# Numerical models to predict steady and unsteady thermal-hydraulic behaviour of supercritical water flow in circular tubes

## Summary (2 min read)

### 1. Introduction

- The THRUST and CFD models are evaluated by comparing the simulation results with the experimental data under various operating conditions.
- Further, both the numerical models are then used to simulate the transient response of the SCWR.
- Subsequently, the step change and periodic variation of various physical variables are introduced with a purpose to assess the capability of the numerical models to predict the heat transfer phenomenon during a transient process.

### 2. Mathematical details of the numerical models

- The mathematical details of the THRUST and CFD models are presented in this section.
- The present analysis is carried out under both steady state and transient conditions.

### 2.1. Mathematical formulations of the 1-D TH model

- After the coefficient and source term are linearized, Eq. ( 6) is discretized with a characteristics-dependent implicit finite-difference scheme where the spatial derivative terms are approximated by a backward or forward difference depending on the sign of the characteristics.
- The resultant discretized equations are then combined together and used for a numerical solution depending on the boundary conditions for the particular problem.

### 2.1.4. Determination of the critical heat flux for DHT

- The above mentioned empirical correlation is based on the mass flux only.
- Therefore, it does not account for other factors that might affect DHT.
- It can predict successfully the occurrence of DHT for the cases under consideration in the present study when comparing with the experimental data.
- But it cannot predict the deteriorated heat transfer zone (DHTZ).

### 3. Results and discussion

- For the purpose of validation of the proposed numerical models and to carry out the intended analysis, 7 different steady state experimental cases are selected.
- The experiments under consideration dealt with supercritical water flowing vertically upwards in bare circular tubes subjected to constant and uniform heat flux in the periphery.
- The selected experimental data sets have broad range of operating conditions in terms of mass flux, heat flux, inlet temperature and operating pressure.
- Cases 4-7 represent the situation where DHT was observed experimentally (q w < q dht ) under low mass flux (Cases 4-6) and high mass flux (Case 7) conditions.

### 3.1. Validation of the numerical models at steady state condition

- The highest average error in the numerical results occurs in Case 7, which is 6.44%.
- In case of CFD simulations, both turbulence models, the RSM and k-ω SST model, are found to comparable to each other for all the cases.
- Therefore, it can be concluded that a good agreement between the numerical results and the experimental data, in general, is obtained; however, the local discrepancies do exist, but generally are confined to a narrow region inside the channel where DHT takes place.

### 3.2. Comparison of the numerical models at the transient condition

- The transient results corresponding to the step change in the wall heat flux rate are shown in Fig. 10 .
- For this transient case study, the mass flux is unchanged and therefore, based on Eq. ( 11) it is also expected that the minimum value of heat flux, at which DHT may take place, also remains the same.
- The outlet bulk temperature, as observed in Fig. 10b , also has similar qualitative trend as the previous case and the initial oscillations are predicted by both CFD model and THRUST.
- The axial variations of the wall temperature and bulk temperature at different time are shown in Fig. 10c .
- Table 5 also confirms the good agreement among the numerical results from the two models.

### 4. Conclusions

- After satisfactory validation of the THRUST and CFD models with 7 different experimental cases of steady state heat transfer, transient simulations under 3 conditions are carried out.
- Out of these 3 conditions, 2 of them involve the step change in the input mass flow rate and heat flux whereas third one is of a sinusoidal variation in the input mass flow rate.
- The THRUST and CFD models are able predict the temporal and axial variations of the wall and bulk temperatures, and the predictions by the THRUST and CFD models are in a good agreement.
- The temporal variation of the outlet mass flow rate and outlet bulk temperature for all the cases obtained by the THRUST and CFD model show the exact value at the final steady state, but the actual time taken to reach to the final steady state is more in the case of the CFD model than the THRUST.

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