Simulation and experimental studies of induction heating during the partial upset-extrusion of a nuclear main pipe

Abstract

As a large, abnormal pipe with branches, the main pipe of an AP1000 nuclear power plant is quite difficult to process integrally. To this end, researchers at Tsinghua University have proposed an integral processing method called partial upset-extrusion, which relies on high-quality online local heating. Induction heating is ideal for this purpose; however, it cannot be directly applied in the partial upset-extruding process without a thorough understanding of the heating pattern of a pipe of the desired type with a prefabricated hole. In this study, the induction heating of such a scaled abnormal pipe during the partial upset-extruding process was investigated numerically and experimentally. A coupled thermal–electromagnetic simulation was performed using the finite element method. It was shown that the prefabricated hole led to local overheating, and that this problem could be solved by placing a lid over the hole. These findings were experimentally verified using thermocouples to acquire the temperature curves of a sample pipe during the heating process. The factors influencing the heating process were further analyzed and optimized numerically. It was shown that the method proposed in this study is suitable for applying online local heating during the integral processing of a nuclear main pipe.

Keywords

Induction heating 316LN AP1000 nuclear main pipe finite element method

Introduction

The AP1000 power plant design belongs to the third generation of nuclear power technology. The main pipe of its reactor, which is regarded as one of the seven key components of the design as well as the main artery of the nuclear island, connects the pressure vessel and the steam generator.¹ To satisfy the service conditions and lifetime requirements of the plant, the main pipe must be forged integrally.² As a large, complex, abnormal pipe, the main pipe is quite difficult to process, and this problem has become a focus of efforts related to AP1000 technology in recent years. The structure of the main pipe is shown in Figure 1.

Figure 1.

Schematic diagram of the structure of the AP1000 nuclear main pipe.

At present, the common method for processing a nuclear main pipe consists of the following steps:³ stretch the 316LN billet, produce a branch pipe by means of open-die forging, machine the inner hole, and bend the pipe. The main drawback of this method is that the machining process severs the metal flow lines of the forged piece, significantly weakening the pipe’s mechanical and corrosion resistance performance; in addition, the complexity of the open-die forging procedure and the high cost of the machining process are also of concern. To overcome these disadvantages, Feng from Tsinghua University designed the partial upset-extruding (PUE) technique, in which a branch pipe on a nuclear main pipe is formed by applying pressure at both ends of the pipe such that the branch pipe is partially extruded in a mold placed for that purpose.⁴ The specific procedure is as follows: (1) machine a prefabricated hole in the middle section of the main pipe; (2) apply local heating until the middle pipe section reaches the forging temperature; and (3) place two mandrels into the pipe, close the dies, and then exert an axial upset-extruding force on both ends of the pipe, eventually causing a branch pipe to form at the position of the prefabricated hole. This method is illustrated in Figure 2. This integral processing technique can help avoid the interruption of the metal flow lines and improve the forging quality. It can also reduce the amounts of materials used and the production costs and is thus a potentially ideal method for processing nuclear main pipes. It has previously been proven in 1:5-scale model experiments that branch pipes can be successfully processed using this method, and that the online local heating applied around the prefabricated hole is the critical step that determines the feasibility of this method.

Figure 2.

Partial upset-extrusion technique.

The online local heating step of the PUE technique is subject to several requirements: (1) the heating rate must be high, (2) the heating range should be limited to the vicinity of the prefabricated hole, and (3) the heating depth should be confined to the thickness of the pipe to avoid heating the mold. Induction heating is an ideal method of local heating for this purpose because it offers the following advantages: (1) high power and high thermal efficiency, (2) a limited heat-affected zone, and (3) a skin effect. However, it is not straightforward to apply induction heating during the PUE process because the presence of the prefabricated hole will inevitably introduce a change in the induction heating behavior compared with that of normal pipes, which may strongly affect the subsequent forging procedures. Moreover, with a diameter of approximately 1 m and a length of over 5 m, a nuclear main pipe is too large to be heated by conventional induction heating devices. Without precise knowledge of the heating pattern in this scenario, it can be difficult to design a suitable induction heating device for a 1:1 nuclear main pipe and to choose the specific heating parameters for the PUE technique. Therefore, it is desirable to investigate the influence of a prefabricated hole on the heating behavior of a pipe by means of numerical simulations and experiments on a scale model.

