If you’re looking for a nice power increase for all-around street driving, a 50-percent increase is more realistic and matching a turbo to this level of increase will produce more satisfactory results. A 300 percent power increase (200 to 600 hp) is possible in many engines, but increases like that are reserved for competition engines that have an array of additional modifications, both internal and external, that all work together to achieve this level of power. One of the most important factors in determining which turbocharger is most appropriate is to have your target horsepower in mind. But you have to be realistic about what you’re shooting for.

The application and intended use of the vehicle is extremely important as well. An autocross car, for example, would require a rapid boost rise for fast acceleration, whereas a Bonneville car running long straights is more concerned with horsepower at higher engine speeds. Indy cars frequently adjust the turbo for short tracks versus long tracks because of how critical the turbo match is to optimize flow at specific engine and vehicle speeds. Tractor pull applications will likely see the highest engine speeds right at the start of competition, and as the pull progresses, the load is progressively increased much like a prony brake until the engine is maximum loaded down by the pulling sled. These different uses require different turbo matches.

...

most of the traditional aftermarket high-performance engine parts essentially raise the engine’s VE. Forced-air induction is all about increasing VE. But what is Volumetric Efficiency exactly?

An engine’s VE is a comparison of an engine’s calculated, or theoretical, volumetric flow rate of air, versus its actual capability. An engine has a fixed displacement, for example, 300 cubic inches. That displacement will theoretically flow 300 ci every two engine revolutions (a four-stroke engine must rotate twice for all cylinders to complete all four cycles). In theory, there would be a linear relation to airflow and engine RPM where doubling the revolutions per minute would double the air displaced by the engine. If an engine were able to flow exactly as much air during operation as the theoretical calculation says is possible, that engine would have a VE of 100 percent. However, in reality that rarely happens

...

During actual engine operation, the intake valve is only opened for a short time. The higher the RPM, the less time the intake valve is off its seat. Therefore actual VE is not a constant. It’s typically an efficiency ratio at one spot in the engine’s operating range.

...

The reason turbocharging has such a dramatic impact to engine performance can be better understood using this concept of volumetric efficiency. In a turbocharged engine, time still limits how long the intake valve is open, but if the intake pressure is greater than atmospheric pressure (boosted), then we can force more total air volume in during the valve opening. The quality of that air is improved for combustion purposes because its density has also been increased. The combination of boost pressure and air density compensate for the time-limiting aspect of the valve events and allow boosted engines to achieve well over 100-percent VE. But when maximizing total horsepower output, even turbocharged engines will benefit from many of the very same design improvements done to enhance VE on naturally aspirated engines.

...

Historically, turbos weren’t marketed in the automotive performance aftermarket as widely as they are today and they were rated only in their mass-flow capability, not in terms of horsepower compatibility. However, a reasonable turbo match can be obtained by using a realistic horsepower target, and simply choosing a turbocharger from a manufacturer where your target horsepower is located right in the middle of the horsepower band it is capable of supporting.

For example, in the above situation where your target is 300 hp (a 50 percent increase over the stock 200 hp) the Garrett brand GT2860RS with a 76 trim, also known as the “Disco Potato,” might be an excellent choice. That turbo is rated to be compatible with horsepower applications of 250 to 360, so 300 is right in the middle of its capacity. This ballpark method allows for both surge margin and broad flow range of operation, as will be discussed in the following paragraphs. This is not the most scientific way to apply a turbo, but it can be done because much of the science of the horsepower match has already been done for you by the manufacturer rating a given turbo in its horsepower compatibility. Also, because many of the turbos offered for sale today have been built with an internally designed wastegate, subtle adjustments in boost pressure optimization can also be performed after the car is test driven. While most turbo experts will raise their eyebrows at this overly simplified approach, it can be very successful for the average turbo car project and it makes the confusion of turbo matching a rather simple process indeed.

...

The process of properly matching a compressor to your engine uses a set of assumptions, all of which are intended to be close and approximate in order to reach a reasonably close turbo match. An approximation is necessary because of an engine’s varied RPM, the entire manifolding system (and its efficiency), corresponding fuel flow, and many other aspects that will affect the final match. This is why most consider turbocharger application both an art and a science. If it were a pure science, then the engine dynamometer cells used to refine turbo matches for production engines would not be necessary.

