Design considerations for combined cooling heating

Design considerations for combined cooling,heating,and power systems at altitude

Nelson Fumo ⇑,Pedro J.Mago,Kenneth Jacobs

Mechanical Engineering Department,Mississippi State University,Mississippi State,MS 39762,USA

a r t i c l e i n f o Article history:

Received 21January 2010

Received in revised form 21September 2010

Accepted 3October 2010

Available online 25October 2010Keywords:

Combined cooling,heating,and power CCHP

Design at altitude

Performance at altitude

a b s t r a c t

Combined cooling,heating,and power (CCHP)is a technology that makes better use of fuels as conse-quence of its high overall efficiency,which can be as high as 80%.CCHP systems aid in the reduction of energy consumption by recovering otherwise wasted heat and using it to provide heating and cooling.As a result,they also have the potential to reduce carbon and other pollutant emissions.Generally,for CCHP systems’components,manufacturers include specifications on the performance of the equipment.However,these specifications are normally given for sea level operation.Changes in altitude affect the performance of any of the CCHP systems’components that are open to the atmosphere due to changes in the properties of the air,such as atmospheric pressure and humidity.This study focuses on consider-ations for CCHP systems design at altitude.The analysis covers the processes affected by altitude and their specific application on how to assess the performance of the individual components of CCHP systems when operating at altitude.This paper also summarizes the analysis by presenting equations that can be used in the design stage of CCHP systems in order to account for equipment capacity variation,or in simplified simulations such as those for screening tools,without having a detailed simulation that some times are not cost-effective due to the time and human effort to accomplish it.

Ó2010Elsevier Ltd.All rights reserved.

1.Introduction

Combined cooling,heating,and power (CCHP)systems could be used on site to save energy by taking advantage of the higher over-all efficiency of this technology,with the additional benefits of reducing operating costs,as well as carbon and other pollutant emissions.CCHP systems work by using a power generation unit (PGU)to generate power for the site.Waste heat from the prime mover is recovered through the jacket water cooling system and exhaust to provide thermal energy to heating systems and to an absorption chiller to provide cooling to the building.According to the US Department of Energy (DOE),most industrial applications of these CCHP systems convert over 80%of the input fuel into use-able energy [1].

Thermal-fluid systems are affected by altitude when the flow of mass is open to the atmosphere at any point in the system.Ther-mal-fluid systems open to the atmosphere are related,among oth-ers,to systems or equipment such as engines,boilers,heat exchangers,pumps,desiccant systems and evaporative cooling systems.For CCHP systems,the effects of altitude are related to the PGU,boiler,exhaust heat exchanger,air-blown cooler heat ex-changer,and absorption chiller/cooling tower.

This paper focuses on the analysis of the parameters affecting CCHP systems energy performance when operating at altitude.Since detailed simulation of CCHP systems will account for the effect of altitude through air properties and manufacture’s perfor-mance curves,the analysis presented in this paper is intended to be used as a reference for the design stage and performance anal-ysis.For the design stage,the information presented in this paper can be used to identify the equipment affected by altitude,as well as the extent affecting the performance in order to help designers in the selection of equipment avoiding oversize or undersize.For the performance analysis,the information provided in this paper can be considered and implemented in simplified models used as screening tools for CCHP systems.Some examples of cities where the information from this paper may be useful in the analysis of CCHP systems are Denver,CO (population 588,349,altitude 1609m/5278ft.),Albuquerque,NM (pop.518,271,1619m/5310ft.),Colorado Springs,CO (pop.372,437,1921m/6300ft.),and Santa Fe,NM (pop.72,056,2133m/6996ft.).

As a first source of information on the performance of equip-ment at altitude,the equipment’s specification given by manufac-turers should be considered.The Boiler Burner Consortium [2]suggests that to account for the density change in air at higher alti-tudes,the air required for any boiler room should be increased by 3%for each 305m (1000ft.)above sea level.Carrier specifies that heating input in Single-Package Rooftop Units is altered by altitude by approximately 4%per 305m (1000ft.)[3].Kohler Power [4]includes correction factors for altitude in their specification sheets of PGU.They state that their natural gas PGUs should be reduced in efficiency by 1.3%for every 100m (328ft.)after the initial 100m

0196-04/$-see front matter Ó2010Elsevier Ltd.All rights reserved.doi:10.1016/j.enconman.2010.10.009

Corresponding author.Tel.:+16623256711;fax:+16623257223.

E-mail address:fumo@me.msstate.edu (N.Fumo).

Cooling tower operation depends on the wet-bulb temperature of the air.This wet-bulb temperature increases with altitude.The efficiency of a cooling tower is a function of the difference in the inlet and outlet water temperatures and the difference in the inlet water temperature and the wet-bulb temperature.As the wet-bulb temperature increases with altitude,it gets closer to the inlet water temperature,raising the efficiency.Hamilton[10]suggests that the performance for the cooling tower increases3–8%at 1500m(5000ft.)above sea level.

