A common problem with 1-pipe heating systems is the unwanted heating of the radiator when the thermostat is in the minimum position and the valve is closed. Unlike 2-pipe systems there is a constant flow of hot water running past the radiator via a bypass, which means that very close to the radiator there will always be both fluid and solids at temperatures as high as 95oC. The construction of a 1-pipe system therefore has the disadvantage of hot water being able to travel in the wrong direction after passing through the bypass and slowly circulate inside the radiator due to buoyancy effects. This slow circulation of water is termed “backflow” and is undesirable since it adds to the heating bill of the consumer even during a closed valve period. Using computational fluid dynamics (CFD), a simplified version of a 1-pipe system with a bypass was investigated with special attention paid to the recirculating flow and the effect of connecting a restriction in the bottom of the radiator. The CFD results, which have been verified against laboratory tests, have been used to gain knowledge about the flow through the suggested restrictor when buoyancy is the dominant effect.

Computational setup
Using the efficient STAR-CCM+ pre-processing tool, a simple model was quickly created enabling an easy study of the design proposal. It was decided, after some trial simulations, not to model the entire radiator for two reasons; 1) modeling the entire radiator heat transfer (i.e. heat transfer from water -> solid -> air) would require a detailed model of the entire system to catch the buoyant features and 2) only the backflow restrictor’s influence on the heat transfer path is of interest. Based on the trial runs a major part of the supply piping was removed and the radiator was replaced with a 300 mm fluid section acting as a heat sink: cooling down the pipe “exhaust” flow to ambient temperatures (see Figure 2).
The solid parts were prescribed a convective heat transfer of 5 W/m2-K @ 20oC ambient temperature, while the pipe end furthest from the heat sink was maintained at a constant temperature of 95oC. The heat sink was prescribed a constant temperature equal to the ambient temperature. For the simulation of buoyancy, the model assumed steady-state, incompressible and laminar flow. A density was specified and hence the buoyancy source term was modeled using the Boussinesq approximation, where body forces are a function of temperature alone.
To obtain a converged solution the coupled steady-state solver was used for initialization of the flow, while the segregated transient solver was used after a few hundred iterations to obtain the final steadystate results. The net heat flux across the plane section combining the heat sink with the rest of the model was used to monitor if a converged solution had been reached based on engineering data (see Figure 3).

Discussion of results

The results from the CFD simulations have been compared to laboratory tests using the same restrictor geometry and, although there were quantitative differences, the major flow features were well predicted. While the laboratory tests were carried using a complete radiator setup (see Figure 1), the CFD model was only a small part of the entire geometry, which would explains the differences in results shown in Figure 4.
When comparing the CFD simulations to experiment, all restrictor results were compared to the net heat flux from a setup where the restrictor was replaced with a straight pipe. As expected, there is not much difference in the net heat flux when the restrictor is horizontally aligned as this would be the same as adding extra pipe length to the existing setup. However, positioning the restrictor with the bend pointing up- or downwards shows a dramatic drop in the net heat flux but more interestingly the efficiency of the restrictor is higher with the bend pointing upwards.
To explain these findings, a sequence of plots showing streamlines and velocity magnitude for the three different positions of the backflow restrictor is shown in Figure 5 through Figure 7. With the restrictor in horizontal mode, the influence of the bend does not seem to have a significant effect on the backflow. This was also not expected as the design of the restrictor was meant to inhibit the flow by using the density differences in the fluid caused by the temperature changes. Rotating the restrictor 90 degrees, however, shows a more dramatic effect as the hot (and thus less dense) water coming from the righthand side is blocked by a layer of relatively cold (and denser) water in the bottom of the restrictor. As a result, two recirculation zones emerge with a very low heat transfer in between.
The last configuration is better in terms of minimizing the net heat flux. Although the temperature of the “exhaust” fluid is almost the same in the two cases, using the restrictor in downward configuration results in average velocities almost 60% higher in the “cold” pipe section due to the longer path over which the fluid can be accelerated. With the restrictor pointing upwards, the same type of acceleration is seen, but since this occurs on the “hot” side of the restrictor, the added momentum does not have an effect on the net heat flux out of the restrictor on the “cold” side. Therefore, the most efficient way of installing a backflow restrictor would be with the bend facing upwards, as the laboratory tests also showed.

Conclusion
A series of simulations have been carried out in order to investigate what effect a backflow restrictor would have on net heat flux going into the radiator system. The simplified model showed similarities to real laboratory tests and the trends found were also replicated in the CFD results, although no direct numerical comparison could be made. With the CFD results it was possible to get a better understanding of the localized flow patterns in different configurations and thus give a better recommendation on how to use the restrictor in a real installation.