Thermal convection and numerical simulation

It is common to compute the energetic fingerprint of buildings during constructions and renovations. Such an analysis computes a balance between heat sources and heat losses in buildings, and helps cut the economic and ecologic cost of cooling and heating. Most of the time, the analysis however only provides a global picture, and cannot predict in detail how the temperature spreads inside building. The physics of thermal convection is highly sophisticated, and massive computer simulations are necessary to produce valid predictions. With help of the simulations, critical mistakes are avoided during a renovation, and the level of comfort of a work or living place can be distinctly improved. Numerical simulation typically provides an answer to questions such as

  • What temperature is felt by an office worker sitting in front of a window in a given building? How strong is the draft at the level of his head or feet? At what distance from the window must the offices be placed ideally?
  • Where to ideally place sources of heat or cooling (floor/walls) to obtain a uniform temperature and miminal drafts?
  • How to protect "critical areas" from impacting negatively on the overall energy fingerprint (e.g. automatic curtains in front of windows with high insulation, or vestibule in front of exposed entrances)?
  • How to place heat diffusers or air conditioners to improve the convection pattern in the building (efficient thermal mixing, but low drafts in inhabited areas)?

Our modeling approach

 We provide a computer analysis of thermal convection by a 4-step approach:

  1. Analysis of the building, identification of heat sources / cold spot, description of global energy balance.
  2. Design of a detailed 3D model of the building, including the identified heat sources and cold spots.
  3. Computer simulation on high-performance computing platforms.
  4. Analysis and presentation of the simulation results.

Our computer model incorporates various types of architectural constructs and thermal devices.

  • Windows with different insulation values (U-factor) and varying outside temperature (summer/winter). Solar radiation through windows.
  • Radiators and heated/cooled floors/ceilings.
  • Heat diffusers, pulsed air conditioners.
  • Internal heat sources (office workers, computers, lightening).

The example below illustrates the abilities of our software. Cold air is injected into a conference room through an air conditioner, and the distribution of the temperature in the room right after the onset of the conditioning system is examined:

flowkit-aircon-2images

As you can see, even tiny flow structures are reproduced sharply in this example. More details of the flow are revealed with the contrasted color scale of the animation below (use full screen mode for further details):

 
The simulation reveals for example the presence of dead spots which are insufficiently cooled by the air conditioning system. This is a simple problem which is for example solved by injecting the air with a sweeping motion:
 

Behind the scenes

Thermal convection results from a coupling between the physics of air flow (which is described by the so-called Navier-Stokes equations) and the convection-diffusion properties of the temperature. This system of equations is highly non-linear, a fact that explains why convection patterns often have a counter-intuitive structure and are difficult to predict.

To get a computer model of such a process, a numerical mesh is generated, which provides a sampling of the temperature and the air velocities in selected points in space. The mesh must be tight enough to capture the details of the flow structure. Some important phenomena occurring during convective heat transfer in a building can happen at such a small scale that the mesh is required to sample the space in intervals of millimeters, in each of the three space directions. A typical simulation of heat convection runs on a mesh with hundreds of million grid points. It is executed on parallel machines: tenth or hundreds of computers collaborate to solve the problem synchronously and provide the results fast.

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