Item 1above, is the solenoid valve, the valve is to prevent the addition of discharge bypass gas when it isn’t wanted. The solenoid valve is usually controlled by a pressure sensing switch which activates if the suction pressure drops below a certain pressure, for air-over evaporators this should be the saturation pressure that coincides with 36 degrees Fahrenheit. The valve could just as easily be controlled by the evaporator temperature.
Item 2 above, is the pressure regulator/flow control. The valve is a spring-loaded regulator that monitors the line pressure downstream of the valve and opens, or closes, to maintain a pre-set pressure against the internal spring. Some have sensing lines, some don’t. They are set to the normal operating pressure of the suction line.
Item 3 above, is the distributor. The distributor is installed after the expansion valve and “distributes” the refrigerant to the various loops of the evaporator for even cooling across the coil. Some distributors have a tap specifically for the hot gas, others will simply be a tee in the line prior the distributor itself.
As mentioned before, but not shown on the sketch, the line can be tapped into the suction line somewhere before the compressor (not recommended). The location should be as far from the compressor as possible.
Air cooled systems that are going to operate during low load and/or low ambient conditions should have a head pressure controller or fan cycling control capable of keeping the condenser pressure at a saturation temperature of 80 degrees Fahrenheit. The system will not function correctly without the control.
Now that we have a description of the system we can add the details. The refrigerant is R-134a designed to operate at a 120-degree saturated condenser and a 45-degree saturated evaporator. There is 9 degrees of sub-cooling and 10 degrees of superheat. The design load is 1 ton, or 12,000 Btu/hour. We know when the ambient temperature is below 70 F, the system will be expected to maintain half the design load, or 6000 Btu/hour.
First, I will plot the two operating conditions without the hot gas.

So, the blue cycle is the design cycle, and the pink is the cycle at low load. The low load cycle evaporator pressure is below freezing (41 psia/ 30 F). This will cause the evaporator to freeze up and slug the compressor with liquid refrigerant.
Hot gas works by modifying two conditions in the evaporator, one, it raises the saturation pressure above freezing, and two, it displaces some liquid refrigerant that does the cooling. So we next need to determine how much hot gas we need to displace 6000 Btu/hour of cooling.
The design cycle has a refrigeration effect of 61 Btu/pound of refrigerant. The 12,000 Btu/hour design divided 60 minutes, is 200 Btu/minute. Divide 200 by 61, and the mass flow of refrigerant per minute is 3.28 pound per minute. This is the design flow rate.
The flow at low load depends on the volume change of the refrigerant at the compressor inlet. For the design cycle the volume is .89 cubic foot per pound, or .89 X 3.28 pounds, 2.93 cubic foot per minute. For the low load inlet conditions the volume is 1.19 cubic foot per pound, so the compressor design cfm, 2.93, divided by the low load specific volume, 1.19, gives 2.46 pounds per minute flow of refrigerant at low load. (Volumes can be found on standard P&H charts).
The refrigeration effect at low load is 72 Btu/pound. Multiply by the flow, 2.46, and the system capacity is 177 Btu/minute. As stated earlier, the system needs to operate at half load, or 6000 Btu/hour = 100 Btu/minute. We need to apply 77 Btu/min (177 – 100) of hot gas bypass to reduce the amount of liquid available for refrigerating with discharge gas.
 What happens when we inject hot gas into the evaporator inlet is we displace liquid droplets that are capable of cooling, the result is a change to the “quality” of the gas in the evaporator, and in turn, a lowering of the refrigeration effect.
The specific enthalpy of the gas at the discharge of the low load compressor is 76 Btu/lb. We need 77 for the evaporator, or 77/76 = 1.01 pound per minute of hot gas bypass.
Another advantage to this approach is that hot gas diverted from the discharge isn’t fed into the condenser and expansion valve so less liquid refrigerant is available for the evaporator. So, we now have 1.01 pound per minute of hot gas and 1.45 pound per minute of liquid feed to the evaporator at an unknown quality.
We can approximate the quality using a mixing equation to find the new quality; {(Mass1 X Quality1) + (Mass2 X Quality2)}/ (Mass1 + Mass2), {(1.45 X .15) + (1.01 X 1)}/ (1.45 + 1.01) = .499 is the new quality of the gas in the evaporator. This looks like the process plotted below.

Changing the quality of the gas reduced the refrigeration effect to 41 Btu/pound. We multiply 41 by the new evaporator flow of 2.46 lb/minute we get 100.86 Btu/minute or 6052 Btu/hour, pretty much half the load.
The introduction of the gas at the prescribed rate will also raise the line pressure to the regulator set pressure of 46 psia (36 degrees F saturation temperature mentioned earlier) getting the coil above freezing. The discharge pressure and temperature will also increase proportionately while the suction superheat will remain controlled by the expansion valve.
When discharge gas is injected in the suction line the behavior is a little different. The effect is to remove gas that could pass through the condenser and evaporator then raise the back pressure to raise the over-all saturation temperature above freezing.
If the hot gas injected into the suction line is before the sensing bulb, the expansion valve will try to compensate by adding liquid to the evaporator to lower the superheat which will lead to a roller coaster ride between the expansion valve and the hot gas regulator.
If the injection point is down stream of the expansion bulb, the heat from the discharge gas will raise the temperature of the gas in the suction line to about 75 degrees which could be above the manufacturer inlet temperature specification for the compressor.