Buildings.Fluid.DXSystems.Cooling.BaseClasses

Package with base classes for Buildings.Fluid.DXSystems.Cooling

Information

This package contains base classes that are used to construct the models in Buildings.Fluid.DXSystems.Cooling.

Extends from Modelica.Icons.BasesPackage (Icon for packages containing base classes).

Package Content

Name	Description
ApparatusDewPoint	Calculates air properties at apparatus dew point
ApparatusDryPoint	Calculates air properties at dry coil surface
CapacityWaterCooled	Calculates cooling capacity at given temperature and flow fraction for water source DX coils
Condensation	Calculates rate of condensation
DXCooling	DX cooling coil operation
DryWetSelector	Selects results from dry or wet coil
EssentialParameters	A partial block for essential parameters for cooling DX coils
Evaporation	Model that computes evaporation of water that accumulated on the coil surface
InputPower	Electrical power consumed by the unit
PartialCapacity	Calculates performance curve value at given temperature and mass flow rate
PartialCoilCondition	Partial block for dry and wet coil conditions
PartialCoilInterface	Partial block for DX coil
PartialDXCoil	Partial model for air or water cooled DX cooling coil
PartialDXCoolingCoil	Partial model for DX cooling coil
PartialSurfaceCondition	Partial block for apparatus dew and dry point calculation
PartialWaterCooledDXCoil	Base class for water source DX coils
SensibleHeatRatio	Calculates the sensible heat ratio
SpeedSelect	Selects the lower specified speed ratio for multispeed model
SpeedShift	Interpolates values between speeds
UACp	Calculates UA/Cp of the coil
WetCoil	Calculates wet coil condition
Functions	Package with functions
Examples	Collection of models that illustrate model use and test models

Buildings.Fluid.DXSystems.Cooling.BaseClasses.ApparatusDewPoint

Calculates air properties at apparatus dew point

Information

This blocks outputs the state of the moist air at the dew point of the coil. The bypass factor of the coil and the resulting enthalpy difference is computed by its base class Buildings.Fluid.DXSystems.Cooling.BaseClasses.PartialSurfaceCondition.

Extends from Buildings.Fluid.DXSystems.Cooling.BaseClasses.PartialSurfaceCondition (Partial block for apparatus dew and dry point calculation).

Parameters

Connectors

Modelica definition

Buildings.Fluid.DXSystems.Cooling.BaseClasses.ApparatusDryPoint

Calculates air properties at dry coil surface

Information

This blocks outputs the state of the moist air at of the coil, assuming no condensation occurs. The bypass factor of the coil and the resulting enthalpy difference is computed by its base class Buildings.Fluid.DXSystems.Cooling.BaseClasses.PartialSurfaceCondition.

Extends from Buildings.Fluid.DXSystems.Cooling.BaseClasses.PartialSurfaceCondition (Partial block for apparatus dew and dry point calculation).

Parameters

Connectors

Modelica definition

Buildings.Fluid.DXSystems.Cooling.BaseClasses.CapacityWaterCooled

Calculates cooling capacity at given temperature and flow fraction for water source DX coils

Information

This model calculates cooling capacity and EIR at off-designed conditions for water source DX coils. The difference between air source and water source DX coils is that water source DX coils require two additional modifer curves for total cooling capacity and EIR as a function of water mass flowrate at the condensers.

Total Cooling Capacity

The total cooling capacity at off-designed conditions for water source DX coils is calculated as:

Q̇(θ_e,in, θ_c,in, ff) = cap_θ(θ_e,in, θ_c,in) cap_FF(ff) cap_FFCon(ffCon) Q̇_nom

where cap_FFCon(ffCon) is the additional modifier for cooling capacity, and calculated as:

capCon_FFCon(ffCon) = b₁ + b₂ ffCon + b₃ ffCon² + b₄ffCon³ + ...

where the variable ffCon is the nomalized mass flow rate at the condenser, and calculated as:

ffCon = ṁCon ⁄ ṁCon_nom

where ṁCon is the mass flow rate at the condenser and ṁCon_nom is the nominal mass flow rate at the condenser.

