### 7.8.1. Interphase Drag

For low Mach number flows, the drag exerted on an immersed body by a moving fluid arises from two mechanisms only. The first is due to the viscous surface shear stress, and is called skin friction. The second is due to the pressure distribution around the body, and is called the form drag. The total drag force is most conveniently expressed in terms of the dimensionless drag coefficient, C D. The calculation of C D is available in Interphase Drag in the CFX-Solver Theory Guide.

#### 7.8.1.1. Interphase Drag for the Particle Model

For a particle of simple shape, immersed in a Newtonian fluid and which is not rotating relative to the surrounding free stream, the drag coefficient, CD, depends only on the particle Reynolds number. The function may be determined experimentally, and is known as the drag curve.

ANSYS CFX offers several different models for the drag curve, and also allows you to specify the drag coefficients directly.

This section describes drag correlations specific to dispersed multiphase flow.

##### 7.8.1.1.1. Specifying a Drag Coefficient

You can choose to specify the dimensionless Drag Coefficients C D directly. This is done by selecting to use the `Drag Coefficient` option on the Fluid Pairs tab in CFX-Pre, and entering the appropriate Drag Coefficient. For details, see Fluid Pair Models Tab in the CFX-Pre User's Guide.

You can supply your own drag coefficient correlation as an expression and you are free to define your own interfacial Reynolds number, or any other dimensionless group.

##### 7.8.1.1.2. Sparsely Distributed Solid Particles

###### 7.8.1.1.2.1. Sparsely Distributed Solid Particles: Schiller Naumann Drag Model

This should only be used for solid spherical particles, or for fluid particles that are sufficiently small that they may be considered spherical. For non-spherical particles, you should supply the drag curve from experiment.

As the Schiller Naumann correlation is derived for flow past a single spherical particle, it is only valid in the dilute limit of very small solid phase volume fractions.

You can select this drag curve by selecting to use the `Schiller Naumann Drag Model` on the Fluid Pairs tab in CFX-Pre. For details, see Fluid Pair Models Tab in the CFX-Pre User's Guide.

##### 7.8.1.1.3. Densely Distributed Solid Particles

###### 7.8.1.1.3.1. Densely Distributed Solid Particles: Wen Yu Drag Model

The Wen Yu correlation is valid for solid phase volume fractions at least up to 0.2, and probably higher.

You can select this Drag Curve by selecting to use the Wen Yu Drag Model on the Fluid Pairs tab in CFX-Pre (Fluid Pair Models Tab in the CFX-Pre User's Guide). Theoretical information about the Wen Yu drag model is given at Densely Distributed Solid Particles: Wen Yu Drag Model in the CFX-Solver Theory Guide.

Note: Although the Wen Yu drag law implemented in ANSYS CFX follows the implementation by Gidaspow [18] and its subsequent wide use, this implementation of the drag law is, in fact, quite different from that given in the original Wen and Yu paper [181].

###### 7.8.1.1.3.2. Densely Distributed Solid Particles: Gidaspow Drag Model

For very dense gas-solid or liquid-solid flows, such as occur in fluidized bed applications, the Gidaspow correlation is recommended.

You can select this drag curve by selecting to use the `Gidaspow Drag Model` on the Fluid Pairs tab in CFX-Pre (Fluid Pair Models Tab in the CFX-Pre User's Guide).

Theoretical information about the Gidaspow drag model is given at Densely Distributed Solid Particles: Gidaspow Drag Model in the CFX-Solver Theory Guide.

##### 7.8.1.1.4. Sparsely Distributed Fluid Particles (drops and bubbles)

###### 7.8.1.1.4.1. Sparsely Distributed Fluid Particles: Ishii-Zuber Drag Model

This is applicable to general fluid particles (drops and bubbles), for any pair of phases. ANSYS CFX automatically takes into account the spherical particle and spherical cap limits and dense fluid particle effects.

You can select this Drag Curve by selecting to use the `Ishii-Zuber Model` on the Fluid Pairs tab in CFX-Pre. For details, see Fluid Pair Models Tab in the CFX-Pre User's Guide. This model is only available when a buoyant flow is specified and a Surface Tension Coefficient has been set.

###### 7.8.1.1.4.2. Sparsely Distributed Fluid Particles: Grace Drag Model

This model was developed using air-water data and produces better results for air-water systems. ANSYS CFX automatically takes into account the spherical particle and spherical cap limits. You can set a Volume Fraction Correction Exponent for this model for use with high bubble volume fractions, see below for details.

You can select this Drag Curve by selecting to use the `Grace Model` on the Fluid Pairs tab in CFX-Pre. For details, see Fluid Pair Models Tab in the CFX-Pre User's Guide. This model is only available when a buoyant flow is specified and a `Surface Tension Coefficient` has been set.

###### 7.8.1.1.4.3. Sparsely Distributed Fluid Particles: Availability

Both the `Ishii Zuber` and `Grace Drag Models` make explicit use of the gravity vector and surface tension coefficient. Hence, both are only available for buoyant multiphase flows when a surface tension coefficient has been specified. The fluid morphologies must be `Continuous` and `Dispersed Fluid` respectively.

##### 7.8.1.1.5. Densely Distributed Fluid Particles

###### 7.8.1.1.5.1. Densely Distributed Fluid Particles: Ishii-Zuber Drag Model

The Ishii Zuber drag model automatically takes into account compact particle effects and is therefore suitable for modeling flows containing high fluid particle volume fractions.

A user-defined maximum packing value can be set. This is defaulted to unity for a dispersed fluid phase. For details, see Maximum Packing.

You can select this drag curve by selecting to use the `Ishii Zuber Model` on the Fluid Pairs tab in CFX-Pre. For details, see Fluid Pair Models Tab in the CFX-Pre User's Guide. This model is available only when a buoyant flow is specified and a surface tension coefficient has been set.

###### 7.8.1.1.5.2. Densely Distributed Fluid Particles: Grace Drag Model

The Grace drag model is formulated for flow past a single bubble. For details, see Sparsely Distributed Fluid Particles (drops and bubbles).

You can select this drag curve by selecting to use the Grace model on the Fluid Pairs tab in CFX-Pre. For details, see Fluid Pair Models Tab in the CFX-Pre User's Guide. This model is only available when a buoyant flow is specified and a Surface Tension Coefficient has been set.

In the dilute limit, leave the Volume Fraction Correction Exponent at its default value of zero. For non-dilute bubble volume fractions, set a non-zero value, depending on the bubble size as discussed below.

Small bubbles tend to rise more slowly at high void fraction, due to an increase in the effective mixture viscosity. To capture this effect, a negative Volume Fraction Correction Exponent should be used. The Ishii Zuber correlation uses an exponent of -1 in this limit. A value of -0.5 has also been used successfully by some investigators.

Large bubbles, on the other hand, tend to rise faster at high void fractions, because they are dragged along by the wakes of other bubbles. This effect may be modeled using a positive Volume Fraction Correction Exponent. The Ishii Zuber correlation uses an exponent of 2 in this regime. A value of 4 has been used successfully by some investigators [74]. If you use a value of 4 and experience poor convergence for the mass equations, try reducing the value to 2.

#### 7.8.1.2. Interphase Drag for the Mixture Model

The mixture model is primarily a tool to permit advanced users to specify their own interfacial transfer models for complex situations. Hence the only drag model available is the specified Drag Coefficient model. This may be a constant, or a function defined using expression language or User Fortran.

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