Kozeny-Carman permeability equation is an important relation for the determination of permeability in porous media. In this study, the permeabilities of porous media that contains rectangular rods are determined, numerically. The applicability of Kozeny-Carman equation for the periodic porous media is investigated and the effects of porosity and pore to throat size ratio on Kozeny constant are studied. The continuity and NavierStokes equations are solved to determine the velocity and pressure fields in the voids between the rods. Based on the obtained flow field, the permeability values for different porosities from 0.2 to 0.9 and pore to throat size ratio values from 1.63 to 7.46 are computed. Then Kozeny constants for different porous media with various porosity and pore to throat size ratios are obtained and a relationship between Kozeny constant, porosity and pore to throat size ratio is constructed. The study reveals that the pore to throat size ratio is an important geometrical parameter that should be taken into account for deriving a correlation for permeability. The suggestion of a fixed value for Kozeny constant makes the application of Kozeny-Carman permeability equation too narrow for a very specific porous medium. However, it is possible to apply the Kozeny-Carman permeability equation for wide ranges of porous media with different geometrical parameters (various porosity, hydraulic diameter, particle size and aspect ratio) if Kozeny constant is a function of two parameters as porosity and pore to throat size ratios.

The two-dimensional through-flow modeling of turbomachinery is still one of the most powerful tools available to the turbomachinery industry for aerodynamic design, analysis, and post-processing of test data due to its robustness and speed. Although variety of aspects of such a modeling approach are discussed in the publicly available literature for compressors and turbines, not much emphasis is placed on combined modeling of the fan and the downstream splitter of turbofan engines. The current article addresses this void by presenting a streamline curvature through-flow methodology that is suitable for inverse design for such a problem. A new split-flow method for the streamline solver, alternative to the publicly available analysis-oriented method, is implemented and initially compared with two-dimensional axisymmetric computational fluid dynamics on two representative geometries for high and low bypass ratios. The empirical models for incidence, deviation, loss, and end-wall blockage are compiled from the literature and calibrated against two test cases: experimental data of NASA two-stage fan and three-dimensional computational fluid dynamics of a custom-designed transonic fan stage. Finally, experimental validation against GE-NASA bypass fan case is accomplished to validate the complete methodology. The proposed method is a simple extension of streamline curvature method and can be applied to existing compressor methodologies with minimum numerical effort.

Purpose -The purpose of this study is to determine interfacial convective heat transfer coefficient numerically, for a porous media consisting of square blocks in inline arrangement under mixed convection heat transfer.Design/methodology/approach -The continuity, momentum and energy equations are solved in dimensionless form for a representative elementary volume of porous media, numerically. The velocity and temperature fields for different values of porosity, Ri and Re numbers are obtained. The study is performed for the range of Ri number from 0.01 to 10, Re number from 100 to 500 and porosity value from 0.51 to 0.96. Based on the obtained results, the value of the interfacial convective heat transfer coefficient is calculated by using volume average method.Findings -It was found that at low porosities (such as 0.51), the interfacial Nusselt number does not considerably change with Ri and Re numbers. However, for porous media with high Ri number and porosity (such as 10 and 0.51, respectively), secondary flows occur in the middle of the channel between rods improving heat transfer between solid and fluid, considerably. It is shown that the available correlations of interfacial heat transfer coefficient suggested for forced convection can be used for mixed convection for the porous media with low porosity (such as 0.51) or for the flow with low Ri number (such as 0.01).Originality/value -To the best of the authors' knowledge, there is no study on determination of interfacial convective heat transfer coefficient for mixed convection in porous media in literature. The present study might be the first study providing an accurate idea on the range of this important parameter, which will be useful particularly for researchers who study on mixed convection heat transfer in porous media, macroscopically.

Thermal dispersion is an important topic in the convective heat transfer in porous media. In order to determine the heat transfer in a packed bed, the effective thermal conductivity including both stagnant and dispersion thermal conductivities should be known. Several theoretical and experimental studies have been performed on the determination of the effective thermal conductivity. The aim of this study is to review the experimental studies done on the determination of the effective thermal conductivity of the packed beds. In this study, firstly brief information on the definition of the thermal dispersion is presented and then the reported experimental studies on the determination of the effective thermal conductivity are summarized and compared. The reported experimental methods are classified into three groups: (1) heat addition/removal at the lateral boundaries, (2) heat addition at the inlet/ outlet boundary, (3) heat addition inside the bed. For each performed study, the experimental details, methods, obtained results, and suggested correlations for the determination of the effective thermal conductivity are presented. The similarities and differences between experimental methods and reported studies are shown by tables. Comparison of the correlations for the effective thermal conductivity is made by using figures and the results of the studies are discussed.

Volume averaged thermal transport properties of two metal foams with 10 and 20 PPI are obtained by using microtomography technique. The digital 3D structures of samples are generated in computer environment. The governing equations are solved for the entire domain and the volume averaged technique is used to determine interfacial heat transfer coefficient, longitudinal and transverse thermal dispersion conductivity. The study is performed for the pore scale Reynolds number from 100 to 600. The obtained results are within the ranges of the suggested correlations in literature. The present study supports the correlations suggested by Calmidi and Mahajan (2000) and Zhang et al. (2016).