VALIDATION OF A FULLY-MIXED MODEL FOR SIMULATING GAS-FIRED WATER STORAGE TANKS. Weimin Wang, Ian Beausoleil-Morrison, Martin Thomas, Alex Ferguson

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1 VALIDATION OF A FULLY-MIXED MODEL FOR SIMULATING GAS-FIRED WATER STORAGE TANKS Weimin Wang, Ian Beausoleil-Morrison, Martin Thomas, Alex Ferguson CANMET Energy Technology Center, Natural Resources Canada 0 Booth Street, Ottawa KA 0E4 ABSTRACT An ESP-r comonent model for gas-fired water storage tanks was develoed within the context of the simulation for building-integrated cogeneration systems. Charged by the cogeneration unit with gas back-u, the tank can be used to satisfy both domestic hot water needs and sace heating. Based on the fully-mixed water assumtion, the model has three control volumes reresenting the water and casing, the combustion chamber, and the flue gas. The exerimental data used in this validation study comes from nine grous of tests, covering four commercial water heaters and three different water drawing schedules. The validation is carried out via a lant network with two comonents: the water tank and a boundary condition. It is found that the model can redict the mean tank temerature well. However, the fully-mixed assumtion may lead to an underestimation of energy consumtion by 8-5%, deending on the water drawing schedule. KEYWORDS Water tanks, Comuter simulation, Emirical validation, Thermal stratification INTRODUCTION There is growing interest in using a water storage tank to satisfy both sace heating and domestic hot water needs for residential buildings. Such a combined system offers the otential advantages of art-load erformance imrovement and caital cost reduction (Weiss Since the water tank is usually charged by the energy from solar collectors or other comonents which may not work continuously, an auxilary heater is needed to maintain a set temeratere in the tank. Modelling water storage tanks has been a research toic for many years. Many mathematical models, exeriments, and simulation rograms have been reorted in the literature, esecially in the field of solar water heating. Since the inlet temerature to solar collectors has substantial imact on the erformance of solar thermal systems, most revious studies focus on modelling thermal stratification and the resulting temerature rofiles in the water tank. The degree of stratification is affected by the following major factors (Shyu et al. 989: thermal mixing and the forced convective flow due to water draws; the natural convective flow due to the heat loss to the surrounding and thermal diffusion from hot layers to cold layers. These factors are considered in available models with varying degrees of comlexity. For examle, two dimensional models are resented in (Cabelli 977; Lightstone et al. 989; Oliveski et al to consider the imact of charging or discharging water on stratification. Shyu et al. (989 investigated the effects of tank wall and insulation on thermal stratification. Zurigat et al. (989 comared six one-dimensional models for stratified water storage tanks. Different mechanisms are emloyed in these one-dimensional models to consider thermal mixing at water inlets. While twodimensional models are more owerful in accounting for different factors affecting stratification, they are comutationally exensive and reuire detailed inut data, which could render them unsuitable for use in building simulations. In TRNSYS, for examle, all four models (Tye 4, 35, 60 and 40 for water storage tanks follow the one-dimensional aroach: the tank is divided into a number of isothermal layers and mass and energy balance euations are established for each layer. These four TRNSYS models have different features such as the number of inlets, outlets, immersed heat exchangers and auxiliary heaters, and the method to consider heat loss to the surrounding (Druck and Pauschinger 997; Klein et al Although the auxiliary heater can be heated by either electricity or gas, the TRNSYS models treat the gas heater simly as an electrical one with a flue. The model examined in this aer was develoed secifically for gas-fired water storage tanks. It was develoed for use in modelling residential cogeneration systems, the erformance of which is less sensitive than solar thermal systems to water inlet temerature. Therefore, stratification is not considered at the current stage for the sake of simlicity. The current aer examines the validity of this model. It studies the model s accuracy in redicting energy consumtion and the difference between simulated tank temerature and the outlet temerature. The uantified deviation will be used as a reference in future erformance assessment of cogeneration systems. This aer is organized as follows. The mathematical model is described next. Then, sections 3 and 4 give an introduction of the - 8 -

