Modifiers: Twist, Noise, TurboSmooth
Particle Systems: Spray
Space Warps: Ripple
Helpers: Atmospheric apparatus
Tub Water / Water Plane:
I added a plane and gave it the water texture. Then, I added a space warp > geometric/deformable > ripple effect and used the bind to space warp tool to bind the ripple to the water plane mesh. I adjusted the flexibility parameters and added a turbosmooth modifier.
I also adjusted the ripple parameters to get a slight, soft ripple in the water. Adjusting the number of circles and segments smoothed out the ripple circles.
I animated the ripples by setting key frames at the first and last frame and changing the phase from 0 (on the first frame) to -5.2 on the last frame.
Faucet Spray/Water Pour:
I added a Particle Systems > Spray effect below the faucet head. I modified the drop size and speed and applied a water texture to the spray.
I adjusted the start to -50 so the spray would already be in motion when the animation began. I also adjusted the render count, speed, drop size, variation and set the type to drops. Then I added a twist modifier to the spray.
For the constant pour, I added a cylinder object and adjusted the mesh so it was pinched in some places, narrowing and widening – curvy. Then I animated the cylinder by setting a key frame on the first and last frames to rotate it. This makes the water flow look like it’s varying in pressure a bit as it widens and narrows.
I created the flames using a helpers > atmospheric apparatus > sphere gizmo.
I added the fire effect to the sphere gizmo on the atmospheres and effects rollout.
I added a noise modifier to the flames/sphere gizmo, too, to animate them a little bit as though they were flickering.