ng

3976

Design at altitudePerformance at altitude

, anefrecothes, monsCCH

their specic application on how to assess the performance of the individual components of CCHP

ower (Cadvanith thes carbosing ae. Was

mal-uid systems open to the atmosphere are related, among oth-ers, to systems or equipment such as engines, boilers, heatexchangers, pumps, desiccant systems and evaporative coolingsystems. For CCHP systems, the effects of altitude are related tothe 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 affectingCCHP systems energy performance when operating at altitude.

As a rst source of information on the performance of equip-ment at altitude, the equipments specication 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 by3% for each 305 m (1000 ft.) above sea level. Carrier species thatheating input in Single-Package Rooftop Units is altered by altitudeby approximately 4% per 305 m (1000 ft.) [3]. Kohler Power [4]includes correction factors for altitude in their specication sheetsof PGU. They state that their natural gas PGUs should be reduced inefciency by 1.3% for every 100 m (328 ft.) after the initial 100 m

Corresponding author. Tel.: +1 662 325 6711; fax: +1 662 325 7223.

Energy Conversion and Management 52 (2011) 14591469

Contents lists availab

n

lseE-mail address: fumo@me.msstate.edu (N. Fumo).mover is recovered through the jacket water cooling system andexhaust to provide thermal energy to heating systems and to anabsorption chiller to provide cooling to the building. According tothe US Department of Energy (DOE), most industrial applicationsof these CCHP systems convert over 80% of the input fuel into use-able energy [1].

Thermal-uid systems are affected by altitude when the ow ofmass is open to the atmosphere at any point in the system. Ther-

the performance analysis, the information provided in this papercan be considered and implemented in simplied models used asscreening tools for CCHP systems. Some examples of cities wherethe information from this paper may be useful in the analysis ofCCHP systems are Denver, CO (population 588,349, altitude1609 m/5278 ft.), Albuquerque, NM (pop. 518,271, 1619 m/5310 ft.),Colorado Springs, CO (pop. 372,437, 1921 m/6300 ft.), and SantaFe, NM (pop. 72,056, 2133 m/6996 ft.).1. Introduction

Combined cooling, heating, and pused on site to save energy by takingall efciency of this technology, wreducing operating costs, as well aemissions. CCHP systems work by u(PGU) to generate power for the sit0196-8904/$ - see front matter 2010 Elsevier Ltd. Adoi:10.1016/j.enconman.2010.10.009systems when operating at altitude. This paper also summarizes the analysis by presenting equationsthat can be used in the design stage of CCHP systems in order to account for equipment capacityvariation, or in simplied simulations such as those for screening tools, without having a detailedsimulation that some times are not cost-effective due to the time and human effort to accomplish it.

2010 Elsevier Ltd. All rights reserved.

CHP) systems could betage of the higher over-additional benets ofn and other pollutantpower generation unitte heat from the prime

Since detailed simulation of CCHP systems will account for theeffect of altitude through air properties and manufactures perfor-mance curves, the analysis presented in this paper is intended tobe used as a reference for the design stage and performance anal-ysis. For the design stage, the information presented in this papercan be used to identify the equipment affected by altitude, as wellas the extent affecting the performance in order to help designersin the selection of equipment avoiding oversize or undersize. ForCombined cooling, heating, and powerCCHP

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 andDesign considerations for combined cooli

Nelson Fumo , Pedro J. Mago, Kenneth JacobsMechanical Engineering Department, Mississippi State University, Mississippi State, MS

a r t i c l e i n f o

Article history:Received 21 January 2010Received in revised form 21 September2010Accepted 3 October 2010Available online 25 October 2010

Keywords:

a b s t r a c t

Combined cooling, heatingquence of its high overallof energy consumption byAs a result, they also haveCCHP systems componentHowever, these specicatiperformance of any of the

Energy Conversio

journal homepage: www.ell rights reserved., heating, and power systems at altitude

2, USA

d power (CCHP) is a technology that makes better use of fuels as conse-ciency, which can be as high as 80%. CCHP systems aid in the reductionvering otherwise wasted heat and using it to provide heating and cooling.potential to reduce carbon and other pollutant emissions. Generally, foranufacturers include specications on the performance of the equipment.are normally given for sea level operation. Changes in altitude affect theP systems components that are open to the atmosphere due to changes

le at ScienceDirect

and Management

vier .com/ locate /enconman

nd Mabove sea level. Generac Power Systems [5] states in their unitsspecication sheets a power adjustment factor that accounts forvariations in ambient conditions, temperature and altitude. Foraltitude, a correction factor of 1% for every 100 m above 183 mor 3% per every 1000 ft. above 600 ft. is given. This derating factoris based on Propane (LPG) while 4% is suggested for Natural Gas.Technical literature also covers engine performance at altitude,such as the 2008 ASHRAE Handbook HVAC Systems and Equip-ment [6] that states naturally aspirated engine output typicallydecreases 3% for each 305 m (1000 ft.) increase in altitude. Re-search results are also available on how altitude affects engine per-formance. Benjumea et al. [7] have conducted research in dieselengines. They found that due to the lower density of the intakeair, more fuel was being used which decreased the efciency. Perezand Boehman [8] have conducted studies for diesel engines to cre-

Nomenclature

CCHP combined cooling, heating, and powerHHV higher heating valueHVAC heating ventilation and air conditioningPGU power generation unitAF airfuel ratioC heat capacity ratioNTU number of transfer unitsP pressureW air humidity ratio

Symbolsn altitude air density ratioe effectivenessg efciencyl boiler efciencyu relative humidityg efciencyl cooling tower efciencyu relative humidity

1460 N. Fumo et al. / Energy Conversion aate a formula for the power correction for the effects of pressure(altitude) and temperature on power output. One way to overcomethe lack of oxygen in the combustion process is turbocharging,which forces more air into the mixture and causes a more completecombustion. This is unfavorable in some situations due to designproblems and the lack of availability of parts for specic engines.The Indian Institute of Petroleum [9] has investigated alternativesto the turbocharger solution, such as to increase the combustionrate by adding a more volatile fuel by way of carburetion. Thesereferences are more related to explain the performance of the sys-tem based on efciency but commercially available technologycompensates for the lack of oxygen by controlling the airfuel ratioand decreasing the output as reported by manufacturers.

