| Method | Pros | Cons |
|---|---|---|
| Comparative | No input problem
Any level of complexity Inexpensive & quick |
No truth standard |
| Analytical | No input uncertainty
Exact truth standard Inexpensive |
No test of model
Limitedno. cases |
| Empirical | Approximate "truth"
Any level of complexity |
Data uncertainty
Expensive & time-consuming Limited number of cases |
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First published as:
`On the thermal interaction of building structure and heating and ventilating
system'.
Doctorate thesis by Jan L. M. Hensen, 1991.
Computer simulation of heat and mass transfer in building and plant configurations may be thought of as a two step process: (1) modelling of the real physical processes at play, allowing the problem to be solved more easily within practical constraints, and (2) numerical solution of the resulting models. Both steps involve simplifications, assumptions, and are likely to introduce errors in the resulting computer code. Verification and validation is necessary, in order to be able to use the program with confidence.
Verification and validation is thus essential when developing computer simulation programs. It should be noted however, that inaccurate prediction results are not always due to program errors. In their report on validation of building energy analysis simulations, Judkoff et al. (1983) identify seven main sources of error, which given the context of heat and mass transfer in building and plant configurations, translate into:
1. differences between the actual weather conditions surrounding the
building and plant and the weather assumed in the simulation;
2. differences between the actual effect of occupant behaviour and those
effects assumed by the user;
3. user error in deriving building and plant input files;
4. differences between the actual thermal and physical properties of the
building and plant and those input by the user;
5. differences between the actual heat and mass transfer mechanisms operative
in individual components and the algorithmic representation of those mechanisms
in the program;
6. differences between the actual interactions of heat and mass transfer
mechanisms and the representation of those in the program; and
7. coding errors.
The error sources 1 through 4 are called external since they are independent of the internal workings of the method of calculation. External errors are not under the control of the developer of the computer program. Error sources 5 through 7 are called internal and are directly linked to the internal workings of a prediction technique. Internal errors are contained within the coding of the program.
This chapter will concentrate on internal errors; i.e. the ability of the simulation program to predict real building and plant performance when given perfect input data. The following sections elaborate the origins of a validation methodology, and by means of specific case studies, how this information may be applied to the program described in this thesis. Although it is recognized that validation is extremely important, the validation activities within the current project, had to be restricted to these examples due to lack of available resources. Two factors may be brought to attention in order to further justify this:
(1) A number of the presented plant component models stem from research projects which incorporated verification and validation of those models (see eg IEA (1984) or Lebrun and Liebecq(1988));
(2) ESP is already the subject of an extensive validation project. This project is briefly introduced in the following section. Finally, the last section of this chapter, identifies possible directions for future validation activities.
Ever since the emerging of building energy simulation models, their developers have been involved in verification and validation studies. Usually this involved comparison of measured data with predictions from some specific model by an individual research team (eg. as reported by Lammers 1978). There have also been at least three studies which attempted to establish a more general validation methodology applicable to building energy simulation programs. The first (IEA 1980) comparison load determination and second, reported by Judkoff et al. (1983), methodology resulted in a three part methodology involving inter-model comparisons, analytical tests, and the use of empirical data. The advantages and disadvantages as summarized by the authors of each of these three parts are indicated in Table 6.1
Table 6.1 Validation techniques from: (Judkoff et al. 1983)
This methodology was further refined and extended in the third study as reported in (BRE/SERC 1988), by Irving (1988) and by Bloomfield (1989). Evaluation procedures building thermal simulation programs. The authors state that:
"The word validation is much misunderstood. It is not feasible
to verify the
correctness of every path through detailed dynamic thermal simulation programs,
to investigate every assumption and approximation, or to take account of
every situation in which a program might be used in practice. A working
definition of validation was adopted: the testing of the theoretical (physical)
correctness of a program and of the mathematical and numerical solution
procedures used." They propose a five stage validation methodology
comprising:
This approach was also adopted by the 'model validation and development sub-group' (MVDS) of a collaborative European Community research project in the field of Passive Solar Architecture known as PASSYS. The principal objective of the MVDS, which involves research consortia from ten EC countries, is to approve/define a European validation methodology and to test this by applying it to a common model, ESP. A complete description of the MVDS work may be found in (CEC 1989). As described by Clarke (1990), some eight climate and building side sub-systems were identified as candidates for validation studies in this way. In addition, and principally by the mechanism of empirical validation and sensitivity analysis, an attempt has been made to evaluate ESP R 's performance at the whole model level. Although none of the validated sub-systems nor the version of ESP R that was researched by the MVDS incorporates plant simulation features, the above is mentioned here to indicate that the current research starts from a sound basis and from notably the most stringently verified and validated building energy simulation model available today. To indicate how the above mentioned methodology may be applied to the current extensions of the ESP energy simulation environment, this section now continues with some case studies exemplifying the various verification and validation stages. Due to the nature of the available data, most case studies incorporate inter-model comparison to some extent.
