Modelling of non-steady-state conditions in a gas boiler heated room

Transcription

1 Proceeings of the 3r IASME/WSEAS Int. Conf. on HEAT TRANSFER THERMAL ENGINEERING AND ENVIRONMENT Corfu Greece August (pp6-11) Moelling of non-steay-state conitions in a gas boiler heate room DR. LÁSZLÓ GARAI DR. LAJOS ARNA Department of uiling Service Engineering uapest University of chnology an Economics 1111 uapest Műegyetem rkp. 9. HUNGARY Abstract: In Hungary the use of gas is of a significant proportion as compare to other energy resources. In the case of the most generally use type gas boilers the coorinate operation of the gas appliance an the chimney as well as the supply of combustion is an important question. esies the construction of the chimney when builing envelops meet moern energetic requirements this coorinate operation also epens on the introuction of the necessary quantity. For the appropriate ajustment of the gas boiler to the conitions of the builing an its heating system computer generate calculation results have to be obtaine that can help the positioning of the appliance an the elaboration of the heating system. For the examination of the coorinate operation of the gas boiler an the heate space a mathematical moel nees to be evelope to escribe the non-steay-state conitions of the heating system an the builing an to help examine the non-steay-state conition of the room s supply appliance chimney. Key wors: heating system gas appliances chimney mathematical moelling supply 1 Introuction In Hungary the use of gas is of a significant proportion as compare to other energy resources. The heating of about 80% of family houses an blocks of flats is provie for by gas boiler operate central heating system. The prevalently use type* gas boilers o not operate continuously but automatically turn on an off epening on the changes of inoor temperature. The temperature of the hot-water heating system connecte to the boiler changes in harmony with the operation of the boiler. In the chimney the extent of the raught epens on the operation of the boiler an the temperature of the flue gas an the heating water. For the appropriate ajustment of the gas boiler to the conitions of the builing an its heating an ventilation system computer generate calculation results have to be obtaine that can help in choosing the appliance an in the planning of the chimney an the supply of the room. Our goal is the evelopment of a physical-mathematical moel that can be use for examining the non-steay-state conition of the room an the gas boiler the chimney an the supply of the room. * Type appliances are connecte to a flue through which combustion proucts can leave an the combustion is rawn irectly from the room. (CEN report CR 1749) The physical moel The evelope physical moel is presente in Fig. 1. A type boiler supplie with an open combustion chamber supplies a hot-water heating system. The heate space is connecte to its environment in part through the heat irecte towar the outoors an in part through the ventilation that evelops ue to the raught of the chimney. See the main characteristics of the energetic connection below. Fig. 1 The physical moel of a flat heate by an iniviual gas boiler

2 Proceeings of the 3r IASME/WSEAS Int. Conf. on HEAT TRANSFER THERMAL ENGINEERING AND ENVIRONMENT Corfu Greece August (pp6-11) On the basis of the physical moel an energetic block iagram of the flat heate with the gas boiler was evelope which in turn le to the elaboration of the mathematic moel. The moel can be ivie into two main parts: the boiler heating system room walls moel an the boiler chimney combustion- supply moel (Fig.). The etails of the sub-moels are as follows. Fig.. Energetic block iagram of a room heate by a gas boiler 3 The calculation moel 3.1. The moel of the heating system The components of the moel: the gas boiler the hot-water heating system the room an its walls. The heat prouce by the gas boiler enters the room through the heating system an the raiator. Depening on the supply an return temperatures an in function of the temperature of the room the heat transmitte by the raiator an therefore the temperature of the of the room both change. The initial equations were the following: the heat balance of the heat circuit: tw s tw r M w = Q& boiler Q& ra (1) τ the heat balance of the room: ( M ti ) = Q& ra Q& tr c p ( ti te ) () where tw s tw r Q & ra = kra Ara ( ti ) (3) is the heat flow transmitte by the raiator an Q & tr = kwall Awall ( ti te ) (4) is the transmission heat loss of the walls. With the introuction of a tag for the meium temperature of the heating meium (t wav ) an its substitution into equations (1) an () the result after the rearrangement of the equations is: Q& boiler kra Ara kra Ara tw av = tw av ti M w M w M w (5) an ti = kra Ara kwall Awall = ( tw av ti ) ( ti te ) M M c kra Ara ( ti te ) = tw av M M k ra Ara kwall Awall c ti M M M k wall Awall c te te (6) M M With the constants combine the equations can also look as follows: tw av = a11 tw av a1 ti a13 an (7) ti = a1 tw av a ti a3 (8) Initial conitions in the moment τ = 0: te0 tv0 tw av = tw av0 = ; an t = t ; t = t = const. i i0 e e0 3. The moel of the boiler The energy flow entering the appliance in the moment when the boiler starts operating: Q& = gas Hs gas c p gas ti comb. c p ti (9) After the burner: Q& = ( gas comb. ) tcombcp = tcombcp (10) Flue gas temperature after the burner calculate from equation (1) an (): gas H s t comb = ti (11) m & c p The energy flow leaving the appliance is Q & = c t w cw ( tw s tw r ) Q& loss (1)