Cooling tower operation depends on the wet-bulb temperatureof the air. This wet-bulb temperature increases with altitude. Theefciency of a cooling tower is a function of the difference in theinlet and outlet water temperatures and the difference in the inletwater temperature and the wet-bulb temperature. As the wet-bulbtemperature increases with altitude, it gets closer to the inletwater temperature, raising the efciency. Hamilton [10] suggeststhat the performance for the cooling tower increases 38% at1500 m (5000 ft.) above sea level.

Heat exchangers, involving atmospheric air as one of the uidsinterchanging thermal energy, are also affected by the psychromet-rics of the atmospheric air. For heat exchangers, altitude affects notonly mass ow rate, but parameters dening the convection heattransfer coefcient. Due to the decrease in air density and massow at altitude, ASHRAE [11], referring to the Thermal Guidelinesfor Data Processing Environments, gives a derating factor of 1 K per300 m (1000 ft.) above 900 m (2950 ft.) for the maximum allow-able temperature of electronic equipment. This derating factorcan be expressed as a decrease of the convection heat transfer ascan be deduced from Belady [12]. According to Belady, the convec-tion heat transfer varies with the density to the power of 0.8 anddensity varies with altitude making the convection heat transfera 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 theequipment. As an example, from data of Carrier manufacturer ofHVAC equipment, the EnergyPlus Engineering Reference [13] inthe section of air-cooled condensers denes a correction factorfor heat removal capacity as a function of altitude as

z altitude (above sea level)z0 critical altitude for theoretical airfuel ratioDn difference between the altitude air density ratio at z and

z0

T* thermodynamic wet-bulb temperature

Subscriptsw water vaporda dry airws saturation of dry airtheoric theoreticalcomb combustiong gas-sidewb wet-bulbi inleto outletmin minimummax maximumr ratioanagement 52 (2011) 14591469[1 7.17E5x (altitude)].Other common processes present in CCHP systems that are af-

fected by altitude are related to fans performance and pumpingsystems. Analysis of the inuence of altitude in fan performancecan 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 becoupled with other thermally activated systems, it is important tomention that processes of heat and mass transfer found in systemssuch 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 arediscussed in Section 2 (Psychrometrics of Air at Altitude), it isimportant to mention here that these properties vary with theweather. Variation of properties with weather is excluded fromthis analysis since the analysis considers that properties such astemperature and relative humidity are known as designparameters.

2. Psychrometrics of air at altitude

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

of these properties only density, relative humidity, and wet-bulb

the partial pressures of dry air, Pda(z), and water vapor, Pw(z), asshown in Eq. (4).

w 0:622 PwP Pw 3

Pz Pdaz Pwz 4Since the partial pressures vary with the amount of moles of dry

air and water vapor in the mixture, a measure is needed for howmuch water is present in the air in order to consider the effect ofaltitude. For the purpose of this paper, relative humidity (u), de-ned by Eq. (5) [18], is used as the parameter to assess how thehumidity ratio changes with altitude. That is, relative humidity isassumed to be known from weather les, which is used as the rel-ative humidity to compute the humidity ratio (w(z)) at altitude byEq. (6). The saturation pressure of water vapor in absence of air(Pws) is a function of temperature, which is denoted by the sub-script T in the equation.

nd Management 52 (2011) 14591469 1461sure to decrease. The pressure will drop with altitude accordingto Eq. (2) [18], where P(z) is the atmospheric pressure at altitudein kPa, P0 is the standard atmospheric pressure at sea level(101.08 kPa), and z is the altitude above sea level in meters.

Pz P01 2:25577105z5:2559 2Eq. (2) is a function of height and standard atmospheric pres-

sure. Since the standard atmospheric pressure at sea level can betaken as a constant, P(z) is only dependent on the altitude. Thisshows that this equation holds true for any point on the earthssurface.

2.3. Air humidity ratioThis equation shows that the standard air temperature decreaseswith altitude, starting with a value of 15 C (60 F) at sea level.The altitude of the highest point on the earths surface is MountEverest, with a standard value of 8900 m (29,190 ft.). For this alti-tude, Eq. (1) denes a standard temperature for the highest pointon the earths surface of 42.85 C (45 F). However, the coldesttemperature on earth, of about 89.2 C (130 F), has been re-corded in Antarctica. Therefore, it must be clear that the word stan-dard refers to the reference temperature for estimating propertiesat various altitudes, and air temperatures vary also with local geog-raphy and weather conditions [18]. For example, Santa Fe (NM) hasan elevation of 2100 m (6890 ft.) and an average temperature of30 C (86 F) for its hottest month, July; while New York City (NY)has an elevation of 10 m (33 ft.) and a lower average temperatureof 28 C (83 F) for July. Therefore, for the purpose of this paper,air temperature on the design, simulation, and operation of CCHPsystems equipment at altitude must be considered through weath-er les, and Eq. (1), as it is dened, 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 effectof altitude in thermal-uid systems. As altitude increases, theamount of air mass decreases. This causes less weight of air on apoint, which, by denition of pressure, causes atmospheric pres-temperature are affected by a change in altitude as consequenceof a change in atmospheric pressure. Schultz [17] mentioned thatbelow 3000 m (10,000 ft.) the effect of altitude on air propertiessuch as specic heat, thermal conductivity, and viscosity can benegligible. However, for important air properties, such as density,enthalpy, and dew-point temperature, the effect of altitude cannotbe ignored. Therefore, the following properties of air are consid-ered in this investigation: temperature, pressure, density, humidityratio, and enthalpy. These are the air properties that affect the per-formance of CCHP systems components due to operation at alti-tudes above sea level.

