Reynolds Number Dependent Coefficients |
 
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Reynolds Number Dependent Coefficients |
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Flexcom also provides a facility to specify hydrodynamic coefficients as a function of Reynolds number (Re). The same five hydrodynamic coefficients are specified on a set by set basis as before, but the terms are repeatedly input for a range of Reynolds numbers to build up a table to data. For values of Re intermediate to the values you specify, the hydrodynamic coefficients are calculated by linear interpolation.
When hydrodynamic coefficients are specified as a function of Re, Flexcom calculates the value of Re at each integration point at each iteration, using the following relation:
(1)
Here Dd is drag diameter and 
is the kinematic viscosity of seawater. 
represents the magnitude of the relative fluid/structure velocity in the direction normal to the element. The manner in which 
is calculated depends on whether you invoke the Constant or Instantaneous Reynolds number computation option.
The default option is Constant, which is valid only for analyses with a single regular Airy wave or a Stokes V waves. When Constant is selected, the computation procedure is as follows. During the first two wave periods, the profile of Re with depth is based only on water particle velocity due to current. During the second wave period the value of 
at each integration point is monitored and the maximum value for the integration point stored. These stored maxima are then used in calculating the Re profile for third wave period, during which the value of 
is again monitored and stored; and so on until the analysis is completed.
If on the other hand you choose the Instantaneous option, hydrodynamic coefficients are computed as a function of the instantaneous value of Re. In this case 
is the magnitude of the instantaneous relative fluid/structure velocity normal to the element at each solution time. Because Re is continuously recomputed, this procedure is valid for any seastate specification, whether regular or random or combinations of these.
One further point to note is that Re is defined in terms of the (unknown) structure velocity. For this reason, regular wave analyses with the default Constant procedure may take longer to reach steady state that would be the case were the hydrodynamic coefficients independent of Re. You should be careful to ensure steady state conditions have indeed been achieved when interpreting the results of regular wave runs that use this facility.
Taking the Pierson-Moskowitz spectrum as an example, the FREQUENCY=AREA input is used to request equal area discretisation, while the FREQUENCY=GP input is used to request geometric progression discretisation.
•*HYDRODYNAMIC SETS is used to assign hydrodynamic coefficients to element sets. Specifically, the TYPE=REYNOLDS input is used to assign hydrodynamic coefficients to element sets where these coefficients are a function of Reynolds number.
•*PRINT is used to request additional printed output to the main output file. Specifically, the OUTPUT=REYNOLDS COF OUTPUT option is used to request output of the instantaneous hydrodynamic coefficients as a function of time. For analyses where you specify that hydrodynamic coefficients are to be computed as a function of instantaneous Re, then for QA purposes a table may be automatically created showing the drag and inertia coefficients actually used by the program in calculating hydrodynamic forces at each integration point on each element. This output is routed to a separate output file named jobname.cof. In the case of a static analysis, the output is produced at the last solution time only. In a dynamic analysis, the output is generated at each solution time which lies within a user-specified range. The default range is from the start of the analysis to the end; if you want to change this, you do so when specifying time variables. The data is in tabular format, in eight columns, these being the following for each location:
1.Element number
2.Integration point number
3.Instantaneous elevation above the mudline
4.Instantaneous water particle velocity
5.Instantaneous structural velocity
6.Instantaneous relative velocity
7.Corresponding normal drag coefficient
8.Corresponding normal inertia coefficient