Presentation Author, 2006

Dynamic Modeling of Mechanical DraftCounter-Flow Wet Cooling Tower with Modelica

Xiao Li and Yaoyu Li

Department of Mechanical Engineering

University of Wisconsin – Milwaukee

4th National Conference of IBPSA-USA, August 11-13, 2010(New York, NY)

John E. Seem

Building Efficiency Research GroupJohnson Controls, Inc.

Aug 12, 2010

Outline

• Research Motivation

• Dynamic Modeling of Cooling Tower

• Further Considerations & Related Components

• Simulation Results

• Conclusion & Future Work

2

Research Motivation• Building operations: 40% energy consumption in the U.S.

• Air conditioning and ventilation account for about 15% of theenergy used in commercial buildings

3

Ventilation and Air ConditioningSystem for Commercial Buildings

• About 2/3 of the totalpower consumptionsis due to the powerconsumption of thecompressors in thechillers and the fansin the cooling tower.

Research Motivation• Although cooling tower consumes

much less power than chiller, itsoperation strongly affects theoverall efficiency: chiller efficiencystrongly affected by cooling tower

• Tradeoff between the energyconsumptions of chiller and coolingtower: one degree drop of thecondensing water 2% increasefor the chiller efficiency

• The chiller efficiency can beimproved by the colder condensingwater provided by the cooling tower

4

Relative Tower Airflow

Pow

er

Tower

Optimal

Chiller

Total

Optimal Fan Speed

minimal power consumption

Research Motivation

5

Relative Tower Flows

Dynamic modeling of coolingtower is desired fordeveloping advanced controlsfor energy saving

ESC method:Online optimization problem : finding an

optimizing inputGenerally unknown and /or time-varying

cost function.

Input dynamics forcontroller design

Accurate performance forsimulation and validation

Overview of Cooling Tower• Typical cooling tower includes

– Fan– Distribution system– Spray nozzles– Fill (packing)– Collection basin

– Condenser pump

• For cooling tower, heat rejection is accomplished via theheat and mass transfer occurring at the direct contact (Fill)between hot water droplets and ambient air

6

Overview of Cooling Tower• The warm water from the condenser is sprayed downward

through the pressurized nozzles and then flows through thefill,

• The evaporation cooling occurs as the air flow is pulledupward by the tower fan though the fill

• The fill is used to increase both the surface area and thecontact time between air and water flows

• An external source of water, called makeup water, is neededto compensate for the water loss due to evaporation and drift

• The condenser pump drives the water back to the chiller

7

Review of Cooling Tower Modeling• First practical cooling tower theory: Merkel (1925)

– Considered both sensible and latent heat transfer based on thedriving potential from enthalpy difference.

– To simplify the analysis, the water loss of evaporation and drift areneglected, and the Lewis number is assumed unity

• Lowe and Christie (1961)– Presented heat transfer and pressure drop data in a cooling tower

with various splash packings– Provided the correlation for calculating the volume transfer

coefficient from a given tower coefficient and tower exponent (basedon manufacturer’s performance data)

• Threlkeld (1970)– Included the water loss due to evaporation– Used the actual Lewis number

8

Review of Cooling Tower Modeling• Sutherland (1983)

– Conducted a more rigorous analysis including water loss byevaporation

– Pointed that the assumptions from Merkel’s model may cause anunderestimation of the effective tower volume by 5-15%

• Braun (1989)– With a detailed analysis, developed effectiveness models– Assumed a linearized air saturation enthalpy– Effectiveness defined with constant saturation specific heat

• Kloppers and Kröger (2003)– Investigated the loss coefficient correlation for wet-cooling tower fills– Proposed a new empirical equation which correlates the fill loss

coefficient data more effectively9

Review of Cooling Tower Modeling• Wetter (2009)

– Proposed a cooling tower model by using static mapping to theperformance curve of a York cooling tower (use Modelica)

• Most existing models are steady-state or effectivenessmodels

• Dynamic model of cooling tower is needed for advancedcontrol design which leads to higher efficiency

• This study aims to develop dynamic model for a mechanicaldraft counter-flow wet cooling tower with Modelica

10

Simulation Platform• Modelica has been adopted for this study on dynamic

modeling of cooling tower– Modelica is an acausal equation based object-oriented language for

multi-physical modeling.

