[TommyM]

Hi All,

Excuse me in advance for such a dumb question, I don't know why but I am stuck on it.

I need to calculate the pressure drop across a pipe.

Working fluid is air and I will simulate both incompressible and compressible flow cases. My issues is related to the incompressible case, thus I will explain that one.

Boundary conditions:
- Inlet mass flow rate (thus velocity) and inlet temperature
- Outlet ambient pressure

The first thing that came to my mind was to use the equation of state (ideal gas law) to obtain the inlet pressure by knowing density and inlet temperature.

Of course, there is something terribly wrong in this reasoning, but I can't figure out what. Any suggestions?

Thanks,

Tommy

[agd]

For true incomporessible flow there is no equation of state like the ideal gas law. And it doesn't really matter what pressure you set at the inlet - the only thing that matters is the pressure difference. Do a search on gauge pressure and its use in incompressible flow simulations. Set the inlet pressure to zero and then the field pressures you compute will be relative to that value. Absolute pressure doesn't really mean anything for true incompressible flows.

[TommyM]

Hi agd,

Thank you very much. I made a trivial mistake by setting both incompressible flow and ideal gas.

By the way, I have a last question related.

Given that imposing both ideal gas law and constant density is not possible, how do I set the density (constant) in an incompressible flow simulation?

I guess that typically one takes reference pressure and temperature, and use them in the ideal gas law to get the reference constant density, isn't it?

Or maybe one can use ideal gas law only to define the density in an incompressible flow simulation. Is it correct?

Tommy

[FMDenaro]

the incompressible flow "model" assume the limit Mach number =0, that is the sound velocity is infinite. Clearly, this model is not physical but the results are in good accordance until real low Mach number.
Since dp ->Inf, there is no thermodinamics in this mathematical model. The "pressure" is only a scalar field, a sort of potential function (actually a lagrangian multiplier) that has the aim of producing gradients that ensure the divergence-free velocity field.
Assuming homogeneous density, this latter is indeed the continuity equation.
Since the only relevant term appears in the momentum equation as a gradient of the "pressure", there is no absolute value for the scalar function. Any field is defined apart an additive function of time.
The value of the constant density is defined by the known physics, is not determined by the equations. The only parameter that defines the solution is the Reynolds number of the flow. This is an input parameter.

[TommyM]

Thank you, Professor Denaro.

A curiosity about density: you mentioned that its constant value is defined by the known physics, thus experimental tables.

But if I look for example at air density tables, I can calculate those same values by applying the ideal gas equation imposing atmospheric pressure and the specified temperature.

This was the reason that misled me in considering the ideal gas equation of state for an incompressible flow.

Tommy

[FMDenaro]

Originally Posted by TommyM

Thank you, Professor Denaro.

A curiosity about density: you mentioned that its constant value is defined by the known physics, thus experimental tables.

But if I look for example at air density tables, I can calculate those same values by applying the ideal gas equation imposing atmospheric pressure and the specified temperature.

This was the reason that misled me in considering the ideal gas equation of state for an incompressible flow.

Tommy

That's ok to use your table to compute a value rho0. This is the value you will use to compute your Re number that is the input value for the incompressible flow model.

You can easily understand why there is no gas equation if you think the incompressible flow model (constant density) with homogenous temperature. The pressure gradient in the momentum equation would be zero and, as a result, you have two equations (continuity and momentum) and only one unknown (velocity).

[TommyM]

Thank you very much for the explanation.

Tommy