Heat exchangers,involving atmospheric air as one of thefluids interchanging thermal energy,are also affected by the psychromet-rics of the atmospheric air.For heat exchangers,altitude affects not only massflow rate,but parameters defining the convection heat transfer coefficient.Due to the decrease in air density and mass flow at altitude,ASHRAE[11],referring to the Thermal Guidelines for Data Processing Environments,gives a derating factor of1K per 300m(1000ft.)above900m(2950ft.)for the maximum allow-able temperature of electronic equipment.This derating factor can be expressed as a decrease of the convection heat transfer as can be deduced from Belady[12].According to Belady,the convec-tion heat transfer varies with the density to the power of0.8and density varies with altitude making the convection heat transfer a function of altitude.For heat exchanger used in heating,ventila-tion,and air conditioning systems(HVAC),it is common that man-ufacturers give correction factors for the capacity of the equipment.As an example,from data of Carrier manufacturer of HVAC equipment,the EnergyPlus Engineering Reference[13]in the section of air-cooled condensers defines a correction factor for heat removal capacity as a function of altitude as [1À7.17EÀ5x(altitude)].

Other common processes present in CCHP systems that are af-fected by altitude are related to fans performance and pumping systems.Analysis of the influence of altitude in fan performance can be evaluated through the fan laws,while for pump perfor-mance the concept of net positive suction head(NPSH)is used.

Since CCHP systems are integrated energy systems that may be coupled with other thermally activated systems,it is important to mention that processes of heat and mass transfer found in systems such as desiccant systems and evaporative cooling systems[14,15], require the consideration of altitude due to the variation of air psy-crometrics with altitude.

The effect of altitude on thermal systems performance is conse-quence of the variation of air properties due to atmospheric pres-sure variation.Although air properties affected by altitude are discussed in Section2(Psychrometrics of Air at Altitude),it is important to mention here that these properties vary with the weather.Variation of properties with weather is excluded from this analysis since the analysis considers that properties such as temperature and relative humidity are known as design parameters.

2.Psychrometrics of air at altitude

Pesaran and Heiden[16]studied the effect of air properties on the performance of desiccant systems at altitude.They considered

Nomenclature

CCHP combined cooling,heating,and power HHV higher heating value

HVAC heating ventilation and air conditioning PGU power generation unit

AF air–fuel ratio

C heat capacity ratio

NTU number of transfer units

P pressure

W air humidity ratio

Symbols

n altitude air density ratio

e effectiveness

g efficiency

l boiler efficiency

u relative humidity

g efficiency

l cooling tower efficiency

u relative humidity z altitude(above sea level)

z0critical altitude for theoretical air–fuel ratio

D n difference between the altitude air density ratio at z and

z0

T*thermodynamic wet-bulb temperature

Subscripts

w water vapor

da dry air

ws saturation of dry air

theoric theoretical

comb combustion

g gas-side

wb wet-bulb

i inlet

o outlet

min minimum

max maximum

r ratio

1460N.Fumo et al./Energy Conversion and Management52(2011)1459–1469density,viscosity,thermal conductivity,specific heat,diffusivity, relative humidity,and wet-bulb temperature,and concluded that of these properties only density,relative humidity,and wet-bulb temperature are affected by a change in altitude as consequence of a change in atmospheric pressure.Schultz[17]mentioned that below3000m(10,000ft.)the effect of altitude on air properties such as specific heat,thermal conductivity,and viscosity can be negligible.However,for important air properties,such as density, enthalpy,and dew-point temperature,the effect of altitude cannot be ignored.Therefore,the following properties of air are consid-ered in this investigation:temperature,pressure,density,humidity ratio,and enthalpy.These are the air properties that affect the per-formance of CCHP system’s components due to operation at alti-tudes above sea level.

2.1.Air temperature

The variation of the standard air temperature with altitude is presented in Eq.(1)[18],with T(z)in°C and z in meters(m).

TðzÞ¼15À0:0065zð1ÞThis equation shows that the standard air temperature decreases with altitude,starting with a value of15°C(60°F)at sea level. The altitude of the highest point on the earth’s surface is Mount Everest,with a standard value of00m(29,190ft.).For this alti-tude,Eq.(1)defines a standard temperature for the highest point on the earth’s surface ofÀ42.85°C(À45°F).However,the coldest temperature on earth,of aboutÀ.2°C(À130°F),has been re-corded in Antarctica.Therefore,it must be clear that the word‘stan-dard’refers to the reference temperature for estimating properties at various altitudes,and air temperatures vary also with local geog-raphy and weather conditions[18].For example,Santa Fe(NM)has an elevation of2100m(60ft.)and an average temperature of 30°C(86°F)for its hottest month,July;while New York City(NY) has an elevation of10m(33ft.)and a lower average temperature of28°C(83°F)for July.Therefore,for the purpose of this paper, air temperature on the design,simulation,and operation of CCHP system’s equipment at altitude must be considered through weath-erfiles,and Eq.(1),as it is defined,should be used only for the eval-uation of standard air properties at altitude.

2.2.Air pressure

Atmospheric pressure is the key property to consider the effect of altitude in thermal-fluid systems.As altitude increases,the amount of air mass decreases.This causes less weight of air on a point,which,by definition of pressure,causes atmospheric pres-sure to decrease.The pressure will drop with altitude according to Eq.(2)[18],where P(z)is the atmospheric pressure at altitude in kPa,P0is the standard atmospheric pressure at sea level (101.08kPa),and z is the altitude above sea level in meters.

PðzÞ¼P0½1Àð2:25577Þð10À5ÞðzÞ 5:2559ð2ÞEq.(2)is a function of height and standard atmospheric pres-sure.Since the standard atmospheric pressure at sea level can be taken as a constant,P(z)is only dependent on the altitude.This shows that this equation holds true for any point on the earth’s surface.

