Development and Validation of Flat-Plate Collector Testing Procedures

Transcription

1 Developmen and Validaion of Fla-Plae Collecor Tesing Procedures Repor for November, 2006 Focus on Energy (FOE) suppors solar hermal sysems ha displace convenional fuels by offering cash-back rebaes ha provide an incenive for residens o inves in his renewable energy echnology. To be eligible for rebaes, FOE requires solar collecors o be cerified by he Solar Raing and Cerificaion Corporaion (SRCC). The cerificaion program involves esing of he solar collecors in accordance wih ASHRAE Sandard Currenly, hese ess are only provided in Florida (oudoors) by he Florida Solar Energy Cener (FSEC). Wisconsin s fla plae collecor esing program will be done a Madison Area Technical College (MATC). The UW-Solar Energy Laboraory is assising MATC personnel in esablishing a suiable implemenaion of he ASHRAE es mehod. The UW furher inends o idenify alernaive es mehods ha can be done indoors or under condiions ha are more suiable o Wisconsin weaher, bu sill provide he informaion required by he ASHRAE es. Wha follows is he second repor of his aciviy.

2 Table of conens 1. Collecor ime consan es Thermal efficiency es Seady sae condiions Solar irradiance Minimum value Maximum variaion Fracion of diffuse radiaion Incidence angle Ambien emperaure Thermal efficiency es Wind speed Flow rae Inle emperaure Conclusion Inciden angle modifier es Tesing mehods Tesing procedure Conclusion Solar Energy Laboraory Page 2 11/30/2006

3 1. Collecor ime consan es The collecor ime consan is a measure of he hermal response ime of he collecor. Knowledge of he response ime is imporan for seing an appropriae ime period for he hermal efficiency es described below as well as for simulaions of collecor energy gain under real condiions. I is also useful for deermining an appropriae period o average and repor experimenal daa colleced during he es. In order o quanify a collecor s ime consan, a collecor ime consan es is performed as-defined in he ASHRAE es sandard. The collecor ime consan es is performed in wo seps as follows. Firs, he collecor is exposed o he sun and he collecor inle emperaure is adjused o he ambien emperaure. As soon as seady sae condiions have been achieved, he solar irradiance is abruply reduced o zero. Removing he solar irradiance can be done by moving he collecor o face norh or by shading he collecor wih an opaque shield. Wih removal of he irradiance, he collecor inle and oule emperaures are coninuously observed unil he difference beween he oule and inle emperaure decreases o 30% of is iniial value. Based on his es, he collecor ime consan is he ime, τ, needed for he emperaure difference beween he collecor oule and inle o decrease o a fracion of 1/e of is iniial value. The following equaion defines he calculaion of he ime consan. τ = f, e, f, i f, e, iniial f, i I is imporan o noe ha he collecor ime consan es requires appropriae conrols o mainain he collecor inle emperaure ( f, i )consan a he ambien emperaure hroughou he es. According o secion of ASHRAE , he collecor inle emperaure mus be adjused o wihin ±1 C (±1.8 F) of he ambien emperaure and conrolled o wihin ±0.05 C (±0.09 F) of he se value. The collecor fluid flow rae mus be mainained as described in Chaper 3.4 of his repor. The inciden solar flux mus be greaer han 790 W/m 2 (250 Bu/h-f 2 ). Wha exacly is mean by mainaining seady sae condiions is discussed in Secion 3 of his repor. (1) Solar Energy Laboraory Page 3 11/30/2006

