CFD in Supercritical Water-cooled Nuclear Reactor (SCWR) with - - PDF document

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CFD in Supercritical Water-cooled Nuclear Reactor (SCWR) with Horizontal Tube Bundles

Zhi Shang Kingston University Faculty of Engineering, London SW15 3DW, UK shangzhi@tsinghua.org.cn Simon Lo CD-adapco Trident House, Basil Hill Road, Didcot OX11 7HJ, UK simon.lo@uk.cd-adapco.com ABSTRACT The commercial CFD code STAR-CD 4.02 is used as a numerical simulation tool for flows in the supercritical water-cooled nuclear reactor (SCWR). The basic heat transfer element in the reactor core can be considered as round tubes and tube bundles. Reactors with vertical or horizontal flow in the core can be found. In vertically oriented core, symmetric characters of flow and heat transfer can be found and two-dimensional analyses are often performed. However, in horizontally oriented core the flow and heat transfer are fully three-dimensional due to the buoyancy effect. In this paper, horizontal tubes and tube bundles at SCWR conditions are studied. Special STAR-CD subroutines were developed by the authors to correctly represent the dramatic change in physical properties of the supercritical water with

• temperature. From the study of single round tubes, the Speziale quadratic non-linear high-Re

k-ε turbulence model with the two-layer model for near wall treatment is found to produce the best results in comparison with experimental data. In tube bundle simulations, it is found that the temperature is higher in the top half of the bundle and the highest tube wall temperature is located at the outside tubes where the flow rate is the lowest. The secondary flows across the bundle are highly complex. Their main effect is to even out the temperature over the area within each individual recirculating region. Similar analysis could be useful in design and safety studies to obtain optimum fuel rod arrangement in a SCWR. KEYWORDS CFD, supercritical water reactor, turbulence model, heat transfer, tube bundle

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• 1. INTRODUCTION

Although heat transfer in supercritical water (SCW) flows has been studied for decades, the subject continues to receive great attention from the research community partly because of its scientific interest and partly because of the interest in using supercritical water in nuclear

• reactors. The Atomic Energy of Canada Limited (AECL) has announced a long-term plan to

develop the supercritical water reactor (SCWR) CANDU [1] as their core nuclear reactor

• technology. Comparing with the current light water reactors (LWR) of generation III and III+

[1], the next generation (Generation IV) nuclear reactors will have much higher thermal

• efficiency. SCWR is a candidate for the Generation IV reactor and several designs have been

studied by Oka et al and Mori et al [2-5]. Figures 1 and 2 show the two basic designs of SCWR. They can be divided into the vertical and horizontal flow types. The study of flow and heat transfer in SCWR must therefore consider these two flow orientation systems. The vertical system has already been studied by several researchers [8-11], the horizontal system is considered in this paper.

• Fig. 1 Vertical flow system in Japanese and European designs

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T1, P1 T2, P2 T3, P3 T1, P1 T2, P2 T3, P3 T1, P1 T2, P2 T3, P3

H.P.

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CONDENSER

H.P.

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CONDENSER

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• Fig. 2 Horizontal flow system in the Canadian design

Supercritical water has some very specific thermal-physical properties that lead to special heat transfer characteristics. At the supercritical pressures there is no phase change from liquid to vapor and the thermal-physical properties have sharp changes in the vicinity of the pseudo- critical temperature, see Figure 3.

200 400 600 800 1000 1200 200 400 600 800 1000

Density Density (kg/m3) Bulk Temperature (

• C)

200 400 600 800 1000 1200 0.00 2.50x10

• 5

5.00x10

• 5

7.50x10

• 5

1.00x10

• 4

1.25x10

• 4

Molecular viscosity Molecular viscosity (Pa s)

200 400 600 800 1000 1200 0.00 0.15 0.30 0.45 0.60 0.75

Thermal conductivity Thermal conductivity (W/m K)

200 400 600 800 1000 1200 25 50 75 100 125

Specific heat Specific heat (kJ/kg K)

• Fig. 3 Variations of thermal-physical properties of SCW under 25MPa

In this paper, the thermal-physical properties are calculated based on the latest data published by the International Association of Properties of Water and Steam (IAPWS). According to the IAPWS data the thermal conductivity, density, molecular viscosity and specific heat are coded in the appropriate user subroutines in STAR-CD for calculations.