2.3.Air humidity ratio

The humidity ratio(w)is defined by Eq.(3)[18],where P is the total pressure of humid air and P w is the partial pressure of water vapor.At altitude,the total pressure of humid air,P(z),is the sum of the partial pressures of dry air,P da(z),and water vapor,P w(z),as shown in Eq.(4).

w¼0:622

P w

w

ð3ÞPðzÞ¼P daðzÞþP wðzÞð4ÞSince the partial pressures vary with the amount of moles of dry air and water vapor in the mixture,a measure is needed for how much water is present in the air in order to consider the effect of altitude.For the purpose of this paper,relative humidity(u),de-fined by Eq.(5)[18],is used as the parameter to assess how the humidity ratio changes with altitude.That is,relative humidity is assumed to be known from weatherfiles,which is used as the rel-ative humidity to compute the humidity ratio(w(z))at altitude by Eq.(6).The saturation pressure of water vapor in absence of air (P ws)is a function of temperature,which is denoted by the sub-script T in the equation.

u¼P w

P ws

T;P

ð5ÞwðzÞ¼0:622

u P ws

PðzÞÀu P ws

T

ð6Þ

To illustrate how the humidity ratio is affected by altitude,Fig.1 shows the variation of the humidity ratio with altitude for relative humidities of30%,50%,and80%.These curves where developed by taking P ws(1.7055kPa)at the standard temperature of15°C(60°F). Fig.1illustrates that the humidity ratio of air increases as altitude increases,with greater variations for higher relative humidity.

2.4.Air density

Air is a compressiblefluid.Therefore,lowering the pressure will ‘expand’a given mass of air to a larger volume,lowering the den-sity.Since atmospheric air can be considered as a mixture of dry air and water vapor,atmospheric air density,defined by Eq.(7)[18], accounts for water content through the humidity ratio.For this study,since R da is the gas constant for dry air and air temperature is said to be considered through weatherfiles,only air pressure and air humidity ratio are affected by altitude which is expressed in Eq.(8).

q¼P

da

ð1þwÞð7ÞqðzÞ¼PðzÞ

da

½1þwðzÞ ð8

Þ

N.Fumo et al./Energy Conversion and Management52(2011)1459–14691461

As an example to illustrate how air density varies with altitude,Fig.2presents the air density for a relative humidity of 30%and four air temperatures.It is important to remember that for the pur-pose of this paper,relative humidity and temperature should be known from local weather files.

Since density is the air property defining the major variations in CCHP systems’equipment performance at altitude,a relationship between the density at altitude and sea level will be useful to de-scribe general performance of equipment as a function of altitude.Therefore,the ‘‘Altitude Air Density Ratio [n (z )]”is defined in this study as

n ðz Þ¼

q ðz Þq

¼½1À2:2557710À5ðz Þ 5:2559

½1þw ðz Þ ð1þw Þ½1þ1:608w ðz Þ ð1þ1:608w Þ

ð9Þ

If humidity ratio would not change with altitude,Eq.(9)would become Eq.(10).

n ðz Þ¼

P ðz Þ

P

¼½1À2:2557710À5ðz Þ 5:2559ð10Þ

To evaluate the effect of humidity ratio on the air density,Eqs.(9)and (10)are plotted in Fig.3for an assumed relative humidity of 30%and air temperature of 25°C.This figure shows that for n (z ),the influence of humidity ratio can be neglected.Since the same behavior was obtained for different relative humidities and temperatures,with the maximum variation of 1.8%for an air temperature of 40°C and 100%relative humidity at the altitude of 4000m (13,120ft.),the altitude air density ratio can be defined by Eq.(10)for all cases.

2.5.Air enthalpy

Specific enthalpy is defined as the energy stored in a system per unit mass [19].In terms of specific enthalpy for psychrometric pro-cesses,it is the amount of energy stored per unit mass of dry air.It is obtained by summing the partial enthalpies of the different com-ponents of a mixture of perfect gases.Specific enthalpy (h ,kJ/kg da )is given by Eq.(11)[18],where w (kg v /kg da )is the humidity ratio,T (°C)is the temperature of the air,1.006T is the approximate spe-cific enthalpy for dry air (kJ/kg da ),and the quantity (2501+1.86T )is the approximate specific enthalpy for saturated water vapor (kJ/kg w ).

h ¼1:006T þw ð2501þ1:86T Þ

ð11Þ

At altitude,Eq.(11)can be changed to the form of Eq.(12).

h ðz Þ¼1:006T þw ðz Þð2501þ1:86T Þ

ð12Þ

3.Thermal-fluid processes affected by altitude

This section considers the thermal-fluid processes influenced by atmospheric property variations due to altitude that are present in CCHP systems’equipment.Combustion is found in the PGU and boiler;heat transfer is found in the exhaust heat exchanger and air-blown cooler heat exchanger;forced air flow is found in the air-blown cooler heat exchanger and cooling tower;and pumping is found in the cooling water loop of the absorption chiller/cooling tower.

3.1.Combustion process at altitude

Russell and Adebiyi [19]define combustion as ‘‘a chemical reac-tion involving a fuel and oxygen ...to form products.”In this sense,combustion will be treated as a chemical reaction without taking into consideration the specifics on how the combustion takes place,i.e.if it takes place in an internal combustion engine or at atmospheric pressure as in burners.This clarification is important because the characteristics of the combustion process are particu-lar to each equipment,and it will be impossible to develop a gen-eral expression that matches exactly the performance of any combustion equipment.Therefore,the following analysis is in-tended to present a method to estimate the performance of equip-ment with a combustion process associated to them when the available amount of air mass for combustion decreases as conse-quence of altitude.

