## 2 Geometry and CFD-Thermal Modeling
### Geometry and Boundary Conditions  
The enhanced CMJICS developed in this study involves CPs with axisymmetric CGVs around them, which are mounted in a hexagonal configuration on the flat base plate of a confined space. An immersed jet of air emerging from a smaller diameter concentric orifice in the confinement plate impinges on the top face of each CP. The wall jet formed on the top face of each CP is deflected toward the base plate by the properly shaped CGV to flow on the lateral face of the CP without separation. The CGV is extended toward the bottom plate to maintain cooling effectiveness by preventing flow separation from the lateral face. As the fluid reaches the base plate, it flows over it and interacts with other streams from neighboring CPs, forming upward fountains, the momentum of which varies with position depending on the strength of the interacting streams in the space between the CPs. The crossflow then interacts with the immersed impinging jets before being discharged from the exhaust ports on the flanks of the confined space. As the height of the CPs is increased,  
Figure 3: Comparison of the local \(Nu\) number distribution on the target plate predicted by CFD on grid M4 with experimental data [74, 75]. interactions of the crossflow with impinging jets weaken rapidly; thereby, their adverse effects on the jet impingement cooling system performance are effectively mitigated. The cooling performance and pressure drop of the enhanced CMJICS in a hexagonal prism shape are calculated by 3D CFD simulations and compared with those obtained for the flat target plate case. The system shown in Figure 4a consists of seven CP-CGV pairs having an interaxial distance of \(5D\) mounted on a hexagonal flat base plate with an inner tangent circle radius of \(8D\) and seven coaxial orifices with a diameter \(D\) of 4 mm drilled into a parallel confinement plate. The upper flat confinement plate is located \(5D\) away from the base plate, while all side faces of the system are exposed to the atmosphere. A CGV is placed around each CP that directs the wall jet formed on the top face of the CP to its lateral face. A planar section view through the axis of a CP and its CGV is presented in Figure 4b. The CGVs are modeled as zero-thickness baffles. The attachments of the CGVs to the confinement plate are not modeled to avoid complexity. As the diameter (\(D_{p}\)) or height (\(H_{p}\)) of a CP is varied, the position of the CGV relative to the CP is maintained. The inlet of a CGV is located far enough from the immersed impinging jet to avoid its interaction with the shear layer of the jet. In CFD simulations, the periodicity condition is applied to the planar boundary faces normal to the azimuthal coordinate of the \(60^{\circ}\) cylindrical sector of the CMJICS shown in Figure 5a. In simulations, the orifice exit velocity profile of a jet is assumed to be flat and the jet \(Re\) number is varied between 5000 and 20,000. The Reynolds-averaged jet velocity at the orifice (\(\overline{u}_{J}\)) is calculated as \(\overline{u}_{J}=(Re\mu)/(\rho D)\) where \(\rho\) and \(\mu\) are the density and dynamic viscosity of the fluid, respectively. It is assumed that the thermophysical  
Figure 4: Novel CMJICS design: (**a**) seven CP-CGV pairs in hexagonal configuration; (**b**) section view of a CP-CGV pair. properties of the cooling air are constant at 1 atm pressure and the Reynolds-averaged jet inlet temperature (\(\overline{T}_{J}\)) is 293 K. The molecular \(Pr\) number of the air is 0.71. Turbulence intensity at the orifice exit of a jet is calculated by \(I=0.16 Re^{(-1/8)}\). The no-slip boundary condition is applied to the walls. The confinement plate is modeled as an adiabatic wall. Uniform Reynolds-averaged wall temperature (\(\overline{T}_{w}\)) of 303 K boundary condition is applied on the top and lateral face of each CP as well as on the base plate.