My Standard Caution About Examples applies to this page.
Start with real input1:
The adiabatic combustion temperatures for natural gas and air as a function of F/A2are shown in table III and in the upper curves of figure 12. The initial temperature of the reactants was assumed to be 298 K. Pressure has no effect on the combustion temperature for fuel-air ratios below 0.04. For fuel-air ratios greater than 0.04, a slight increase in combustion temperature occurs with pressure. The highest combustion temperatures of 2242 and 2262 K are attained at the stoichiometric F/A for pressures of 3 and 10 atmospheres (3.04×105 and 10.13×105 N/m2), respectively.
The effect of F/A on the thermodynamic and transport properties at 3 atmospheres (3.04×105 N/m2) is shown in table IV and in figures 1 to 6. The properties were calculated for fuel-air ratios from zero (air) to stoichiometric and for temperatures from 300 to 2500 K. The ratio of specific heats, molecular weight, and viscosity decrease with increasing F/A, while the specific heat at constant pressure and thermal conductivity show the opposite trend. For temperatures lower than approximately 1400 K, the Prandtl number increases with increasing F/A, whereas above 1400 K the effect is reversed.
The corresponding data at 10 atmospheres (10.13×105 N/m2) are given in table V and in figures 7 to 11. Over the range of F/A investigated, the effect of pressure on the properties of the combustion products of natural gas and air is essentially the same as that described for air, with pressure having a negligible effect until the temperature exceeds approximately 1700 K. As was the case for air, the viscosity is essentially independent of pressure, and, thus, figure 3 can be used for the viscosity data at 3 and 10 atmospheres (3.04×105 and 10.13×105 N/m2).
Discussion
Object/Process: Combustion Products, Natural Gas in Air
I construed “Combustion Products” as an object (pluralization notwithstanding). With suitable tweaking of subsequent nomenclature, I could as easily construe this as a process: “Combustion, Natural Gas/Air”. I see no philosophical reason to prefer one over the other.
Topic: Combustion Product Characteristics (reference)
By not specifying additional modifiers (“thermal” or “transport” ), I’ve allowed for the future addition of new parameters from other sources. “Natural Gas in Air” does not repeat in the nomenclature because the topic is hierarchically subordinate to the object being characterized.
I would (however) have accepted the two topics instead of one if somebody felt strongly about it. The finer granularity would have more closely matched some approaches to skill (domain) definition. I would also have accepted those two hierarchically subordinate to the one given above. The only down side is that finer granularity leads to proliferation of topics, adversely impacting management thereof. As with many such issues, this one is more a matter of organizational preference (that is, “style”) than anything else.
It probably appears tempting to consider several other things as topics. For example, you might have defined a topic called “Maximum Combustion Temperature” which is the grammatical subject of the last sentence in the first paragraph. I would have considered that to be improper: “Maximum Combustion Temperature” directly takes a nominal value3, so is properly considered a Parameter associated with the topic. I raise this counter-example here in order to observe that “grammatical subject” and “topic” are not the same thing, which is my entire reason for using the word “topic” instead of the word “subject”.
Automated extraction of “topic” as used here relies on more than just grammar. In my experience, a proper “topic” is often more strongly associated with an entire paragraph or section than with an individual sentence, but there are probably as many exceptions to that generalization as there are compositional styles. The objective of this exercise is to extract useful data into a single organization scheme of storage and execution: to remove the issues of compositional style and make all such interpretation plain in order to mitigate the potential for cognitive biases in that process.
Parameterization (reference)
We want to clearly distinguish between parameters that measure properties of the topic, and those to which those properties are sensitive (“parameters of circumstance”). The former would customarily be those found to the left of the = sign in an equation (the “output” side); the later would customarily be found on the right (as “inputs”).
Properties with commentary where it seems appropriate
Adiabatic Combustion Temperature (Tad)
I might have accepted “Theoretical” in place of “Adiabatic”, but there are other theories that could be considered; the selected nomenclature will allow future extension if that proves necessary. Leaving the modifier altogether off would NOT have been acceptable, because the document clearly represents an analytical result rather than test data (although test data are reported on later in the same document). [Note that the nomenclature is exactly as shown in the reference’s table III.]
Maximum Adiabatic Combustion Temperature (Tadmax)
I would accept this as not being a proper parameter if a good argument were made. It could be calculated instead. On the other hand, conservative engineering practice might make it explicit just because observance of this some specific nominal value would eliminate an entire class of possible failures (due to real-time error in controlling the fuel/air ratio). The practicality of that question depends on the speed of calculating that maximum possible value (if conservatism is desired) versus the cost of storing an additional parameter. The issue is not a major discriminator.
Ratio of specific heats (γ)
As with all parameters extracted from the second paragraph, we could have written a topic (and associated parameters) that characterized the immediate products, before any heat loss could occur. In that case, this (and subsequent parameters) would have a single nominal value for the mixture. However, the intent of the TN appears to have been more comprehensive: it appears that it addresses how the transport properties change as the products move down stream from the combustion chamber (cooling along the way). I had to actually go look at the tables and charts in order to assure myself that I’d correctly captured that apparent intent(which is pretty useful).
