Methodology for identifying parameters for the TRNSYS model Type 210 -wood pellet stoves and boilers

Transcription

1 Methodology for identifying paraeters for the TRSYS odel Type 1 -wood pellet stoves and boilers Toas Persson, Frank Fiedler and Svante ordlander Version ISS ISR DU-SERC SE April 6

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3 Acknowledgeents This work has been financed by Foras, STEM, ordic Energy Research and Högskolan Dalarna. We also would like to thank the different copanies for the opportunity to easure their boilers and stoves to be able to verify the odel towards real products. Abstract This report describes a ethod how to perfor easureents on boilers and stoves and how to identify paraeters fro the easureents for the boiler/stove-odel TRSYS Type 1. The odel can be used for detailed annual syste siulations using TRSYS. Experience fro easureents on three different pellet stoves and four boilers were used to develop this ethodology. Recoendations for the setup of easureents are given and the required cobustion theory for the data evaluation and data preparation are given. The data evaluation showed that the uncertainties are quite large for the easured flue gas flow rate and for boilers and stoves with high fraction of energy going to the water jacket also the calculated heat rate to the roo ay have large uncertainties. A ethodology for the paraeter identification process and identified paraeters for two different stoves and three boilers are given. Finally the identified odels are copared with easured data showing that the odel generally agreed well with easured data during both stationary and dynaic conditions. Keywords: Wood pellets; boiler; stove; cobustion calculations; TRSYS; siulation odel, easureents; validation. 1

4 Contents 1 ITRODUCTIO... 4 METHOD THE SIMULATIO MODEL MEASUREMETS Set up of the easureents COMBUSTIO CALCULATIOS Cobustion power Cheical coposition for air Cheical copositions of soft wood pellet Cobustion reactions Methodology for cobustion calculations Calculation of air factor fro easureents of CO Calculation of air factor fro easureents of O Heat rate to the water circuit Heat rate to the flue gasses Density of the flue gas Density of air Heat capacity of the flue gas Heat capacity of air Heat rate to the abient and full energy balance of the boiler Efficiency of boilers and stoves Eission calculations Conversion to other units PARAMETER IDETIFICATIO Procedure Paraeters for the Theria Bionet boiler Minial and axial cobustion power UA value identification Theral asses Air factor CO factor CO eission for start/stop Duration of the two start phases Fan operation and ass flow after stop Leakage flow rate Electricity consuption... 35

5 6.3 Paraeters for the Rebus boiler Minial and axial cobustion power UA value identification Theral asses Air factor CO factor CO eission for start/stop Duration of the two start phases Fan operation and ass flow after stop Leakage flow rate Electricity consuption Characteristics of the odels VERIFICATIO AD VALIDATIO OMECLATURE REFERECES APPEDIX 1. Identified paraeters for the boilers and stoves

6 1 Introduction This report describes a ethod how to perfor easureents on boilers and stoves and how to identify paraeters fro the easureents for the boiler/stove-odel Type 1 (ordlander, 3). The odel can be used for detailed annual syste siulations using TRSYS (Klein et al., ). Method This work is based on easureents on three pellet stoves; one traditional with only convection/radiation to the roo and two water antled (jacketed) stoves and four different boilers. One boiler with an integrated solar store of.63 3 and heat exchangers for hot water preparation, one boiler with integrated DHW (hot water) preparation and a relatively large volue and two boilers without DHW preparation and a saller water volue. Paraeters were identified for three boilers and two stoves. In addition preliinary paraeters were identified for the boiler with integrated hot water preparation. Fro the experiences of the easureents and paraeter identification process this ethodology was developed. It contains detailed inforation about the setup of the easureents and necessary easureent sequences, the data evaluation, necessary cobustion calculations and the paraeter identification process and the verification and validation. 3 The siulation odel The siulation odel is described by ordlander (3), so only a general description is given here. The odel is illustrated in Fig Fuel and cobustion air enter the stove and cobust to for a hot flue gas. Energy is transferred fro the gas to a first theral ass, 1, representing the part of the stove that transfers heat to the abient air. Having passed 1 the gas has tepera-ture Tg1 and heat is transferred to, which represents the gas-liquid heat exchanger in the stove. Finally the gas leaves the stove at teperature Tg. Heat transfer between the roo and 1 is governed by the coefficient UAa and heat transfer between and the liquid flow strea is governed by UAliq. Heat transfer between 1 and is governed by UA, etc. Abient air Liquid UA a UA liq UA 1 T 1 T Fuel UA g1 Hot gas T g T g1 UA g T g Air Solid arrow = ass flow Dashed arrow = heat transfer Fig Scheatic structure of the odel Type 1 (ordlander, 3). 4

7 4 Measureents 4.1 Set up of the easureents Recoended set up of the easureent equipent and the sensors are illustrated in Fig The weight of the pellets store is continuously easured by WS1 and if the pellets store is integrated in the boiler/burner, the whole unit can be placed on the scale as in Fig Flexible connections of silicone for the chiney ust then be used to ensure that teperature expansion don't affect the weight easureents. Also the flexible pipes and cables ust be carefully connected not to influence the scale due to teperature or pressure. The value of the scale ust be corrected for the density difference due to the varying teperature of the water volue in the boiler. The gas analyser GA1 is easuring the volue coponents on dry gas, as a cooling unit is built in the achine to condensate the water in the flue gas. The pressure eter PS1 easure the dynaic pressure in the chiney fro the Prandtl tube. Water flow rate through the boiler is easured by a flow sensor VF1 and the inlet and outlet teperatures are easured as close as possible to the boiler/stove. A coplete list of the different variables that should be easured is listed in Table 4.1. The heat loss easureents at no cobustion is perfored by circulating the water through the boiler and the electric heater ELAUX and easure the electricity consuption to the heater and the pup. The heat losses for the heating circuit is also without the boiler connected in the circuit. TS5 PS1 GA1 Cooling Load or cooled buffer store CV1 ELAUX TS6 TS7 Wood pellets store TS9 TS3 TS8 TS4 Wood pellet boiler/stove TS TS1 TS1 P1 VFS1 WS1 Fig Scheatic of the test apparatus for the boilers and stoves. 5

8 Table 4.1 The different paraeters that are easured during the tests of boilers and stoves. VFS1 Flow rate through the boiler 3 /s TS1 Water inlet teperature to boiler/stove C TS Water outlet teperature fro boiler/stove C TS3 Boiler/stove water teperature C TS4 Flue gas teperature at outlet of boiler/stove C TS5 Flue gas teperature at position of flow sensor C TS6, TS7 Roo air teperature in different heights C TS8 Teperature of cobustion air C TS9 Surface teperature of hot surfaces on stove/boiler C TS1 Teperature of hot air outlet of stove C GA1 Oxygen concentration in flue gas % GA1 Carbon dioxide concentration in flue gas % GA1 Carbon onoxide concentration in flue gas PPM GA1 O x concentration in flue gas PPM PS1 Dynaic pressure in chiney Pa WS1 Weight of pellet store or boiler/stove (integrated pellets store) kg - Voltage to the screw otor or nuber of rotations V, rp - Voltage to the fan otor or nuber of rotations V, rp 6

9 5 Cobustion calculations The paraeter identification process for Type 1 requires input data which can be taken directly fro the easureent or need to be calculated fro the easureent data. The following input data are necessary: 1. The axial cobustion power of the boiler/stove. The heating value of the fuel 3. The boiler inlet teperature 4. The teperature of the cobustion air 5. The air factor labda 6. The air teperature in the boiler roo 7. The liquid ass flow through the boiler 8. The cobustion (fuel) power 9. The heat rate to the liquid 1. And the heat rate to the flue gas The values need to be deterined for steady state conditions and for several sequences over the whole cobustion range of the boiler/stove. The following chapter describe how to obtain the values, 5, 8, 9 and 1. Especially the heat rate to the flue gas requires extensive calculations to deterine the flue gas coposition and flue gas rate. 5.1 Cobustion power The cobustion power is calculated fro the weight easureents and the lower heating value of the pellet. To iniize the fluctuations the pellet consuption were soothed. Q LHW cob pell Equ. 5.1 Where LHW is the lower heating value of the pellet and pell is the ass flow rate of consued pellet. The lower heating value should be defined by a laboratory for the particular pellet that is used. The pellet should be stored in a tight container or plastic bag until it is used, so that the huidity of the pellet does not change. 5. Cheical coposition for air Wester () gives the olar coposition of dry air in to Table 5.1. The values in Table 5.1 show that the nuber of oles of, is 3.77 ties the aount of O and the nuber of oles of air is 4,773 ties the aount of O assuing that the olar concentration and the volue concentration is the sae. The olecular weight of the air ixture can be calculated fro MW ix MW n i1 i i Equ. 5. 7

