I thought we’d have a look at some interesting non-automotive applications for my next few blog posts. I’ve been meaning to write some for a while. Speaking to one of my colleagues in South Africa I learnt about his area’s reduced domestic water flow in a bid to save water. I was interested to find out what the implications are in terms of additional energy required, for example, to run a bath to a desired temperature over a longer filling time period and how much of an energy usage increase we can expect?
When filling a bath we tend to mix the hot and cold water to a desired temperature. Let’s assume we are using a mixer tap. Typically the temperature of the water coming out of a mixer tap will be higher than the desired bath temperature to account for the heat losses through the bath tub, heating its thermal mass and also convecting to the environment through the water surface. A longer pouring time will inevitably lead to higher thermal losses during the filling period.
The following investigation assumes a fibreglass bath tub with the following characteristics:
- length: 1.6m
- width: 0.55m
- height: 0.35m
- wall thickness: 4mm
The cold and hot water copper pipes are assumed not to be insulated and to have:
- diameter: 15mm
- wall thickness: 1mm
The boiler will heat the cold supply water up to a temperature of 60 degC.
The boundary conditions for the experiment will be a target bath water temperature of 38 degC and a desired filling height of 60% of the total height.
Heat transfer:
The heat transfer is assumed as follows.
For the pipes we are convecting heat from the wall outer surface to ambient. The heat transfer from the fluid to the internal pipe wall is modelled according to flow regime conditions and surface roughness.
For the bath tub we assume heat transfer from the water to the bath tub and also convecting from the water surface and outer bath tub surface to the surrounding air.
DYMOLA diagram layer of the multi-domain representation of the bath filling system. We used a combination of Modelica.Fluid and advanced pipe models from our specialised Claytex.Fluid library.
All components in the bathroom are initialised at ambient conditions for the house which are 21 degC. The water supply is set at 18 degC. Because the spec of the boiler is not known, but we know that the outlet temperature is 60 degC, we can exploit the acausal nature of the underlying MODELICA language and force the boiler water to 60 degC. The heating power required to do this will be automatically calculated for us. Assuming a constant efficiency of 90% this power is then integrated over time to calculate the energy usage for filling the bathtub to the required temperature.
At the start of the simulation, the mixer tap will open and the outlet temperature controlled to ensure that the bath water temperature is kept at 38 degC. Although in reality we most likely won’t have this automated system, it is a way to ensure a repeatable boundary in this respect. In reality we would be checking the water temperature as we fill the bath and adjust the mixer outlet temperature to suit.
Once the desired bath fill level has been reached, the flow is stopped and the total energy usage for heating the water recorded.
The model has a tunable restrictor immediately downstream of the supply whose discharge coefficient has been calibrated to deliver a fifth of the unrestricted mass flow rate for the restricted case.
The total energy required to produce enough hot water to fill the bath to 60% of its total volume with a final temperature of 38 degC with unrestricted (baseline) and restricted flow are 4.46 kWh and 4.93 kWh respectively indicating a total increase in required energy of 10.5% with reduced flow.
We then used the model to tell us what final temperature would be required in order to reduce the energy consumption to our baseline of 4.46 kWh. The end temperature would have to be 36.4 degC. Alternatively if we only filled the bath to 54% of it’s volume (18 litres less than our baseline) we could achieve the same baseline energy usage.
Reduction of water supply flow can achieve lower usage if the customer is prepared to take a hit on volume of water used for the same end temperature. If they are prepared to take a temperature hit for the same volume and are prepared to wait longer then there will be no water saved.
In the next post we will look at what detail can be added to more closely represent the system, for example pipe bend losses, thermal insulation of the pipes and bath, thickness and material of the bath, material of the pipes, thermal losses of the taps and the influence of storey height on the filling performance of the bath and the hot water energy consumption.
The model was built in DYMOLA using a combination of the Modelica.Fluid library and the Claytex.Fluid advanced thermo-fluids modelling library. A Modelica.Fluid only version of the model is also available on request for those who do not have a Claytex library licence.
Tip: When creating your fluid system model you might want to set the following command: Advanced.MediaPropagation = 1 or 2. Setting this command will make the task of setting and propagating the medium model in each fluid component that you drag and connect much easier and automated. The setting 1 or 2 will change the amount of detail in the automated settings within the pop-up windows.
Written by: Alessandro Picarelli – Engineering Director
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