4 2. Thermal efficiency es The hermal efficiency es was described in he Chaper Inroducion o inle emperaure disribuions in he las repor. While he measuremens required for he es and he analysis of he es daa are relaively simple, he es sandard requiremens concerning seady-sae condiions are demanding. A complee hermal efficiency ess requires 16 measuremens (called daa poins) as described in he las repor. The efficiency for one daa poin is calculaed from measuremens aken over a defined ime period, here called he daa period. Seady-sae condiions mus be mainained during he daa period. Only he daa from measuremens aken during his daa period are used o calculae he efficiency for each daa poin. However, seady-sae condiions mus also be mainained during a defined ime inerval prior called he pre-daa period. In secion 3.1 of he Sandard, he es period is defined as he ime over which seady sae condiions are mainained for a single measured efficiency poin. This means ha he es period as defined in he Sandard consiss of he pre-daa period and he daa period defined in his repor. The siuaion is visualized in Figure 1. In general: Pre-daa period Tes period Daa period Oudoor es 1 : 15 min MAX(5 min, τ) Oudoor + alazimuh moun: Indoor es: MAX(5 min, τ/2) MAX(5 min, τ) MAX(5 min, τ) Figure 1 Tes and predaa periods for he efficiency ess (τ = collecor ime consan 1 fixed es moun) The lenghs of he pre-daa period are defined in secion of he Sandard. The lenghs of he pre-daa periods depend on he kind of es apparaus used. For he oudoor ess wih a fixed es moun, he pre-daa period is 15 min; for oudoor ess wih an alazimuh (adjusable azimuh) moun (which allows o rack he sun) pre-daa period is reduced o 5 minues or half of he collecor ime consan, whichever is larger; and for he indoor es wih a solar irradiance simulaor, no pre-daa period is required. The lengh of he daa period is, independen of he es apparaus and is he greaer of a 5 minue inerval or he collecor ime consan. Pre-daa periods have a large effec on he ime required for a collecor es. In fac, he pre-daa period is responsible for he main par of ime consumed for a single oudoor fixed-moun es. Assuming a collecor ime consan of less han 5 minues (ypical for fla plae collecors), he daa period during which he efficiency measuremens are recorded would be 5 minues long while he pre-daa period is 15 minues. So 75% of he Solar Energy Laboraory Page 4 11/30/2006

5 minimum ime required for he es is used for he pre-daa period and any measuremens aken during his period do no direcly conribue o he archived es resuls. I is no clear if he long pre-daa period resuls in an increase in es qualiy.. A his poin, hree differen ime periods relevan for he efficiency ess are defined. During hese periods, seady-sae condiions mus be mainained. The following secion will deal wih hese seady-sae condiions. Solar Energy Laboraory Page 5 11/30/2006

6 3. Seady sae condiions The ASHRAE Sandard describes es mehods for seady-sae or quasi-seadysae hermal performance, ime response and angular response ess. The purpose of performing he ess under seady-sae condiions is o avoid ransien influences during he es ha could inflae he measured performance of a collecor. The Sandard rigorously defines he condiions for seady-sae condiions, as lised in Table 1. Table 1 Seady sae condiions of he ASHRAE sandard for oudoor ess Variable Maximum variaion Lower Upper In beween daa Wihin daa limi limi Reference periods period Toal irradiance - ±32 W/m normal o sun (±10 Bu/f2 h) W/m Fracion of diffuse % radiaion Inciden angle - ±2% modifier 2) Ambien emperaure range < 30 C (54 F) ±1..5 C ±2.7 F Wind m/s 4.5 m/s Flow rae same flow rae for all daa poins (0.02 kg/sm ) ±0.005 gpm 1) Inle emperaure - ±Max of (1.0 C/1.8 F, 2%) Inciden angle 3) - ± Symmery o solar noon 4) ) 2) 3) 4) A a given flow rae of 2.3 gpm his would mean a maximum variaion of % (!). Only for hermal efficiency ess Only for inciden angle modifier es Only for fixed-moun es apparaus: for every inle emperaure wo measuremens shall be aken before and wo afer solar noon, addiionally hose measuremens mus form symmeric pairs wih respec o solar noon. Clearly, several of he variables have exremely igh olerances on variabiliy. These olerances make he ess boh difficul and ime-consuming. A his poin, we are opimisic ha alernaive es mehodologies which relax he curren olerances are possible while sill preserving he inegriy of he collecor efficiency derived from he daa. If alernaive mehods can be idenified and validaed, he cos of collecor esing along wih he ime required may be significanly reduced. 3.1 Solar irradiance Minimum value Secion of ASHRAE 93 requires ha he average global solar irradiance on a surface normal o direc beam radiaion no less han 790 W/m 2 (250 Bu/f2-h). Solar Energy Laboraory Page 6 11/30/2006