10 and is kg/kol with the values of Table 5.1. The nuber of oles of a substance can be calculated fro i i MW i Equ. 5.3 The water content of the air is defined as kg of water per kg of dry air (Alvarez, 199): x H O,air H O air,dry Equ. 5.4 Table 5.1 Molar fraction and olecular weight of the copositions in dry air. The values are taken fro Wester () and are given as volue fraction, however the volue fraction and olar fraction can be considered as equal if the gasses are assued to behave as ideal gasses. For the pressures and teperatures related to the equations here only CO cannot be considered as an ideal gas (Wester, ), however, the ole fraction of CO is so low that the influence on the final result can be neglected. Mole fraction in dry air χ Mole fraction copared to O MW χ MW Mass fraction Y [kol/kol] [kol/kol] [kg/kol] [kg/kol] [kg/kg] itrogen Oxygen O Argon Ar Carbon dioxide CO Total Cheical copositions of soft wood pellet The wood pellet that was used during the easureents was sent to a laboratory to deterine the cheical coposition of the pellet and the heating value. The values in Table 5. are an exaple to describe a ethod for the cobustion calculations used for paraetric identification of wood pellet boilers and pellet stoves. The oisture content of the pellet was between 5.8 and 6.% (6.% for the pellet directly fro the package). The oisture content was defined per kg of oisture pellet. The LHW was defined to be MJ/kg for the pellet with 5.8% oisture content and MJ/kg for the pellet with 6.% oisture content. is given per kg of huid wood pellet, thus the follow- As the oisture content of the fuel ing correlation is valid. H O, fuel H O, fuel Y H O, fuel fuel,h Equ. 5.5 or H O, fuel Y H O, fuel fuel,dry H O, fuel Equ

11 Solving for H O, fuel gives the following expression Y 1 Y H O, fuel H O, fuel H O, fuel fuel,dry Equ. 5.7 Table 5. The analysed copositions (ass fraction) of the dry wood pellet fro (reference). Y [%] Carbon C 51.3 Hydrogen H 6. itrogen <.1 Oxygen O 4. Ashes Cobustion reactions For a fuel containing C (Carbon) H (Hydrogen), (itrogen), O (Oxygen) and A, (ashes) the cheical reactions for the cobustion (oxidation) can be written C O CO 1 H O H O Equ. 5.8 Equ. 5.9 Here we assue that no CO Carbon onoxide or O x is produced. Usually the concentration of O x and CO in the flue ga is far below 1 pp (1%) for wod pellet boilers (Äfab/Konsuentverket, 5). so the influence on the energy efficiency is sall. Fro the cheical reactions in Equ. 5.8 and Equ. 5.9 an expression for the required aount of oxygen for stoichioetric cobustion can be derived. The oxygen in the fuel is used during the cobustion and the oxygen deand is therefore reduced by the oxygen content in the fuel. Stoichioetric cobustion is coplete cobustion with iniu required aount of oxygen. The ashes are not taking part in the reactions C, fuel H, fuel O, fuel O stoic MWC MWH MW O Equ. 5.1 Fro Table 5.1 it can be calculated that the total aount (nuber of oles) of air will be ties the aount of oxygen for stoichioetric cobustion. air,stoic C, MW fuel C H, MW fuel H MW O, fuel O Equ The nuber of oles of the different copositions in the cobustion air can also be calculated separately in relation to the stoichioetric O deand as 9

12 CO,stoic,air. 14 O,stoic Equ. 5.1,stoic,air O,stoic Equ Ar,stoic,air. 444 O,stoic Equ where the coefficients coe fro Table 5.1. air,stoic O,stoic CO,stoic,air,stoic,air Ar,stoic,air Equ The total aount of dry flue gasses is calculated fro the su of CO, and Ar in the flue gases. flue,stoic CO,stoic,stoic Ar,stoic Equ The nuber of oles of in the flue gas at stoichioetric cobustion as:, stoic can be assued, stoic, stoic, air, fuel Equ The olar concentration of species i in a ixture of species can be calculated by i i tot Equ and ass fractions can be calculated by Y i i tot i MW MW ix i Equ which is a general for of Equ The air factor λ is defined as the rate between real dry air consuption and the theoretical aount of dry air required to achieve stoichioetric cobustion: air air,stoic Equ. 5. This relation can be used to calculate the aount of excess air in the cobustion, which is the extra air that is not used in the cobustion. The dry aount of excess air can be calculated air,exc 1 air air,stoic air, stoic Equ. 5.1 Fro the knowledge of the consued wood pellet, the aount of stoichioetric air and excess air the total ass of flue gas can be calculated 1

13 g fuel H O, fuel aches air,stoic H O,air,stoic air,exc H O,air,exc Equ. 5. The total ass can also be calculated fro the coponents in the flue gas as g H MW MW MW MW MW O H O CO CO Ar Ar O O Equ. 5.3 Fro the cheical reactions above and fro the stoichioetric air consuption O stoic the nuber of oles of the carbon dioxide at stoichioetric conditions can be calculated. The non-burning coponents in the fuel: nitrogen and ashes is assued to have negligible ipact on the flue gases. Also the relatively low production of CO and O x is ignored (Äfab/Konsuentverket, 5). CO,stoic MW C, fuel C CO,air O,air O,stoic Equ. 5.4 Where CO air is the ole fraction of CO in the dry air and O air is the ole fraction of O in the dry air. The first ter in Equ. 5.4 is the aount of carbon dioxide that is produced fro the carbon in the fuel according to Equ The second ter is the aount of carbon dioxide in the air (identical with Equ. 5.1) that is used for stoichioetric cobustion. It relates the concentration of carbon dioxide in the air to the concentration of oxygen in the air and by ultiplying this ratio with the oxygen consuption at stoichioetric conditions, the aount of carbon dioxide in the air is calculated. The concentration of CO at real cobustion also includes the aount of CO in the extra air, though this is alost zero (Table 5.1) and therefore alost the sae as the concentration of CO at stoichioetric cobustion. CO MW C, fuel C CO,air O,air O stoic air,exc CO,air CO,stoic Equ. 5.5 The third ter is the aount of carbon dioxide that is coing fro the extra aount of air and because of that the concentration of carbon dioxide in air is nearly zero, CO CO, stoic., fuel,air O,stoic air,exc MW O,air,air Equ. 5.6 Ar Ar,air O air O stoic air,exc Ar,air Equ. 5.7 O air,exc O,air Equ. 5.8 The water in the flue gasses coes fro the oxidation of hydrogen in the fuel, fro the huidity in the fuel and fro the huidity in the cobustion air and can be expressed. 11

14 H O MW H, MW H, fuel H fuel H MW H MW H O, fuel H O O, fuel H O x x H O,air H O,air MW air H O MW air,stoic MW H O air MW air x H O,air MW air,exc H O MW air Equ. 5.9 The air/fuel ratio at stoichioetric cobustion conditions is a paraeter required in the TRSYS odel of the boiler and it can be calculated as A f air,stoic fuel H O,air,stoic H O, fuel Equ Methodology for cobustion calculations The ain reason for perforing the cobustion calculations is to evaluate the olar fractions andass fractions of the different copositions in the flue gas and in that way be able to calculate the ass flow rate of the flue gas as well as the heat capacity and the density of the flue gas. It will be seen that the ajor paraeters affecting the properties is the teperature and the air factor. The oisture content of the wood pellet and the oisture content of the air are considered to be constant. An exaple of a cobustion calculation perfored in a spread sheet is suarized in Table 5.3. The calculation is perfored for 1 kg of dry wood pellet. The ass fractions of the different copositions in the dry wood pellet fro Table 5. is given in C3 to C7, and the olar weights of the species are given in B3 to B6. The nuber of oles of the different species are calculated in D3 to D6 using Equ The nuber of oles of O required to cobust the fuel is then calculated in E8 by Equ. 5.1, which is a su of the values in E3 to E6. Finally the nuber of oles of H O, CO and fro the fuel and the oxygen is calculated in F4, G3 and H5 respectively. The fuel oisture ratio is given in C9 and the additional oisture content for 1 kg dry fuel is calculated in C1 using Equ The olecule weight of water is given in B1 and the nuber of oles of water is calculated in D1 by Equ The nuber of oles of CO, and Ar and in the air for stoichioetric cobustion is calculated in G1, H1 and I1, by Equ. 5.1, Equ and Equ The total nuber of oles of, Ar and CO is then suarized in E1 and the stoichioetric dry air deand in E13 is calculated by suing the nuber of oles of oxygen in E8 and the nuber of oles of, Ar and CO in E1 using Equ The ass of the stoichioetric air deand is calculated in E14 using Equ The olecule weight of the air is calculated in Table 5.1. The air oisture ratio is given in C15. The nuber of kg of huidity in the air is calculated in E16 by Equ. 5.4 and the nuber of oles of huidity is calculated in E17 by Equ The value of E17 is also inserted in F17. The Stoichioetric huid air deand in E18 is calculated in E18 by suing upp the stoichioetric dry air deand in E13 with the Huidity in the air in E17. The total aount of CO, and Ar in the flue gas is sued upp in G19, H19 and I19 (full expression for CO is shown in Equ. 5.4). And the total aount of stoichioetric dry flue gas is calculated in E19 by using Equ (suing G19, H19 and I19). Finally the olar concentration of CO, and 1

