### 5.6.2. Solids Pressure

#### 5.6.2.1. Empirical Constitutive Equations

The most popular constitutive equations for solids pressure are due to (Gidaspow [18]). These actually specify the solids pressure gradient, rather than solids pressure directly:

| (5–90)

| (5–91)

Where is the Elasticity Modulus, is the Reference Elasticity Modulus, is the Compaction Modulus, and is the Maximum Packing Parameter.

The Gidaspow model is implemented with an option for specifying the Reference Elasticity Modulus and Compaction Modulus. There is also an option to specify the Elasticity Modulus directly. There is also an option to specify the solids pressure directly. This permits more general constitutive relations than those where the solids pressure is a function of volume fraction only.

#### 5.6.2.2. Kinetic Theory Models for Solids Pressure

The kinetic theory model for solids pressure is similar to the equation of state for ideal gases, modified to take account of inelastic collisions, and maximum solid packing.

| (5–92)

Here, denotes the coefficient of restitution for solid-solid collisions, and denotes the radial distribution function. Popular models for the radial distribution function are given by:

Gidaspow (1994) [18]:

| (5–93)

Lun and Savage (1986) [100]:

| (5–94)

Note that the radial distribution function tends to infinity as . The singularity is removed in CFX by setting:

| (5–95)

where and:

| (5–96)

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