## onsdag 4 maj 2011

### Why Measure Viscosity and Temperature? To measure viscosity is possible for heavily viscous fluids, but difficult for slightly viscous fluids.

Here is a response to a question by Anders Nordenfelt about how to measure temperature:

To measure a coefficient of viscosity of slightly viscous fluid is difficult, or more precisely virtually impossible, since it is defined as shear stress per shear deformation (velocity), which in turbulent slightly viscous flow is severely dependent on the fluid flow and not only on the fluid itself.

It is thus necessary to make a distinction between different viscosity coefficients of vastly varying size from laminar viscosity to turbulent viscosity for different elementary flow patterns. To use the appropriate viscosity coefficient in a fluid simulation thus poses the requirement that the flow is known beforehand as well as its viscosity coefficients for all elementary flows involved, which is difficult to meet.

In the books Computational Turbulent Incompressible Flow and Computational Thermodynamics we show a way out of this dead end which starts with the following question:
• Why are viscosity coefficients required?
In the case of turbulent (incompressible) flow one answer is: To compute turbulent dissipation from turbulent shear force as viscosity coefficient times shear deformation (velocity).

In the books it is shown that that turbulent dissipation can be computed as a transfer from kinetic energy to internal energy, without making an explicit computation of turbulent dissipation through viscosity coefficients combined with shear deformation. The computation uses a certain form of numerical viscosity automatically introduced by residual stabilization and the only input is that the physical viscosity is small, whatever else it may be.

The net result is that it is possible to simulate slightly viscous flow without any precise input of viscosity coefficients, only that the viscosity is small.

Similarly, coefficients of heat capacity as a measure of heat energy per unit of temperature and mass, as well as temperature as heat energy per unit mass, may be difficult to define and measure, since the required precise definition of heat energy is difficult to give.

An alternative is to again view internal energy/heat energy as arising from transfer of energy from kinetic energy which makes it accessible indirectly thus avoiding the difficulty of computing internal energy through temperature and heat capacity coefficients.