AixLib.Fluid.FixedResistances.BaseClasses.PlugFlowTransportDelay

# .AixLib.Fluid.FixedResistances.BaseClasses.PlugFlowTransportDelay

Delay time for given normalized velocity

## Information

Calculates time delay at both sides of the pipe as the difference between the current simulation time and the inlet time of the fluid at both ends of the pipe.

#### Main equation

∂z(x,t)/∂t + v(t) ∂z(x,t)/∂x = 0,

where z(x,t) is the spatial distribution as a function of time of any property z of the fluid. For the inlet time propagation, z will be replaced by the inlet time of the fluid tin.

#### Implementation

The inlet time is approached as a fluid property and its propagation follows the one-dimensional wave equation, implemented using the spatialDistribution function. This components requires the mass flow through the pipe and the pipe dimensions in order to derive information about the fluid propagation.

The component calculates the delay time at the inlet and the outlet port of the pipe. For the forward flow, the time delay is exposed at the output `tau`, and for the backward flow, the time delay is exposed at the output `tauRev`.

#### Assumption

No axial mixing takes place in the pipe.

## Revisions

- December 2, 2020, by Philipp Mehrfeld:
  Corrected calculation of `tau` and `tauRev` to be be only positive.
  This is for #1427.
- December 14, 2018, by Michael Wetter:
  Corrected argument of `spatialDistribution` operator to be a parameter expression.
  This is for #1055.
- September 9, 2016 by Bram van der Heijde:
  Rename from PDETime_massFlowMod to PlugFlowTransportDelayMod
- December 2015 by Carles Ribas Tugores:
  Modification in delay calculation to fix issues.
- November 6, 2015 by Bram van der Heijde:
  Adapted flow parameter to mass flow rate instead of velocity. This change should also fix the reverse and zero flow issues.
- October 13, 2015 by Marcus Fuchs:
  Use `abs()` of normalized velocity input in order to avoid negative delay times.
- July 2015 by Arnout Aertgeerts:
  First implementation.

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