Energy Input Ratio (EIR)

The Energy Input Ratio (EIR) is the inverse of the Coefficient of Performance (COP). Similar to the cooling capacity modifiers, the change in EIR due to change in water mass flow rate at the condenser is

EIR_FFCon(ffCon) = b₁ + b₂ ffCon + b₃ ffCon² + b₄ffCon³ + ...

where the six coefficients are obtained from the coil performance data record. See Buildings.Fluid.DXSystems.Cooling.BaseClasses.PartialCapacity for more information.

Extends from Buildings.Fluid.DXSystems.Cooling.BaseClasses.PartialCapacity (Calculates performance curve value at given temperature and mass flow rate).

Parameters

Connectors

Modelica definition

Buildings.Fluid.DXSystems.Cooling.BaseClasses.Condensation

Calculates rate of condensation

Information

This block computes the water mass flow rate that condenses.

Extends from Modelica.Blocks.Icons.Block (Basic graphical layout of input/output block).

Connectors

Modelica definition

Buildings.Fluid.DXSystems.Cooling.BaseClasses.DXCooling

DX cooling coil operation

Information

This block combines the models for the dry coil and the wet coil. Output of the block is the coil performance which, depending on the mass fraction at the apparatus dew point temperature and the mass fraction of the coil inlet air, may be from the dry coil, the wet coil, or a weighted average of the two.

Extends from Buildings.Fluid.DXSystems.Cooling.BaseClasses.PartialCoilInterface (Partial block for DX coil).

Parameters

Connectors

Modelica definition

Buildings.Fluid.DXSystems.Cooling.BaseClasses.DryWetSelector

Selects results from dry or wet coil

Information

This block smoothly transitions the results from the dry coil and the wet coil computation. The independent variable for the transition is the difference between the water mass fractions at the apparatus dew point, as computed by the wet coil model, and the coil inlet mass fraction.

Connectors

Modelica definition

Buildings.Fluid.DXSystems.Cooling.BaseClasses.EssentialParameters

A partial block for essential parameters for cooling DX coils

Information

This partial block declares parameters that are required by most classes for cooling DX coils in the package Buildings.Fluid.DXSystems.

Parameters

Modelica definition

Buildings.Fluid.DXSystems.Cooling.BaseClasses.Evaporation

Model that computes evaporation of water that accumulated on the coil surface

Information

This model computes the water accumulation on the surface of a cooling coil. When the cooling coil operates, water is accumulated on the coil surface up to a maximum amount of water before water starts to drain away from the coil. When the coil is off, the accumulated water evaporates into the air stream.

Physical description

The calculations are based on Shirey et al. (2006).

Parameters

The maximum amount of water that can be accumulated is computed based on the following model, where we used the convention that latent heat removed from the air is negative: The parameter t_wet defines how long it takes for condensate to drip of the coil, assuming the coil starts completely dry and operates at the nominal operating point. Henderson et al. (2003) measured values for t_wet from 16.5 minutes (990 seconds) to 29 minutes (1740 seconds). Thus, we use a default value of t_wet=1400 seconds. The maximum amount of water that can accumulate on the coil is

m_max = -Q̇_L,nom   t_wet ⁄ h_fg

where Q̇_L,nom<0 is the latent capacity at the nominal conditions and h_fg is the latent heat of evaporation.

When the coil is off, the water that has been accumulated on the coil evaporates into the air. The rate of water vapor evaporation at nominal operating conditions is defined by the parameter γ_nom. The definition of γ_nom is

γ_nom = Q̇_e,nom ⁄ Q̇_L,nom,

where Q̇_e,nom<0 is the rate of evaporation from the coil surface into the air stream right after the coil is switched off. The default value is γ_nom = 1.5.

Time dependent calculations

First, we discuss the accumulation of water on the coil. The rate of water accumulation is computed as

dm(t)⁄dt = -ṁ_wat(t)

where ṁ_wat(t) ≤ 0 is the water vapor mass flow rate that is extracted from the air at the current operating conditions. The actual water vapor mass flow rate that is removed from the air stream is as computed by the steady-state cooling coil performance model because for the coil outlet conditions, it does not matter whether the water accumulates on the coil or drips away from the coil. The initial value for the water accumulation is zero at the start of the simulation, and set to whatever water remains after the coil has been switched off and the water partially or completely evaporated into the air stream.

