K20Z3 Turbocharger Analysis

[DetachmentBravo]

NOTE: The following is original research and may contain errors. If you spot any errors in any of the equations, spreadsheets or graphs, please contact me and I will correct them as soon as possible.

Introduction:

This thread is meant to explain some of the science behind turbocharger selection. To make the information contained herein more applicable to the 8thCivic community, the K20Z3 engine is used for all examples. It is my that this thread, with contributions from the community, will become a reference for Si owners who are considering turbocharging.

Calculation:

Several processes are detailed online for analyzing compressor maps and selecting the proper turbo for your application. The system used here takes a slightly different approach to maximize the range of applications addressed and to allow for changes in elevation. Living in Colorado, the effects of altitude have a significant impact on the data. All of the spreadsheets and charts included will have two versions: one for an altitude of 5280 ft and one for sea level.

You will also notice that all calculations are done in SI units and then converted into imperial units as needed.

Step 1: Volumetric Displacement

The first step is to calculate the approximate airflow through the engine as a function of RPM. In theory, a four stroke engine (also known as an "Otto Cycle" engine) will move a volume of air equal to its total displacement every two complete revolutions. In reality, airflow restrictions and other sources of inefficiency prevent an engine from flowing all of the air it is theoretically capable of. The amount of air that an engine will actually flow is dictated by its Volumetric Efficiency. To get an exact value for Volumetric Efficiency requires testing an engine on a flow bench. For our purposes, we are going to assume that the K20Z3 has a high Volumetric Efficiency of 90%.



Step 2: Air Density

Calculating the density of air the plenum is where we can account for changes in elevation. It is also where we could go way overboard on the math, accounting for water vapor, compressor efficiency, intercooler efficiency, etc. To keep things simple, but maintain accuracy, we assume a constant intake temperature for an intercooled system of 338 K (~ 130 F) and that the incoming air has no water vapor. (Anyone who has been to Colorado knows this isn't far from the truth ). The intake pressure is equal to the atmospheric pressure adjusted for altitude minus 6.8 kPa (~ 1 psi) to account for restrictions in the intake and air filter. Our variable in this equation is the Compressor Pressure Ratio, the value commonly seen on the y-axis of compressor flow maps.



Step 3: Mass Flow

Step three is a fairly basic application of volume and density to find mass. We take our Volumetric Flow from step 1 and multiply it by the Air Density from step 3. The result is our mass flow rate for our engine at a certain Compressor Pressure Ratio and RPM.



Step 4: Power

While not necessary for analysis of compressor maps, having an estimate of your engines power output under boost conditions is always handy. To calculate power output we are going to use a value known as Brake Specific Fuel Consumption (BSFC). BSFC is a measure of how much fuel an engine consumes to create a certain amount of power. Lower values of BSFC indicate a more efficient engine because less fuel is needed to create the same amount of hp. To get an accurate estimate of the BSFC for the K20Z3 I used the known hp number published on the Honda website (197 hp @ 7800 rpm). Amazingly, the result was 218 g/kW*hr. The average four stroke gasoline engine has a BSFC of 322 g/kW*hr! Having a BSFC as low as 218 is usually only found in diesel engines!



As a side note, using the data from the above calculations matched perfectly with AJP's dyno results when adjusted for sea level.

[DetachmentBravo]

Excel File:

To make it easier for people to help correct any errors and expand the number of maps we have available, I'm going to include a link to my original excel files. This link will be kept updated along with the rest of this thread, so any added charts will also be added to the file. I'm going to upload it to a free file server instead of attaching it to this post because the file is pushing the 976.6 kB file limit as it is, so any additions may push it over the limit.

Excel Files

How to Generate Your Own Turbo Maps:

The following is a "How-To" describing the process I used to create the maps featured later in this thread. To make this a process available to everyone, I have simplified it to use only two basic programs, Excel and Paint. A link to the required .xls can be found above. All steps are accompanied by visual aides. (Click to enlarge.)

Step 1:

Get a hold of a flow map for the turbocharger you wish to analyze. They can usually be found on the internet in GIF form. Our first step is to determine the range of the Pressure Ratio and Air Flow axis of the original chart. Doing so will allow us to properly scale our map.

In our example map the Air Flow axis has a range of 0-50 lb/min with an interval of 5 lb/min, and the Pressure Ratio axis has a range of 1-4 with an interval of .5.

Step 2:

Creating a new chart from scratch would require a good deal more work, so we are just going to modify an existing one instead. But first, we have to make a copy of the existing map so we don't erase our previous hard work. To to this, open up the Excel file and select a chart that uses the same units as the map you are going to analyze. The example map we are using is a Garret map, so the units are imperial (lb/min). If we were using a Mitsubishi map the units would be in SI (kg/s). Once you have found a chart, right click on its tab bottom of the screen and select "Move or Copy...". A window will pop up prompting you to select the destination of the chart. Because we are creating a copy, do not modify the destination parameters, just select the "Creat a copy" check box at the bottom of the window and hit "Ok".