2.1. Air temperature

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

Tz 15 0:0065z 1density, viscosity, thermal conductivity, specic heat, diffusivity,relative humidity, and wet-bulb temperature, and concluded that

N. Fumo et al. / Energy Conversion aThe humidity ratio (w) is dened by Eq. (3) [18], where P is thetotal pressure of humid air and Pw is the partial pressure of watervapor. At altitude, the total pressure of humid air, P(z), is the sum ofu PwPws

T;P

5

wz 0:622 uPwsPz uPws

T

6

To illustrate how the humidity ratio is affected by altitude, Fig. 1shows the variation of the humidity ratio with altitude for relativehumidities of 30%, 50%, and 80%. These curves where developed bytaking Pws (1.7055 kPa) at the standard temperature of 15 C (60 F).Fig. 1 illustrates that the humidity ratio of air increases as altitudeincreases, with greater variations for higher relative humidity.

2.4. Air density

Air is a compressible uid. Therefore, lowering the pressure willexpand a given mass of air to a larger volume, lowering the den-sity. Since atmospheric air can be considered as a mixture of dry airand water vapor, atmospheric air density, dened by Eq. (7) [18],accounts for water content through the humidity ratio. For thisstudy, since Rda is the gas constant for dry air and air temperatureis said to be considered through weather les, only air pressure andair humidity ratio are affected by altitude which is expressed inEq. (8).

q PRdaT1 1:608w 1w 7

qz PzRdaT1 1:608wz 1wz 8Fig. 1. Humidity ratio of air at altitude for 80%, 50%, and 30% relative humidity.

Natural gas is composed of hydrocarbon gases, typically 7090%

Fig. 2. Air density variation with altitude for relative humidity of 30%.

1462 N. Fumo et al. / Energy Conversion and MAs an example to illustrate how air density varies with altitude,Fig. 2 presents the air density for a relative humidity of 30% andfour air temperatures. It is important to remember that for the pur-pose of this paper, relative humidity and temperature should beknown from local weather les.

Since density is the air property dening the major variations inCCHP systems equipment performance at altitude, a relationshipbetween 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 dened in thisstudy as

nz qzq

1 2:25577105z5:2559 1wz1w1 1:608wz1 1:608w 9

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

nz PzP

1 2:25577105z5:2559 10

To evaluate the effect of humidity ratio on the air density,Eqs. (9) and (10) are plotted in Fig. 3 for an assumed relativehumidity of 30% and air temperature of 25 C. This gure showsthat for n(z), the inuence of humidity ratio can be neglected. Sincethe same behavior was obtained for different relative humiditiesand temperatures, with the maximum variation of 1.8% for an airtemperature of 40 C and 100% relative humidity at the altitudeof 4000 m (13,120 ft.), the altitude air density ratio can be dened

by Eq. (10) for all cases.

Fig. 3. Comparison of Eqs. (9) and (10).methane (CH4), 020% ethane (C2H6), propane (C3H8), and butane(C4H10), with small amounts (05%) of hydrogen (H2), carbon diox-ide (CO2), and hydrogen sulphide (H2S) [20]. Since commonly nat-ural gas is the fuel used in CCHP systems, in this paper methane isthe fuel used for all analysis as reference for natural gas. Completecombustion occurs when there is enough oxygen in the reactantsto completely oxidize all of the hydrogen and carbon, leavingmostly H2O and CO2, which are both stable. Eq. (13) shows thechemical reaction equation for complete combustion of methane:

CH4 2O2 3:76N2 ! CO2 2H2O 7:52N2 13A denition regarding the minimum theoretical air required for

the incomplete combustion of a fuel is the theoretical airfuel ratio(AFtheoric). For Eq. (13), the theoretical airfuel ratio is

AFtheoric 24:76 mol of air1 mol of fuel 9:52 142.5. Air enthalpy

Specic enthalpy is dened as the energy stored in a system perunit mass [19]. In terms of specic enthalpy for psychrometric pro-cesses, it is the amount of energy stored per unit mass of dry air. Itis obtained by summing the partial enthalpies of the different com-ponents of a mixture of perfect gases. Specic enthalpy (h, kJ/kgda)is given by Eq. (11) [18], where w (kgv/kgda) is the humidity ratio,T (C) is the temperature of the air, 1.006T is the approximate spe-cic enthalpy for dry air (kJ/kgda), and the quantity (2501 + 1.86T)is the approximate specic enthalpy for saturated water vapor(kJ/kgw).

h 1:006T w2501 1:86T 11At altitude, Eq. (11) can be changed to the form of Eq. (12).

hz 1:006T wz2501 1:86T 12

3. Thermal-uid processes affected by altitude

This section considers the thermal-uid processes inuenced byatmospheric property variations due to altitude that are present inCCHP systems equipment. Combustion is found in the PGU andboiler; heat transfer is found in the exhaust heat exchanger andair-blown cooler heat exchanger; forced air ow is found in theair-blown cooler heat exchanger and cooling tower; and pumpingis found in the cooling water loop of the absorption chiller/coolingtower.

