Impinging premixed methane-air flame jet of tube burner: thermal performance analysis for varied equivalence ratios

Abstract

Thermally efficient gas burners can be designed by optimising the parameters associated with combustion and heat transfer mechanisms. The current study presents the thermal analysis of the premixed methane-air flame jets of circular tube gas burner impinging on a target surface. The effect of flame jet parameters such as mixture Reynolds number, equivalence ratio and burner to target surface spacing on heat transfer characteristics is investigated. The thermal performance is quantified in terms of thermal efficiency. The lean and stoichiometric mixtures release maximum amount of thermal energy. However, in lean flames, a part of the energy released is used for rising the temperature of excess air. Though the combustion is incomplete for fuel rich flames, higher heat transfer is achieved because of higher flame height. The optimal thermal performance is observed when the mixture is near stoichiometric and the burner is spaced from the target surface such that the premixed cone tip just touches the surface.

Appendix

1.1 Determination of rate of heat transfer from impinging flame jet to square target plate

The steady state wall heat flux is Gaussian in nature. A Gaussian curve of the form ${q}^{{\prime\prime} }(r)={q}_0^{{\prime\prime}}\mathit{\exp}\left(-a{\left(\frac{r}{R}\right)}^2+b\right)$ is fitted to the heat flux data and further analysed to obtain rate of heat transfer from the flame to plate.

$$ {\dot{Q}}_{ht}={\int}_A{q}^{{\prime\prime} } dA $$

$$ \kern1.75em =\underset{Circular\ Part}{\underbrace{\int_0^{2\pi }{\int}_0^R{q}^{{\prime\prime} }(r).r. d\theta . d r\ }}+\underset{\begin{array}{c} Corners\ of\ the\ plate\\ {} excluding\ circle\end{array}}{\underbrace{\left(\left(4-\pi \right){R}^2{q}^{{\prime\prime} }(R)\right)}} $$

$$ \kern1.75em ={\int}_0^{2\pi }{\int}_0^R{q}_0^{{\prime\prime}}\mathit{\exp}\left(-a{\left(\frac{r}{R}\right)}^2+b\right).r. d\theta . d r+\left(\left(4-\pi \right){R}^2{q}^{{\prime\prime} }(R)\right) $$

$$ \kern1.75em =2\pi q{{\prime\prime}}_0{e}^b{\int}_0^R\mathit{\exp}\left(-a{\left(\frac{r}{R}\right)}^2\right).r. dr+\left(\left(4-\pi \right){R}^2{q}^{{\prime\prime} }(R)\right) $$

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Let r² = u, then 2r. dr = du.

$$ {\dot{Q}}_{ht}=\frac{2\pi {q}_0^{{\prime\prime} }{e}^b}{2}{\int}_0^{R^2}\mathit{\exp}\left(\frac{- au}{R^2}\right). du+\left(\left(4-\pi \right){R}^2{q}^{{\prime\prime} }(R)\right) $$

$$ \kern1.75em =\pi {q}_0^{{\prime\prime} }{e}^b{\left[\frac{-{R}^2}{a}\mathit{\exp}\left(\frac{- au}{R^2}\right)\right]}_0^{R^2}+\left(\left(4-\pi \right){R}^2{q}^{{\prime\prime} }(R)\right) $$

$$ \kern1.75em =\frac{-\pi {q}_0^{{\prime\prime} }{e}^b{R}^2}{a}\left[{e}^{-a}-1\right]+\left(\left(4-\pi \right){R}^2{q}^{{\prime\prime} }(R)\right) $$

$$ \kern1.75em =\frac{\pi q{{\prime\prime}}_0{R}^2}{a}\left[{e}^b-{e}^{\left(b-a\right)}\right]+\left(\left(4-\pi \right){R}^2{q}^{{\prime\prime} }(R)\right) $$

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