Measuring and Improving Cooling System Performance – Part 7: Overall Performance

Now that we have modeled cooling system performance, used math to figure out what's going on, measured a bunch of parameters to determine what it's doing in real life, and built a physical model that gave insight into what's happening under the hood, we can move on to making it better. Here's where it gets fun; you don't have to be satisfied with your car's cooling system as is. Do you need greater cooling capacity because you track your car in Phoenix in the summer? Do you want less cooling drag and can sacrifice some cooling capacity because you compete at the Green Grand Prix in New York in the cool of early spring? Do you want to reduce drag while increasing cooling capacity just a little? Do you want to rig up an actuator or system to vary outlet area so you can adjust cooling capacity and drag on the fly? Any of those, and infinitely more, are possible. You don't have to fall into the trap of thinking your car is as perfect as it can be from the factory; your individual set of compromises in its design will always be slightly different than what the manufacturer predicted. You can modify it stupidly, following convention and the ever-changing dictates of tuner culture and style or internet rules-of-thumb; or, you can modify it smartly, understanding how the various systems on your car function, what drives their performance, and how best to alter them to achieve your goals.

This 1938 Miller-Tucker (the first rear-engine car to qualify for the Indianapolis 500) has an interesting cooling system arrangement. Not visible: on the other side of the car is a large air-to-air heat exchanger, along with an air-to-liquid exchanger in the conventional location at the front, behind a grill. You can see this car at the Indianapolis Museum of Art, on loan from the Indianapolis Motor Speedway Museum.

Let's go step-by-step through the cooling system again to figure out where and how we can change it and how to measure its performance.
 
INLET
 
We want a capture area smaller than the actual opening so that we get static pressure increase from the freestream/ambient condition. This reduces the chance of separation inside the diffuser by reducing the strength of the adverse pressure gradient. Do this in conjunction with outlet sizing since, absent constriction by the physical inlet area (which we don't want, since it will mean a reduction in static pressure and stronger adverse pressure gradient), outlet conditions will determine the mass flow rate through the system and thus the inlet streamtube area.
 
Test: Measure static pressure at the grill inlet compared to freestream. If p₁ > p_a, the streamtube area is smaller than the physical inlet opening and the adverse pressure gradient inside the diffuser is minimized.
 
If you find that there is separation around the inlet, round the edges and check with tufts for attached flow. Look at commercial jet engine nacelles for inspiration on shaping; they are designed for spillage with attached flow at cruise.
 
Test: Use tufts taped around the inlet opening to check for separation.
 
Remove mesh or bars in grill openings and check for reduction in total pressure loss.
 
Test: Measure total pressure loss, p_0a – p₀₁, across the grill (or measure total pressure loss across the entire cooling system).
 
DIFFUSER
 
Duct the inlet opening to the heat exchanger inlet using smooth surfaces and gentle curves to support attached flow. Check for reduction in total pressure loss.
 
Test: Measure total pressure loss, p₀₁ – p₀₂, from the grill to the heat exchanger (or measure total pressure loss across the entire cooling system).
 
Raise p₂/reduce u_core as much as possible. u_core will get lower as the mass flow rate is reduced (assuming a duct or at least baffling to seal the inlet opening to the heat exchanger core and a smooth-sided duct)—again, this means you will want to check this in conjunction with modifying the outlet and vents since, if your inlet is sized appropriately, the outlet area and pressure boundary will determine the mass flow rate.
 
Test: Find dynamic pressure at the heat exchanger face, q₂ = p₀₂ – p₂, and normalize to freestream dynamic pressure to find u_core/u_∞. The lower this ratio, the less internal drag the cooling system will develop.
 
HEAT EXCHANGER
 
If you are designing a cooling system from scratch and have complete control over the sizing, or if you are replacing an existing cooling system in its entirety or building a custom setup, use as large an exchanger as you can fit with the lowest fin density for lowest drag.
 
For more cooling capacity, increase u_core/u_∞ (flow velocity into the heat exchanger). For lower drag, reduce u_core/u_∞.
 
OUTLET
 
Adjust ṁ for required cooling capacity with minimum total pressure loss for your desired design condition. Modify this mass flow rate using the outlet and vent sizing.  If your car has a fan shroud/nozzle, use q₄ measured at its outlet to check for changes in ṁ.
 
Test: Measure q₄ = p₀₄ – p₄ and normalize to freestream dynamic pressure. For fixed nozzle outlet area, the larger this ratio is, the more mass flow goes through the cooling system.
 
Site vents on the hood, engine undertray, fender/body side, or wheel housings (where it can "bleed" out attached to body surfaces), with minimal or no opening area normal to the vehicle longitudinal (front-to-back) axis.

 
Place vents in areas of negative C_P (low static pressure).
 
Test: Measure static pressure difference between the body panel location and freestream and normalize to freestream dynamic pressure. The more strongly negative C_P is, the better the location is for a vent.
 
