Why do you say DNS and RANS should match each other? They are very different approaches, so isn't some variation to be expected?

Of course it is, but I compared the results with some other and the result of RANS matched in all cases the DNS-data and the wall function. So I think my results should do the same.
I my thinking the first calculated y+ value should be identical with the exported y+ value for the first node. And that's why i came to this modification...

Your results are already pretty close so you know you are not far wrong. If you expect that you can get your results closer to the DNS line then you need to do a careful validation of mesh size, convergence and time step size.

OK I will try this suggestions.

Thank you very much for your help Garrocks.