Vaillant Heat Pump Controls: Part 1: The heat curves.

Friends, I live and learn.

When I wrote previously about my radiator replacement therapy, I mentioned briefly the Vaillant control system with its mysteriously numbered control curves and arcanely inarticulate descriptions.

Afterwards, several people contacted me on Twitter, Mastodon and in the comments and suggested I had read the manual incorrectly. And I realised – not for the first time – that I had been an idiot. And I further realised that an issue raised by a correspondent about radiator de-rating was central to my misunderstanding of this issue.

This is a rather technical article: sorry. But please allow me to explain.

The Vaillant Heat Curve Diagram

In the Vaillant manual there is an arcane diagram which is designed to help users set up their weather compensation. It looks like this:

Click on image for a larger version. This is the Weather Compensation diagram from the Vaillant Manual.

• The vertical axis is the flow temperature of the water in the radiators (°C)
• The horizontal axis shows the outside temperature (°C). This is plotted in reverse i.e. bigger numbers are to the left.
• Both axes meet at 20 °C i.e. when the outside temperature is 20 °C and the flow temperature of water in the radiators is 20 °C. Unsurprisingly, this diagram is only correct if you want your home to be at… 20 °C!
• The various curves show different ways in which the control system will adjust the flow temperature of water flowing through radiators as the outside temperature falls.
• Each curve is labelled with an apparently arbitrary number between 0.1 and 4.0.

The first thing we need to understand is why the diagram above looks like it does, and in particular, why the curves are curved, and not straight lines. This will take the whole of the rest of this article! I’ll talk about adjustments in a follow up.

How Radiators Work

I have written about how radiators work before, but I didn’t do a very good job. I concluded that for many purposes, one can assume that the heating power (watts) of a radiator is proportional to the difference between the average temperature of the water in the radiator and the room temperature. However, if one looks in detail, this is really not a very good approximation.

The figure below shows (red line) how the heating power of a typical radiator varies as the flow temperature increases. The calculation assumes that the room is at 20 °C. Also shown (green dotted line) is the assumption of proportionality.

Click on image for a larger version. Graph showing the heating power of a typical radiator versus the temperature of water flowing through the radiator. Also shown as a dotted green line is the heating power if the output were directly proportional to the temperature difference between the flow temperature and room temperature.

Increasing the flow temperature, increases the heat output of the radiator, but the curvature means that increasing the flow temperature by a fixed amount results in different amounts of additional heating depending on what the flow temperature is.

Click on image for a larger version. Graph showing the slope of the curves and lines in the previous graph versus flow temperature. For a real radiator the output power from increasing flow temperature by 1 °C varies from 10 W/°C to over 25 W/°C at high temperature.

For example, at the lowest flow temperatures, increasing the flow temperature by 1 °C results in an additional 10 W of heating power. But at the highest flow temperatures, increasing the flow temperature by 1 °C results in more than 25 W of extra heating power.

Click for a larger image. A typical dual-panel radiator transfers heat from the hot water flowing through it to the room in two quite distinct ways. By direct heating of the air in contact with the metal surfaces, and by radiation from the outer metal surface.

Why is this? It’s because radiators heat a room by two mechanisms: convection and radiation. Over this temperature range, radiation is completely linear i.e. the heating power is directly proportional to the difference between the average temperature of the radiator and the room. But heat transfer by convection is more complex.

One can consider heat transfer by convection in two stages. In the first stage, air immediately next to the radiators metal parts is heated. In the second stage, this air leaves the radiator and heats the room. It is this second stage where the complexity arises:

• The heat transfer rate in the first stage is proportional to the temperature difference between the air and the radiator.
• The heat transfer rate in the second stage depends on the speed of air flow moving past the metal surfaces of the radiator. At low radiator temperatures the air rises only slowly, but as the temperature difference between the radiator surface and room-temperature air increases, so does the speed of the air flow: colloquially there is a chimney effect.

Combined, these lead to low rates of convective heat transfer at low temperature differences, and higher rates of convective heat transfer at higher temperature differences.

So now we understand how radiators work, let’s think about how a control system will use radiators to control the temperature of a dwelling.

How Weather Compensation Works

The rate at which heat that leaks out of a house is proportional to the temperature difference between the inside and the outside. People have investigated this thoroughly and it is substantially correct. Weather Compensation is a control scheme which exploits this proportionality.

Weather Compensation increases heating power in proportion to the temperature difference between the inside and the outside. If adjusted just right, the heating power exactly matches the rate at which heat is lost to the outside, and the temperature stays constant. Notice that this control system works without a conventional internal thermostat.

Analogy. This is to equivalent stabilising the level of water in a bucket without using a level sensor. Imagine having a bucket with a leak in the bottom. As the bucket fills up, the rate at which water leaves the bottom of the bucket increases in proportion to the depth of water in the bucket. If we use a pump to fill the bucket at a rate which just matches the rate at which water leaves, then the water level will stay constant.

Notice that in order for weather compensation to work for a wide range of outside temperatures, it’s important that the heating power is varied in proportion to the temperature difference between the inside and outside of the house. This is where the non-linearity of radiator output that I mentioned at the start of the article becomes important.

The weather compensation schemes in all devices (boilers or heat pumps) works by increasing the flow temperature in radiators when the outside temperature falls. But the weather compensation scheme must account for the non-linear output as the flow temperature changes. To see how it does this, we need to re-plot the first graph in this article – the radiator de-rating graph – and plot it with the axes swapped over.

Click on image for a larger version. This is the same data as plotted in the first graph, but with the axes swapped. This graph shows the flow temperature required to cause a radiator to emit a given heating power.

