.ThermoPower.Gas.Flow1DFV

Information

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.

Contents

Revisions

• 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.