You should now have a copy of the original chart. You can rename this new chart by right clicking on the chart's tab and selecting "Rename". You can also change the title on the top of the chart by selecting it and then clicking somewhere within the text. (Do not double click however, this is a different function.)

Step 3:

The chart must now be adjusted to the ranges found in Step 1. To do this, right click on an axis and select "Format Axis...". A new window will open up. Go to the "Scale" tab and enter in the new range data. When you are finished hit "Ok". Repeat this for the other axis.


Step 4:

Here comes the sneaky bit that makes this so simple. Excel allows us to use a custom background for our chart area, and because Excel generates all of the axises and titles for us, all we need to do is cut out the center section of our turbo flow map. Open up your turbocharger flow map in paint and select just the inner part of the map with the rectangular selection tool. Got to "Edit->Cut" or hit 'Ctrl-X' to cut out the selected area.

Next, open a new image using "File->New" or 'Ctrl-N', and paste the selected area into it using "Edit->Paste" or 'Ctrl-V'. You can now save this new area in any format you like (preferably GIF or JPEG) by going to "File->Save As...".

Step 5:

To tell Excel to use this new image as the background for our chart, right click within the plot area and select "Format Plot Area...". A new window will pop up. Hit the "Fill Effects..." button. Another new window will pop up. Hit the "Select Picture..." button and navigate to where you saved your map section from Step 4. After selecting your saved image, hit "Open" and then hit "Ok" on the two other open windows.

TADA! You have just created a turbocharger flow map with an overlay of the data for the K20Z3 engine!

[DetachmentBravo]

Explanation of Turbocharger Maps:

Now that we have covered the equations behind how the engine maps are generated, we are going to look at how to read these maps. Below is an example map of the GT3582R. Important features are indicated and explained below. (Click to enlarge.)

Pressure Lines
The blue pressure lines indicate a certain manifold gauge pressure. These values are referred to as the "boost pressure" of the turbo. Each dot on the pressure line corresponds to a certain engine rpm, starting at 2,000 RPM and going to the engine's rev limit of 8,500 RPM.

RPM Lines
The green RPM lines indicate a certain engine RPM. They serve as guides for interpolating mass flow rates that do not lie perfectly on a pressure line. You'll notice that the RPM lines are not always even spaced. This is due to the fact that I decided to chart 7,800 RPM (where maximum hp is created on the stock engine) and at 8,500 RPM (the rev limit of the engine).

Surge Line
On a compressor map, the "Surge Line" is the left most boundary of a compressor map. When a compressor is in surge conditions, it does not have sufficient flow to maintain the pressure ratio across its inlet and outlet. This condition normally occurs when the throttle body is closed suddenly and pressure backs up in the intake. A BOV is used to prevent this condition from occurring. The surge line can also indicate how your turbo will spool up. For instance, if your target boost pressure is 16 psi, then you can see that the surge line intersects with the 16.4 psi pressure line at about 5,000 rpm. This indicates that you will achieve your maximum boost pressure around 5,000 rpm. A turbocharger just doesn't suddenly jump to a target pressure however, it will slowly build up over the rpm range. To see when the turbocharger will start creating pressure, we move down the map and to the left to find the first intersection of the surge line and an rpm line. In our example this occurs between the 3.3 psi and 6.6 psi pressure lines and between the 3,0000 RPM and 4,000 RPM lines. This tells us that the turbo will likely start generating pressure at around 4,000 RPM.

Efficiency Islands
Each ring on the compressor map shows the approximate efficiency of the compressor in that area. Compressor efficiency is an advanced subject so I will only give a simple explanation of it here. The higher the compressor efficiency, the less heat is being transfered to the air as it is being compressed. As the heat of the air increases, its density decreases which has a negative effect on power. Eventually it is a matter of diminishing returns. The extra pressure created by the compressor is negated by the heat generated. This is a gross oversimplification, and if you would like to learn more about compressor efficiency see the links posted at the end of this section. NOTE: Compressor efficiency has not been factored into the spreadsheets and charts used here to make the calculations more manageable.

Efficiency Centerline
The "Efficiency Centerline" shows where the compressor achieves its maximum efficiency for a given pressure ratio.

Choke Line
The rightmost bound of the compressor map is known at the "Choke Line". The choke line indicates where the compressor efficiency drops below a certain point (usually 55%) and the compressor is no longer having a positive impact on horsepower.

Speed Lines
The speed lines on a compressor map show the estimate RPMs of the compressor at a given point.

