1、4708 Calibration and Testing of Thermal Simulation Models of Air Heaters Per Blomberg, Ph.D. Elisabeth Mundt, Ph.D. ABSTRACT Detailed measurements of the thermal Characteristics of one one-row and one four-row ducted, hydronic air heating coil have been performed. The measurements were made in a car
2、efully designed andproduced laboratory setup, capable of creating almost perfect step changes of both water flow rate and supply temperature. The heater 3 steady-state character- istics were first modeled. The model was then calibrated with a set of measurements by means ofparameter estimation. Then
3、 a couple of dynamic models, based on the calibrated steady- state models, were tested. Both the calibrations and the behav- ior of the dynamic models are discussed. It is shown that ifthe base has careful calibration of the steady-state characteristics, simple uncalibrated dynamic models can be use
4、d. The measurementfiles are available on CD for anyone interested in testing heater simulation models. INTRODUCTION Computer simulation based on first principle models may well serve in all phases of the building process. In the design phase, simulation may be used to compare alternatives on the bui
5、lding level, determine the characteristics of heating and cooling loads, and make various detailed design studies. Furthermore, simulation may be used to verify that the design fulfils the performance requirements. In the realization phase, simulation may be used to analyze the consequences of chang
6、es. In the commissioning phase, simulation with a detailed model could positively support analysis of the plant and optimization of its operation. When calibrated, the detailed simulation model could predict characteristics of the energy consumption for reference cases and thus help to decide whethe
7、r the building fulfils the performance require- Tor-Gran Malmstrm, Ph.D. Member ASHRAE ments. In the operating phase, the calibrated simulation model could serve a number of purposes. It is a great help when educating the operation and maintenance personnel. The oper- ator could use it to answer “wh
8、at if questions, to produce reference behavior for equipment performing suspiciously, and more. The model could be used in a continuous-commis- sioning scheme and not least in FDD-systems (fault detection and diagnosis). Simulation, thus, is a powerful tool for creating a good indoor climate and for
9、 saving energy. However, many of the options need detailed knowledge of the characteristics of the components. This is especially true for the use of models in the commissioning and operation phases. Model calibration is important to reach this level of detail. This paper has a focus on validation a
10、nd validation meth- ods. The components chosen for the study of the calibration process are air heating coils, common and, from an energy use point of view, important HVAC components. There are two basic modes for control of the heat output from air heaters: Water flow rate control Water temperature
11、 control (with constant water flow) Models should be able to simulate both these function modes. This makes it necessary to calibrate them for both temperature and flow rate changes. Both steady-state calibration and testing of dynamic model characteristics are done. It is shown that if the base has
12、 careful calibration of the steady-state characteristics, simple uncalibrated dynamic models can be used. Useful information about heat transfer characteristics is also presented, as well as examples of simple but good dynamic models. Per Blomberg is with AF Installationsteknik, Stockholm, Sweden. E
13、lisabeth Mundt and Tor-Gran Malstrm are professors, Division of Building Services Engineering, KTH, Stockholm, Sweden. 158 02004 ASHRAE. The base for the calibrations and testing is detailed, with careful laboratory measurements made with an experimental apparatus able to create almost perfect step
14、changes. Many measurements have been made, which can also be used for testing other models. The files can be ordered on a CD. STATIC MODEL Heat Transfer Calculations An air heater is a heat exchanger between water and air. The basis for the modeling, thus, is heat exchanger theory, which is well kno
15、wn and will not be described here. A static model can be used if the time step is much longer than the time constant and the time delay for the whole heating coil. Using the definition of temperature effectiveness, the outlet temperatures then can be expressed as: Two = T,j - Esf. (T,j - Ta,) (la) T
