Similarity analysis and verification of the relationship between resistance coefficients in porous media of different scales: Focusing on slatted floor

livestock houses, the slatted floor is one of the challenges to be modelled in CFD due to its small sizes of slots and large number of solid surfaces. Porous media modelling, with resistance coefficients derived from scaled experimental tests and full-scale CFD simulations, offers a practical approach to addressing these challenges. Clarifying the relationship between the resistance coefficients of slatted floors at different scales is crucial for optimising computational resource consumption and simplifying the research process. This paper, using similarity theory, explores the relationship of resistance coefficients of porous media modelling at different geometric scales. The similarity analysis revealed that the viscous resistance coefficient similarity constant is inversely proportional to the square of the geometric similarity constant ($c_D=1/{c_l}^2$), while the inertial resistance coefficient similarity constant is inverselIn %y proportional to the geometric similarity constant ($c_C=1/c_l$). And, CFD simulations of slatted floors at three different geometric similarity scales (1:1, 1:2.5, and 1:5) confirmed the validity of these relationships. The predictions of similarity theory showed strong agreement with the simulation results, with an average error of 2.1 % for the 1:1 scale (prototype) and 1.6 % for the 1:5 scale. Furthermore, a detailed CFD validation was conducted using a 1:2.5 scaled pig pen model by incorporating the resistance coefficients derived from direct geometric modelling into a porous media model. Comparison with experimental data demonstrated good agreement in both air velocity and temperature, with a maximum air velocity error of 0.34 m/s and an overall relative air temperature error of 1.98 %.