CYLINDER LEAK DOWN TESTER

Forum about flow calculators available on pipeflowcalculations.com and how to find solution for your fluid flow problem.
HenriMalcorps
Posts: 8
Joined: Wed Mar 20, 2013 1:27 pm

CYLINDER LEAK DOWN TESTER

Post by HenriMalcorps »

A few weeks ago I bought a cylinder leak down tester. The principle is that the cylinder of the motor is put under pressure (a few bar) and that the flow rate, necessary to maintain the pressure, is measured. To measure the flow rate, a tube with a restriction is put between the air compressor and the cylinder. The internal diameter of the tube is 10 mm, the cylindrical restriction has a diameter of 1 mm and is 6.4 mm long, the pressure at the entrance and the outflow is measured. The pressure difference should be a measure for the flow rate.
The results I became where strange and I got the impression that nobody really understands how this instrument works. I was very happy to find this flow calculator, it is a beautiful instrument and I feel it should allow me to understand the working of the leak down tester. I also appreciate very much theory chapter and the forum.
I used the air pressure drop calculator to find the relation between the pressure difference and the flow rate for a sudden restriction and a sudden enlargement connected by a cylinder (1mm diameter and 6 mm long). For the sudden enlargement and restriction, two values for K (K1 and K2) are given, in function if they are "related to the smallest or greatest opening". I didn't (still don't) know what this means in this pressure drop calculator and which to choose, but if I used K1, I found unrealistic values. Using K2 gave acceptable values. Can somebody clarify my mind concerning the choice between K1 and K2?

I would have inserted a report, but was unable to copy and paste it.

Kind regards,

Henri Malcorps
admin
Site Admin
Posts: 375
Joined: Mon Feb 08, 2010 7:47 pm

Re: CYLINDER LEAK DOWN TESTER

Post by admin »

First of all try with this to enable copy/paste:
https://blogs.oracle.com/kyle/entry/cop ... va_in_java .
For some reason copy/paste stopped working in new version of windows web browsers.

Also, if you click "report" button all results will open in web page so you can copy/paste from there.

Now, to your question. K1 and K2 are minor losses coefficient that are used with corresponding velocity (diameter). If you calculate pressure drop and for minor losses use velocity V1 that is on D1 than you should use K1.
For that: Delta p = K1 * (rho * V1^2 / 2) and similar for K2 and V2. In the calculator - air pressure drop calculation - K should be used with internal pipe diameter which is K2, V2, D2, as you already did.

But for your problem I would suggest you to also try with gas discharge calculator. That calculator uses D and it is the restriction diameter in your situation.
It would be very interesting to me if you can do some testing and validate results from both calculators?
Pipe flow calculations - since 2000
HenriMalcorps
Posts: 8
Joined: Wed Mar 20, 2013 1:27 pm

Re: CYLINDER LEAK DOWN TESTER

Post by HenriMalcorps »

Thank you very much for your answer.
Below you will find my reports for the air pressure drop and the gas pressure drop.
The conclusions I could drew for the cylinder leak down tester are very interesting. I don't know if people on this forum are interested in this. If so, I am willing to write them down. I would not have been able to get there witgout this calculator.
Best regards,

Henri Malcorps

Air pressure drop calculator

1. volumetric flow rate at normal conditions (qn):
qn : 0.0058822595 l/s

2. mass flow rate (w):
w : 0.027380722 kg/h

3. length (L):
L : 6 mm

4. diameter (D):
D : 1 mm

5. pipe roughness (kr):
kr : 0.02 mm

6. local resistence coefficient (K):
K : 15000

7. velocity (v1):
v1 : 1.2617905 m/s

8. velocity (v2):
v2 : 1.5147061 m/s

9. cross section area (A):
A : 0.78539824 mm2

10. friction coefficient (f):
f : 0.11279753

11. Reynolds number (Re1):
Re1 : 567.3883

12. pressure on the pipe start (p1):
p1 : 6 bar

13. pressure on the pipe end (p2):
p2 : 5 bar

14. pressure drop (p1-p2):
p1-p2 : 1 bar

15. temperature (T):
T : 0 C

Isothermal gas flow rate amd pressure drop calculator

1. volumetric flow rate at normal conditions (qn):
qn : 0.0058844946 l/s

2. mass flow rate (w):
w : 0.027380722 kg/h

3. length (L):
L : 6 mm

4. diameter (D):
D : 1 mm

5. pipe roughness (kr):
kr : 0.02 mm

6. local resistence coefficient (K):
K : 15000

7. velocity (v1):
v1 : 1.2617905 m/s

8. velocity (v2):
v2 : 1.5147061 m/s

9. cross section area (A):
A : 0.78539824 mm2

10. friction coefficient (f):
f : 0.11275469

11. Reynolds number (Re1):
Re1 : 567.6039

12. pressure on the pipe start (p1):
p1 : 6 bar

13. pressure on the pipe end (p2):
p2 : 5 bar

14. pressure drop (p1-p2):
p1-p2 : 1 bar

15. temperature (T):
T : 0 C

16. kinematic viscosity (ν):
ν : 2.2230127 mm2/s

17. dynamic viscosity (μ):
μ : 1.7061117E-005 Pas

18. gas constant (R):
R : 287 J/kgK

19. critical pressure (pcrit.):
pcrit. : 37.7 bar

20. critical temperature (Tcrit.):
Tcrit. : 132.2 K
admin
Site Admin
Posts: 375
Joined: Mon Feb 08, 2010 7:47 pm

