## 3 Measurement Techniques  
### CFD Study  
Numerical simulation was carried out via the ANSYS 19.0 software package. The mesh preparation and generation was carried out via the Meshing module. Simulation of the fluid flow took place in the Fluent module. Based on three-dimensional models, three computational regions were obtained, consisting of unstructured grids with a total number of cells of about 250,000. The grids mainly consisted of the hexahedron families in the bulk and prismatic cells near the physical walls of the geometric model. The characteristic cell size lies in the range of 0.001-1 mm, depending on the local thickening of the grid. The parietal region consists of six layers of prismatic cells with the size of 0.005 mm or more.  
Simulation of the flow process is based on the Navier-Stokes equations solutions. In this paper, we considered the stationary flow of a viscous fluid in a hydraulic system consisting of tube cross-sections located in a horizontal plane. Due to the action of viscous friction forces, the velocity of a fluid particle varies depending on its distance \(R\) to the axis of symmetry of each section of the hydraulic system. Due to the fact that the expected flow type in the tubes will be mainly laminar, the value determination of the Reynolds number dimensionless coefficient can be obtained via the equation:  
\[Re=\frac{\rho VR}{\mu} \tag{1}\]  
where, \(\rho\) is the fluid density, \(V\) is an average velocity, \(R\) is a tube radius, \(\mu\) is a fluid viscosity.  
Figure 5: Windows of each pass in the TCPC-3 image with particle image velocimetry (PIV) settings.  
In general, the fluid flow in this case is described by the Bernoulli equation, expressed in terms of pressure:  
\[\frac{V}{2g}^{2}+\frac{P}{\rho g}=H, \tag{2}\]  
where \(P\) is a static pressure and \(H\) is the total head.  
The flow simulation was based on the stationary condition, since the nonfunctional right ventricle is excluded for the circulation. For healthy patients from the age group of five years old children, the venous blood flow distribution between the superior and inferior vena cava is characterized by a ratio of 37%-63%, respectively. The cardiac output value is of 2.2 L/min [15]. The mean arterial pressure in the pulmonary arteries corresponds to 11 mmHg [16]. The efficiency of TCPCs was estimated via hydraulic power losses magnitude (see Equation (3)). Since there is no heat transfer, the hydraulic power losses magnitude is the only criterion for evaluating the efficiency of the hydraulic system. As a result, it is determined only by the flow part geometry. Hydraulic power losses are equal to the difference of total pressure at the inlet and outlet of the system. The total pressure is the sum of the average static and dynamic pressures in the cross-section of the tube. Hydraulic losses are determined by the difference in static pressures at the system inlet and outlet.  
\[\begin{split} Power\ Loss=F_{IVC}\cdot U_{IVC}\cdot\left(P_{static }+P_{dynamic}\right)_{IVC}+F_{SVC}\cdot U_{SVC}\cdot\left(P_{static}+P_{ dynamic}\right)_{SVC}\\ -F_{LPA}\cdot U_{LPA}\cdot\left(P_{static}+P_{dynamic}\right)_ {LPA}-F_{RPA}\cdot U_{RPA}\cdot\left(P_{static}+P_{dynamic}\right)_{RPA} \end{split} \tag{3}\]  
where \(F\) is a cross-section area (m\({}^{2}\)), \(U\) is a mean value of velocity magnitude in a cross-section (m/s), \(P_{static}\) is mean static pressure (Pa) in a cross-section, \(P_{dyn}=\frac{1}{2}\rho\left|\vec{v}\right|^{2}\) is mean dynamic pressure (Pa) in a cross-section, and Power loss is power loss in the system (W). Subscripts \(IVC\) and \(SVC\) designate the inferior and superior vena cava, respectively. Subscripts \(LPA\) and \(RPA\) designate the left and right pulmonary artery, respectively.  
Due to higher stability parameters of the implicit formulation, a converged steady-state solution was used. The convergence was carried out for the following parameters: velocity, pressure at the entrances, mass flow rates at the output, and was assessed using reference values which were below 0.001.