Measuring and Improving Cooling System Performance – Part 8: Modification

Production car cooling systems are always beholden to styling considerations, packaging issues, and cost constraints (design cost, materials cost, manufacturing cost, etc.). Because of this, most leave room for improvement if your goals and requirements are different than the manufacturer's. We've seen so far that a few simple measurements on your car will give you a lot of information about how well its cooling system works and where it can be made better. If you don't mind getting your hands dirty, you should be able to reduce cooling drag on your car while maintaining or even increasing cooling capacity.

How big should inlets be? Outlets? How should they be shaped? How much will internal smoothing reduce drag? How much will mass flow increase if we reduce system losses? Don't try to modify any of these things by guessing! The engineers behind this 2019 Porsche 911 certainly didn't.

Modifying Cooling System Flow
 
As an example, I'll modify the cooling system of my 2013 Prius to decrease its drag while maintaining factory cooling capacity. I've previously tried to reduce cooling drag on this car by blocking the inlet but did not test anything aside from some static pressure measurements that I didn't really understand at the time. Now I'll have another go at this as an engineer.
 
The first question is, what can I easily modify without getting too far into the weeds? In the last post, I wrote out a list of the various changes you could make to your car's cooling system but obviously some of them are quite difficult to do. I'm not interested (for now) in re-engineering the engine bay or cutting into structural components in the front end of the car, for example, and I cannot modify any of the car's safety equipment if I want to continue to compete in the Green Grand Prix.
 
If you look at your car and how everything is packaged, you will probably find that there's very little room behind the fans and more real estate available to modify the space in front of the heat exchangers. Designers hate "wasted" space (and apparently view the diffuser duct as one such waste), so you might find that there's all sorts of stuff in there anyway: horns, bumper beam, absorber, temperature sensor, and—on newer cars—movable grill shutters, radar, and camera sensors. But there's probably enough room to fit panels or baffles, change the shape of cooling air openings, and more.
 
So I'll focus on the front, starting with the inlet.
 
License Plate Removal
 
I first removed the license plate and tufted the front of the car. Over the past few months as I've driven around, I've paid more attention to the placement of license plate holders on various cars and trucks; lots of them hang down over the lower cooling air opening, which means they're contributing to losses in the inlet and diffuser (and I'm not the only one complaining about these afterthought plate mounts, since they almost always require drilling into the bumper cover).
 
Everything looks good without the plate obstructing the top of the inlet:

There's attached flow all the way around the inlet, and we can see the "spillage" around the opening, especially over the splitter. In a minute we'll see what effect this has on inlet and diffuser performance.
 
Lower Grill Removal
 
Earlier, I wrote that the grills and fascia ornamentation on modern cars dissipate energy (through shear layers in separated flow behind them and friction over the slats, bars, and mesh themselves; look again at the image of the Porsche 911 cooling inlets above and take note of what's missing) and that removing them can reduce total pressure loss. How much?
 
Engineers justify with numbers. Any time you see someone arguing the results or merit or performance of an aerodynamic modification to their car by asserting the difference is "noticeable" without some measurement or calculation based on a test to back that up, don't believe it. That includes me, before I became an engineer. So, in the name of science I'll break some eggs and then measure stuff:

175,000 miles of gravel, dirt, and bugs have bent or broken some of the fins on the condenser. Because all those things are heavier than air, the localized damage to the core doesn't necessarily tell us where there is more airflow through it.

The grill serves another purpose in addition to styling, namely keeping large objects out of the cooling system. I'm not really worried about that; as I wrote before, I've owned cars in the past with no grills in the cooling air openings and have been just fine (and I've been running an engine air inlet on this car with no grill for several years with no issues). If you're not comfortable with that, don't do this modification.

As with cooling air intakes, we want the engine air intake to be sited in an area of high total pressure i.e. as close to the very front of the car as possible.

If you are comfortable with it, however, the potential gains can be significant. Diffuser efficiency and static pressure coefficient, measured in the same location on the heat exchanger core as previous testing, both increased much more than I expected:

Think about why these parameters changed the way they did. Removing the grill preserves energy in the flow by reducing dissipation and entropy; with more energy (total pressure) available, static pressure at the core is higher and, since diffuser efficiency is a function of total pressure loss, that has also been improved. Both of these I expected; what was surprising was how much these things changed. It turns out, simply removing the grill across the main cooling air opening may be enough if all you're after is a little more cooling capacity and reduced drag through improved diffuser efficiency.
 
