Drag Coefficient Reference

Standard drag coefficients are used for drag force models that are composed of a Standard Drag Coefficient for a single particle together with a Drag Correction factor to account for multi-particle effects. Linearized drag coefficients are used for integrated models for the interphase drag or friction force.

The Drag Coefficient node is a child node of the Drag Force model.

Continuous-Dispersed Topology Drag Coefficient Properties

For a Continuous-Dispersed Topology phase interaction use one of the following methods for specifying the drag coefficient:

Method	Corresponding Properties/Method Nodes
Arastoopour The Arastoopour drag coefficient method is provided for solid dispersed-phase applications such as fluidized beds, where particle loadings are high. This method is available only when the dispersed phase is a solid.	Exponent The exponent $n$ in Eqn. (2331).
Bozzano-Dente The Bozzano-Dente drag coefficient method defines the standard drag coefficient using the Bozzano and Dente correlation. See Eqn. (1958). The Bozzano-Dente correlation is suitable for a wide range of liquid-gas bubble systems including water at low and high pressure, and highly viscous liquids such as some oils, glycerol, or molten glass. For small bubble diameters in low viscosity systems (for example, water), the Bozzano-Dente method gives a different asymptote to other standard drag correlations. The Bozzano-Dente correlation requires that gravity is activated for the physics continuum. This method is available only when the dispersed phase is a gas.	The surface tension value must be specified in the Multiphase Material > Material Properties > Surface Tension node for the parent phase interaction. The Surface Tension node appears automatically when the Bozzano-Dente correlation is selected.
EMMS The EMMS (energy minimization multi-scale) drag coefficient method is suitable for applications involving a dispersed solid phase, particularly for modeling fluidized bed systems where the influence of heterogeneity from particle clusters becomes significant. This method is available only when the dispersed phase is a solid.	Particle Type Selects one of the following methods for specifying the dispersed phase particle type: Geldart A Sets the particle type to Geldart A particles. These (aeratable) particles are fine, cohesive powders with a size and density range based on Geldart powder groups for fluidization. Geldart B Sets the particle type to Geldart B particles. These (sand-like) particles are less cohesive than Geldart A particles, with a size and density range based on Geldart powder groups for fluidization. Fluidization Regime Selects one of the following methods for specifying the flow regimes relative to the gas-solid fluidization: Bubbly Available only for the Geldart A particle type. Applies to cases where the fluid velocity leads to the formation of bubbles within the bed. This regime is characterized by intermittent bubbling and solid particles movement. Fast Applies to cases where the fluid velocity through the bed is greater than the minimum fluidization velocity, leading to a turbulent behavior of solid particles. Pneumatic Applies to cases with high fluid velocity where the particle bed expands, lifting and suspending solid particles within the conveying medium, resulting in a fluid-like behavior. This approach is well-suited for modeling pneumatic conveyors.
Field Function	Scalar Defines the standard drag coefficient ${C_{i j}}^{D}$ in Eqn. (1931).
Field Function (Linearized Coefficient)	Scalar Defines the linearized drag coefficient ${A_{i j}}^{D}$ in Eqn. (1930).
Gidaspaw The Gidaspow drag coefficient method is appropriate for solid dispersed-phase applications, such as fluidized beds, that have high particle loading. This method is available only when the dispersed phase is a solid.	Exponent The hindered settling exponent $n$ in Eqn. (2333). Transition Volume Fraction When the particle volume fraction is below this value a modified form of Stoke’s law is used to compute the drag, as shown in Eqn. (2333). The Ergun equation is used for loadings above this value. The Gidaspow drag coefficient method reduces to the Wen and Yu correlation when the transition volume fraction is set to 1.0.
Hamard and Rybczynski The Hamard and Rybczynski drag coefficient method is used for viscous Newtonian fluid droplets dispersed in a second immiscible viscous Newtonian fluid. See Eqn. (1964). The Hamard and Rybczynski drag model is not valid for high Reynolds numbers, where the Schiller-Naumann model is expected to be more accurate. This method is suitable for spherical liquid droplets.	None.
