Well, you know that to charge a capacitor instantly will require infinite current, right? And we know that all real-world power sources have some finite resistance associated with them, as do capacitors (ESR). However, as your intuition suggests, if you just pop your capacitor across a supply you are depending on the parasitic resistance to limit your current. If it doesn't limit your current enough your supply may not be able to handle it and you can get droop or brownout.
So it's better to control the charging impedance to a known value that doesn't stress the rest of the system.
Sometimes, especially in AC/DC supplies a positive tempco thermistor is used to limit the inrush that charges the main cap. As it heats up the resistance decreases and the circuit begins operation.
Before you design your smoothing capability, you need to specify what you want it to do.
'The current coming out should preferably be maintained around 180Amps.'
This is not a specification, and around is not a tolerance. It does sound like you want a constant current output, rather than a constant voltage. Or are you just using 'current' loosely? Would a constant voltage be OK?
At the risk of being obvious (this is to illustrate the need for a specification), you can approach zero voltage ripple on the output as you approach infinite capacitance. The two are precisely in inverse proportion. Less capacitance, more ripple. So, as capacitance costs money and takes up space, you can work out exactly how much capacitance you need, from how much ripple your application can tolerate.
The easiest way to produce a high ripple, high value capacitor, is to parallel several lower value caps. So yes, your idea of 90 off 2A capable caps to handle 180A is OK. You may not need as many as 90.
There are better ways to reduce the output ripple than simply racking up the capacitance, once the ripple becomes a critical specification.
The first is use of three phase power. The problem with single phase is the long period with no effective power coming from the mains, that has to be held over by the capacitors. Three phase reduces the ripple from raw rectified mains to a few percent, rather than the 100% of single phase.
The alternative is to use a SMPS, switched mode power supply. At this power, getting for 4kW, it should be power factor corrected. The design of a SMPS at this power level is non-trivial, and you would do best to buy something.
Best Answer
A typical DC power supply (like you might find in your phone charger) will look something like this (probably with more protection devices and other extras). The AC will be rectified by a bridge rectifier and smoothed by a capacitor to create high voltage DC. Then a power supply IC will quickly switch the current through a transformer on and off to step down the voltage to say 5V. The output is once again rectified and smoothed, then fed to your phone:
simulate this circuit – Schematic created using CircuitLab
The resistors across the capacitors (especially R1/C1 because they are at high voltage) are there to discharge the capacitors when the device is unplugged, so that if someone touches the output they won't get shocked. Because the capacitors are there only for smoothing, and not to allow the device to function for a while after power is removed, having the capacitors discharge quickly when the device is unplugged does not hinder their operation and improves safety, so they're included almost everywhere.
Note: I have omitted several things from the schematic, such as a power rail for the converter chip, feedback windings, or flyback configuration, as they do not help to illustrate the functioning of the capacitors and discharge resistors.