As a thermal–electromagnetic coupling process, induction heating is typically simulated using the finite element method (FEM) and via indirect coupling, namely, by alternately calculating the harmonic electromagnetic field and the transient temperature field.⁵ Many studies have focused on the changes in the temperature field that occur during induction heating and during subsequent welding or forging processes.^6–10 For example, Hansson and Fisk¹¹ analyzed the variations in the temperature and flow stress of 353MA and SAF2057 stainless steel pipes during induction heating, expansion, and extrusion, whereas Shokouhmand and Ghaffari¹² used the FEM to analyze the dynamic temperature field of a pipe heated by moving induction coils. However, because of the influence of the material and the prefabricated hole, controlling the temperature field during the induction heating of a nuclear main pipe is different from the above examples, and no related reports have been published to date.

This study investigated the induction heating of a scale model of an AP1000 nuclear main pipe for application in the PUE technique. The temperature field of the pipe was analyzed using the FEM and was found to be improved by covering the prefabricated hole with a lid. Induction heating experiments were performed to verify the validity of the numerical model, and the factors influencing the heating process were further discussed and optimized.

Materials and methods

Materials and methods for the simulations

Geometrical models

Two kinds of geometrical models were used in our study. Figure 3 shows a 1:5-scale model of the induction heating of an actual nuclear main pipe, which consists of an air space, an induction coil, and a pipe made of 316LN austenitic stainless steel, with its middle section enclosed in the coil. For computational efficiency, the induction coil was simplified as a thin-walled cylinder. The diameter of the prefabricated hole was defined to be 72 mm, and the other important geometrical parameters were specified as follows: air space D × L = 640 mm × 1200 mm, coil D_o × D_i × L = 256 mm × 250 mm × 280 mm, and pipe D_o × D_i × L = 190 mm × 170 mm × 700 mm. A more complex model with the same dimensions was also considered, in which a lid made of the same material as the pipe was placed precisely over the prefabricated hole. A rectangular coordinate system was used, in which the z-axis coincided with the axis of the model.

Figure 3.

Geometrical model for induction heating simulations (for the pipe without the lid).

Material properties

The material properties that are relevant to induction heating problems are the density $ρ$ , the specific heat C_P, the thermal conductivity $λ$ , the electrical conductivity $σ$ , and the relative permeability $μ_{r}$ . Because 316L and 316LN are highly similar in composition (316LN contains an additional 0.01%–0.16% N), the $σ$ and $μ_{r}$ values for 316L were used.¹³ The temperature characteristic curves of $C_{P}$ , $λ$ , and $σ$ are shown in Figure 4.

Figure 4.

Several temperature characteristic curves of 316LN (316L): (a) specific heat, (b) thermal conductivity, and (c) electrical conductivity.

Because 316LN is a paramagnetic material, its relative permeability $μ_{r}$ is close to that of the atmosphere at room temperature. As the temperature increases, the $μ_{r}$ of a paramagnetic material decreases but always remains greater than 1; thus, we assumed a constant value of $μ_{r} = 1.008$ for 316LN.¹³

Governing equations

The simulations were performed via indirect coupling, that is, the harmonic electromagnetic field and the transient temperature field were calculated alternately. The governing equation for the harmonic electromagnetic field, which applies to the entire domain, is derived from Maxwell’s equations as follows¹⁴

j ω σ A - \frac{1}{μ} \nabla^{2} A = J_{s}

(1)

where $ω$ denotes the angular frequency, $σ$ is the electrical conductivity, and $μ$ is the permittivity of the material. By generating an excitation current density $J_{s}$ in the coil, we produce a magnetic vector potential $A$ and an eddy current density $J = j ω σ A$ in the workpiece. The heat source density $\overset{\cdot}{q}$ due to the Joule effect is a function of $J$ and is calculated as follows for use in the subsequent heat analysis

\overset{\cdot}{q} = \frac{{[Re (J)]}^{2}}{σ}

(2)

