Development of one-dimensional two-fluid model with consideration of void fraction covariance effect

Figures & data

Table 1. Constitutive equations implemented in TRAC-BF1 code

Item	Model
Distribution parameter, C0	$C_0=1.1-0.1\sqrt{\frac{{\rho }_g}{{\rho }_f}},\mathrm{for}\mathrm{bulk}\mathrm{boiling}\mathrm{condition}$ [11, 12]
	$C_0=\left(1.1-0.1\sqrt{\frac{{\rho }_g}{{\rho }_f}}\right)\left(1-e^{-12.1{⟨{\alpha }_g⟩}^{0.701}}\right),\mathrm{for}\mathrm{sub}\text{-}\mathrm{cooled}\mathrm{boiling}\mathrm{condition}$ [17]
Drift velocity, ⟨⟨vgj⟩⟩	$\begin{array}{c}⟨⟨V_{gj}^{+}⟩⟩+⟨⟨V_{gj,B}^{+}⟩⟩exp\left(-1.39⟨J_g^{+}⟩\right)+⟨V_{gj,P}^{+}⟩\left\{1-exp\left(-1.39⟨J_g^{+}⟩\right)\right\}\hfill \end{array}\left[26\right]$
	$⟨V_{gj,B}^{+}⟩=\sqrt{2}{\left(1-⟨\alpha ⟩\right)}^{1.75}\left[10\right]$
	$\begin{array}{c}\mathrm{when}{N}_{uf}\le 2.25\times {10}^{-8}\hfill \\ ⟨⟨V_{gj,P}^{+}⟩⟩=0.0019{\left(D_H^{+}\right)}^{0.809}{\left(\frac{{\rho }_g}{{\rho }_f}\right)}^{-0.157}{N}_{\mu f}^{-0.562}for{D}_H^{+}\le 30\hfill \\ ⟨⟨V_{gj,P}^{+}⟩⟩=0.030{\left(\frac{{\rho }_g}{{\rho }_f}\right)}^{-0.562}{N}_{\mu f}^{-0.562}for{D}_H^{+}\ge 30\hfill \\ \mathrm{when}{N}_{\mu f}\ge 2.25\times {10}^{-3}\hfill \\ ⟨⟨V_{gj,P}^{+}⟩⟩=0.92{\left(\frac{{\rho }_g}{{\rho }_f}\right)}^{-0.157}\mathrm{for}{D}_H^{+}\ge 30\left[27\right]\hfill \end{array}$
	$⟨⟨V_{gj}^{+}⟩⟩=\frac{⟨⟨v_{gj}⟩⟩}{{\left(\frac{\sigma g\Delta \rho }{{\rho }_f^2}\right)}^{1/4}},⟨j_g^{+}⟩=\frac{⟨j_g⟩}{{\left(\frac{\sigma g\Delta \rho }{{\rho }_f^2}\right)}^{1/4}},D_H^{+}=\frac{D_H}{\sqrt{\frac{\sigma }{g\Delta \rho }}},N_{\mu f}=\frac{{\mu }_f}{{\left({\rho }_f\sigma \sqrt{\frac{\sigma }{g\Delta \rho }}\right)}^{1/2}}$
Void fraction covariance, Cα	$C_{\alpha ,\mathrm{BB}}=1+\left\{9.38{\left(⟨{\alpha }_g⟩-0.5\right)}^4+0.414\right\}\left\{1-{\left(\frac{{\rho }_g}{{\rho }_f}\right)}^2\right\}⟨{\alpha }_f⟩$ [17]
	$C_{\alpha ,\mathrm{SB}}=\frac{0.190}{{⟨{\alpha }_g⟩}^{0.855}}$ [17]
	Cα(⟨αg⟩) = max (Cα, SB, Cα, BB)for⟨αcrit⟩ > ⟨αg⟩
	$C_{\alpha }\left(⟨{\alpha }_g⟩\right)=\frac{1-C_{\alpha }\left(⟨{\alpha }_{\mathrm{crit}}⟩\right)}{1-\left(⟨{\alpha }_{\mathrm{crit}}⟩\right)}\left(⟨{\alpha }_g⟩-1\right)+1\mathrm{for}⟨{\alpha }_{\mathrm{crit}}⟩\le ⟨{\alpha }_g⟩$
	⟨αcrit⟩ = 0.84

Figure 1. Void fraction covariance and relative velocity covariance calculated by Ozaki and Hibiki [17] model at a pressure of 7 MPa.

Figure 2. Calculation model and nodalization of TRAC-BF1 for rod bundle under two-phase flow (steady-state simulation case).

Table 2. Boundary conditions of inlet flow rate, outlet pressure and bundle power conditions for steady-state simulations

Run	Inlet mass	Mass flux in	Outlet pressure	Bundle power
no.	flow rate (kg/s)	bundle (kg/m^2s)	(MPa)	(MW)
1	1.5	154	7.0	1.5
2	2.0	205	7.0	1.7
3	2.5	256	7.0	1.9
4	3.0	308	7.0	2.1
5	3.5	359	7.0	2.3
6	4.0	410	7.0	2.5
7	5.0	513	7.0	2.9
8	10.0	1025	7.0	4.9
9	15.0	1538	7.0	6.9

Figure 3. Comparisons of axial void fraction profiles for steady-state simulation cases at targeted void fraction of 0.8 and mass flow rate of (a) 5, (b) 10, and (c) 15 kg/s.

Figure 4. Comparisons of the void fraction at (a) 26th cell, (b) 35th cell, (c) 40th cell, and (d) 45th cell from the inlet of CHAN component with the conditions of mass flux.

Figure 5. Calculation model and nodalization of TRAC-BF1 for rod bundle under two-phase flow (transient simulation case).

Table 3. Pressure boundary conditions and initial power and void fraction conditions for transient simulations

Run	Inlet pressure	Outlet pressure	Initial bundle	Initial targeted outlet
no.	(MPa)	(MPa)	power (MW)	void fraction (-)
10	7.04	7.0	1.15	0.4
11	7.04	7.0	1.50	0.5
12	7.04	7.0	2.03	0.6
13	7.05	7.0	2.95	0.7

Figure 6. Bundle power perturbation applied for transient simulation case.

Figure 7. Comparison of area-averaged void fraction trend at the 45th cell from the inlet of CHAN component.

Figure 8. Comparison of inlet flow rate of CHAN component.

Figure 9. Comparisons of dumping ratio for inlet flow rate and void fraction oscillation.

Ozaki T, Hibiki T. Modeling of distribution parameter, void fraction covariance and relative velocity covariance for upward steam-water boiling flow in vertical rod bundle. J Nucl Sci Technol. 2018; 55:386–399.

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