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Steam Flow through a fine orifice

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norm norton08/09/2020 17:07:35
139 forum posts
7 photos

This is a bit of a specialist question, but perhaps a fluid flow specialist might know the answer, and others might like to speculate.

I have built a pair of safety valves for a 5"G locomotive, and to make them more prototypical in appearance have drilled the vent cap with two rows of very fine holes (18 off 0.9mm dia. and 18 off 1.2mm dia.), rather than a single row of larger holes (12 off 1.7mm dia.). Now the cross sectional area of my two rows is substantially greater than the singe row, but I am concerned that the diameter of the holes is such that they act as critical flow orifices. However, if the flow through the single row is not supersonic, it cannot be so in the two rows. Or am I missing something?

I have used this website that provides a calculator

but if I plot the data for smaller and smaller orifices I still see a liner flow vs. area response, so has this calculator allowed for a critical behaviour? I don't think so but what do others think?

I appreciate that I could answer this if my physics knowledge included Reynolds number and fluid physics, etc. but it dosen't. Anyone have a quick answer? Sorry I don't have a ready number for the mass of steam that the valves have to shift other than an estimate that we are talking about 10 to 20kW of thermal energy generating that steam.


Dave Halford08/09/2020 17:25:16
1023 forum posts
9 photos

Wire drawing applies.

stephen goodbody08/09/2020 17:46:22
56 forum posts
40 photos

Hi Norm,

I believe you'll be fine given that your total relief orifice area is significantly greater than the total relief orifice area for the original valves, and assuming that the original relief orifice area was correctly calculated in the first place to relieve the maximum steam generation capacity of the boiler.

Think of it this way - If the safety valve plug (or ball) were to fully lift, giving little pressure-drop across the valve seat and hence almost full boiler pressure on the underside of the vent cap, then the differential pressure across the vent cap is equal to the boiler pressure and the original 1.7mm vent cap orifices would themselves vent at critical flow.

In other words, there's nothing fundamentally wrong with having critical flow orifices, I deliberately used them as idiot-proof metering devices in high-end gas blending systems many years ago, it just means that you have reached the venting limit of the hole.

The only caveat is that smaller holes are easier to block than larger holes and, while blocked holes are unlikely in a safety-valve exposed only to steam, it's still worth noting given the safety-critical nature of the device. Hence check that the valves relieve properly each time you steam the engine, as I'm sure you do anyway.

Best regards


duncan webster08/09/2020 20:06:48
2853 forum posts
43 photos

As long as your flow area is sufficient it won't make a lot of difference whether a few big or a lot of little holes

Gareth Jones 909/09/2020 09:31:32
20 forum posts

Hi Norm, looks like you will have critical flow in all the orifices, as this does not depend on the orifice diameter. If you take the upstream pressure in absolute units and multiply by 0.55 for superheated steam or by 0.58 for saturated steam, then this will give the critical pressure. If the downstream pressure is less than the critical pressure then critical flow occurs.

If the orifice is flowing steam directly to atmosphere (1.01bar absolute) then critical flow occurs when upstream pressure on the orifice (boiler pressure) is more than 1.74bar absolute (0.73barg).

Calculation of flow through the orifice is straight forward, so if you know the max rate of steam you can get the required number of orifices. As Stephen says above, if the total area of orifices exceed the original, then the relieving flow will be greater than the original, assuming none are blocked.


Edit: added the word Area

Edited By Gareth Jones 9 on 09/09/2020 09:33:50

norm norton09/09/2020 14:22:05
139 forum posts
7 photos

Thanks, reassuring answers regarding the conclusion that as long as I have a greater total area, the actual diameter of the holes does not matter (seems counter intuitive to me, is this true even with a large number of (e.g.) 0.1mm dia. holes? which then create very long, narrow cylinders? but lets go with it for now).

I though that if a fluid flow system got anywhere near to criticality then the pressure drop rose rapidly to become a flow limiting absolute. I can't see that these vent holes could work if they were anywhere near that. I clearly need to know the volume of steam generated per second and then calculate the steam velocity.

I am trying to work out the implications of your comment Gareth. The boiler will be 6 barg (90psi). Perhaps in a safety valve most all the pressure drop is across the ball to seat gap, and this gap increases as a greater volume of steam has to be released. Meanwhile, the pressure drop across the vent cap is only a small fraction of the ball to seat one and thus the small holes stay away from criticality?

