Reconciliation of measured and predicted unsteady skin friction

Fundamental differences between measured and predicted skin friction forces in unsteady pipe flows are addressed. Strong evidence is presented to demonstrate the existence of three types of behaviour that are characterised as (i) approximately frozen turbulent viscosity, (ii) rapidly changing viscosity and (iii) gradually evolving viscosity. All three types are illustrated for the particular case of constant uniform acceleration from an initially steady flow. It is shown: that frozen viscosity assumptions are suitable after sudden changes from steady flow and that they remain applicable for significant time; that frozen-viscosity models can give reasonable predictions of damping of pressure waves measured in well known laboratory experiments; that experimental measurements with which the frozen-viscosity models have been compared unfavourably were obtained during periods of gradually-evolving viscosity; that the behaviour of flows during the period of gradually-evolving viscosity can be interpreted in a physically plausible manner. Much of the evidence used to justify the above deductions is obtained from a CFD analysis using a low Reynolds number RANS approach. The use of this model is itself justified by comparison with experiments that demonstrate its ability to predict delays in turbulence responses with sufficient accuracy for the purposes of this paper.