15 Ar in the dry flue gas at stoichioetric conditions can be calculated in G, H and I by using Equ On line 1 the nuber of oles of huidity in the air and the huidity produced at the cobustion is added, but not the huidity in the fuel. Table 5.3 Calculation of olar concentrations and ass concentrations of the copositions in the flue gas both for dry flue gas at stoichioetric cobustion and real cobustion with huidity in fuel and air. Explanations of the calculation ethod are given in section 5.5. A B C D E F G H I J K 1 Äne MW O Flue gas (kol) (kg/kol) (kg) (kol) (kol) H O CO Ar O 3 C H O Aches.5 8 Total dry= 1. kg Fuel oisture ratio=.59 kg/kg total 1 Moisture *** 11 Totalt fuel= 1.67 kg 1,Ar och CO i luft =3.773*O = kol 13 air,stoic =Stochioetric dry air=.143 kol 14 Stochioetric dry air= kg 15 Air oisture ratio=.4 kg/kg dry 16 Huidity in air=.483 kg 17 Huidity in air= kol 18 Stochioetric huid air deand=.157 kol 19 flue,stoic = stochioetric dry flue gas= kol Concentration in dry gas, stochioetric= kol/kol 1 stochioetric flue gas, dry fuel, huid air= kol air factor= 3. 3 Dry excess air= kol 4 Dry excess air= kg 5 Huidity in excess air=.4966 kg 6 Huidity in excess air= kol 7 Aount of huid excess air= kol 8 Total dry flue gases= kol 9 Huidity fro fuel=.348 kol 3 Total huid flue gases= kol 31 Aount of flue gas= kg Molar concentration [kol/kol] 3 Molar concentration in dry gas== kol/kol 33 Molar concentration in huid gas== kol/kol 34 Mass concentration Y [kg/kg] 35 MW= kg/kol 36 MW= kg/kol 37 Mass concentration in huid gas=y= kg/kg 38 Air/fuel ratio= kg huid air per kg huid fuel 13

16 In C the air factor is given and the aount of dry excess air is calculated in E3 using Equ The aount of the different coponents in this air is calculated in G3 to J3 using Equ The ole fractions of the different coponents in air are given in Table 5.1. The nuber of kg of excess air is calculated in E4 using Equ The nuber of kg of huidity in the excess air is calculated in E5 using Equ. 5.4 and the nuber of oles of huidity in the excess air is calculated in E6 using Equ The value of E6 is also inserted in F6. The aount of huid excess air is calculated in E7 by suing up the dry excess air in E3 with the Huidity in the excess air in E6. The total aount of the copositions in the flue gas except fro the water is sued up in line 8 (Equ. 5.6, Equ. 5.7 and Equ. 5.8 give give the whole calculation procedure. The nuber of oles of huidity in the fuel calculated in D1 is now inserted in F9 and the total aount of huid flue gasses are sued up in line 3. The water in the flue gas now coes fro the cobustion reactions, fro the huidity in the fuel, fro the huidity in the stoichioetric air deand and fro the huidity in the excess air and can directly be calculated using Equ In line 3 the olar concentrations of the coponents in the dry flue gas are calculated using Equ In line 33 the olar concentrations of the coponents in the huid flue gas are calculated using Equ In line 35 the olecule weight of the different coponents in the flue gas are given and the ass fractions are ultiplied with the olecular weights in line 36. The olecular weight of the ixture is calculated in E36 using Equ. 5.. The ass fractions of the coponents are then calculated in line 37 using Equ The theoretical air/fuel ratio at stoichioetric cobustion is a paraeter in the TRSYS odel and calculated in line 37 using Equ Finally also the total aount of flue gas per kg fuel can be calculated in C31 using Equ. 5.3 or Equ. 5. by suing the values in C11, E14, E16, E4 and E5 and by subtracting the aount of ashes in C Calculation of air factor fro easureents of CO Most often the eission easureents are on the concentration for dry gasses, thus there is a dehuidifier in the instruent. The following derivation is for easureents of olar concentration of CO on dry gasses. The nuber of oles of CO in the dry flue gas can be calculated fro CO CO flue Equ Where CO is the olar concentration of CO in the dry flue gas and flue is the total nuber of oles of dry flue gas. For the stoichioetric case the nuber of oles of CO in the flue gas is the sae as for real cobustion (assuing that the concentration of CO in air = %) CO,stoic CO CO,stoic flue,stoic Equ. 5.3 The total aount of dry flue gas is the su of the aount of dry flue gas at stoichioetric cobustion and the aount of the dry extra air (λ-1) that is used and it can be expressed flue 1 flue,stoic air, stoic Equ

17 Where flue,stoic is the nuber of oles of dry flue gas per kg of dry fuel at stoichioetric cobustion. Cobining Equ. 5.31, Equ. 5.3 and Equ to express the nuber of oles of CO gives the following expression 1 CO CO,stoic flue,stoic CO flue,stoic Solving for λ gives air,stoic Equ flue,stoic CO,stoic 1 1 air,stoic CO Equ If flue,stoic air,stoic, the following siplification is possible CO CO,stoic Equ The value of CO, stoic can be calculated fro the knowledge of the copositions of the different substances in the wood pellet and in the air and have been calculated to.163 in Table 5.3. The value of flue,stoic is.115 and air,stoic is.143 according to Table Calculation of air factor fro easureents of O The air factor can also be calculated fro the easured concentration of O in the exhaust gasses. The following is a derivation for easureents on dry gasses. Assuing that there is.95% O in the air the concentration of O in the dry flue gas can be expressed as O O flue. 95 flue,stoic 1 air,stoic 1 air, stoic Equ Solving for λ gives 1 flue,stoic air,stoic O. 95 O Equ Fro Table 5.3 it can be seen that flue,stoic =.115 air,stoic =.143 aking the following siplification possible O O O Equ The average of the values calculated by Equ and Equ was used during the paraeter identification process. 15

18 5.8 Heat rate to the water circuit The heat rate to the water circuit Q wat V wat wat Q wat can be calculated as t.15 c t c p, wat, out out 73 p, wat, in in Equ. 5.4 Where V wat is the easured volue flow rate of water, T bout and T bin is the outlet and inlet water teperature of the boiler respectively and ρ wat is the density of the water and c pwat is the heat capacity of the water evaluated at the average water teperature. Polynoial functions have been derived fro values fro Incropera and DeWitt (1996) for a teperature range fro C to 1 C in Fig. 5.1 = ρ wat t t t ( C<t<1 C) Equ where t is the teperature of the water passing through the flow sensor. The hat capacity can be calculated fro: c p, wat = t t t where t is the inlet or outlet teperature t ( C<t<1 C) Equ. 5.4 The functions above give the agreeent with data fro Incropera and De Witt according to Fig. 5.1 Heat capacity cp [J/(kg K)] Heat capacity Density Teperature t [ C] Density [kg/ 3 ] Fig Values of density and heat capacity of water fro Incropera and DeWitt (1996) displayed as dots in coparison with the polynoial functions Equ and Equ. 5.4 displayed as lines. 5.9 Heat rate to the flue gasses According to Wester () the flue gas losses can be calculated by (assuing no condensation) Q flu g c pg, out Tgout c pg, in T gin Equ