The Fourier equation is then applied to calculate the transient temperature field

ρ C_{P} \frac{\partial T}{\partial t} - \nabla \cdot (λ \nabla T) = \overset{\cdot}{q}

(3)

where $ρ$ is the density, $C_{P}$ is the specific heat, $λ$ is the thermal conductivity, and T is the temperature. The workpiece is subject to boundary conditions in terms of radiation and convection, which can be combined as follows

- λ \frac{\partial T}{\partial n} = h (T - T_{amb}) + ε σ_{b} (T^{4} - T_{ext}^{4})

(4)

where $n$ is the normal vector, h is the convection coefficient, $ε$ is the material emissivity, $σ_{b}$ is the Stefan–Boltzmann constant, $T_{amb}$ is the ambient temperature, and $T_{ext}$ is the temperature of the air close to the surface of the workpiece.

On the boundaries of the entire computational domain, magnetic and thermal insulation conditions apply, namely

n \times A = 0

(5)

n \cdot (λ \nabla T) = 0

(6)

To simulate the induction heating of the pipe with the lid, an additional contact pair analysis was conducted for the numerical model, including a thermal contact pair and an electrical contact pair.

The thermal contact pair analysis was based on the Cooper–Mikic–Yovanovich interfacial thermal resistance theory.¹⁵ This theory posits that the thermal streamlines at an interface become denser at discrete contact points that form because of the microscopic roughness of the materials in contact. Under the assumption of no friction loss, the heat fluxes at the contact between the lid and the pipe are calculated as

\begin{matrix} - n_{l} \cdot (- λ_{l} \nabla T_{l}) = - h_{j} (T_{p} - T_{l}) \\ - n_{p} \cdot (- λ_{p} \nabla T_{p}) = - h_{j} (T_{l} - T_{p}) \end{matrix}

(7)

where the indices l and p refer to the lid and pipe, respectively. The joint conductance at the interface, $h_{j}$ , is the sum of the constriction conductance $h_{c}$ at the microscopic contact points, the gap conductance $h_{g}$ , and the radiative conductance $h_{r}$ , namely

h_{j} = h_{c} + h_{g} + h_{r}

(8)

$h_{c}$ is given as a function of several microscopic contact parameters

h_{c} = 1.25 λ_{contact} \frac{m_{asp}}{σ_{asp}} {(\frac{p}{H_{c}})}^{0.95}

(9)

where $m_{asp}$ and $σ_{asp}$ are the average slope and height, respectively, of the microscopic roughness profile; p is the contact pressure; and $H_{c}$ is the micro-hardness. The harmonic mean of the conductivities for the contact pair, $λ_{contact}$ , was set equal to the $λ$ of 316LN in our case.

Similarly, the electrical contact pair is also subject to a contraction effect. Moreover, the air layer and oxide layer at the interface have a hindering effect on the electrical conduction. These effects lead to a significant decrease in the electrical conductivity at the interface; therefore, we simplified the electrical contact pair as a thin layer with a much lower conductance.

Simulation setup

For both models, the parameters of the boundary conditions were selected to represent typical working conditions. Because thermal radiation occurs predominantly in the high-temperature zone (greater than 800 °C) and the radiative power loss is quite limited compared with the heating power in this case, the variations in the emissivity $ε$ with temperature were not considered. Some articles have indicated that the $ε$ of 316LN depends on the actual conditions, but it is typically not lower than 0.80 at temperatures higher than 800 °C.^16,17 Therefore, we set $ε = 0.80$ . Under the assumption of no forced convection, the convection loss is much lower than the radiative loss.¹⁴ Therefore, we simply set the natural convection coefficient $h = 5 W / (m^{2} \cdot K)$ . The ambient temperature was assumed to be 20 °C.

For the heating problem with the lid, the interfacial thermal and electrical attributes involve many physical parameters; conservative estimates of these parameters were obtained from the literature and are listed in Tables 1 and 2.^18,19

Table 1.

Parameter values for the thermal contact pair.

