A Nozzle Is Said To Have Choked Flow When Turbo Calculator Explained

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Turbo Calculator Explained

Turbo calculators are useful software applications that help you choose the right turbocharger for your build up. Good calculators have additional features that help you maximize the potential of your turbo setup including improving the spool characteristic and maintaining reliable control over your boost pressure.

Intro to turbos

Turbochargers are air compressors that are typically attached to an engine to improve its performance. The compressor side of the turbocharger intercepts the air coming into the engine’s intake system and compresses it before it reaches the cylinders. This compression increases the air density allowing the engine to ingest more oxygen molecules (which are essential to the combustion process) in the same cylinder volume, ergo making the engine breathe like a larger displacement engine and ultimately allowing it to produce more power.

The turbine side of the turbocharger is what drives the compressor wheel described above. The turbine intercepts the exhaust gasses coming out of the engine, and uses part of the thermodynamic energy stored in those hot and rapidly moving gasses to spin the turbine wheel. This turbine wheel is physically connected to the compressor wheel and as it picks up speed the turbo starts to spool – which is the point at which the compressor reaches a high enough speed where it can start to compress the air to overfeed the intake side of the engine as described earlier.

Matching turbo size to engine demand

Now there are many possible combinations of different sizes of compressors and turbines creating an array of turbochargers to work on any vehicle. For example a very large displacement engine that does not have a high horsepower target will have require a larger turbine that will not choke the exhaust flow but a smaller turbo that does not have to do that much work compressing air for such a small power target. Alternatively, a small displacement engine with a very high power target, such as a drag racing four cylinder engine will require a smaller turbine side for quicker spool, but with an over-sized compressor side to be able to deliver a very high power target at a very high pressure ratio.

What a good turbo calculator does is help you choose the right turbocharger to match both the intake side and the exhaust side of your engine to give the best balance between quick spool and reaching our overall power targets.

Generally speaking, larger turbines and larger compressor wheels are larger and heavier… and require more time and more energy to spool them up. At the same time larger turbines and larger compressor wheels are able to support higher power targets without choking off or limiting the engine flow. This is the inherent trade off between spool and peak power that is the nature of the turbo sizing game.

Factors affecting engine demand

Knowing that the turbo is both driven by the engine exhaust flow, and also knowing that the turbo needs to ultimately have a higher peak air flow than our engine (in order to force feed it and raise our power levels)… then at the core of any good turbo calculator is a good engine model that understands how much power and flow the engine is already making in order to choose an appropriate turbocharger.

The are several factors that affect engine demands that most performance enthusiasts are very likely to perform on their cars prior to, or during doing a turbo conversion or installing a turbocharger kit.

For example:

* Increasing the displacement of the engine will typically increase the engine’s power between 2% and 15% depending on the type of over-bore or stroker kit used.

* Raising the rpm at which the engine produces its peak power level will affect power by the ratio of those two rpms… for example using an aftermarket camshaft to allow the engine to produce peak power at 7500 rpms as opposed to 6500 rpms for the stock camshaft should increase power delivery by roughly 15% depending on the exact tune.

* Other modifications such as a new intake manifold or a larger exhaust system and a better designed exhaust manifold for the turbo system may raise the engine’s volumetric efficiency at peak flow by anywhere between 5 and 15%

Combining all of those factors together, it is possible that the engine that you are trying to turbocharge is already producing up to 50% more power (and thus has 50% higher demands from the proposed turbocharger) than a stock engine that is still performing to its original manufactured parameters.

Now that we know our new engine demand and power levels (after factoring in any modifications we have performed as mentioned earlier), we can then move on to choosing a turbocharger that is matched to this exact engine combination.

Normal engines breathe under the sole effect of ambient air pressure due to the Earth’s atmospheric conditions. These conditions vary with things like elevation and humidity; however, in general most engines breathe due to a pressure differential of 1 bar of boost (or 1 atmosphere) between the outside air, and the vacuum inside the cylinder.

If our current engine produces 450 horsepower at 1 atmosphere in naturally aspirated form, and we would like to make 750 horsepower with a turbocharger then the logic goes as follows:

To force the engine to flow 750 horsepower instead of 450 horsepower, the turbocharger needs to create a condition where the intake manifold of the car is operating above the normal atmospheric pressure of 1bar. The exact pressure level required in an ideal world is actually the ratio of those two power levels which is 1.66 bar (or 1.66 atmosphere) of pressure since air flow and air pressure are linearly related.

Knowing this now, we know that we are looking for a turbocharger that can flow 750 horsepower worth of air (roughly 1125 cubic feet per minute) at a pressure ratio of 1.66.

This figure of 1125 cfm @ 1.66 PR is the key to choosing the right compressor wheel that is capable of flowing that much air, at that pressure level, at a high enough efficiency level.

The real Density Ratio vs the ideal Pressure ratio

As stated earlier, in ideal conditions a pressure ratio of 1.66 is enough to reach our power goals. However, in the real world, air temperature rises when air is compressed. This temperature rise causes the air to expand as we are trying to compress it which reduces its density.

The combination of this thermal expansion is a loss in compressor efficiency. The ideal compressor has a density ratio of 2.0 at a pressure ratio of 2.0, i.e. when the air is compressed to twice the pressure, it is now at half the size, and at double the density… However in the real world, the density ratio always lags behind the pressure ratio depending on the thermal efficiency of the compressor wheel where it is possible that our target pressure ratio of 1.66 that our actual density ratio is 1.5 which means the actual power we will make at this boost level will be 675 horsepower rather than the target of 750.