Molecular weight (m)
Viscosity (μ)
Specific heat (constant pressure) (Cp)
Thermal conductivity (k)
Prandtl number (Pr)
This is a similarity parameter used to compare rates of two different physical diffusion phenomena (momentum/thermal). It can be used to apply the results for diffusion of one mixture of gases to those of another having the same nominal value. The value also strongly suggests what type of thermal model is most appropriate when assessing heat transfer.
Circumstances
Fuel/Air Ratio (F/A)
Initial Temperature (T0)
Pressure (Pcomb)
Tdown
The “down stream” reference is inferred4 as noted above. Some sort of designation was necessary to clearly distinguish this parameter from the combustion temperature itself. I would be open to other clearly distinguishing nomenclatures.
Evaluation (reference)
I will work through only the first parameter here. Development of values for the other parameters adds nothing of philosophical interest.
Adiabatic Combustion Temperature:
I include four distinct methods for supplying nominal values for the parameters in question. Each of the three has advantages and disadvantages as noted. I have included a brief discussion regarding uncertainty and limit handling at the end of this section.
Method 1: Tabulation5
|
F/A Ratio () |
Pressure
(N/m2) |
Adiabatic Combustion
Temperature (K) |
| 0 | 3.04×105 | 298 |
| 0.01 | 3.04×105 | 745 |
| 0.02 | 3.04×105 | 1130 |
| 0.04 | 3.04×105 | 1770 |
| 0.06 | 3.04×105 | 2242 |
| 0 | 10.13×105 | 298 |
| 0.01 | 10.13×105 | 745 |
| 0.02 | 10.13×105 | 1130 |
| 0.04 | 10.13×105 | 1771 |
| 0.05 | 10.13×105 | 2262 |
Method 1 leaves all interpolation to the individual modeler.
Method 2: Statistical Fitting
Tad = NASA_TN_D_5452(FA,Pcomb,conf);
Method 2 effectively executes all interpolation ahead of time, but inhibits the discretion of the individual modeler. See the algorithms and embedded comments in NASA_TN_D_54526. Set the file extension to “m” to execute in Matlab.
This method probably results in the least potential for bias: it not only makes clear the interpretation and interpolation, it enforces consistency of usage through reusable code. As written (however) the code maximally restricts the latitude available to the individual modeler. (Of course, additional interpolation methods can be written into such a code base, somewhat alleviating that issue.)
Method 3: Reimplementation
Noting that the reference supplies (in turn) a reference for the specific model used to generate the adiabatic temperatures, we could obtain that second reference (NASA Sp-3011, 1964) and implement the model ourselves. This would (of course) entail validation of that new implementation; reference 1 includes only a subset of the data required to do so. I do not presently have access to the secondary reference, so cannot fully develop this approach.
Method 4: Reference
Poferl, Davis J., et al, “Thermodynamic and Transport Properties of Air and the Combustion Products of Natural Gas and of ASTM-A-1 Fuel with Air” (NASA TN D-5452); National Aeronautics and Space Administration, Washington, D.C., October 1969); Table III.
“By reference” is the most complete method with regard to any limitations on interpretation because it makes none. It is also the least useful in terms of data storage or actual analytical calculations. Note that the other evaluation methods effectively incorporate this method through their traceability.
A Note With Regard to Uncertainty and Limits of Applicability:
Uncertainty should be quoted along with the nominal values as shown above. All four methods should admit to uncertainty with respect to the reference’s limited test data. Both of the first two methods are also impacted by uncertainty propagated through the modeling of the secondary reference.
Note that, as implemented, the second method incorporates the uncertainty added by the regression technique: the modeler can (and should) consider the confidence interval question, and implement accordingly. The statistical component of uncertainty can be dealt with in worst-case analysis by using an offset. If (however) different “directions” of uncertainty are “worst case” for different issues, a Monte Carlo analysis would be more appropriate, selecting randomly within the desired confidence interval on each of many model executions.
All four methods are susceptible to misuse with regard to limits: none contain information regarding initial temperatures different from 298K, for pressures other than those given, or for F/A above 0.06. If implemented as a model, either method has to “handle” the issue, whether clamping, extrapolating, or throwing an error (see the crude input checking of the code in Method 2 for a simplistic example).
Footnotes
- Poferl, Davis J., et al, “Thermodynamic and Transport Properties of Air and the Combustion Products of Natural Gas and of ASTM-A-1 Fuel with Air” (NASA TN D-5452); National Aeronautics and Space Administration, Washington, D.C., October 1969[↩]
- Fuel/Air Ratio)[↩]
- For a given set of circumstances (see below).[↩]
- By me![↩]
- From the reference’s table III[↩]
- Because I’m lazy, that’s why.[↩]