There is no shortage of reference materials on the subject of how to match a turbocharger to an engine. Most all are very sound, and some make it very difficult to follow along. We’ll attempt to progressively work our way through the math involved and explain what we are doing as we go. This way the concepts of what we are doing, and why, are best understood. After all, the objective of this book is to help you apply a turbocharger to your project and obtain good results, not confuse you with overly complicated math.

...

Let’s assume we intend to turbo a 3.0-liter gas engine rated at 190 hp at 6,500 rpm in our street/strip car. The next assumption is that we wish to operate the turbo with 10 lbs of boost pressure (a reasonable boost level for which we can obtain proper fuel octane levels to control fuel ignition and avoid detonation). The first thing we do is to convert its displacement into cubic inches, allowing easier conversion into our ultimate objective of determining lbs/min of air mass flow.

3.0 liters =

3,000 cubic centimeters (cc)

Displacement in cc / 16.387 =

Cubic Inch Displacement

3,000 cc / 16.387 = 183 ci

Now that we have our displacement in cubic inches we need to calculate the engine’s airflow in CFM in its naturally aspirated state. This is very easily done as follows.

CID x 0.5 x Max RPM / 1,728 = CFM

This formula simply takes the engine’s size in cubic inches times .5 because in a four-cycle engine it takes two complete engine revolutions for all cylinders to complete their cycles. This value is then converted from cubic inches per minute to CFM by dividing it by 1,728, the number of cubic inches in one cubic foot (12 x 12 x 12 = 1,728).

So, this formula with our engine looks like this,

183 x .5 x 6,500 / 1,728 = 344 CFM

Next we take the 344 CFM and we adjust it to reality. The above calculation contains an assumption of 100- percent VE. Since most engines in a naturally aspirated state do not operate at 100 percent VE, we must adjust our calculation to compensate for this. While VE varies with engine speed, valve, etc., timing experts have historically agreed that an average of 80 percent is logical in most cases. However, in many of today’s engines operating with four valves, variable valve timing, and computer designed induction systems, it may be more logical to use a higher figure. For the sake of your calculations, you can use the following suggestions regarding what VE value to assume.

Typical two-valves-per-cylinder, push-rod engine: 80% VE

Four-valve engine: 85% VE

Four-valve engine w/variable valve timing: 95% VE

So for our example, we’ll assume it’s a four-valve engine: 344 CFM x .85 = 292.4 CFM

Now that we have the CFM flow potential of the engine in its naturally aspirated state we need to adjust it by the rise in actual airflow once turbocharged. We do this using a density ratio chart. It is possible to calculate a density ratio for each level of compressor efficiency at a given pressure ratio. This calculation says for any given compressor efficiency line there will be a resulting increase in air density at a given pressure. The density ratio chart plots air density as a function of compressor efficiency and pressure ratio. The pressure ratio is easily determined by taking ambient pressure, which is 14.7 lbs at sea level, adding it to your boost pressure, and then dividing it by ambient pressure. This gives you the absolute pressure ratio.

Boost Pressure + Ambient Pressure, P2

Ambient Pressure, P1

= Pressure Ratio

10 + 14.7 / 14.7 = 1.68 PR

Now that we know the pressure ratio is about 1.7 we can obtain the density ratio (DR) from one of our density ratio (aftercooled or nonaftercooled) charts. If boost is expected to exceed 7 lbs, it’s advisable to use an aftercooler. In the example, we’re talking about 10 lbs, so I’ve used the aftercooled chart.

...

By looking across the X-axis to the 1.7 PR and extending up to the 74 percent compressor efficiency line, we can then read across to find a density ratio of 1.5. The 74 percent number is used because it ends up being a conservative and realistic efficiency average to expect.

CFM x DR = CFM with our turbo

292.4 x 1.5 DR = 438.6 CFM turbocharged

Next we simply convert the turbocharged CFM into lbs/minute mass flow by multiplying it times standard air density, which is .069 lbs mass/cubic foot of air.

