.Buildings.Fluid.DXSystems.Cooling.BaseClasses.PartialCapacity

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.

Revisions

• April 5, 2023, by Xing Lu:
  Changed class name from PartialCoolingCapacity to PartialCoilCapacity.
• November 8, 2022, by Michael Wetter:
  Corrected calculation of performance which used the wrong upper bound.
  This is for issue 3146.
• October 21, 2019, by Michael Wetter:
  Ensured that transition interval for computation of corFac is non-zero.
  This is for issue 1202.
• February 27, 2017 by Yangyang Fu:
  Revised the documentation.
• December 18, 2012 by Michael Wetter:
  Added warning if the evaporator or condenser inlet temperature of the current stage cross the minimum and maximum allowed values.
• September 20, 2012 by Michael Wetter:
  Revised model and documentation.
• May 18, 2012 by Kaustubh Phalak:
  Combined cooling capacity and EIR modifier function together to avoid repeatation of same variable calculations. Added heaviside function.
• April 20, 2012 by Michael Wetter:
  Added unit conversion directly to function calls to avoid doing the conversion when the coil is switched off.
• April 6, 2012 by Kaustubh Phalak:
  First implementation.