Numerical optimization of radial graded porosity and cell size in volumetric solar air receivers for enhanced thermal–hydraulic performance

Volumetric solar receivers (VSRs) enable deep radiative penetration and efficient solid–fluid heat interactions, making them attractive for high–temperature concentrating solar power applications. However, their performance is highly sensitive to foam morphology, and uniform structures often exhibit a thermal–hydraulic trade–off in which enhanced heat absorption is accompanied by large hydraulic losses. This study utilizes an evolutionary design approach in which a constant solid volume of a uniform silicon carbide (SiC) foam is radially redistributed into discrete double– and triple–layer graded configurations. Various porosity and cell size combinations are refined to simultaneously enhance thermal performance and reduce flow resistance. A numerical analysis employing the extended Darcy–Forchheimer equation for fluid transport, the local thermal non–equilibrium (LTNE) model for energy exchange, and the P1 approximation for radiation transfer is implemented to assess the performance of the redesigned foam structures under identical boundary conditions. The results show that radial grading greatly improves overall performance while maintaining the same material content. Double–layered receivers raise outflow temperature by up to 25% and achieve performance evaluation coefficient (PEC) values exceeding 1.30. Triple–layered designs incorporating porosities of 0.65, 0.80, and 0.95 consistently provide the most effective balance between radiative absorption, solid–fluid interaction, and flow permeability. Further optimization of cell size distributions shows that coarse inner core pores combined with finer outer layers maximize radiative penetration and improve interfacial convective heat transfer between the solid and fluid phases, yielding the highest outlet fluid temperature of 1000 K for the best graded porosity configuration of (ϕ₁ = 0.95, ϕ₂ = 0.65, ϕ₃ = 0.80) and cell size distribution of (dc1 = 3.0, dc2 = 1.5, dc3 = 1.5 mm).