Abstract
Our interest now is to derive guidence for design or for performance predictions of combustion devices. The word design refers to the determination of the geometry (length, diameter, shape) of the device and ensuring safety (Nowhere in the device should the temperature exceed a prespecified value, which is often dictated by metallurgical limits.) for the desired product composition. Performance prediction implies the reverse—that is, determining product composition for a given geometry under safe operating conditions.
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Notes
- 1.
Nowhere in the device should the temperature exceed a prespecified value, which is often dictated by metallurgical limits.
- 2.
- 3.
For a fuel-rich mixture, the blow-off limit will be controlled by oxygen mass fraction.
- 4.
This assumption of decoupling NO formation from the main combustion reaction is justified on the grounds that NO mass fractions are usually very small and their influence on other mass fractions is negligible.
- 5.
A WSTCR is assumed to operate at constant pressure.
- 6.
- 7.
- 8.
Longwell and Weiss plotted values of \(\dot{m}/ (V_{cv} \times p^{1.8}_{1}) \). They found that for \(\Phi = 1\), the value of this parameter was \({\simeq }0.247 \times 10^{-5}\). Note that the exponent value 1.8 is very close to x \(+\) y \(=\) 1.75 used here.
- 9.
The variation of \(R_{fu}\) with T shown in the left figure is typical for all fuels. Only the magnitudes differ. Note that \(T_{2}\) is replaced by T on the x-axis.
- 10.
The intermediate solution 2, which occurs on the rapidly rising portion of the \(R^{*} \sim T^{*}\) curve, is essentially unstable, because in a practical reactor, the conditions are never perfectly steady. Thus, for example, if the value of \(\Phi \), were to increase slightly above the preset value, then the temperature will also increase, owing to the availability of extra fuel, further increasing \(R_{fu}\). This increase will further increase T and so on. Eventually, solution 3 will be reached in this way. Solution 1 will be reached if the converse were to happen owing to a momentary increase in \(\dot{m}\).
- 11.
Incidentally, the time required to reach \(T^{*} = 0.1\) is identified with ignition delay, as will be discussed in Chap. 3.
- 12.
The expressions for \(V_{cv}\), \(x_{p}\), and \(u_{p}\) can be derived as
$$\begin{aligned} V_{cv}= & {} A_{c}\,( x_{0} + x_{p} ) \end{aligned}$$(7.111)$$\begin{aligned} x_{p}= & {} c\,( 1 - \text{ cos }\,\theta ) + b - \sqrt{b^{2} - c^{2}\,\text{ sin }^{2}\,\theta } \end{aligned}$$(7.108)$$\begin{aligned} u_{p}= & {} \frac{d\, x_{p}}{dt} = c\,\Omega \,\text{ sin }\,\theta \,\left[ 1 + \frac{c\,\text{ cos }\,\theta }{\sqrt{ b^{2} - c^{2}\,\text{ sin }^{2}\,\theta }}\,\right] \,, \end{aligned}$$(7.109)where b and c are lengths of the connecting rod and crank, respectively, \(x_{0}\) is the clearance at TDC, and \(\Omega = 2\,\pi \, N/60\) is the angular velocity of the crank in radians/s, and N is RPM. The crank angle \(\theta \) is measured clockwise and \(\theta = 0\) coincides with TDC.
- 13.
Borman and Ragland [19] recommend the following empirical formula for engine work:
$$\alpha _{eff}\,\left( \frac{\mathrm{kW}}{\mathrm{m}^{2}\text {-}\mathrm{K}} \right) = 0.82\, d^{-0.2}\, U^{0.8}_{g}\, p^{0.8}\, T^{-0.53}\,.$$
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Date, A.W. (2020). Thermochemical Reactors. In: Analytic Combustion. Springer, Singapore. https://doi.org/10.1007/978-981-15-1853-9_7
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DOI: https://doi.org/10.1007/978-981-15-1853-9_7
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