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• 2. PHYSICAL PROBLEM AND COMPUTATIONAL PARAMETERS

2.1. Horizontal Tube Horizontal tube and tube bundle are studied in this paper. In a horizontal tube flow, buoyancy affects both the flow and heat transfer. This combined effect often leads to different wall temperatures and heat transfer coefficients on the top and bottom surfaces of the tube. The horizontal tube flow is fully three-dimensional (3D) and cannot be simplified to 2D or quasi- 3D flow as often done for vertical tube flows [8-11]. Figure 4 shows the geometry of the test case studied. The calculation parameters and boundary conditions are listed in Table 1 [7]. The flow enters the tube with uniform mass flux, is heated by the wall with uniform heat flux in Table 1 and flows out the tube from the outlet. STAR-CD can automatically choose the suitable outflow boundary conditions for the numerical simulations.

• Fig. 4 Geometry of the horizontal tube

Table 1 Parameters of the horizontal tube test case Parameters (boundary conditions) Value Units Mass flux (inlet) 340 kg/m2s Heat flux (wall) 300 kW/m2 Pressure (reference) 24.4 MPa

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5 / 14 2.2. Horizontal Tube Bundle in a Cylinder Figure 5 shows the geometry of the horizontal tube bundle in a cylinder. Table 2 shows the calculation parameters and boundary conditions used [11]. Again fully developed flow is assumed at the outlet. Figure 6 shows the computational mesh at a cross section. Finer meshes are employed in the near wall regions to resolve the flow and thermal boundary layers at the wall.

• Fig. 5 Geometry of the horizontal tube bundle in a cylinder
• Fig. 6 Mesh distribution at a cross section

Table 2 Parameters of the horizontal tube bundle test case Parameters (boundary conditions) Value Units Mass flux (inlet) 1050 kg/m2s Heat flux (wall) 600 kW/m2 Pressure (reference) 25 MPa

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• 3. RESULTS AND ANALYSES

It is well known that the accuracy of the CFD results is strongly dependent on the turbulence model used. Several turbulence models are tested to determine their suitability of modeling supercritical water flows. Tests of the turbulence models are carried out for the horizontal tube

• case. The chosen turbulence model is then applied to the tube bundle test case afterwards.

3.1. Horizontal Tube Previous studies on supercritical water flow and heat transfer in vertical tubes have concluded that CFD methods can be employed to study the heat transfer phenomena of supercritical water with the rapid changes of thermal-physical properties near the pseudo-critical temperature [8-11]. Heat transfer in a horizontal tube is much more complex than the vertical systems. Due to the buoyancy effect the wall temperature distributions at the top and bottom surfaces are different [7]. Secondary flow can also be found across the tube. Previous CFD study using the STAR- CD code [12] revealed that the non-linear turbulence model, which includes anisotropic effects, could capture the secondary flow better. In the vertical tube studies, it was found that Speziale quadratic non-linear high-Re k-ε turbulence model gives good results comparing with experimental data [6]. Comparison studies of three non-linear turbulence models provided by the STAR-CD code are conducted. These studies include the Speziale quadratic high-Re k-ε turbulence model, the standard quadratic high-Re k-ε turbulence model and the standard cubic high-Re k-ε turbulence model. All simulations use the two-layer (Hassid and Poreh) model for the near- wall treatment [9] and keeping y+<1 in the near well cells. In order to keep the y+<1, the stretched structure mesh partition near the tube wall is adopted. Figure 7 shows the comparisons of computed results from CFD based on 3D simulations against the experimental data of Bazargan et al [7]. Heat transfer coefficients along the top and bottom surface of the tube from inlet to outlet are plotted against bulk temperature, fluid temperature averaged across the tube.

