Improved drift-flux correlation to enhance the prediction of void fraction in nuclear reactor fuel bundles at low flow and elevated pressure conditions

Figures & data

Figure 1. Drift-flux correlation development timeline.

Table 1. Relevant drift-flux correlations.

Reference	C0 correlation	≪vgj≫ correlation
Ishii [24]	$\begin{array}{rl}& C_0=C_{\mathrm{\infty }}-\left(C_{\mathrm{\infty }}-1\right)\sqrt{\frac{{\rho }_g}{{\rho }_f}}\\ & C_{\mathrm{\infty }}=1.2\end{array}$	$⟨⟨v_{gj}⟩⟩=\sqrt{2}{\left(\frac{\sigma g\mathrm{\Delta }\rho }{{\rho }_f^2}\right)}^{1/4}{\left(1-⟨\alpha ⟩\right)}^{1.75}$
EPRI [16]	$\begin{array}{rl}& C_0=\frac{L}{K_0+\left(1-K_0\right){⟨\alpha ⟩}^r}\\ & L=\frac{1-e^{-C_1⟨\alpha ⟩}}{1-e^{-C_1}},C_1=\frac{4P_{crit}^2}{P\left(P_{crit}-P\right)}\\ & K_0=B_1+\left(1-B_1\right){\left(\frac{{\rho }_g}{{\rho }_f}\right)}^{1/4},r=\frac{1+1.57\left(\frac{{\rho }_g}{{\rho }_f}\right)}{1-B_1}\\ & B_1=min\left(0.8,\frac{1}{1+exp\left(\frac{-Re}{60000}\right)}\right),Re=max\left(R{e}_f,R{e}_g\right)\end{array}$	$\begin{array}{rl}& ⟨⟨v_{gj}⟩⟩=1.41{\left(\frac{g\sigma \mathrm{\Delta }\rho }{{\rho }_f^2}\right)}^{1/4}{C}_2{C}_3{C}_4{C}_9\\ & C_2=\left\{\begin{array}{c}0.4757{\left(ln\left(\frac{{\rho }_g}{{\rho }_f}\right)\right)}^{0.7}\mathrm{i}\mathrm{f}\frac{{\rho }_f}{{\rho }_g}\le 18\\ \left\{\begin{array}{c}1\\ \\ \\ \mathrm{i}\mathrm{f}{C}_5\ge 1\\ {\left(1-exp\left(\frac{-C_5}{1-C_5}\right)\right)}^{-1}\mathrm{i}\mathrm{f}{C}_5<1\end{array}\right.\mathrm{i}\mathrm{f}\frac{{\rho }_f}{{\rho }_g}>18\end{array}\right.\\ & C_3=max\left(0.5,2exp\left(\frac{-\left|R{e}_f\right|}{60000}\right)\right)\\ & C_4=\left\{\begin{array}{c}1\mathrm{i}\mathrm{f}{C}_7\ge 1\\ {\left(1-exp\left(\frac{-C_7}{1-C_7}\right)\right)}^{-1}\mathrm{i}\mathrm{f}{C}_7<1\end{array}\right.\\ & C_5=\sqrt{150\frac{{\rho }_g}{{\rho }_f}},C_7={\left(\frac{0.09144}{D_H}\right)}^{0.6},C_9={\left(1-⟨\alpha ⟩\right)}^{B_1}\end{array}$
Kataoka and Ishii [25]	$\begin{array}{c}{C}_0=C_{\mathrm{\infty }}-\left(C_{\mathrm{\infty }}-1\right)\sqrt{\frac{{\rho }_g}{{\rho }_f}}\\ C_{\mathrm{\infty }}=1.2\end{array}$	$\begin{array}{rl}& \mathrm{w}\mathrm{h}\mathrm{e}\mathrm{n}{\mathrm{N}}_{\mu f}\le 2.25\times {10}^{-3}\\ & ⟨⟨V_{gj}^{+}⟩⟩=\left\{\begin{array}{c}0.0019{\left(D_H^{+}\right)}^{0.809}{\left(\frac{{\rho }_g}{{\rho }_f}\right)}^{-0.157}{N}_{\mu f}^{-0.562}\mathrm{f}\mathrm{o}\mathrm{r}{D}_H^{\ast }\le 30\\ 0.030{\left(\frac{{\rho }_g}{{\rho }_f}\right)}^{-0.157}{N}_{\mu f}^{-0.562}\\ \mathrm{f}\mathrm{o}\mathrm{r}{D}_H^{\ast }>30\\ \end{array}\right.\\ & \mathrm{w}\mathrm{h}\mathrm{e}\mathrm{n}{N}_{\mu f}\ge 2.25\times {10}^{-3}\\ & ⟨⟨V_{gj}^{+}⟩⟩=0.92{\left(\frac{{\rho }_g}{{\rho }_f}\right)}^{-0.157}\mathrm{f}\mathrm{o}\mathrm{r}{D}_H^{\ast }\ge 30\\ \end{array}$
