### 6.2.2. Modeling Errors

In industrial CFD methods, numerous physical and chemical models are incorporated. Models are usually applied to avoid the resolution of a large range of scales, which would result in excessive computing requirements.

The classical model used in almost all industrial CFD applications is a turbulence model. It is based on time or ensemble averaging of the equations resulting in the so-called Reynolds Averaged Navier-Stokes (RANS) equations. Due to the averaging procedure, information from the full Navier-Stokes equations is lost. It is supplied back into the code by the turbulence model. The most widely used industrial models are two-equation models, such as the or models.

The statistical model approach reduces the resolution requirements in time and space by many orders of magnitude, but requires the calibration of model coefficients for certain classes of flows against experimental data. There is a wide variety of models that are introduced to reduce the resolution requirements for CFD simulations, including:

- Turbulence models

- Multi-phase models

- Combustion models

- Radiation models.

In combustion models, the reduction can be both in terms of the chemical species and in terms of the turbulence-combustion interaction. In radiation, the reduction is typically in terms of the wavelength and/or the directional information. For multi-phase flows, it is usually not possible to resolve a large number of individual bubbles or droplets. In this case, the equations are averaged over the different phases to produce continuous distributions for each phase in space and time.

As all of these models are based on a reduction of the ‘real’ physics to a reduced ‘resolution’, information has to be introduced from outside the original equations. This is usually achieved by experimental calibration, or by available DNS results.

Once a model has been selected, the accuracy of the simulation cannot be increased beyond the capabilities of the model. This is the largest factor of uncertainty in CFD methods, as modeling errors can be of the order of 100% or more. These large errors occur in cases where the CFD solution is very sensitive to the model assumptions and where a model is applied outside its range of calibration.

Because of the complexity of industrial simulations, it cannot be ensured that the models available in a given CFD code are suitable for a new application. While in most industrial codes a number of different models are available, there is no a priori criterion as to the selection of the most appropriate one. Successful model selection is largely based on the expertise and the knowledge of the CFD user.

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