This model describes the flow of a gas in a rigid tube. The basic modelling assumptions are:

- Uniform velocity is assumed on the cross section, leading to a 1-D distributed parameter model.
- Turbulent friction is always assumed; a small linear term is added to avoid numerical singularities at zero flowrate. The friction effects are not accurately computed in the laminar and transitional flow regimes, which however should not be an issue in most power generation applications.
- The model is based on dynamic mass, momentum, and energy balances. The dynamic momentum term can be switched off, to avoid the fast oscillations that can arise from its coupling with the mass balance (sound wave dynamics).
- The longitudinal heat diffusion term is neglected.
- The energy balance equation is written by assuming a uniform pressure distribution; the pressure drop is lumped either at the inlet or at the outlet.
- The fluid flow can exchange thermal power through the lateral
tube boundary, by means of the
`wall`connector, that actually represents the wall surface with its temperature. The heat flow is computed by an instance of the replaceable HeatTransfer model; various heat transfer models are available in the ThermoPower.Thermal.HeatTransferFV package.

The mass, momentum and energy balance equation are discretised with the finite volume method. The state variables are one pressure, one flowrate (optional), N-1 temperatures, and either one or N-1 gas composition vectors.

The turbulent friction factor can be either assumed as a
constant, or computed by Colebrook's equation. In the former case,
the friction factor can be supplied directly, or given implicitly
by a specified operating point. In any case, the multiplicative
correction coefficient `Kfc` can be used to modify the
friction coefficient, e.g. to fit experimental data.

A small linear pressure drop is added to avoid numerical
singularities at low or zero flowrate. The `wnom` parameter
must be always specified: the additional linear pressure drop is
such that it is equal to the turbulent pressure drop when the
flowrate is equal to `wnf*wnom` (the default value is 1% of
the nominal flowrate). Increase `wnf` if numerical problems
occur in tubes with very low pressure drops.

Flow reversal is not supported by this model; if you need flow reversal, please consider using the Flow1DFEM model.

**Modelling options**

The actual gas used in the component is determined by the
replaceable `Medium` package.In the case of multiple
component, variable composition gases, the start composition is
given by `Xstart`, whose default value is
`Medium.reference_X`.

Thermal variables (enthalpy, temperature, density) are computed
in `N` equally spaced nodes, including the inlet (node 1)
and the outlet (node N); `N` must be greater than or equal
to 2.

if `UniformComposition` is true, then a uniform
compostion is assumed for the gas through the entire tube length;
otherwise, the gas compostion is computed in `N` equally
spaced nodes, as in the case of thermal variables.

The following options are available to specify the friction coefficient:

`FFtype = FFtypes.Kfnom`: the hydraulic friction coefficient`Kf`is set directly to`Kfnom`.`FFtype = FFtypes.OpPoint`: the hydraulic friction coefficient is specified by a nominal operating point (`wnom`,`dpnom`,`rhonom`).`FFtype = FFtypes.Cfnom`: the friction coefficient is computed by giving the (constant) value of the Fanning friction factor`Cfnom`.`FFtype = FFtypes.Colebrook`: the Fanning friction factor is computed by Colebrook's equation (assuming Re > 2100, e.g. turbulent flow).`FFtype = FFtypes.NoFriction`: no friction is assumed across the pipe.

If `QuasiStatic` is set to true, the dynamic terms are
neglected in the mass, momentum, and energy balances, i.e.,
quasi-static behaviour is modelled. It is also possible to neglect
only the dynamic momentum term by setting `DynamicMomentum =
false`.

If `HydraulicCapacitance = 2` (default option) then the
mass buildup term depending on the pressure is lumped at the
outlet, while the optional momentum buildup term depending on the
flowrate is lumped at the inlet; therefore, the state variables are
the outlet pressure and the inlet flowrate. If
`HydraulicCapacitance = 1` the reverse takes place.

Start values for the pressure and flowrate state variables are
specified by `pstart`, `wstart`. The start values for
the node temperatures are linearly distributed from
`Tstartin` at the inlet to `Tstartout` at the outlet.
The (uniform) start value of the gas composition is specified by
`Xstart`.

A bank of `Nt` identical tubes working in parallel can be
modelled by setting `Nt > 1`. The geometric parameters
always refer to a *single* tube.

This models makes the temperature and external heat flow
distributions available to connected components through the
`wall` connector. If other variables (e.g. the heat transfer
coefficient) are needed by external components to compute the
actual heat flow, the `wall` connector can be replaced by an
extended version of the `DHT` connector.

Name | Description |
---|---|

HeatTransfer |

*30 May 2005*by Francesco Casella:

Initialisation support added.*24 Mar 2005*by Francesco Casella:

`QuasiStatic`added.

`FFtypes`package and`NoFriction`option added.*19 Nov 2004*by Francesco Casella:

Adapted to Modelica.Media.*5 Mar 2004*by Francesco Casella:

First release.

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