Power conversion and heat dissipation systems

PROCESS takes into account all the systems required to perform the necessary conversion of fusion power to electricity, from the coolant systems in the plant components to the heat exchangers and turbines. Figure 1 shows the power flow.

Figure 1: Power flows

Divertor

All of the charged particle transport power leaving the plasma (excluding the 1-f_alpha_plasma portion of the alpha power that escapes directly to the first wall) is assumed to be absorbed in the divertor, along with a proportion fdiv of the radiation power and the neutron power.

Switch iprimdiv may be used to specify whether the thermal power deposited in the divertor becomes high-grade thermal power (iprimdiv = 1) or low-grade waste heat (see Figure 1).

First wall

The photon power is divided into three parts: absorbed by the first wall; incident upon the divertor; and lost through ports. Power due to ions derived from the neutral beams but lost before being thermalised ("first orbit loss"), and from the fast alpha particles lost before being thermalised, also contribute to the total thermal power absorbed by the first wall.

Thermal cycling package

This performs calculations on the first wall of the machine. Evaluations of the mechanical and thermal stresses on this component lead to a measure of the maximum number of cycles to which the first wall can be subjected, and hence to the minimum allowable length of each reactor cycle for a specified first wall lifetime. The cycle time can be constrained to be at least the minimum value by turning on constraint equation no. 42 with iteration variable no 67 (ftcycl).

Power conversion cycle

The primary coolant (less any thermal power required to produce hydrogen in a hydrogen production plant) is used to heat the secondary coolant to turn the turbines, which power the generator. The remainder is dumped to the environment. All of the low-grade heat is dumped to the environment.

primary_pumping : This switch controls the calculation of the mechanical pumping power required for the primary coolant.

• If primary_pumping = 0, the user sets mechanical pumping directly
• If primary_pumping = 1, the user sets mechanical pumping power as a fraction of thermal power removed by coolant.
• If primary_pumping = 2, the mechanical pumping power is calculated, as follows:
  • User inputs for the coolant outlets temperature (which may be used as an iteration variable), the coolant channel diameter, and the segmentation of the blanket are used. The peak temperature in the first wall material (underneath the armour) is derived. The user can apply an upper limit to this temperature, and if this constraint is used then it is strongly recommended to set the length of the first wall pipe (fw_channel_length) as an iteration variable. The Gnielinski correlation is used to determine the heat transfer in the channel. The stresses in the first wall are currently taken into account.
  • The mechanical pumping power required for the first wall and breeder zone is calculated using the Darcy friction factor, estimated from the Haaland equation, an approximation to the ColebrookWhite equation. (If you consider that the calculated value for the pumping power is too low, then you can add an additional electric power requirement using baseel. Do not use htpmw_min as this prevents the optimisation of the first wall.) The inlet and outlet temperatures of the first wall and blanket can be different. The isentropic efficiency of the first wall and blanket coolant pumps (enthalpy increase in the fluid for isentropic compression divided by the mechanical power used) is specified by the parameter etaiso. Note that the mechanical pumping power for the shield and divertor are still calculated using the simplified method (a fixed fraction of the heat transported).

• If primary_pumping = 3, the mechanical pumping power is calculated using specified pressure drop. The pressures and temperatures are set by the user.

  • When used with the DCLL model a different set of pressure drop variables are used, which are outlined below:

  Variable	Units	Default	Description
  dp_fw_blnkt	Pa	1.5D5	Pressure drop in FW and blanket coolant including heat exchanger and pipes
  dp_fw	Pa	1.5D5	Pressure drop in FW coolant including heat exchanger and pipes
  dp_blkt	Pa	3.5D3	Pressure drop in blanket coolant including heat exchanger and pipes
  dp_liq	Pa	1.0D7	Pressure drop in liquid metal blanket coolant including heat exchanger and pipes

  • The defaults for these variables are geared towards a WCLL concept, so different values should be used with Helium cooling.

secondary_cycle : This switch controls the calculation of the thermal to electric conversion efficiency in the secondary cycle.

• If secondary_cycle = 0, the efficiency of the power generation cycle is set to a single value obtained from previous cycle modelling studies. The heat deposited in the Toroidal Field coils divertor coolant is assumed to be at such low temperature that it cannot be used for power generation and is dumped to the environment.
• In the remaining options (secondary_cycle = 1, 2 or 3), the heat deposited in the divertor coolant is used for power generation
• If secondary cycle = 1, the efficiency of the power generation cycle is set as above, but the divertor heat is used for electricity generation.
• If secondary_cycle = 2, the efficiency of the power generation cycle is input by the user.

• If secondary_cycle = 3, a steam Rankine cycle is assumed. The secondary cycle thermal efficiency (etath) is calculated from the coolant outlet temperature using simple relations between temperature and efficiency¹:

  $\begin{eqnarray*} \eta & = & -2.0219 + 0.3720 \, \mathrm{ln}(T) \,\, \mathrm{(water \, coolant; saturated \, steam \, Rankine \, cycle)} \\ \eta & = & -0.8002 + 0.1802 \, \mathrm{ln}(T) \,\, \mathrm{(helium \, coolant; superheated \, steam \, Rankine \, cycle)} \end{eqnarray*}$

• If secondary_cycle = 4, a supercritical CO$_2$ Brayton cycle is assumed. The secondary cycle efficiency (etath) is calculated from the coolant outlet temperature using simple relations between temperature and efficiency from ¹:

  $$\eta = -2.5043 + 0.4347 \mathrm{log}(T) \,\, \mathrm{(water or helium coolant)}$$

In the above three equations, T is the temperature (K) of the (secondary) coolant at the inlet to the turbine, assumed to be 20 K below the outlet temperature of the primary coolant.

The electrical power required to operate the power plant itself is the so-called recirculating electric power (precircmw). Any surplus is exported to the electricity grid as net electric power (pnetelmw).

The recirculating power comprises the electrical power required to run all of the associated electrical systems surrounding the fusion power core, plus the on-site building services, offices, etc., as shown in Figure 1. Of these, the cryogenic plant power includes the power required to cool the TF coils from the neutron power absorbed by the coils, the PF coils (as defined by the ratio of the total PF coil stored energy to the fusion power pulse time t_pulse_repetition), and other 'cold' components.

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1. C. Harrington, "Development and Implementation of Improved Balance of Plant Models for PROCESS", CCFE C5.M15 Milestone Report, August 2014 (copy stored as CCFE internal note T&M/PKNIGHT/PROCESS/027) ↩↩