2 exerimental data and how the model inut data are reared based on the exerimental data. The ESP-r simulation model is briefly resented in section 5. The simulation results are comared with the exerimental data in section 6. Some concluding remarks are made finally. GAS-FIRED WATER STORAGE TANK MODEL In ESP-r (Clarke 200, each lant comonent is reresented by one or more discrete control volumes (nodes. For each node, the governing euations are established according to the rinciles of conservation for mass, energy and momentum. For the gas-fired water storage tank, the model was develoed with three nodes (Figure : node for the water and casing; node 2 for the combustion chamber; and node 3 for the flue. This three-node aroach was used because it facilitates future exansion to incororate exlicit combustion modeling and the heat transfer rocesses between the flue and the water tank (Beausoleil-Morrison 200. The energy balance euation for each node is described next. from cogeneration (T cg loss to cogeneration fuel air exhaust-gases flue (node 3 flue-gases combustion chamber (node 2 water & casing (node DHW to fan coil from fan coil (T coil from mains (T m Figure Three-node reresentation of gas-fired storage water tank Energy balance for node The water tank model was develoed within the context of the simulation for building-integrated cogeneration systems. Charged by the cogeneration unit with gas back-u, the hot water can be sulied to the fan coil for sace heating and various outlets for domestic hot water (DHW needs. Based on the connection scheme in Figure, the energy balance for the water and casing (node is given as: T (Mc = loss + (mc & t + (mc & (T + (mc & coil r cg DHW (T (T cg m ( where, the term on the left side reresents the heat storage of the water tank; on the right side, is the heat transferred to the water from the flue gases, loss is the skin heat loss from the tank casing, the 3 rd to 5 th terms reresent the net energy flows from the cogeneration unit, the fan-coil for sace heating, and the water mains for DHW make-u, resectively. Since the heat transfer rocess between the flue and the water tank is not exlicitly modeled in the current stage, the term is simly derived from the the following euation: = μ (2 burner where, burner is the energy released by the fuel s combustion and μ is the overall efficiency of combustion and of the heat transfer between the flue and water. The value of μ is eual to the fraction of the energy released by the fuel s combustion that is transferred to the water. The overall efficiency is assumed to be constant in this model and given as a user inut. The skin heat loss from the water tank to its surrounding is calculated with loss = (UA (T (3 env where, UA is heat loss coefficient, T env temerature of environment. Energy balance for nodes 2 and 3 is the The energy balance euations for node 2 and node 3 are given as: & + & & (4 ( mh fuel (mh air + burner = (mh flue gases ( mh & & + (5 flue gases = (mh exhaust gases In the above euations, the flow rate of fuel, air, and flue gases, and the enthaly of the fuel and air streams entering the combustion chamber are calculated based on the molar fraction of fuel constituents, the excess air ratio, and the burner caacity. The linearization aroach can be used to relate the enthaly of flue gases and exhaust gases to the corresonding node temerature. The detailed descrition of these calculations can be found in (Beausoleil-Morrison 200. According to the chosen imlicit/exlicit scheme, euations, 4, and 5 are used to derive the energy balance matrix coefficients for the gas-fired water tank. These coefficients are then embedded into the integrated matrix for all the lant comonents of the HVAC system. The matrix euation is solved in ESP-r with a direct solution aroach to obtain the three node temeratures. Since the euation set is - 9 -

3 highly nonlinear, iteration is reuired to udate and resolve the matrix until convergence is achieved. EXPERIMENTAL DATA Exerimental data were gathered from a series of tests carried out at Natural Resources Canada. The urose of these tests was to measure the energy consumtion and efficiency of gas-fired water heaters. Four different water heater models were used in the tests: model A is a ower-vented water heater, which uses draft fans to ush the exhaust gases away; models B and C are conventional water heaters, which use room air for combustion and natural draft for the exhaust; model D is a direct-vented water heater, which draws air from outside the building directly into the combustion chamber. Three water draw schedules were used in the tests: the draw schedule secified in the standard CAN/CSA-P.3-04 (CSA 