Buoyancy effects in heat exchangers & CFD models

Conventionally, two regimes of flow are typically discussed in the context of heat exchange. Forced flow, where the flow is driven by a pump, fan, stirrer or other prime mover, is by far the most common process used industrially. This mode provides efficient, predictable, controllable heat transfer. Free convection (or natural convection) is the opposite case. In this case, the flow is driven entirely by buoyancy – hotter fluid is denser, and so rises in the surrounding fluid. Industrial examples include tank heaters (used in storage tanks containing viscous or high melting point liquids). It’s worth pointing out that both forced flow and free convection can be laminar or turbulent.

In heat exchangers a combination of these two flow regimes can occur, known as mixed convection. In mixed convection, the buoyancy of the heated or cooled fluid influences the forced flow. Gas flows under high temperature gradients and low flowrates are particularly sensitive to mixed convection effects. The contribution of mixed convection changes the velocity profile, and can lead to new flow structures or changes in the boundary layer. So the possibility of mixed convection has consequences in laminar-turbulent transitions, prediction of heat transfer and in computational fluid dynamics modelling of heat exchange surfaces.

Particularly in CFD, when buoyancy forces are in equilibrium with velocity forces, this can make convergence difficult.

You can determine whether mixed convection is important in your modelling work using the Richardson number. The Richardson number determines whether the flow is dominated by buoyancy (Ri above 1) or forced flow (Ri below 1). Richardson numbers between 0.1 and 10 indicate mixed convection. Richardson number is the ratio of the Grashof number to the square of the Reynolds number.

In my simulation work, I’ve used the Richardson number to try and give me an idea of whether buoyancy effects were affecting the convergence. It turned out that the Richardson number in my work is very small, and so this event is unlikely. I also compared the convergence of two runs (with gravity on and with gravity off) and got similar results. Buoyancy relies on gravity to take effect, so this showed me that the problems I am having with convergence are unlikely to be due to buoyancy effects in the fluid. So I am satisfied with this level of detail, but mixed convection heat exchange and buoyancy modelling in CFD is a rabbit’s hole of a subject area, and there are many aspects of the problem I haven’t covered in this blog entry.