438.6 CFM x .069 = 30.26 lbs/min of air mass flow

The entire formula look like this, (0.5 x CID x Max RPM / 1,728) x VE x DR x .069

It’s really just that easy. One of the double checks is a basic ratio of 1 to 10. It takes about 1 lb mass of air per minute to make 10 horsepower. To double-check our example, we need about 30 lbs/min of mass flow and 30 lbs/min x 10 = 300 horsepower, so we should meet our goal.

To improve the accuracy of your calculations it may be worthwhile to use the 1:10 air mass-flow to horsepower ratio initially to basically “shop” for the potential turbo of choice. Then, using compressor maps (see Chapter 5), determine the turbocharger that has your basic mass-flow and pressure ratio located right in the middle of its highest efficiency. Using that efficiency number, go back through the calculations for mass flow to verify your match.

...

Today’s turbocharger compressors will commonly hit efficiencies as high as 78 to 80 percent. But the wide operating RPM band of gasoline engines will operate any given compressor through a wide range of flow efficiencies. Each compressor has areas of varying efficiency called efficiency islands.

Find the nearby compressor map of the Garrett “Disco Potato.” As we can see our 30 lbs/min requirement at max RPM of 6,500 rpm shows up in a nice high efficiency island of about 72 percent, at a 1.7:1 pressure ratio. If we consider the fact that we’re going to be running our wastegate at 10 lbs boost, and that we want full boost at about 4,000 rpm, we can also calculate this point using the same formula as above except we use 4,000 rpm instead of 6,500 rpm. This will calculate about 19 lbs/min at a 1.7:1 pressure ratio, which is also in a high efficiency island over 76 percent. Once you plot both points on the map, you can see that from 4,000 rpm through 6,500 rpm with boost controlled at a 1.7:1 pressure ratio, the turbo will be running around 110,000 rpm turbine speed and it will flow right through the highest efficiency part of the compressor map. This would represent a very good match.

...

The trim of a wheel is a ratio used to describe both the turbine and compressor wheels. Trim is used in reference to the basic flow potential of a given wheel’s machining dimensions. Every wheel, both compressor and turbine, may have several trim configurations within that wheel casting. A given compressor wheel casting for example, could be “trimmed” such that it has two, three, or more trim configurations available. It is the trim that determines the wheel’s flow range and pressure characteristics.

Trim is calculated using the inducer and exducer diameters of the wheels. Note that the inducer of the compressor wheel is the smaller inlet diameter where the fresh air is induced into the compressor wheel, while the exducer is at the maximum diameter. The exducer has two primary components, the overall diameter and the tip width, sometimes called the tip height. In a trim calculation, however, the tip height is not part of the trim calculation.

Trim is calculated as:

(Inducer / Exducer) x 100

Example: Inducer diameter = 88mm

Exducer diameter = 117.5mm (88 / 117.5) x 100 = 56 trim

As a rule, as the trim is increased, the wheel can support more mass flow of air. Turbines are typically not as sensitive to flow changes as compressors. Because of this, it’s common for there to be more selections of compressor trims within a turbo model family than turbine trims.

For the most part, compressors with large inducers and smaller exducer diameters will flow large volumes of air (mass flow) at lower pressures, while smaller inducers with larger exducer diameters will flow less mass at slightly higher pressures. A large inducer with a large exducer diameter is a high-pressure, highflow compressor used in competition applications such as tractor pulling.

The trim characteristics of a compressor wheel will greatly influence the compressor map and thus that turbo’s flow potential. An example can be seen in the comparison in maps between the GT2860R and the GT2860RS, on page 66 in Chapter 5. They are very similar turbos from the same family except the 2860R uses a 55 trim while the 2860RS uses a 62 trim. Both compressor wheels are 60mm in diameter, but the 2860RS has about a 3mm larger inducer diameter. So, when tweaking your match and you wish to change compressors, if your pressure ratio is working fine, but you suspect you’re a bit short on air, a larger trim may be what you want, but make sure the trim you are switching to has a larger inducer by comparing the new wheel OD (outside diameter) to your wheel’s OD, if they are the same, but the new wheel has a larger trim, then the inducer is larger and this formula will tell you by how much.