3.1. Combustion process at altitude

Russell and Adebiyi [19] dene 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 takinginto consideration the specics on how the combustion takesplace, i.e. if it takes place in an internal combustion engine or atatmospheric pressure as in burners. This clarication is importantbecause 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 anycombustion 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 theavailable amount of air mass for combustion decreases as conse-quence of altitude.

anagement 52 (2011) 14591469In combustion equipment, if the fuel input remains constant whenthe equipment is placed at altitude, the airfuel ratio will be low-ered and the efciency will drop as consequence of incomplete

nd Mcombustion. To avoid the direct and indirect consequences ofincomplete combustion, manufacturers design the equipment tokeep constant the design airfuel ratio. For this reason, manufactur-ers report a derating factor or derated output for equipment operat-ing at altitude. If the amount of air mass available for combustiondecreases with altitude, in order to keep constant the airfuel ratio,the amount of fuel must be decreased in the same proportion asshown in Eq. (15) and the stoichiometric reaction given in Eq. (16).

AF v airv fuel AFdesing 15

vCH4 v2O2 3:76N2 ! vCO2 v2H2O v7:52N2 16where v represents the fraction of theoretical air in the combustionprocess due to air density reduction with altitude.

Although the combustion process depends on factors such asappropriate mixing of the fuel and air and sufcient chamber pres-sure and temperature [19], based on how the manufactures reportthe performance of equipment at altitude, it suggests that the ef-ciency of the equipment remains close to its design value. There-fore, for combustion equipment, a reasonable approach is toestimate the derating factor for the equipment output as the airdensity changes with altitude. This consideration indicates thatthe output of combustion equipment at altitude can be estimatedas

Outputz nz Outputnominal 17Although n(z) does not have a linear behavior, by using Eq. (17), itcan be noticed that the output of combustion equipment dropsabout 1% for every 100 m (3% for every 1000 ft.) as the values foundfrom 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 altitudeas a result of air density variation. Heat transfer by convection oc-curs when one uid ows over a surface, gaining or removing heatfrom the surface based on the temperature difference. For the focusof this paper, air or exhaust gases are the gas uids owing over asurface which has an inner liquid uid such as water with someadditive to change its boiling and freezing points if needed. Sinceit is well known that the heat transfer coefcient on the gas-sideis much lower than those on the liquid-side, extended surface heatexchangers are used. The twomost common types of extended sur-face heat exchangers are plate-n and tube-n heat exchangers[21]. Therefore, this section is developed by keeping in mind thatone of these heat exchangers will be used on the CCHP system.

One of the methods to analyze heat exchangers performance isthe e-NTUmethod. 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 (Cr) dened as

NTU UACmin

18

Cr CminCmax 19

where A is the heat transfer area, U is the overall heat transfer coef-cient, and Cmin and Cmax are the smaller and larger of the heatcapacity rates of the two uids. The heat capacity rates are denedas

C _mcp _VqCp 20

N. Fumo et al. / Energy Conversion aHeat exchanger effectiveness relations have been developed for dif-ferent types of heat exchangers and ow arrangements. For plate-n and tube-n heat exchangers, the ow arrangement is cross-ow (single pass) with (a) both uids unmixed, (b) Cmin unmixedand Cmax mixed, and (c) Cmin mixed and Cmax unmixed. For cross-ow with both uids unmixed, the heat exchanger effectiveness is

e 1 exp 1Cr

NTU0:22fexpCrNTU0:78 1g

21

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

Re DhGl

22

where Dh is the hydraulic diameter (m), l is the dynamic viscosityof the uid (Pa s), and G is the mass velocity or mass ux (kg/m2 s)dened as

G qUmax _m

Amin23

where q is the density of the uid, Umax is the uid velocity (m/s)based on the minimum free-ow cross-sectional area, Amin, and _mis the total mass ow rate of uid. Since for Re the density is theonly property that varies due to the change in altitude, it can besaid that Re is directly proportional to the density of the air, leadingto a decrease in Re with altitude. Eq. (24) gives the Reynoldsnumber as a function of altitude by incorporating the altitude airdensity ratio.

Rez nzRe 24For extended surface heat exchangers, the heat transfer coefcientcan be dened as a function of the ChiltonColburn modulus, j, as

h j GcpPr2=3

25

where cp is the specic heat of the uid (J/kg K), and Pr is the Prandltnumber, which can be assumed constant for the range of tempera-ture operation in the heat exchanger present in CCHP systems. Foraltitude, Eq. (25) becomes

hz jznzGcpPr2=3

26

where jz is the ChiltonColburn modulus found based on Re(z). Theheat transfer coefcient of an extended surface heat exchanger isusually given by the relationship between the ChiltonColburnmodulus and the Reynolds number [21]. Using the example plots gi-ven by Kaka and Liu [21] of j vs. Re for different extended surfaceheat exchangers, their analysis for altitude leads to the followingrelationship

jzj 1 5 105z 27

where j is obtained with Re and jz is obtained with Re(z).It must be understood that the ChiltonColburn modulus is par-

ticular for each heat exchanger but Eq. (27) gives a good referencefor the objective of this paper which is to provide estimation forthe design stage or screening tools of CCHP systems. As an exam-ple, Orth et al. [23] investigated the air-side heat transfer processof an air cooled condenser nding that their heat exchange followsthe correlation j 0:166Re0:4air . This correlation, by using Eq. (24),denes its ratio as jzj nz0:4. Comparison of results from thiscorrelation with results from Eq. (27) shows a maximum variation

anagement 52 (2011) 14591469 1463in the order of 1.7% for an altitude of 4000 m.By using Eqs. (25), (27), and (26) can be modied to dene the

variation of the heat transfer coefcient as a function of altitude as

Rz R1 5 105znz 39

It should be noted that fg will never reach zero because there mustbe some resistance on both sides (gas and liquid) where heat trans-fer takes place. How close fg gets to zero is based on the heatexchanger design. However, since the idea is to simplify computa-tions at altitude, in this study a general case is dened based onfg = 0.113 in order for

1fg;z1fg to reach the value of 1.