Natural gas is composed of hydrocarbon gases,typically 70–90%methane (CH 4),0–20%ethane (C 2H 6),propane (C 3H 8),and butane (C 4H 10),with small amounts (0–5%)of hydrogen (H 2),carbon diox-ide (CO 2),and hydrogen sulphide (H 2S)[20].Since commonly nat-ural gas is the fuel used in CCHP systems,in this paper methane is the fuel used for all analysis as reference for natural gas.Complete combustion occurs when there is enough oxygen in the reactants to completely oxidize all of the hydrogen and carbon,leaving mostly H 2O and CO 2,which are both stable.Eq.(13)shows the chemical reaction equation for complete combustion of methane:

CH 4þ2ðO 2þ3:76N 2Þ!CO 2þ2H 2O þ7:52N 2ð13Þ

A definition regarding the minimum theoretical air required for the incomplete combustion of a fuel is the theoretical air–fuel ratio (AF theoric ).For Eq.(13),the theoretical air–fuel ratio is

AF theoric ¼

2ð4:76Þmol of air

1mol of fuel

¼9:52

ð14Þ

In combustion equipment,if the fuel input remains constant when the equipment is placed at altitude,the air–fuel ratio will be low-ered and the efficiency will drop as consequence of

incomplete

1462N.Fumo et al./Energy Conversion and Management 52(2011)1459–1469

AF¼v air

v¼AF desingð15Þ

v CH4þv2ðO2þ3:76N2Þ!v CO2þv2H2Oþv7:52N2ð16Þwhere v represents the fraction of theoretical air in the combustion process due to air density reduction with altitude.

Although the combustion process depends on factors such as appropriate mixing of the fuel and air and sufficient chamber pres-sure and temperature[19],based on how the manufactures report the performance of equipment at altitude,it suggests that the effi-ciency of the equipment remains close to its design value.There-fore,for combustion equipment,a reasonable approach is to estimate the derating factor for the equipment output as the air density changes with altitude.This consideration indicates that the output of combustion equipment at altitude can be estimated as

OutputðzÞ¼nðzÞOutput

nominal

ð17ÞAlthough n(z)does not have a linear behavior,by using Eq.(17),it can be noticed that the output of combustion equipment drops about1%for every100m(3%for every1000ft.)as the values found from the literature review.

3.2.Heat transfer process at altitude

Among the three heat transfer processes(conduction,convec-tion,and radiation),only convection may be affected by altitude as a result of air density variation.Heat transfer by convection oc-curs when onefluidflows over a surface,gaining or removing heat from the surface based on the temperature difference.For the focus of this paper,air or exhaust gases are the gasfluidsflowing over a surface which has an inner liquidfluid such as water with some additive to change its boiling and freezing points if needed.Since it is well known that the heat transfer coefficient on the gas-side is much lower than those on the liquid-side,extended surface heat exchangers are used.The two most common types of extended sur-face heat exchangers are plate-fin and tube-fin heat exchangers [21].Therefore,this section is developed by keeping in mind that one of these heat exchangers will be used on the CCHP system.

One of the methods to analyze heat exchangers’performance is the e-NTU method.For this method the performance of the heat ex-changer is described based on the effectiveness(e)of the heat ex-changer.Effectiveness is a function of the number of transfer units (NTU)and the capacity rate ratio(C r)defined as

NTU¼UA

C min

ð18Þ

C r¼C min

C max

ð19Þ

where A is the heat transfer area,U is the overall heat transfer coef-ficient,and C min and C max are the smaller and larger of the heat capacity rates of the twofluids.The heat capacity rates are defined as

C¼_mc p¼_V q C pð20ÞHeat exchanger effectiveness relations have been developed for dif-ferent types of heat exchangers andflow arrangements.For plate-fin and tube-fin heat exchangers,theflow arrangement is cross-flow(single pass)with(a)bothfluids unmixed,(b)C min unmixed and C max mixed,and(c)C min mixed and C max unmixed.For cross-flow with bothfluids unmixed,the heat exchanger effectiveness is e¼1Àexp1

C r

ðNTUÞ0:22f exp½ÀC rðNTUÞ0:78 À1g

ð21Þ

To assess the effect of altitude on heat exchanger effectiveness,the following analysis is done to derive Eq.(21)for altitude.As the anal-ysis illustrates,both NTU and C r,in effectiveness equations,are af-fected by altitude.A deciding factor in the amount of heat transfer due to convection is the Reynolds number[22]

Re¼

D h G

lð22Þ

where D h is the hydraulic diameter(m),l is the dynamic viscosity of thefluid(Pa s),and G is the mass velocity or massflux(kg/m2s) defined as

G¼q U max¼

_m

A min

ð23Þ

where q is the density of thefluid,U max is thefluid velocity(m/s) based on the minimum free-flow cross-sectional area,A min,and_m is the total massflow rate offluid.Since for Re the density is the only property that varies due to the change in altitude,it can be said that Re is directly proportional to the density of the air,leading to a decrease in Re with altitude.Eq.(24)gives the Reynolds number as a function of altitude by incorporating the altitude air density ratio.