2004, the draw schedule used at the Canadian Center for Housing Technology (CCHT 2007, and a hyothetical draw schedule seculated by the tester. The CSA schedule has a total of six draws for a simulated day. Each draw starts at the beginning of the first six hours and has a volume about 40.6 L. The CCHT schedule has a total of eight draws er day. The corresonding volume and time for each of the eight draws are secified as 25 L/7:00, L/8:00, 8 L/3:00, 27 L/8:00, 4 L/9:00, 9 L/20:00, 34 L/2:00, and 39 L/23:00. The hyothetical schedule has a draw every hour. Each draw starts at the th minute and has a volume of about 6 L. All water heater models were tested following the CSA schedule while only model A was tested following the CCHT schedule and the hyothetical schedule. Table gives an overview of all the tests covering different water heater models and water draw schedules. HEATER MODEL A B Table : Overview of tests VENT TYPE ower-vented conventional TEST DRAW SCHEDULE A- CSA A-2 CSA A-3 CCHT A-4 CCHT A-5 hyothetical B- CSA B-2 CSA C conventional C- CSA D direct-vented D- CSA The exeriment was set u according to the standard CAN/CSA-P.3-04 (CSA All tests start just after cut-out, which is the moment in time when the water heater thermostat has acted to reduce the fuel suly to the burner to its minimum (zero if no ilot ower exists. Due to different uroses of the original tests, the CSA scheduled tests differ from the tests with the other two schedules in the following two asects: The inlet water temerature. For the CSA scheduled tests, the water suly to the water heater inlet is maintained at a constant temerature of about 4 ºC. In contrast, for the tests with the CCHT and hyothetical schedules, the suly water is directly taken from the water mains and its temerature may vary between 5 and 0 ºC. The data measurement in terms of scoe and freuency. For the CSA scheduled tests, the following data were measured every two seconds during the six water-drawing eriods and ten seconds during the standby eriod: the concentration of O 2, CO, CO 2, and NO in the flue gas, the water inlet and outlet temerature, the water flow, the room temerature, the flue gas temerature, and the tank water temerature. In articular, the tank water temeratures were measured with six thermocoules eually distributed along the vertical line of the tank. Besides the above regular measurements, gas consumtion was measured for all burner-on eriods during the test. For the tests with the CCHT and hyothetical schedules, the measurements are limited to the water inlet and outlet temerature, the water flow, the room temerature, and the gas consumtion. These measurements are recorded every twenty seconds. CALIBRATING MODEL The exerimental data are used to calibrate the reviously described model in order to establish the model inuts. The calibrated model inuts include the heat loss coefficient UA, the overall efficiency μ, the ilot ower ilot, and the excess air ratio. Since the tests originally aimed at determining the efficiency of gas-fired water heaters, the measured data can be conveniently emloyed to calculate the water heater s recovery efficiency, which is defined as the ratio of the energy imarted to the water to the energy content of the fuel consumed by the burner during the eriod that the water temerature is raised from the inlet temerature to the final temerature, with the tank filled to caacity (CSA The recovery efficiency is then used as the basis to calculate both UA and μ

4 The recovery efficiency η of a gas-fired water heater is comuted as (CSA 2004: Mc(Tout in + Mc2(Tmax, 0 η = (6 Q where, M is the mass of water withdrawn during the first draw, M is the mass of water in the tank, Tout and Tin are the average outlet and inlet temerature for the first draw, Tmax, is the maximum mean tank temerature recorded after the first cut-out, T0 is the mean tank temerature rior to the first draw, c and c2 are the secific heat of water resectively at ( Tout + Tin / 2 and ( Tmax + T0 / 2, Q is the energy consumed in the first drawing eriod (from the start of the test to the first cut-out. Considering that the heat loss coefficient UA is regarded as a constant in the model, it is better to derive its value that can mostly reresent the water heater states in terms of the mean tank temerature and the burner status. Therefore, the calculation of UA is based on the standby eriod lasting from the time at which the maximum mean tank temerature is observed after the sixth draw to the end of the test. The UA is calculated as: UA = T Q = τ t, η Mc (T a, t, (T 24 a, max,6 (7 where, is the standby loss rate, Q is the total energy consumtion during the standby eriod, Tt, and Ta, are resectively the average water temerature and ambient temerature during the