Since R 1UA, from Eq. (39), the overall heat transfer coefcientat altitude can be dened as

Uz 1 5x105znzU 40

nd Management 52 (2011) 14591469hz 1 5 105znzh 28In the study Design Considerations for Air Cooling Electronic Sys-tems in High Altitude Conditions conducted by Belady [12], theconvection heat transfer coefcient is dened as h = Ch-turbq0.8G0.8.Although this correction factor does not account for the geometricof a heat exchanger, comparison of results from this correlationand Eq. (28) gives a maximum error of 8.6% for the altitude of4000 m. However, the use of Eq. (28) in later analysis illustrateslower errors for the type of heat exchangers considered in thisstudy.

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

R Rg Rg;f Rcond Rl Rl;f 29where Rg is the resistance for the gas-side, Rg,f is the fouling resis-tance for the gas-side, Rcond is the conduction resistance throughthe tube, Rl is the resistance for the liquid-side, and Rl,f is the foulingresistance for the water-side, all with units of K/W.

1UA

1hiAi

R00f ;i

Ai ln D0=Di

2pkL R

00f ;o

Ao 1hoAo

30

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

R Rg R0 31If, as a measure of the magnitude of Rg with respect to R0, the gas-side resistance ratio (fg) is dened as

fg R0

Rg32

Eq. (31) can be rewritten as

R Rg1 fg 33This equation as a function of altitude becomes

Rz Rgz1 fg;z 34where fg,z is dened as

fg;z R0

Rgz 35

and by using Eq. (28) Rg(z) is dened as

Rgz Rg1 5 105znz 36

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

RzR

11 5 105znz1 fg;z1 fg 37

From Eq. (37) it can be noticed that the ratio 1fg;z1fg is not a functionof altitude, but of fg (at sea level and at altitude). It can be veriedthat by assuming values of fg, the plot of

1fg;z1fg vs. altitude is approx-

imately a straight line, which let conclude that for a particular fg theratio 1fg;z1fg can be considered independent of altitude. With this re-sult, by plotting 1fg;z1fg vs. fg it is found that the ratio follows thecurve t given in Eq. (38).

1 fg ; z1 fg 0:5256f

0:295g 38

Since the resistance for the gas-side is much greater than the liquid-side [18], Rg R0, for Eq. (38), as fg approaches zero, the ratio 1fg;z1f

1464 N. Fumo et al. / Energy Conversion ag

approaches 1. Then, Eq. (37) can be simplied toSince the heat capacity rate for the gas-side is affected by altitude,two cases arise when Eqs. (18), (19), and (21) are dened for alti-tude. Case 1 refers to the case when the air-side heat capacity rateCg is the lower (Cmin) of the two uids, and Case 2 refers to the casewhen Cg is the greater (Cmax) of the two uids.

Case 1 (cg = cmin):

NTUz 1 5 105zNTU 41Crz nzCr 42

ez 1 exp 1nzCr

NTUz0:22fexpnzCr NTUz0:78 1g

43Case 2 (cg = cmax):

NTUz 1 5x105znzNTU 44

Crz 1nzCr 45

ez 1 exp nzCr

NTUz0:22 exp Cr

nz NTUz0:78

1

46In order to validate Eqs. (41)(46), the correction factors obtainedusing Eqs. (41)(43) (Case 1) were compared with the altitude cor-rection factor given in the EnergyPlus Engineering Reference [13] inthe section of air-cooled condensers. The correction in this refer-ence is dened as [1 7.17E5(z)]. Since this correction factor isonly function of altitude, comparison using different values ofNTU and Cr were done. For a NTU of 4 and Cr of 1, the maximumvariation of 0.8% was found for an altitude of about 2000 m. AsNTU decreases while holding Cr equal to 1, the variation increaseswith a maximum of 1.9% for an altitude of 4000 m. As Cr decreaseswhile holding NTU equal to 4, the variation increases with a maxi-mum of 10% at 4000 m when Cr is 0.5. However, if both parameterdecreases, increases in a lower proportion, i.e. for Cr equal to 0.5 butwith a NTU of 2, the variation is only 6%.Fig. 4. Correction data for NTU at different altitudes (Case 1).

nd MFig. 5. Correction data for NTU at different altitudes (Case 2).N. Fumo et al. / Energy Conversion aFigs. 4 and 5 show how NTU varies with altitude based on Eqs.(41) and (44) respectively.

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

If the heat exchanger does not have both uids unmixed, theeffectiveness equation of the specic heat exchanger type can bemodied using Eqs. (41) and (42) if Cg = Cmin and Eqs. (44) and(45) if Cg = Cmax.

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 volumetricow rate, static pressure, and horsepower [24].

altitude, n(z) can be used to estimate the static pressure the fan willFig. 6. Effectiveness vs. NTU at different altitudes for C = 0.75 (Case 1).