ReðzÞ¼nðzÞReð24ÞFor extended surface heat exchangers,the heat transfer coefficient can be defined as a function of the Chilton–Colburn modulus,j,as h¼j

Gc p

Pr2=3

ð25Þ

where c p is the specific heat of thefluid(J/kg K),and Pr is the Prandlt number,which can be assumed constant for the range of tempera-ture operation in the heat exchanger present in CCHP systems.For altitude,Eq.(25)becomes

hðzÞ¼

j

z

nðzÞðGc pÞ

Pr2=3

ð26Þ

where j z is the Chilton–Colburn modulus found based on Re(z).The heat transfer coefficient of an extended surface heat exchanger is usually given by the relationship between the Chilton–Colburn modulus and the Reynolds number[21].Using the example plots gi-ven by Kakaçand Liu[21]of j vs.Re for different extended surface heat exchangers,their analysis for altitude leads to the following relationship

j

z¼1þ5Â10À5ðzÞð27Þ

where j is obtained with Re and jz is obtained with Re(z).

It must be understood that the Chilton–Colburn modulus is par-ticular for each heat exchanger but Eq.(27)gives a good reference for the objective of this paper which is to provide estimation for the design stage or screening tools of CCHP systems.As an exam-ple,Orth et al.[23]investigated the air-side heat transfer process of an air cooled condenserfinding that their heat exchange follows

the correlation j¼0:166ReÀ0:4

air

.This correlation,by using Eq.(24), defines its ratio as j z¼nðzÞÀ0:4.Comparison of results from this correlation with results from Eq.(27)shows a maximum variation in the order of1.7%for an altitude of4000m.

By using Eqs.(25),(27),and(26)can be modified to define the variation of the heat transfer coefficient as a function of altitude as

N.Fumo et al./Energy Conversion and Management52(2011)1459–14691463hðzÞ¼½1þ5Â10À5ðzÞ nðzÞhð28ÞIn the study‘‘Design Considerations for Air Cooling Electronic Sys-tems in High Altitude Conditions”conducted by Belady[12],the convection heat transfer coefficient is defined as h=C h-turb q0.8G0.8. Although this correction factor does not account for the geometric of a heat exchanger,comparison of results from this correlation and Eq.(28)gives a maximum error of8.6%for the altitude of 4000m.However,the use of Eq.(28)in later analysis illustrates lower errors for the type of heat exchangers considered in this study.

For extended surface heat exchangers,the total resistance for heat transfer is given by Eq.(29),which can be written with more detail as Eq.(30).

R¼R gþR g;fþR condþR lþR l;fð29Þwhere R g is the resistance for the gas-side,R g,f is the fouling resis-tance for the gas-side,R cond is the conduction resistance through the tube,R l is the resistance for the liquid-side,and R l,f is the fouling resistance for the water-side,all with units of K/W.

1 UA ¼

1

h i A i

þ

R00

f;i

A i

þ

ln D0=D i

ðÞ

2p kL

þ

R00

f;o

A o

þ

1

h o A o

ð30Þ

Since only the heat transfer resistance of the gas-side is affected by altitude,a more useful form of Eq.(29)is

R¼R gþR0ð31ÞIf,as a measure of the magnitude of R g with respect to R0,the‘‘gas-side resistance ratio(f g)”is defined as

f g¼R0

R g

ð32Þ

Eq.(31)can be rewritten as

R¼R gð1þf gÞð33ÞThis equation as a function of altitude becomes

RðzÞ¼R gðzÞð1þf g;zÞð34Þwhere f g,z is defined as

f g;z¼

R0

R gðzÞ

ð35Þ

and by using Eq.(28)R g(z)is defined as

R gðzÞ¼

R g

½1þ5Â10ðzÞ nðzÞ

ð36Þ

Dividing Eq.(34)by Eq.(33)yields

RðzÞR ¼

1

½1þ5Â10ðzÞ nðzÞ

ð1þf g;zÞ

ð1þf gÞ

ð37Þ

From Eq.(37)it can be noticed that the ratioð1þf g;zÞ

g

is not a function

of altitude,but of f g(at sea level and at altitude).It can be verified

that by assuming values of f g,the plot ofð1þf g;zÞ

ð1þf gÞ

vs.altitude is approx-imately a straight line,which let conclude that for a particular f g the

ratioð1þf g;zÞ

ð1þf gÞ

can be considered independent of altitude.With this re-

sult,by plottingð1þf g;zÞ

ð1þf gÞ

vs.f g it is found that the ratio follows the curvefit given in Eq.(38).

ð1þf g;zÞð1þf gÞ¼0:5256fÀ0:295

g

ð38Þ

Since the resistance for the gas-side is much greater than the liquid-side[18],R g)R0,for Eq.(38),as f g approaches zero,the ratioð1þf g;zÞ

g approaches1.Then,Eq.(37)can be simplified to RðzÞ¼

R

½1þ5Â10À5ðzÞ nðzÞ

ð39Þ

It should be noted that f g will never reach zero because there must be some resistance on both sides(gas and liquid)where heat trans-fer takes place.How close f g gets to zero is based on the heat exchanger design.However,since the idea is to simplify computa-tions at altitude,in this study a general case is defined based on

f g=0.113in order forð1þf g;zÞ

ð1þf gÞ

to reach the value of1.

Since R¼1,from Eq.(39),the overall heat transfer coefficient at altitude can be defined as

UðzÞ¼½1þ5x10À5ðzÞ nðzÞUð40ÞSince the heat capacity rate for the gas-side is affected by altitude, two cases arise when Eqs.(18),(19),and(21)are defined for alti-tude.Case1refers to the case when the air-side heat capacity rate C g is the lower(C min)of the twofluids,and Case2refers to the case when C g is the greater(C max)of the twofluids.