...

the math for turbine matching is accurate and specific, but the variables are many and almost never known for sure. The following section on turbines will not necessarily give you a cut and dry manner in which to match a turbine to your engine. It is intended more to increase your comprehension of what is going on inside of a turbine and how to consider adjusting your match for optimum performance.

Perhaps the very best thing you can do for your turbo project is to not forget to place a pressure tap in the turbine inlet just past the turbine foot. Most people only focus on boost, but if all you’re looking at is boost you’re only measuing one side of the equation. You must know your turbine pressure or you’re flying blind. This can be easily accomplished by creating a 1/8-inch pipe tapped hole and installing an air tight fitting as a pressure tap. Run a couple of feet minimum, of steel tubing from the turbine to separate it from the heat of the exhaust before connecting it to a high-temp flexible line. This line will essentially be your “turbine boost gage” line, or actually turbine inlet pressure. You want to make sure that your turbine inlet pressure does not dramatically exceed your boost pressure or you’re developing too much back pressure and killing your power.

...

However, done properly, the realistic sizing of the compressor will place you in a model series that will likely have a suitable turbine selection for your application. This is because turbine and compressors are relatively matched in flow range because of the power balance necessary between the compressor and turbine ends of the turbocharger.

While the process of mathematically performing a turbine match is not really logical for an aftermarket application, understanding why and the elements necessary do help in understanding turbines in general.

...

Let’s revisit the A/R ratio, or literally, Area divided by Radius. It’s a simple mathematical relationship between the size of the turbine wheel, which dictates the radius, and the throat square area of the turbine housing. You can think of it as a rating of the exhaust gas swallowing capacity of the turbine section. To calculate the A/R ratio the, area of the turbine housing is measured in square inches of a cutting plane line that passes through the turbine’s gas passage at the tip of the tongue, divided by the radius from the center of the turbine wheel’s axis of rotation, to the centroid of the volute.

...

Turbine housing designs utilize what is called a free-vortex flow field. In this design, the exhaust gas tangential velocity will vary inversely with radius. The tangential velocity component approaching the wheel tip will have approximately the same value as the wheel tip peripheral velocity. This is why it would be a mistake to assume that the same A/R ratio used in different diameter turbine wheels would have similar volumetric flow patterns. A smaller A/R will raise exhaust pressure but only within that turbine family where the same turbine wheel is used.

Examples:

1) 3-inch area / 3-inch radius = A/R of 1

Versus

2) 1.5-inch area / 1.5-inch radius = A/R of 1

In each of these examples the A/R is “1.” However the volumetric flow capacity of each is dramatically different from the other. Imagine a 3-square-inch orifice feeding a 6 inch diameter turbine as in example 1, versus only a 1.5-inch orifice feeding a 3-inch diameter turbine wheel. In this case it can be easily understood how different the volumetric flow of each combination is, yet the A/R of each turbine is the same. Remember that A/R is only a ratio of the values within a given turbine housing, not the values themselves.

...

Lastly, if your turbo selection uses an internally wastegated turbine housing, chances are the turbine trim of the wheel and the choices of turbine housings available have taken the wastegate’s presence into account by allowing exhaust backpressure to rise more quickly for drivability and response since the wastegate is present.

...

The wastegate performs a very valuable function. The wastegate is simply a valve that opens the turbine housing to relieve excess exhaust backpressure, triggered by a boost pressure actuator. The actuator is activated by boost pressure fed from the compressor. It is adjusted such that a small turbine housing A/R that provides boost pressure at a low to mid-range RPM, doesn’t over boost as the engine climbs in speed thereby over speeding the turbo and over boosting the engine.

Many off-the-shelf-turbo models will have a wastegate built integral into the turbine housing and that makes your application much easier. However, in-line wastegates are also available on those turbo models where a wastegate is not designed integral to the turbocharger.

...

https://www.musclecardiy.com/performance/match-turbocharger-engine-step-step-guide/