Re: CYLINDER LEAK DOWN TESTER

Post by admin »

Thank you for your data, but I suggested you to use GAS DISCHARGE CALCULATOR and not isothermal just to check from the other point of view.
Your experience with tester for sure will be of interest for others as well as for me also.
Pipe flow calculations - since 2000
HenriMalcorps
Posts: 8
Joined: Wed Mar 20, 2013 1:27 pm

Re: CYLINDER LEAK DOWN TESTER

Post by HenriMalcorps »

I am sorry; I confused the isothermal gas pressure drop with the gas outflow. I don’t know how to apply the “gas outflow calculator” to the leak tester. Compressed air is indeed leaking to the atmosphere through the tester and the motor cylinder, but I have no idea what the "K" of the cylinder could be. In fact the idea of the “garage leak down tester” is not to measure the leak (in l/s) but to compare the air resistance of the motor cylinder with a reference, which is the hole in the tester. The result is expressed in % which is obtained by dividing the pressure drop over the tester by the pressure at the outlet of the tester, while it is connected to the cylinder of the motor. The idea is probably inspired by what is happening in electricity, where the ratio of the value of two resistors connected in series, may be obtained from the distribution of the potential drop over the resistors. The problem is that for fluid flow the pressure drop depends on the square of the flow rate and the pressure. Probably this is the main reason why it is difficult to obtain coherent measurements with those instruments; I have to think about it. On top of that they are often sold without a users guide.
I think that an easier and more reliable method to measure the leak of a cylinder is to put it under pressure, close the cylinder and measure the time needed to get to 63% of the starting pressure. The result will of course depend upon the volume of the cylinder that is under pressure. The advantage of the down leak tester is that it is faster.
Maybe the gas outflow calculator opens possibilities in the field of leak testing in motor cylinders, but at this stage I am not sufficiently familiar with the calculator to discover this.
HenriMalcorps
Posts: 8
Joined: Wed Mar 20, 2013 1:27 pm

Re: CYLINDER LEAK DOWN TESTER

Post by HenriMalcorps »

I continued experimenting with the calculator and followed the suggestion of admin concerning the gas outflow calculator.
I remenber that the model I used for the leak down tester, was a pipe with 10 mm diameter and "a cylindrical restriction with a diameter of 1 mm and a length of 6 mm. Following the figures of the "K calculator" with alpa 180°, K at the entrance of the restriction is about 5000 and at the expansion side 10000. Total K is 15000. I didn't understand the suggestion of admin, but I think the idea for the gas outflow was to consider only a pipe of 1mm ending in a pipe of 10 mm. In this case K should be 10000.
I calculationed the volume and mass outflow for pressure difference between 0 and 5 bar, using the "air pressure drop" - and the "gas discharge calculator".
It is a pitty I can't publish the graph I obtained from those calculations, but roughly I can say that:
- the volume outflow obtained with the gas outflow calculator was about twice that of the air pressure drop;
- the mass outflow was at least 10 times greater;
- during the calculation with the gas outfow calculator with K=10000 I got a warning about the "pipe resistance in terms of the diameter" beeing to high. I had to increase the restriction to 3 mm (K=100) before this warning dissapeared. Changing K between 10000 and 100 didn't change the outflow. I don't understand physically the reason of this.
- Flow was always laminair for the "air pressure drop" and the outled was not choked for the "gas discharge".
That the outflow of the gas outflow calculator gives higher results seems logical, because the same pressure is put at the entrance of the outflow neglecting the rest of the cylindrical restriction. But why is the mass outfow multiplied by ten, while the volume out flow only by two.
I don't know if admin wanted to draw my attention on something specific. In any case it escapes me until now, but I ended up with several other questions and the conclusion that pipe flow has many mysteries to me. Maybe I will translate them to electrical analogies which I seem to understand more easily.
admin
Site Admin
Posts: 375
Joined: Mon Feb 08, 2010 7:47 pm

Re: CYLINDER LEAK DOWN TESTER

Post by admin »

what you are measuring is actualy pressure difference in front and after 1 mm orifice - am I right? So with discharge calculator you can calculate how much air is flowing through discharge orifice.

I here show my results for 5 bar pressure drop over 1 mm pipe with 6 mm length and K = 1.5 for entrance and exit.