Theory and code examination is perhaps the most important step of the verification and validation methodology. However, this step is often underestimated. Good examples of theory examination may be found in the IEA Annex X (Lebrun and Liebecq 1988) and the PASSYS (CEC 1989) reports. Both cases involved cross referencing of each other work by different research groups. Regarding examination of the underlying theory of fluid flow and plant simulation in the present work, the reader is referred to the previous chapters. Inspection of the corresponding source code is difficult to exemplify. Suffices to remark that all code has been thoroughly checked with computer aided software engineering (CASE) tools (Kruyt 1989) for any syntax errors. The code is very modular structured and heavily commented in order to be more or less self documentary.
The inbuilt trace facilities may be enabled by the user to track the simulation process at a detailed level during run-time. Were possible, the user supplied input data is checked prior to the actual simulation (for example whether or not the user has defined a valid plant network). As indicated in the previous chapters, a number of parameters is checked during run-time (for instance whether or not the flow is actually laminar in a component expecting such).
Figure 6.1 Network of fluid flow components arranged in series and parallel
As an example of analytical verification, consider the network of fluid flow components which is schematically drawn in Figure 6.1. This problem was introduced by Walton (1989) to test his AIRNET air flow network simulator. It is a relatively complex network of 'common orifice flow' components (type 40). The problem involves 12 nodes and 20 fluid flow components arranged in series and parallel. The pressure-flow relationship for these type of components (see Section 4.4.4.) can be written as:
(6.1)
where C=CdAsqrt{2 rho}, in which Cd is the discharge factor (-), A is the opening area (m2), and rho is the fluid density (kg/m3). Starting from equation (6.1), it is easy to combine parallel flow components into a single replacement component. For example the combination say Ca of the components C1, C2, and C3 is given by:
(6.2)
It is also possible to convert components in series into a single replacement component. For instance the combination say Cb of C10 through C14, is given by:
(6.3)
Table 6.2 Discharge factor CD and area A of fluid flow components (type 40: common orifice flow) in Figure 6.1
In this way it is feasible to derive one single replacement component Ctot for the whole network, for which it is then easy to analytically compute the fluid mass flow rate given some pressure difference between the two outermost nodes. Starting from the parameter values as indicated in Table 6.2., it may be deduced that for this network the mass flow rate evaluates to dot{m}=0.0611024kg-1 for P1- P2=100 (Pa) and rho=1.20415(kgm -3). Actually, by choosing the parameters to represent a combination of large and small flow resistances, a network results which is known to be difficult to solve. When setting the relative and absolute convergence criteria parameters to 1x10-4 and 1x10-4kg-1 respectively, mfs computes the 'true' mass flow rate dot{m}=0.06110 kg-1 in 32 iterations. Walton's AIRNET needs 12 iterations for the same result. It should be noted however that AIRNET needs additional input parameters, in order to enable its linear initalization process. It is also worth mentioning here that when the Steffensen convergence acceleration mechanism (see Section 4.3.3.) would be disabled, mfs would not converge to a solution. Probably due to its previously mentioned linear initalization process, AIRNET will converge without the convergence accelerator, but would need 157 iterations under these circumstances.
As an example of inter-model comparison, simulation results for the boiler model with aquastat control (type 260; see Section 5.4.8.) were compared with results as reported by Dachelet et al. (1988). They compared experimental data with results calculated with the (original) TRNSYS (SEL 1988) version of the boiler model. Here, results calculated with the bps implementation of the same boiler model are compared to both the experimental data and to the results as computed with TRNSYS.
The boiler under consideration is a relatively small unit of 27 (kW) nominal heat output. The parameters describing the boiler are collated in Table 6.3.