19 Where T gin is the incoing cobustion air teperature abient air teperrature T. The heat capacity should be evaluated at the average teperature of T gout and T gin or better the average heat capacity over the entire teperature range. The ass flow in the exhaust gasses flu and thereby the energy to the flue gases can be calculated fro g Av g Equ Where v is the average gas velocity and A is the chiney area. The average gas velocity can be calculated fro the dynaic pressure p d easured in the iddle of the chiney by the Prandtl tube using the definition of dynaic pressure p d and a correction factor for the velocity profile in the chiney which was identified to v corr.85 by easureents in different points. v v corr P g d Equ The upper two equations lead to the following equation for the ass flow rate g Av corr P g d Equ Using the cobustion calculations there is also a second way to calculate g g fuel,h g fuel,h Equ where g can be calculated fro Equ. 5.. The ratio g / fuel depends ainly on the air factor λ and is plotted in Fig. 5. for the actual type of pellet in this work. A regression gives the following polynoial function g -15 fuel,h λ λ (1<λ<1) Equ If the consued pellet is easured in that way that the ashes is not leaving the weight stack what is easured is fuel,h - ashes and the ratio in Equ 5.47 should be g /( fuel,h - ashes ). The polynoial function becoes fuel,h g -15 ash (1<λ<1) Equ There is also Siegerts equation that can be used for calculating the flue gas losses (Wester, ): Q flu Q cob T gout T k CO Equ. 5.5 where the coefficient k depends on the fuel type, fuel oisture content and the carbon dioxide concentration. Extrapolating the fuel oisture rate to 6% fro Wester () and takes into account that are given as olar fraction or volue fraction and not % give: CO 17

20 k. 85 CO. 68 Equ g/fuel,h [-] λ [-] Fig. 5.. The ratio g / fuel as a function of λ. The dots show the results calculated by Equ. 5. and the line show the regression with Equ The cobustion power is calculated fro the ass flow of cobusted pellet and the LHW as Q cob fuel, h LHW Equ. 5.5 If the consued pellet is easured in that way that the ash is not leaving the weight stack the easured part will be and the cobustion power can be calculated fro Q cob however fuel,h fuel,h ash ash ash LHW ash is unknown, but can be calculated Equ ash ash fuel,h fuel,h fuel,h ash ash fuel,h ash Equ thus the cobustion power is Q cob ash LHW fuel,h ash fuel,h ash fuel,h ash Equ The ass of the ashes, ash can be obtained fro Table 5.3 to.5 kg and the ass of the fuel, fuel,h to 1.67 kg. 5.1 Density of the flue gas The density of the flue gasses (ρ g ) can be estiated fro the general gas law if the flue gasses are assued to behave as ideal gases. 18

21 i P MW R u T i Equ Where the general gas constant R u is J/(kol K). itrogen ( ) and oxygen (O ) can be considered as ideal gases, however vapor (H O) and carbon dioxide (CO ) are not ideal gases and could therefore cause probles in the accuracy when using the general gas law (Wester, 1991). The following correlation is therefore suggested i P MW z i R u i T Equ Where z is the copressibility factor, which is dependent on the type of gas, the teperature and the pressure (Alvares, 199). For the teperatures and pressures that is relevant here the copressibility factor can be assued to be constant and for water vapour z =.945 and for carbon dioxide z =.993 (Vester, ). For the other gases actual in this work the copressibility factor z is close to unity. The average density of the gas ixture can then be calculated fro the olar concentration g n i1 i i Equ The full expression of the density for the flue gases is g P R T u g H O,wf z Ar,wf MW HO z MW Ar HO Ar O CO,wf,wf z z MW MW O CO O CO,wf z MW Equ The density will vary depending on the air factor, the oisture content in the air, etc, however the variations are relatively sall. With the coposition of the wood pellet that is used here (Table 5. and oisture rate of.59 kg/kg), an assued air factor of., an air oisture ratio of.4 kg/kg and, a pressure of 1135 Pa, the equation can be reduced to: g K T g Equ. 5.6 Where K for an air factor of.. This is a value calculated for this particular pellet fuel specified in Table 5., oisture content specified in Table 5.3 and for the assued oisture content in the air. Plotting the value of K depending on air factor and aking a polynoial approxiation for K give the results as in Fig For the calculation of density for dry flue gases K dry can be calculated in a siilar way, just ignoring the water content g,dry K T dry g Equ

22 K, Kdry Dry gas 355 Huid gas Fig The value of K in as a function of the air factor. The dots are calculated using Equ and Equ. 5.6 and the curves are calculated with the polynos in Equ. 5.6 and Equ Making a linear regression of the influence for the air factor λ between 1. and (Fig. 5.3) give the following correlation for K and K dry, The oisture content of the air is assued to be constant.4 kg/kg. The oisture content of the wood pellet is assued to be.59 kg/kg. K K dry (1<λ<) (1<λ<) Equ. 5.6 Equ Density of air The density of dry air at atospheric pressure aking a regression fro data in Incropera and DeWitt (1996) for teperatures between 3 and 5 K give the following expression. =. 584T T (3K<T<5K) air Equ ] g / [k 1. [J/kg-K] dry air T [K] Fig Values of density of dry air fro Incropera and DeWitt (1996) displayed as dots in coparison with the polynoial function in Equ displayed as a curve

23 5.1 Heat capacity of the flue gas According to Wester () the heat capacity of the flue gases can be estiated by weighting the heat capacity for the different species by the ass fractions c p,g Y H c Y c Y c Y Y O p,h O CO p,co p, Ar p,ar O p, O c c Equ The ass fractions for the different species are calculated in Table 5.3. To be able to take into account the influence fro varying air factors, the ass fractions of the different species have to be expressed as a function of the air factor. cp [J/kg-K] cp [J/kg-K] 5 3 HO T [K] T [K] cp [J/kg-K] cp [J/kg-K] p CO T [K] O T [K] Fig Heat capacity for the different species in the flue gas as a function of teperature. Data for water vapour at atospheric pressure have been taken fro Granryd (1995). The other values have been taken fro Incropera and DeWitt (1996) for atospheric pressure. Data fro Granryd (1995) also show that the heat capacity for Argon is alost independent fro the teperature and a value of 51 J/(kg K) can be used over the entire teperature range. Influence fro the teperature on the different c p - values is shown in Fig And the regressions for teperatures between 3 and 5 give the following expressions for the heat capacity c p, HO = T T T T T Equ c p, = T (3 K<T<5 K) c CO p, = c Ar. 349 T T (3 K<T<5 K) p, = 51 (3 K<T<5 K) c p, =. 6 T (3 K<T<5 K) O Equ Equ Equ Equ

24 Plotting the results fro using Equ To Equ. 5.7 and using ass fractions (Y) fro six different air factors give the points in Fig The lines show the calculated values using Equ. 5.7, which is a regression of both T and λ. The curves are quite linear, thus evaluating cp at the average teperature between flue gas and abient is a good assuption for the average cp in the teperature range. cp,g [J/kg-K] T [K] λ=1. λ=1.5 λ=5. λ=. dry air Fig Heat capacity of the flue gas depending on teperature and air factor. The dots show calculated values using Equ and the data fro Table 5.3 and Equ to Equ The curves show the result calculated by Equ The line for dry air is calculated fro Equ These values are calculated for this particular pellet fuel specified in Table 5., oisture content specified in Table 5.3 and for the assued oisture content in the air. c p,g =.138 T ln.76 T T T ln (1. < λ < ) Equ To be able to find a suitable correlation like Equ the following procedure can be followed. Express the heat capacity as a function of the air factor in an equation of the following type ln + K ln + K3 c p,g = K1 Equ. 5.7 where K 1 K and K 3 is constants that can be identified for each teperature using the "Solver" in Microsoft Excel trying to iniize the absolute difference between heat capacity calculated by Equ and Equ Then plot the constants towards the teperature and use a linear regression to express K 1 and K and a polynoial of the second order to express K 3. For this case then the constants are found to be K 1 =.138 T K = -.76 T K 3 =.785 T T Equ Equ Equ. 5.75