Parameter	Conservative estimate
Gap conductance $h_{g}$	$400 W / (m^{2} \cdot K)$
Average asperity height $σ_{asp}$	$3.2 μ m$
Average asperity slope $m_{asp}$	0.4
Contact pressure p	$10 kPa$
Micro-hardness $H_{c}$	$1.519 GPa$

Table 2.

Parameter values for the electrical contact pair.

Parameter	Conservative estimate
Relative permeability $μ_{r}$	1
Relative permittivity $ε_{r}$	1
Electrical contact conductance $σ$	$80, 000 S / m$
Width of transition zone d	$0.01 m$

The load in the coil was selected to satisfy the heating requirements for the PUE process, namely, that the outer surface of the middle pipe section should be heated to 1200 °C–1250 °C within 1–2 min, with the inner surface reaching not less than 1100 °C. The excitation current density $J_{s}$ was assumed to be constant, with a typical order of magnitude of $10^{7} A / m m^{2}$ , neglecting the axial and radial components. We set $| J_{s} | = 40 \times 10^{6} A / m m^{2}$ , a heating frequency of 1000 Hz, and a heating time of 90 s.

Separate numerical simulations were performed using ANSYS and COMSOL Multiphysics. The grid generated in COMSOL is shown in Figure 5. Note that the current density is expected to vary considerably over the surface layer of the pipe because of the skin effect; therefore, a polarized mesh was used to reduce the computational error. The BiCGStab and GMRES solvers were applied to solve for the electromagnetic and temperature fields, respectively.

Figure 5.

Mesh generation in COMSOL (for the pipe without the lid).

Materials and methods for the experiments

To verify the simulations, induction heating experiments were performed using a semi-closed induction heating furnace. Because the furnace geometry was not identical to that in the models described above, the following approach was taken to verify the numerical analysis: (1) a pipe without a prefabricated hole was heated, temperature curves were measured at several axially distributed points, and these curves were compared with the results of a simulation under the same conditions to confirm the accuracy of the numerical method; and (2) then, a pipe with a prefabricated hole was heated to verify the phenomena observed in the simulations.

The experimental setup is illustrated in Figure 6: a 316LN pipe (D_o × D_i × L = 120 mm × 104 mm ×438 mm, 1:8 scale) was placed in a GT-300-1 medium-frequency induction heating furnace (Rontai, Shandong, China; as shown in Figure 7), with the symmetry plane of the pipe coinciding exactly with the end of the induction coil. K-type thermocouple wires and a TP-1000 temperature recorder (Toprie, Shenzhen, China) were used to record the temperatures at several axial points, whose locations are shown in Figure 8. A CY-RCT Rogowski coil (Chuangyin, Shenzhen, China) was used to measure the strength and frequency of the excitation current. The root mean square (RMS) of the excitation current was 1.74 kA, corresponding to an equivalent current density of $62.1 A / m m^{2}$ . The heating frequency was 480 Hz, and the total power was 66 kW. The heating duration was 600 s.

Figure 6.

Schematic diagram of the induction heating experiments.

Figure 7.

Induction heating device.

Figure 8.

Distribution of the temperature measurement points for experiment 1 (the pipe without the hole).

Results and analysis

Results and analysis of the simulations

The pipe without the lid

As shown in Figure 9, the temperature contours acquired after 90 s of heating using ANSYS and COMSOL are identical, with an error not greater than 2%. The prefabricated hole in the middle section of the pipe results in a non-uniform temperature field with a high local temperature: once the entire middle section of the pipe reaches 1250 °C, both axial sides of the prefabricated hole are at a temperature higher than 2000 °C, which is far above the melting point of 316LN (1400 °C). In reality, a temperature of 2000 °C would not be reached; such temperatures arose in the simulations only because melting was not considered. However, the simulation results indicate that the melted region would expand during the heating process, making it necessary to scrap the pipe.

Figure 9.

Temperature field results (for the pipe without the lid): (a) ANSYS and (b) COMSOL.