Now, we discuss the evaporation of the water on the coil surface into the air when the coil is off. The model in Shirey et al. (2006) is based on the assumption that the wet coil acts as an evaporative cooler. The change of water on the coil is

dm(t)⁄dt = -ṁ_max(t) η(t),

where ṁ_max(t) > 0 is the maximum water mass flow rate from the coil to the air and η(t) ∈ [0, 1] is the mass transfer effectiveness. For an evaporative cooler,

η(t) = 1-exp(-NTU(t)),

where NTU(t)=(hA)_m/Ċ_a are the number of mass transfer units and Ċ_a is the air capacity flow rate. The mass transfer coefficient (hA)_m is assumed to be proportional to the wet coil area, which is assumed to be equal to the ratio m(t) ⁄ m_max(t). Hence,

(hA)_m(t) ∝ m(t) ⁄ m_max(t).

Furthermore, the mass transfer coefficient depends on the velocity, and hence mass flow rate, as

(hA)_m(t) ∝ ṁ_a(t)^0.8,

where ṁ_a(t) is the current air mass flow rate, from which follows that

NTU(t) ∝ ṁ_a(t)^-0.2.

Therefore, the water mass flow rate from the coil into the air stream is

ṁ_wat(t) = ṁ_max(t) (1-exp(-K (m(t) ⁄ m_tot) (ṁ_a(t) ⁄ ṁ_a,nom)^-0.2 )),

where K > 0 is a constant to be determined below and the rate of change of water on the coil surface is as before

dm(t)⁄dt = -ṁ_wat(t).

The maximum mass transfer is

ṁ_max = ṁ_a (x_wb(t) - x(t)),

where x_wb(t) is the moisture content of air at the wet bulb state and x(t) is the actual moisture content of the air.

The constant K is determined from the nominal conditions as follows: At the nominal condition, we have m(t) ⁄ m_tot=1 and ṁ_a(t) ⁄ ṁ_a,nom=1, and, hence,

ṁ_nom = ṁ_max,nom (1-e^-K).

Because

ṁ_nom = - γ Q̇_L,nom ⁄ h_fg,

it follows that

K = -ln( 1 + γ_nom Q̇_L,nom ⁄ ṁ_a,nom ⁄ h_fg ⁄ (x_nom-x_wb,nom) ),

where x_nom is the humidity ratio at the coil at nominal condition and x_wb,nom is the humidity ratio at the wet bulb condition. Note that the ln(·) in the above equation requires that the argument is positive. See the implementation section below for how this is implemented.

Implementation

Potential for moisture transfer

For the potential that causes the moisture transfer, the difference in mass fraction between the current coil air and the coil air at the wet bulb conditions is used, provided that the air mass flow rate is within 1⁄3 of the nominal mass flow rate. For smaller air mass flow rates, the outlet conditions are used to ensure that the outlet conditions are not supersaturated air. The transition between these two driving potential is continuously differentiable in the mass flow rate.

Computation of mass transfer effectiveness

To evaluate

K = -ln( 1 + γ_nom Q̇_L,nom ⁄ ṁ_a,nom ⁄ h_fg ⁄ (x_nom-x_wb,nom) ),

the argument of the ln(·) function must be positive. However, often the parameter γ_nom is not known, and the default value of γ_nom = 1.5 may yield negative arguments for the function ln(·). We therefore set a lower bound on γ_nom as follows: Note that γ_nom must be such that 0 < ṁ_wat,nom < ṁ_max,nom. This condition is equivalent to

0 < γ_nom < ṁ_a,nom (x_nom-x_wb,nom) h_fg ⁄ Q̇_L,nom

If γ_nom were equal to the right hand side, then the mass transfer effectiveness would be one. Hence, we set the maximum value of γ_nom,max to

γ_nom,max = 0.8 ṁ_a,nom (x_nom-x_wb,nom) h_fg ⁄ Q̇_L,nom,

which corresponds to a mass transfer effectiveness of 0.8. If γ_nom > γ_nom,max, the model sets γ_nom=γ_nom,max and writes a warning message.

Regularization near zero air mass flow rate

To regularize the equations near zero air mass flow rate and zero humidity on the coil, the following conditions have been imposed in such a way that the model is once continuously differentiable with bounded derivatives on compact sets:

• We impose that ṁ_wat(t) → 0 as m → 0 to ensure that there is no evaporation if no water remains on the coil.
• We impose that ṁ_wat(t) ⁄ ṁ_a(t) → 0 as ṁ_a(t) → 0 to ensure that the evaporation mass flow rate remains bounded at zero air flow rate and that it is symmetric near zero without having to trigger an event.

