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L. 

Wang, 

P. 

Haves 

& 

F. 

Buhl

Lawrence Berkeley National 

Laboratory Berkeley, CA

An Improved Simple Chilled 

Water 

Cooling 

Coil 

Model

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Motivation 

and 

History

Purpose:

•Energy simulation

•Model‐

based 

FDDIssues:

•Model ‘equations’: scope, approximations …

•Input data: physical or rating point

NTU-  / LMTD Holmes (1982)

Elmhardy & Mitalas (1977)CCDET

Braun (1988)CCSIM

Brandemuehl (1993)

Chillar&Liesen (2004)

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Overall 

Thermal 

Resistance 

 – (ratio?)

 Rn AUA row facetotholmes  /=

Holmes

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Dry and Wet Sections

where: C = UAtot,des / UAtot, holmes

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Three Modes of  Operation

Completely dry

EDB, ERH (EWB)LDB,

 LRH

EWTLWT

Partially wet

EDB, ERH (EWB)

LWT

LDB, LRH 

EWT

IF   tDewPt (Entering air dew point)< tSurfExt (Surface temperature at air exit)  THEN

ELSE  Assume fully wet coil

IF 

tDewPt (Entering air dew point)>tSurfEnt(Surface temperature at air entrance)  THEN 

ELSE

Completely wet

EDB, ERH (EWB)

LWT EWT

LDB, LRH 

1. Assume dry coil:

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Algorithm

DesignOperation

Input Rating

Condition,

OperationConditions

Calculate:

LWTdes, DewPtdes,

UAholmes,des

Calculate:

UAtot,des, C

Determine coil

operation mode

Calculate: LWT

,Qsen

Calculate:

UAext,des / UAint,des

UAext,des, UAint,des

UAext, UAint

,

LDB LW Qtot ,Fwet

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Validation using Purdue Measurements 

Zhou, X. , (2005). Dynamic modeling of  chilled water cooling coils. PhD thesis, Purdue University.

Cooling coil specification:

•8-row, 8 tubes/row, 8 circuits

•ID: 0.0119 m

•Face area: 0.3716 m2

Data Set:

•32 cases (16 dry, 16 wet)

•Measurements:

• EDB, ERH, LDB, LRH, ma

• EWT, mw

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Comparison of  Proposed Model and Chillar and Liesen 

Model with Purdue Measurements (Dry Coil)

Maximum Fractional Error 

Proposed model: 9.3%

CL model: 16.3%

Mean Fractional Error 

Proposed model: 4.3%

CL model: 5.6%

Chillar,R. and Liesen, R. (2004). Improvement of the ASHRAE secondary HVAC toolkit simple cooling coil model for simulation. SimBuild 2004, IBPSA-USA

National Conference Boulder, CO, August 4-6, 2004. (CL model)

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Maximum Fractional Error 

Proposed model: 7.7%

CL model: 24.8%

Mean Fractional Error

Proposed model: 3.4%

CL model: 13.3%

Comparison of  Proposed Model and Chillar and Liesen 

Model with Purdue Measurements (Wet Coil)

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Maximum fractional error

Proposed model : 4.7 %

Mean fractional error 

Proposed model : 2.3 %

Heat transfer rate imbalance for wet

cases measurement : 0.1%-6.2%

Wet Coil Comparison using Adjusted RH Measurements

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Sensitivity to Number of  Coil Circuits

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100% water flow rate 30% water flow rate

100% air flow rate   1 3

30% air flow rate   4 2

Model 

Simplification 

using 

Fixed 

Ratio 

of  

UAext to 

UAint

• Operating condition: inlet air temperature 27˚C, inlet water temperature 7˚C

• Design velocities: va= 2.5 m.s-1 v

w= 1.4 m.s-1

• High Fin Spacing: UAint  :UA

ext= 5.15

• Low Fin Spacing: UAint  :UA

ext= 3.45

Proposed default ratio UAint  :UA

ext= 4.3

Max diff: 3% duty

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Conclusions

•  Use of  Holmes’ empirical model allows configuration of  a partly wet coil model from a single rating point and 

limited geometrical

 data:

 – Face area

 – Tube diameter

 – Number of  rows

 – (Number of  circuits)

•  Relatively small accuracy degradation from using 4.3 as 

the default value of  the ratio of  the water‐side to the 

air‐side

 overall

 heat

 transfer

 coefficient

  – no

geometrical data required,  just a single rating point.

Method especially useful for existing buildings where 

manufacturer’s data

 difficult

 to

 obtain