Rusche-Issa The Rusche-Issa drag coefficient method is appropriate when the dispersed phase volume fraction becomes high. This model accounts for the modification of the drag force due to the presence of other particles when the particles are densely-packed. For example, you would use this model when predicting the separation of oil and water in an emulsion settling experiment. See Eqn. (1954).	Simcenter STAR-CCM+ includes two implementations of this model. The particular implementation that Simcenter STAR-CCM+ uses depends on the two phases: Both phases liquid: Simcenter STAR-CCM+ applies the Inversion Rusche-Issa drag model. One liquid phase and one gas or particle phase: Simcenter STAR-CCM+ applies the standard Rusche-Issa drag model. See Rusche-Issa Drag Coefficient Properties.
Linearized Emulsion Topology Inversion The Linearized Emulsion Topology Inversion drag coefficient method allows the phases to invert when the volume fraction of the dispersed phase reaches the specified Inversion Volume Fraction. When the dispersed volume fraction becomes larger than the specified value, the drag, the relative viscosity, and the normal relative viscosities are swapped between the phases. After inversion, the relative viscosities are calculated using a new value for the maximum packing in the relative viscosity models. This method is available only when the Emulsion Rheology model is selected.	Inversion Volume Fraction The volume fraction of the dispersed phase at which the phase properties are inverted: the drag, the relative viscosity, and the normal relative viscosities are swapped between the phases. Inversion Maximum Packing The maximum packing value that is used in the relative viscosity models after phase inversion.
Schiller-Naumann Suitable for spherical solid particles, liquid droplets, and small-diameter (spherical) bubbles. This method is available only when the continuous phase is viscous. However, the continuous phase can be either Newtonian or non-Newtonian. See Eqn. (1946).	None.
Symmetric The Symmetric drag coefficient method is recommended for flows where phase topology inversion occurs, that is, the dispersed phase in one region of the domain becomes the continuous phase in another.	Inverted Topology Length Scale You specify the appropriate method and value for Eqn. (1955).
Syamlal-O’Brien The Syamlal-O’Brien drag coefficient method is based on measurements of terminal velocity that is made in settling beds. The Syamlal-O’Brien drag coefficient properties should be adjusted according to the parameters of the simulation. For more information and an example case, see the technical report Study of Gas-Solid Fluidized Bed - Tuning Syamlal-O'Brien Drag Model in the Technical Library on the Support Center portal, https://support.sw.siemens.com/en-US/product/226870983/downloads. This method is available only when the dispersed phase is a solid.	Transition Volume Fraction The cut-off volume fraction $α_{t r}$ in Eqn. (2343). C1 Value that is used as the exponent of $ϵ$ above the cut-off volume fraction in Eqn. (2343). C2 Value that is used as the multiplier of $ϵ$ below the cut-off volume fraction in Eqn. (2343).
Tomiyama The Tomiyama drag coefficient method determines the drag force depending on how contaminated the bulk flow is by impurities, such as surfactants. Surfactants reduce the liquid surface tension and prevent internal circulation in bubbles, hence increasing drag. The Tomiyama drag coefficient method is suitable for liquid-gas bubble systems with a low Reynolds number and low Morton number flow, for example, small bubbles in an air-water system. In such cases, the Bozzano-Dente model over-predicts the drag coefficient. The Tomiyama correlation requires that gravity is activated for the physics continuum. This method is available only when the continuous phase is viscous, and when the dispersed phase is a gas. It is not available for solid particles.	Contamination State Selects one of the method to use for specifying contamination: Pure Uses the drag coefficient that is described by Eqn. (1968). Moderate Specifies a higher drag coefficient than the Pure option, before bubble deformation effects become dominant. See Eqn. (1969). Contaminated Specifies a higher drag coefficient than the Moderate and Pure options to account for the presence of surfactants. See Eqn. (1970). The Contaminated water option is the default option since it applies to most industrial cases. The surface tension value must be specified in the Multiphase Material > Material Properties > Surface Tension node for the parent phase interaction. The Surface Tension node appears automatically when the Tomiyama correlation is selected.
Wang Curve Fit Suitable for water-air bubble systems or similar systems at near atmospheric pressure, and should be used with care in any other conditions. See Eqn. (1973). The Wang Curve Fit drag coefficient method is available only when the continuous phase is viscous, and when the dispersed phase is a fluid. This method is not available for solid particles.	None.
Suspension The Suspension drag coefficient method is a linearized form of the Schiller-Neumann drag model which allows $A_{D}$ to become infinitely large when maximum packing is reached. The maximum-packed structure prevents slip from occurring between the phases. This method is available only when the Suspension Rheology model is selected.	None.