7 The sandard does no specify wheher he average of he daa period or he complee es period (pre-daa and daa period) shall be used. Addiionally, if a fixed es moun is used, he inciden angle of direc beam radiaion is no necessary normal o he collecor plane. The pyranomeer measures he oal irradiance upon he collecor plane bu no necessarily normal o direc beam radiaion. If he Sandard requiremen described above were realized exacly, a second sun racking pyranomeer would be required o measure he oal normal direc beam radiaion or a calculaion mehod for he oal normal direc beam radiaion should be provided by he Sandard. The requiremen o measure efficiency a near-normal incidence condiions as defined in secion of he Sandard requires ha he collecor orienaion be adjused such ha he inciden angle modifier is wihin a range of ±2% of he normal value. This can, depending on he collecor angular response, allow inciden angles up o 40, as shown in Chaper of his repor Maximum variaion The maximum allowed variaion in solar irradiance upon he collecor plane is ±32 W/m 2 (±10 Bu/f 2 h). For some reason a his poin new ime inervals are defined in he Sandard. The maximum variaion shall no occur for duraions of 10 minues or wo ime consans, whichever is greaer, boh prior o and during he period when daa are aken. (ASHRAE , ). Figure 2 ries o relae he new ime inervals for seady-sae solar irradiance o he previously defined requiremens. Does he new required ime inerval increase he ime needed for a single es? For oudoor ess wih a fixed es moun, more ime is required only if he collecor ime consan is greaer han 7.5 min. As mos fla plae collecors have smaller ime consans he required ime is no increased. However, for he oudoor es wih an alazimuh moun he pre-daa period would a leas double in lengh, in he wors case (τ > 10 min) he lengh would be four imes he lengh defined above for he pre-daa period. I is no clear how he irradiance variaion relaed o a ime inerval wih a lengh of MAX(10 min,2τ) should be applied o a daa period (= period when daa are aken ) wih lengh MAX(5 min, τ). The Sandard needs o be clarified in his area Fracion of diffuse radiaion The Sandard requires ha he diffuse irradiance on he aperure plane be a maximum of 20% of he oal irradiance on he collecor aperure plane. The diffuse fracion can be calculaed by he following equaion (ASHRAE , eq. 8.19). G = G G cos( θ ) (2) d DN G is he oal irradiance, measured by he pyranomeer in he collecor plane, and G DN is he direc beam radiaion, measured by he sun-racking pyrheliomeer. The diffuse fracion shall have a value of less han 20% hroughou he es. Table 9.1 in ASHRAE requires reporing he diffuse fracion only a he beginning and he end of he daa period. Solar Energy Laboraory Page 7 11/30/2006

8 In general: Pre-daa period Daa period Oudoor es 1) : 15 min MAX(5 min, τ) Oudoor + varying azimuh moun: Variaion of solar irradiance: MAX(10 min,2τ) MAX(5 min, τ /2) MAX(5 min, τ) MAX(10 min,2τ) Figure 2 Variaion of solar irradiance, 1) fixed es moun Incidence angle The incidence angle, θ, is he angle beween he inciden direc beam radiaion and he normal o he collecor plane. ASHRAE defines he following incidence angle modifier-relaed requiremens: 8.3.3: Experimenal Deerminaion of Collecor Thermal Efficiency: For ess conduced o deermine he hermal efficiency a near-normal inciden condiions, he angle of incidence shall be in he range in which he inciden angle modifier varies no more han ±2% from he normal incidence value. For ess conduced o deermine he inciden angle modifier, he orienaion of he collecor shall be such ha he collecor is mainained wihin ±2.5 degrees of he angle of incidence for which he es is conduced, hroughou he es period. The definiion relaed o he incidence angle modifier ess refers o a cerain range of inciden angles (±2.5 ). This means ha for example he inciden angle modifier es for an inciden angle of 60 can be performed wih acual incidence angles beween 58 and 62. Furhermore his means ha he collecor orienaion mus be adjused, wih respec o he solar direc beam irradiance, o mee hese requiremens. The incidence angle modifier es is discussed in more deail in he nex secion of his repor. This incidence angle requiremen is no a problem for he acual es seup a MATC. The second definiion in he cied paragraph of he es sandard is relaed o he hermal efficiency ess. The mos imporan quesion is if he defined range of allowed incidence angle modifier values requires ha he collecor rack he sun during he efficiency ess. If so, manual adjusmens in collecor orienaion hroughou he ess would be required. The following analyses show ha solar racking is no required. For he following consideraions, a precise definiion of he possible es mouns is required. The differen kinds of es mouns are no defined in secion 3.1 of he ASHRAE Sandard. However an implici definiion can be found in he following ciaion from he Sandard : Number of Daa Poins. For he case wih a fixed-moun es apparaus, wo of he four daa poins shall be aken during he ime period preceding solar noon and he oher wo shall be aken in he period following solar noon, he specified periods being chosen so ha he daa poins represen imes symmerical o solar noon. This Solar Energy Laboraory Page 8 11/30/2006