Fig. 7. Effectiveness vs. NTU at different altitudes for C = 0.75 (Case 2).be able to create Pz and the power to be consumed (hpz) as

Pz nzP0 50hpz nzhp0 51

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 somepoint. 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 ofaltitude on pump performance is considered through the conceptof net positive suction head (NPSH). The NPSH of a pump allowsusers to maintain proper static pressure on the suction side ofthe pump. If the suction pressure drops to the vapor pressure ofthe liquid, then the liquid will begin to vaporize. The bubbles thatform from the vaporization can then collapse on the impeller of thepump, reducing the efciency and causing cavitation and vibration.Eq. (52) shows that the NPSH available (NPSHa) to the pump is cal-culated as the difference between the suction head (hs) at theimpeller and the vapor head (hv) of the uid. Eq. (53) denes hsas function of the suction pressure (Ps), the velocity of the waterat the inlet of the pump (Vs), and the head loss due to major andminor losses in the pipe hl. On the other hand, Eq. (54) denes hvas the ratio of the vapor pressure and specic weight of the uid.While Eq. (55) denes Ps as the sum of the atmospheric pressure(Patm) and the pressure due to the column of water (h).

NPSHa hs hv 52

hs Psc V2s2g

hl 53

h Pv 54_V1_V2

rpm1rpm2

47a

P1P2

rpm1rpm2

247b

hP1hP2

rpm1rpm2

347c

These equations are used to compare fans performance at the sameair 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 thedensity 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 altitudewith respect to the design conditions (sea level), it is assumed thatthe rpm are kept at the nominal value of the fans motor; therefore,the volumetric ow rate will be the same at any altitude and Eq.(47a) applies. Volumetric ow rate is dened by Eq. (48), where_m is the mass ow rate (kg/s) and q is the density (kg/m3). Substi-tuting Eq. (48) into Eq. (47a) yields Eq. (49), where the subscripts zand 0 denote altitude and sea level, respectively.

_V _mq

48

_mz _m0 qzq0 nz _m0 49

Since the air at altitude weighs less, the fan will require less powerbut also create less pressure than specied. For fans operating at

anagement 52 (2011) 14591469 1465v cPs Patm hc 55

4. CCHP system

A schematic of the combined cooling, heating, and power(CCHP) system considered in this study is shown in Fig. 10. TheCCHP system operates on a topping cycle, which means the poweris generated rst and then the heat is recovered for further use.CCHP systems produce electric power with a PGU. The primemover for the PGU can be a reciprocating engine, a gas or steamturbine, microturbines, or fuel cells. Heat is recovered from thecombustion process of the engine which in turn is used as thermal

thermal energy demand, a boiler provides the supplemental ther-mal energy. On the other hand, if the recovered thermal energy

nd Management 52 (2011) 14591469Pump

Absorption Chiller

Cooling Tower

Hot Cooling Water

Cold Cooling Water

Water Level

h

h

Fig. 8. Schematic of cooling tower.

1466 N. Fumo et al. / Energy Conversion aBy substituting Eqs. (53)(55) into Eq. (52), NPSHa can be rewrittenas

NPSHa Patmc hV2s2g

hl Pvc 56

In Eq. (56) the only parameter affected by altitude is the atmo-spheric pressure, which decreases with altitude. Therefore, NPSHadecreases with altitude. To avoid a decrease in pump performance,NPSHa must remain above the NPSH required for the pump (NPSHr),which is given by the manufacturer. In order to keep constant theNPSHa after a variation of atmospheric pressure due to altitude, asshown in Fig. 8, the column of water, Dh, need to be increased.The required increase of the water column can be found by sub-tracting the NPSHa at 0 m reference and at altitude as

Dh NPSHa NPSHaz Poc Pzc

57

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

Dh Poc1 nz 58

Since P0 = 101.08 kPa, and the specic weight of water for thetemperature range of operation in the cooling tower can be consid-ered constant, by assuming c 9810 N=m3, Eq. (58) becomes

Dh 10:31 nzm 59

Fig. 9 illustrates the magnitude of Dh as function of altitude.

Fig. 9. Increase of water column at pump suction due to altitude.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 coolingpurposes, the thermal energy is used to power an absorption chil-ler to handle the cooling load. A cooling tower is used to cool thewater 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 toeach specic CCHP system component in order to obtain equationsthat can be used in approaches to evaluate their performance ataltitude. These equations are intended to be used in the designstage of CCHP systems in the selection of equipment affected byaltitude, and for their use in simulations in screening tools forCCHP systems feasibility.

4.1. Power generation unit at altitude

The PGU in a small scale CCHP system is typically a natural gasor diesel internal combustion engine. This study deals solely withthe natural gas internal combustion engine; however, there isinformation on diesel engines that is related to the natural gas per-formance. The lower density of the air at higher altitudes can leadto different derating factors in engine performance. As indicated byspecication sheets of PGUs from different manufacturers con-sulted in the literature review, the performance of this type ofequipment is specied by the derate power output at altitude. Asderived from Section 3.1, the derating factor for power output forthe PGUs in CCHP systems can be estimated by Eq. (60).

PGUoutputz nzPGUnominal output 60

4.2. Boiler at altitude

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

Exhaust HX Bo

iler

Coo

ling

Tow

er

Air-Blown PGU

Absorption Chiller

Heater

Heating

Coolingenergy source for heating and cooling and purposes [25]. This isfavorable due to the increase in efciency of the system since theheat and power are produced simultaneously instead of by sepa-rate processes. If the recovered heat is not enough to satisfy theCooler

Fig. 10. CCHP system schematic.

range Ti To 62

peratures. Fig. 12 shows the cooling capacity factor as a function ofthe inlet cooling water temperature (exiting water temperaturefrom the cooling tower). It can be seen in the gure that the coolingcapacity of the condenser can be increased by decreasing the inletcooling water temperature. By using Eq. (65) to nd the outlet tem-perature of the cooling tower, Fig. 12 can be used to determine thecooling capacity for this specic absorption chiller.