25 5.13 Heat capacity of air The heat capacity of dry air at atospheric pressure fro Incropera and DeWitt (1996) are shown in Fig The data give the following expression when aking a regression. c p,air = T T (3 K < T < 5 K) Equ The heat capacity of the air can also be calculated using the sae ethodology as for the cobustion reactions (Equ. 5.65) and with the properties of dry air fro Table 5.1 and Equ to Equ. 5.7 alost the sae results as with Equ is obtained. Including a oisture content of.4 kg water per kg dry air have any significant influence on the heat capacity. cp [J/kg-K] T [K] dry air Fig Heat capacity of dry air fro Incropera and DeWitt (1996) displayed as dots in coparison with the polynoial functions (Equ. 5.76) displayed as lines Heat rate to the abient and full energy balance of the boiler With the setup of the easureents as described in this work it is ipossible to directly easure heat rate to the abient (the roo). It can only be calculated fro the energy balance of the boiler. The energy balance of the boiler for stationary conditions are: Q pell Q ab Q wat Q flu Equ Or in ters of heat rate Q pell Q ab Q wat Q flu Equ If the teperature of the boiler is changed during the easureents also a ter of internal energy change ust be included. Q pell Q ab Q wat Q flu Q int Equ

26 And it can be calculated as Q int wat c T c T c T T p, wat b p, wat t b1 t 1 steal p, steel b b1 Equ. 5.8 When identifying the paraeters for the UA-values using a spreadsheet with the boiler odel included the average heat rates of cobustion, to the water, to the flue gas and to the abient should be given. If the boiler water teperature have changed during the easureent sequence a correction due to the internal energy change ust be ade. As the change of the teperature of the water in the boiler is energy ainly up taken by the water and the steal it is suggested that the heat rate to the water includes both the tersq Q. wat int 5.15 Efficiency of boilers and stoves The efficiency for a boiler can be calculated fro boil Qwat Q Q pell int Equ where Q wat is the energy to the water and Q pell is the energy content of the consued pellet. In a stove also the heat rate to the abient air is considered to be useful heat and the efficiency can be calculated as stove Q wat Q Q ab pell Q int Equ Eission calculations The eissions are easured as volue concentrations in dry gases in PPM (parts per illion). Higher air factor will give lower values in PPM, though the eissions are constant which akes it necessary to relate the eissions to the cobusted pellet in [kg/(j fuel)] or siilar to be useful as a paraeter in the siulation odel. The cobustion calculation in Table 5.3 give the nuber of oles of dry flue gases as a function of the air factor, where the nuber of oles of CO can be calculated fro the following equation during stationary cobustion conditions. CO CO flue Equ Where flue is the nuber of oles of dry flue gas given fro the cobustion calculations in Table 5.3 or by Equ flue is dependent on the air factor and for the actual fuel in this study a linear regression give the following correlation with λ. flue = λ Equ Multiplying with the olecular weight of CO (=8.1 kg/kol) gives the ass of CO and by dividing with the heating value of the wood pellet and the consued wood pellet give the CO eissions per J fuel. 4

27 Q CO cob CO flue LHW MW pell CO Equ When flue is calculated fro the cobustion calculations in Table 5.3 it assues cobustion of 1.67 kg huid pellet, which ust be correlated to the actual aount of cobusted pellet Q CO cob CO pell LHW flue pell MW CO CO flue MW LHW CO Equ Assuing that CO CO will ake it possible to use the above equation for calculating the CO eissions. During the start and stop sequences the CO eissions cannot be calculated fro the knowledge of the cobustion conditions, as they are not known. Here the CO ust be calculated in absolute ters based on the easured flow rate of the flue gas. For easureents of one tie step the CO-eissions are CO V CO CO t s Equ The ass of CO-eissions for at tie step will be calculated based on the following equation. CO CO Vg, dry, Tref CO, Tref t s Equ Where the volue flow rate of the dry flue gas can be estiated the following way V g, dry, C g H O, g g, dry, Tref g g Y g, dry, Tref H O, g g g x g, dry, Tref H O, air Equ Where g can be calculated using Equ or Equ The reference teperature should theoretically be the teperature of the flue gas inside the instruent, when the concentration is easured, however due to calibration issues it ay be better to relate to the reference teperature of the calibration gas, which is usually 15 C. The cobustion calculations in Table 5.3 can be used to estiate the ass flow of water in the flue gas depending on the air factor. A correlation can be found in Equ If it is assued to be ainly air in the flue gas the assued oisture ratio in the air can be used. Observe that the siplified expression using the oisture content of air ( xh O, air ) does not follow the definition in Equ. 5.4, however the influence on the accuracy is sall copared to the uncertainty in the flow rate easureents. A regression of the ass fraction of water in the flue gas as a function of λ fro the cobustion calculation in Table 5.3 are shown in Fig. 5.8 and give the following correlation. Y HO,g = λ (1.<λ<3) Equ. 5.9 During ignition and cooling down phase the air factors are large and the cobustion calculations cannot be used. For these operation ties the huidity of air should be used. 5

28 Mass fraction of water in the flue gas [kg/kg] Air factor λ [-] Fig The ass fraction of water in the flue gas YH O,g as a function of the air factor λ fro the cobustion calculation in Table 5.3 displayed as dots and the values of Equ. 5.9 as a curve Conversion to other units Concentrations of the species have previously been expressed only in olar fraction, while easureent instruents usually give the readings in volue fraction. To convert fro volue fraction to olar fraction, the following equation can be used (Wester ), where values of z for different spices are given in section 5.1: i zi Equ i n i zi i1 6

29 6 Paraeter identification 6.1 Procedure The following procedure can be recoended in order to identify paraeters and verify the Type 1 fro easureents on a boiler or a water jacket stove. 1) The lower heating value (paraeter 3) of a test saple is deterined by an authorised test institute. Fro the cobustion calculations (Table 5.3) paraeters can be identified. ) Fro the easureents of stationary operation data for ax, in and operation power, the UA values (paraeter 1 to 3) can be identified using a separate excel sheet with the theory of the odel ipleented as a Visual Basic progra. To iniise the error any sequences shall be used, but with an even distribution of heat rate. The heat rate to the water circuit, the heat rate to the flue gases and the heat rate to the abient air is copared in the identification process. To avoid the deviation between the teperature in ass and the easured water teperature, the UA value between the water and ass (paraeter 7) shall be very large. The paraeters defining the heat losses at no cobustion UA 1-Ab and UA 1- (paraeters 5 and 9) shall be correlated to each other by the following equation UA 1 Ab 1 Equ UA UA loss 1 where the heat loss coefficient is calculated fro a test where the boiler is heated by electricity with the chiney blocked to avoid all chiney losses. The following equation can be used to calculate the heat loss coefficient fro heat loss easureents for the boiler. UA loss T Q el,hb boil,hb Tab,hb t T boil,h Q el,h T ab,h t Equ 6. The first ter is total heat loss coefficient fro the boiler and the electrical heating circuit and the second ter the heat loss coefficient for only the heater. 3) Fro the stationary cobustion easureents also the axiu cobustion power and the iniu cobustion power (paraeter 7 and 8), the air factor (inputs and 3) and the CO-eission paraeters (paraeters 31 and 3) can be identified fro these data. Fro the sae easureents also data of electricity consuption should be taken and the paraeters 11 and 1 can be identified. 4) Fro a start and a stop sequence where the operation of the fan and the pellet feeder are easured the paraeters 13, 14 and 15, can be identified. By using the flow rates easured by the Prandtl tube, the flue gas ass flow rate during the stop phase and during standby (paraeters 17 and 18) can be identified. The sequence ight be different depending if the boiler is war or cold and if the boiler is operating with stand by cobustion or not. The average values of several easureent sequences should be used. 7

30 5) The leak flow rate is set by paraeter 18 and is calculated the following way internally in the odel according to ordlander (3) which eans that it varies with the outgoing gas teperature and the outdoor teperature. Tg Toutd air air5 Equ In practise the leak flow rate will not only vary depending on the outdoor teperature and the outgoing gas teperature but also with the chiney height and diaeter, the theral ass and the insulation standard of the chiney, if there is a valve that axiise the under pressure in the chiney and the actual pressure in the boiler roo relative the outdoor pressure. It is good if the total heat loss coefficient of the boiler have been easured at different under pressures in the cobustion chaber like in Fig If the easureents have been perfored at a specific under pressure in the cobustion chaber and the easureents shall be used for the validation sequence an artificial outdoor teperature ust be calculated to give the right leak flow rate at no cobustion. The following equation, derived fro Equ. 6.3 and shall be used. T outd T g 5 air air5 Equ 6.4 The coefficient air5 is the leakage flow rate of air at 5K difference between the gas leaving the boiler and the outdoor teperature (ordlander 3). Assuing this teperature difference for an outdoor teperature of C and a 5 high chiney and ignoring friction losses, that the gas is cooled down along the chiney and that the gas ight contain other substances near a cobustion period it cause an under pressure of g H p Equ 6.5 air, 5C air, C Evaluating the densities using Equ and assuing a chiney height of 5 give the actual under pressure fro Equ 6.5. The heat loss coefficient for the self draught UA los,flu can be derived fro Fig. 6.1, where the heat losses have been easured depending on the under pressure in the chiney. The ass flow rate at this particular condition can then be calculated as UAlos, flu air Equ 6.6 c p,air, 5C 6) Electricity consuption paraeters (Paraeters 1, 11 and 1) shall be identified fro electric consuption easureents of the boiler. An average power consuption during the start sequence shall be easured and for the operation electricity consuption should be easured at different cobustion powers and at standby. The odel assues a linear dependence on cobustion power. 7) Fro a cooling off sequence where the chiney is blocked to avoid flue gas losses the theral asses of the boiler (paraeters 5 and 6) can be adjusted during siulations of the cooling of sequence. The asses shall be adjusted so that the siulated teperatures of the asses correspond well with the easured boiler water teperature during the whole cool- 8

