# Finding the Peak Pressure of a Diesel Injection Pump

• Automotive
I am trying to find peak pressure of a diesel engine injection pump.. It doesn't have to be exact but +/- 1000psi would be fine. The basic principle is the same as an engine. Piston goes up and covers a fill hole, once it is covered the only way it can flow fuel is through the injector, so injection starts the instant that fill hole is covered. The injector itself will not open until 4500psi and there is a delivery valve (check valve) at the top of the piston to prevent the pressure from bleeding back and having to build pressure throughout the injection line which would delay timing and cause bad things to happen. I attached a pic of this for better understanding.

Also there is a cam with a roller tappet that rides the cam profile. On the actual pump I used a dial indicator and measured the lift of the plunger at every single degree of cam rotation. From this I found that from one degree to the next the biggest difference was 0.017 inches, so this would be the peak piston velocity per degree.

To get a flow calculation, I just assumed it to have a constant "pumping" lift rate of 0.017" per degree the entire time. I realize this is not true by design but being all I want to know is the peak pressure at this velocity, I decided to use it get a flow measurement. So I took 0.017*360 to get a full pump rotation since it is gallons per minute I'm after and the pump uses revolutions a minute. This gets me to 6.12 of total virtual stroke at the continuous 0.017" lift per degree velocity.

Use that as the height for the volume of a cylinder formula and I end up with 1.259 cubic inches. The piston is 13mm so I did all the conversions there.. Multiply that by 2000 for 2000RPM and you get 2518.2 CI per Minute. Multiply by 0.004329 to get GPM and you're at 10.9GPM

Then it goes through a little 2ft injection line 0.120" diameter, then through the injector and out the tip. The pintle in the injector will not open until 4500psi is reached. There are 5 holes in the injector each 0.035" in diameter and that comes out to a combined cross sectional area of 0.00481 sq. in.

Apparently this needs to be in sq. ft. for a formula I found so that converts to 0.0000334067 sq. ft. I then converted the GPM from earlier into Cubic Feet a second and got 0.024289. Then I divided that by the hole area and got the final velocity of 727 fps.

Density of diesel is 1.64 slugs. Using pressure formula of 0.5 * density * velocity and converting to PSI I get 3010psi.

The injector doesn't pop until 4500psi though so I assume since it is a positive displacement pump it would be shoving 3010psi out in addition to the 4500, for a total peak pump pressure of 7510psi.

This seems very low to me and if I use a smaller injector which is what was on the engine stock, I'm seeing almost 200,000psi. So I think my math is wrong somewhere.

I attached a spreadsheet that I've been doing this math with.

Anyone that can help is much appreciated.

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## Answers and Replies

Baluncore
Welcome to PF.

The pintle lifts at 4500 psi. The fuel is vaporised there. The vapour is then distributed through the 5 holes into the combustion chamber.

You cannot combine the holes into one area as fluid flow through an orifice is not a linear function of area.
Fuel jets are not cold liquid but are vapour. They are injected into a hot environment. The viscosity of vapour in the 5 jet director holes are not the same as the viscosity of cold liquid fuel.
There is no sudden start to flow so we can ignore transmission line effects. Injector pintle lift pressure will control the pump pressure.

Fuel injector lines are elastic so increase diameter when under pressure. You can measure diameter with a piezo displacement sensor clamped to the injection line. Calibrate with a hydraulic hand pump and pressure gauge.

anorlunda
Baluncore
Density of diesel is 1.64 slugs. Using pressure formula of 0.5 * density * velocity and converting to PSI I get 3010psi.
I think that is dynamic pressure and like KE is proportional to velocity squared.
That appears across the pintle lift.

Theres definitely more than 4500psi, tons of articles including straight from bosch say the pumps peak pressure is something around 20,000psi. If the pump couldn't keep up with the injector holes then I could see that but it is pumping so fast and hard that it shoves the fuel through at great pressure above 4500. As far as the pump is concerned it is pumping liquid fuel, it isn't burning until it leaves the injector. I'm not sure it is even vapor until it actually leaves the injector being its a diesel. I understand gasoline vapor is actually what burns but I don't think diesel is entirely vapor until it leaves the injector.

Of course I'm not 100% on all of this but diesel is definitely heavier than gasoline and not as combustible or volatile. You can pour diesel on the ground and throw a match on it and it won't ignite and it won't evaporate for quite a long while.