Ran

geac

h

Entering Water Temperature

Exiting Water Temperature

nd Management 52 (2011) 14591469 1467approach To Twb 63l range

range approach Ti ToTo Twb 64

Assuming that the boiler will allow for the heat medium inlet tem-perature for the absorption chiller to be constant by using a modu-nominal mass ow 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 canbe estimated by Eq. (61).

Boileroutputz nzBoilernominal output 61

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 arethe heat exchanger for the exhaust (exhaust heat exchanger), andthe emergency heat exchanger (air-blown cooler) used to removeany unused recovered thermal energy in order to prevent over-heating the prime mover. For the exhaust heat exchanger, sincethe exhaust mass ow rate is very low compared with the liquid-side mass ow rate, usually the gas-side has the lower heat capac-ity ratio (Cg = Cmin) and Eq. (43) from Section 3.2 applies for theheat exchanger effectiveness. While for the air-blown air heat ex-changer, since for safety reasons the air leaving the heat exchangercannot have high temperature, the gas-side may have the greaterheat capacity ratio and Eq. (46) from Section 3.2 would apply forthe heat exchanger effectiveness. Therefore, depending on the de-sign of the heat exchanger of the CCHP system at sea level, theeffectiveness of the heat exchanger at altitude can be estimatedfrom

Case 1, Cg = Cmin:

ez 1 exp 1nzCr

NTUz0:22 expnzCr NTUz0:78

h i 1

n o

NTU(Z) = [1 + 6 105(z)]NTUCase 2, Cg = Cmax:

ez 1 exp nzCr

NTUz0:22 exp Cr

nz NTUz0:78

1

NTU(Z) = [1 + 6 105(z)]n(z)NTUThe equations for effectiveness are for both uids unmixed in

the cross-ow heat exchanger conguration. For other congura-tions, the same methodology used in Section 3.2 can be appliedin order to nd the effectiveness at altitude for other type of owor heat exchanger.

4.4. Absorption chiller/cooling tower at altitude

Performance of cooling towers is related to the denitions ofrange and approach [26]. The range is dened as the difference be-tween the entering (Ti) and exiting (To) water temperatures to andfrom the cooling tower (Eq. (62)). The approach is dened by thedifference between the exiting water temperature from the coolingtower (To) and the entering air wet-bulb temperature to the cool-ing tower (Twb) (Eq. (63)). These are illustrated in Fig. 11. By relat-ing the range and the approach, the cooling tower performance canbe evaluated through its effectiveness (l) as shown in Eq. (64).

N. Fumo et al. / Energy Conversion alating control [27], and the cooling tower efciency is constantbased 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-bulbtemperature will increase with increasing humidity ratio, whichwas 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 les for a specic location, thewet-bulb temperature can be found. By rearranging Eq. (64) andconsidering the change in wet-bulb temperature for altitude, Eq.(65) can be used to nd the outlet temperature of the water tothe absorption chiller.

Toz Ti lTi Twbz 65The outlet water of the cooling tower is sent through the con-

denser in the absorption chiller to condense the refrigerant onthe coils containing the water. From Yazaki Energy Systems waterred chillers specications sheet for model WFC-SC30/SH30 [28],the standard rating for the heat medium inlet temperature is takento be 90 C (193 F). Using this standard temperature, a gure wascreated using the cooling capacities for various cooling water tem-

Appr

o

Entering Air Wet-Bulb Temperature

Fig. 11. Range and approach of a cooling tower.Fig. 12. Example of absorption chiller cooling capacity factor as a function of inletcooling water temperature.

[consulted on September 2009].

nd MSince the cooling tower exit temperature decreases with alti-tude, Fig. 12 shows that the cooling capacity of the absorption chil-ler increases. This implies a positive boost in the performance ofthe absorption chiller. This can be expressed in two ways. If the in-let temperature of the cooling water to the cooling tower is to re-main a constant, then less fan power is required for the coolingtower since less air needs to be passed through the cooling tower.If the fan power remains constant because no variation in the fanmotor is allowed, then the inlet temperature of the cooling towerwill decrease with altitude, increasing the cooling capacity of theabsorption chiller.

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

Above freezing point:

wz 2501 2:326Twsz 1:006T T

2501 1:86T 4:186T 66a

Below freezing point:

wz 2830 2:4Twsz 1:006T T

2830 1:86T 2:1 66b

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

wsz 0:622 Pwspz Pws

T

67

The saturation pressure of water vapor (Pws) for T* can be computedusing Eq. (68) [18].

lnpws CaT

Cb CcT CdT2 CeT3 Cf T4Cd ln T 68

The coefcients for Eq. (68) are given in Table 1.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 ataltitude, which is given by Eq. (6) (Section 2.3)

wz 0:622 uPwsPz uPws

T

By solving these equations simultaneously, or through an iterative

Table 1Coefcient values for Eq. (68) [18].

100 to 0 C 0200 CCa 5.6745359E+03 5.8002206E+03Cb 6.3925247E+00 1.3914993E+00Cc 9.6778430E03 4.8640239E02Cd 6.2215701E07 4.1764768E05Ce 2.0747825E09 1.4452093E08Cf 9.4840240E13 0Cg 4.1635019E+00 6.5459673E+00

1468 N. Fumo et al. / Energy Conversion aapproach, T* can be found. This temperature denes the wet-bulbtemperature Twb(z) to be used in Eq. (65).

5. Conclusion

In this study the effect of altitude on the performance of CCHPsystems components is analyzed. The analysis is oriented to thedevelopment of equations that can be used during the design stageor CCHP screening tools developed with simplied models. Theanalysis is based on the assumption that atmospheric propertiesfor the site, temperature and relative humidity, are known throughthe use of site weather data such as weather les. Equipment inCCHP systems that are affected by altitude include the power gen-[4] Kohler Co. Kohler power systems, model: 60REZG, gas; 2009. [consulted on September2009].

