.ThermoPower.Water.Flow1D2ph

Information

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

• The fluid state is either one-phase, or a two-phase mixture.
• In case of two-phase flow, the same velocity is assumed for both phases (homogeneous model).
• 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 applications using water or steam as a working fluid.
• 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 surface, which is represented by the wall connector. The actual heat flux must be computed by a connected component (heat transfer computation module).

The mass, momentum, and energy balance equation are discretised with the finite volume method. The state variables are one pressure, one flowrate (optional) and N-1 specific enthalpies.

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 instabilities occur in tubes with very low pressure drops.

The model assumes that the mass flow rate is always from the inlet to the outlet. Small reverse flow is allowed (e.g. when closing a valve at the outlet), but the model will not account for it explicitly.

Modelling options

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.

The dynamic momentum term is included or neglected depending on the DynamicMomentum parameter.

The density is computed assuming a linear distribution of the specific enthalpy between the nodes; this requires the availability of the time derivative of the inlet enthalpy. If this is not available, it is possible to set avoidInletEnthalpyDerivative to true, which will cause the mean density of the first volume to be approximated as its outlet density, thus avoiding the need of the inlet enthalpy derivative.

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 HydraulicCapacitance = 2 (default option) then the mass storage term depending on the pressure is lumped at the outlet, while the optional momentum storage term depending on the flowrate is lumped at the inlet. If HydraulicCapacitance = 1 the reverse takes place.

Start values for pressure and flowrate are specified by pstart, wstart. The start values for the node enthalpies are linearly distributed from hstartin at the inlet to hstartout at the outlet.

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 visible 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.

Revisions

• 27 Jul 2007 by Francesco Casella:
  Corrected error in the mass balance equation, which lead to loss/gain of mass during transients.
• 30 May 2005 by Francesco Casella:
  Initialisation support added.
• 24 Mar 2005 by Francesco Casella:
  FFtypes package and NoFriction option added.
• 16 Dec 2004 by Francesco Casella:
  Standard medium definition added.
• 8 Oct 2004 by Francesco Casella:
  Model now based on Flow1DBase.
• 24 Sep 2004 by Francesco Casella:
  Removed wstart, pstart. Added pstartin, pstartout.
• 28 Jul 2004 by Francesco Casella:
  Adapted to Modelica.Media.
• 15 Jan 2004 by Francesco Casella:
  Computation of fluid velocity u added. Improved treatment of geometric parameters
• 1 Oct 2003 by Francesco Casella:
  First release.