– In Modelica, modeling of thermofluid system components can bedirectly represented by differential algebraic equations (DAE)

• Simulation Platform: Dymola + TIL– Dymola is an integrated development environment for Modelica based

modeling, which contains Modelica translator to perform symbolictransformations, index reduction algorithms for reducing the DOFcaused by constraints, and can better handle algebraic loops

– TIL is a Modelica library developed by TLK-Thermo GmbH for steady-state and transient simulation of thermofluid systems

11

Modeling Assumptions• Heat and mass transfer in the direction normal to the flows

only

• Negligible heat and mass transfer through the tower walls tothe environment

• Negligible heat transfer from the tower fans to the air orwater streams

• The mass fraction of water vapor in the moist air isapproximately equal to the humidity ratio

• Uniform temperature throughout the water stream at anycross section

• Uniform cross-sectional area inside the tower

12Assumptions Adopted from Braun (1989)

Modeling Strategy

• Instead of treating the specific heats as constants, themutative water and air specific heats are considered (withthe property calculation capability available in the TILMedia Library)

• The formulation of Lewis relation in Bosnjakovic (1965) isfollowed instead of considering it as unity

• The finite volume method is applied in order to achievemore robust performance for start-up and all load-changetransients (Bendapudi, Braun & Groll, 2008)

• The transient mass and energy storage is considered at thewater side but neglected at the air side

13

Finite Volume Method

14

The control volumes ofwater and moist air aredefined separately, inopposite flow directions

Dynamic mass andenergy balances areevaluated for eachcontrol volumes

The heat and masstransfer are consideredbetween each pair ofwater and moist-aircontrol volumes

The balance betweenwater loss and humidityincrease in the moist-airis reinforced through allthe control volumes

Energy Balance• For the ith water-side control

volume, the energy balanceleads to

15

• The equation can be expanded to

, , , , ,w i w in i w out i iH H H q (1)

,, , , , , , , , , , , , ,

w iw i p w i w in i w in i w i w out i w out i w i i

dTm c m h h m h h q

dt(2)

• On the air side, the transient energy storage is neglected, theenergy balance results in

, , , , 0a in i a out i iH H q (3)

Energy Balance

• The heat flow transferred from the neighbored water cell iscombination of the sensible and the latent heat flow

16

, ,i sen i lat iq q q (4)

, , , ,sen i C i V cell w i a iq h A V T T

, , , , , , , , , ,lat i f g i evap i f g i D i V cell s w i a iq h m h h A V

(5)

(6)

ContactTime ?

ContactArea ?

Uncertaintiesfrom Fouling

(Fill)!

Overall Heat/Mass Transfer Coefficients• The overall heat and mass transfer coefficients can be

determined by:

17

,a inD V

T

NTU mh A

V, ,

,f pm i a in

C i VT

Le NTU c mh A

V

• NTU can be determined from experimental data usingempirical equations of thermal properties

• According to Kloppers and Kröger (2005), it is moreappropriate to calculate Lef with the equation byBosnjakovic (1965)

• A numerical value of 0.92 is recommended

Mass Balance• For the water-side control volumes

18

,, , , , ,

w iw in i w out i evap i

dmm m m

dt(7)

where , ,w i effective w im V

• Veffective is the water droplet volume in the cell

• The ratio of water droplet volume per unit volume of the tower isaround the level of 0.001(Bernier, 1994)

,, , , , ,

,,

effective w iw i effe

effecctive

tive w iw in i w out i evap i

dV ddt dt

d VV m m m

dt

(8)

(9)

Water Droplet Volume in Cell : Veffective

• Veffective can be obtained by (Bernier, 1994)

19

,,

celleffective w in

w i w

V mAV

V (10)

• Vw is the velocity when the water droplets fall freely (nopacking), which is assumed as constant

,,

effective w incellw i

w

dV dmVA tV ddt

(11)

• If w,in does not vary much, Veffective can be assumed as constant;otherwise, the gradient of w,in is needed to account for thechange of Veffective

Local Water Density: w,i

• The time derivatives of pressure, specific enthalpy and density ineach control volume are related by (Richter, 2008):

20

h P

d dP dhdt P dt h dt

(12)

• The cell pressure is approximately constant

pw

d dh dTdt c dt dt

(13)

where is the isobaric coefficient of expansion:1

PT

,, , , , , , ,

,w iw in i w out i evap i effective w i w

w inc

wi

elldTm m m V

ddmV

AVt dt (14)

• Mass balance:

Further Considerations• It is hard to measure the outlet water temperature of the fill

from the cooling tower

• Collection basin model is needed to describe the dynamicbehavior of the condenser water back to chiller, which iseasier to measured

• The fan and pump models are needed for control design andenergy consumption evaluation

• Valve model is needed if no variable speed pump isavailable

21

Fan & Pump

22

• The fan and pump models are derived following the basicmodels provided by the TIL library for now, which are basedon the fan and pump affinity laws and squaredcharacteristics.

