated results were compared with experiment and the predicted pressure has a good consistence with the measurement at large flow rate while the predicted pressure was lower at low flow rate, which was attributed to the failure of 2D model for simulating 3D flow phenomenon in the pump. Kirillov and Obukhov [12] also developed a similar 2D model to study DSF fluctuation and internal vortex flow. A numerical model based on time harmonics finite difference method was created by Kim and Lee [13], and they studied some important ALIP characteristics, such as eddy current, DSF pressure pulsation, and Lorentz force under various flow rates. Until recently, Asada et al. [14] used commercial CFD software and combined with home-made electro-magnetic solver to simulate a 3D ALIP model. The results showed pressure pulsation and reverse flow at the outlet under severe working conditions. However, only small vortices in the radial plane and near the outer duct wall were observed in the simulation. Roman et al. [15, 16] used the commercial software FLUENT and COMSOL to solve fluid and magnetic fields, respectively, and global performances in the various flow regimes were investigated. The equivalent circuit model was also applied to forecast the ALIP working characteristics and to optimize the pump performance. Kim and Yong [17] used the equivalent circuit model to establish the correlations of the input current, voltage and power with the developed pressure and efficiency and the results were well consistent with the experiments. Nashine and Rao [18] used the same method to develop the expression for calculating the pump developed pressure with the considerations of both the end effect and hydraulic losses in the pipe. Kim and Kwak [19] further applied the equivalent circuit model to analyze the influences of some pump design variables on the developed pressure and efficiency, and proposed the optimal pump design variables. In designing the commercial ALIP prototype, the pump channel will be indispensably widened. To increase the induced magnetic field in the wider channel, the windings are arranged at both inner and outer sides of the pump channel [3]. The influence of the double-sided (DS) winding scheme on the pump performance and internal flow characteristics has yet to be deeply revealed for optimizing the design of large ALIP.

Figure 1.

Schematic of different winding schemes, a) SS winding model (SS pump), b) DS winding model 1 (DS1 pump), c) DS winding model 2 (DS2 pump).

From the literature review, most numerical work was focused on 2D model as it is simple to solve and can provide reliable results of the ALIP working parameters. In this work, we created a 2D model where the meridian plane of the pump channel was simulated. The single-sided (SS) winding and two different DS winding arrangements were compared. Except for the performance characteristic, the velocity, Lorentz force and induced magnetic field at different positions in the pump channel were studied. The aim of this work is to study the effects of different winding schemes on both the pump performance and the internal flow and electromagnetic field.

2. Numerical model

2.1 Physical models

A 2D symmetrical ALIP model simulating the meridian plane of the pump is created in this work, as shown in Fig. 1. The modeling domain consists of the inner and outer stators, windings, inner and outer ducts, pump channel between two ducts and the inner and outer air gaps between ducts and stators. A large air domain is defined to surround the ALIP components. The stator is ferromagnetic material, the duct is made of steel and liquid sodium flows in the channel. The SS winding scheme is reproduced based on the ALIP’s parameters reported in Ref. [10], as shown in Fig. 1a. Figure 1b–c show the schematic of two different DS winding schemes referred to as DS1 and DS2 pump, respectively. It is noticed that the winding area in stators keeps constant for three pumps. In the DS1 pump, the windings are equally distributed in the inner and outer stators while the windings number in the outer stator is double than that in the inner stator of DS2 pump. Assuming the input current density is constant, the input energy will be the same in all scenarios but distributed differently in the inner and outer stators. The pump channel is extended out of the magnetic influencing area at both ends and the flow can be fully developed in the channel before entering into the ALIP section.

2.2 Governing equations

The governing equations are Maxwell equations and Navier-Stokes equations. In this work, the system is assumed in isothermal condition and the energy equation is therefore ignored.

$\displaystyle\nabla\times H=J$ (1) $\displaystyle B=\nabla\times A$ (2) $\displaystyle J=\sigma E+\sigma u\times B+J_{e}$ (3) $\displaystyle E=-\frac{\partial A}{\partial t}$ (4) $\displaystyle F_{L}=J\times B$ (5) $\displaystyle\rho\frac{\partial u}{\partial t}+\rho(u\cdot\nabla)u=\nabla\cdot% [-pI+(\mu+\mu_{T})(\nabla u+(\nabla u)^{T})]+F_{L}$ (6)

where $A$ is magnetic vector potential, $\sigma$ is conductivity, $H$ is magnetic field intensity, $B$ is magnetic flux density, $u$ is flow velocity, $J$ is current density, $F_{L}$ is Lorentz force, $p$ is pressure, $\mu$ is flow viscosity, $\mu_{T}$ is turbulence viscosity.