Table 6.3 Parameters describing the boiler under consideration (ie of
type
260:2 node model & aquastat control)
This boiler was subjected to a series of tests in a laboratory facility, covering full as well as part load and stand-by conditions. Table 6.4. comprises all test conditions which are necessary as inputs to the model as well as some of the results.
Table 6.4 Inputs to the boiler model and some results; experimental data (derived from: Dachelet et al. 1988)
In bps the boiler model was incorporated in a small plant network consisting of a temperature source component model (type 900), the boiler, and a pump (type 240). The water node of the temperature source was controlled to set the supply temperature for the boiler (theta1), and the pump was controlled to deliver the water mass flow rate (dot{m}w); both are inputs as defined in Table 6.4. This plant network was then simulated during a number of time steps so as to achieve steady-state conditions. The final results with respect to computed global boiler efficiency and burner operation rate are collected in respectively Figure 6.2 and Figure 6.3. These figures also show the results as predicted by the TRNSYS version of the boiler model, and enable comparison of predictions with measurements results.
From Figure 6.2 and 6.3, it is apparent that the TRNSYS version of the boiler model and the bps implementation give almost identical results. Some discrepancy may be observed for the results for test 13 of Table 6.4. Given that the inputs for test 13 seem to be exactly the same as for test 9, it was concluded that there is probably a typing error in the data as presented by Dachelet et al. (1988). This is indeed the case, as was found out after communication with the authors. The boiler inlet temperature for test 13 should read 45.2 instead of 54.3°C. With the new inlet temperature, the results for the two models were almost identical.
Figure 6.2 Inter-model comparison of boiler component predicted versus measured global efficiency
Figure 6.3 Inter-model comparison of boiler component predicted versus measured burner operation rate.
Although it would perhaps be preferable to conduct a whole model validation exercise, this was not done in the present research due to lack of available resources. Also the full scale measurements as mentioned in Chapter 2. are not suitable for this purpose. Instead, the radiator plant component models (type 210 (2 node) and 270 (8 node)), as described in Section 5.4.9., were selected as subjects in an example of empirical validation. In their publications, Crommelin and Ham (1982), and Ham (1988) report extensive measurements and modelling theory regarding dynamic thermal behaviour of different radiators and convectors. One of the tests they performed concerned a step change in radiator inlet water temperature at a constant water mass flow rate. It should be noted that step change experiments constitute one of the most rigorous experimental methods to investigate the dynamic behaviour of some system. The radiator under investigation was a single plate radiator of 800 mm height and 960 mm length. The parameters describing this radiator are collated in Table 6.5.
Table 6.5 Parameters describing the radiator (ie of type 210 or 270) subjected to a step change in inlet water temperature
The nominal values as presented in Table 6.5 were derived from the measurement results as presented in the above mentioned publications. Transformed to the commonly used nominal temperatures 90/70/20 for thetas,0 /thetax,0 / theta sube,0, the nominal heat emission would evaluate to phi0=1100 (W) when using the logarithmic mean temperature difference (see Section 5.4.9.) and to phi0=1105(W) when using the arithmetic mean temperature difference. These values differ markedly from the manufacturers data which states phi0=1005 (W). The above merely serves to exemplify one of the error sources as indicated in the introduction to this chapter. The radiator model was incorporated in a small plant network consisting of a temperature source component model (type 900), the radiator, and a pump (type 240). The water node of the temperature source was controlled to set the supply temperature for the radiator, and the pump was controlled to deliver the constant water flow rate (qw=1.092 x 10-5m3s-1). This plant network was then simulated during a number of time steps so as to achieve steady-state conditions. At a certain point in time, say t=0, the temperature of radiator supply water was suddenly changed from 91.0 to 70.4°C after which the simulation was carried on long enough to achieve steady-state conditions again. The bps simulation results and the measurement and simulation results as reported by Crommelin and Ham (1982) are shown in Figure 6.4 for the radiator heat emission and in Figure 6.5 for the radiator outlet water temperature. The bps simulation results comprise those for the two different radiator models when using different simulation time-steps. It should be noted that the graphs are arrived at by connecting the centre points of the successive time step; eg in the case of the 900 (s) time steps, the resultat t=-450(s) is connected with the result at t=+450 (s), etc. Graphs using stair step display of the results turned out to be very confusing, i.e. it is then very difficult to distinguish the differences between the investigated cases.