[5] Generac Power Systems, Inc. Product overview, spec sheets. [consulted on October 2009].

[6] ASHRAE handbook. HVAC systems and equipment; 2008 [chapter 7].[7] Benjumea Perdo, Agudelo John, Agudelo Andrs. Effect of altitude and palm oil

biodiesel fuelling on the performance and combustion characteristics of a HSDIdiesel engine. Fuel 2009;88(4):72531.

[8] Perez PL, Boehman AL. Performance of a single-cylinder diesel engine usingoxygen-enriched intake air at simulated high-altitude conditions. AerospaceSci Technol 2009;14(2):8394.

[9] Sivasankaran GA, Jain SK. Performance of diesel engines at high altitudes. DefSci J 1988;38(3):30113.

[10] Thomas H. Hamilton. Effect of altitude on cooling tower rating andperformance. Bibliography of technical papers thermal performance, TPR-125. Cooling Technology Institute; 1962. .

[11] ASHRAE handbook. HVAC applications; 2007 [chapter 17].[12] Belady Christian L. Design considerations for air cooling electronic systems in

high altitude conditions. IEEE Tran Compon Pack Manuf Technol Part A1996;19(4):495500.

[13] The US Department of Energy, Ofce of Energy Efciency and RenewableEnergy. Building technology program, EnergyPlus simulation software,EnergyPlus engineering reference (available in the Documentation folder ofthe software).

[14] Pasaran A, Heiden R. The inuence of altitude on the performance of desiccant-cooling systems. Energy 1994;19(11):116579.

[15] Camargo JR, Godoy Jr E, Ebinuma CD. An evaporative and desiccant coolingsystem for air conditioning in humid climates. J Braz Soc Mech Sci Eng 2005;XXVII(3):2437.

[16] Pesaran Ahmad A, Heiden Rick. The inuence of altitude on the performance ofdesiccant-cooling systems. Energy 1994;19(11):116579.

[17] Carl C. Schultz. Engineering for high altitude. Engineered systems magazine,eration unit, the boiler, heat exchangers, the absorption chiller/cooling tower, and any pump with the suction side open to theatmosphere. Due to reduction of air mass with altitude, compo-nents having a combustion process associated to them, such asthe power generation unit and the boiler, will be negatively af-fected. Effect of altitude on heat exchanger processes, such as thefound 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 theair will increase its ability to hold heat as altitude increases. Thisincrease in cooling tower performance has a positive effect onthe absorption chiller since the absorption chiller relies directlyupon the cooling water inlet temperature. Pumps in the systemwhich have suction-side reservoirs open to the atmosphere willnot necessarily be affected negative or positively, but must be con-sidered in the design of the system due to vaporization. If waterstarts to evaporate due to a decrease of pressure as consequenceof altitude, a decrease of pump efciency and damage to the impel-ler blades will be the consequences. The equations proposed toestimate performance of CCHP systems equipment at altitudeare presented as function of altitude. At the design stage, theseequations can be used to estimate performance reduction in orderto select equipment with higher capacity. For simulations, theequations can be incorporated in the code to assess the perfor-mance of CCHP systems at altitude.

References

[1] The US Department of Energy, Energy Efciency and Renewable Energy.Industrial technology program, industrial distribution energy. Cooling, heating,and power for industry: a market assessment; August 2003. [consulted on September 2009].

[2] The Energy Solutions Center, Inc. The natural gas boiler burner consortium.Air supply. [consulted on October 2009].

[3] Carrier Corp. Single-package rooftop units, natural gas high altitude conversionkit accessory, installation instructions; March 2005.

anagement 52 (2011) 145914692006 December issue, cover story; 2006. [consulted on September 2009].

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[22] Incropera Frank P, DeWitt David P, Bergman Theodore L, Lavine Adrienne S.Fundamentals of heat and mass transfer. Hoboken (NJ): Wiley; 2006.

[23] Orth L, Zietlow DC, Pedersen CO. Predicting refrigerant inventory of HFC 134ain air cooled condensers. Report project ACRC TR-34, Air Conditioning andRefrigeration Center, University of Illinois, Urbana, IL; 1993.

[24] McQuiston Faye C. Heating, ventilating, and air conditioning analysis anddesign. Hoboken (NJ): John Wiley & Sons; 2005.

[25] Fumo N, Mago PJ, Chamra LM. Hybrid-cooling, combined cooling, heating, andpower systems. In: Proceedings of IMechE, vol. 223. Part A J Power Energy;2009.

[26] ASHRAE handbook. HVAC systems and equipment; 2008 [chapter 39].[27] ASHRAE handbook. HVAC systems and equipment; 2008 [chapter 31].[28] YASAKI Energy Systems, Inc. Products, literature, water red chiller/chiller

heater WFC-S series: 10, 20 and 30 RT cooling. [consulted on September 2009].

N. Fumo et al. / Energy Conversion and Management 52 (2011) 14591469 1469

Design considerations for combined cooling, heating, and power systems at altitudeIntroductionPsychrometrics of air at altitudeAir temperatureAir pressureAir humidity ratioAir densityAir enthalpy

Thermal-fluid processes affected by altitudeCombustion process at altitudeHeat transfer process at altitudeFan performance at altitudePump performance at altitude

CCHP systemPower generation unit at altitudeBoiler at altitudeHeat exchangers at altitudeAbsorption chiller/cooling tower at altitude

ConclusionReferences