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250 300 350 400 450 500 550 600 650 2 4 6 8 10 12 14

Heat Transfer Coefficients (kW/m

2

• C)

Bulk Temperature (

• C)

Experiment Data Speziale quadratic high Re k-ε Standard quadratic high Re k-ε Standard cubic high Re k-ε Bottom Surface

(a) Bottom surface

250 300 350 400 450 500 550 600 650 2 4 6 8 10 12 14

Experiment Data Speziale quadratic high Re k-ε Standard quadratic high Re k-ε Standard cubic high Re k-ε Heat transfer Coefficients (kW/m

2

• C)

Bulk Temperature (

• C)

Top Surface

(b) Top surface

• Fig. 7 Comparison of turbulence models on heat transfer coefficients.

It can be seen that the Speziale quadratic high-Re k-ε turbulence model gives the best results comparing with the experimental data [7]. Results from the other two models are rather poor and some extremely large oscillations can be seen in the vicinity of the pseudo-critical temperature. (a) Temperature distribution (b) Secondary flow

• Fig. 8 Temperature and secondary flow along tube length.

Figure 8 shows the temperature distribution and the secondary flows at the different cross sections along the tube length. Figure 8(a) shows the fluid and tube wall temperatures increase from inlet to outlet due to heating along the tube. It is interesting to note the wall temperature distribution in the circumferential direction is fairly uniform when the

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8 / 14 temperature is lower than 350oC or higher than 550oC but rather non-uniform within this temperature range from the contour lines. This temperature range happens to cover the sharp changes in physical properties in the vicinity of the pseudo-critical temperature shown in Figure 3. It is interesting to note in Figure 8(b) that the secondary flow is stronger in locations within this temperature range from the vector plots. These results indicate that the physical properties of the supercritical water in the vicinity of the pseudo-critical temperature have strong effects on the fluid flow and heat transfer with buoyancy as the main contributing factor. 3.2. Horizontal Tube Bundle in a Cylinder Since the heat transfer element in a reactor is usually in form of a tube bundle, it is necessary to study the flow and heat transfer inside a tube bundle. Figure 5 shows the geometry of the tube bundle studied. According to the design of Cheng [11], the tube diameter is 8mm, pitch is 10mm and bundle length is 3000mm. The tube walls have the heat flux given in table 2. The

• utside cylinder wall is adiabatic.

3.2.1. Mesh sensitive study The mesh sensitivity study is aimed to eliminate numerical effects due to the size of computational meshes and their distributions. Table 3 lists the three meshes used in this study. In all the three cases y+ is kept less than 1 in the near wall cells with the stretched mesh partitions same as the horizontal tube. These meshes were constructed by varying number of elements in each direction in order to fully assess the mesh sensitivity. During the mesh sensitive studies, the flow parameters are kept unchanged as listed in Table 2.

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9 / 14 Table 3. Meshes of the horizontal tube bundle Mesh Number of computational cells 1 1,188,000 2 792,000 3 396,000 Three monitoring points are defined to monitor the flow behaviour at critical areas during the computations, see Figure 6. According to the reactor design, the maximum tube wall temperature is one of the critical criteria for safe operation of the reactor [3-5]. The sensitive study is therefore focused on the wall temperature variations at the three monitoring points along the bundle. The monitoring points are selected to cover the maximum, minimum and the mid-range wall temperatures in the bundle. Figure 9 shows the results of the mesh sensitivity study. It can be seen that the temperature profiles obtained from the three meshes are almost the same at the three monitoring points. Table 4 gives the relative error among the test cases with Mesh 1 as the reference. The maximum relative error is around 1%. Numerical errors from the mesh partitions can therefore be ignored. With the consideration of computing efficiency and numerical accuracy, Mesh 2 which is enough to keep the accuracy of the numerical simulations was chosen for the analyses presented in this paper. Table 4. Relative error of mesh sensitive tests Mesh Error at point 1 |TMesh1 – TMesh|/TMesh1 Error at point 2 |TMesh1 – TMesh|/TMesh1 Error at point 3 |TMesh1 – TMesh|/TMesh1 1 0.000 0.000 0.000 2 0.005 0.001 0.001 3 0.011 0.009 0.011

