Pressure Drop Across Radiator And Air Flow

[KLoux]

Hello all,

I have some performance data on a particular radiator, and I want to model the system and see if I can't get a simple analytical model to match the data. The problem I'm having is with the air flow rate through the radiator. The only relevant data made available to me is the pressure drop across the radiator. So far, it seems as though this isn't enough.

It's not quite the same as a venturi, because the pressure difference is between the front and back of the radiator, not the front and middle (where the area change occurs). I also considered treating it as an orfice plate, but that introduces another lot of unknowns (coefficient of discharge, ratio of frontal area to solid area, etc.). I also tried just making an assumption about the speed of the air as it hits the radiator, but the model is pretty sensitive to this input, so I don't feel confident making this assumption.

Am I approaching this the wrong way? Is it possible to calculate the mass air flow across a radiator knowing only the pressure drop, exterior dimensions of the radiator and inlet air temperature?

Thanks,

Kerry

 

[Effort]

Maybe I'm just simplifying this a little much, but you can calculate the air velovity from
bernouliis equation... static pressure + dynamic Pressure = total pressure. Since you know the change in pressure, the air velocity can be calculated from

V^2 = 2*(change in pressure)*(1/denisty).

with the velocity and the radiator dimensions you should be able to get the mass flow rate.

 

[minger]

The change in pressure is mostly going to be losses in the radiator. Small tubing + many bends = large losses.

You could try to guess the losses assuming that they are all just 180° bends and straight sections.

 

[KLoux]

Thanks for the input!

Maybe I'm just simplifying this a little much, but you can calculate the air velovity from
bernouliis equation... static pressure + dynamic Pressure = total pressure. Since you know the change in pressure, the air velocity can be calculated from

V^2 = 2*(change in pressure)*(1/denisty).

with the velocity and the radiator dimensions you should be able to get the mass flow rate.

I was assuming that the delta pressure is actually delta static pressure... I guess this isn't necessarily true, but I think that's how it's typically measured.

The change in pressure is mostly going to be losses in the radiator. Small tubing + many bends = large losses.

You could try to guess the losses assuming that they are all just 180° bends and straight sections.

Hmmm. This is an interesting approach - but the air isn't flowing through any bends, it's kind of flowing around (through?) an obstruction. Is there a way to estimate these losses? I'm familiar with computing losses due to different styles of elbows and reducers, but not through a radiator.

-Kerry

 

[minger]

OOooh, AIR flow, whoops. How are you measuing these pressures? Is it open like an automobile radiator or closed ala a shell-tube heat exchanger?

 

[KLoux]

It's open like in a car. I assumed that they were using pressure taps perpendicular to the airstream, one on either side of the radiator - but as Effort pointed out, that may not be the case (but I still think that it is the case).

-Kerry

 

[Q_Goest]

I have some performance data on a particular radiator, and I want to model the system and see if I can't get a simple analytical model to match the data.

What kind of data do you have? Note that for a conventional radiator dHair = dHcoolant. In other words, the change in enthalpy of the air must equal the change in enthalpy of the coolant. You can also write dH = m*cp*dT. Given this, you can equate the enthalpy of air and coolant and solve for a single unknown such as mass flow rate of air as long as you have the other variables.

Regarding other ways to do this, I'd be skeptical of calculating the mass flow from pressure drop across the radiator for 2 reasons.
1) The dP across the radiator might not be the same at all points across the radiator unless it's inside a housing of some kind. With an open radiator, flow around the edges of the radiator will reduce the dP there, and the dP near the center will be highest. Flow then requires an integration across the entire flow area.
2) Even if you had dP across the radiator, you need to have some kind of value for the restriction it represents, otherwise there's no way to determine the flow rate of air through it. To determine restriction you need area and a coefficient, or some equivalent value that can be plugged into a flow equation. To get this information, you either need to determine flow area and guess at the coefficient, or preferably, have some kind of test data.

If you could be more specific about what information you have and what you're trying to do, it might help.

 

[KLoux]

Here's the information I've got:

Heat transfer rate (units of power)
Delta pressure across the radiator (this was measured in a test rig - it might have been in a duct of some kind - I'll make another call and see if I can find out)
Exterior dimensions of the radiator
Inlet air temp
Water flow rate
Inlet water temp

With this I was able to calculate the outlet water temperature, but I need either the air flow rate or the outlet air temperature to solve for the other.

I begged for more information, but this is not from a recent test, and they don't usually test these things, so unfortunately this was all they had. This does not mean that it is sufficient...

Thanks for the help!

-Kerry

 

[Q_Goest]

If you had air temp downstream of the radiator, you'd have everything you need. But without it, you can't determine mass flow. See if you can get air temp downstream or if there might be a rough estimate of it. Once you have that, calculate mass flow from the first law. With mass flow, you can then determine an equivalent restriction for the radiator.

 

[KLoux]

Thanks! That's what I'll have to do. I appreciate all of the responses!

-Kerry