# Turbine Bypass system

Hi,
I am a mechanical engineering student, and my group and I were given this problem:
Emergency Steam Dump System An nuclear power plant has 4 steam
generators that produce 1000 kg/s steam at 50 bar absolute and saturated under normal operating conditions. However under emergency conditions, where the turbines cannot accept steam (turbine trip), 60% of the steam must bypass the turbines and be dumped directly to the condensers through a 50 m long piping system. The condensers are at a pressure of 4 kPa absolute. Design the steam dump line and as much as possible avoid pipeline vibration which is typical of these installations.
Anybody could help us with this? We haven't learned compressible flow yet, and our prof. just expects us to learn it on our own. He told us to read about Fanno Flow... I kinda understand it, but not quite. Could anybody give me basic equations to work with (I've been reading a textbook, and with all the derivations, it's hard to tell what I should be using). Any help of any kind would be greatly apprciated.
Thanks,
S
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Could he be referring to the Fanning dimensionless number - 2 tau / ( rho. V^2) for shear stress / dynamic pressure? [viscous flow] ...or the Fliegner number - Q subm (Csubp. T ) ^1/2 / (A(p subs + rho.V^2) [compressible flow] ???
I probably lost the significance of the tip - but providing a reasonably damped expansion seems like the way to go.
Brian Whatcott Altus OK
On 4 Feb 2007 18:41:23 -0800, snipped-for-privacy@gmail.com wrote:

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On Mon, 05 Feb 2007 02:54:19 GMT, in sci.engr.mech Brian Whatcott

Yes. Fanno flow is compressible flow with friction. In a constant area pipe the effect of friction in compressible flow will drive the Mach number towards Mach 1, whether the flow is either subsonic or supersonic.
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Ed Ruf ( snipped-for-privacy@EdwardGRuf.com)

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On Mon, 05 Feb 2007 05:41:25 -0500, "Ed Ruf (REPLY to E-MAIL IN

Ah yes: how foolish of me not to have googled first.
e.g.
Fanno Flow The most important model in compressible flow was suggested by Gino Fanno in his Master's thesis (1904). The model bears his name. Yet, according to Dr. Rudolf Mumenthaler from UTH University, no copy of the thesis can be found in the original University and perhaps only in the personal custody of the Fanno family.
Fanno attributes the main pressure reduction to friction. Thus, flow that is dominantly adiabatic could be simplified and analyzed. The friction factor is the main component in the analysis as Darcy had already proposed in 1845.
The arrival of the Moody diagram, which built on Hunter Rouse's (194x) work made Darcy-Weisbach's equation universally useful. Without the existence of the friction factor data, the Fanno model wasn't able to produce a prediction useful for the industry.....
Thanks
Brian Whatcott Altus OK
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On 4 Feb 2007 18:41:23 -0800, in sci.engr.mech snipped-for-privacy@gmail.com wrote:

http://www.tfd.chalmers.se/~ulfh/gas_dyn_h/lecture_notes/05-fanno/sld004.htm http://www.potto.org/fanno.pdf
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Ed Ruf ( snipped-for-privacy@EdwardGRuf.com)

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Thank you folks,
I really appreciate the help. I think i understand it a little better now (thanks to your help).
Cheers,
Sébastien
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On Feb 4, 9:41 pm, snipped-for-privacy@gmail.com wrote:

Fanno flow is constant area compressible flow of a PERFECT GAS with friction. Saturated steam is not a perfect gas - p does not equal rho*R*T, particularly when you reduce the pressure and condensation occurs. Perhaps you can use steam properties to see how far off p=rho*R*T is, if the error is small perhaps you can justify using Fanno flow equations to size the pipe. You should certainly make note of the assumption in your design calculations.
Also you'd have to assume there are no other losses in the system other than friction in the pipe (i.e., no turbine bleed loss, no flow measurement orifice, no flow control valve, no turns, etc). In reality pipe friction losses are usually small in comparison to these other losses.
If you can make these assumptions then the basics of Fanno flow are given below: 1) Guess a Diameter, D 2) Calculate the pipe inlet Mach Number using isentropic relations: Area, A = (pi/4) * (D)^2 Inlet Total Pressure, Pt1 = From Problem Inlet Total Temperature, Tt1 = From Steam Properties (Saturated) Flow Rate, w = From Problem Specific Heat Ratio, gamma = From Steam properties Gas Constant, R = From Steam properties Solve Isentropic Compressible Flow Equation to get Mach Number (solve iteratively): [w * sqrt(Tt*R/gamma)] / [A * Pt] = M1 / [1+ (gamma-1)/ 2*M1^2]^[(gamma+1)/(2*gamma-2)] 3) Calculate choked Fanno parameter (4*f*Lmax/D) for inlet mach number calculated above: (4*f*L/D)max = (1-M1^2) / (gamma*M1^2) + (gamma+1)/ (2*gamma)*LN{ [(gamma+1)*M1^2] / [2* (1+(gamma-1)/2*M1^2)] } 4) Calculate the minimum diameter required to pass the desired flow with choke conditions at the pipe exit: D = 4*f*L / (4*f*L/D)max where, Friction factor, f = function of pipe roughness/diameter and Reynold's number, use Moody chart or correlation by Colebrook or Miller. Pipe Length, L = From problem You can use this result to calculate the maximum pipe length for a given diameter or the minimum diameter for a given length that will result in choked conditions at the pipe exit. 5) Plug this value of D back into step 1 and iterate until D converges.
Try to borrow a compressible flow book from someone who has taken the course or the library for more insight. Don't use a Fanno flow table (precalculated values of 4*f*Lmax/D) - they are usually based on air properties.
Dave Parker
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