Case1(c g=c min):

NTUðzÞ¼½1þ5Â10À5ðzÞ NTUð41ÞC rðzÞ¼nðzÞC rð42Þ

eðzÞ¼1Àexp1

nðzÞC r

½NTUðzÞ 0:22f exp½ÀnðzÞC r½NTUðzÞ 0:78 À1g

ð43ÞCase2(c g=c max):

NTUðzÞ¼½1þ5x10À5ðzÞ nðzÞNTUð44Þ

C rðzÞ¼

1

nðzÞ

C rð45Þ

eðzÞ¼1Àexp nðzÞ

r

½NTUðzÞ 0:22expÀ

C r

½NTUðzÞ 0:78

À1

ð46ÞIn order to validate Eqs.(41)–(46),the correction factors obtained using Eqs.(41)–(43)(Case1)were compared with the altitude cor-rection factor given in the EnergyPlus Engineering Reference[13]in the section of air-cooled condensers.The correction in this refer-ence is defined as[1À7.17EÀ5(z)].Since this correction factor is only function of altitude,comparison using different values of NTU and C r were done.For a NTU of4and C r of1,the maximum variation of0.8%was found for an altitude of about2000m.As NTU decreases while holding C r equal to1,the variation increases with a maximum of1.9%for an altitude of4000m.As C r decreases while holding NTU equal to4,the variation increases with a maxi-mum of10%at4000m when C r is0.5.However,if both parameter decreases,increases in a lower proportion,i.e.for C r equal to0.5but with a NTU of2,the variation is only

6%.

14N.Fumo et al./Energy Conversion and Management52(2011)1459–1469

Figs.4and 5show how NTU varies with altitude based on Eqs.(41)and (44)respectively.

To illustrate how the effectiveness of a heat exchanger varies with altitude,Figs.6and 7shows the plot of Eqs.(43)and (46)respectively,for an arbitrary C r =0.75.

If the heat exchanger does not have both fluids unmixed,the effectiveness equation of the specific heat exchanger type can be modified using Eqs.(41)and (42)if C g =C min and Eqs.(44)and (45)if C g =C max .

3.3.Fan performance at altitude

The performance of a fan can be summed up in a group of equa-tions called the fan laws.These laws,shown in Eqs.(47a),(47b),(47c),compare the ratio of two fans’rpm with their volumetric flow rate,static pressure,and horsepower [24].

_V 1_V 2¼rpm 1

rpm 2

ð47a ÞP 1P 2¼rpm 1

rpm 2

2

ð47b ÞhP 1hP 2¼rpm 1

rpm 2

3

ð47c Þ

These equations are used to compare fans performance at the same air conditions,which it is not the case considered in this paper.When the fan performance at altitude is compared with the perfor-mance at sea level,Eqs.(47b)and (47c)do not apply because the density varies.That is why fan manufacturers supply correction fac-tors for the pressure and power for fans to be operated at altitude.When comparing the performance of a fan working at altitude with respect to the design conditions (sea level),it is assumed that the rpm are kept at the nominal value of the fan’s motor;therefore,the volumetric flow rate will be the same at any altitude and Eq.(47a)applies.Volumetric flow rate is defined by Eq.(48),where _m

is the mass flow rate (kg/s)and q is the density (kg/m 3).Substi-tuting Eq.(48)into Eq.(47a)yields Eq.(49),where the subscripts z and 0denote altitude and sea level,respectively.

_V

¼_m q

ð48Þ

_m

z ¼_m 0q z

q 0

¼n ðz Þ_m

0ð49Þ

Since the air at altitude weighs less,the fan will require less power but also create less pressure than specified.For fans operating at altitude,n (z )can be used to estimate the static pressure the fan will be able to create P z and the power to be consumed (hp z )as

P z ¼n ðz ÞP 0ð50Þhp z ¼n ðz Þhp 0

ð51Þ

3.4.Pump performance at altitude

In pumping systems,the variation in altitude will affect the sys-tem only when the system is open to the atmosphere in some point.For the purpose of this paper,this means that only the suc-tion side of the circulation pump for the cooling water of the cool-ing tower may be affected by altitude.Therefore,the effect of altitude on pump performance is considered through the concept of net positive suction head (NPSH ).The NPSH of a pump allows users to maintain proper static pressure on the suction side of the pump.If the suction pressure drops to the vapor pressure of the liquid,then the liquid will begin to vaporize.The bubbles that form from the vaporization can then collapse on the impeller of the pump,reducing the efficiency and causing cavitation and vibration.Eq.(52)shows that the NPSH available (NPSH a )to the pump is cal-culated as the difference between the suction head (h s )at the impeller and the vapor head (h v )of the fluid.Eq.(53)defines h s as function of the suction pressure (P s ),the velocity of the water at the inlet of the pump (V s ),and the head loss due to major and minor losses in the pipe h l .On the other hand,Eq.(54)defines h v as the ratio of the vapor pressure and specific weight of the fluid.While Eq.(55)defines P s as the sum of the atmospheric pressure (P atm )and the pressure due to the column of water (h ).