This is implemented by replacing for |ṁ_a(t)| < δ the equation for the evaporation mass flow rate by

ṁ_wat(t) = -C m ṁ_a²(t) (x_nom-x_wb,nom),

where C=K δ^-0.2 which approximates continuity at |ṁ_a|=δ. Note that differentiability is ensured because the two equations are combined using the function Buildings.Utilities.Math.Functions.spliceFunction. Also note that based on physics, we would not have to square ṁ_a, but this was done to avoid an event that would be triggered if |ṁ_a| would have been used. Since the equation is active only at very small air flow rates when the fan is off, the error is negligible for typical applications.

References

Hugh I. Henderson, Jr., Don B. Shirey III and Richard A. Raustad. Understanding the Dehumidification Performance of Air-Conditioning Equipment at Part-Load Conditions. CIBSE/ASHRAE Conference, Edinburgh, Scotland, September 2003.

Don B. Shirey III, Hugh I. Henderson, Jr. and Richard A. Raustad. Understanding the Dehumidification Performance of Air-Conditioning Equipment at Part-Load Conditions. Florida Solar Energy Center, Technical Report FSEC-CR-1537-05, January 2006.

Extends from Modelica.Blocks.Icons.Block (Basic graphical layout of input/output block).

Parameters

Connectors

Modelica definition

Buildings.Fluid.DXSystems.Cooling.BaseClasses.InputPower

Electrical power consumed by the unit

Information

This block calculates total electrical energy consumed by the unit using the rate of cooling and the energy input ratio EIR.

The electrical energy consumed by the unit is

P = -Q_cool EIR

Extends from Modelica.Blocks.Icons.Block (Basic graphical layout of input/output block).

Connectors

Modelica definition

Buildings.Fluid.DXSystems.Cooling.BaseClasses.PartialCapacity

Calculates performance curve value at given temperature and mass flow rate

Information

Cooling capacity modifiers

There are two cooling capacity modifier functions: The function cap_θ accounts for a performance change due to different temperatures at the condenser and evaporator and the function cap_FF accounts for a performance change due to different air flow rates at the evaporator, relative to the nominal condition. These cooling capacity modifiers are multiplied with nominal cooling capacity to obtain the cooling capacity of the coil at given inlet temperatures and mass flow rate. See Buildings.Fluid.DXSystems.BaseClasses.CapacityAirSource.

The temperature dependent cooling capacity modifier function is

cap_θ(θ_e,in, θ_c,in) = a₁ + a₂ θ_e,in + a₃ θ_e,in ² + a₄ θ_c,in + a₅ θ_c,in ² + a₆ θ_e,in θ_c,in,

where the six coefficients are obtained from the coil performance data record.

The flow fraction dependent cooling capacity modifier function is a polynomial with the normalized mass flow rate ff (flow fraction) at the evaporator as the time dependent variable. The normalized mass flow rate is defined as

ff = ṁ ⁄ ṁ_nom,

where ṁ is the mass flow rate at the evaporator and ṁ_nom is the nominal mass flow rate. If the coil has multiple stages, then the nominal mass flow rate of the respective stage is used. Hence,

cap_FF(ff) = b₁ + b₂ ff + b₃ ff² + b₄ff³ + ...

The coefficients of the equation are obtained from the coil performance data record.

It is important to specify limits of the flow fraction to ensure validity of the cap_FF(⋅) function in performance record. A non-zero value of cap_FF(0) will lead to an infinite large change in fluid temperatures because Q̇ ≠ 0 but ṁ = 0. Hence, when ṁ ≠ 0 is below the valid range of the flow modifier function, the coil capacity will be reduced and set to zero near ṁ = 0.

Energy Input Ratio (EIR) modifiers

The Energy Input Ratio (EIR) is the inverse of the Coefficient of Performance (COP). Similar to the cooling rate, the EIR of the coil is the product of a function that takes into account changes in condenser and evaporator inlet temperatures, and changes in mass flow rate.

