# Simulation

The essential elements of filter unit design are determining the required filter surface, the pressure loss in the filter medium and in the filter unit as a whole, and the flow rates occurring in the filter element. The required filter surface is determined by the volumetric flow rate to be filtered and the optimal flow rate at the filter surface for the separation required. The final size of a filter is determined by the filter surface and the type of filter construction used, while the type of filter construction significantly affects the overall hydraulic conditions as well as the incoming volumetric flow rate. It is also important to know the heat transfer, if, for example, hot fluids or gases are to be filtered, or very high pressures and/or pressure variations, which produce strong temperature changes, are involved.
In addition to laboratory and test trials of the media to be filtered, we also use computational fluid dynamics to reduce the number of trials to a minimum and to minimise development times. We are able to use our simulation software to conduct flow and heat analyses. The result is flow-optimized filters that do not have dead zones or flow regions, in which unwanted turbulence would dissipate excessive flow energy.

## Pressure losses

The pressure loss through the filter medium depends on the mean inflow velocity vF, the viscosity η, and the density ϱ of the fluid, as described in the following equation:

$$\Delta p = K_1\cdot \eta \cdot v_F + K_2\cdot \rho\cdot {v_F}^2 .$$

Here the constants K1 and K2 are resistance coefficients that depend on the respective filter medium. The first viscosity-influenced summand describes the laminar flow through the medium, while the second summand represents the contribution of turbulent flow. In some applications the turbulent part is negligible and the pressure loss can be calculated by means of the Darcy equation:

$$\frac{dp}{dz} = \frac{1}{k( \epsilon )} \cdot \eta \cdot v_F .$$

Here k(ε) is known as the Darcy constant that depends on the porosity of the filter medium.
The hydraulic conditions within the filter and the rheological properties of the fluid being considered determine whether laminar flow prevails or if turbulent flow must also be taken into account. The constants K1 and K2, as well as the Darcy constant, express the flow resistance of porous layers. In addition to the filter medium, these include the filter cake, whose thickness increases with increasing filtration time. Furthermore the cake porosity may change with time and height. Thus, in many cases the above-mentioned equations can only be solved iteratively, depending on the cake compressibility and fluid properties.
While the density of incompressible liquids is only temperature dependent, with gases the equation of state must be solved locally, due to their compressibility.

## Non-Newtonian fluids

Modelling hydraulic conditions within a filter becomes more complex if the fluid to be filtered is Non-Newtonian. As a Newtonian fluid exhibits linear viscous behaviour, its viscosity η is only temperature dependent and is defined as ratio of the appearing shear stress τ and the shear velocity γ ̇.

$$\tau = \eta \cdot \dot{\gamma} .$$

Typical Newtonian fluids are water, diluted, aqueous solutions, and all gases. In contrast, solutions of very large molecules like polymers or surfactants, polymer melts, adhesives, blood, and a large variety of dispersions from different industries like printing colours, dispersion colours, mayonnaise, tooth paste, and others exhibit Non-Newtonian behaviour. There are different manifestations of Non-Newtonian behaviour. With shear thinning fluids, for example with polymer melts, the viscosity decreases with increasing shear velocity. The viscosity of shear thickening (dilatant) fluids increases with increasing shear velocity. Pseudoplastic fluids exhibit certain elasticity like solid bodies. Some substances have a defined yield strength (a minimum shear stress at which flowing sets in). This behaviour is required with paints and fluids that are dispensed from collapsible tubes. In certain cases, the viscosity of some fluids does not only depend on the shear velocity, but also on the temporal change of shear velocity. This makes flow modelling even more complex, due to the additional variable time within the rheological equation.
In some mixtures of substances the flow behaviour changes with changes in the concentration of components. This must be considered in the calculation of filtration processes, in which certain ingredients are continuously concentrated. There are different models for predicting elastic and viscous behaviour. They were developed from measuring rheological properties and are integrated in existing flow simulation tools. This has enabled the calculation of the structural behaviour of even complex fluids.

## Flow simulation

Besides laboratory and pilot tests, the methods of numerical fluid dynamics are applied in order to minimize the number of experiments and development times. Our simulation software makes the description of flow conditions and temperature profiles in filter geometries possible. The flow through all common filter media can be simulated, and the rheological properties of a large variety of fluids can be considered. Besides standard fluids like water, oil, air, methane or ammonia, these also include Non-Newtonian fluids like polymer melts, polymer solutions and even fluids with inherent phase transitions.
The simulation results provide the optimum operational parameters for the desired filtration task. These are the filtration pressure, the temperature, and the required filter areas and cycle times for filtration and backwash. The make-up of the filter medium (flat or cylindrical, smooth or pleated) is defined during the simulation. Filter media are installed in filter housings that are hydraulically optimized so that they do not have either dead zones or regions, in which unwanted turbulences cause excessive dissipation of flow energy.

## Services offered by Seebach /Fluid Dynamics Analysis

Modern flow simulations are increasingly used to identify the root cause of filtration problems, and in the development of the filtration solutions for custom applications. The main challenges addressed by Seebach‘s modern flow simulation relate to the scientific characteristics of the fluids to be filtered and the filter media to be used. The foundation of the Seebach approach is our extensive knowledge and experience in the filtration of non-Newtonian fluids which change their viscosity with applied shear.

Seebach has extensive experience in the simulation of fluid and media flow characteris­tics. Utilizing the simulation process we can optimize existing systems or design new systems optimized for specific applications.

Seebach has developed the possibility to describe the dynamics for classical fluids such as gases and liquids, and also for non-classical fluids such as polymers and resins.

As a result, we are able to provide the following data (graphically expressed diagram):
– Expected Start pressure loss
– Velocity profile within the filter
– Shear stress and viscosity profiles
– In case of a temperature-dependent simulation: temperature gradient

For the simulation, we require the following data:
– Drawings (preferred 3D models) of existing filtration system
– Information on flow rate, temperature conditions, desired
filtration rating and filtration
– Fluid data (density, viscosity curves, temperature transition coefficient, etc.)

Depending on the quality of the existing data our time requirement to complete a simulation is:
– about 1 – 3 working days for creating the simulation model
– about 1 – 3 working days for the definition of the fluid and filter media data
and the configuration of the simulation
– 1 – 2 working days for the generated report