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.