Why are aerodynamic models without stall used in research papers?

Question

Some papers that I'm reading in the Journal of Fluid Mechanics give aerodynamic models in which the lift force appears to not take stall into account -- unless I am misinterpreting the math model, but I don't think I am.

Is it reasonable to use a model without stall? What would be the advantages of doing so?

Answer 1

Because they don't need to. Scientists and engineers always have to trade-off between efficiency (speed, computational resources needed,...) and accuracy when doing calculations. If the calculations to be performed are not expected to be in the stall region, it's easier to use simple models without modelling the stall behaviour.

It's not only about doing more calculation steps but also about the methods you can apply. For example, the lift coefficient $C_L$ is often defined as a function of the angle of attack $\alpha$:

$C_L= C_{L\alpha} \cdot \alpha$.

This equation doesn't take stall into account and can lead to infinite lift coefficients. A slightly more accurate formula, which limits the maximum lift coefficient, is the following:

$C_L = C_{L\alpha}\cdot \sin\alpha$.

Why don't we always use the second one? Computing a sine isn't that expensive, isn't it? Well, for example, control engineers usually use state-space models, which require linear terms. Also, the derivative of the first formula is a constant, while the derivative of the second one is still a function of $\alpha$. Doing mathematical calculations or deriving formulas is much easier using the first one.

Obviously, care should be taken to not use the simplified formulas in design regions where they are not valid.