1. What's the temperature of a house during different periods of the day?
How can the insulating material influence the heating energy? To answer this question, we build up a simulation model based on a system approach and take in account different influences, like the outdoor environment, insulating material. The multi-physics libraries in LMS Imagine.Lab Amesim facilitate to assembly all components and simulate within seconds different possible scenarios.
2. Modelling a house and its thermal behavior with LMS Imagine.Lab Amesim
LMS Amesim software offers a huge amount of ready-to-use components stored in different physical and application libraries. To model a house and its thermal behavior, we mainly use the thermal library. This library includes components to model thermal conductive effects, like thermal capacities or components to model solar radiation on opaque surface.
2.1 Outdoor Environments:
In this model we take into account the thermal heating or cooling induced by the solar radiation on the external walls and on the glass windows. In order to model the solar radiation and its thermodynamic effects, we use dedicated components from the thermal library, which take into account the solar incidence angle and the general radiative effect. By connecting these components with thermal wall models using convective components, we create a model for wall and window thermal heating. We can define for each of these walls the orientation. In the figure below you see a model considering the solar radiation for 4 walls of the house, by meaning of north, south, east and west.
The wall model used consists of two layers representing the insulating material (layer 1), in this case expanded polystyrene, which is insulating the second layer (layer2), the concrete.
For the window model we use a thermal wall model with 3 layers. The first and third layers are defined as glass having between them an air layer.
At port 2 we define the external temperature of the outdoor environment, which can be constant or variable to represent the temperature progress during the day. In this example the duration of the simulation is 24 hours.
2.2 Internal heat sources
Each person seating in the house produces a certain amount of heat. The average heat source emitted by a person is set 100W and is modeled using a thermal heat source component in LMS Amesim. You can directly define the number of persons using the parameter k.
To model the heating from the equipment, like the TV or washing machine, we define directly a heat flow source in Watt. The heat flow in this example is set to 1000 W.
2.3 Heating System
The heater with the thermostat is functionally modeled using components from the thermal library. You can use between 5 levels of heating intensity, similar to the thermostat you have home. To calculate the heat flow induced by the heating system and transported by radiation to the house we use following equation:Where:
A = Surface of the heater
ɛ = Emission rate
Cs = Radiation coefficient
T1 = Temperature of the heater
T2 = Temperature of the house
We assume a total surface of all heaters in the house to be 12 m². The emission rate of a heater is set to 0.88 and the radiation coefficient to 5.77 W/(m²K4)
The equation is implemented using a function block from the signal library in LMS Amesim and using a temperature sensor from the thermal library to get the current house temperature.
In order to calculate the costs of the heating for house, we have integrated a simple function, which multiplies the cost of 1kWh with the actual heating consumption.
2.4 House rooms:
To make this model as simple as possible we model the different rooms of the house as one chamber, which has the volume of the entire house. This volume can be change according to your home.
For this purpose we use the moist air chamber with heat flux from the thermal library. A moist air source with inputs like, humidity, is connected to this chamber.
2.5 Ambient Conditions:
In the thermal library we can define globally the ambient conditions. It allows to set the actual location or the starting date and time.
2.6 Final House Model
To create one thermal model we connect all components together.
To better organize the model from a functional point view we encapsulate the sub-systems into super-components. By using them, we simplify the visual appearance of the model and facilitate the parameterization of the model.
3.1. Different Heating levels
Different heating levels [1...5] allow to adapt easily the amount of energy used for heating the house. To study the temperature change during the day as a function of the heating level, we use batch runs to calculate these different scenarios.
As expected, the temperature of the house varies depending on the heating level. According to the specific ambient temperature described in chapter 2.1 (Outdoor Environments) the simulation results show a maximum temperature variation between 26 °C and 27.3 °C.
3.1. Insulating material
Now we can see for example the influence of the insulating material on the room temperature. We vary the thermal conductivity of the insulating material between 0.027 W/(m.K), 0.054 W/(m.K) and 0.108 W/(m.K). Plotting the temperature of the walls for these 3 runs allow us to see the difference.
From the results, we can easily see that the thermal conductivity of the insulating material has a big influence on the room temperature. With a constant heating, an insulating material with 4 times less thermal conductivity leads to a higher temperature of 1.5 degrees.
You can use this model in LMS Amesim V15.1 as a start to model your own house. You can extend this thermal model by including the heat exchange between different floors, model different rooms of your house or use different ambient temperatures scenarios.