Upper Grill Removal and Duct Smoothing
 
There are, of course, slats not just across the lower opening but also the upper "mustache" inlets on this car (and on most other cars, where the upper inlet tends to be a lot larger and heavily styled). I initially thought about blocking these and ducting the lower opening to the full core area (as modeled in Part 6) but found this unworkable: there just isn't enough space. There's only about half a foot from the inlet opening to the core on the centerline of the car, and a large part of this area is taken up by the crash structure:

Additionally, the two horns sit behind the upper inlets, blocking more of the area where I would want a duct to go (you can see one behind the upper inlet grill in one of the images above). I tried multiple duct versions but wasn't happy with any of them, and as I thought more about it I decided not to block off any cooling air opening without determining mass flow first. So, back to the drawing board.
 
This got me thinking about my immediate goal in this phase of modification, and that goal is to preserve total pressure in the flow through the cooling system as much as possible (as I wrote in the previous post and will explain in a minute, I'll adjust mass flow by changing the outlet conditions later). To that end, I next cut out the grills in the mustache inlets and relocated the horns to the open spaces in front of the wheel housings, where there is ample room for them and they won't obstruct the path of cooling air (and there are several unused, threaded bosses—an advantage of owning a base trim car):

Since it's easy to get to and simple to fabricate, I added a smooth piece of HDPE sheet to the bottom side of the lower inlet, covering up the very rough factory paneling there and sealing better to the bottom of the core inlet with some gasket tape. I also stuffed some closed-cell foam pipe insulation around the passenger side of the exchanger core (where there was a factory opening in the shroud, perhaps to feed air with higher total pressure to the stock engine air intake pickup which I'm no longer using on this car):

Did these improve things? Yes! Again, more than I expected:

Diffuser efficiency jumped again, along with static pressure coefficient at the diffuser outlet/heat exchanger core inlet which has now tripled from what it was before modification. Since the whole point of a diffuser is the recovery of internal energy (static pressure) from total pressure, it should be no surprise that static pressure coefficient goes up as total pressure loss is reduced and the diffuser functions more efficiently.
 
According to Hoerner, the best aircraft cooling system diffuser ducts approach an efficiency of 90% or more; those are very well-designed ducts, with adequate length, smooth and gradual changes in cross section area, and smooth internal surfaces. In the case of a production car—whose cooling system ducting has almost none of those qualities—I'm quite happy with ~80% diffuser efficiency, doubled from ~40% before with just a few easy modifications (try these on your own car if you're so inclined, but make sure you measure their performance. Their effect may be different than what I found on my car!).
 
Before I go on, one note about the flow through the exchanger cores. Here's a plot of the measured velocity ratio at the center of the core area with each modification:

Notice that, aside from some small variation which is probably attributable to the coarseness of my measurement device or some other test uncertainty, it hasn't really changed despite the expectation that, as loss coefficient of the diffuser is reduced, mass flow rate should go up. I'll explain later what's going on with this.
 
System Parameters
 
That takes care of the easy stuff. Now, to compare overall performance of the modified cooling system to the baseline before I changed anything, I will remeasure and calculate the same parameters I did in Part 7, ξ_system and C_P,out. This will indicate the changes in loss coefficient and mass flow rate (using the equations in that post), if any.
 
System loss coefficient and outlet static pressure coefficient now look like:

And change in calculated mass flow, which is equal to the change in velocity ratio as given by the momentum equation:

This suggests cooling capacity (mass flow) has increased an average 6% while internal losses have been reduced an average 25%. But this doesn't quite tell me how much cooling drag has decreased because these two things combined—total pressure loss and mass flow rate—determine drag. Some modeling will show why.
 
Modeling Cooling Drag Increment
 
Generally, there are two model frameworks you can use to characterize cooling system internal drag. If you go back and review Part 4, you can guess what these are: momentum and energy.
 