3 Proceeings of the 3r IASME/WSEAS Int. Conf. on HEAT TRANSFER THERMAL ENGINEERING AND ENVIRONMENT Corfu Greece August (pp6-11) where Q & loss is the heat loss of the appliances cause by convection an raiation. Neglecting the appliance s convection an raiation losses the heat flow transmitte by the hot flue gas an the heate water within the heat exchanger is: c p ( tcomb t ) = w cw ( tw s tw r ) = = Ahe khe tav (13) After reuctions an the introuction of constants (A 0 A 1 A A 3 ) the form of equation (13) is: c p ( tcomb t ) = (14) = A0 A1 tcomb A0 A1 t A0 A A3 From the equations the temperature of flue gas leaving the appliance is: A0 A A3 t = (15) A0 A1 c p 3.3 The moel of the chimney an the inlet Draft inuce by the ensity ifference at H long vertical section of the chimney covers: flow resistance of the inlet pressure ifference necessary to increase the velocity of room entering the raft hoo the flow resistance of chimney an the win pressure. Using the tags from Fig. 1: ρ p = g H ( ρe ρmix.av) = pin w (16) p p p. raft hoo chimney win Assuming that the characteristic of the inlet is: p = C 1 s where C 1 = const. equation (16) will become: g H ( ρe ρmix.av ) = s ρi A raft hoo ρi ρ (17) i ζ raft hoo A raft hoo ρi H mix ρ mixav λ ζ C D A ρmixav where C = p win = const. After simplifying an reucing equation (17) the result is: p e T e g H 1 = s R T e T mixav 1 R Ti (1 ζ raft hoo) A p raft hoo i H 1 R Tmixav λ ζ mmix C. D & A pmixav (18) In orer to receive an equation easier to hanle the following notations are introuce: pe g H = R 1 R Ti ( 1 raft hoo ) = 1 A p rafthoo ζ i H 1 R λ ζ = D A pmixav Thus the new form of the equation (14) is: 1 1 = s Tmixav C Tmixav mix. (19) As m & s = comb. és mix = equation (19) expresse in a ifferent way is: 1 1 = ( comb. ) T mixav C Tmixav ( m m ). & & 0 (0) After raising the equation to secon power an rearranging it: C = Tmix av m T mix av & 0 comb. Tmix0 3 Tmix av mav & (1) 0 3 C m comb. m Tmix av & &. 0