Figure 10 shows that the distortions in the temperature field on the axial sides of the prefabricated hole are caused by distortions in the eddy current field. In Figure 10(a), the eddy current field far from the prefabricated hole is uniformly distributed in the circumferential direction, but the eddy current field near the prefabricated hole is distorted. Figure 10(b) shows that the prefabricated hole exerts a splitting effect, leading to the changes in the directions of the eddy current vectors and a significant increase in the local current density. The magnitude of the current density at points C and D (Figure 10) is $10^{5} - 10^{6} A / m m^{2}$ , considerably lower than that of the excitation current. Meanwhile, the current that is diverted around the prefabricated hole becomes concentrated at points A and B, causing the current at these points to reach a considerably higher magnitude. Therefore, the heat generation rate and temperature at A and B increase sharply, whereas the temperature at C and D is lower than that in a pipe without a prefabricated hole. Similar distortion can also be observed in the magnetic field, as shown in Figure 11.

Figure 10.

Distribution of the eddy current field (in the pipe without the lid): (a) overall and (b) near the prefabricated hole.

Figure 11.

Global distribution of the magnetic field (in the pipe without the lid).

The pipe with the lid

As shown in Figure 12, when the other simulation settings remain unchanged, adding the lid improves the global temperature field of the pipe. After 90 s of heating, the heated region reaches an overall temperature of 1250 °C, with a maximum temperature of 1336 °C.

Figure 12.

Temperature contours after 90 s of heating (in the pipe with the lid).

Figure 13 shows the temperature distributions on the cross sections at z = 0, 36, 50, 100, 140, and 200 mm; with the exception of the case of z = 0 shown in Figure 13(a), in which the circumferential sides of the prefabricated hole reach a temperature higher than 1300 °C, the temperature distributions in these regions are quite uniform. As shown in Figure 14, the global eddy current field becomes uniform when the lid is used, and the eddy current flows through the lid so smoothly that the contraction on the axial sides no longer dominates.

Figure 13.

Temperature distributions on the cross sections at z = 0, 36, 50, 100, 140, and 200 mm (in the pipe with the lid).

Figure 14.

Global eddy current field distribution (in the pipe with the lid).

The distribution in Figure 13(a) is different from the others because z = 0 mm is the only cross section depicted in Figure 13 that includes the lid. As shown more clearly in Figure 15, there is a “jump” in temperature of approximately 100 °C at the interface of the contact pair, which is a spontaneous effect of the contraction of the thermal and eddy currents caused by the microscopic roughness of the surfaces in contact. Figure 13(a) also shows that the temperature in the lid is slightly lower than that in the pipe; the reason for this is that the eddy current generated in the lid itself, which is of a smaller order of magnitude, partially counteracts the current that is conducted from the interface into the lid. Despite the jump in the temperature at the interface, this behavior is considerably preferable to the distortion discussed above.

Figure 15.

Temperature distribution on the external surface of the cross section at z = 0 mm.

Figures 16 and 17 show the eddy current density and temperature distributions, respectively, in the radial direction on the cross sections at z = 36, 50, 75, and 100 mm. The eddy current is biased toward the external surface; however, because of surface radiation and convection, the point with the maximum temperature is located several millimeters below the external surface. This phenomenon is a result of both the skin effect and heat loss. For the cross sections at higher temperatures in Figure 17, the maximum is located deeper inside the material because the heat loss at the surface is greater.

Figure 16.

Eddy current density distributions in the radial direction on the cross sections at z = 36, 50, 75, and 100 mm.

Figure 17.

Temperature distributions in the radial direction on the cross sections at z = 36, 50, 75, and 100 mm.

Figure 18 shows the temperature curves at 10 axially distributed points on the cross sections at z = 36, 50, 100, 140, and 200 mm. A steady heating rate was assumed for the pipe with the lid, corresponding to the use of a constant power to heat the pipe. Both Figures 17 and 18 indicate a maximum temperature difference in the radial direction of less than 150 °C during the heating process, which satisfies the requirement that the entire middle section should reach the forging temperature approximately simultaneously.

Figure 18.

Temperature curves at key axial points. The solid and dashed lines correspond to points on the outer and inner surfaces, respectively.

As described above, the simulations yielded satisfying results. However, in other cases in which the outlines of the lid and the hole do not match well, there is still a risk of high local temperatures; this implies that the requirements for the geometric precision of the lid are quite high. Other specific measures for improving the thermal distribution in the pipe include removing any oxide coating or greasy dirt from the lid to ensure good conductivity and increasing the contact pressure between the interfacial surfaces to reduce the gap and mitigate the current contraction effect.