Hibiki and Ishii [2]	$\begin{array}{rl}& C_0\mathrm{a}\mathrm{n}\mathrm{d}⟨⟨v_{gj}⟩⟩\mathrm{d}\mathrm{e}\mathrm{p}\mathrm{e}\mathrm{n}\mathrm{d}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{o}\mathrm{n}\mathrm{f}\mathrm{l}\mathrm{o}\mathrm{w}\\ & \mathrm{r}\mathrm{e}\mathrm{g}\mathrm{i}\mathrm{m}\mathrm{e}\mathrm{a}\mathrm{n}\mathrm{d}\mathrm{i}\mathrm{n}\mathrm{l}\mathrm{e}\mathrm{t}\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{d}\mathrm{i}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s}\end{array}$	$\begin{array}{rl}& ⟨⟨V_{gj}^{+}⟩⟩=⟨⟨V_{gj,B}^{+}⟩⟩e^{\left(-1.39⟨j_g^{+}⟩\right)}+⟨⟨V_{gj,P}^{+}⟩⟩\left[1-e^{\left(-1.39⟨j_g^{+}⟩\right)}\right]\\ & ⟨⟨V_{gj,B}^{+}⟩⟩=\sqrt{2}{\left(1-⟨\alpha ⟩\right)}^{1.75}\\ & ⟨⟨V_{gj,P}^{+}⟩⟩=\mathrm{K}\mathrm{a}\mathrm{t}\mathrm{a}\mathrm{o}\mathrm{k}\mathrm{a}\text{\&}\mathrm{I}\mathrm{s}\mathrm{h}\mathrm{i}\mathrm{i}(1987)\end{array}$
Ozaki et al. [17] Ozaki and Hibiki [18]	$\begin{array}{rl}& C_0=C_{\mathrm{\infty }}-\left(C_{\mathrm{\infty }}-1\right)\sqrt{\frac{{\rho }_g}{{\rho }_f}}\\ & C_{\mathrm{\infty }}=1.10\end{array}$	$⟨⟨V_{gj}^{+}⟩⟩=⟨⟨V_{gj,B}^{+}⟩⟩e^{\left(-1.39⟨j_g^{+}⟩\right)}+⟨⟨V_{gj,P}^{+}⟩⟩\left[1-e^{\left(-1.39⟨j_g^{+}⟩\right)}\right]$
Clark et al. [6]	$C_0=C_{\mathrm{\infty }}-\left(C_{\mathrm{\infty }}-1\right)\sqrt{\frac{{\rho }_g}{{\rho }_f}}{C}_{\mathrm{\infty }}=\left\{\begin{array}{c}{C}_{\mathrm{\infty }L}\mathrm{f}\mathrm{o}\mathrm{r}⟨j^{+}⟩\le {⟨j^{+}⟩}_{C_{\mathrm{\infty }}max}\\ C_{\mathrm{\infty }H}\mathrm{f}\mathrm{o}\mathrm{r}⟨j^{+}⟩>{⟨j^{+}⟩}_{C_{\mathrm{\infty }}max}\end{array}\right\}{C}_{\mathrm{\infty }H}\left(⟨j^{+}⟩\right)=1.1+1.84e^{-0.100⟨j^{+}⟩}{C}_{\mathrm{\infty }L}=\left[\frac{C_{\mathrm{\infty }H}\left({⟨j^{+}⟩}_{C_{\mathrm{\infty }}max}\right)-1}{{⟨j^{+}⟩}_{C_{\mathrm{\infty }}max}-⟨j_f^{+}⟩}\right]\left(⟨j_g^{+}⟩\right)+1{⟨j^{+}⟩}_{C_{\mathrm{\infty }}max}=m⟨j_f^{+}⟩+bm=\frac{1}{1-{⟨\alpha ⟩}_{crit}{C}_0};b=\frac{⟨⟨V_{gj}^{+}⟩⟩{⟨\alpha ⟩}_{crit}}{1-{⟨\alpha ⟩}_{crit}{C}_0}{⟨\alpha ⟩}_{crit}=min\left(0.0284⟨j_f^{+}⟩+0.125,0.52\right)$	$⟨⟨V_{gj}^{+}⟩⟩=⟨⟨V_{gj,B}^{+}⟩⟩e^{\left(-1.39⟨j_g^{+}⟩\right)}+⟨⟨V_{gj,P}^{+}⟩⟩\left[1-e^{\left(-1.39⟨j_g^{+}⟩\right)}\right]$

