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Flow Models
The Flow module solves for conservation of mass and momentum, using the transient Navier-Stokes Equations H.Ding, F.C. Visser, Y.Jiang, and M. Furmanczyk, “Demonstration and Validation of a 3-D CFD Simulation Tool Predicting Pump Performance and Cavitation for Industrial Applications,” FEDSM2009-78256, 2009..
The integral form (conservative) of Reynold’s Averaged Navier-Stokes Equations (RANS) are as follows:
Continuity
Momentum
Stress Tensor
where,
 τij effective shear stress (molecular+turbulent) f body force n surface normal ρ static pressure(Pa) t time v fluid velocity vσ mesh velocity Ω(t) control volume as a function of time r average local fluid density (kg/m3) σ surface of control volume µ dynamic viscosity (Poise or Pa-s) µt turbulent dynamic viscosity δij Kronecker delta(=1 for i=j, =0 for i≠j)
Viscosity Models
Constant Dynamic Viscosity—Specifies the fluid viscosity in a selected volume. The unit of dynamic viscosity is Pa-s or N-s/m2.
The value of the dynamic viscosity is specified in the box under the Constant Dynamic Viscosity selection.
Constant Kinematic Viscosity—Specifies the fluid viscosity in a selected volume. The unit of kinematic viscosity is m2/s. The value of the kinematic viscosity is specified in the box under the Constant Kinematic Viscosity selection.
Sutherland Law—Specifies the fluid viscosity in a selected volume in terms of the dynamic viscosity (Pa-s). The equation and inputs are as follows:
where,
 T temperature (K) µref viscosity at reference temperature (Pa-s) S Sutherland Temperature (K)
 T is the fluid Temperature (K) required as an input if the energy module is not active.
Sutherland Law is used to compute the viscosity of an ideal gas as a function of temperature. Sutherland, W. (1893), "The viscosity of gases and molecular force," Philosophical Magazine, S. 5, 36, pp. 507-531 (1893). The following table shows Sutherland's constant and reference temperature for selected gases. Ref: en.wikipedia.org/wiki/viscosity.
 Gas S (K) Tref (K) mref (Pa-s) air 120 291.15 18.27 e-6 nitrogen 111 300.55 17.81 e-6 oxygen 127 292.25 20.81 e-6 carbon dioxide 240 293.15 14.8 e-6 carbon monoxide 118 288.15 17.2 e-6 hydrogen 72 293.85 8.76 e-6 ammonia 370 293.15 9.82 e-6 sulphur dioxide 416 293.65 12.54 e-6 helium 79.4 273 19 e-6
NonNewtonian Viscosity Models
The nonNewtonian viscosity models are:
Herschel-Bulkley Model
Bingham Models
These models provide the appropriate viscosity for various types of fluids that exhibit nonNewtonian flow properties. The Herschel-Bulkley model and Bingham models relate the shear stress to the shear rate as follows:
where,
 e0 critical shear rate k consistency index τ0 yield stress of the fluid n Power Law index. For Bingham model, n=1
 The shear rate of 0 is the same as the gamma dot in the plot above.
Resistance Model
Resistance Model is a Flow module option that you can use to set a resistance in a selected volume. The Resistance Model contains the following two models:
Pressure Loss: based on the following equation:
where,
 Cl linear drag coefficient (Pa-s/m2) Cd quadratic drag coefficient (1/m) β porosity ρ density
Darcy's Law: model based on the following equation:
where,
 β porosity α permeability µ dynamic viscosity V velocity Cd quadratic drag coefficient (1/m)
The velocity used in the resistance equation is the local velocity. F in the equation is measured in the unit N/m3, such as force/volume, or pressure gradient (Dp/Dx), or rg. The pressure drop across the interface is computed by multiplying F by a finite thickness. The porosity is set in the Common module.