Tamaño del negocio, Factores determinantes

In the current study, the flow path was divided into a number of small segments in the flow direction. A nodalization sensitivity study was performed for both the straight-channel and the zigzag-channel PCHEs. The helium inlet temperatures and mass flow rates on both sides of the PCHEs were obtained from steady-state calculations. The second terms on the left hand of Equations (5.5), (5.6), (5.8), and (5.9) for the fluid energy balance can be modified using a finite difference technique, converting all the partial differential equations (PDEs) to ordinary differential equations (ODEs). Transient scenarios were simulated using a MATLAB code that was developed in this study. Figure 5-10 presents the PCHE system nodal structure. Nodalization sensitivity study was performed to determine the effective number of segments used in the transient simulations based on the nominal operating conditions. The helium temperatures at the

These two helium outlet temperatures were compared to the nominal operation parameters that were used in the heat exchanger rating or sizing process.

Figure 5-10. PCHE nodal structure.

5.4.1 Straight-channel PCHE

Five different numbers of segments were used in the nodalization sensitivity study. The helium inlet temperatures on both the hot and cold sides were kept at constants of 465.6 and 207.6 °C, respectively. The temperatures at the hot-side and cold-side outlets were recorded after the system reached a steady state in the calculations using the numerical model. These two helium outlet temperatures were compared to the values that were obtained from the heat exchanger rating process using the e-NTU method. It can be seen from Table 5-2 that these five cases presented similar results without significant deviations for the straight-channel PCHE. The hot-side and cold- side temperature differences between the values using the e -NTU method and the results obtained from the simulations for the five cases were mainly attributed to the fluid thermophysical properties. The fluid thermophysical properties were evaluated based on the average temperature for each helium stream in the heat exchanger rating process while the temperature-dependent properties were employed in each segment in the numerical simulations. Note that increasing the number of segments would considerably increase the computational time. It was observed from Table 5-2 that the helium outlet temperature differences on both sides tended to diminish when the

total number of segments were greater than 500. Therefore, a total of 500 segments were selected for the PCHE to simulate the transient scenarios in this study.

Table 5-2. Results of nodalization sensitivity study for the straight-channel PCHE.

PCHE NTU e - rating value Number of segments 50 100 300 500 1,000

Hot-side helium outlet temperature (°C) 294 294 293.7 293.6 293.6 293.5

Cold-side helium outlet temperature (°C) 379.2 379.5 379.2 379.0 379.0 379.0

To predict the dynamic behavior of the straight-channel PCHE, steady-state operating parameters were first calculated by assuming constant helium fluid properties. The input parameters for the calculation included the helium inlet temperatures on both the hot and cold sides. The temperature distributions inside the PCHE, as shown in Figure 5-11, were obtained by dividing one hot helium stream, one cold helium stream, and one plate into 500 axial segments along the helium flow direction. The steady-state temperatures inside the PCHE and helium mass flow rates can serve as the initial condition for the transient simulations.

Figure 5-11. Temperature distributions inside the straight-channel PCHE.

5.4.2 Zigzag-channel PCHE

Similar to the straight-channel PCHE, five cases were carried out for the zigzag-channel PCHE and Table 5-3 presents the similar results without significant deviations for these five cases. The hot-side and cold-side temperature differences between the nominal values used in the heat exchanger sizing process (i.e., LMTD method) and the results obtained from the five cases with different segments were mainly attributed to the fluid thermophysical properties. A total of 500 segments of the PCHE were also selected to simulate the transient scenarios for the zigzag-channel PCHE. The steady-state temperature distributions inside the PCHE, as shown in Figure 5-12, were obtained by equally dividing each stream and plate into 500 segments along the helium flow direction. The temperature distributions inside the heat exchanger and helium mass flow rates can be used as the initial condition for the transient simulations.

Table 5-3. Results of nodalization sensitivity study for the zigzag-channel PCHE. Used in the LMTD method Number of segments 50 100 300 500 1,000

Hot-side helium outlet temperature (°C) 462 463.7 463.1 462.7 462.6 462.6

Cold-side helium outlet temperature (°C) 688 687.3 686.5 686.0 685.9 685.8

Figure 5-12. Temperature distributions inside the zigzag-channel PCHE.

5.4.3 Heat exchanger model verification

The dynamic model described above was verified in a previous study (Chen et al., 2015b) by comparing the numerical solution with the results obtained from a commercial software DYNSIM. A general countercurrent two-stream heat exchanger was adopted, and the parameters obtained from the thermal design of the heat exchanger under a steady-state condition were fed into

DYNSIM to simulate the dynamic behavior of the heat exchanger. Comparison of the results obtained from the dynamic model and DYNSIM simulations is shown in Figure 5-13. It was evident that the results obtained from the dynamic model and DYNSIM software presented a good agreement in depicting the dynamic behavior for a 10%-step increase in fluid mass flow rate on the cold side of the heat exchanger starting at 100 seconds.

Figure 5-13. Heat exchanger model verification under flow step change condition (Chen et al., 2015b).