2.3 Initial and boundary conditions

The main parameters of the ALIP are adopted from the previous work [10] and listed in Table 1. 36 windings are arranged along the pump length and each two windings share the same current phase. Since three phase alternating current is applied, each pole occupies 6 windings and 6 poles are created in the stator. At the boundary of the domain, parallel magnetic flux lines are defined, indicating the magnetic vector potential is zero through the boundary. Depending on the flow rate, a uniform velocity is defined at the inlet of the channel and zero pressure is imposed at the outlet with 1 atm as the reference pressure. Non-slip condition is assumed on the channel walls and wall roughness is 3.2 $\mu$ m by default. The standard k- $\varepsilon$ model is employed to consider turbulence in the domain. Although the presence of magnetic field can significantly influence the turbulence flow near wall, the interaction is not considered in this work.

Table 1
Parameters of the modeled SS pump, adopted from Ref. [10] ( $T=$ 200 ${}^{\circ}$ C)

Parameters value	Value
Density of the liquid sodium	903.56 kg $\cdot$ m ${}^{-3}$
Electrical conductivity of the liquid sodium at 200 ${}^{\circ}$ C	7.4 $\times$ 10 ${}^{6}$ S $\cdot$ m ${}^{-1}$
Dynamic viscosity	2.13 $\times$ 10 ${}^{-4}$ Pa $\cdot$ s
Relative permeability of the yoke	1000
Relative permeability of sodium	1
Frequency	50 Hz
Inner duct length	0.001 m
Stator height	0.85 m
Channel width	0.012 m
Stator outer diameter	0.564 m
Teeth pitch	0.0233 m
Teeth width	0.0063 m
Outer duct thickness	0.0035 m
Outer diameter of inner core	0.284 m
Current	280 A
Number of poles	6
Number of slots	36
Winding connection	Y

2.4 Mesh independent study

Hybrid meshes are created in the modeling domain for solving the governing equations. Structure mesh is created in the flow channel and the meshes near wall are refined for the requirement of 30 $<$ y ${}^{+}<$ 200 on the wall. Structure mesh is also used for the duct as the duct thickness is much smaller than its length. In other areas, unstructured meshes are used for solving magnetic field.

Table 2
Mesh independent study

Grid number	66099 (coarse)	83459 (normal)	168598 (refined)
Differential pressure [Pa]	177182	176646	176125

The mesh independence is studied by solving the coupled equations in three meshes. The differential pressure between inlet (S1) and outlet (S7) of the SS pump model at the mass flow rate of 7.45 m ${}^{3}$ /min is obtained within different meshes as presented in Table 2. The difference between the coarse and refined meshes is about 1000 Pa while that between the normal and refined meshes is only half of that. Figure 2a–b show the comparisons of time averaged Lorentz force along the pump length and the radial velocity distribution at S6 in the channel using the different meshes. It is found that there is small discrepancies in both the averaged Lorentz force and the velocity profile predicted by the coarse mesh while the results within normal mesh agree well with the refined one. Therefore, the normal mesh with 83459 elements is used in the following simulations by considering both result accuracy and less computational burden.

Figure 2.

Comparisons of the results within different meshes, a) time averaged Lorentz force along the pump length, b) time averaged radial velocity profile in the pump channel.

3. Results and discussion

3.1 Pump performance characteristics

The pump performance curves (H-Q curve) are obtained by calculating at various flow rates for both the SS and DS-type pumps (DS1 and DS2) and are compared with the experimental result of the referred ALIP [10] in Fig. 3. In the simulations, the inlet and outlet pressure are obtained at the positions very close to the ALIP ends (0.1 m away from the inlet and outlet) while the pressures measured in the experiment undergone a significant pressure loss due to the flow separation and deflection in the duct and bend. Fortunately, the pressures at the inlet and outlet of ALIP section were also measured in the experiment and the ratio of pressure pulsation to the differential pressure between the inlet and outlet of ALIP section was reported for two specific flow rates. By estimating the values of the pressure pulsation from the figures, a corrected differential pressure is obtained without any hydraulic loss and they are also presented in Fig. 3. The error bars indicate the possible error due to our coarse estimation of the relative pressure pulsation from the original figures. It shows that the simulation can give very accurate pressure at 7 m ${}^{3}$ /min, which is the nominal flow rate of the ALIP while it significantly underestimates the pressure at 5.3 m ${}^{3}$ /min. The reason was attributed to the failure of the 2D model for simulating complex 3D flow phenomenon. In a real ALIP, large pressure pulsation with low frequency was observed and several numerical models revealed large scale vortex occurring in the pump channel at the outlet side [7], especially at low flow rate. Comparing the three pumps under the same energy input condition, the SS winding gives a little higher differential pressure than both the DS pumps. In the experiment, there is a dimple occurring in the P-Q curve when the flow rate is 4–5 m ${}^{3}$ /min while a dimple with much smaller strength is observed in the SS pump.