Approximating differences in static pressure and streamtube area of a control volume drawn upstream and downstream as negligible (which isn't a valid assumption if we consider the cooling system exit as the fan shroud into the engine bay, but is if you draw your control volume somewhere outside the vehicle and downstream of any engine bay vents), drag force is a function of momentum loss in the flow as it interacts with the duct and all surfaces within it. Convection of momentum is given by mass flow rate times velocity, so momentum loss is equal to mass flow rate times the change in velocity (this is the "momentum deficit" method of drag calculation). Mass flow rate can be referenced to any point in the duct because of continuity, so

where x denotes the station in the duct used as a reference. In cooling system design, the most convenient reference is the heat exchanger core(s), giving

…where A_ref is vehicle reference area (typically frontal projected area for ground vehicles, wing plan area for aircraft). From this you can derive an expression for the internal drag coefficient of the cooling system (assuming axial flow at the outlet):

If we include the difference in pressure at the outlet in the engine bay, this equation contains an additional term:

It would seem that the necessary information is easy to obtain from measurements made on your car. However, this is not quite the case—one datum, u_out, is not readily calculable since we need to know either the density directly or temperature and static pressure of the air at the fan outlet.
 
You could get around this by making an assumption of constant density (which is an approximation we've made implicitly for a lot of the analysis over this series), in which case the square root of the dynamic pressure ratio would be enough to give us that last term. However, I'm sitting here looking at sunlight streaming in through my living room window and reflecting off the blank white page of the notebook in front of me, the "shimmer" in the rising warm air just inside the window clearly visible in the reflected image on the paper. These shimmers arise from changes in density in the air, which even at this small temperature difference are enough to change its refractive index so that the density waves are visible in reflection—the same theory behind schlieren imagery, which is used to observe shock and expansion waves in supersonic nozzle outlets.

Schlieren image of shock wave formation behind a jet nozzle outlet, from a laboratory experiment last year. As total pressure in the air feeding the jet is raised, the speed of the outlet flow approaches and then reaches the local speed of sound ("sonic condition"; accelerating past this would require a converging-diverging nozzle design, which this jet did not have). When the flow becomes underexpanded (p_e > p_a), the classic "shock diamond" pattern emerges as the flow is processed. Reflection off a series of mirrors allows the camera to "see" the density changes in the air.

All that is to argue, I don't think it's a valid assumption to just say density of the cooling outflow is the same as freestream density and leave it at that. Because of this, we can't use a simple ratio of measured q_out to find u_out.
 
The other option is the energy (or power, the time derivative or rate of energy) approach. Modeling aerodynamic power requirements for the whole car with and without cooling drag results in the formulation of cooling drag coefficient we saw in Part 7 (referenced to vehicle area and freestream dynamic pressure),

These are all easy to find: system loss coefficient as in Part 5 and 7, average velocity ratio from the momentum balance in Part 7, and the last term by inspection.
 
Now you should see the problem with simply reducing losses; as I did that above, u_core/u_∞ must also increase. Because this term is cubed in the expression above, it has an outsized effect: increasing mass flow rate 10% will increase internal drag more than 30% if total pressure loss is held constant. This also explains what was going on with the measured velocity ratio at the center of the core face: it didn't change because the velocity into the core at that spot didn't change (despite a sharp increase in static pressure there!). Because the properties across the heat exchanger face are not uniform—as I explained in Part 6 and we observed in the physical model—the velocity ratio has to have gone up in other spots since momentum through the cooling system has increased by reducing total pressure losses.

This points to a persistent (and unsolvable) real-world problem of measurement in general: often, we just can't get complete information—like total pressure across the entire heat exchanger core face, for example—and even when we can, the inherent instability and unsteadiness of real airflow defies absolute certainty. Try to place probes and sensors in the same location when repeating tests, recognize that measurement values are averages and approximations, do your best to minimize error (for example, by normalizing or nondimensionalizing measurements), and focus on the change in measured parameters rather than their absolute values. Real airflows are complex and wildly chaotic; even the most sensitive equipment used to calculate the drag coefficient of the F-16 during its development, for example, showed a spread of 12% depending which test data were used for the calculation. It is an unfortunate reality of modern amateur aerodynamicists—most of them raised on a diet of (bad) CFD—that we tend to think aerodynamic coefficients and values are constant, specific, and absolute when nothing could be further from the truth.

 
That said, calculating C_D,int using the power equation before and after modification shows the following approximate change:

This is exactly what I wanted (and you probably do too, on your car): reduced cooling drag, an average 11%. However, I'm not looking for an increase in mass flow so there may be opportunity for further drag reduction. To bring it back down, I'll turn next to the area behind the heat exchangers.
 