9 requiremen is made so ha any ransien effecs ha may be presen will no bias he es resuls when hey are used for design purposes. The requiremen for obaining daa poins equally divided beween morning and afernoon is no mandaory when esed wih an alazimuh moun. An alazimuh moun can be used o move an insrumen along wo perpendicular axes of moion (verical movemen = aliude or il, horizonal = azimuh). So he alazimuh moun can rack he sun hroughou he day and mainain an inciden angle close o normal (0 ). This means he alazimuh moun can perform hermal efficiency ess during he whole day and comply wih he incidence angle requiremen. The fixed moun es apparaus as menioned in he cied paragraph mus be fixed in a leas one of he possible dimensions (il, azimuh). The es moun a MATC can be manually adjused in azimuh. So i is desirable o perform he es wih he es moun fixed facing souh as his reduces he effor. Wha does he requiremen of mainaining he angle of incidence in a range where he inciden angle modifier varies no more han ±2% mean for a fixed es moun? To answer his quesion, he inciden angle modifier curve for a single glass cover collecor given in he Sandard (ASHRAE , Figure 9) is evaluaed. Normal incidence is defined as an angle of incidence, θ, of zero. The normal incidence value of he inciden angle modifier (8.3.3, ASHRAE ) is he value of he inciden angle modifier a an incidence angle of zero. A his angle, he value of he inciden angle modifier is always uniy by definiion. According o secion (ASHRAE ), he hermal efficiency es is o be conduced a near-normal inciden condiions. The laer are defined as all angles of incidence for which he value of he inciden angle modifier varies no more han ±2% from is normal incidence value. As he normal incidence value is uniy and he inciden angle modifier is beween zero and uniy per definiion, he range of inciden angles is deermined by he value of 1 2% * 1 = 0.98 for he incidence angle modifier. For a single glass cover collecor given in he Sandard, a range of incidence angle modifiers beween 1 and 0.98 yields a corresponding range of allowed incidence angles from 0 o 41 as shown in he modified figure below. Solar Energy Laboraory Page 9 11/30/2006

10 0.98 = 1.0 * (100 2)% 41 Figure 3 Range of incidence angles for near-normal condiion, based on ASHRAE Figure 9 Using a fixed moun apparaus (fixed azimuh angle and slope of he collecor) he calculaed range of allowed inciden angles deermines a ime window in which he ess can be conduced during he day. However, he range of allowed incidence angles is sufficienly wide such ha he possibiliies for hermal efficiency ess a MATC are no affeced. 3.2 Ambien emperaure Thermal efficiency es The range of ambien emperaures of all daa periods shall be less han 30 C (54 F) (ASHRAE : ). This requiremen relaes differen daa poins of one complee es wih each oher. Wihin one es period, he es sandard requires o mainain he ambien emperaure wihin a variaion of ±1.5 C (2.7 F) during he predaa period. Alhough no menioned explicily in he sandard, he same requiremen should be applied for he daa period. 3.3 Wind speed The Sandard requires he wind speed lie beween 2.2 and 4.5 m/s (5 and 10 mph) (ASHRAE ). This requiremen applies o he es period and a MAX(10 min,2τ) inerval prior o he es period. The Sandard furher sipulaes ha some Solar Energy Laboraory Page 10 11/30/2006