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0.0 0.5 1.0 1.5 2.0 2.5 3.0

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350 400 450 500 550 600 650

Temperature (

• C)

z (m) case 1 case 2 case 3 At point 1

(a) Point 1

0.0 0.5 1.0 1.5 2.0 2.5 3.0 380 400 420 440 460 480

temperature (

• C)

z (m) case 1 case 2 case 3 At point 2

(b) Point 2

0.0 0.5 1.0 1.5 2.0 2.5 3.0 370 380 390 400 410 420 430 440 450

Temperature (

• C)

z (m) case 1 case 2 case 3 At point 3

(c) Point 3

• Fig. 9 Temperature profile of mesh sensitive tests

3.2.2. Numerical Results Figure 10 shows the temperature distribution in the tube bundle. Due to the buoyancy effect, the higher temperature (low density) fluid moves to the top region and the lower temperature (high density) fluid moves to the bottom. The maximum temperature is located at the top row

• f tubes near the outlet. The tube wall temperature is non-uniform both in the axial and

circumferential directions. This non-uniformity in the tube wall temperature can cause thermal stresses and must be given attention during the design stage.

• Fig. 10 Temperature distribution in the tube bundle

Figure 11 shows the temperature distribution at a cross section near the outlet, z=2.7m. The highest temperature can be found at the top and outer tubes (no.1, 2, 5 and 6). Temperatures of the bottom and middle tubes are lower.

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• Fig. 11 Temperature distribution at the cross section z=2.7m

Figure 12 shows the corresponding distributions of density and axial velocity that affect the convective heat transfer. It can be seen in Figure 12(a) that due to buoyancy the higher density (low temperature) fluid settles to the bottom region and lower density (high temperature) fluid rises to the top. Since lighter fluid is easier to accelerate, higher velocity is therefore found in the top region and lower velocity in the bottom as shown in Figure 12(b). (a) Density distribution (b) Axial velocity magnitude distribution

• Fig. 12 Density and velocity magnitude distribution at the cross section z=2.7m

The combined effect of density and velocity discussed above can be described in terms of mass flux ( w w v u ρ ρ ≈ + +

2 2 2

). The mass flux distribution at cross section z=2.7m is

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12 / 14 shown in Figure 13. It can be seen that the mass flux is lower in the high temperature regions indicating the lack of fluid flow to carry the accumulated heat away causes the higher fluid and wall temperatures in these areas as shown in Figure 11.

• Fig. 13 Mass flux distribution at the cross section z=2.7m

Figure 14 shows the secondary flows at the cross section z=2.7m. The magnitude of the velocity is indicated by the secondary mass flux defined as

2 2

v u + ρ . It can be seen that the secondary flows are highly complex. The maximum velocity is located between tubes 1 and 6. In this region, the fluid is driven by buoyancy up from the top of tube 7 and is further heated by tubes 1 and 6. Due to the converging effect created by tubes 1 and 6, the fluid is accelerated to give the strongest upward velocity in the narrow gap region even thought the temperature locally is not the highest. The minimum velocity is found around tube 7. The flow pattern of the secondary flow is strongly dependent on the geometry. The secondary flow tends to even out the temperature within the area of recirculation.

• Fig. 14 Secondary flow distribution at the cross section z=2.7m

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13 / 14 3.2.3. Computing time The calculations presented in this paper were performed on a computer with a 2.40GHz Intel Core, 2 CPU and 3.24GB of RAM for parallel calculations. The single round tube case took about 8 hours and the tube bundle case took 20 hours. 4. CONCLUSIONS Flow and heat transfer of supercritical water in horizontal tube and horizontal tube bundle are studied using the STAR-CD CFD software. The Speziale quadratic high-Re k-ε turbulence model with the two-layer model for near wall treatment is found to predict the heat transfer coefficient in good agreement with experimental data. The model is found suitable for the simulation of supercritical water flows in horizontal tubes and tube bundles, hence should also be suitable for studying SCWR core design. From the simulations of a horizontal tube bundle, it is found that the temperature is non- uniformly distributed both axially and across the bundle. The mass flux across the bundle is also non-uniform. It is believed that these non-uniformities are caused by the buoyancy effect. The secondary flows across the bundle are very complex and they tend to even out the temperature within the recirculating region. The results are found to be symmetrical above the vertical central plane so that only half of the geometry needs to be modeled in future analyses. REFERENCES

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