Outlet
 
Now I have two options to reduce mass flow rate, and by doing that reduce drag even further: change the size of the outlet or change the pressure boundary condition. Why not block the inlet opening? There are a few reasons that isn't a good idea. First, blocking with sharp-edged boards (as many Ecomodders/hypermilers do and I have done on this and other cars in the past—see the image below) may increase losses in the diffuser from separation, reducing diffuser efficiency and increasing drag for a given mass flow. Second, the flow into the system will try to "adjust" based on the outlet conditions and sizing, and if the physical inlet area is smaller than the streamtube captured by the system this may increase the strength of the adverse pressure gradient in the diffuser, which could result in greater losses. Third, since the streamtube capture area is smaller than the physical opening anyway right now (which I know from calculated velocity ratio; this ratio is the same as required inlet opening size to core area), constricting the opening won't really do anything anyway and may have adverse effects on diffuser efficiency.
 
So, the outlet it is. I have two choices to reduce ṁ to around what it was before modification: reduce the outlet area of the fan shroud or raise the static pressure in the engine bay. Use the momentum equation in Part 7 and rearrange it to figure out how much either of those will need to change; on my car, I will have to cover about 15 in² of outlet area or raise C_P,out to slightly less than 0.1.
 
One of those is a lot easier to adjust than the other. In fact, outlet area can be restricted using just tape if you want, as has been done on production cars in the past (see Wolf [2004] for a surprising example). However, since the cooling air here is venting into the engine bay and I want to minimize system losses behind the shroud outlet, I want to avoid having a sharp edge on any outlet block—so I'll curve the edge as much as possible to try to direct flow out more or less axially and minimize total pressure loss behind the plate:

This is the ideal use case for coroplast (corrugated polypropylene): in the engine bay, it will be shielded from UV light, and temperature in the bay won't come close to the melting point of the sheet. Add in cost (these were free, from a political campaign I worked on this spring) and ease of workmanship, and it's a no-brainer material choice here.

With these in place and mass flow restricted to approximately what it was before I modified the inlet and diffuser, internal drag is likely reduced an average 25% from the stock system while maintaining factory cooling capacity—not too shabby!

A long validation drive in hot weather just a few days after installing these (to the outskirts of Chicago, where I visited the Volo Museum) showed no change in coolant temperature from what it typically was before I started modifying the cooling system—an indication that mass flow rate may be the same as before, although I won't know for sure until I take the car to an extreme environment, like the Continental Divide in July. The car's economy over the ~350 mi freeway trip was just over 60 MPG, a bit more than expected based on previous, similar summer Chicago trips.

I went primarily to see the museum's collection of film cars, including this screen-used Vanquish (built on a Mustang chassis) from Die Another Day (2002).

Final Results
 
Pick one, but choose wisely:

Cooling system modification, guess-and-hope version.

Cooling system modification, engineered version.

The first example was modified by guess and rule-of-thumb, back when I believed such simplistic nonsense as "cooling air openings should be a slot as wide as the radiator and 1/6 the height" and other "rules." This was completely informed by what I had read on various web forums and discussion boards, which amounts to little more than belief in magic as an effective engineering process.
 
The second example is the result of building a conceptual (mathematical) model, measuring performance parameters of the system in (close to) stock form, using these values to predict the result of changes by the model equations, then implementing these changes and measuring the improvements in performance. Notice also that the end result is a string of modifications that run exactly counter to prevailing internet wisdom. Where most people think you should block the inlet opening to reduce drag, you can actually increase mass flow and decrease drag simultaneously by opening up the inlet and diffuser, removing obstructions and smoothing surfaces to reduce total pressure loss. Where most people don't pay any attention to sharp edges on inlet blocks, careful smoothing of inlet edges and internal duct surfaces can improve mass flow while reducing drag. Where most people think that cooling system mass flow is regulated by the size of the inlet, you should close down the outlet opening instead to restrict mass flow and decrease drag if desired, or open it up to increase cooling capacity.

 
It's a lot more work but the results are real and measurable—and what's more, this process has been a lot more fun than guessing! Try it out on your car.
 
Next time: a final note, on pressure measurement across heat exchangers.

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