Howard Lewis09/09/2020 15:16:05
3783 forum posts
3 photos

Surely, the essential thing is that the safety valve is capable of releasing more steam than the boiler can produce, so that pressure cannot rise above the setting.

Not being a steam man, I believe that this is one of the parameters checked during a boiler steam test.


stephen goodbody09/09/2020 20:18:40
56 forum posts
40 photos

Hi Norm,

To clarify, the design basis for the safety valve vent-cap orifice cross-sectional area should actually assume critical flow through the orifices. In other words, if the valve design is correct then the critical flow-rate through the vent-cap orifices must exceed the steam-generating capacity of the boiler.

That's the reason that I feel confident that you'll be fine with your modifications provided that the original valve design was sound - you have a greater total vent-cap orifice cross-sectional area now than had the original design.

If you want to It's pretty straightforward to calculate the critical flow-rate for your orifices and it looks like you've already figured that out. You don't need to worry about velocity, and Gareth has provided the pressure-drop ratios in his Email above. As Gareth mentions, make sure you're using absolute pressure and not gauge pressure.

Taking things further, the trick is to work backwards. You know the steam leaves the vent cap at atmospheric pressure - that's your starting point. Hence you know the pressure on the other side of the vent cap when the valve is maxed out is the critical pressure. Hence you know that the limiting pressure drop across your valve seat will be the difference between maximum boiler pressure and that critical pressure. Hence you can calculate the valve's Cv (which is a measure of the valve's flow capacity) and hence come up with an appropriately-sized plug and seat arrangement to achieve the needed flowrate given your calculated across-the-seat pressure drop.  

You do raise another question which is reasonable but which would be much more difficult to answer without a doctorate in computational fluid dynamics and/or extensive lab testing. To paraphrase your question, "how small a hole is too small and how long a hole is too long"? I for one don't know an easy way to answer that when working at the micro-extreme. I imagine that the orifice shape, length, interior surface roughness, and steam viscosity play a part however.

Best regards



Edited By stephen goodbody on 09/09/2020 20:20:10

Edited By stephen goodbody on 09/09/2020 20:32:00

norm norton09/09/2020 21:15:35
139 forum posts
7 photos

Steve, thank you, your comments are helpful in that you have not challenged anything I am doing. I shall have to read a little more elsewhere as I would like to understand whether my limited understanding from 40 years ago (viz: a CFO is a pure hole with no length and the critical flow point is related to the speed of sound in that fluid) is correct or not.

To help others who are wondering what I am doing with this safety valve, it is a proven design that adequately discharges the necessary steam, but I have changed the holes in its vent cap for appearance only and I want to understand whether, theoretically, this may adversely affect its safe operation. I have also made the single row caps and I can, and will, compare the two versions in an actual test in a few months. For now, the feedback above, gives me confidence that the modifications will be ok.


stephen goodbody09/09/2020 21:51:42
56 forum posts
40 photos

No problem Norm.

For reference, the critical flow most definitely is related to the local speed of sound, but that's essentially irrelevant to addressing the practical question posed.

Additionally your definition of a CFO is correct, but again we're dealing with a practical problem and the approximations we're making are likely fine if the original design was sound. Presumably you've not changed the orifice area-to-length ratio by an order-of-magnitude or more.

If your vent-cap holes were very long indeed, such that the frictional pressure-drop occurring within the holes resulted in additional back-pressure within the valve such that the pressure drop across the valve seat were significantly reduced, then there'd indeed be a potential problem. In that case the back-pressure on the valve plug would reduce the valve's flow capacity.

Best regards - let us know how things work out,


Gareth Jones 910/09/2020 09:18:55
20 forum posts

Hi Norm and Stephen, my comments above refer to a sharp edged orifice plate where the inside diameter of the orifice is much larger than the thickness of the orifice plate. If the system consists of longer small diameter holes in a thick plate, then the pressure drop through is more like flow through a pipe where the physical properties of the fluid change due to the large change in pressure between pipe entrance and exit. This is similar to a flare system in the oil and gas industry and that flow would be calculated by use of the isothermal flow equation. The above comments wrt critical flow apply as flow can be critical or chocked flow, or not. Expanding on what Stephen has said above, you will need the pipe ID, internal roughness, length, fluid density, viscosity and mass rate to calculate the pressure drop. The calculation can be solved by equation or more easier by use of isothermal flow graphs. I can add more detail if you require.


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