16、wo = water outlet temperature (OC) TWi = water inlet temperature (“C) E = temperature effectiveness Tui = air inlet temperature (“C) Tao = air outlet temperature (“C) crr = ratio of the heat capacity flow rates m;c a hw Cp, crr = ma = air mass flow rate (kgls) h, = water mass flow rate (kg/s) cPa =
17、air specific heat capacity (J/(kg*K) = water specific heat capacity (J/(kg*K) In this study, tests have been made with two air heaters, one-row and four-row. The effectivenesses for two idealized configurations are given in Equations 3 and 4. The one-row cross-flow heating coil is approximated with
18、a cross-flow heat exchanger with one mixed flow and the other flow unmixed (see Incropera and de Witt 1990): 1 - exp(-crr. (1 - exp(-NTU)J err The four-row cross flow is approximated as ideal cross flow with both flows unmixed (Incropera and de Witt 1990): (3) Esf = Eff = 1 - ep(S . (exp(-err . NTU0
19、78) - 1) (4) NTU = number of heat transfer units UA 111,. c NTU = - Pa U A = heat exchanging area (m2) = overall heat transfer coefficient (W/(m2*K) The overall heat transfer is calculated with Equation 6 using the fin efficiency, 6 (see Schmidt 1949). fin surface (m2) tube outer free surface (m2) t
20、ube inner surface (m2) log mean area for the tube wall (m2) tube wall thickness (m) heat transfer coefficient for the water, at the tube inner surface (W/(m*K) heat conductivity for the tube material (W/(m*K) heat transfer coefficient for the fins (W/(m2*K) The flow in the pipes is disturbed by bend
21、s, etc. There- fore, the equations for calculating the pipe inside heat transfer coefficients should be valid for developing flow. The follow- ing two equations were found suitable from an extensive study by the first author (Blomberg 1992). 2300) heat transfer inside the pipes can be calculated wit
22、h Equation 7 formulated by Stephan (1959). For laminar flow (Re (7) 0.0677 . (Re . Pr . u/L). 1 + 0.1 . Pr . (Re. d/L)083 Nulam = 3.66+ Nu = Nusseltsnumber Re = Reynoldsnumber Pr = Prandtlsnumber d = inner diameter of the pipe (m) L = length of the pipe (m) For turbulent flow (Re 2300) heat transfer
23、 inside the pipes can be calculated with Equation 8 formulated by Hausen (1983). 0.8 Nuturb = 0.0235 . (Re - 230) . (1.8 . - 0.8) QJ = dynamic viscosity of the fluid at mean temperature qCis = dynamic viscosity of the fluid at the pipe wall (kgl (kgl(s*ms) (s*ms) In the transient region where the fl
24、ow changes from lami- nar to turbulent flow, the two heat transfer equations are weighted together in order to avoid the discontinuity at Re = 2300, see Equation 9. ASHRAE Transactions: Research 159 2 2 Nu, = Nu, . cos cp +Nutur6. sin nals I 65 60 50 * 45 40 3 55 354 I I I I I I l I i 650 875 700 72
25、5 750 775 800 825 850 Semnds Twcm - Tw71 - Fgure 5 A selection from the measured data $le. The upperjgure shows the temperatures, in “c, which are from the top curve water inlet, water outlet, and air outlet and air inlet. The lower $re shows the mass flow rates. Figure 6 Comparison between the meas
26、ured output and the simulated one (T7lY using the dynamic model with one weighted time constant. The top figure shows the air outlet temperature and the other one the water outlet temperature. Finite-Element Model This finite-element model has a local time step so the liquid flows through one elemen
27、t per local time step. The model has the maximum number of elements set to 200. This number should be behveen 20 and 200 according to experi- ence. The model runs a couple of local time steps and then interpolates to get the temperatures for the global time step. The model sets up the heat transfer
28、for one element taking the heat capacitance of the elements and solves it numerically. COMPARISON WITH MEASURED DATA FOR ONE-ROW COIL In this section, comparison with measured data for a one- row heater is done by inspection of the outlet temperatures for the static and dynamic heating coil models d
29、escribed above. For the calculations, the mean values of the calibration factors were used, for residual minimizing on the air side and water side, respectively. When comparing the simulations (with the different models) and the measured data, the data file shown in Figure 5 was used. The set consis
30、ts of both temperature and flow rate changes. Measurements were taken at 4 Hz, with 0.25 second intervals. Dynamic Model Using One Weighted Time Constant The calculations were made with a time step of 0.25 second, the same as the measurement frequency. For this model, using one weighted time constan
31、t, the predictions follow the measured air outlet temperature quite well. The water outlet temperature is a coupIe of seconds early but reacts slower than the measured outlet water temperature. The temperature water mass flow rate changes are followed quite well. The model seems to work well. Finite