Results and analysis of the experiments

The temperature curves measured in experiment 1 for the pipe with no prefabricated hole are shown in Figure 19 (curves labeled 1–5). These curves show that the temperature increased approximately linearly up to 600 °C, above which point the heating rate began to decrease; the temperature increased only slightly thereafter, up to approximately 1100 °C. Below 600 °C, the eddy current heat dominated, and radiation loss was negligible; consequently, the temperature increased approximately linearly under the application of a constant power. In contrast, above 800 °C, the magnitude of the radiation loss was close to that of the heat generated by the eddy currents, so the temperature could not continue to rise at the same rate; finally, the system reached a dynamic balance at approximately 1100 °C. If a higher temperature were to be required, it would be necessary to apply more power at a higher frequency.

Figure 19.

Comparison of the temperature curves. The experimental curves are labeled 1–5; the simulated curves are labeled 1′-5′.

The simulated curves exhibit similar shapes to the experimental ones, as shown in Figure 19. The curves simulated for the points inside the coil (points 1 and 2) are particularly close to their experimental counterparts. Although there is a difference in temperature of tens of degrees between the experimental and simulated curves for points 4 and 5 after 400 s of heating, the general heating patterns are the same. Two possible reasons for the discrepancy between these curves can be identified: first, the heating conditions were simplified in the simulation, and several factors that might lead to such an error were not considered, such as the possibility of off-center placement and contact with the furnace; second, the physical parameters of the material were considered in the form of polynomial fits instead of diagrams, and fitting errors might exist. Despite the discrepancy, the above results demonstrate the accuracy of the numerical model.

In experiment 2, using the pipe with the prefabricated hole, the overheating at the axial sides of the prefabricated hole and the effect of the lid on improving the temperature field were verified. As shown in Figure 20(a), both axial sides of the prefabricated hole tended to overheat. If the pipe was to be continuously heated at a constant power, the overheated zone would melt at approximately 1400 °C (a temperature as high as 2000 °C, as indicated in Figure 9, would not be reached). In contrast, after the addition of the lid, the non-uniformity of the temperature field around the prefabricated hole was considerably mitigated. This phenomenon is also shown quantitatively in Figure 21 in the form of the temperature curves at points A and B. After a heating time of 150 s, in the case with the lid, the temperature at point A was 100 °C–200 °C lower than that in the case without the lid. Moreover, the temperature difference between A and B was also reduced; the remaining temperature difference can be primarily attributed to the fact that A was located deeper inside the induction coil.

Figure 20.

Comparison of the heating effect: (a) without a lid and (b) with a lid.

Figure 21.

Temperature curves at points A and B in Figure 20.

Further discussion

This section presents a parameter analysis to determine suitable parameter values for satisfying the previously stated heating requirements for the PUE processing of a nuclear main pipe. The related factors can be classified into three categories: (1) geometric parameters, including the size and shape of the coil and the gap between the coil and the pipe; (2) current parameters, including the excitation current frequency and density; and (3) other factors related to the actual working conditions, such as insulation measures and whether the pipe is placed in an eccentric orientation in the furnace. Based on the simulation of the pipe with the lid, this study primarily addresses the influences on the heating quality of the frequency, density, and strength of the excitation current; the thickness of the coil; and the gap between the coil and the pipe. Here, the heating quality is characterized in terms of the temperature difference between the inside and outside surfaces (ΔT); the heating time, defined as the time required for the outer surface of the middle section to reach 1250 °C; and the size of the heat-affected zone, defined as the axial distance from the end of the coil to the cross section at which the temperature is only 50 °C.

Influence of frequency

The control variable method was used in this study to analyze the influence of frequencies ranging from 500 to 4000 Hz. The current density was set to $40 A / m m^{2}$ , the equivalent thickness of the coil was set to 6 mm, and the gap between the coil and the pipe was set to 3 cm. The simulation results are shown in Figures 22 and 23.

Figure 22.