standby eriod, T 24 is the mean water temerature at the end of the test, T su is the maximum mean water temerature observed after the sixth draw, τstdby is the length of the standby eriod. The overall efficiency (μ used in the model does not take the same value as the recovery efficiency (η calculated from Euation 6. This is because the heat loss to the surrounding is considered by η but not by μ. Therefore, the following euation is emloyed to calculate μ from η: UA τ (T t, a, μ = η + (8 Q where, Tt, and Ta, are resectively the average water temerature and ambient temerature during the first drawing eriod, τ is the length of the first drawing eriod. It is observed that for the tested water heaters with ermanent ilot, the burner is not activated during the standby eriod. Hence, the ilot ower can be simly calculated as: ilot Q = (9 τ The excess air ratio is calculated based on the O 2 concentration in flue gas, the molar fraction of fuel constituents, and the chemical reactions involved in fuel combustion. The details are not resented here due to sace limitation. With all the euations described in this section, the model inut data for the CSA-scheduled tests are calculated and the results are given in Table 2. The model inut data for the tests with the CCHT schedule (A-3 and A-4 and the hyothetical schedule (A-5 take the average of tests A- and A-2 because the tank temerature was not recorded. Table 2 also lists the rated burner-on caacity and the calibrated tank volume. burner on ESP-R SIMULATIONS Since this study aims to validate the tank model s rediction when subjected to external loads, a lant network is created with two comonents: a gas-fired water tank and a boundary condition. The boundary condition is used as the water flow source for the tank. With only one connection alicable in this study, the 3 rd and the 4 th items at the right side of euation will vanish while for the existing 5 th item, both the water flow rate and water inlet temerature are fed from a boundary condition file. This file has a one-minute freuency of data records; therefore, the original test data are rocessed in the following ways to obtain the reuired boundary conditions: The water flow rate in kg/s derives from the measured water flow in L for every minute. Since the water flow may not last for a whole minute, the derived flow rate may take different values during the water drawing eriods. This difference has negligible imact on simulation results because each draw is short in time (about 4 minutes and for each draw the total volume withdrawn from the tank kees the same value as that for the exeriment. The water inlet temerature T m is averaged only for those data records with non-zero water flow, instead of all data records within a minute. This treatment is necessary because a water draw may not last for a whole minute. In this ESP-r simulation model, the gas-fired water tank uses a temerature-based control. The burner is fired if the tank temerature is less than the signal on setoint temerature or if it was on for the Tset on

5 revious time ste and the tank temerature is less than the signal off setoint temerature Tset off. The well-mixed nature of the water tank model determines that the mean tank temerature needs to be used as the setoints. Therefore, both and Tset off Tset on are extracted from the exerimental data by averaging the mean tank temeratures corresonding to the change of burner status from off to on or vice versa during a test. The established ESP-r model assumes that the tank locates at a room with a constant temerature, which takes the average value of all measured room temertatures for each test. This assumtion is reasonable because the room temerature has only a small fluctuation of about 0.5 ºC. COMPARISON OF MODEL PREDICTIONS TO EXPERIMENTAL DATA After running the simulation, the results are comared with the exerimental data. The comarison in this aer concentrates on the tank temerature and the energy consumtion. Figures 2 and 3 resectively show the change of tank temerature during the water-drawing eriods and the standby eriod for test B-. These two figures lead to the following observations: Generally, the redicted mean tank temerature comlies well with the test data. One most significant temerature difference (about.4 ºC occurs at the end of cut-out following the first draw (Figure 2. This difference is mainly due to the deviation of observed temerature setoints for different on-off cycles. It is found that the mean tank temerature at the first cut-out is about 0.9 ºC lower than the Tset off value used in the model inut. During the subseuent hour after each cut-out, the redicted tank temerature decreases faster than the test data (Figure 2. This is because thermal mixing and the residual heat