32、-Element Model The model has a good time delay for the outlet air temper- ature, but reacts too quickly, and for the water outlet temper- ature, it has a good agreement on the time delay but then a little too fast response. 164 ASHRAE Transactions: Research 32 30 28 28 24 22 20 1 I Taam Ta74 - - 650
33、 675 700 725 750 775 800 825 850 Seconds 70 65 60 - - TWWn 55 Tw74 50 0 45 40 35 - “ . 650 675 700 725 750 775 800 825 850 swo see Figure 8. CONCLUSIONS Calibration of air heaters has been studied. The studies showed that excellent simulation results were obtained with models with simple dynamics bu
34、t based on careful steady- state calibrations. The steady-state heat transfer modeling used was based on idealized equations for the thermal effectiveness of air heat- ers. The heat transfer coefficients on the air side have been evaluated by fitting measurements to a function: The need for further
35、calibration of the steady-state heat transfer was studied, but in the cases tested, only minor improvements could be gained. Although such calibrations are not simple, they are possible to make also in real building installations. Calibration of dynamic models is much more 32 30 Taom Tan - * 28 1 26
36、 - 24 22 20 4 I I l I I 650 875 700 725 750 775 8M) 825 850 sem* I Figure 8 Comparison between measured air temperature values and values simulated with a model taken from a well-known simulation package. The mass pow rate changes in the last hundred seconds of thejle cause instability in the calcul
37、ations. This didnt occur at smaller change rates. difficult, as there is a need for controlled step and ramp flow rate and water temperature changes. Therefore, no rigorous calibration of the dynamic part of the models was performed. Instead all the models used the calibrated steady-state part in or
38、der to make comparisons of the dynamics possible, and the dynamics even of simple models were found good enough for HVAC simulations. It is interesting to note that more detailed dynamic model- ing had a rather small impact on the results and caused no improvements in the cases tested. This is not g
39、enerally the case-for instance, it does not apply to pipes. For coils with more than one row, the situation is more complex than for one-row heaters, both for static and dynamic models as indicated earlier. This is due to the often very irreg- ular pipe arrangement, introduced to achieve certain fea
40、tures in coil function (cross-flow or counterflow). The numerical implementation of such cases also is more complicated regarding the administration of calculation routines. However, according to our experimental results, the dynamic responses (as expected) are slower than for one-row coils, i.e., t
41、he effec- tive time constant is longer due to the larger heat capacity. This decreases the impact of fluid transport delay within the coil. Thus, it is reasonable to expect that model dynamics working for one-row coils will be approximately applicable to multi- row coils. The study was made for coil
42、s with a front area of 0.3*0.3 m2. We feel, however, that the results can be applied also to larger coils (limitations are as mentioned, that the air front velocity should be in the range 1-5 ds and the length ofpipes between distributor and collector tube between 3 and 10 m). The methodology descri
43、bed can also be applied to dry cooling coils. ACKNOWLEDGMENTS The authors are indebted to FORMAS (The Swedish Research Council for Environment, Agricultural Sciences and Spatial Planning) and STEM (The Swedish Energy Agency) for funding this work. ASHRAE Transactions: Research 165 REFERENCES Blomber
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48、rflow, Parallel Flow und Crossflow. Mc Graw-Hill, pp. 22-37. Holmes, M.J. 1982. The simulation of heating and cooling coils for performance analysis. Proc. System Simulation in Buildings. Lige. 75-87. Incropera, F.P., and D.P. de Witt. 1990. Fundamentals of Heat and Mass Transfer. New York: John Wil
49、ey&Sons. Isermann, R. and H. Jantschke. 1970. Das regeldynamischen verhalten Wasser- und dampfbeheizter kreuzstrom- wrmebertrager in klimaanlagen. Regelungstechnik und prozessdatenverarbeitung. Heft 3. Jensen, L. 1978. Digital reglenng av klimatprocesser. LTH, Lund. Novakovich V. 1982. Digital regulering av varmebatterier. NTH Trondheim. Schmidt, T.E. 1949. Heat transfer calculations for extended surfaces. Journal of the ASRE, April, pp. 351-357. Spirkl, W. 1990. Dynamic SDHW testing. J. of Solar Energy Eng., Transaction of the ASME, 112:98-101.
