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

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:

$$\underset{\mathbf{¯}}{\mathbf{H}}={\underset{\mathbf{¯}}{\mathbf{H}}}^i-{\underset{\mathbf{¯}}{\mathbf{H}}}^v=\left(\begin{array}{c}\rho \mathbf{v}\\ \rho \mathbf{vv}\\ \mathbf{v}\left(\rho E+p\right)\\ \rho \mathbf{v}c\end{array}\right)+\frac{1}{R{e}_0}\left(\begin{array}{c}0\\ \underset{¯}{\mathit{\tau }}\\ \underset{¯}{\mathit{\tau }}\mathbf{v}+\mathbf{q}\\ {\mathbf{J}}_c\end{array}\right)$$

(2)

$$\dot{\mathbf{W}}={\left(0,\mathbf{0},\mathcal{Q}{\overline{\dot{\omega }}}_c,{\overline{\dot{\omega }}}_c\right)}^T$$

(7)

$$\frac{\partial \check{G}}{\partial t}+\left(\tilde{\mathbf{v}}+\frac{{\rho }_{\infty ,u}}{\overline{\rho }}{\widehat{\tilde{s}}}_{t,u}\check{\mathbf{n}}\right)·\nabla \check{G}=0$$

(8)

$$\check{\mathbf{n}}=-\frac{1}{|\nabla \check{G}|}{\left(\partial \check{G}/\partial x,\partial \check{G}/\partial y,\partial \check{G}/\partial z\right)}^T$$

(9)

$$\frac{\partial p^a}{\partial t}+\overline{a^2}\mathbf{\nabla }·\left(\overline{\rho }{\mathbf{v}}^a+\overline{\mathbf{v}}\frac{p^a}{\overline{a^2}}\right)=\overline{a^2}{q}_c+q_e-︸\underset{q_{c\text{\&}e}}{\overline{a^2}\mathbf{\nabla }·\left(\overline{\mathbf{v}}{\rho }_e\right)}$$

(15)

$$\begin{array}{l}\frac{\partial {\mathbf{v}}^a}{\partial t}+\mathbf{\nabla }\left(\overline{\mathbf{v}}·{\mathbf{v}}^a\right)+\mathbf{\nabla }\left(\frac{p^a}{\overline{\rho }}\right)={\mathbf{q}}_{\mathbf{m}}\end{array}$$

(16)

$$q_c=-\mathbf{\nabla }·{\left({\rho }^{\prime }{\mathbf{v}}^{\prime }\right)}^{\prime }$$

(17)

$$q_e=\frac{\partial p\prime }{\partial t}-\overline{a^2}\frac{\partial \rho \prime }{\partial t}$$

(18)

$$\begin{array}{l}{\mathbf{q}}_{\mathbf{m}}={\left(\mathit{\omega }\times \mathbf{v}\right)}^{\prime }-\mathbf{\nabla }{k}^{\prime }\\ +\mathbf{\nabla }\left(\frac{p^{\prime }}{\overline{\rho }}\right)-{\left(\frac{\mathbf{\nabla }p}{\rho }\right)}^{\prime }+{\left(\frac{\mathbf{\nabla }·\underset{¯}{\mathit{\tau }}}{\rho }\right)}^{\prime }\end{array}$$

(20)