Figure 6.4 Radiator heat emission following a step change in inlet water temperature (91.0 -> 70.4°C), as computed by bps with the two radiator models using different simulation time-steps. To the right are measured (dots) and computed (+) results as presented by Crommelin and Ham (1982). Some measurement results were copied to the left graph.
Figure 6.5 Radiator outlet water temperature following a step change in inlet water temperature (91.0 -> 70.4°C), as computed by bps with the two radiator models using different simulation time-steps. To the right are measured (dots) and computed (+) results as presented by Crommelin and Ham (1982). Some measurement results were copied to the left graph.
From Figure 6.4, it may be concluded that the 8 node radiator model, accurately describes the heat emission dynamics given the time step which was used. From the 2-node model results, it is apparent that the time step length plays an important role. It may be concluded that the error in computed heat emission increases with the time step length. The time constant of this radiator, given the current mass flow rate, is in the order of 300 (s). It can be seen that the error does not increase excessively for time steps much larger than the components time constant. This is probably due to the fact that the solution method switches from a Crank-Nicholson scheme to fully implicit for those conditions. Whether or not the errors introduced by increasing the time step length are acceptable, depends on the problem at hand. When for instance the primary interest is the total heat output during a certain period, the errors as shown in Figure 6.4 may be quite acceptable. The error in total radiator heat emission for the period shown when compared to the 8 node / 60 s time step case, is largest for the 2 node / 900 s time step case but is still only 3%.
From Figure 6.5, it may also be concluded that the 8 node radiator model, given the time step used, prvides the most accurate outlet water temperature predictions. For the 2 node model the same remarks as above apply. Again, whether errors introduced by employing a less rigorous model or larger simulation time steps will be acceptable or not, depends on the problem at hand.
Another experiment reported by Crommelin and Ham (1982) and Ham (1988), concerned a step change in radiator water flow rate with (nearly) constant inlet water temperature. One of the radiators they experimented on, was a single plate radiator of 400 mm height and 1920 mm length. The parameters describing this radiator are collated in Table 6.6.
Table 6.6 Parameters describing the radiator (ie of type 210 or 270) subjected to a step change in water flow rate.
As with the previous radiator, the nominal values as presented in Table 6.6 were derived from measurements. These were then transformed to the commonly used nominal temperatures 90/70/20 for thetas,0 /thetax,0 / thetae,0, the nominal heat emission would be equivalent to phi0 of approximately 1105 (W). These values also differ markedly from the manufacturers data which states phi0=1041 (W).
For the simulations, the small plant network as described above was used. The water node of the temperature source was controlled to set the supply temperature for the radiator (89.7, 88.6°C before, respectively after the step change), and the pump was controlled to deliver the water flow rates. The plant network was then simulated. At a certain point
Figure 6.6 Radiator heat emission following a step change in water flow
rate (1.193x10-5 -> 5.524x10-6m3/s),
as computed by bps with the two radiator models using different simulation
time-steps. To the right are measured (dots) and computed (+) results as
presented by Crommelin and Ham (1982). Some measurement results
were copied to the left graph.
in time, say t=0, the water flow rate through the network was suddenly decreased from qw= 1.193x10-5m3/s to qw= 5.524x10-6m3/s, after which the simulation continued long enough to achieve steady-state conditions again. The bps simulation results and the measurement and simulation results as reported by Crommelin and Ham (1982) are shown in Figure 6.6 for the radiator heat emission and in Figure 6.7 for the radiator outlet water temperature.
From Figure 6.6, it is apparent that both the 8 node model and the 2 node model describe the dynamic behaviour of the radiator heat emission very well provided that the simulation time step is small enough. At larger time steps the errors increase. The differences between the various time step lengths are larger than in the case of the inlet temperature step change. This is due to the fact that the radiator model uses the first node's temperature to decide whether iteration is necessary (see also Section 5.4.9.). This results in a too high heat emission immediately after the flow rate step change, which is most apparent for the larger time steps. As mentioned before, whether the errors introduced by increasing the time step length are acceptable, depends on the problem at hand. For the simulation period as shown in Figure 6.6, the error in total radiator heat emission when compared to the 8 node / 60 s time step case, is largest for the 2 node / 900 s time step case but is still only 4%.