Using a good inter-cooler, after the turbocharger can bring the overall system efficiency up close to 85% or 90%. But this means that in most cases, you have to know that most turbo calculators are about 10 to 15% off of your target power level and that you will need slightly more boost pressure to reach your target power goal. That is unless the turbo calculator knows the exact point on the compressor map where you will make peak power, and unless it corrects for both the compressor efficiency at that point as well as the inter cooler efficiency (which are the two factors affecting the gap between the real density ratio and the ideal pressure ratio),

As the turbo calculator gives you a short list of possible turbochargers that will meet your power and boost pressure goals to match your engine demands, it is a good habit to choose a slightly over-sized turbocharger where your data point (1125 cfm @ 1.66 PR) is sitting in the middle of the compressor map on a high efficiency island, rather than at the far right of the compressor map of a smaller turbocharger that is almost maxed out for this engine combination. Having a slightly over-sized turbocharger allows you to compensate for the slight difference between the actual density ratio and the calculated pressure ratio that most calculators can’t correct for, and with this larger turbo you will be able to slightly raise your actual boost pressure to make sure you still reach your target power goal. A smaller turbocharger that has your target data point at the far edge of the compressor map will ultimately have a lower compressor efficiency on that larger outer island and will have no more room to grow with you for any future modifications or power increases.

Turbine Aspect Ratio Sizing

Now that we have found the compressor wheel that matches our engine demands, we must move on to choose the right turbine aspect ratio to get the best spool characteristics out of our turbocharger. On most street engines running pressure ratios in the 2.0 range you will find that turbocharger manufacturers have already coupled adequately sized turbine wheels to match the compressor wheel to give good overall performance.

However, even having that already taken care of by the manufacturer, the customer is still left with a choice turbine aspect ratios which helps target a certain spool rpm in trade-off for peak flow.

The turbine aspect ratio is the ratio of the diameter of the turbine inlet pipe to the radius of the turbine wheel. To simplify this explanation think of a fan mounted with pin on a long straw. The fastest way to get the fan to spin up is typically to blow on the outer edge of the fan lobes by focusing all of your breathe as a tight stream of air on that outer rim. This ‘nozzle’ like air injection helps spool the fan but ultimately shaping your mouth into a nozzle limits the amount of peak air that you will be able to blow at the fan before back pressure builds up in your moth.

Alternately, opening your mouth and blowing on a larger area of the fan takes longer for the fan to reach its peak speed but in the end you are able to blow larger amounts of air through the fan without building up pressure in your mouth.

The turbine aspect ratio is the ratio of the inlet area of the turbo to the turbine wheel diameter, and so having chosen a single turbine wheel and fixing that diameter, altering the size of the turbine housing inlet changes the size of the air ‘nozzle’ injection into the turbine for the air coming out of the engine’s exhaust ports.

A smaller aspect ratio has a smaller inlet area which enhances the nozzle effect and gives faster spool. A larger aspect ratio has a larger inlet area which distributes the air across a larger area of the turbine wheel, which does not promote spool, but ultimately helps the engine breathe more easily at peak flow levels without creating so much back pressure in the exhaust manifold.

Generally speaking the turbine aspect ratio (A/R) is chosen based on:

* Displacement: The larger the engine displacement, the more power it can produce at lower rpms levels, the less ‘nozzle’ assist it needs from the turbine housing, the larger the aspect ratio can be.

* Engine redline and target spool rpm: The higher the engine redline, the wider the range of rpms we have to make power in, the less urgent it is to spool the turbo at 2500 rpms (when you have up to 10,000 rpms to make power with) and the more likely we are to choose a larger aspect ratio.

* The peak pressure ratio: The higher the pressure ratio we are shooting for, the wider the dynamic range of power output that we will see from the engine between being off boost and on boost, and the higher the flow requirement will be on the typically smaller turbine side (which is matched to the smaller engine to get any kind of spool in the first place) and thus the larger the aspect ratio will be chosen (albeit on typically a smaller radius turbine for these cases).

A good turbo calculator is able to take into account these different factors and recommend an aspect ratio that will give a good compromise between spool rpm (the rpm at which the turbo first starts to produce power) and the peak flow capacity of the turbine wheel (which can degrade by up to 25% – a significant amount – for a 0.40 A/R housing vs a 1.20 A/R housing for example).

Waste-gate sizing

The waste-gate is an exhaust port that is controlled by turbo pressure. Once the pressure in the intake manifold reaches our desired pressure ratio, the waste-gate port is opened to direct exhaust gasses away from the turbine wheel and directly into the exhaust system. This bypass prevents more energy from reaching the turbine and regulates the turbine wheel rpm.

The general concept behind waste-gate sizing is two fold:

1- The larger the waste-gate the more energy you can take away from the turbine, and the more accurate your boost control can be. Smaller waste-gates can be overwhelmed at higher flow levels and show side-effects like ‘boost creep’ at high rpms.

2- The waste-gate needs to flow a percentage of the total exhaust airflow related to percentage utilization of the turbocharger. For example, a turbocharger that fully spools at 2500 rpms on an engine that has a 7500 rpm redline needs to bypass two thirds of the exhaust air away from the turbine since only one third of the engine output is enough to spool the turbo.

Similarly, the larger your turbocharger is compared to your power goals (having a 1000hp capable turbocharger on a 600hp engine for example) the larger the waste-gate needs to be in order to move exhaust energy away from the turbine preventing the turbo from going to its maximum rpms and producing too much boost and too much power (which the engine may not be prepared to fuel or handle).

So either way, there is a minimum waste-gate port size that will be able to handle a reasonably matched turbocharger to your engine demands. As you oversize the turbocharger larger and larger (leaving room for future upgrades and more power) and as you lower your spool rpm and your turbine A/R lower and lower, then you need to compensate by using an even larger waste-gate port to manage your boost levels properly.

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