Rusche-Issa Drag Coefficient Properties

Depending on the selection of phases for the drag force phase interaction model, the following properties are available:

Method	Corresponding Properties/Method Nodes
Inversion Rusche-Issa This model allows you to model immiscible liquid (such as oil-water) separation without turning on all the detailed physics of the Emulsion rheology model.	Parameter Options Specifies the choice of parameters that are used in the Rusche-Issa drag coefficient, Eqn. (1954). Simcenter STAR-CCM+ detects the type of dispersed phase and sets the default option accordingly to one of the following: Gas Bubble Liquid Droplet Solid Particle User Parameters Available only when the Parameters Options property setting is User Parameters. K1, K2 The parameter values ( $K_{1}$ and $K_{2}$ in Eqn. (1954)) are set automatically for the default dispersed phase type. These values are based on the averages that were obtained by Rusche [538]. These parameters are editable Start Volume Fraction (mixture regime), End Volume Fraction (mixture regime) The start and end values specify the range across which the drag limits are blended. Inversion Length Scale Specifies the size of the dispersed liquid drops after inversion.
Rusche-Issa This drag model allows hindered settling in a similar way to the Richardson-Zaki drag correction.	Parameter Options same as above.

Method

Corresponding Properties/Method Nodes

Inversion Rusche-Issa

This model allows you to model immiscible liquid (such as oil-water) separation without turning on all the detailed physics of the Emulsion rheology model.

Parameter Options

Specifies the choice of parameters that are used in the Rusche-Issa drag coefficient, Eqn. (1954).

Simcenter STAR-CCM+ detects the type of dispersed phase and sets the default option accordingly to one of the following:

Gas Bubble
Liquid Droplet
Solid Particle
User Parameters

Available only when the Parameters Options property setting is User Parameters.

K1, K2

The parameter values ( $K_{1}$ and $K_{2}$ in Eqn. (1954)) are set automatically for the default dispersed phase type. These values are based on the averages that were obtained by Rusche [538]. These parameters are editable

Start Volume Fraction (mixture regime), End Volume Fraction (mixture regime)

The start and end values specify the range across which the drag limits are blended.

Inversion Length Scale

Specifies the size of the dispersed liquid drops after inversion.

Rusche-Issa

This drag model allows hindered settling in a similar way to the Richardson-Zaki drag correction.

Parameter Options: same as above.

The Rusche-Issa drag coefficient has a value that ranges from one at zero dispersed phase volume fraction and increases exponentially [537].

Multiple Flow Regime Topology Drag Coefficient Properties

For a Multiple Flow Regime Topology phase interaction, you set the appropriate Drag Coefficient method for each phase interaction regime.

Method	Corresponding Properties/Method Nodes
Field Function This method is available only for the first dispersed and second dispersed regimes.	Scalar Defines the standard drag coefficient ${C_{i j}}^{D}$ in Eqn. (1931).
Field Function (Linearized Coefficient)	Scalar Defines the linearized drag coefficient ${A_{i j}}^{D}$ in Eqn. (1930).
Schiller-Naumann With this methods the drag coefficient is computed using the Schiller-Naumann correlation. This method is available only for the first dispersed and second dispersed regimes.	None.
Tomiyama The drag coefficient is computed using the Tomiyama drag coefficient method. Available for the first dispersed regime when the secondary phase is a gas and available for the second dispersed regime when the primary phase is a gas. The Tomiyama drag coefficient determines the drag force depending on how contaminated the bulk flow is by impurities, such as surfactants. Surfactants reduce the liquid surface tension and prevent internal circulation in bubbles, hence increasing drag. The Tomiyama correlation requires that gravity is activated for the physics continuum.	Contamination State Select one of the following; Pure Uses the drag coefficient that is described by Eqn. (1968). Moderate Specifies a higher drag coefficient than the Pure option, before bubble deformation effects become dominant. See Eqn. (1969). Contaminated Specifies a higher drag coefficient than the Moderate and Pure options to account for the presence of surfactants. See Eqn. (1970). The Contaminated water option is the default option since it applies to most industrial cases. The surface tension value must be specified in the Multiphase Material > Material Properties > Surface Tension node for the parent phase interaction. The Surface Tension node appears automatically when the Tomiyama correlation is selected.
Blended The intermediate regime drag is calculated by blending the drags of the first dispersed regime and the second dispersed regime on either side of the interface (see Eqn. (1977)). This method is available only for the intermediate regime.	None.
Strubelj-Tiselj The drag coefficient is computed using the Strubelj and Tiselj interface drag method [549]. This method is available only for the intermediate regime.	Relaxation Time Scale A low value of the relaxation time scale helps in instantaneous equalizing of velocities of both of the phases. Increasing this value leads to reduced interface drag and slower equalizing of velocities of both of the phases. This value is t_sc in Eqn. (1976). For air-water flows, t_sc value of 0.01s is sufficient.