Generalized Equation for Airflow Resistance of Bulk Grains With Variable Density, Moisture Content and Fines∗

Abstract

The pressure drop versus airflow data for several types of grains were compiled and a grain specific generalized pressure drop versus airflow equation was developed. The equation predicted pressure drop as a function of airflow when porosity, moisture content and fine concentration were specified. The effect of properties of airflow on the resistance of bulk grain to airflow was also considered in the generalized equation. A modified Leva's equation was developed. The similarity between the grain specific equation and the modified Leva's equation led to a method for estimating the shape factor for irregularly shaped particles. LElTRODUCTIONThe ASAE Standard D272.2 (ASAE, 1992) has more than 20 individual curves relating pressure drop to airflow. The main problems with these curves are: (1) their range * Journal Paper No. MS-930806 TN. LI AND SOKHANSANJof applicability is limited; (2) their accuracy is questionable when applied to different varieties of a grain type; and (3) for a new type of grain for which pressure-airflow rate c w e is not available, only a visual interpolation is possibte.Factors that affect the resistance of bulk grains to airflow include air viscosity and density, porosity of the bulk material. orientation of the particles in the buk. size, shape and panicle surface condition. These factors are highly interdependent and thus it is difficult to develop a unique curve or mathematical model to relate pressure drop to air flow as a function of these factors. Equation 1 developed by Shedd (1953), and Eq. 2 developed by Hukill and Ives (1955) are used extensively to relate airflow to pressure drop in agricultural grains. The symbols and units in Eqs. 1 and 2 and in subsequent equations are defined in nomenclature. Equations 1 and 2 are specific to the experimental condition. They do not provide sufficient understanding of the importance of various factors affecting the pressure drop. The objective of this research was: (1) to review literature pertaining to pressure drop in bulk particulate materials; (2) to compiIe pressure drop data over a wide range of grain types (size and shape), densities (fines content), airflow rates; (3) to develop a generalized mathematical model of pressure drop versus airflow for agricultural grains. Generalized flow eauations through oorous media Ergun (1952) studied the pressure drop through fixed bed of granular solid materials. He confirmed the Reynolds theory that the pressure loss can be treated as the sum of the kinetic and viscous energy losses. Based on the work of Kozeny (1927), Carman (1937), and Burke and Plurnrner (1928). Ergun (1952) proposed chat the viscous energy losses in a granular fixed bed are proportional to (~-e )~/ &~ and the kinetic energy losses to (1-&)I€*, and hence suggested the following generalized equation to predict the pressure drop in a packed column: Downloaded by [RMIT University] at 16:18 15 March 2015 AIRFLOW RESISTANCE OF BULK GRAINS where fE is the modified friction coefficient and The particle diameter Dp in Eq. 3 is defined by...

Airflow Resistance of Seeds at Different Bulk Densities Using Ergun’s Equation

“…This assumption is not correct, because the density and porosity of grain in the silo changes along the height due to compaction from the grain load (Grundas et al, 1978;Bakker-Arkema et al, 1969). Li and Sokhansanj (1994) compiled the pressure drop versus airflow resistance of numerous grains to develop a generalized equation based on Ergun's (1952) equation or Leva's (1959) equation that are both physical models based on a semi-theoretical analysis.…”

“…Other researchers have investigated the effect of fines (Haque et al, 1978;Grama et al, 1984), moisture content (Haque et al, 1982), combination of fines and moisture content (Abdelmonsin, 1983), the effect of filling method Foster, 1976, 1978), and the effect of airflow direction (Kumar and Muir, 1986) on the pressure drop versus airflow rate. Li and Sokhansanj (1994) and Bakker-Arkema et al (1969) concluded that Ergun's equation could be the basis for a generalized model of airflow resistance through agricultural products. Based on Reynolds' theory for resistance to fluid flow, Ergun (1952) hypothesized that the pressure drop was the summation of the viscous and kinetic energy losses.…”

“…Based on Reynolds' theory for resistance to fluid flow, Ergun (1952) hypothesized that the pressure drop was the summation of the viscous and kinetic energy losses. Ergun's general equation for uniform products can be written as (Li and Sokhansanj, 1994):…”

Resistance to forced airflow through layers of composting organic material

“…The static pressure gradient of forced air in the layers of organic material depends on flow rate, viscosity and density of the air, in addition to the size, shape, surface roughness and orientation of the particles, water content, degree of degradation and compaction of the material (Li and Sokhansanj, 1994;Yazdanpanah et al, 2011). Some researches carried out with different organic waste provided different results for the static pressure gradient of airflow.…”

“…The static pressure gradient of airflow through a layer of organic material for composting may be represented by the same models used for grains, i.e., power (Shedd's Equation), logarithmic (Hukill & Ives' Equation) and quadratic (Ergun's Equation) (Kashaninejad et al, 2010;Li and Sokhansanj, 1994;Matos et al, 2012;McGuckin et al, 1999;Yazdanpanah et al, 2011). These models were developed empirically or theoretically, in which the material's physical properties and air characteristics were taken into consideration (McGuckin et al, 1999;Navarro and Noyes, 2002;Ray et al, 2004).…”