In his next column, Griff Thomas from heatly, looks at what can affect flow rate in a heat pump system and consequently the amount of energy needed to keep a house warm, while explaining the calculations needed to work this out accurately.
All wet heating systems rely on warm water flowing through pipes and radiators or underfloor heating circuits. In the case of a heat pump (and any low or standard temperature system), correctly calculating any resistance that may compromise flow and therefore reduce performance is key – every part of the system can impact the flow.
Get these calculations wrong and you may end up with a heat pump system that fails to keep customers’ warm and/or costs more to run.
Pipes
The length of the pipe, diameter and the number of branches, changes of direction you have throughout the configuration all effect the amount of friction and consequently potentially the flow rate.
You will be aware that low temperature heat pump systems require a greater volumetric flow than gas boilers for the same kW transfer due to the narrow dt by comparison. A heat pump can work with smaller diameter pipes, but you may have to increase the circulator pump pressure to deliver that flow and therefore the energy used (and costs associated).
Where possible, pipe runs should be short and bends kept to a minimum, valves, filters, radiators etc., all induce resistance which increases our index circuit calculation.
When calculating the flow rate, you need to consider the radiator output required in kW, pipe sizing formulas and specific product friction loss. If the correct volumetric/mass flowrate through the radiator is not achieved, the radiator mean water temperature and consequent room temperature will not be reached.
If water moves flows at a reduced rate, the differential temperature (dt) will be wider and therefore the required flow temperature from the heat pump will need to increase to compensate, raising the mean water temperature, this will reduce efficiency and increase running costs.
Example calculations
To work out velocity, volumetric and mass flow rates, the calculation is: V = Q (m3/hr)) ÷ (Area (m2) x 3600 seconds).
In my opinion, it helps to understand how the constituent parts interact and set out each step clearly. For example, a 7kW heat pump, Delta T 5 specific heat capacity (shc) 4.2 requires 7kW ÷ (5 x 4.2) = 0.333333kg/s – these are generic numbers, for example purposes only.
Industry usually uses the equation 1kg/s = 1L/s, but in reality, this is almost never the case. The flow temperature affects the density and the shc of water. At 40 degrees, shc is 4.18kj/kg/°c (not 4.2) and its density is 0.99423kg/L.
For example, a 7kw Arotherm has a max flow of 1205 L/hr, because the water is warmer the density per litre is less, consequently the volumetric flow rate value is numerically greater than the mass flow rate value.
1205L/hr x 0.99423kg/L = 1,198.04715kg/hr
1,198.04715 ÷ 3600 = 0.332790875 kg/s
As opposed to: (1205 ÷ 3600)= 0.33472 L/s
At A-3°/W40° 8.6kw is the stated output
Consequently: 8.6 ÷ (mass flow 0.332790875 x shc 4.18) = dt 6.18 required.
When we look at how many watts are being transferred per L, 8600w ÷ 1205L = 7.14w/L
To calculate a theoretical figure to the nth degree it’s necessary to move from volumetric flow rates to mass flow rates and vice versa.
So, in the simplest form volumetric flow in L/s x density in kg/L at the chosen flow temp = mass flow in kg/s.
0.33472L/s x 3.6 = 1.205m3/hr volumetric flow
0.332790875 x 3.6 = 1198.047kg/hr mass flow
28mm pipe diameter has an internal diameter of 26.2mm.
We need to convert the diameter from mm to metres, to do this we must divide by 1000 = 0.0262m. Using the formula below we can calculate the velocity of a fluid through a pipe if we know the volumetric flow rate in m3/hr and the pipe diameter in metres.
Flow through a 28mm pipe will have a velocity of 0.6208m/s. The formula in the diagram is based upon 1.2m3/hr rather than 1.205m3/hr, this is why it’s important to know the min/max flow rates of appliances.
Based upon the detail below when 1.205m3/hr @ 40°c the return leg would flow at 33.82°c, the 1.205m3/hr would be denser, @0.9955kg/L or 1199.6kg/hr.
To average this out we use the mean water temperature (40+33.82) 2 = 36.91°c. At 36.91°c the mass is 0.9948kg/L
The maximum volumetric flow 0.33472L/s has a mass flow equivalent of 0.33472 x 0.9948 = 0.33297kg/s. The shc at 36.91°c is 4.178.
The 8.6kw output ÷ (4.178×0.33297) = 6.18°dt
But what about the minimum output?
The same heat pump has a minimum flow rate of 540L/hr, that’s 540 ÷ 3600 = 0.15L/s. Our kw load is typically 25% of peak at base temp, i.e. 2.15kw and therefore would require a flow temp of 30°c or mwt of 26.91°c (@ dt 6.18). The shc is then 4.179, the mass per kg has changed because the cooler water is denser, so:
0.15 l/s x .9968kg/l = 0.1495kg/s
0.1495kg/s x 4.179 shc x 6.18 dt = 3.86kw
This assumes dt can remain constant. 3860w ÷540 L/hr = 7.15w/L. If the dt across the emitters is not maintained, due to flow rates not modulating low enough to match the kw load required, the dt would narrow, which changes the minimum output.
If the max mass flow rate 0.33365kg/s continued – as is common with fixed speed circulators in some heat pumps – then at what point would the heat pump cycle? What minimum dt would be tolerable for the heat pump?
Just assume for this example a dt lower than 3°C would lead to the heat pump cycling:
0.33365kg/s x 4.179shc x dt3 = 4.183kw
4183w ÷ 1205L/hr = 3.485w/L, which is significantly less than by modulating the flow proportionately to the kw output and maintaining dt… its over 50% less. This has the effect of increased circulator running costs, as the dt narrows the mwt increases from 26.91c to 28.5c.
Fully modulating the volumetric flow rate is more efficient in terms of circulator running costs, the lower rate at 0.540m3/hr has a velocity through the same 28mm diameter pipe of 0.278m/s, almost 50% lower, consequently friction losses are similarly reduced.
The conundrum for system design, peak load and pipe lengths, fittings, cumulative resistance pressure drops all figure in pipe sizing and velocities, yet most of the year the velocity would then be lower than guidance 0.5m/s … but its only guidance, in my view needs addressing.
The relationship between kw outputs, velocity, volumetric flow rates, mass flow rates, changing mean water temperature through weather comp / load compensation, are all interwoven.
All the above feeds into the Reynolds number formula, the friction factor formula and pressure drop per m formula – something for another day.
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