Thursday, March 15, 2012

Thermal storage simulations

If you have visited this blog before, you’ll know that I have been working on a new concept for passive solar thermal power generation.  The concept involves a thermodynamic cycle based on evaporative cooling of hot air at reduced pressure.  The energy to power the engine is provided by sunshine and collected passively under a transparent insulated canopy.

Details can be found at

Thermal energy can be stored in a bed of rocks simply by blowing hot air from the canopy through the bed during the day.  At night, cool air is drawn through the bed by the engine, heating up in the process, and then the reclaimed thermal energy is converted into electrical power.

That highlights the need to develop simulation tools so that important questions can be answered.  For a given rock mass in the bed, how much energy is stored?  What size should the rocks be, and how much energy is required to pump air through the bed?  How sharp is the interface between hot rocks and cold rocks?  How does one simulate a charge/discharge cycle?

I started to think about these issues in early 2011 and wrote down the elements of a mathematical model for the storage simulations. Subsequently my focus switched elsewhere and I made no further progress on the work until early 2012, at which point I discovered an important paper by Hänchen et al. [1]  Their work contained a comprehensive literature review, model equations, numerical algorithms, validations, and computer simulations of various storage scenarios.

The mathematical model in [1] is different to mine.  They assume the air has constant density, the pressure is constant, rock particles heat and cool instantly (as fast as heat can be supplied/removed at the particle surface), and there is no diffusion in the air but some inter-particle diffusion in the rock bed.  The relevant equations are solved by a finite difference technique.

In my model, air is an ideal gas with variable density but constant pressure and constant specific heat capacities.  I allow heat to diffuse radially in the rock particles.  I include diffusion in the air but no inter-particle diffusivity.  And I solved my equations by a finite volume procedure.

The variation in air density with temperature is significant: my engine will operate over a range of say 20-140°C, for which the density ranges between 1.20 and 0.85 kg/m^3.  In [1], the maximum temperature considered was 550°C, for which the air density is 0.43 kg/m^3.  So you can imagine my surprise when I found that my simulations gave the same answer as [1] for a validation test.

Why is this so?  It turns out that the chosen coefficient for heat exchange between air and rock particles depends on the mass flow-rate of air, and not separately on the air density or bulk flow speed.  As the air temperature goes up, the density goes down and the bulk air speed goes up, so that the mass flow-rate stays approximately constant.  Moreover, the crucial feature of the thermal storage simulations is the heat exchange between particles and air.  So that’s the nub of the explanation.

My simulation codes need tweaking to control wiggles and instabilities, but that can be managed by attention to the timestep and spatial resolution.  It also helped to ensure that the initial and boundary data for simulations is specified in a consistent way.

I hope to publish this work later this year, so I won’t provide further mathematical or computational details here.   I do however provide below a 16-hour simulation of a charge-discharge cycle, as appropriate for my evaporation engine.  A pdf file that gives a coarse movie of the simulations can be found at (look for the link to “Thermal storage simulations” in the panel on the right-hand side).

I’m excited about possible applications for these new simulation tools.  If you would like to have a conversation about air-blown thermal storage, please get in touch.
Fig 1:  Simulation of air-blown thermal storage in a bed of steatite rocks.  Inlet temperatures 140°C (charge, 0 to 8 hrs) and 20°C (discharge, 8-16 hrs), initial bed temperature 20°C, inlet bulk air speed 0.4 m/s, particle diameter 0.040 m, bed height 5 m.  The air temperature is shown as a function of depth at each hour.  [Click to enlarge.]

[ 1]  M Hänchen, S Brückner & A Steinfeld, “High-temperature thermal storage using a packed bed of rocks – heat transfer analysis and experimental validation”, Applied Thermal Engineering 31 (2011), 1798-1806.