Characterization of the external and internal flow structure of an aerated-liquid injector using X-ray radiography and fluorescence

Abstract

In the present study, the internal flowfield of aerated-liquid fuel injectors is examined through X-ray radiography and X-ray fluorescence. An inside–out injector, consisting of a perforated aerating tube within an annular liquid stream, sprays into a quiescent environment at a fixed mass flow rate of water and nitrogen gas. The liquid is doped with bromine (in the form of NaBr) to create an X-ray fluorescence signal. This allows for reasonable absorption and fluorescence signals, and one or both diagnostics can be used to track the liquid distribution. The injector housing is fabricated from beryllium (Be), which allows the internal flowfield to be examined (as Be has relatively low X-ray attenuation coefficient). Two injector geometries are compared, illustrating the effects of aerating orifice size and location on the flow evolution. Time-averaged equivalent pathlength and line-of-sight averaged density ρ(y) reveal the formation of the two-phase mixture, showing that the liquid film thickness along the injector walls is a function of the aerating tube geometry, though only upstream of the nozzle. These differences in gas and liquid distribution (between injectors with different aerating tube designs) are suppressed as the mixture traverses the nozzle contraction. The averaged liquid velocity (computed from the density and liquid mass flow rate) reveals a similar trend. This suggests that at least for the current configurations, the plume width, liquid mass distribution, and averaged liquid velocity for the time-averaged external spray are insensitive to the aerating tube geometry.

Appendix: Uncertainty Quantification

The uncertainty of the EPL and the resulting derived quantities (line-of-sight averaged density and average liquid velocity) are computed from the procedure of Kline and McClintock (1953), in which the principal uncertainties are weighted by the respective sensitivity coefficients and combined as a root-sum-of-squares. As described in Sect. 2.4, the EPL of the two-phase mixture is found by removing the attenuation through the beryllium injector body:

$${\text{EPL}} = \frac{{ - \ln \left( {I/I_{0} } \right)_{\text{corr}} }}{{\beta_{\text{liquid}} \;\rho_{\text{liquid}} }} = \frac{{\left[ { - \ln \left( {I/I_{0} } \right)_{\text{meas}} } \right] - \left[ { - \ln \left( {I/I_{0} } \right)_{\text{Be}} } \right]}}{{\beta_{\text{liquid}} \;\rho_{\text{liquid}} }},$$

(6)

where the subscript corr indicates the corrected intensity ratio, and meas is the measured value. The uncertainty can, therefore, be calculated as

$$\varepsilon_{\text{EPL}} = \sqrt {\left( {\frac{{\partial {\text{EPL}}}}{{\partial \beta_{\text{liquid}} }}\varepsilon_{{\beta_{\text{liquid}} }} } \right)^{2} + \left( {\frac{{\partial {\text{EPL}}}}{{\partial \rho_{\text{liquid}} }}\varepsilon_{{\rho_{\text{liquid}} }} } \right)^{2} + \left( {\frac{{\partial {\text{EPL}}}}{{\partial \left( {I/I_{0} } \right)_{\text{meas}} }}\varepsilon_{{\left( {I/I_{0} } \right)_{\text{meas}} }} } \right)^{2} + \left( {\frac{{\partial {\text{EPL}}}}{{\partial \left( {I/I_{0} } \right)_{\text{Be}} }}\varepsilon_{{\left( {I/I_{0} } \right)_{\text{Be}} }} } \right)^{2} } .$$

(7)

The uncertainties for (I/I ₀)_meas and (I/I ₀)_Be are computed in a similar fashion, using the previously described procedure from Sect. 2.4 to compute (I/I ₀)_Be:

$$\varepsilon_{{\left( {I/I_{0} } \right)_{\text{meas}} }} = \sqrt {\left( {\frac{{\partial \left( {I/I_{0} } \right)_{\text{meas}} }}{\partial I}\varepsilon_{I} } \right)^{2} + \left( {\frac{{\partial \left( {I/I_{0} } \right)_{\text{meas}} }}{{\partial I_{0} }}\varepsilon_{{I_{0} }} } \right)^{2} }$$

