It's simple enough to calculate. If you know the cylinder diameter, stroke, maximum engine rpm and cutoff percentage one can calculate the volumetric flow rate. Assuming that the flow speed is around 4000-6000 ft/min (well below the speed of sound, so no compressibility effects) one can then calculate the pipe area, and thus diameter, needed. If you know the boiler pressure, and degree of any superheat, one can also calculate the mass flow rate.

If one really wants to get into detail one can also calculate the Reynolds number of the flow to ensure that the flow is turbulent rather than laminar, as that should result in a lower pressure drop.

In practice, for a small model that isn't likely to be doing any significant work, it probably doesn't matter. The engine will run even if a significant proportion of the boiler pressure is lost on the way to the valve chest. Just use the biggest practical pipe. Of the two the exhaust is probably the more important, as if one can't get the steam out, it's going to be more difficult to get it in on the other side of the piston. Clearly the exhaust passages need to be bigger, as the pressure is lower, assuming some expansion in the cylinder. As stated, times two is a good starting point. The exhaust is particularly important if it is also used to provide a draught for the fire; one needs to ensure that a draught is created in the chimney, without causing backpressure in the cylinder.

Regards,

Andrew

That's very interesting; I am currently looking at the maths of compounding, and then intend to move onto steam flows to ensure that the passage ways in my traction engine are not overly constrictive. The basic steam passages are about 15mm diameter, at around 10 bar. With those numbers, assuming saturated steam, I expect a Reynolds number on the order of 140000. That should put the flow comfortably into the turbulent regime. I'd be interested to understand better what happens with relatively short pipes. Does the flow start out laminar and stay laminar, or degenerate into a turbulent flow if the Reynolds number is large enough? If so what would you estimate the pipe length to be to ensure a transition to turbulent flow?

Regards,

Andrew

The following applies to reasonably well behaved fluids and subsonic flow .

(1) Flow in short ducts is determined almost entirely by nozzle characteristics of duct and only a little by frictional effects and laminar/turbulent conditions .

(2) Turbulent v laminar flow settling down distance for a long straight uniform pipe is typically from 20 diameters to 100 diameters . Very uncertain in reality and for general purpose estimates it is often taken arbitrarily as 60 diameters . So for 15 mm pipe about 900 mm – ie in a normal steam cylinder passage or the like it never settles down at all .

(3) When duct is anything other than a long straight uniform pipe there are no rules at all – much more detail calculation or practical tests are needed .

(4) Where the transition from previous flow conditions into duct is reasonably smooth then generally what goes in is what comes out – turbulent in turbulent out / laminar in laminar out .

(5) Where transition from previous flow conditions into duct is not reasonably smooth then flow can be tripped from laminar to turbulent by local disturbances . Examples are abrupt change of flow area , sharp edges , sharp changes of direction and projections .

The reverse of turbulent tripped into laminar flow very rarely occurs naturally thogh it can be contrived by , for example , passing flow through a nest of short fine tubes .

Where transitional control of flow matters critically then smooth slow area transitions , slow bends and possibly internal guide vanes are needed .

There is a particular problem with steam in ducts in that it may change state at transitions – ie becoming more/less wet/superheated .

This effect can trip flow from laminar to turbulent in higher speed flows .

(6) A useful tool for quick estimates of how well behaved flow will be at transitions is to draw out by eye the streamline pattern . I’ll describe this further if wanted .

The flow can actually be fully modelled on computer but there are many pitfalls and the sketch is always a good start anyway .

(7) Reynolds number is a measure of the ratio of inertia to viscous forces in a particular flow .

That’s what it says in books anyway . Really it is the ratio between forces tending to destabilise the flow – and forces tending to stabilise the flow .

Thus a thick slow moving fluid flow is likely to be stable (ie laminar) whereas a thin fast moving fluid flow is likely to be unstable (ie turbulent) .

Reynolds number is useful for estimates but not for detail calculations . Really the whole theory was developed for sewers and drains and becomes less reliable when used on more sophisticated flows .

MikeW

Edited By MICHAEL WILLIAMS on 22/01/2014 10:58:15

Edited By MICHAEL WILLIAMS on 22/01/2014 11:20:41

hi michael,

could you possibly summarise the above so that those of us without a detailed engineering background can understand, and put it in simple language for miniature loco builders please? what does the above mean for miniature locos? the late jim ewins was of the view that so long as our locos were superheated the steam was (until expansion) much more fluid than fullsize and that flow problems encountered in fullsize werent such a problem.

cheers,

julian

> Disturbed flow will often trip laminar flow into turbulent .

I'm reminded of 'turbulators' – lengths of cotton glued along the wings of model gliders.

Neil

Standard on full size sailplanes too, except we don't use cotton. The turbulator is normally a zigzag plastic strip running along the wing at about 2/3 to 3/4 chord. The plastic is hard, and surprisingly sharp, it'll shred your fingers if you're not careful. And oddly enough pilots get sulky if you get blood all over their nice polished wing.

Regards,

Andrew

Some interesting points raised by MikeW. The steam flow from boiler to HP valve chest in my traction engine is fairly convoluted, with several changes of section and bends. The steam is saturated, and most likely wet, which complicates the calculations. I doubt that the flow will be laminar. I am going to base my port size calculations on a flow speed of about 5000 ft/min, so well subsonic, but still a high enough Reynolds number to ensure, in theory, turbulent flow. When I finish the engines it will be interesting to measure the pressure drop from boiler to HP valve chest under varying conditions. When the regulator is partially closed there is a sharp edged transition into the safety valve chest. I am assuming that this will approximate an isenthalpic expansion, with the benefit that it will dry the steam.

I've found Reynolds numbers to be fairly useful in aerodynamics, at least for ensuring that experimental results are comparing like for like, at least for subsonic flows. Supersonic is a whole different ball game. Boundary layer control is of particular interest for sailplanes. Most of the modern wing sections control laminar flow boundary layers by controlling pressure gradients. Although in the past holes for blowing/sucking air have been tried to ensure that the boundary layer stays attached.

Andrew

A very interesting discussion, but I suspect way beyond what we actually need in order to make some sensible calculations looking at port sizes and the steam flow from the boiler to HP valve chest and beyond to check that the passages are of a sensible size.

Regards,

Andrew