## 3 Numerical Methods  
In this article, the effect of circuit number on the FTHX performance was explored with EVAP-COND 4.0 software, a widely accepted and highly accurate simulation tool for the FTHXs. More detailed information about the EVAP-COND series can be found in References [8; 23; 24]. The heat transfer model for the outdoor FTHX was established in EVAP-COND 4.0 first. The arrangement of the coil and its interfacing with the airflow are schematically shown in Figure 2; the geometric parameters of the coil are very similar to the real ones. Note that the airflow onto the FTHX was actually two-dimensional, but the EVAP-COND series adopted a one-dimensional airflow. Therefore, the real air velocity was first experimentally measured over the whole FTHX and then integrated in the horizontal direction, as shown in Figure 2. Note that the non-uniformity of the airflow distribution was relatively mild due to the suction pattern of the airflow through the FTHX and the axial fan successively. Therefore, the four-circuit division of the FTHX was the same in the commercial prototype. \begin{table}
\begin{tabular}{c c c c c c} \hline \multirow{2}{*}{**Conditions**} & **Outdoor Tem.** & **Indoor Temp.** & **Compressor** & **EEV Target** & **Out FTHX** \\  & **(Dry/Wet Bulb)** & **(Dry/Wet Bulb)** & **Speed** & **Discharge Temp.** & **Air Flowrate** \\ \hline Rated cooling & 35/24 \({}^{\circ}\)C & 27/19 \({}^{\circ}\)C & 55 Hz & 79 \({}^{\circ}\)C & 1800 m\({}^{3}\)/h \\ Rated heating & 7/6 \({}^{\circ}\)C & 20/15 \({}^{\circ}\)C & 90 Hz & 73 \({}^{\circ}\)C & 2400 m\({}^{3}\)/h \\ \hline \end{tabular}
\end{table} 
Table 2: Conditions and control parameters of the tested ASHP. The equations to calculate the heat transfer coefficients and pressure drops for both sides were applied before the simulations. For the refrigerant side, the boiling and condensing heat transfer coefficients were obtained with the Thome [25] and Shah Equations [26], respectively, while the single-phase heat transfer coefficient was calculated with McAdams Equation [27]. The pressure drop equations for straight tubes and bends are different. In the tubes, single- and two-phase pressure drops are obtained with Blasius and Muller-Steinhagen Equations, respectively [28]. In the bends, by contrast, the single- and two-phase pressure drops are calculated with Chisholm [29] and Idelchik [30] Equations, respectively. For the air side, however, the pressure drop was not calculated by the software, and the heat transfer coefficient was obtained with Wang Equation [31]. The original outdoor FTHX in the ASHP was four-circuit reversely fixed, and its heat transfer performance in both condenser and evaporator modes were tested first for the optimization and validation of the simulations. The obtained constraint parameters for the FTHX simulations are listed in Table 3. Note that to improve the reliability of the evaporator simulations, the outlet quality of the evaporator was set to 0.98, which differed from the actual slightly superheated state, but this had a little effect on the overall capacity. All the heat transfer tubes were labelled with numbers, 1-24, from the top down, as shown in Figure 2. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Nodes** & **Condenser** & \multicolumn{3}{c}{**Evaporator**} \\ \hline \multirow{3}{*}{Refrigerant} & Inlet temperature/\({}^{\circ}\)C & 48.5 & Outlet sat. temperature/\({}^{\circ}\)C & 0.8 \\ \cline{2-5}  & Inlet superheat/\({}^{\circ}\)C & 34.8 & Outlet quality & 0.98 \\ \cline{2-5}  & Subcooling/\({}^{\circ}\)C & 1.3 & Inlet quality & 0.15 \\ \hline \multirow{3}{*}{Air} & Air inlet temperature/\({}^{\circ}\)C & 35 & Air inlet temperature/\({}^{\circ}\)C & 7 \\ \cline{2-5}  & Air inlet pressure/MPa & 0.101 & Air inlet pressure/MPa & 0.101 \\ \cline{2-5}  & Air inlet relative humidity & 0.40 & Air inlet relative humidity & 0.86 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Constraint parameters for the FTHX simulations. Figure 2: Schematic diagram of the FTHX and airflow arrangement in EVAP-COND.