(8)

and

$$\varepsilon_{{\left( {I/I_{0} } \right){\text{Be}}}} = \sqrt {\left( {\frac{{\partial \left( {I/I_{0} } \right)_{\text{Be}} }}{{\partial \alpha_{\text{Be}} }}\varepsilon_{{\alpha_{\text{Be}} }} } \right)^{2} + \left( {\frac{{\partial \left( {I/I_{0} } \right)_{\text{Be}} }}{{\partial z_{\text{Be}} }}\varepsilon_{{z_{\text{Be}} }} } \right)^{2} }$$

(9)

Note that the uncertainty in Eq. (9) is a function of the chord length z _Be through the injector body, computed as

$$z_{\text{Be}} = 2\sqrt {R_{1}^{2} - y^{2} } - 2\sqrt {R_{2}^{2} - y^{2} } = 2\sqrt {R_{1}^{2} - y^{2} } - D,$$

(10)

where R ₁ and R ₂ are the outer and inner radii of the injector body, respectively. Using the principal uncertainty values in Table 2, the uncertainty of EPL can be calculated (Fig. 19). In the aerating region for Case A, the uncertainty increases from nominally 1–7% as the two-phase mixture flows downward toward the mixing region.

Table 2 Principal uncertainties and nominal values

Fig. 19

EPL uncertainty of Case A, showing only the left half of the aerating region

The uncertainty of the line-of-sight averaged density ρ(y) is computed by applying the above procedure to Eq. (3), leading to

$$\varepsilon_{\rho } = \sqrt {\left( {\frac{\partial \rho }{{\partial {\text{EPL}}}}\varepsilon_{\text{EPL}} } \right)^{2} + \left( {\frac{\partial \rho }{\partial D}\varepsilon_{D} } \right)^{2} + \left( {\frac{\partial \rho }{{\partial \rho_{\text{water}} }}\varepsilon_{{\rho_{\text{water}} }} } \right)^{2} }$$

(11)

Due to the iterative nature of the signal trapping fluorescence correction, a closed-form solution for Eq. (7) was not available for the nozzle and spray regions. Instead, Eq. (11) was calculated by estimating ε _EPL as 2% of the local value, based upon inspection of the aerating and mixing regions. The density uncertainty in the aerating region has been shown in Fig. 10, depicting the elevated uncertainty levels near the injector wall. This trend is attributed to the uncertainty of D(y) shown in Fig. 20, which increases as y approaches R ₂.

Fig. 20

Chord D(y) uncertainty of Case A, showing only the left half of the aerating region

The axial velocity uncertainty ε _u is computed from Eq. (4) as

$$\varepsilon_{u} = \sqrt {\left( {\frac{\partial u}{{\partial m_{\text{L}} }}\varepsilon_{{m_{\text{L}} }} } \right)^{2} + \left( {\frac{\partial u}{{\partial {\text{TIM}}}}\varepsilon_{\text{TIM}} } \right)^{2} } ,$$

(12)

where the uncertainty of the TIM is

$$\varepsilon_{\text{TIM}} = \sqrt {\left( {\frac{{\partial {\text{TIM}}}}{\partial \rho \left( y \right)}\varepsilon_{\rho \left( y \right)} } \right)^{2} + \left( {\frac{{\partial {\text{TIM}}}}{\partial D\left( y \right)}\varepsilon_{D\left( y \right)} } \right)^{2} + \left( {\frac{{\partial {\text{TIM}}}}{\partial \Delta y}\varepsilon_{\Delta y} } \right)^{2} } .$$

(13)

The spanwise spacing of the measurement locations is represented by Δy. Figure 17 shows the uncertainty plotted as error bars, indicating that the uncertainty is approximately 10% of the local velocity for most locations. The magnitude of the uncertainty can be explained by D(y) (Fig. 20). Due to the summation in Eq. (4), the uncertainty of TIM is biased towards larger values by the elevated uncertainty of D(y) at the periphery of the measurement region.