Figure 3.

Pump performance curves (H-Q curve).

The time averaged Lorentz force along the pump channel is shown in Fig. 4 for the three modeled pumps. Two flow rates, i.e. 2.91 and 7.45 m ${}^{3}$ /min, are shown in the figure to refer to as the “low” and “high” flow rate conditions. The end effect is large at high flow rate and the negative Lorentz force at the outlet is larger than that at the inlet. The averaged Lorentz force is larger at low flow rate and pressure pulsation is also small. At high flow rate, the spatial pressure variation of the DS-type pumps is slightly larger than the SS pump.

Figure 4.

Time averaged Lorentz force along the pump length at high and low flow rates.

The pumping efficiency is also an important parameter to estimate the pump performance. The efficiency is defined as the ratio between the mechanical energy transferred into the liquid sodium and the total input electrical energy in the coils. The former is the product of the developed pressure and the pumping flow rate while the latter is the total input energy in the coils. At the high flow rate, the efficiency of SS pump is 27.7% while it is 45.5% and 44.9 % for DS1 and DS2 pumps, respectively. The results show that the DS winding scheme can significantly increase the efficiency, which is attributed to less consuming electrical energy in the coils due to the reduced total electrical resistance and the almost same transferred mechanical energy in sodium. At the low flow rate, the pump efficiency shows 8% for the SS pump and 11.2% and 10.9% for the DS pumps. The much smaller values are due to the deviation of the flow rate from the designed point. The efficiency may be slightly overestimated as the magnetic hysteresis effect in stators was not considered. Overall, the DS winding scheme shows an overwhelming advantage from the perspective of pumping efficiency and the difference between the DS1 and DS2 is negligible.

3.2 Velocity distribution in pump channel

The radial velocity profiles in the pump channel of both the SS pump and DS pumps are presented in Figs 5 and 6 for the “high” and “low” flow rates. Seven positions chosen along the pump length (named as S1–S7 in Fig. 1a) are studied to understand the velocity variation throughout the pump channel. The velocity is also temporally varied because of the sinusoidal incitation current imposed in windings. Herein, the velocity is time averaged for a period of 5 cycles after the simulation running 35 cycles and reaching the convergence.

Figure 5.

Radial distributions of velocity at the high flow rate, a) at S1, b) at S2, c) at S3, d) at S4, e) at S5, f) at S6, g) at S7.

Figure 6.

Radial distributions of velocity at the low flow rate, a) at S1, b) at S2, c) at S3, d) at S4, e) at S5, f) at S6, g) at S7.

At high flow rate, the velocity profiles are almost the same for all three pumps at S1–S3, as shown in Fig. 5a–c. They are distributed in the similar manner like a common channel flow, but show a slightly flattened curve in the middle range of the channel due to the influence of magnetic field. As sodium flowing inward to S4 (the middle of first pole), the velocity distribution in Fig. 5d demonstrates a strong Hartman effect because the flow is suffering a strong electromagnetic force. The velocity at the inner side is larger and the peak value appears in the vicinity of the inner duct. The velocity distributions show little change when the sodium fluxes over S5 and S6. However, at the last position S7, which is 0.05 m outside of the outlet, the velocity distributions of DS1 and DS2 pumps show quietly uniform in the channel while the SS pump keeps in its original pattern.

The discrepancy of velocity profiles is more significant when the low flow rate is simulated, as shown in Fig. 6a–g. The velocity distribution starts to diverge when the sodium flow arrives at S2. When the flow moves to S3, large discrepancy of velocity distribution occurs among the pumps. For SS pump, the velocity at the outer side is larger and the peak value is in the vicinity of the outer duct while the pattern is completely opposite for DS1 pump. For DS2 pump, the velocity distribution shows a good uniform in the channel. When the sodium goes further, the velocity distributions in all pumps tend to be in the same manner at S4–S7, i.e., the velocity at the inner side is larger and the peak value is in the vicinity of the inner duct. However, the most severe non-uniformity is found in the DS1 pump at S4 and S5 while it occurs in the SS pump at S6 and S7. At all positions, the DS2 pump shows a moderate performance between the other two pumps.