As for the cooling rate, EIR_θ(⋅, ⋅) is

EIR_θ(θ_e,in, θ_c,in) = c₁ + c₂ θ_e,in + c₃ θ_e,in ² + c₄ θ_c,in + c₅ θ_c,in ² + c₆ θ_e,in θ_c,in.

where the six coefficients are obtained from the coil performance data record, and θ_e,in is the dry-bulb temperature if the coil is dry, or the wet-bulb temperature otherwise.

Similar to the cooling ratio, the change in EIR due to a change in air mass flow rate is

EIR_FF(ff) = d₁ + d₂ ff + d₃ ff² + d₄ff³ + ...

Obtaining the polynomial coefficients

The package Buildings.Fluid.DXSystems.Cooling.AirSource.Examples.PerformanceCurves contains performance curves. Alternatively, users can enter their own performance curves by making an instance of a curve in Buildings.Fluid.DXSystems.Cooling.AirSource.Examples.PerformanceCurves and specifying custom coefficients for the above polynomials. The polynomial coefficients can be obtained by doing a curve fit that fits the polynomials to a set of data. The site http://www.scipy.org/Cookbook/FittingData shows examples for how to fit data. If a coil has multiple stages, then the fit need to be done for each stage. For variable frequency coils, multiple fits need to be done for user selected compressor speeds. For intermediate speeds, the performance data will be interpolated by the model Buildings.Fluid.DXSystems.Cooling.AirSource.VariableSpeed.

The table below shows the polynomials explained above, the name of the polynomial coefficients in Buildings.Fluid.DXSystems.Cooling.AirSource.Examples.PerformanceCurves and the independent parameters against which the data need to be fitted.

Note that for the above polynomials, the units for temperature is degree Celsius and not Kelvins.

Implementation

A parameter of the performance curve is the range of mass flow fraction ff for which the data are valid. Below this range, this model reduces the cooling capacity and the energy input ratio so that both are zero if ff < ff_min/4, where ff_min is the minimum flow fraction for which the performance curves are valid.

Extends from Modelica.Blocks.Icons.Block (Basic graphical layout of input/output block).

Parameters

Connectors

Modelica definition

Buildings.Fluid.DXSystems.Cooling.BaseClasses.PartialCoilCondition

Partial block for dry and wet coil conditions

Information

This partial block is the base class for Buildings.Fluid.DXSystems.BaseClasses.DryCoil and Buildings.Fluid.DXSystems.Cooling.BaseClasses.WetCoil.

Extends from Buildings.Fluid.DXSystems.Cooling.BaseClasses.PartialCoilInterface (Partial block for DX coil).

Parameters

Connectors

Modelica definition

Buildings.Fluid.DXSystems.Cooling.BaseClasses.PartialCoilInterface

Partial block for DX coil

Information

This partial block declares the inputs and outputs that are common for Buildings.Fluid.DXSystems.BaseClasses.DryCoil and Buildings.Fluid.DXSystems.Cooling.BaseClasses.DXCooling.

Extends from Modelica.Blocks.Icons.Block (Basic graphical layout of input/output block), Buildings.Fluid.DXSystems.Cooling.BaseClasses.EssentialParameters (A partial block for essential parameters for cooling DX coils).

Parameters

Connectors

Modelica definition

Buildings.Fluid.DXSystems.Cooling.BaseClasses.PartialDXCoil

Partial model for air or water cooled DX cooling coil

Information

This partial model is the base class for Buildings.Fluid.DXSystems.Cooling.BaseClasses.PartialDXCoolingCoil.

Extends from Buildings.Fluid.DXSystems.Cooling.BaseClasses.EssentialParameters (A partial block for essential parameters for cooling DX coils), Buildings.Fluid.Interfaces.TwoPortHeatMassExchanger (Partial model transporting one fluid stream with storing mass or energy).

Parameters

Connectors

Modelica definition

Buildings.Fluid.DXSystems.Cooling.BaseClasses.PartialDXCoolingCoil

Partial model for DX cooling coil

Information

This partial model is the base class for Buildings.Fluid.DXSystems.Cooling.AirSource.SingleSpeed, Buildings.Fluid.DXSystems.Cooling.AirSource.MultiStage and Buildings.Fluid.DXSystems.Cooling.AirSource.VariableSpeed.