Baluncore
The 4500 psi injector is a differential pressure in series with the combustion chamber pressure. So add the two to get the required pump pressure. Compression during starting will only be about 300 psi. The cylinder pressure in the combustion chamber during injection and combustion is significantly greater.

What is the injector? Is it the pressure step across the pintle that generates the vapour, or is it the outlet of the holes that guide the vapour jets and screen the pintle from the combustion? What advantage is there in having small director holes with insufficient capacity for the fuel vapour generated at high flow rates?

The energy released at the step change in pressure through the injector causes the atomisation. As that pressure step is increased, the ability to quickly and cleanly burn more difficult fuels improves. There have been several generations of fuel injection system development. You started discussing a first generation jerk pump. Later generations have much higher common rail pressures and so injection is from the common rail, with transducers controlling the release of fuel into the combustion chamber. Take care not to confuse later common rail pressures with earlier jerk pump pressures.

I am not sure weather you are looking for the pressure the pump is outputting as connected or, what the max. pressure is possible by the pump.

If you are looking for the pressure being provided during operation....I would think it would be the 4500 psi as controlled by the injector opening value. If you are looking for the max. pressure the pump is capable of, you must consider the following. Diesel fuel is a liquid, and for all practicable purposes can be considered uncompressible. If we close-off the pump’s cylinder at the top to allow no fuel to escape, the highest pressure possible is controlled by the fit of the piston to the cylinder walls and the amount of force that can be applied to the piston from the cam and the ultimate strength of the materials involved. If the piston to cylinder fit is such that it allows no (or very little) blow-by. Then max. pressure, inside the cylinder, is controlled by how much force can be applied to the bottom of the piston and the strength of the materials used. If the piston is very small in diameter and the force applied very large, any amount of pressure can be achieved, up to rupture of the materials. The psi can be calculated using the force applied and the area of the piston.

Baluncore
Eilts, P., Stoeber-Schmidt, C., and Wolf, R., "Investigation of Extreme Mean Effective and Maximum Cylinder Pressures in a Passenger Car Diesel Engine," SAE Technical Paper 2013-01-1622, 2013. https://doi.org/10.4271/2013-01-1622. Gives the following; “The current level of mean effective pressure (mep) of automotive diesel engines is 20 to 30 bar. Maximum pressure (pmax) is about 180 to 200 bar”.
200 bar is 2900 psi. So add the injector pressure drop of 4500 psi to get pump pressure = 7400 psi.

anorlunda
Staff Emeritus
Fuel injector lines are elastic so increase diameter when under pressure. You can measure diameter with a piezo displacement sensor clamped to the injection line. Calibrate with a hydraulic hand pump and pressure gauge.

That point seems to have been ignored in this discussion. If the fluid is very incompressible, then even a tiny change in volume is sufficient to mitigate high pressures. So the elasticity becomes the dominant effect in determining peak pressure.

The goal is to find the max pressure exerted within the chamber of the pumping piston. The amount of force is basically unlimited as the engine runs the pump and it will destroy the pump if it gets to that point of pressure. But I guess at this point I'm lost as to how to find that pressure using the flow rate out of the injectors.

Baluncore
That point seems to have been ignored in this discussion. If the fluid is very incompressible, then even a tiny change in volume is sufficient to mitigate high pressures. So the elasticity becomes the dominant effect in determining peak pressure.
Not quite, the lines must not be that elastic.
But it is the another reason why the injector pintle is designed to lift at such a high set pressure. The pump and injector lines will expand until the pressure is sufficient to lift the injector pintle. That line pressure rise-time introduces a delay to the start of injection and is largely eliminated by setting the timing of the engine.

If fluid flowed due only to the plunger stroke there would be a dribble at the start and another at the end of each fuel slug pumped that would not be vaporised, so would not burn clean and would produce black smoke.

So what has flow rate got to do with it? By having a set pintle lift pressure it is guaranteed that sufficient energy is released during injection to vaporise all the fuel injected. That is largely independent of the fuel injection rate because energy_released = volume_flow * pressure_difference.

But I guess at this point I'm lost as to how to find that pressure using the flow rate out of the injectors.
You cannot calculate the peak pump pressure from the flow.
You need to add two things, the pintle lift pressure and the peak cylinder pressure during injection.

The injection pump will not break before the cylinder head bolts are stripped, the pistons and bearings are crushed, or the cylinder sleeves split.