Relationship between the frequency and the heating time.

Figure 23.

Relationship between the frequency and the temperature difference between the inside and outside surfaces (ΔT).

The above figures indicate that when all the other factors are held constant, a higher frequency leads to a shorter heating time and a larger temperature difference between the inside and outside surfaces. The formula for the current penetration depth δ is as follows²⁰

δ = 503 \sqrt{\frac{ρ}{μ_{r} f}}

(10)

$ρ$ is the resistivity of the material $(Ω \cdot m)$ $μ_{r}$ is the relative permeability of the material, and f is the frequency (Hz).

According to this formula, as the frequency increases, δ decreases, intensifying the skin effect. Although frequency is not an energy parameter, the energy will also be more strongly concentrated in the surface layer, resulting in a greater ΔT and a reduction in the time required for the outer surface to reach the desired temperature.

Influence of current density

For a frequency of 1000 Hz, an equivalent coil thickness of 6 mm, and a gap width of 3 cm, the influence of the current densities in the range of $20 - 80 A / m m^{2}$ was analyzed, as shown in Figures 24 and 25. Increasing the current density leads to a shorter heating time and a larger ΔT. Because the current density is positively correlated with the heating power, a higher current density implies a higher heating rate and a shorter heating time; the absolute gap in the eddy current density along the radial direction also increases, as does the temperature difference between the inside and outside surfaces.

Figure 24.

Relationship between the current density and the heating time.

Figure 25.

Relationship between the current density and ΔT.

During induction heating, the excitation current will be redistributed in the coil in accordance with the skin effect; therefore, it is more convenient to control the current strength than the current density.

Influence of the gap between the coil and the pipe

For gap widths ranging between 0.5 and 6 cm, the influence of the gap between the coil and the pipe was analyzed for a frequency of 1000 Hz, a current density of $40 A / m m^{2}$ , and an equivalent coil thickness of 6 mm. The simulation results indicate that the width of the gap has only a slight impact on the heating time and the temperature difference ΔT but is positively correlated with the size of the heat-affected zone, as shown in Figure 26. When the gap width decreases, the magnetic field becomes more concentrated inside the coil, reducing the size of the heat-affected zone.

Figure 26.

Relationship between the gap width and the size of the heat-affected zone.

In summary, the parameters investigated above have the following effects: (1) the strength of the excitation current predominantly determines the heating time, whereas the frequency also influences the heating time; (2) the frequency predominantly determines the temperature difference between the inside and outside surfaces (ΔT), whereas the current strength also influences ΔT; and (3) the width of the gap between the coil and the pipe predominantly determines the size of the heat-affected zone. For a 1:5-scale model, it is preferable for the product of the equivalent thickness of the coil and the current density to be in the $200 - 280 A / mm$ range and for the gap to be 1–3 cm. Such parameter values can guarantee a 1–2 min heating time, a ΔT of <100 °C, and a heat-affected zone of <60 mm.

Conclusion

Induction heating is a potential online local heating method for processing AP1000 nuclear main pipes using the partial upset-extrusion technique. However, to enable the application of this heating method for this purpose, the heating pattern of this abnormally shaped type of pipe must be thoroughly investigated. In this article, we report on the induction heating of a pipe with a prefabricated hole during the PUE process. Both numerical and experimental studies revealed a tendency toward overheating close to the prefabricated hole, which is caused by the distortion of the eddy current field in the pipe. It was proven that by covering the prefabricated hole with a lid, the eddy current can be conducted from the pipe into the lid, thereby mitigating the non-uniformity of the temperature field. Based on the simulations of a model with such a lid, the excitation current density and frequency and the gap between the coil and the pipe were verified to be the dominant factors determining the induction heating quality, and the values of these parameters were optimized to satisfy the requirements of the partial upset-extrusion technique. This method was demonstrated to be a feasible online local heating solution that can be applied for the integral processing of AP1000 nuclear main pipes.

Footnotes

Academic Editor: Jiin-Yuh Jang

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This research was supported by the National Science and Technology Major Project of China (grant no. 2012ZX0401008) and the National High-tech R&D Program of China (863 Program, grant no. 2012AA040202).

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