Electronic – Value of the capacitor required for smoothing

The current thru a capacitor is the rate of change of the voltage times the capacitance. At the same voltage, higher frequencies have a higher rate of change (derivative), so a capacitor conducts more current at higher frequencies, all else being equal.

Another way to look at this is to imagine a capacitor driven with different frequencies, all with the same peak to peak voltage. That peak to peak voltage dictates how much charge is sloshed around each ½ cycle. The higher frequencies will cause the same charge to be sloshed more often. Charge moving per time is current, so the higher frequency voltages cause a higher current thru the capacitor.

Don't get so hung up on names of how a capacitor is used in a circuit. Not all uses have short names, so don't try to force one onto every occasion. Generally bypass capacitor is used for the relatively small and high frequency cap close the the point of use of power. It's job is to be a short term but immediately responsive reservoir to keep the voltage smooth as the current demand changes quickly.

You can call C1 a DC blocking cap. I wouldn't try to put a particular name on the use of C2.

Without reading through the Instructable I think what you want is this:

^{simulate this circuit – Schematic created using CircuitLab}

Figure 1. Multi-piezo rectification.

The piezo output will exhibit a very high internal resistance. Once they are loaded the output voltage will collapse. In practice the capacitor loads the piezo so that each piezo pulse will add a little charge to the capacitor. The max voltage the capacitor sees will depend on the rate of charge versus the rate of discharge.

^{simulate this circuit}

Figure 2. Six-piezo rectification. All rectified outputs joined in parallel.