Extends from Buildings.Fluid.DXSystems.Cooling.BaseClasses.PartialDXCoil (Partial model for air or water cooled DX cooling coil).

Parameters

Connectors

Modelica definition

Buildings.Fluid.DXSystems.Cooling.BaseClasses.PartialSurfaceCondition

Partial block for apparatus dew and dry point calculation

Information

This partial block is the base class for Buildings.Fluid.DXSystems.Cooling.BaseClasses.ApparatusDewPoint and Buildings.Fluid.DXSystems.Cooling.BaseClasses.ApparatusDryPoint.

This block calculates the UA/c_p value, the bypass factor and the enthalpy difference across the coil. It uses the function Buildings.Fluid.DXSystems.Cooling.BaseClasses.Functions.speedShift for intermediate compressor speeds.

Implementation

For coils that only have discrete compressor speeds, this block does not do an interpolation for intermediate speeds. For coils with variable speed compressors, the computations are also done if the coil is off, as this ensures that the derivatives are continuous near the off conditions.

Extends from Modelica.Blocks.Icons.Block (Basic graphical layout of input/output block), Buildings.Fluid.DXSystems.Cooling.BaseClasses.EssentialParameters (A partial block for essential parameters for cooling DX coils).

Parameters

Connectors

Modelica definition

Buildings.Fluid.DXSystems.Cooling.BaseClasses.PartialWaterCooledDXCoil

Base class for water source DX coils

Information

This model can be used to simulate a water source DX cooling coil with single speed compressor.

See Buildings.Fluid.DXSystems.Cooling.UsersGuide for an explanation of the model.

Extends from Buildings.BaseClasses.BaseIcon (Base icon), Buildings.Fluid.DXSystems.Cooling.BaseClasses.EssentialParameters (A partial block for essential parameters for cooling DX coils).

Parameters

Connectors

Modelica definition

Buildings.Fluid.DXSystems.Cooling.BaseClasses.SensibleHeatRatio

Calculates the sensible heat ratio

Information

This block computes the sensible heat ratio.

Extends from Modelica.Blocks.Icons.Block (Basic graphical layout of input/output block).

Parameters

Connectors

Modelica definition

Buildings.Fluid.DXSystems.Cooling.BaseClasses.SpeedSelect

Selects the lower specified speed ratio for multispeed model

Information

This blocks outputs the normalized speed of the compressor, whereas the highest stage is assigned a normalized speed of one, and all other stages are proportional to their actual speed.

Extends from Modelica.Blocks.Icons.Block (Basic graphical layout of input/output block).

Parameters

Connectors

Modelica definition

Buildings.Fluid.DXSystems.Cooling.BaseClasses.SpeedShift

Interpolates values between speeds

Information

This block uses the Buildings.Fluid.DXSystems.Cooling.BaseClasses.Functions.speedShift function to interpolate the input array. Depending on input speed ratio and speed set array the input array u is interpolated.

Parameters

Connectors

Modelica definition

Buildings.Fluid.DXSystems.Cooling.BaseClasses.UACp

Calculates UA/Cp of the coil

Information

This model calculates the UA/c_p value and the bypass factor of the coil from the nominal inlet and outlet air properties.

For a heat exchanger where one medium changes phase, the NTU-ε relation is

ε = 1 - exp(-NTU) = 1-exp(-UA ⁄ c_p ⁄ ṁ).

Since the bypass factor b is defined as b=1-ε, one can write

b = exp(-UA ⁄ c_p ⁄ ṁ)

and, hence,

UA ⁄ c_p = - ṁ log(b).

Extends from Modelica.Blocks.Icons.Block (Basic graphical layout of input/output block).

Parameters

Connectors

Modelica definition

Buildings.Fluid.DXSystems.Cooling.BaseClasses.WetCoil

Calculates wet coil condition

Information

This block calculates the rate of cooling and the coil surface condition under the assumption that the coil is wet.

The dry coil conditions are computed in Buildings.Fluid.DXSystems.BaseClasses.DryCoil. See Buildings.Fluid.DXSystems.Cooling.UsersGuide for an explanation of the model.

Extends from Buildings.Fluid.DXSystems.Cooling.BaseClasses.PartialCoilCondition (Partial block for dry and wet coil conditions).

Parameters

Connectors

Modelica definition