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Very interesting problem you have here. Both Mitch and Michael are right and cover the potential problems. I'm gonna add a third observation. I personally would NEVER allow heated water to infiltrate the cold water supply. The water coming from most water heaters is filthy, dirty and full of bacteria.(especially if temp is set below 140F) The sediment in the bottom of most heaters is nasty! I always advise my customers to never use hot water for potable purposes unless it is going to be boiled in the process. With that said, the closed systems I have had installed cycle the unused hot water back into the cold water supply to the heater tank with a back flow preventer installed in the cold feed to prevent the warm water from entering the cold supply by siphoning. The system as pictured looks to me like a quasi sediment agitating system, by pumping water in from the bottom of the tank. NASTY!!!! There is a reason for a drain at the bottom; to get rid of sediment as well as drain the tank to replace it. I would rethink this system, get some advice from a Master Plumber that knows how to install a recycling system if you feel you need it. Most residential users do not need instant hot water, have the high volume usage or have hot water outlets located so far from the heater to justify the additional operating costs of this type of system. Don't get me wrong, loop systems are great if the lines are well insulated, and the volume of hot water required can justify the cost.

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First off, it's quite possible that the segment of pipe between the pump and the "tee" attached to the drain valve is completely or partially clogged with (corrosive) scale/sediment buildup. Judging by the scale buildup on the outside of the pipe just below the tee, it looks like the tee is leaking (why? corrosion?). I can only imagine that the inside is worse. Even the check valve and the ball valve upstream from the pump look like crap. In fact, I'm pretty sure that's calcium on the ground below the check valve (thing between the pump and the drain with a hex bolt -shaped top on it), indicating that it too is already leaking. The check valve almost certainly isn't functioning properly (check valves are intended to only allow water to flow one way,) which is possibly why you are having to constantly readjust the temperature in your shower. The cold water gets injected into the tank at the bottom (via a long "dip tube" that enters at the top and travels down to the bottom.) If this check valve is being held open by sediment, or if it has failed due to corrosion, then cold water could be coming out of the water heater from the drain at the bottom, making your "hot" water turn merely "warm" after about 10-15 gallons of use, which is one possible explanation for your "shower get[ting] colder during use" problem.

I see a line (the CPVC that goes into the wall) for what I hope to be a T&P valve, but I can't see where the actual T&P valve is. If it's tee'd off of the hot water outlet, then that's fine. I'd hope it's not simply laying on top, not connected to anything, but I don't have enough faith in whoever installed this to take that for granted.

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Actually the return loop line coming back to the tank should have the pump at that point. After the pump the return line should run back to the cold supply line to the top of the take with a tee and shut off valve on both legs of the tee. One leg should go to the cold supply in with a check valve on the cold supply side to prevent the hot water from backflowing into the cold supply. The other side of the tee should go to the hot supply line to feed the house with a check valve to prevent backflow. the shut off valves on each leg should be close 1/2 to divert roughly equal flow to the tank and the hot supply. This configuration will give you true circulation of the hot loop as intended.

This device recirculates the water in those hot water lines by placing a sensor and a valve at the farthest end of your hot water line that senses when the water in the hot water line has dropped below 95° F, opens the valve and “trickles” the water out of the hot water line into the cold water line until the water in the hot water pipes gets back up to 95° F or so.

What the manual is describing is a system without a dedicated return line. The valve at the furthest point allows previously hot water that is now cool to go into the cold water pipes backwards and the pump pushes hot water back into the hot pipes up to that valve. With an existing install, this is probably the easiest way to do it, but I prefer an install with a dedicated return to avoid getting the water from the hot water tank in the cold lines (not a fan of the mineral taste). It looks like you have the latter setup.

check valve is looking a little crusty. they dont hold up well in potable water. cold water from the bottom of the tank will "back" through the pump amd mix with the hot giving you the diminished hot water that you descriped.

I'm having some problems with it now, as it's no longer providing hot water as quickly as it used to. I looked up the service manual for it, and it calls for an installation different than what I'm actually seeing (not sure if this is the problem, but I want to understand). The manual specifies:

You're sorta kinda in a bit of trouble here. This system is close to being good, but because of a seemingly minor screw-up, you're going to have major problems here. The recirculating pump SHOULD NOT be connected to the drain.

My advice would be to get this junk removed ASAP before something bursts and you have a disaster on your hands. Get rid of it completely, or if you want to get it fixed up, get a new pump (Grundfos makes great pumps, but I can't imagine that this pump is usable at this point) and tell the plumber to connect the recirculating pump to the T&P relief valve inlet, which is not currently being used(?), rather than the drain. Doing this would reduce the scale/sediment buildup greatly, which happens mostly near the bottom of the tank. Replace all of the pipe in the vicinity of the pump as well, as it is probably completely scaled up and corroded. Everything else should be ok.

Moved into a house recently that was built in 2006. There is a hot water recirculating pump installed (Grundfos UP 15-10 pump). I'm not very knowledgeable about plumbing from a DIY perspective, so I could use some help here.

The first thing I'd check if you're having problems is when the timer is set. You typically want this to run shortly before you get up in the morning to use the sink/shower. Over time, with a power outage now and then, it may be running after you need the hot water.

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My perfect advice would be to return the feed immediately back to the top of the tank on the cold side, check valve included. This way continuous circulation happens inside the tank rather than taking chances with a whole house system. You might also install an extra pump at the top of the loop to help balance out the bottom pump, etc. A third pump in between is optional although highly recommended. The idea here is to get the water spinning fast enough to cause friction ergo the generation of heat.