modelSolAbsForristal
1D radial energy balance around the Heat Transfer Element based on the Forristal
Information
Model SolAbsForristal represents the one-dimensional radial energy balance between the Heat Collector Element (HCE) and the atmosphere based on the Forristal model.
The terms in the energy balance depends on the collector type, the HCE condition, the optical properties and the ambient condition.
The phenomena represented by the model are:
The model assumptions are:
Parameters
| Type | Name | Default | Description |
|---|---|---|---|
| Real | pi | Modelica.Constants.pi | |
| Real | Sigma | Modelica.Constants.sigma | Stefan-Boltzmann constant |
| Real | gg | Modelica.Constants.g_n | Standard acceleration of gravity on earth |
| Integer | N | 2 | number of cells |
| Integer | Nt | 1 | number of tubes |
| Modelica.SIunits.Length | L | length of tubes | |
| Modelica.SIunits.Length | A_P | Aperture of the parabola | |
| Real | P_mmhg | Pvacuum/133.322368 | |
| General › Optical Properties | |||
| Real | eps1 | HCE Shadowing | |
| Real | eps2 | Tracking error | |
| Real | eps3 | Geometry error | |
| Real | rho_cl | Mirror reflectivity | |
| Real | eps4 | Dirt on Mirrors | |
| Real | eps5 | Dirt on HCE | |
| Real | eps6 | Unaccounted | |
| Real | Tau_g | 0.963 | Glass Transmissivity |
| Real | Alpha_g | 0.02 | Glass Absorptivity CONSTANT see Forristal pag 18 |
| Real | Eps_g | 0.89 | Glass emissivity CONSTANT see Forristal pag 18 |
| Real | Alpha_t | 0.97 | Tube Absorptivity |
| General › GeometriesAndProperties of the glass envelope | |||
| Modelica.SIunits.Length | Dext_g | 0.12 | External glass diameter |
| Modelica.SIunits.Length | th_g | 0.0025 | Glass thickness |
| Modelica.SIunits.Length | rext_g | Dext_g/2 | External Radius Glass |
| Modelica.SIunits.Length | rint_g | rext_g - th_g | Internal Radius Glass |
| Modelica.SIunits.Density | rho_g | Glass density | |
| Modelica.SIunits.SpecificHeatCapacity | Cp_g | Specific heat capacity of the glass | |
| Modelica.SIunits.ThermalConductivity | lambda_g | Thermal conductivity of the glass | |
| General › GeometriesAndProperties of the metal envelope | |||
| Modelica.SIunits.Length | Dext_t | 0.07 | External diameter tube |
| Modelica.SIunits.Length | th_t | 0.002 | tube thickness |
| Modelica.SIunits.Length | rext_t | Dext_t/2 | External Radius Glass |
| Modelica.SIunits.Length | rint_t | rext_t - th_t | Internal Radius Glass |
| Modelica.SIunits.Density | rho_t | tube density | |
| Modelica.SIunits.SpecificHeatCapacity | Cp_t | Specific heat capacity of the tube | |
| Modelica.SIunits.ThermalConductivity | lambda_t | Thermal conductivity of the tube | |
| General › Atmospheric characteristic | |||
| Modelica.SIunits.Pressure | Patm | Atmospheric pressure | |
| Modelica.SIunits.ThermalConductivity | k_air | 0.025574811 | Thermal conductivity of air at constant pressure |
| Modelica.SIunits.Density | rho_air | 1.183650626 | Density of air |
| Modelica.SIunits.DynamicViscosity | mu_air | 1.83055E-05 | Dynamic viscosity of air at glass temperature |
| Real | Pr | ||
| General › Vacuum properties: between metal and glass envelope | |||
| Modelica.SIunits.Pressure | Pvacuum | Vacuum Pressure [Pa] | |
| Real | GAMMA | 1.39 | Ratio of specific heats for the annulus gas |
| Real | DELTA | 3.53e-8 | Molecular diameter for the annulus gas [cm] |
| Real | BB | 1.571 | Interaction coefficient |
| Modelica.SIunits.ThermalConductivity | k_st | 0.02551 | Thermal conductivity at standard pressure and temperature |
| Initialization | |||
| Modelica.SIunits.Temperature | T_g_start_in | Temperature of the glass_inlet | |
| Modelica.SIunits.Temperature | T_g_start_out | Temperature of the glass outlet | |
| Modelica.SIunits.Temperature[N] | T_g_start | linspace(T_g_start_in, T_g_start_out, N) | start value of the tube temperature vector |
| Modelica.SIunits.Temperature | T_t_start_in | Temperature of the tube inlet | |
| Modelica.SIunits.Temperature | T_t_start_out | Average temperature of the tube outlet | |