In order to quantitatively identify the uniformity of velocity distributions, the root mean square deviation (RMSD) of the velocity profiles are calculated for all pumps at the high and low flow rates. It is noted that the nearest four points to both the inner and outer duct walls are excluded because the velocity at these points is rapidly decreased due to the constraint of no-slip condition on the wall. The RMSD at S1 and S2 are not calculated since the Hartman effect is not obvious at the entrance. As seen in Fig. 7, the velocity profiles at high flow rate is much more uniform than at the flow rate. Compared among the pumps, DS2 pump shows the smallest RMSD at all positions when the pump is running at high flow rate. DS1 and SS pumps perform in worse conditions but the deterioration is very limited. However, things become complicated when the pumps run in low flow rate. There is no pump showing the best performance throughout all positions. SS pump gives a better velocity profile at S4 and S5 while the DS-type pumps do better at S6 and S7. Viewing the data through S3–S7, the RMSD of DS2 pump is more stable, even though not being always smallest.

Figure 7.

RMSD of the velocity profiles of SS and DS-type pumps at different positions.

3.3 Lorentz force in pump channel

Figure 8.

Radial distributions of Lorentz force at the high flow rate, a) at S1, b) at S2, c) at S3, d) at S4, e) at S5, f) at S6, g) at S7.

Figure 9.

Radial distributions of Lorentz force at the low flow rate, a) at S1, b) at S2, c) at S3, d) at S4, e) at S5, f) at S6, g) at S7.

The Lorentz force acting on liquid sodium is the main reason of Hartmann effect in the channel. The time averaged Lorentz force in radial direction at S1–S7 in pump channel are presented in Figs 8 and 9 for both high and low flow rates. From Fig. 8a before entering the pump, the Lorentz force is small and smooth. When entering the pump inlet at S2, the end effect creates a considerable negative force as seen in Fig. 8b. However, the distribution pattern is completely opposite between SS pump and DS1 pump. In the SS pump, the largest negative force occurs in the vicinity of outer side and it is linearly reduced in magnitude toward to the inner side. The DS1 pump shows a peak value close to the inner side and its magnitude is rapidly decreased as moving to the outer side. The DS2 pump presents the best uniform distribution. When the flow moves over the entrance, the Lorentz force pattern changes to be similar as shown in Fig. 8c (S3). The maximum positive force occurs in the vicinities of both inner and outer ducts, then rapidly decreased, and finally reduced to the minimum level in the middle of the channel. The magnitude of the force is generally a litter smaller in the DS pumps than in the SS pump. Nevertheless, the force pattern in the DS-type pumps becomes worse again when the sodium flows into the downstream half part, as shown in Fig. 8d–e (S4 and S5). At the high flow rate, a highly non-uniform distribution is found, compared with a relatively smooth force profile in the SS pump. A significant hump pointing downward is presented close to the inner side for the DS pumps, which may create large unstable pressure in the liquid. At the exit of the channel (Fig. 8f), the Lorentz force becomes negative again due to the end-effect and the humps appear in all three pumps. However, the largest one is found in the DS1 pump and the DS2 pump performs better with an attenuated hump which can compete with the performance of SS pump. When the flow leaves the pump, the Lorentz force become stable and no big discrepancy is found among the pumps.

When the flow rate is reduced to low level, the Lorentz force distribution shows the similar pattern with those of high flow rate at S1 and S2, as shown in Fig. 9a and b. After the sodium moving over the entrance, the force distribution in the SS pump becomes smoother compared with those in the two DS-type pumps while the force magnitude is generally larger in the DS pumps. However, when the flow reaches S6 and S7 (Fig. 9f and g), the force distribution in SS pump also show a significant non-uniformity, which is comparable with that in DS pumps.

Figure 10.

Radial distributions of magnetic flux density at the high flow rate, a) at S2, b) at S3, c) at S4, d) at S5, e) at S6.