31 ing down period. Particularly for a stove with large aount of heat rate to the roo it is ore iportant to copare the easured teperature at the convection air outlet and the glass surface with the siulated heat rate to the roo both at the start up period and the cooling down period. Increasing the theral ass 1 will have a delaying effect on the heat rate to the abient. 8) The tie constant for the after glow phase can be identified by siulating a easured stop sequence and copare the easured boiler water teperature (or air outlet teperature and glass teperature for a stove) with the teperature of the theral asses. 9) Verification of the odel should be perfored to show that the odel can ake predictions during real operation conditions. For this a sequence including real operation conditions should be used. The easureent data should be prepared in that way that cobustion power abient air teperature inlet water teperature and inlet water flow rate are used as input. If a real chiney is used during the easureents the outdoor teperature is given as input and if a fan with a constant draught is used a fictive outdoor teperature is calculated using Equ Paraeters for the Theria Bionet boiler In this section the paraeter identification of the Bionet boiler serves as an exaple of the ethodology. The paraeters are given in Appendix 1 together with the identified paraeters for the other stoves and boilers. The boiler can be operated at three different cobustion steps and adjustent of the fuel and air settings were carefully perfored at an constant under pressure of 11 Pa in the cobustion chaber. The lowest possible air factor was adjusted trying to aintain low eissions of CO and O x. The easured air factors are given in Fig Identified paraeters for the different boilers that have been tested are collected in Appendix 1. The table also shows all inputs to the odel, where the air factor for soe boilers are odelled externally. The paraeters are collected fro the following references: Persson (3), Persson (4), ordlander (4a) and ordlander (4b). In Persson (3) and Persson (4) an old version of the boiler odel was used, but the paraeters are converted to the relevant paraeters for type 1 in Appendix 1. For the odel of Biosolpannan that is cobined with the type 14 odel (Drück, ), also these paraeters are given in Appendix Minial and axial cobustion power The axiu and iniu cobustion power was calculated fro an average of pellet consuption during stationary operation on highest respective lowest cobustion power. The values was identified to kj/hr and 16 6 kj/hr respectively. 6.. UA value identification 9

32 Microsoft Excel was used for autoatic generation of the UA values, however two restrictions were used. The UA value between the water and ass was fixed to7 kj/(hr K) to keep the outlet water teperature close to the teperature of ass. The UA value between the ass 1 and the abient air was described using equ. 6.1, where UA loss are 4.4 W/K fro Fig UA los [W/K] P [Pa] Fig Heat loss coefficient as a function of the under pressure P in the cobustion chaber for the Theria Bionet boiler Theral asses The theral asses (paraeters 5 and 6) and the tie constant for the after glow phase (paraeter 16) should be identified. A easured cooling down period with blocked chiney and a start and stop sequence where the water circulation stops at the sae tie as the fuel feeding stops is used for that purpose (Fig. 6. part (a)). The teperature of the theral ass that odels the heated water and the steal in the boiler is adjusted so that the siulated teperature of ass agree with the easured boiler water teperature. In the atheatical odel there are no theral ass of the water, thus the teperature difference between the theral ass and the water is dependant on the heat rate and the UA-value (paraeters 3 and 4). For this reason it can be advantages if paraeter 3 has a large value. One way to get a proper water teperature is to cobine the odel with a ass of water like type 14 (storage tank odel). This can be done either by just odel the water using type 14 and ove the theral ass fro ass to the storage tank odel or by using the boiler odel only to produce hot flue gas that goes through one heat exchanger of the boiler odel. In Fig. 6. part (b), theral ass 1 and the tie constant for the after glow phase are identified. Paraeter 5 are adjusted until the siulated heat rate to the water circuit and to the abient follows the easured data and paraeter 16 is adjusted until the teperature increase of ass after the stop agree with the easured water teperature. 3

33 Measured water teperature Calculated teperature of ass Measured water teperature Calculated teperature of ass Measured heat rate to water Calculated heat rate to water (a) Fig. 6.. (a) shows siulated teperature of the theral ass in coparison with easured boiler water teperature for a cooling of sequence with blocked chiney. (b) shows a start and a stop sequence with siulated heat rate to the water and teperature of ass in coparison with the easured heat rate to the water and boiler water teperature. (b) 6..4 Air factor The easured air factor (calculated fro and average of Equ and Equ. 5.38) is plotted as a function of the cobustion power in Fig. 6.3 and a regression is perfored giving the following correlation [-] Equ Q Pell where Q Pell shall be given in [kj/hr]. A linear correlation as is suggested by the odel is not considered to be accurate enough for this type of boiler, thus the air factor ust be odelled externally using Equ 6.7. Air factor [-] P pell [kj/h] Fig Measured (as dots) and odelled (as a curve) air factor as a function of cobustion power for the Theria Bionet boiler. 31

34 6..5 CO factor The CO eissions during stationary operation are plotted in Fig. 6.4 expressed both in [g/mj] and in [g/h] and the regressions are the following: CO Q Pell [g/mj fuel] Equ. 6.8 [g/hr] Equ CO Q Pell where Q Pell shall be given in [kj/hr]. The odel assues a linear correlation for the eissions, however better agreeent with the easured data will be achieved using an exponential function. Thus the eissions are odelled externally using the exponential function in Equ 6.9. The COeissions during the start sequence was identified to be. g/start. y = x y = x CO-eission (g/mj) P pell [kj/h] CO-eission (g/h) P pell [kj/h] Fig Measured (as dots) and odelled (as a curve) CO eissions as a function of cobustion power for the Theria Bionet boiler CO eission for start/stop During the stop sequence the CO-eissions arise through a long tie span according to Fig Thus the eissions ust be stopped if the burner starts again during this tie span. The stop eissions are therefore odelled externally according to Fig The ass flow of the eissions are odelled as. h average values for the first three hours and with one hour average values for the last three hours. 3

35 5 5 CO-eissions [g] Mass flow of CO [g/hr] Tie [h] Tie [h] Fig Acuulated CO-eissions and ass flow of CO-eissions during the stop sequence. Average value of two independent stop sequences Duration of the two start phases Fro easureents of start sequences in Fig. 6.6 (starting by aking a new ignition) the duration of the start phases can be identified. The start tie of the pellet feder is found fro the voltage easureent of the screw otor. Phase one is assued to start when the pellet feeder starts and phase when the ignition ocours. There is a period with low fan operation and no pellet feeding during phase before the therostat is allowed to control the burner. % :: C :: :51:4 weight pellets = kg O = % Start pellet feeder Diff pressure =.8 Pa Ignition Phase 1 Phase TS 1 = 67. C weight pellets = kg End of start sequence CO = 4.11 % TS 1 = 6.4 C kg Pa C : : : : Fig Measureents of a start sequence, starting by aking a new ignition. The start tie of the pellet feder is found fro the voltage easureent of the screw otor. Phase one is assued to start when the pellet feeder starts and phase when the ignition ocours. There is a period with low fan operation and no pellet feeding during phase before the therostat is allowed to control the burner. TS 1 is the flue gas teperature and TS 1 is the boiler water teperature. 33

