Erratum to “impact of burner plenum acoustics on the sound emission of a turbulent lean premixed open flame”

Abstract

Herff S, Pausch K, Nawroth H, et al. Impact of burner plenum acoustics on the sound emission of a turbulent lean premixed open flame. International Journal of Spray and Combustion Dynamics 2020; 12: 1–20. doi: 10.1177/1756827720956906

In the above-referenced article, the correct version of the equations (2), (7), (8), (9), (15), (16), (17), (18), and (20) are below:

\underline{H} = {\underline{H}}^{i} - {\underline{H}}^{v} = (\begin{matrix} ρ v \\ ρ vv \\ v (ρ E + p) \\ ρ v c \end{matrix}) + \frac{1}{R e_{0}} (\begin{matrix} 0 \\ \underline{τ} \\ \underline{τ} v + q \\ J_{c} \end{matrix})

(2)

\dot{W} = {(0, 0, Q {\bar{\dot{ω}}}_{c}, {\bar{\dot{ω}}}_{c})}^{T}

(7)

\frac{\partial \overset{ˇ}{G}}{\partial t} + (\tilde{v} + \frac{ρ_{\infty, u}}{\bar{ρ}} {\hat{\tilde{s}}}_{t, u} \overset{ˇ}{n}) \cdot \nabla \overset{ˇ}{G} = 0

(8)

\overset{ˇ}{n} = - \frac{1}{| \nabla \overset{ˇ}{G} |} {(\partial \overset{ˇ}{G} / \partial x, \partial \overset{ˇ}{G} / \partial y, \partial \overset{ˇ}{G} / \partial z)}^{T}

(9)

\frac{\partial p^{a}}{\partial t} + \bar{a^{2}} \nabla \cdot (\bar{ρ} v^{a} + \bar{v} \frac{p^{a}}{\bar{a^{2}}}) = \bar{a^{2}} q_{c} + q_{e} - ︸ \underset{q_{c & e}}{\bar{a^{2}} \nabla \cdot (\bar{v} ρ_{e})}

(15)

\begin{array}{l} \frac{\partial v^{a}}{\partial t} + \nabla (\bar{v} \cdot v^{a}) + \nabla (\frac{p^{a}}{\bar{ρ}}) = q_{m} \end{array}

(16)

q_{c} = - \nabla \cdot {(ρ^{'} v^{'})}^{'}

(17)

q_{e} = \frac{\partial p'}{\partial t} - \bar{a^{2}} \frac{\partial ρ'}{\partial t}

(18)

\begin{array}{l} q_{m} = {(ω \times v)}^{'} - \nabla k^{'} \\ + \nabla (\frac{p^{'}}{\bar{ρ}}) - {(\frac{\nabla p}{ρ})}^{'} + {(\frac{\nabla \cdot \underline{τ}}{ρ})}^{'} \end{array}

(20)