From Figure 6.7, it may be concluded that the 8 node radiator model, given the time step utilised, yields the most accurate outlet water temperature predictions. For the 2 node model the same remarks in the paragraph above apply. Because, for the larger time steps the initial heat emission after the step change is too large, it is evident that the return water temperatures will be too low. Again, whether errors introduced by employing a less rigorous model or larger simulation time steps will be acceptable or not, will depend on the problem at hand.
Figure 6.7 indicates the radiator outlet water temperature following
a step change in the
water flow rate (1.193x10-5-> 5.524x10-6m3/s),
as computed by bps with the two radiator models using different simulation
time-steps. To the right are measured (dots) and computed (+) results as
presented by Crommelin and Ham (1982). Some measurement results were copied
to the left graph.
From the above follows that when larger time steps are to be allowed, it is probably better to not only use the first node's temperature but also it's mass flow rate as an indication of iteration necessity. Finally, and in support of similar remarks in Section 5.3.4., it may also be concluded from the above that it is probably worthwhile to investigate whether a combination of simulation time step control and iteration procedures would be beneficial for the accuracy and CPU resources.
Parametric sensitivity analysis can be used to establish the model predictions uncertainty band associated with the input data. As an example of this technique, one of the previous step change experiments was repeated with small changes in some of the input parameters. For this the radiator described by Table 6.5 and the experiments involving a step change in inlet water temperature were chosen. As described above, the difference between the measured nominal heat emission and manufacturers data was approximately 6% for this radiator. For the radiator described by Table 6.6, this difference was approximately 9%. It was decided to repeat the simulations with changes in the nominal heat emission of +/- 8%.
Another input parameter which was subjected to small changes, is the radiator's total heat capacitance (ie. product of total mass and mass weighted average specific heat). It was assumed that the uncertainty associated with this parameter is in the order of say 2.5%.
Figure 6.8 Uncertainty band for bps predicted radiator heat emission associated with input parameters. The simulation (with 2 node radiator model using 60 s time steps) involved a step change in inlet water temperature (91.0 -> 70.4°C).
Figure 6.9 Uncertainty band for bps predicted radiator outlet water temperature associated with input parameters. The simulation (with 2 node radiator model using 60s time steps) involved a step change in inlet water temperature (91.0 -> 70.4°C).
The inlet water temperature step changes described in the previous section, were repeated using the 2 node radiator model and with simulation time steps of 60s. The results with respect to predicted heat emission are shown in Figure 6.8. From this, it is clear that the nominal heat emission is an important parameter, and any uncertainty in this parameter causes an almost equal relative uncertainty in the heat emission predictions (in fact: phi1 /phi2=( phi0,1 /phi0,2 )n).
From the results it is also apparent that the uncertainty in nominal heat emission only affects the absolute value of the heat output and not the dynamic behaviour. The effects of changes in total heat capacitance on the other hand, are negligible, both in an absolute sense and with respect to dynamic behaviour.
Lastly, the results with respect to the uncertainty band for predicted outlet water temperature are shown in Figure 6.9. As may be expected from the above, any uncertainty in nominal heat emission has a much stronger influence on the predictions uncertainty, than the uncertainty in total radiator heat capacitance. Again, this only affects the temperatures in an absolute sense. Neither uncertainty will affect the dynamic behaviourof the predicted outlet water temperatures.
As explained before, the verification and validation efforts in the current project have been mostly directed towards the first phases or steps of the validation methodology:
Because the other methodology steps have been applied selectively only, there is still a lot of work to be done in those areas. This does not only apply to plant and fluid flow component models as such, but also to the interaction of those models with the building model and to the overall building/plant configuration model as a whole.
This chapter focussed on internal errors. There remains however the issue of external errors which often cause much larger uncertainties than internal errors. Evidence suggesing this may be found in the previous sections. In terms of plant simulation, the necessaryinput parameters are often difficult to extract from published data. Manufacturers data is usually related to specific test conditions under steady full load operation; part load steady-state data is scarce and dynamic performance test results are even more scarce. It is necessary for all parties which are involved in or benefit from system simulation to agree that this sort of data is crucial and to act accordingly; ie to persuade the industry to publish appropriate data, and to develop standardized procedures and reporting formats for dynamic performance tests.
Another way of trying to prevent external errors, is by user guidance via a so called 'intelligent front-end'. This issue will be discussed further in Chapter 8.