36 6..8 Fan operation and ass flow after stop Paraeter (15 and 16) have been identified fro easureents of a stop sequence (Fig. 6.7). The stop tie of the pellet feeder is found fro the voltage easureent of the screw otor and the stop of the fan is found fro the voltage easureent of the fan. The ass flow during the fan operation is the calculated average fro the Prandtl easureents during the period between the screw otor stops and the fan stops. pp :59: C :59:7 1.5 t :3: % Pa C Fre O = % CO = pp TS 1 = C CO = % Diff pressure = Pa : : : : Fig Measureents of a stop sequence. The stop tie of the pellet feeder is found fro the voltage easureent of the screw otor and the stop of the fan is found fro the voltage easureent of the fan. TS 1 is the flue gas teperature Leakage flow rate. When identifying the leakage losses through the chiney during standby (paraeter 18) the chiney length ust be taken into account. If easureents like in Fig. 6.1 are available, the data ust be recalculated for a certain chiney height. The draught in a particular chiney can be calculated fro the air density using Equ and assuing a chiney height of 5 give an under pressure of 8.57 Pa using Equ Using Fig. 6.1 this pressure causing a heat loss coefficient for the self draught UA los,flu of.98 W/K. The ass flow rate at these particular conditions can then be calcu- 34

37 lated as using Equ 6.6: UAlos, flu kg / s 3. c 17. air 5 p,air, 5C kg / hr 6..1 Electricity consuption The electrical consuption is odelled as a linear function depending on the cobustion power using paraeter 11 and 1. Measured electricity consuption at stand by and at axiu cobustion power (Fig. 6.8) is used to identify the paraeters. The electricity power consuption during the start sequence is calculated fro a easured average and was found to be 194 kj/hr. Pel [kj/h] P pell /P pell,ax [-] Fig Measured (as dots) and odelled (as a line) electrical consuption of the Theria Bionet boiler. 6.3 Paraeters for the Rebus boiler The so called REBUS boiler is a prototype of a very copact odulating pellet boiler with a noinal cobustion power range between 3.4 and 1 kw. The original pellet heater is anufactured by the Austrian copany RIKA and arketed under the nae EVO AQUA. This is in fact a water antled pellet stove that is usually installed in the living area of a house. The reason to use this stove for the REBUS project was that the core part of the stove, the water antled cobustion unit, is very copact and fits into a 6x6c cabinet. The front window was replaced by a door and insulation was placed around the boiler, reducing the heat transfer to the abient to a iniu. Furtherore, odifications of the pellet transport syste were accoplished. However, odifications of the heat flows have influence on the cobustion so that the original settings for the cobustion had to be adapted to the changes Minial and axial cobustion power The original water antles stove has a total cobustion power range fro 3.6 to 1.7 kw (BLT, 3). The pellet supply and by that the cobustion power is controlled by the frequency of the feeding screw. This eans the rotation speed is constant but the otor is clocked. The boiler has 1 cobustion stages with default clocking ties. For each cobustion stage the boiler is doing a fine 35

38 regulation based on the flae teperature easureent in the cobustion chaber. After the feeding screw was replaced by a longer flexible feeding screw an adjustent of the otor speed was necessary in order to aintain the sae power range. Later, steady state tests with 3 different cobustion power stages were perfored. Fro the pellet weight easureent the three cobustion powers have been calculated. In figure these powers are presented in coparison with the original stove for the 1 power stages. It can be seen that the new feeding screw has a non linear characteristic, which has ade it necessary to odify also the cobustion settings. Using a polynoial fit, the cobustion power for the lowest heating stage is 3.4 kw. The axial cobustion power for H1 is 1.4 kw Cobustion power [kw] Cobustion power original stove Cobustion power odified boiler 6 4 Feeding rate [kg/hr] Feeding rate original stove H H 1 H H 3 H 4 H 5 H 6 H 7 H 8 H 9 H 1 H 11 Heating stages Fig Cobustion power of the heating stages for the original and odified pellet heater UA value identification Type 1 odels the heat transfer of the boiler by two theral asses and five heat transfer coefficients (see figure 3.1). These UA-values are not constant rather depending on power and/or teperature. Thus, Type 1 odels the UA-values with a constant and a variable coefficient which is dependent on the cobustion power. Consequently, 1 values need to be identified with the solver in Excel paraeter identification sheet. As input values data fro several sequences with constant cobustion power are necessary. The sequences should cover the whole cobustion power range of the boiler and as ore sequences as ore accurate results can be expected. The great nuber of paraeter akes it necessary to reduce the range of paraeter so that the solver is not looking for solutions far fro realistic values. Here start paraeter can be defined which are known fro other siilar boiler and the first runs can be liited to only a few paraeter. It is also possible to let the solver only search for solutions for the power independent paraeters. Furtherore restrictions can be added, ranges were the paraeter are expected to be found. Moreover the inial heat loss coefficient can be identified by easureents and can be given as a boundary condition for the paraeter identification. For the Rebus boiler the inial heat loss coefficient has been deterined by several tests where the boiler was heated by puping water, which is heated by an electrical heater, through the water antle of the boiler. The obtained heat loss coefficient depends on the water teperature and can be seen in figure For noral operation conditions that gives heat losses of 15 W to 5 W depending on the boiler teperature. 36

39 7 6 5 UAlstot UA [W/K] dt [K] Fig Heat loss coefficient to the abient depending on the teperature difference between boiler and abient without cobustion In reality the heat losses during operation of the boiler are uch higher (5W 1W) since this test does not siulate the heat losses fro the front door of the boiler. The largest part of the losses occur fro the front door since the door is not water antled and reaches teperatures above C even if insulated fro inside. However, the identified value can be used as a lower liit for the solver. The identified heat loss coefficient can not directly be assigned to the boiler odel. The heat losses of the boiler are governed by the heat loss factor UA 1-Ab and UA 1-. Both represent the total heat losses fro the boiler to the abient and can be expressed as (see also chapter 6.1): 1 UA loss 1 1 Equ. 6.1 UA UA 1 Ab 1 For UA lstot the value fro the heat loss test is applied and added as a condition for the solver. That allows the solver only to find solutions were UA loss is greater than 5.5 W/K (see also Equ.6.1). The paraeter finally identified for all UA-values can be found in Appendix Theral asses Before is going to be deterined the after glowing tie should be identified (paraeter 16). In the case of the REBUS boiler this was done for by looking at the flue gas teperature during the stop phase of the boiler. The tie between the boiler was stopped and the flue gas teperature starts to decrease drastically was easured for several sequences. A value of about.5 in was identified. Subsequently, paraeter 6 for the theral ass was identified by siulating a easured cooling down phase of the boiler and varying the value for. The gradient of the easured and siulated boiler teperature curves should be as siilar as possible (figure 6.3.3a). The theral ass 1 was identified by siulating a easured start phase of the boiler. Here 1 is varied until the teperature of 1 (this is an output of Type 1) is between the boiler and flue gas teperature with a siilar slope (figure 6.3.3b). The two siulations need to be done in turn since the 1 and influence both start and stop phase. 37

40 easured flue gas teperature siulated boiler teperature teperature of 1 easured boiler teperature easured boiler teperature siulated boiler teperature (a) (b) Fig Measured and siulated boiler teperature during cooling down phase of the boiler (a). Measured and siulated boiler teperature, siulated teperature of 1 and siulated flue gas teperature (b) Air factor An equation for the air factors has been deterined for three easureents with steady state conditions for different cobustion powers of the boiler. The air factors have been calculated based on O values in the flue gas. For each of the three sequences an average O value has been calculated applying equation The O value was used due to better calibration of the flue gas analyzer for O copared to CO. The correlation between cobustion power and air factor are shown in figure Labda [kol/kol] y =.395x Labda CO Labda O Power (Labda CO) Xpel [kw/kw] Fig Air factor Labda calculated with equation 5.35 and equation

41 6.3.5 CO factor The values for the CO eissions have been deterined after the boiler design odified. Due to these odifications it was also necessary to adjust the cobustion settings. The flae set teperature was increased by 3%. Furtherore the cobustion air flow was adjusted by decreasing the air flow by 7% for 4 kw, by 5% for 7 kw and % for 1 kw. The adjustent criteria were the CO eission. The values are presented in figure The CO factors are odelled as a fixed and power dependent paraeter for Type 1 which akes it difficult used the power fit of the CO eissions. Consequently, the siplified less accurate linear fit was used for the paraeter. If the boiler is operated on/off or with a fixed cobustion power the correct value should be chosen fro the power fit, otherwise the error can be significantly. A siilar fit was found for the Bionet boiler so that it is suggested to change the CO eissions fro a paraeter to a input so that the CO eission can be odelled with an external equation. 5 Linear fit: y = x Power fit: y = x CO eissions [g/mj] CO Linear fit Power fit Xpel [kw/kw] Fig CO eissions depending on the fraction of the axial cobustion power CO eission for start/stop The paraeters for the CO eissions during start and stop/start have been deterined fro the test sequences in figure In the first sequence the boiler starts with a cold water volue and cobustion chaber whereas a war start was perfored for the second and third sequence. For the start eissions and average value of 4.4 g CO has been deterined and for the stop eissions an average value of 1.4 g CO has been deterined. 39