Gas discharge calculator

1. pressure in position 1 (p1):
p1 : 6 bar

2. pressure in position 2 (p2):
p2 : 1 bar

3. pressure drop (p1-p2):
p1-p2 : 5 bar

4. tube diameter (D):
D : 1 mm

5. volume flow rate (q1):
q1 : 0.44992828 m3/h

6. weight flow rate (w):
w : 3.26603 kg/h

7. velocity (V1):
V1 : 159.12967 m/s

8. expansion factor (Y):
Y : 0.6236117

9. Reynolds number in front of orifice (ReD):
ReD : 11893.101

10. temperature (T1):
T1 : 288 K

11. density (ρ1):
ρ1 : 7.2590013 kg/m3

12. gas constant (R):
R : 287 J/kgK

13. K factor - minor losses coefficient (K ):
K : 1.5

14. friction coefficient (f):
f : 0.10293295

15. pipe length (L):
L : 6 mm

16. kinematic viscosity (ν):
ν : 13.38 mm2/s

17. dynamic viscosity (μ):
μ : 9.712544E-005 Pas

18. pipe roughness (kr):
kr : 0.1 mm


Gas discharge calculator - results end

Very important to tell that calculator gives CHOKED flow condition so volume flow rate is much lower than expected without this chek.
I strongly suggest not to use air pressure drop calculator for this kind of calculation because that calculator is for isothermal flow which can be possible in long lines with small pressure drop over that length. With 5 bar pressure drop over 6 mm long pipe, flow condition is defenitly not isothermal and that calculator should not be used.

Isothermal flow is with constant temperature. Now as pressure drops due to obstacles or friction temperature drops as well. If that pressure is not changing suddenly, heat from surrounding area is used and temperature of flow stays constant.
Pipe flow calculations - since 2000
HenriMalcorps
Posts: 8
Joined: Wed Mar 20, 2013 1:27 pm

Re: CYLINDER LEAK DOWN TESTER

Post by HenriMalcorps »

Indeed, that's it. Why do you use 1.5 for K ? I considert the discharge as a sudden enlargement and used 10000 for K; see below.
In this case the speed is 27 m/s instead of 163m/s and the flow is not choked. I am still in doubt if I understood correctly how to determine K.
The process is probably not isothermal nor adiabatic, but to my understanding air is compressed at the entrance and temperature increases, but it expands again at the outlet, where it will cool. The pipe is in fact manufactured in a small blok of aluminium, which has a relatively important heat capacity.
Is the isothermal condition not necessary for the gasdischarge? Is this condition not tied up with the Darcy equation on which also the gas discharge is based?
Maybe I should start some experiments. I disemantled a cheap commercial leak down tester, because I think it had a bad pressure regulator and unadapted manometers. I will get new components next week. It should not be to difficult to measure the airspeed at the output with a hot wire anemometer, although I doubt it will work at 163m/s.



Gas discharge calculator

1. pressure in position 1 (p1):
p1 : 6 bar

2. pressure in position 2 (p2):
p2 : 1 bar

3. pressure drop (p1-p2):
p1-p2 : 5 bar

4. tube diameter (D):
D : 1 mm

5. volume flow rate (q1):
q1 : 0.07759098 m3/h

6. weight flow rate (w):
w : 0.56352645 kg/h

7. velocity (V1):
V1 : 27.44221 m/s

8. expansion factor (Y):
Y : 0.7389997

9. Reynolds number in front of orifice (ReD):
ReD : 2050.9875

10. temperature (T1):
T1 : 14.850006 C

11. density (ρ1):
ρ1 : 7.2627835 kg/m3

12. gas constant (R):
R : 287 J/kgK

13. K factor - minor losses coefficient (K ):
K : 10000

14. friction coefficient (f):
f : 0.03120448

15. pipe length (L):
L : 5 mm

16. kinematic viscosity (ν):
ν : 13.38 mm2/s

17. dynamic viscosity (μ):
μ : 9.7176046E-005 Pas

18. pipe roughness (kr):
kr : 0.1 mm
admin
Site Admin
Posts: 375
Joined: Mon Feb 08, 2010 7:47 pm

Re: CYLINDER LEAK DOWN TESTER

Post by admin »

On the other hand I don't know how did you get K=10000?
It is well known that for pipe entrance K=0.5 and for pipe exit K=1.0 for pipes with sharp edges.
As the pipe length is very small, flow can be considered as adiabatic as there is not enough time to exchange heat with surroundings.
That high speed is result of expected 5 bar pressure difference which is very unlikely in your conditions. Leak from cylinder will probably be very small and I think that 5 bar will not be possible to achieve in front of orifice which is all the time open to atmosphere. So what you will have is much lower air speed than it is for 5 bar pressure difference.
Pipe flow calculations - since 2000
HenriMalcorps
Posts: 8
Joined: Wed Mar 20, 2013 1:27 pm

Re: CYLINDER LEAK DOWN TESTER

Post by HenriMalcorps »

I see. The leak down tester is a pipe of about 150 mm long and a diameter of 10 mm (in relality it is a aluminium blok with a hole in it of 10 mm diameter) with in the center a restriction of 1mm diameter and 6 mm long. The outflow of the 1mm restriction is thus ending in a pipe of 10 mm and not in the free air. So, I considered this as a sudden enlargement with D1=1 and D2=10, alpha equal to 180°. As I measure the pressure in the enlarged part D2, I used K2 which is 9801.
I expect to feel the tester heating up while air is passing through it, if this occurs the system would not be adiabatic. Maybe you are rigth and will I not be able to get a pressure difference of 5 bar.
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