4 Proceeings of the 3r IASME/WSEAS Int. Conf. on HEAT TRANSFER THERMAL ENGINEERING AND ENVIRONMENT Corfu Greece August (pp6-11) As the next step the constants in equation (1) are substitute with the constants shown below: C 1 3 a0 = 1 a1 = a = a3 = 3 a4 = comb. a5 = a6 = 3 a7 = comb. a8 = a9 = The new form of the equation is: = a0 ( a1 a Tmix0 a3 Tmixav ) Tmixav ( a4 a5 Tmix0 a6 Tmixav ) ( a7 a8 Tmix0 a9 Tmixav ). () The unknowns in equation () are: Tmix0 és Tmix av while the other factors can be etermine from the combustial equations an from the flow an geometric characteristics of the combustion gas outlet. Further equations are: Initial temperature of flue gas after mixing combustion an room : T Ti Tmix = T z 0 mix0 =. (3) = The meium temperature of the mixture flowing through the chimney can also be escribe on the basis of the temperature of the mixture that enters an then leaves the chimney (if we conceive the chimney as a heat exchanger): Tmix0 Tmix ( H ) Tmix av = = Tmix0 k U (4) H 1 ( ) c p mix ( Tmix0 To ) e Equations () (3) an (4) form an equation system. It can be use for the examination an sizing of chimneys as regars thermal an flui ynamics but can also be utilise for the etermination of the chimney s operating point when the heating system connecte to the appliance is in a non-steay-state. 4 Steps of calculation The steps of moelling were the following: Initially the gas boiler is not in operation a temperature evolves in the room an a given current evelops through the gas appliance an the chimney. At the sign of the room thermostat at a τ = 0 moment the gas appliance starts its operation an transmits Q heat quantity into its surrounings uring a τ perio. As a result the supply water temperature increases. At the flue gas outlet of the appliance a flue gas mass flow of t temperature appears. The of the room mixes to this in the raft hoo an an initial mixture temperature evelops together with an increasing flow through the chimney. The operating point of the chimney can be calculate with iteration cycles by repeating the following steps: 1. From the heat loa of the gas appliance as given by the manufacturer it is possible to calculate the mass flow of the flue gas which leaves the heat exchanger.. The temperature of flue gas can be calculate from equation (15) accoring to the actual return temperature of the heating circuit. 3. y assuming an initial mass flow value for the combustion entering the raft hoo t mix0 an t mixav can be calculate from (3) an (4) respectively. 4. Room mass flow can be etermine with equation () an can be compare with the assume value. 5. Shoul they iffer mass flow has to be moifie an the above escribe iteration process has to be repeate. Iteration is to be continue until esire accuracy is met. At which point the ata for the chimney s operating point is available for the given conition of the heating circuit. 6. The mass flow of combustion has to be recalculate an checke by taking into account the pressure ifference between what is calculate in the raft hoo an what is measure in the room as well as the pressure ifference necessary to accelerate the combustion an the flow resistance of the gas appliance. To calculate the next chimney operating point for the given heating circuit the above escribe metho has to be repeate. 5 Calculation results ase on the moel a calculation program has been create which can calculate the mass-flow of the room entering the raft hoo though not yet the heat balance of the heating system an the room. The program was use in orer to etermine the chimney point an the mass-flow of the room entering the

5 Proceeings of the 3r IASME/WSEAS Int. Conf. on HEAT TRANSFER THERMAL ENGINEERING AND ENVIRONMENT Corfu Greece August (pp6-11) raft hoo when a gas appliance is turne on an the return water temperature is still col. Afterwars the above escribe factors were examine for the case when the return water temperature is alreay hot. Fig.3 reveals an example of the results of the calculation. The mean flue gas temperature the raft cause by the ensity ifference in the vertical section of the chimney an therefore the mass flow of the room all steaily increase. As follows the changes of the characteristic temperature ata of a Vaillant VU18 type wall mounte boiler an the ajoining chimney are presente. In the initial state the boiler is col. In the course of the measurement the boiler an the chimney heat up. Once the operating balance is reache the boiler shuts own followe by a perio of falling temperature. The measure environmental gas- an water-sie characteristics: t room = 11 C t gas = 187 C p gas = 3040 Pa t wsupply = 511 C t wreturn = 83 C m w = 50 Litre/h Figures 4 an 5 inicate a few measurement results. Fig.4 mperature change aroun the appliance Fig.3 Calculation results 6 Examination of the non-steay-state process through measurement Establishing the initial ata for moelling requires measurement ata which escribe the operating parameters of the gas appliances with special regar to non-steay-state operating conitions. Therefore measurements have been conucte to escribe the operating conitions of the boiler an the chimney. The following temperature measurement points were establishe on the equipment in the university epartment s gas technical laboratory: the temperature of the flue gas leaving the gas appliance the temperature of the flue gas mixture close to the point it entere the flue pipe the inner wall temperature of the flue liner once the mixture got into the funnel close to the chimney outlet along the iameter the temperature of the gas mixture an the inner wall temperature of the flue liner. Fig.5 mperature change at the chimney entrance 7 Conclusions In Hungary in the case of the generally use type gas boilers the coorinate operation of the gas appliance an the chimney as well as the supply of combustion is an important question. For the examination of the coorinate operation of the gas boiler an the heate space a mathematical moel nees to be evelope to help escribe the non-steay-state conitions of the heating system an the builing an can also be