NPSH a ¼h s Àh v ð52Þh s ¼P s

c þV 2

s 2g þh l

ð53Þh v ¼

P v c

ð54ÞP s ¼P atm þh c

ð55

Þ

NPSH a¼P atm

cþhþ

V2

sþh

l

À

P v

cð56Þ

In Eq.(56)the only parameter affected by altitude is the atmo-spheric pressure,which decreases with altitude.Therefore,NPSH a decreases with altitude.To avoid a decrease in pump performance, NPSH a must remain above the NPSH required for the pump(NPSH r), which is given by the manufacturer.In order to keep constant the NPSH a after a variation of atmospheric pressure due to altitude,as shown in Fig.8,the column of water,D h,need to be increased. The required increase of the water column can be found by sub-tracting the NPSH a at0m reference and at altitude as

D h¼NPSH aÀNPSH aðzÞ¼P o

cÀ

P z

cð57Þ

By using the altitude air density ratio,Eq.(57)becomes

D h¼P o

cð1ÀnðzÞÞð58Þ

Since P0=101.08kPa,and the specific weight of water for the temperature range of operation in the cooling tower can be consid-ered constant,by assuming c¼9810N=m3,Eq.(58)becomes

D h¼10:3½1ÀnðzÞ ½m ð59ÞFig.9illustrates the magnitude of D h as function of altitude.4.CCHP system

A schematic of the combined cooling,heating,and power (CCHP)system considered in this study is shown in Fig.10.The CCHP system operates on a topping cycle,which means the power is generatedfirst and then the heat is recovered for further use. CCHP systems produce electric power with a PGU.The prime mover for the PGU can be a reciprocating engine,a gas or steam turbine,microturbines,or fuel cells.Heat is recovered from the combustion process of the engine which in turn is used as thermal energy source for heating and cooling and purposes[25].This is favorable due to the increase in efficiency of the system since the heat and power are produced simultaneously instead of by sepa-rate processes.If the recovered heat is not enough to satisfy the thermal energy demand,a boiler provides the supplemental ther-mal energy.On the other hand,if the recovered thermal energy is not used or stored,a second heat exchanger(air-blown cooler) is used to remove any unused heat to ensure cool enough temper-atures to prevent the prime mover from overheating.For cooling purposes,the thermal energy is used to power an absorption chil-ler to handle the cooling load.A cooling tower is used to cool the water used in the condenser of the absorption chiller.The con-denser of the absorption chiller in turn heats the water,which re-turns to the cooling tower and the process is repeated.

The topics discussed in previous sections will now be applied to each specific CCHP system component in order to obtain equations that can be used in approaches to evaluate their performance at altitude.These equations are intended to be used in the design stage of CCHP systems in the selection of equipment affected by altitude,and for their use in simulations in screening tools for CCHP systems feasibility.

4.1.Power generation unit at altitude

The PGU in a small scale CCHP system is typically a natural gas or diesel internal combustion engine.This study deals solely with the natural gas internal combustion engine;however,there is information on diesel engines that is related to the natural gas per-formance.The lower density of the air at higher altitudes can lead to different derating factors in engine performance.As indicated by specification sheets of PGUs from different manufacturers con-sulted in the literature review,the performance of this type of equipment is specified by the derate power output at altitude.As derived from Section3.1,the derating factor for power output for the PGUs in CCHP systems can be estimated by Eq.(60).

PGU outputðzÞ¼nðzÞPGU nominal outputð60Þ4.2.Boiler at altitude

The boiler is another component of the CCHP system that loses performance with altitude.Due to the lower density of the air,the

nominal mass flow rate of natural gas in the burners need to be re-duced due to the lack of oxygen,as discussed in Section 3.1.Simi-larly to the analysis for the PGU,the dirate output for the boiler can be estimated by Eq.(61).

Boiler output ðz Þ¼n ðz ÞBoiler nominal

output

ð61Þ

4.3.Heat exchangers at altitude

For the CCHP system of Fig.10,the two heat exchangers work-ing at atmospheric pressure that may be affected by altitude are the heat exchanger for the exhaust (exhaust heat exchanger),and the emergency heat exchanger (air-blown cooler)used to remove any unused recovered thermal energy in order to prevent over-heating the prime mover.For the exhaust heat exchanger,since the exhaust mass flow rate is very low compared with the liquid-side mass flow rate,usually the gas-side has the lower heat capac-ity ratio (C g =C min )and Eq.(43)from Section 3.2applies for the heat exchanger effectiveness.While for the air-blown air heat ex-changer,since for safety reasons the air leaving the heat exchanger cannot have high temperature,the gas-side may have the greater heat capacity ratio and Eq.(46)from Section 3.2would apply for the heat exchanger effectiveness.Therefore,depending on the de-sign of the heat exchanger of the CCHP system at sea level,the effectiveness of the heat exchanger at altitude can be estimated from

Case 1,C g =C min :

e ðz Þ¼1Àexp

1n ðz ÞC r

½NTU ðz Þ 0:22exp ½Àn ðz ÞC r NTU ðz Þ

0:78h i À1n o NTU (Z )=[1+6Â10À5(z )]NTU

Case 2,C g =C max :e ðz Þ¼1Àexp

n ðz ÞC r

½NTU ðz Þ 0:22exp ÀC r n ðz Þ

½NTU ðz Þ 0:78

À1

NTU (Z )=[1+6Â10À5(z )]n (z )NTU

The equations for effectiveness are for both fluids unmixed in the cross-flow heat exchanger configuration.For other configura-tions,the same methodology used in Section 3.2can be applied in order to find the effectiveness at altitude for other type of flow or heat exchanger.