11 collecors wih glass glazing may require a longer inerval of up o 20 minues or four ime consans. If aken lierally, his requiremen would mean ha ahead of every es period (which is defined by he Sandard as he ime over which quasi-seady-sae condiions are mainained, ASHRAE , 3.1) an addiional ime period wih he described wind condiions would be required. The siuaion is shown in he figure below. In general: MAX(10 min,2τ) Predaa period Daa Oudoor es 1) : MAX(10 min,2τ) 15 min Oudoor + alazimuh moun: MAX(10 min,2τ) Variaion of wind speed Figure 4 Variaion of wind speed, alernaive 1 1) fixed es moun This inerpreaion would furher increase he required pre-daa ime period. I is more likely ha here is an inconsisen use of he expression es period in he Sandard. If he requiremens for he wind speed are applied in he same way as hose for he solar irradiance as described in chaper of his repor, he requiremens for he wind speed mus be me prior o he daa period insead of he whole es period. This alernaive inerpreaion is shown in Figure 5. In general: Predaa period Daa period Oudoor es 1) : 15 min MAX(5 min, τ) Oudoor + alazimuh moun: MAX(5 min, τ/2) MAX(5 min, τ) Variaion of wind speed: MAX(10 min,2τ MAX(5 min, τ) Figure 5 Variaion of wind speed, alernaive 2 1) fixed es moun Now, he ime inerval wih consan wind speed is direcly prior o he daa period. This inerpreaion should be used a MATC. 3.4 Flow rae The hea ransfer fluid flow rae remains fixed for all daa poins. The recommended mass flow rae per aperure area for a liquid fluid is 0.02 kg/s-m 2 (14.7 lb m /hr-f 2 ). An excepion is made for collecors which are designed for special flow raes. These collecors should operae wih heir design flow raes (ASHRAE , ). The flow rae shall be mainained consan a he recommended flow rae wihin ±0.005 gpm ( lier/sec). (ASHRAE , ). Solar Energy Laboraory Page 11 11/30/2006

12 For he collecor acually esed a MATC, he recommended flow rae is 3.2 gpm. A difference of gpm requires mainaining he operaing flow rae o wihin % of is nominal value! This requiremen is very resricive when compared o he inle emperaure which is allowed o vary wihin ±1.8 F or ±2%, whichever is larger. I seems ha he Sandard should prescribe he flow rae accuracy as a percenage of he nominal flow rae, raher han an absolue value. 3.5 Inle emperaure The Sandard requires ha he inle emperaure be mainained consan (wihin ±1 C [±1.8 F], ASHRAE , and ) during he pre-daa and daa periods. However, in secion 7.1.7, he sandard requires he inle emperaure o be conrolled wihin ±0.05 C (±0.09 F) during he complee es period. Why is a device required in he es seup which can conrol he inle emperaure wihin ±0.09 F, if he allowed inle emperaure variaion for seady sae condiions is ±Max of (1.8 F, 2%), which is in he lowes case 20 imes greaer han he conrol uni could provide? Again, here seems o be inconsisencies in he variaion in conrolled and unconrolled variable relaed o collecor esing. The variables ha have exremely narrow olerances significanly complicae he daa collecion process for measuring collecor performance. 3.6 Conclusion The seady sae condiions defined in he Sandard are very challenging and perhaps more resricive han originally inended. A resul of hese requiremens could be ha ess in Wisconsin can be performed in only very few days of he year. This issue will be evaluaed in more deail by he SEL. Solar Energy Laboraory Page 12 11/30/2006

13 4. Inciden angle modifier es The hermal efficiency ess are performed a near normal inciden angles of he solar beam radiaion upon he collecor plane. However, he hermal efficiency of a collecor depends on he angle of incidence of he solar radiaion. The inciden angle modifier K τα is used o describe his dependence, which can be imporan for simulaing he collecor behavior under some condiions. Figure 6 Incidence angle modifier (ASHRAE sandard , Figure 9) Figure 7 Incidence angle modifier (ASHRAE sandard , Figure 10) The resuls of he hermal efficiency ess look qualiaively like shown in Figure 8. The efficiency has been measured a four differen inle emperaures bu a abou he same inciden angle (close o normal incidence) for all daa poins (compare o Figure 6 in repor 1). Solar Energy Laboraory Page 13 11/30/2006

14 η η θ = 0 (normal incidence) θ = 30 θ = 45 θ = 60 0 f,i = a f, i G a 0 f, i = a f, i G a Figure 8 Resuls of he hermal efficiency es (all a normal inciden angle) Figure 9 Thermal efficiencies a differen inciden angles The purpose of he incidence angle modifier es is o deermine he efficiency of he collecor a a fixed inle emperaure and differen inciden angles. The Sandard prescribes he collecor inle emperaure be mainained a ambien emperaure. For he example shown in Figure 8 his would mean, ha he efficiency ess have o be repeaed for ha poin of he x-axis where he collecor inle emperaure f,i equals he ambien emperaure a (highlighed wih a dashed line circle and box in Figure 8). Performing ess a hese condiions and varying he incidence angles lead o resuls as shown in Figure 9. For a ypical fla plae collecor, he hermal efficiency decreases as he incidence angle increases. Figure 10 shows a plo of efficiency versus incidence angle. The incidence angle modifier is he raio of he efficiency o he efficiency a he same operaing condiions bu wih normal incidence radiaion: η( θ ) K τα ( θ ) = (3) η The incidence angle modifier is a funcion of angle, bu in he following secions, he (θ) behind he symbol K τα is no shown for breviy. The plo of he inciden angle modifier defined by equaion (3) is shown in Figure 11. I has he same shape as he efficiency curve in Figure 10. Obviously he incidence angle modifier is no a linear funcion of he inciden angle. normal Solar Energy Laboraory Page 14 11/30/2006

