3D printed electrolyzer with different inlets
To systematically investigate inlet effects, we developed a modular 3D printed electrolyzer with exchangeable inlets. Three types of inlets were used: a conic inlet, a tube inlet and a divider type inlet (shown in figure 4). Results for these inlets are shown in figure 9. All three inlets produce higher rates of mass transfer than expected from the predictions by Pickett et al (eq 2.). Furthermore, for the conic and divider type inlet, a region with a smaller slope and a (Re < 300) region with a larger slope (Re > 300) can be discerned. The tube inlet shows a large slope at all flow rates. The aforementioned regions represent laminar and turbulent flow respectively. In the laminar region, a similar performance is seen for the conic and divider inlet. Therefore, only one mass transfer correlation is established (eq.6) for both inlets in laminar flow (Re <300).
\(Conic,divider\ inlet:\ Re<300:\ \ \ \ Sh\ =1.72\ Re^{0.247}Sc^{0.33}\)eq. 6
Compared to eq.3a a higher rate of mass transfer is observed. This could be due to protrusions resulting from imperfections in the printed parts or the rubber seals between them. Additionally, the Reynolds power in eq.6 is 0.247 compared to the power of 0.33 in eq.3a. The likely reason for this is that the current at low flow rates is not fully stabilized, as shown in figure 2. The effect likely also contributes to the higher performance in eq.6 compared to eq.3a.
[FIGURE 9]
In the turbulent region the rate of mass transfer with the conic inlet is a factor 1.4 higher (at Re = 1000) compared to the divider inlet. Mass transfer with the tube inlet is a factor 2.3 higher (at Re = 1000) compared to the divider inlet. This difference is the result of an earlier transition to the turbulent regime, which in turn is caused by the sudden expansion of the inlet to the channel. Djati et al. [19] investigated the effect of these expansions on the rate of mass transfer in slit and tube inlets. They established a correlation using the inlet to channel cross sectional area ratio Ain/Ach as a parameter (eq. 6). If Ain/Ach = 1, no expansion occurs and the equation describes hydrodynamically developed turbulent flow comparable to equation 5a. The difference between eq.7 and eq.5a or eq.5b is small. [19]
\(Sh\ =\ 0.068\ \ \left(\frac{A_{\text{in}}}{A_{\text{ch}}}\right)^{-0.5}Re^{0.72}Sc^{0.33}\)eq. 7
In our case, the tube inlet has an area ratio of 0.07. The divider inlet is a series of slits, with the ratio of the area of all openings to the channel being 0.52. The conic inlet ends in the same cross-sectional area as the channel, which implies that the ratio is 1.0. Using these values, eq. 7 results in a good prediction for the divider inlet at Re > 500 (max deviation < 8%) and to a lesser extent the tube inlet (max deviation <18%). For the conic inlet on the other hand the prediction appears to be inaccurate. This is because the ratio of 1.0 implies that there is no expansion, but expansion is occurring in the inlet. Therefore, we used the geometric mean to determine the ratio:\(A_{\text{in}}=\sqrt{A_{in,0}*A_{in,1}}\), where \(A_{in,0}\) is the area at the beginning of the inlet and \(A_{in,1}\)the area and the end of the inlet. For the conic inlet the area ratio then becomes 0.26. With this ratio, the prediction closely matches the experimental results at Re > 300 (max deviation < 6%)
By finding the intersect of the laminar and turbulent correlations, the Reynolds number at which the transition occurs \(Re_{t}\) can be determined. When combined, and solved for Re, eq.6 and eq.7 lead to eq.8, which gives \(Re_{t}\) as a function of the cross-sectional area ratio of the inlet to the channel.
\(\text{\ R}e_{t}=925\ \left(\frac{A_{\text{in}}}{A_{\text{ch}}}\right)^{1.06}\ \)eq. 8
Eq. 8 predicts that the flow transition occurs at \(Re_{t}\) = 223 for the conic inlet, \(Re_{t}\) = 463 for the divider inlet and \(Re_{t}\) = 56 for the tube inlet. The transition for the conic and divider inlet are observed in figure 9. For the tube inlet \(Re_{t}\) is near the first datapoint of the graph and therefore the transition cannot be seen. When Ain/Ach = 1, no expansion takes place and \(Re_{t}\) = 925. This is far earlier than expected from the work of Ong and Pickett [12,13], possibly due to the imperfections in the printed parts and the assembly thereof.