We see that plotted this way, heating power is on the horizontal axis and flow temperature is on the vertical axis. We can now see the curvature familiar from the Vaillant weather compensation diagram. As I mentioned above, heating power needs to be proportional to the difference between the internal temperature and the external temperature. So we can re-plot the graph above like this:

Click on image for a larger version. This is the same as the previous graph, but the heating power on horizontal axis has been replaced by the outside temperature. Notice that the horizontal axis is plotted in reverse so that zero heating power corresponds to 20 °C.

This is the same data as the previous graph but the horizontal axis has been re-labelled as the “Outside Temperature”. This particular curve describes one particular response of a control system seeking to stabilise internal temperature as the outside temperature falls. But depending on the installation, more or less heating power may be required. Depending on how much more or less heating power is required we can generate a family of curves that a control system could use. We would just need to pick the correct curve.

Click on image for a larger version. This is the same as the previous graph, but with additional heating curves added corresponding different radiator systems.

So I think now one can see the origin of the diagram in the Vaillant manual. The curves are curved because they compensate for the non-linear output power of radiators as the flow temperature is increased. There are a family of curves depending on the thermal properties of the dwelling and the radiator system.

Heat Transfer Coefficients (HTCs)

A heat transfer coefficient (HTC) is a number which occurs in the description many heat transfer situations, and characterises the rate at which heat flows across a boundary due to a temperature difference of 1 °C.

When considering this control problem, there are two important temperature differences, and two important heat transfer coefficients. The first heat transfer coefficient (HTC_ext) describes the way the heat is lost from the inside of a dwelling to the outside. The second heat transfer coefficient (HTC_int) describes the way the heat is transferred from the hot water in the radiators to the inside of the dwelling.

Click on image for a larger version. Illustration of the two important heat transfer processes. Left. HTC_ext describes how much heat flows out of the house when it inside temperature is raised a further 1 °C above the outside temperature. Right. HTC_int describes how much heat flows out of the radiator when the flow temperature is increase by a further 1 °C above the room temperature.

• The external HTC (HTC_ext) describes how much heat leaves a house when its temperature increases by 1 °C above the outside temperature. Insulating a house reduces this number. For my home, the heat loss is about 4,000 W when the external temperature is -5 °C and the internal temperature is 20 °C. So the heat transfer coefficient is 4,000 W/25 °C = 160 W/°C.

• The internal HTC (HTC_int) describes how much heat leaves the radiators when their temperature increases by 1 °C above the internal temperature. Adding more radiators increases this number. For my home, I measured that:
  • When the flow temperature was 46 °C the heat transfer coefficient for the new radiator system was ~220 W/°C.
  • When the flow temperature was 32 °C the heat transfer coefficient for the new radiator system was ~200 W/°C.

So now we can re-write the labels on the previous graph using HTCs.

Click on image for a larger version. This is the same as the previous graph, but now with additional labels showing how the temperatures on the previous graph are related to heat flows, and the heat transfer coefficients..

We now see that the graph is really a graph of Heating Output versus Heating Demand, and that the curved lines reflect the fact HTC_int varies with flow temperature because of the non-linear physics of convection.

For my home,

• HTC_ext = 160 W/°C. So for every 1 °C that the external temperature falls I need 160 extra watts of heating. This is true at all temperatures.
• HTC_int ~ 200 W/°C at low flow temperatures and 220 W/°C at higher flow temperatures. So to match the heat loss caused by 1 °C fall in external temperatures, I need to increase the flow temperature by different amounts depending on what the flow temperature already is.
  • If the flow temperature is around 32 °C, I need to increase the flow temperature by around 160/200 =0.8 °C
  • If the flow temperature is around 46 °C, I only need to increase the flow temperature by around 160/220 =0.73 °C

Notice that HTC_ext is dependent only on the fabric of the house but  HTC_int depends on the radiator system and the temperature of water flowing through the radiators. One can affect HTC_ext by reducing draughts, and improving household insulation. But to improve HTC_int one must add more radiators, or increase the size of existing radiators, or add fans to existing radiators.

Curve Labels

So one mystery remains. What is the origin of the seemingly arbitrary labelling of the curves. My surmise was that the curve labelling convention is based on the ratio of HTC_ext to HTC_int at some arbitrarily chosen temperature. So for example:

• If (at some arbitrarily chosen temperature) one needs to make the flow temperature 4 °C hotter when the external falls by 1 °C, then the curve is labelled 4.
• Similarly, if (at some arbitrarily chosen temperature)  one needs to make the flow temperature only 0.6 °C hotter when the external temperature falls by 1 °C, then the curve is labelled o.6.

So the curve labelled “1” would describe a situation where the flow temperature needed to increase by exactly 1 °C for each additional 1 °C that the  external temperature fell.

Now I have obviously checked this – and it doesn’t quite work! So the mystery remains!

Summary 

In this article I have been explaining to myself the origin of the curves of the Vaillant temperature control diagram. I say explaining to myself because almost 2,000 words in, I am sure that most humans will no longer be reading this!

Basically the curves reflect the non-linear behaviour of radiators. But I am sceptical that all radiators behave similarly, so these curves are likely conventional only. The control system also ignores the fact that there are other sources of heating in most dwellings (people and electrical items in particular) and so the heating demand is typically zero or negative until the external temperature falls below about 17 °C.

In the next article, I will look at the three modes of room temperature modulation offered by Vaillant, and the how the diagram is affected when the internal temperature is not 20 °C.

If you still want more, check out this article which has much more detail than this one!

Tags: Convection, Radiators