15 η f,i = a K τα f, i = a θ [ ] θ [ ] Figure 10 Thermal efficiency as funcion of incidence angle Figure 11 Incidence angle modifier as funcion of incidence The Sandard assumes, ha for non-concenraing collecors, he following equaion (4) can be used o describe he behavior of he inciden angle modifier depending on he inciden angle θ (ASHRAE sandard , eq. (8.18)). 1 Kτα = 1 b o 1 cos( θ ) (4) To reach a linear relaion, he erm in parenheses is named o 1 x = 1 ( 5) cos( θ ) and he equaion for he incidence angle modifier hen simplifies o K = τα b x. 1 o The daa poins shown in Figure 11 are now ploed in Figure 12 using equaion (6). The values of x are shown in Table 2. Wih he mehod of he leas-squares fi, a sraigh line is deermined as shown in Figure 13. The slope of his line is he coefficien, b 0, from equaions (4) and (6). The coefficien, b 0, is called he incidence angle modifier coefficien and generally a posiive number. As soon as b 0 is deermined, he inciden angle modifier for all angles can be calculaed by equaion (4). (6) Table 2 x-axis values for cerain inciden angles θ [ ] x [-] Solar Energy Laboraory Page 15 11/30/2006

16 K τα f,i = a K τα f, i = a slope = b 0 x(0) x(30) x(45) x(60) x x(0) x(30) x(45) x(60) x Figure 12 Incidence angle modifier as funcion of x = Figure 13 Deermining he incidence angle modifier coefficien Resuls of such ess are shown in Figure 6 and Figure 7 for differen kinds of collecors. For some reason he Sandard uses K ατ (wih inerchanged indices) as he symbol for he inciden angle modifier. As he subscrip is based on he ransmiance-absorpance produc τα, he symbol K τα will be used in his repor. 4.1 Tesing mehods The ASHRAE Sandard describes wo mehods for measuring he collecor inciden angle modifier (ASHRAE : ). As described above, he inciden angle modifier is no measured direcly bu is derived from a series of hermal efficiency measuremens. The procedure for measuring he hermal efficiency is described in secion of he Sandard. Boh mehods for measuring he collecor inciden angle modifier require mainaining he inle emperaure a ambien emperaure. The measuremens for he differen angles are recommended o be aken on he same day. Mehod 1 can be used for indoor or oudoor esing wih a movable es rack (collecor azimuh angle can be adjused). In sum, four hermal efficiency measuremens are required, a inciden angles of 0, 30, 45, and 60 degrees. Mehod 2 can be used for oudoor ess wih a es rack which can be adjused in il bu no in azimuh angle. The inciden angle is adjused o 0, 30, 45, and 60 degrees by varying he il angle of he collecor. For every inciden angle wo measuremens symmeric o solar noon are necessary. The average efficiency values of he symmeric measuremens shall be used for he angle modifier calculaions. The orienaion of es rack used a MATC can be adjused wih respec o he norh-souh line (azimuh angle), bu no in il. As a resul, only mehod 1 can be used for he inciden angle modifier es. The procedure is described in he following secion. 4.2 Tesing procedure The movable rack allows inciden angle modifier ess o be conduced whenever he condiions for hermal efficiency ess are me. A hermal efficiency es as described in secion of he Sandard mus be performed a incidence angles of 0, 30, 45, and 60 degree and wih a collecor inle emperaure equal o ambien emperaure. The required azimuh angle mus be calculaed before he ess are iniiaed. The proper azimuh angle Solar Energy Laboraory Page 16 11/30/2006