transfer from the flue to the tank after the burner off are not considered in the model. In addition, because the thermal mixing due to water draws and the start-u characteristics of the burner are not considered in the model, the tank temerature increases right after the burner is fired while there is a time lag in the test. The time lag can exlain the difference of about.5 ºC between the simulation and the test when the tank temerature begins to increase (Figure 2. In the standby eriod (Figure 3, the temerature vs. time curves for the simulation and the test are close and almost arallel with each other. This Temerature ( o C Temerature ( o C observation demonstrates that the heat loss to the surrounding is modeled correctly with its UA value. 48 simulation test 46 09:49 0:49 :49 2:49 0:49 02:49 03:49 Time Figure 2 Comarison of tank temerature in the water drawing eriods for test B simulation test 46 03: 05: 07: 09: : 0: 03: 05: 07: Time Figure 3 Comarison of tank temerature in the standby eriod for test B- Similar trends of tank temerature change with time are found for other CSA-scheduled tests excet for the water heater model A. For examle, Figure 4 shows the change of tank temerature for test A-. In contrast to other tests, the burner is fired in the standby eriod because the model A has no ilot ower. Moreover, there is an asynchronous change of burner status: the burner is fired earlier and shorter in the test than it in the simulation. This difference can be exlained via the temerature setoints defined in this study. Recall that the setoints are derived by averaging the mean tank temeratures corresonding to the change of burner status. Hence, the control used in the simulation is an aroximation of the actual control, which deends on the thermostat located in between the 3 rd and the 4 th thermocoules. Meanwhile, the change of sensed

6 temeratures has different characteristics due to water draws and standby losses. As illustrated in Figure 5, the lower arts of the tank (e.g., T 4 and T 6 have much lower temeratures after the water drawing than they have in the standby eriod, while the uer arts of the tank (e.g., T and T 3 have higher temeratures after the water drawing than they have in the standby. In other words, the tank is more stratified after the water drawing. The overall conseuence is that in the standby eriod, the mean tank temerature is still higher than the derived value Tset on (=. ºC when the burner is fired in the test while it is still lower than Tset off (=.46 ºC when the burner is off. Temerature ( o C Temerature ( o C simulation test 48 0:36 3:36 6:36 9:36 22:36 :36 4:36 7:36 Time Figure 4 Comarison of tank temerature over the whole test eriod for test A- interval between 5th and 6th draw th draw and the following burner-on standby T T3 T4 T6 Tavg 34 4: 5:38 7:35 20:55 0:5 3:35 Time Figure 5: Measured temeratures at different levels and the mean tank temerature for test A- The third column in Table 3 lists the redicted energy consumtion for all cases. Comared with the exeriment, the simulation model has about 8% underestimation for the two CCHT scheduled tests (A-3 and A-4. The degree of underestimation is as large as about 5% for all other tests with the CSA schedule and the hyothetical schedule. The underestimation comes from the assumtion of wellmixed water in the tank. Under this assumtion, the energy delivery due to water flow is calculated as ( c m & DHW(Tm, instead of ( c m & DHW(Tm out. However, due to stratification, the mean tank temerature T differs from the outlet temerature T out. For examle, Figure 6 shows their difference for the six water draws in test B-. This figure demonstrates that T may be more than 0 ºC lower than T out. To examine the imact of using different temeratures T and Tout on energy consumtion, the delivered energy is calculated in the above two ways for each time ste. Then, the delivered energy is integrated together for all time stes and the results are given in Table 4. This table demonstrates that the temerature difference between T and T out causes about 65-95% of the underestimated energy consumtion. The rest of underestimation may be due to other factors such as the inaccuracy of exerimental measurements and the simulation model inuts. Temerature ( o C Draw Tout T Figure 6 Comarison of outlet temerature T out and mean temerature T over the six draws in test B- The imroved accuracy of redicted energy consumtion using the outlet temerature Tout motivates the idea of reresenting the items of delivered energy from the tank connections in Euation directly as the energy flow. For examle, the third item and the fourth item can be relaced with the useable heat generation rate of the cogeneration unit and the heating load of the sace, resectively. Thus, the modified euation takes the following form for this study: T (Mc = t = loss loss + + (mc & delivered DHW (T m out (

