Inflow boundary condition states in your model should be "controllable", as well as "observable". Assuming there are pressure or mechanical (vanes etc) control effectors that establish a "controllability", then place sensors such that your model is "observable". Sources of process noise and model uncertainty should also be understood, so sensors can placed to minimize those effects.

Thank you for your answer, dear John Vian.

I'am aware of the notions of observability and controllability. It was a mistake not to include those in the topics. But whenever I saw these, in the frame of fluids, they always concern 2D examples with regular geometries, mainly for the problem of the flow around an obstacle. Making my question more precise, I would like to know if there is a practical criteria to verify the observability and controllability properties, that can be applied with an irregular 3D domain (like part of an artery), even if at the discrete level. Do you have any suggestion on this?

In a practical sense, it's usually best to place the sensor in the same position as a sensor in your experiment. This way, when you write up, the explanation of why you chose a position, and the observed value is simple. For instance matching Pitot pressure at a known point will usually result in good estimation of the inflow conditions.

If you have more than one sensor to match, and you are matching the conditon by changing the inflow boundary, when it might help to have the sensor closer to the inflow. This will depend on the response of your system. For a highly elliptical system like an incompressible pipe flow, all points in the solution affect the mass flow through the pipe, and then regardless of the sensor position, the time-constant of your system will be some multiple of the speed of sound times the flow length in the domain.

Only sensors which are "well positioned" are going to give you the control effect which you want. This means: in a part of the flow which is linear, ie not in a separation or lee region and far enough away from any problematic boundary conditions (inflow, outflow, symmetry, periodic) that unphysical effects of the boundary condition will not have nonlinear effects on the sensor.

Dear Jorge Tiago

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The question may seem simple, but as the subject is studied blood within an artery that you take some care.

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First, the pseudo-Reynolds the case is low (less than 2000), is non-Newtonian fluid (blood) and the third and most important, is non-steady state, and as the flexibility of the walls is high propagation velocity can be very low, then I suggest a control by amount.

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Dear Anthony, thank you for your detailed answer. I do have more than one sensor to match and I also want to control by changing the inflow. I the case where my geometry induces a recirculation, do you thing I should place the sensor on the recirculation area?

Dear Rogerio, thank you for your answer. When you refer to "control by amount" do you mean quantities as the flow rate, instead of the velocity field? Or are you having something different in mind?

Hi Jorge,

you probably won't get the answer you want by placing your sensor in the recirculation region, although it depends on the flow. I don't know your exact situation, but mostly you want a sensor for which (Sensor pressure too low)-->(increase inflow pressure)-->(sensor pressure increases), and its converse will be a valid control strategy. This is nearly always true for points where the pressure is controlled by the potential flow. For points in recircultion regions, or which can move in and out of a recirculation region this is not always true, and can lead to a failure of your feedback module.

I would suggest putting your sensor for control outside the recircultion region and then varying other things (turbulence model, wall temperature, fluid mixture) so that you get the size of recirculation region which you expect. Since you mention wall profiles: it may be necessary to add a (non-physical) lead-in to your pipe if you're not using periodic walls to get fully developed pipe flow.