17 for a specified incidence angle depends on he day of year, ime of day, locaion of he es faciliy, he collecor il angle and he desired incidence angle. The siuaion is shown in Figure 14. N W E Posiive values Negaive values Collecor azimuh angle S Sun Figure 14 Collecor orienaion for inciden angle modifier ess The following se of equaions allows calculaing he azimuh angle based on his informaion. All equaions are aken from Duffie and Beckman (2006). ( 1) ( ) [ deg] B = n / ( ) ( ) ( ) ( ) Cos B sin B E = [ min] Cos 2 B sin 2 B ( [ ] ( s loc ) ) solime sandime = 4 min/deg L L + E [min] (9) [ ] ( solime ) ω= 15 deg/h 12 h (10) ( ) ( ) ( ) ( ) ( ) ( ) ( ( ) ( ) ( ) ( ) ( )) δ= Cos B sin B Cos 2 B sin 2 B Cos 3 B sin 3 B (7) (8) (11) θ z = arccos cos φ cos δ cos ω+ sin φ sin δ (12) ( δ ) ( φ ) ( β) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) sin sin cos sin δ cos φ sin β cos γ θ= arccos + cos δ cos φ cos β cos ω + cos δ sin φ sin β cos γ cos ω + cos δ sin β sin γ sin ω (13) Solar Energy Laboraory Page 17 11/30/2006

18 ( θz ) ( φ) ( δ) sin( θ ) cos ( φ) cos sin sin γ S = Sign ( ω) ABS arccos z γ A (14) = ( γ γ ) (15) S The parameers for hese equaions are lised below. Table 3 Parameer for collecor orienaion during K τα es Symbol Descripion Value for MATC es faciliy N Day of year (1 365) The es day is he n h day of he year. Tes dae n Solime Solar ime (noon is defined by he zenih of he sun) sandime Sandard ime of local ime zone Use he ime in he middle of he daa period. During dayligh saving ime subrac 1 h from local clock ime. L Sandard meridian for local ime zone 90.0 s L loc Longiude of he locaion 89.4 Ω Δ Φ θ z Β Θ Γ γ S Γ Hour angle Declinaion of he sun Laiude Zenih angle, angle beween beam radiaion and horizonal plane Slope or il, angle beween collecor and horizonal Incidence angle, angle beween beam radiaion and collecor plane Collecor azimuh angle, deviaion from norhsouh orienaion, eas negaive, wes posiive. Solar azimuh angle, deviaion from norhsouh orienaion, eas negaive, wes posiive. Alernaive collecor azimuh angle, deviaion from norh-souh orienaion, eas negaive, wes posiive , 30, 45, 60 For he given purpose he shaded cells in he hird column of he able are calculaed, all o her daa mus be provided o deermine a collecor azimuh angle for a collecor inciden angle modifier es. The following example shows how a complee inciden angle modifier es could be performed a Nov. 22 for he parameers given in Table 4. The imes are chosen arbirarily, excep for he zero degree es (Tes 2). Solar Energy Laboraory Page 18 11/30/2006

19 Tes number Table 4 Example collecor orienaion Solar ime Sandard ime Inciden angle Solar azimuh Collecor azimuh Al. collecor azimuh Tes 1 11:30 11: Tes 2 12:00 11:44 (0) 1) Tes 3 12:30 12: Tes 4 13:00 12: ) Tes a 0 incidence angle no possible wih a fixed collecor il of 50.5 a Nov. 22 (minimum 13 ) A his day, he z enih angle reaches is minimum (a solar noon) a abou 63. This means ha a collecor wih a il fixed o 50.5 can no be o rienaed in a way ha he incide n angle reaches 0. The siuaion is shown in Figu re 15. In such a siuaion he collecor should be orienaed facing he sun a solar noon for he es a 0 inciden angle. For his exampl e he achieved inciden angle a solar noon is (min. zenih angle) Solar beam radiaion 90 Collecor 12.5 (incidence angle) (collecor slope) Figure 15 Inciden angle and zenih angle 4.3 Conclusion As soon as he required azimuh angles for he four incidence angle modifier ess are calculaed, a normal hermal efficiency es mus be performed. The proper azimuh angles will be provided by a se of ables or a program. All incidence angle modifier ess mus be performed a ambien emperaure. If he ambien emperaure is below 0 C (32 C), hese ess canno be performed wih waer as hea ransfer fluid. 1 ANSI/ASHRAE Sandard , Mehods of Tesing o Deermine he Thermal Performance of Solar collecors. ISSN , ASHRAE, Inc., 2003, 1791 Tullie Circle, Ne, Alana, GA30329 Solar Energy Laboraory Page 19 11/30/2006