Links:

These are the two sites that I found the most helpful in my research:

Garret's Turbo 103 (General Overview)
Stealth 316's Site (Very Technical)

Spreadsheets:

Plugging the above equations into Excel lets us calculate Mass flow data for a range of altitudes and Compressor Pressure Ratios. (Click to enlarge.)



Maps:

The data from the spreadsheets can now be plotted and applied to various compressor maps. (Click to enlarge.)

K20Z3 Charts



Mitsubishi Maps



Garrett T3-T4 Maps



Garret GT Maps

[GalaxyGreySi]

Looking forward to this... 8thcivic.com needs more math and physics geeks. + rep, DetachmentBravo!

[DetachmentBravo]

Well thats all the data I have for now. I'm working on charts for sea level and alot more compressors so stay tuned.

[06Si_LoveR]

Ya... that looks about right...

[DetachmentBravo]

Okay updated the two compressor maps with the maps for sea level. Any suggestions which compressors to do next?

[GalaxyGreySi]

I'd REALLY like to see the Trust T517Z and the Precision SC6169E and SC6176 if you can find maps for them, since they are the turbos that nearly every boosted member on here is running.

[DetachmentBravo]

Yes, I too would love to do those as they are the two most used turbochargers.

One little problem... Trust doesn't release maps for their turbos and I can't find any maps for Precision turbos. Perhaps one of the AJP guys could be so kind as to donate a SC6169E map?

[GalaxyGreySi]

Is there any sort of computer program available that can generate a simulated map based of of the specs of the turbo? That would be so handy; seems like a lot of these companies do not release compressor maps. I wonder why that is...

[DetachmentBravo]

I don't know of any programs unfortunately. And while I do know several languages (Java, C/++, LUA, ASM) I do not know any of the fluid dynamics behind impeller design.

[sickyute]

check garrett's site for compressor maps .... they build the precision turbos ...even if u don't see the exact turbo on there ... there's one to match the precision u would be looking for ...

atleast i think so.

[DetachmentBravo]

Very true, Precision Turbo does use Garret turbos as a base. The only catch is that I can only find maps for GT series turbochargers and T3/T4 turbochargers. I'm having trouble figuring out which maps would best represent the SC6169E. All I really know about the SC6169E is that it has a 61 mm compressor wheel, 56 trim and a T04E style housing. That doesn't match up perfectly with any of the maps I have. The closest I have is an old T04E map for a 57 trim.

I'm not certain what effect the size of the compressor is going to have on the map. Also, Precision turbo designs their own housings which is going to alter the turbo characteristics somewhat. I'll post the T04E map when its done, but I am not certain how accurate it is.

[DetachmentBravo]

UPDATE: I just added the T04E and GT35R maps. Check 'em out on the first page.

I know that blueroadster is using the GT35R. He might be having a little bit of turbo lag... but he's making a hell of alot of power when it kicks in.

[webby]

well done

[DetachmentBravo]

Originally Posted by webby

well done

Holy crap! From Webby that is high praise! Am not worthy.

[sickyute]

Originally Posted by DetachmentBravo

UPDATE: I just added the T04E and GT35R maps. Check 'em out on the first page.

I know that blueroadster is using the GT35R. He might be having a little bit of turbo lag... but he's making a hell of alot of power when it kicks in.

ball bearing ...
so he's spooling faster ...

i can tell u that at idle (on the ajp car) that u could almost hear the GT35r wanting to spool ... no exageration here ...

so whatever it would have, if any, would be minimal.

[F.I.A.T]

compressor maps are a good baseline to start with but altering the motors charateristics will affect your formula. not to mention if we still went solely by compressor maps instead of real world experience we would never be runnning anything larger than a T3 turbo and no where near the GT42R that we run now.

The maps for the Precision turbos are not going to be found. They do their own R&D outside of Garrett and now make some of their own wheels. so simply relying on the garrett mmaps would not be correct in any of your calculations. esspecially since they dont use standard garrett turbine wheels which alter spool and output of each turbo.

[DetachmentBravo]

Originally Posted by F.I.A.T

compressor maps are a good baseline to start with but altering the motors charateristics will affect your formula. not to mention if we still went solely by compressor maps instead of real world experience we would never be runnning anything larger than a T3 turbo and no where near the GT42R that we run now.

The maps for the Precision turbos are not going to be found. They do their own R&D outside of Garrett and now make some of their own wheels. so simply relying on the garrett mmaps would not be correct in any of your calculations. esspecially since they dont use standard garrett turbine wheels which alter spool and output of each turbo.

As I had feared with the Precision Turbo's.

Remember, I have designed these calculations to simply be baselines for people interested in the turbocharger selection process. They are a trade off between accuracy and convenience.

By assuming constant values for such things as intake plenum temperature and pressure