3.4 Magnetic flux density in pump channel

Although the Lorentz force profiles are more uniform for all pumps at high flow rate, the divergence and humps still exist at some positions, such as at S2, S4, S5, and S6. From the Ampere’s law, Eq. (1), the induced current is correlated with the gradient components of magnetic field and the Lorentz force is determined by the multiply of induced current and magnetic flux density. Therefore, the magnetic flux density $B$ at S2–S6 is depicted in Fig. 10a–e for the high flow rate condition. The figures show that $B$ is distributed differently among each other. In SS pump, $B$ is smaller at the inner side and monotonously increases to the outer side, because the magnetic field is incited from the outer side windings. In DS-type pumps, $B$ is presented in parabola, because the magnetic field is incited from both side windings. The minimum magnetic flux density is located in the area near the channel center. In the SS pump, the curve incline of $B$ at the inner side is gentle but it becomes very steep at the outer side at some positions, such as S2 (Fig. 10a), S4 (Fig. 10c) and S6 (Fig. 10e). This can explain why large non-uniformity or humps occur in Fig. 8b, d and f for the SS pump, because the more steep the curve, the larger the induced current created in the channel, resulting in large difference in the Lorentz force.

Differently from the SS pump, the DS-type pumps appear a large hump in the Lorentz force profile at S4 (Fig. 8d) and small humps at S3 (Fig. 8c) and S5 (Fig. 8e) at the inner side, besides of the entrance (S2) and exit (S6) of ALIP section. For the DS1 pump, Fig. 10 demonstrates that $B$ is always large in the vicinity of inner side so as to create a steep curve with large slope while $B$ is relative small at the outer side with gentler curves. This distribution pattern creates a large gradient of the magnetic flux density at the inner side which is attributed to the humps in the profiles of Lorentz force. When adjusting the inner and outer winding areas by the scheme DS2, the discrepancy of maximum values between the inner and outer sides has been tuned down, especially for the positions of S2 and S6. Therefore, the DS2 pump gives a more uniform distribution of Lorentz force at the entrance and exit of the ALIP section, seen in Fig. 8b and f. Inside of the channel, e.g., S3, S4 and S5, the DS2 pump still improves somehow the discrepancy and the curve slops, but not reaching effective levels.

Based on aforementioned results, the DS-type pumps can give a more uniform velocity distribution throughout the pump channel, especially at the pump exit. However, they may create a highly non-uniformity in the distribution of Lorentz force in the channel. The improvements in the Lorentz force profiles and the induced magnetic field by DS2 winding scheme implies that effort should be paid on how to determine an appropriate ratio of the winding numbers between inner and outer stators with respect to high uniformity in both magnetic field and Lorentz force.

4. Conclusions

This work simulated the liquid sodium flowing in ALIP with both SS and DS arrangements of windings. The total input energy is retained the same by keeping constant total winding area and current density. The pump performance characteristics is obtained and some internal characteristics are studied. Some important conclusions are summarized as below:

Based on the P-Q curve, the DS-type pumps cannot increase the pressure at outlet. Moreover, they create lower pressure at high flow rate compared with the SS pump.

The DS-type pumps perform better than the SS pump with respect to the velocity distribution in the radial direction of pump channel. Compared between the schemes of DS1 and DS2, the latter creates less RMSD values of the velocity profiles at the pump nominal flow rate.

The DS-type pumps create high discrepancy in the Lorentz force profile and the time averaged force is smaller than that in SS pump, particularly at high flow rate. By peeking into the magnetic field, the DS winding arrangement results in steeper magnetic flux density profiles, which introduces the divergence and humps in the Lorentz force profiles. However, the scheme of DS2 can mitigate the curve slope somehow, in particularly at the entrance and exit of the ALIP section. Therefore, the DS-type winding scheme can bring out a more stable output of the flow at the pump exit. However, the ratio of winding area at inner and outer side should be optimized in order to create more uniform distributions of Lorentz force and induced magnetic field in the pump channel.

Footnotes

Acknowledgments

We are grateful to the financial supports by the National Natural Science Foundation of China (Grant No. 51509110), the China Postdoctoral Science Foundation (Grant No. 2015M581736) and the Senior Talent Fund of Jiangsu University (Fund No. 5501440001).

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Numerical investigation of pump performance and internal characteristics in ALIP with different winding schemes

Abstract

Keywords

1. Introduction

2.1 Physical models

2.2 Governing equations

Table 1 Parameters of the modeled SS pump, adopted from Ref. [10] ( T = 200 ∘ C)

Table 2 Mesh independent study

3.1 Pump performance characteristics

4. Conclusions

Footnotes

Acknowledgments

References

Table 1
Parameters of the modeled SS pump, adopted from Ref. [10] ( $T=$ 200 ${}^{\circ}$ C)

Table 2
Mesh independent study