Use vents with guide vanes or ducting to bend outlet flow as close to the direction of the vehicle's longitudinal axis as possible. Check for outlet flow attachment with tufts; if separation is found, round outlets with gentle curves and recheck.
 
Test: Tape tufts to the trailing edge and panel behind the vent to check for flow direction and attachment.
 
Simulating Cooling System Flow
 
Now that we've identified the various ways you might modify your cooling system to improve its performance, let's do some simple modeling to try and predict the result of changes. This may give us insight into what sorts of parameter changes will yield the greatest effects.
 
Following the method of Schmitt (1940) repeated by Wolf (2004), the total aerodynamic power requirement of a vehicle with cooling airflow is,

…and without cooling, the power requirement would be,

The power requirement for the cooling system alone is,

Redefine total power as the sum of these last two and we get,

Solve for the drag coefficient of the cooling system:

Further, we can derive core velocity ratio from momentum loss and static pressure coefficient at the outlet by,

Note that A_core here isn’t necessarily the physical area of the core; as we saw in Part 4 and Part 6, the effective core area can be smaller than its actual size. Also, as in the thought experiment I related in Part 6, once C_P,out = 1 (i.e. static pressure in the engine bay equals total pressure in the engine bay equals freestream total pressure), u_core is 0 and no flow crosses the heat exchanger. You should be able to see this in the equation above (work out or plot what happens as C_P,out approaches 1, then compare to the simulations below); this is a mathematical proof from a momentum balance to back up what I wrote before about total pressure and static pressure changes through a duct—which might be contrary to what you've read online or understood before! Raising or lowering outlet static pressure influences the mass flow rate through the cooling system, as we will see in the plots below, but it does not tell us the direction of flow through the system and it is not the sole determinant of mass flow rate.
 
While this derivation models the power requirement for cooling airflow, it also follows from a momentum balance. Hoerner shows that momentum drag coefficient referenced to core area can be approximated as (you can derive this yourself from the momentum equation above if you choose the right assumptions),

Referenced to vehicle area, this gives

…exactly the same result as the power derivation.
 
Great—so what can we do with this? Well, now I'll measure ξ_system and C_P,out of the cooling duct on my car (I already measured outlet area in Part 5) by placing total and static probes in the freestream (Station a), at the heat exchanger core inlet and outlet (Stations 2 and 3) and behind the fan outlet (Station 4):

Station a (freestream).

Station 2 (heat exchanger inlet).

Station 3 (heat exchanger outlet).

Station 4 (fan shroud outlet).

Then, measure total pressure loss, outlet static pressure, freestream dynamic pressure, and average core dynamic pressure to find ξ_system and C_P,out (revisit the relevant sections in this series if you're confused as to what values to measure or how to calculate these). Plotted over a range of speeds, these show on my car as:

Next, I can use these to predict the change in internal drag coefficient and mass flow rate using the equations above while varying ξ_system, C_P,out, and A_out to see what happens (try this yourself too, using the values you measured on your own car). Assuming effective core area equal to physical area, this gives changes:

What do these tell us?
 
1) As system loss coefficient is reduced, drag coefficient should go down and mass flow up.
2) As outlet static pressure coefficient goes up, drag coefficient and mass flow should go down (drag decreasing faster than mass flow) and vice versa. When C_P,out = 1, there is no drag from the cooling system or mass flow through it because there is no flow through the duct.
3) As outlet area is made smaller, drag coefficient and mass flow should go down (drag decreasing faster than mass flow) and vice versa.
 
Further, the slope of these lines tells us where the greatest potential for changing mass flow and drag coefficient lies. Reducing total pressure losses by 50% reduces drag 22%, while reducing outlet area the same percentage reduces drag 74% and reducing outlet static pressure coefficient increases drag 80%. The same changes increase mass flow 16%, decrease it 36%, and increase it 22% respectively. Plotting these shows (similar to a chart in Wolf [2004]):

Thus, it should be beneficial to first reduce system loss coefficient as much as possible, reducing drag and increasing mass flow rate. Think about what this means physically: with less total pressure loss but the same static pressure boundary at the outlet, the dynamic pressure must be higher there and thus the mass flow rate (and this is a good example of what we found before—measuring static pressure change alone doesn't give you enough information to determine what the flow through a duct or heat exchanger looks like).
 
Then ṁ can be adjusted to whatever value I desire by raising or lowering outlet static pressure (by opening or closing engine bay vents) and increasing or decreasing A_out, and these last two should reduce drag significantly if I close down the area or raise static pressure to reduce mass flow rate.
 
This suggests an order of operations. First, fabricate and test modifications to reduce total pressure loss; then, based on those results, trial modifications to engine bay vents and fan shroud outlet sizing until the change in mass flow rate is where you want it to be. In this way, it may be possible to both increase cooling air mass flow rate and decrease cooling drag.
 
Next time: putting it all together to modify and test a real car.

Previous: Measuring and Improving Cooling System Performance – Part 6: Physical Model