[moros]

Hello,

I am modelling a thin filter in an air venting system using a porous jump. The vent manafacturer supplied a graph for the filter of pressure drop (y) vs. flow velocity (x). Using the method outlined in the fluent manual, I found the line equation for the graph using excel which was of the form y=ax²+bx-c.

From this, I calculated the face permeability and the pressure-jump coefficient using equation 7.2-2 in the fluent manual section 7.2.3 Porous Media Conditions. However, the equation returns a negative face permeability and a negative pressure-jump coefficient.

I understand that you can define a negative pressure-jump coefficient in Fluent but not a negative face permeability. What is the nature of positive and negative values for these parameters? Are negative values a valid solution?

[vinerm]

Before you try to use the equation, I'd suggest you to check the validity of the equation returned by Excel. Excel is not very good at predicting trendline equations, actually, it is bad at it. Try using same data in Matlab or Octave or some online tool to determine the equation coefficients. Furthermore, you can check the validity of the equation within the Excel by plotting it against the data.

If the equation returned by Excel turns out to be good, which would be an ugly duckling, then you may have to modify your equation slightly so as to get positive coefficients. The curve does not have to be the best fit but a valid fit.

[moros]

The equation seems valid after cross checking it against other trendline applications online. In fact, the problem lies in the sign of the coefficients being positive (i.e. +x² and +x) which is generally true for all trendlines representing filter behaviour for plots of pressure drop against flow velocity. Therefore, I am failing to see how calculating a positive permeability is even possible.

Even in the fluent manual 7.2.3 Porous Media Conditions (Deriving the Porous Coefficients Based on Experimental pressure and Velocity Data), a negative permeability value is calculated. Is

[vinerm]

Yes, that is true and it is an example to show that the data may lead to negative values for coefficients but it should not be used. All you need to ensure is that if you use the calculated coefficients and then plot the pressure drop based on velocity, do you get the similar trend or not.

[moros]

I do get a similar trend but my question is, how do I input a negative face permeability into fluent when there is no option to (presumably because it's invalid)?

[vinerm]

My point is that you should check if you get similar trend by using positive value. If Fluent has an inbuilt fail-safe, which it has for quite a few parameters, then it will not allow you to enter negative coefficients. In the end, all that matters is that total of the equation should be positive, i.e., the linear and the quadratic part. If total is positive, then pressure drop will increase with increase in velocity.

[LuckyTran]

How do you get negative values for both the pressure jump coefficient and permeability? It's not even possible to get wrong signs for both of those unless the manufacturer gave you pressure-rise data... The signs can only be wrong if you get one positive and one negative. If both, are negative/positive then you've done something silly.

Check your formula in excel.... Maybe you implicitly assumed that pressure drop as having positive values. What does the curve data look like? Is the pressure drop curve positive of negative? And does your formula reflect that?

[moros]

I've made a test case in Fluent and by changing both the face permeability and pressure-jump coefficient to positive. I've obtained a very similar trend to the original data by doing this so it seems your advice was correct.
Thanks for the help vinerm.

[vinerm]

Nice to know that it worked.

[moros]

Originally Posted by LuckyTran

How do you get negative values for both the pressure jump coefficient and permeability? It's not even possible to get wrong signs for both of those unless the manufacturer gave you pressure-rise data... The signs can only be wrong if you get one positive and one negative. If both, are negative/positive then you've done something silly.

Check your formula in excel.... Maybe you implicitly assumed that pressure drop as having positive values. What does the curve data look like? Is the pressure drop curve positive of negative? And does your formula reflect that?

My curve is of the polynomial form ax² + bx - c (where c not shown for in the supplied data and is negligible in my excel generated polynomial). Using this polynomial I used the following 2 equations to find these values:

face permeability = -(fluid viscosity*filter width)/b
pressure-jump coefficient = -(2*a)/(fluid density*filter width)

The manafacturer supplied the graph as pressure loss (Pa) vs. flow rate (m/s). I have assumed positive pressure values in this as that was how the graph was supplied. Should I have assumed negative values for pressure loss to calculate the porous jump parameters?

[LuckyTran]

Originally Posted by moros

The manafacturer supplied the graph as pressure loss (Pa) vs. flow rate (m/s). I have assumed positive pressure values in this as that was how the graph was supplied. Should I have assumed negative values for pressure loss to calculate the porous jump parameters?

Yes because is a pressure difference, not pressure drop. When someone gives you "pressure drop data" in positive values, you need to have the faculty to understand to convert that to negative 's.

[moros]

Originally Posted by LuckyTran

Yes because is a pressure difference, not pressure drop. When someone gives you "pressure drop data" in positive values, you need to have the faculty to understand to convert that to negative 's.

I understand this, and fortunately did have this faculty as I came to that conclusion in the above discussion. However, I fail to see why ANSYS define a negative face permeability (which is invalid) in the ANSYS manual.

[LuckyTran]

Originally Posted by moros

However, I fail to see why ANSYS define a negative face permeability (which is invalid) in the ANSYS manual.

It doesn't.

[vinerm]

In reality, permeability is not a scalar or vector rather a second rank symmetric tensor. The permeability value being used in porous model is a simplification with an assumption that the flow in a particular direction is dependent on pressure gradient in its principal direction. That's why Fluent requires users to define principal directions. So, the question whether the pressure drop is negative or positive or is it drop or difference is not irrelevant but incorrect. If the flow is in positive x-direction, then pressure at higher x value has to be smaller than that at lower x value, leading to negative pressure gradient. If, however, the direction considered is negative x-direction, then the pressure at higher x value has to be more than that at lower x value, leading to positive pressure gradient. Do note, however, that the velocity now is negative.