6 Proceeings of the 3r IASME/WSEAS Int. Conf. on HEAT TRANSFER THERMAL ENGINEERING AND ENVIRONMENT Corfu Greece August (pp6-11) use also for the examination of the non-steay-state conition of the room s supply appliance chimney. ase on the moel a calculation program has been create which can calculate the mass-flow of the room entering the raft hoo though not yet the heat balance of the heating system an the room. Establishing the initial ata for moelling requires measurement ata. Therefore measurements have been conucte to escribe the operating conitions of the boiler an the chimney. The measurements conucte so far clearly emonstrate the non-steay character of the early stage of the process namely that the ilute flue gas temperature an the inner wall temperature constantly change in the case of intermittently operating boilers. Further steps of moelling inclue the comparison of calculate an measure parameters an improvements on the moel. Nomenclature: A flow cross-section m ; c p specific heat J/kg K; D the characteristic size of the chimney (iameter) m; g gravity acceleration m/s ; H average height of the chimney m; H s combustion heat of the natural gas J/m 3 ; k heat transmission coefficient J/m K; mass flow rate kg/s; M heat capacity p pressure Pa; Q & energy flow rate heat flow rate W; R gas constant J/kgK; t temperature C; T absolute temperature K; U specific surface of the wall of the chimney (surface/length) m; V volume m 3 ; V gas natural gas mass flow entering the gas appliance m 3 /s; w spee m/s; Greek symbols v specific volume m 3 /kg; λ friction factor (-); ρ ensity kg/m 3 ; Subscripts av average comb combustion e outsie flue gas i insie mix mixture r return ra raiator s supply w water References: [1] arna L. Poroszlai I. Légbevezető elemek alkalmazása gázkészülékek helyiségeinek szellőzőlevegő ellátására (Application of Air Inlets for Ventilating-Air Supply of Rooms with Gas Appliances) in: Magyar Épületgépészet Vol. L 001/8 p [] arna L. Gázkészülékek égési levegő ellátásának méretezése 1. rész: A típusú gázkészülékek (Sizing of Air Supply in the Room of Gas Appliances 1 st Part: A Type Gas Appliances) in: Magyar Épületgépészet Vol. LI 00/3 p [3] arna L. Gázkészülékek égési levegő ellátásának méretezése. rész: típusú gázkészülékek (Sizing of Air Supply in the Room of Gas Appliances n Part: Type Gas Appliances) in: Magyar Épületgépészet Vol. LI 00/8 p [4] Homonnay G. (e.) Épületgépészet 000 Vol. I Fűtéstechnika (HVAC 000 Vol. I Heating chnic Épületgépészet Kiaó uapest 001. [5] Krope J. Goricanec D. Analysis of pipe networks incluing pumps. Energy buil.. [Print e.] 1991 Vol. 17 pp [6] Garbai L. arna L. Vigh G. Moelling of Instacioner Conitions in a Space Heate by an Iniviual Gas oiler Gépészet 004 Conference uapest University of chnology an Economics 004 Proceeings pp [7] Garbai L. arna L. Air Supply Moelling in a Room Heate by an Iniviual Gas oiler Energy for uilings 6 th International Conference Vilnius Lithuania 004 Proceeings pp