7 The T out values are fed into the model via the boundary condition file and they are obtained from the exerimental data through the same rocessing rocedure as those for the item T m. Based on Euation 0, the simulation model is rerun for each case and the results are resented in the rightmost column of Table 3. Because the imact of stratification on energy consumtion has decreased significantly in Euation 0, the degree of underestimation reduces to less 6%. For some cases such as A-3, B- and B-2, there is negligible deviation between the simulation and test in terms of energy consumtion. CONCLUSIONS A model for simulating gas-fired water storage tanks is resented in this aer. This model assumes that the tank water is well-mixed. The model s accuracy in redicting tank temerature and energy consumtion is comared with nine grous of exerimental data for commercial water heaters. The comarison leads to the following conclusions: The redicted mean tank temerature generally comlies well with the test data. The major source of redication error comes from the temerature setoints. The redicted mean temerature is about 4-2 ºC lower than the outlet temerature for most draws. Because of the fully-mixed assumtion, the model underestimates energy consumtion. The degree of underestimation deends on the water draw schedules: 8% of underestimation is found for the schedule imitating a normal house in Canada and about 5% of underestimation found for freuent, large volume water draws. The difference of outlet temerature and mean temerature is the main reason of underestimation. The error of redicted energy consumtion can be reduced to less 6% by directly using the energy flow to establish the energy balance euation for node. Major future work lies in two asects: the consideration of stratification and the exlicit modeling of combustion and flue-to-water heater transfer. NOMENCLATURE C secific heat (J/kg-K h enthaly (J/kg M mass (kg m& mass flow rate (kg/s heat flow rate (W Q energy (J T temerature (K UA heat loss coefficient (W/K t, τ time (s η recovery efficiency of water heater μ overall efficiency of burner REFERENCES Beausoleil-Morrison I Design of fuel cell comonent model for FCT roject, Internal Reort for CANMET Energy Technology Center in Ottawa, Natural Resources Canada, 6 ages. Cabelli A Storage tanks-a numerical exeriment, Solar Energy. 9:45-. CCHT htt:// accessed in February, Clarke JA Energy Simulation in Building Design, 2 nd edition. Oxford: Butterworth- Heinemann. CSA National Standard of Canada CAN/CSA- P Testing Method for Measuring Energy Consumtion and Determining Efficiencies of Gas-fired Water Heaters. Canadian Standards Association. Druck F, and Pauschinger T Multiort Store: model for TRNSYS Tye 40. University of Stuttgart (Germany, 25 ages. Klein SA, et al TRNSYS, version 6. Solar Energy Laboratory, University of Wisconsin. Lightstone MF, Raithby GD, and Hollands KGT Numerical simulation of the charging of liuid storage tanks: comarison with exeriment, ASME Journal of Solar Energy Engineering. (3: Oliveski RC, Krenzinger A, and Vielmo HA Comarison between models for the simulation of hot water storage tanks, Solar Energy. 75(2: Shyu RJ, Lin JY, and Fang LJ Thermal analysis of stratified storage tanks, ASME Journal of Solar Energy Engineering. : -6. Weiss W. (Editor Solar heating systems for houses: a design handbook for solar combisystems. London : James & James. Zurigat YH, Maloney KJ, and Ghajar AJ A comarison study of one-dimensional models for stratified thermal storage tanks, ASME Journal of Solar Energy Engineering. (3:

8 Table 2: Technical arameters and model inuts for CSA-scheduled tests TEST η UA μ ilot burner-on VOLUME (W/K (W (kw (L A A B B C D Table 3: Comarison of energy consumtion between exeriment and simulation based on different energy balance euations on node BASED ON EQUATION BASED ON EQUATION 0 MEASUREMENT TEST (KJ PREDICTION DEVIATION PREDICTION 2 DEVIATION 2 (KJ (% (KJ (% A- * A-2 * A A A B B C D * Note: the energy consumed in the standby eriod is not accounted because of the serious asynchronous change of burner status as shown in Figure 4. Table 4: Comarison of delivered energy using different temeratures and its imact on simulation results TEST [] DELIVERED ENERGY (KJ [2] DELIVERED ENERGY 2 (KJ [3] cm(t & m out cm(t & m RESULTED DIFF. IN GAS ENERGY (KJ [4] ([ 2] [3] / η SIMULATION DEVIATION (KJ [5] # measurement rediction A A A A A B B C D ACCOUNTABLE DEVIATION (% [6] # Note: the values in column [5] are calculated as the difference of energy consumtion between measurement and the simulation based on euation, the values of which are from Table