42 Boiler on/off [1/] Boiler on/off Mflue [kg/hr] CO [pp/1] COcu [g] Cocu, Mflue, CO [g, kg/hr, pp/1 14:4 14:45 15:7 15:8 15:5 16:1 16:33 16:55 17:16 17:38 18: 18:1 18:43 19:4 19:6 19:48 :9 :31 :5 1:14 1:36 Fig Continuous and cuulated CO eissions for three cobustion sequences Duration of the two start phases The first start phase without cobustion (paraeter 13) was easured to be approxiately 9 inutes. This is the tie the boiler is perforing the cleaning of the grate and filling the cobustion chaber with the start aount of pellets. The second start phase has been set to zero and the corresponding cobustion power for this phase to 1.4 kw (paraeter 9). It has been shown that it is not necessary to odel a second start phase since the identified theral asses create the sae effect as a lower cobustion power during start a slow heating up of the boiler Fan operation and ass flow after stop Both paraeter (15 and 16) have been identified fro lab easureents of the boiler. The values given in Appendix 1.1 are deterined for stops when the boiler was before the stop operating with the lowest cobustion power. This is assued to be the noral case when the boiler is operating with odulating power. If the boiler was operating with higher cobustion power (e.g. when the boiler is on/off controlled) these values are usually different since the fan is speed controlled depending on the teperature in the cobustion chaber Leakage flow rate. The leakage flow rate has been deterined fro the easureents of the flue gas ass flow easureents. The accuracy of the flue gas ass flow easureent based on the dynaic pressure easureent is rather low. By contrast, for steady conditions the flue gas ass flow rate can be rather exactly deterined based on the cobustion calculations described in chapter 5. Fro the three stationary easureents a correction factor for the flue gas ass flow rate was deterined and applied. With this calibration the leakage ass flow rate was easured after the boiler was stopped for a teperature difference of 5 K between boiler teperature and abient (outside) teperature. Fro two sequences an average value of 1.8 kg/hr was calculated. The obtained value should be validated by other easureents as perfored by ordlander (4a). Furtherore the effect of under pressure in the cobustion chaber should be studied as for the Bionet boiler (chapter 6.). 4

43 6.3.1 Electricity consuption The paraeters for the electricity consuption (par. 1-1) have not been easured for the actual boiler. The values presented in the paraeter list in Appendix 1.1 have been taken fro the test report for the Evo Aqua stove (BLT, 3). The values for the boiler ignition power (paraeter 1) and the standby operation should be equal since the construction is identical. The power dependent value ight deviate as the otor for the actual feeding screw has a higher electrical power than the original one. However, no final decision was ade what otor will be used in future. 6.4 Characteristics of the odels Heat (kw), air factor air factor fraction of heat to water K stove, Persson (4) CO-eissions efficiency heat to water heat to roo start and stop eissions of CO = 3. g/start P pellets (kw) Efficiency, fraction to water, CO (g/mj) Heat (kw), air factor Wodtke Sart stove, Fiedler et al., (6b) start and stop eissions of CO = 3. g/start efficiency fraction of heat to water air factor CO-eissions heat to water heat to roo P pellets (kw) Efficiency, fraction to water, CO (g/mj) 1 9 Pitekainen stove, Persson (4) 1. efficiency.9 1 Wodtke Sart stove, Persson (4) 1. 9 efficiency.9 Heat (kw), air factor heat to roo air factor CO-eissions start and stop eissions of CO = 1.85 g/start P pellets (kw) Efficiency, CO (g/mj) Heat (kw), air factor fraction of heat to water CO-eissions heat to water air factor heat to roo start and stop eissions of CO = 3. g/start P pellets (kw) Efficiency, fraction to water, CO (g/mj) Fig Characteristics of four stove odels (Pitekainen, two versions of Wodtke Sart and K) at stationary conditions. The inlet water teperature is 55 C for the water jacketed stoves. The water flow rate is.111 kg/s for the water jacketed stove and abient air teperature is C. The stove K is a generic stove (a odified version of Wodtke sart used by Persson (4). The paraeters for the odels are collected in Appendix 1:1. 41

44 Perforance charts of two boiler and two stove odels during stationary operation are presented in Fig and Fig Characteristic for all boilers and stoves are decreased air factor and COeissions with increased cobustion power, except for the Pitekainen, that has a sall increasing air factor for increasing cobustion power. The efficiency is higher for the stoves than for the boilers as the heat rate to the roo is considered as losses in the efficiency calculation for the boilers, but not for the stoves. The efficiency decreases with increased cobustion power for the stoves indicating that the flue gas teperature increase with the cobustion power. For the boilers the efficiency is quite constant over the entire operation range with the axiu efficiency at the average cobustion power. The ajor paraeters influencing the efficiency is the air factor and the flue gas teperature, and for the boilers of course the heat losses to the roo. Theria Bionet boiler, Persson et al. (6) Heat [kw], Air factor start eissions of CO =. g/start stop eissions of CO = 1 g/stop heat to water CO-eissions efficiency air factor 1.1 heat to roo Cobustion power [kw] Efficiency, CO [g/mj] Theria Bioatic boiler, Fiedler et al. (6b) Heat [kw], Air factor start eissions of CO = 1 g/start stop eissions of CO = 6 g/stop heat to water efficiency air factor 1 heat to roo CO-eissions Cobustion power [kw] Efficiency, CO [g/mj] Rebus boiler (Rika), Fiedler et al. (6a) 11 1 start eissions of CO = 4.4 g/start stop eissions of CO = 1.4 g/stop Pell-X burner + Biosol boiler, Fiedler et al. (6b) 11 1 start eissions of CO = 1. g/start stop eissions of CO = 6.4 g/stop efficiency efficiency.9.8 Heat [kw], Air factor 7.7 heat to water air factor.3. CO-eissions 1.1 heat to roo Cobustion power [kw] Efficiency, CO [g/mj] Heat [kw], Air factor heat to water air factor. CO-eissions 1.1 heat to roo Cobustion power [kw] Efficiency, CO [g/mj] Fig Characteristics of four different boiler odels (Theria Bionet, Theria Bioatic, Rebus and Pell-X burner + Biosol boiler) at stationary conditions. The inlet water teperature is 65 C for the boilers, the water flow rate is. kg/s for the boilers and abient air teperature is C. The Theria Bioatic boiler is considered to be a generic boiler as the paraeter identification process was very siplified. The paraeters for the odels are collected in Appendix 1:1 and 1:. 4

45 7 Verification and validation Coparisons between easureents and siulations during stationary operation and dynaic conditions showing high agreeent between the easureents and the siulations. The results are shown in figures 7.1 to 7.5 below. Validation or verification of the odels coparing with a sequence with realistic operation conditions that not have been used during the identification process has not yet been perfored. kw P roo eas Proo si P gas eas P gas si Eff eas Eff si 1% 9% 8% 7% 6% 5% 4% 3% % 1% % A B C D E Fig Coparison between easured and siulated values for the stove "Pitekainen" during stationary operation conditions. kw Pliq Pliq si Pab Pab si Pg Pg si A B C D E F G H I J K L M Fig. 7.. Coparison between easured and siulated values for the stove "Wodtke Sart" during stationary operation conditions. 43

46 Heat [kw], air factor Calculated Measured air factor CO-eissions heat to roo Theria Bionet heat to water efficiency P pellets [kw] Efficiency, CO [g/mj] Fig Coparision between easured and siulated values during stationary conditions for the Theria Bionet boiler and the Rebus boiler. Heat [kw] CO-eissions heat to roo Calculated Measured Rebus heat to water efficiency Air factor P pellets [kw] Efficiency 3 Measured flue gas tep. 5 Calculated flue gas tep. 16 Effekt Heat (kw), rate [kw], Energi Energy (kwh) [kwh] Measured flue gas tep. Measured energy to the flue gas Measured energy to roo air Calculated energy to roo air Calculated energy to the flue gas Teperature [ C] (C) 44 Tie [hours] Cobustion power Fig Coparison between easured and siulated values for the stove "Pitekainen" during dynaic operation conditions