Figure 2. Velocity scaling of drift-flux parameters.

Figure 3. Distribution parameter of Clark et al. correlation [5].

Figure 4. Rod bundle test section of the Purdue University 8 × 8 bundle [4].

Figure 5. Rod bundle data of the Purdue University 8 × 8 bundle [4].

Figure 6. Rod bundle data of the ORNL/THTF 8 × 8 bundle [19].

Table 2. Analysis cases for Purdue University rod bundle tests.

Series No.	Measured <jf> [m/s]	Measured <jg> [m/s]	Measured <α> [-]
Series 1	0.00	0.06–9.89	0.14–0.93
Series 2	0.09–0.11	0.03–9.66	0.06–0.90
Series 3	0.25–0.27	0.03–9.24	0.01–0.83
Series 4	0.49–0.50	0.06–8.29	0.08–0.79
Series 5	0.76–0.77	0.13–7.04	0.09–0.74
Series 6	1.01–1.03	0.25–6.33	0.15–0.70

Figure 7. Nodalization for Purdue University bundle analyses.

Figure 8. Predicted void fraction profiles (Measured void fractions are also plotted with the ±10% error band).

Figure 9. Void fraction prediction for Purdue University bundle tests.

Figure 10. Nodalization for ORNL/THTF bundle analyses.

Table 3. Analysis cases for ORNL/THTF rod bundle tests.

Test No.	Power [kW/m]	Pressure [MPa]	Measured <α> [-]
Test 3.09.10 J	1.07	4.20	0.09–0.64
Test 3.09.10 K	0.32	4.01	0.08–0.25
Test 3.09.10 M	1.02	6.96	0.18–0.56
Test 3.09.10 N	0.47	7.08	0.11–0.29
Test 3.09.10AA	1.27	4.04	0.23–0.76
Test 3.09.10BB	0.64	3.86	0.16–0.54
Test 3.09.10CC	0.33	3.59	0.06–0.42
Test 3.09.10DD	1.29	8.09	0.14–0.64
Test 3.09.10EE	0.64	7.71	0.07–0.42
Test 3.09.10FF	0.32	7.53	0.08–0.30

Figure 11. Predicted void fraction profiles.

Figure 12. Void fraction prediction for ORNL/THTF bundle tests.

Figure 13. Correction factor.

Figure 14. Distribution parameters.

Figure 15. Predicted void fraction profiles.

Figure 16. Void fraction prediction for ORNL/THTF bundle tests.

Table 4. Prediction uncertainty of drift-flux correlations for ORNL/THTF data.

Correlations	md	sd	Remarks
EPRI [16]	3.02%	5.10%	Completely empirical model
Clark et al. [6]	−10.83%	10.74%	Limited applicable pressure range
New correlation	0.12%	5.89%	Corrected pressure scaling

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