4.4.Absorption chiller/cooling tower at altitude

Performance of cooling towers is related to the definitions of range and approach [26].The range is defined as the difference be-tween the entering (T i )and exiting (T o )water temperatures to and from the cooling tower (Eq.(62)).The approach is defined by the difference between the exiting water temperature from the cooling tower (T o )and the entering air wet-bulb temperature to the cool-ing tower (T wb )(Eq.(63)).These are illustrated in Fig.11.By relat-ing the range and the approach,the cooling tower performance can be evaluated through its effectiveness (l )as shown in Eq.().

range ¼T i ÀT o

ð62Þapproach ¼T o ÀT wb

ð63Þl ¼

range range þapproach ¼T i ÀT o

T o ÀT wb

ðÞ

Assuming that the boiler will allow for the heat medium inlet tem-perature for the absorption chiller to be constant by using a modu-lating control [27],and the cooling tower efficiency is constant based on the manufacturers’data;then,the outlet water tempera-ture is a function of the wet-bulb temperature of the air.By consult-

ing a psychrometric chart,it can be seen that the wet-bulb temperature will increase with increasing humidity ratio,which was shown to be true for increasing altitude.ASHRAE provides psy-chrometric charts for different elevations [18].By using the neces-sary chart along with weather files for a specific location,the wet-bulb temperature can be found.By rearranging Eq.()and considering the change in wet-bulb temperature for altitude,Eq.(65)can be used to find the outlet temperature of the water to the absorption chiller.

T o ðz Þ¼T i Àl ðT i ÀT wb ðz ÞÞ

ð65Þ

The outlet water of the cooling tower is sent through the con-denser in the absorption chiller to condense the refrigerant on the coils containing the water.From Yazaki Energy Systems water fired chillers specifications sheet for model WFC-SC30/SH30[28],the standard rating for the heat medium inlet temperature is taken to be 90°C (193°F).Using this standard temperature,a figure was created using the cooling capacities for various cooling water tem-peratures.Fig.12shows the cooling capacity factor as a function of the inlet cooling water temperature (exiting water temperature from the cooling tower).It can be seen in the figure that the cooling capacity of the condenser can be increased by decreasing the inlet cooling water temperature.By using Eq.(65)to find the outlet tem-perature of the cooling tower,Fig.12can be used to determine the cooling capacity for this specific absorption chiller.

In order to perform simulations,the following approach can be used tofind the web bulb temperature at altitude,T wb(z).The ap-proach is as follows.Eq.(66)[18]defines the humidity ratio at alti-tude as function of the thermodynamic wet-bulb temperature,T*.

Above freezing point:

wðzÞ¼½2501À2:326TÃ w sðzÞÃÀ1:006½TÀTÃ

2501þ1:86TÀ4:186TÃ

ð66aÞ

Below freezing point:

wðzÞ¼½2830À2:4TÃ w sðzÞÃÀ1:006½TÀTÃ

Ã

ð66bÞ

For Eq.(66),the humidity ratio at the saturation point for T*is com-puted using Eq.(67)[15].

w sðzÞü0:622P ws

pðzÞÀP ws

TÃ

ð67Þ

The saturation pressure of water vapor(P ws)for T*can be computed using Eq.(68)[18].

lnðp

w sÞ¼

C a

Ã

þC bþC c TÃþC d TÃ2þC e TÃ3þC f TÃ4C d ln TÃð68Þ

The coefficients for Eq.(68)are given in Table1.By using Eqs.(66), (67),and(68),w(z)can be found for any T*.To validate this humid-ity ratio,it must be compared with the actual humidity ratio com-puted using the temperature and relative humidity of the site at altitude,which is given by Eq.(6)(Section2.3)

wðzÞ¼0:622u P ws

u ws

T

By solving these equations simultaneously,or through an iterative approach,T*can be found.This temperature defines the wet-bulb temperature T wb(z)to be used in Eq.(65).

5.Conclusion

In this study the effect of altitude on the performance of CCHP systems’components is analyzed.The analysis is oriented to the development of equations that can be used during the design stage or CCHP screening tools developed with simplified models.The analysis is based on the assumption that atmospheric properties for the site,temperature and relative humidity,are known through the use of site weather data such as weatherfiles.Equipment in CCHP systems that are affected by altitude include the power gen-eration unit,the boiler,heat exchangers,the absorption chiller/ cooling tower,and any pump with the suction side open to the atmosphere.Due to reduction of air mass with altitude,compo-nents having a combustion process associated to them,such as the power generation unit and the boiler,will be negatively af-fected.Effect of altitude on heat exchanger processes,such as the found in the exhaust heat exchanger and the air-blown cooler, are evaluated by computing the effectiveness at altitude.The cool-ing tower will experience a positive change in performance as the air will increase its ability to hold heat as altitude increases.This increase in cooling tower performance has a positive effect on the absorption chiller since the absorption chiller relies directly upon the cooling water inlet temperature.Pumps in the system which have suction-side reservoirs open to the atmosphere will not necessarily be affected negative or positively,but must be con-sidered in the design of the system due to vaporization.If water starts to evaporate due to a decrease of pressure as consequence of altitude,a decrease of pump efficiency and damage to the impel-ler blades will be the consequences.The equations proposed to estimate performance of CCHP systems’equipment at altitude are presented as function of altitude.At the design stage,these equations can be used to estimate performance reduction in order to select equipment with higher capacity.For simulations,the equations can be incorporated in the code to assess the perfor-mance of CCHP systems at altitude.

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C b 6.3925247E+00 1.3914993E+00

C cÀ9.6778430E–03À4.80239E–02

C d 6.2215701E–07 4.17768E–05

C e 2.0747825E–09À1.4452093E–08

C fÀ9.4840240E–130

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