Thermal Simulation of a Metro System
Jorge Amaya
Roberto Román
Takeshi Asahi (Research Engineer)
Guillermo Poblete (Research Engineer)
Jose Antonio Sanchez (Research Engineer)
Universidad de Chile
We present a brief outline of the hypothesis behind our model, the way it was conceived and how one can use it to deal with "what-if" scenarios. We have made some simplifications, but this actual model can be improved.
Basic Approach
Instead of using empirical parameters for the model, we decided that the best approach was from a strictly physical point of view. Thus the system is modelled as dynamic systems (the trains) that move between stations and this system has certain energy inputs and outputs.
Then we have the tunnel system that interacts with the energy exchanges that rise from the train system.
Train model:
The train was modelled as a dynamic system that moves along rails. The train has a certain mass (tare weight, load and rolling inertial mass) and one wants it to follow a certain acceleration and deceleration curve.
Forces that act on the train are: inertia, rolling friction, air drag. From the basic equations one can calculate the required force for the train to accelerate and thus the input power as well as the energy losses.
Speed / distance track:
From basic kinematics, we use the speed versus distance for this simple model. We had to use a 1 meter interval to have good enough approximations. One can input and change parameters such as: mass (empty, passengers and inertia), the acceleration versus distance profile, rolling resistance, drag coefficient and the power dissipated by auxiliaries.
Braking efficiency actually can be modified.
Kinematics results:
Besides the speed versus distance profile, one also obtains the force necessary to accelerate the train and also the different losses, including braking losses. These are presented both as kW as well as kJ per meter. From these results it is evident that, except during braking, one important loss to the tunnel is due to auxiliaries.
As the train moves along the track, there is power dissipating as heat. This is then calculated as energy dissipated per meter of track when a train passes.
For the moment, we suppose the track is horizontal and straight. It should not be too difficult to incorporate slopes and curves.
The basic idea of this approach was to have a good breakdown of the different forces that act upon the train and then compare these with real cases of study.