| Modelica.SIunits.Temperature[N] | T_t_start | linspace(T_t_start_in, T_t_start_out, N) | start value of the tube temperature vector |
Connectors
| Type | Name | Default | Description |
|---|---|---|---|
| Modelica.Blocks.Interfaces.RealInput | DNI | ||
| Modelica.Blocks.Interfaces.RealInput | v_wind | ||
| Modelica.Blocks.Interfaces.RealInput | Theta | In radiants | |
| Modelica.Blocks.Interfaces.RealInput | Tamb | ||
| Interfaces.HeatTransfer.ThermalPort | wall_int |
Components
| Type | Name | Default | Description |
|---|---|---|---|
| Real[N] | Eps_t | Coating emissivity funzione della temperature Forristal pag 18 | |
| Real | C | if Re < 40 then 0.75 else if Re > 40 and Re < 1000 then 0.51 else if Re > 1000 and Re < 200000 then 0.26 else 0.076 | Coefficient for Nusselt number from Forristal |
| Real | m | if Re < 40 then 0.4 else if Re > 40 and Re < 1000 then 0.5 else if Re > 1000 and Re < 200000 then 0.6 else 0.7 | Coefficient for Nusselt number from Forristal |
| Real | n | if Pr < 10 then 0.37 else 0.36 | Coefficient for Nusselt number from Forristal |
| Real | Re | Reynolds number of atmosphere | |
| Real | Nu | Nusselt number of atmophere | |
| Modelica.SIunits.Area | A_ext_g | Lateral external area of the glass | |
| Modelica.SIunits.Area | A_ext_t | Lateral external area of the tube | |
| Modelica.SIunits.Area | A_ref | Area of the reflector | |
| Modelica.SIunits.Area | Am_t | Area of the metal cross section | |
| Modelica.SIunits.Area | Am_g | Area of the glass cross section | |
| Modelica.SIunits.CoefficientOfHeatTransfer[N] | Gamma_vacuum | Coefficient of heat transfer vacuum | |
| Modelica.SIunits.CoefficientOfHeatTransfer | Gamma_air | coefficient of heat transfer | |
| Real[N] | LAMBDA | mean free-path between collisions of a molecule [m] | |
| Modelica.SIunits.Temperature | Tsky | Sky temperature | |
| Modelica.SIunits.Temperature[N] | T_int_t | temperature of the internal tube | |
| Modelica.SIunits.Temperature[N] | T_t | temperature at the center of the tube | |
| Modelica.SIunits.Temperature[N] | T_ext_t | temperature of the external tube | |
| Modelica.SIunits.Temperature[N] | T_g_t | Average temperature of the inner glass and the external tube | |
| Modelica.SIunits.Temperature[N] | T_int_g | temperature of the internal glass | |
| Modelica.SIunits.Temperature[N] | T_g | temperature at the center of the glass | |
| Modelica.SIunits.Temperature[N] | T_ext_g | temperature of the external glass | |
| Modelica.SIunits.HeatFlowRate | Q_glass_tot | ||
| Modelica.SIunits.HeatFlowRate | Q_tube_tot | ||
| Modelica.SIunits.HeatFlowRate[N] | Q_abs | ||
| Modelica.SIunits.HeatFlux | Phi_glass_tot | heat flux absorbed by the glass | |
| Modelica.SIunits.HeatFlux[N] | Phi_glass_tot_N | Heat flux from the sun to the glass at each node | |
| Modelica.SIunits.HeatFlux | Phi_tube_tot | Heat flux absorbed by the tube | |
| Modelica.SIunits.HeatFlux[N] | Phi_tube_tot_N | Heat flux from the sun to the tube at each node | |
| Modelica.SIunits.HeatFlux[N] | Phi_tube_int | Heat flux of tube internal | |
| Modelica.SIunits.HeatFlux[N] | Phi_tube_ext | Heat flux of the tube external | |
| Modelica.SIunits.HeatFlux[N] | Phi_conv_gas | heat flux convection in the vacuum | |
| Modelica.SIunits.HeatFlux[N] | Phi_rad_gas | heat flux radiation in the vaccum | |
| Modelica.SIunits.HeatFlux[N] | Phi_glass_int | heat flux of the glass internal | |
| Modelica.SIunits.HeatFlux[N] | Phi_glass_ext | heat flux of the glass external | |
| Modelica.SIunits.HeatFlux[N] | Phi_conv_air | Heat flux convection in the air | |
| Modelica.SIunits.HeatFlux[N] | Phi_rad_air | heat flux radiation in the air | |
| Modelica.SIunits.HeatFlux | Phi_loss | Heat losses with respect to the reflector surface | |
| Real | eta_opt | ||
| Real | eta_opt_g | ||
| Real | eta_opt_t | ||
| Real | IAM | Incident Angle Modifier | |
| Real[N] | eta_th | Thermal efficiency at each node | |
| Real[N] | eta_TOT | Total efficiency : eta_th * eta_opt_t | |
| Real | Eta_th | Average Thermal efficiency | |
| Real | Eta_TOT | Average Total efficiency |