, ,0 ,0,0

fanfan affinity fan

fan

nQ Q

n

2

, ,0 ,0,0

fanfan affinity fan

fan

np p

n

2

, ,0, ,0

1 fanfan fan affinity

fan affinity

Qp p

Q

(15)

(16)

(17)

Collection Basin

23

• The energy and mass balance equations of collection basin

win out makeup w cb

dTm m m Vdt

in in cb out out cb makeup makeup cbwpw

w cb

m h h m h h m h hdTc

dt V

(18)

(19)

• The dynamic model of collection basin will help construethe additional transient behavior to the transientperformance of evaporation process of cooling tower

Assumptions• Constant volume of water in the collection basin (Vcb)• Flow rate of make-up water = water loss by evaporation

SIMULATION RESULTS

24

Dymola Layout for Developed Model

25

Water Inlet Flow Rate

Water Inlet Temperature

Air Inlet Humidity Ratio

Air Inlet Temperature

Air Inlet Flow Rate

• Dymola layout for the evaporation cooling process of coolingtower and the whole system of cooling tower

Valve

Fan

CollectionBasin

CondenserPump

TowerBody

Represented ChillerSide Pressure Change

Air Temp.Makeup Water

Humidity Ratio

Fan Speed

Valve Opening

Water Temp.

Evaluation of Steady-state Performance

• The model is evaluated withthe experimental data fromSimpson & Sherwood (1946)

• The prediction error has themean of 0.334K and thestandard derivation of 0.428K

26

Case Tw,in (oC) Tw,out (oC) Tdb,in (oC) Twb,in (oC) Tdb,out (oC) a,in (kg/s) w,in (kg/s) Tw,out,cal (oC)

1 33.22 25.50 28.83 21.11 28.44 1.1871 1.0088 25.462 34.39 29.0 31.78 26.67 31.22 1.1653 1.0088 28.783 43.61 27.89 35.0 23.89 32.78 1.1584 0.7548 28.124 38.78 29.33 35.0 26.67 33.28 1.2653 1.0088 29.875 43.06 29.72 35.72 26.67 33.89 1.1566 0.7548 29.94

296

297

298

299

300

301

302

303

304

305

306

307

296 298 300 302 304 306

Mea

sure

dOut

let W

ater T

empe

ratu

re

Model Predict Outlet Water Temperature

Mea

sure

d O

utle

t Wat

er T

empe

ratu

re (K

)

Model Predicted Outlet Water Temperature (K)

Lewis RelationThe Lef valuecalculated by theequation fromBosnjakovic(1965) is within(0.910, 0.916):compatible withthe suggestedvalue of 0.92 inKloppers &Kröger (2005).

27

0 500 1000 1500 2000 25000.910

0.911

0.912

0.913

0.914

0.915

0.916

0.917

Lewis Relation

Dynamic Behavior

28

Wat

er O

utle

t Tem

pera

ture

(K)

Time (s)40 50302.85

+0.05

+0.10

+0.15

+0.20

+0.25

+0.30Water Outlet Temperature • Demonstrated scenario is inlet

temperatures increase, leading to anincrease of the water outlettemperature

• The increase of the differencebetween the dry-bulb and wet-bulbtemperatures indicates a decreaseof the relative humidity of the inletair, resulting in a decrease of thewater outlet temperature

• The transient: an undershoot ratherthan a smooth transient

Case Tw,in(oC)

Tw,out(oC)

Tdb,in(oC)

Twb,in(oC)

Tdb,out(oC)

a,in(kg/s)

w,in(kg/s)

Tw,out,cal(oC)

4 38.78 29.33 35.0 26.67 33.28 1.2653 1.0088 29.875 43.06 29.72 35.72 26.67 33.89 1.1566 0.7548 29.94

Additional Transient from Basin Dynamics

29

0 500 1000 1500 2000 2500292

294

296

298

300

302

304

306

308

Out of Tower Body Out of Collection BasinW

ater

Out

let T

empe

ratu

re (K

)

Time(s)

Conclusion & Future Work

• The dynamic model of cooling tower is derived usingthe finite volume method

• Some relevant components are also modeled for futureneed in optimization and control development

• Steady-state performance is evaluated with theexperimental data from Simpson and Sherwood (1946),with good match

• The transient behavior is also simulated under thechanges of tower inlet conditions, with the performanceto be evaluated in the future with field test data

30

31

Thanks for Listening!

Questions?

Dynamic Modeling of Mechanical DraftCounter-Flow Wet Cooling Tower with Modelica

Xiao Li and Yaoyu LiDepartment of Mechanical Engineering

University of Wisconsin – Milwaukee

John E. SeemBuilding Efficiency Research Group

Johnson Controls, Inc.