Establishing the geometry of foam cells is useful in developing microstructure-based acoustic and structural models. Since experimental data on the geometry of the foam cells are limited, most modeling efforts use the three-dimensional, space-filling Kelvin tetrakaidecahedron. The validity of this assumption is investigated in the present paper. Several FeCrAlY foams with relative densities varying between 3 and 15% and cells per mm (c.p.mm.) varying between 0.2 and 3.9 c.p.mm. were microstructurally evaluated. The number of edges per face for each foam specimen was counted by approximating the cell faces by regular polygons, where the number of cell faces measured varied between 207 and 745. The present observations revealed that 50 to 57% of the cell faces were pentagonal while 24 to 28% were quadrilateral and 15 to 22% were hexagonal. The present measurements are shown to be in excellent agreement with literature data. It is demonstrated that the Kelvin model, as well as other proposed theoretical models, cannot accurately describe the FeCrAlY foam cell structure. Instead, it is suggested that the ideal foam cell geometry consists of 11 faces with 3 quadrilateral, 6 pentagonal faces and 2 hexagonal faces consistent with the 3-6-2 cell.
IntroductionAircraft engine noise is a major environmental concern especially in regions surrounding an airport during takeoff and landing (Ref. 1). Significant progress has been made since the advent of the first commercial jet engine-powered airplanes with current ultrahigh bypass engines being much quieter than the first generation engines. For example, the effective perceived noise level in decibels (EPNdB) relative to the International Civil Aviation Organization's (ICAO) Chapter 3 certification standards decreased from about +5 EPNdB for aircraft engines developed in the 1960s to -5 EPNdB for modern engines (Refs. 2 and 3). Despite this large improvement in engine design, there is still a great desire among policy makers and designers to reduce noise much below current levels. For example, the National Aeronautics and Space Administration (NASA) has set ambitious goals to further reduce aircraft noise by -52 db with respect to the newly adapted ICAO's Chapter 4 certification standards by the year 2020 under its Subsonic Fixed Wing (SFW) project (Ref. 4). It is expected that these noise reduction goals will be achieved through a combination of design changes and development of suitable materials (Refs. 3 and 4).Polymeric foams have been historically used for sound absorption in several applications (Ref. 5). More recently, metal foams are being investigated for their flow resistance (Refs. 6 and 7) and sound absorption properties (Refs. 8, 9, and 10). Metal foams have been proposed for use in jet engines as acoustic treatment over rotors (Ref. 11), fan blades (Ref. 12) and other applications (Ref. 13). The acoustic and other properties of foams are dependent on their relative density, */ s , where * and s are the densities of the foam and the solid material, r...