TRANSIENT FLOW 1

[masaflu]

Hi,
I have been working on a solution for a transient flow problem for a week now. I'm trying to calculate the Transit Time in a Dry Pipe System. I have used the unsteady flow differential equations ( in one attempt 11 equations, and in the second attempt 9 equations)in a spreadsheet using Runge-Kutta, then using charts to graph the results. The results don't agree to what I expect. I expect some pressre and velocity fluctuations, followed by steady flow. Anyone can help? Specifically, I don't know how to use the time step in my numerical analysis.
Thank you.
Mehdi

 

[a1j2]

Probably the best but not the most economic solution is trying some simulation tool like PIPESYS, PROFES, HYSYS 3.0.1 that calculate transient pressures/flow.

I really admire your effort in dealing yourself with a spreadsheet.

Good Luck and best regards

 

[Tremolo]

masaflu,

It has been a while since your original post, so I don't know if you have solved your problem yet.

Regarding the time step, a differential time, dt, should appear in the transient terms of your differential equations. When the mathematical equations are converted into numerical form, the dt becomes the time step.

I am not sure of the details of your numerical model, but to get reliable transient answers the time step must be smaller than the "Courant limit". Often, the time step must be 10 times smaller than the Courant limit to get numerically stable answers. The Courant limit is simply calculated as x/a, where "x" is the length of a fluid node and "a" is the sonic velocity of the fluid. Physically, this is saying that you do not want a pressure wave to travel completely through a fluid node in a single time step.

Regardless of your time step, you should arrive at a stable steady state answer which can be verified with straight forward hand calculations. If your time step selection is bad, then the transient time will be off, but you should still arrive at the proper steady state solution.

I would be happy to review your equations or provide additional information if you are still working on this problem.

Tremolo.

 

[LSThill]

Hi masaflu (Mechanical)

This is a simple problem if you were to use BOS/FLUIDS:

BOS/Fluids

http://www.paulin.com/newprg/bos_fluids.htm

BOS Fluids is the engineering software package that analyzes fluid transients in pipe systems and relates this information back to the mechanical piping system transferring the fluid.

For years piping engineers have labored with simplifying hand methods, cumbersome analog computers, or user-unfriendly software products when needing basic steady state and transient fluid analysis capability. BOS Fluids was written specifically to address the need of the piping engineer for fluid reaction forces, and to provide a system whereby the fluid simulation results can be easily integrated back into the piping system design and analysis.

BOS Fluids is an interactive computer simulation package that models steady state and transient flow in liquid or gas carrying piping systems. The procedure is easy to use and interfaces with most pipe stress programs. The package contains the elements required to model most common unsteady flow conditions. The elements included in the simulation package are pipes, valves, pressure relief valves, vacuum breaker, air valves, pumps, equipment, surge vessels, inlets, outlets, and orifices. BOS Fluids makes fluid simulation simple and easily accessible and yet gives the analyst pressure transients and dynamic force results with an engineering accuracy.

Based on a number of realistic assumptions a simplified form of the time dependent conservation (Navier-Stokes) equations are solved for the internal channel flow. The assumptions made are:

1. Fluid behavior in pipes is one dimensional i.e. similarity of cross sectional distribution of properties does exist.
2. Fluid transport velocity is small compared to wave speed.
3. Wave fronts remain plane while propagating.
4. Gas simulations assume that flow velocities are below sonic, and that pressure drops through the system are less than 30%.

Based on these approximations friction effects are lumped. The present friction model used is Colebrook-White. The Darcy-Weisbach flow model is used for steady state pressure drop calculations and the basic theory applied in BOS Fluids can be found in Wylie & Streeter's "Fluid Transients" published by FEB Press. BOS Fluids is capable of simulating both the steady and transient behavior of liquid carrying closed conduit systems of pipes, valves, pumps and surge relief devices. The following special features are available:

1. Pipe stress models from either CAESAR or PipePak can be downloaded for fluid analysis.
2. The analyst can pick different fluids from a database or add their own fluids to the database
3. Two different models are available to simulate column separation: Concentrated Air Pocket (CAP) model and the Vapor Cavity Model (VCM).
4. Various pipe materials can be applied-both isotropic (Metals) and Orthotropic (FRP) materials are included.
5. Based on geometry typical pump properties are generated automatically.
6. Buried and above ground systems can be simulated.
7. Simultaneously the transient response of multiple sources: Pump starts, Pump Failures, Valve Operations can be simulated.
8. Harmonic option allows an analysis of the occurrence of standing waves.
9. Maximum and minimum pressures and velocities occurring during transient and/or harmonics are traced.
10. The force processor allows an analyst to survey the time history of the unbalanced forces on pipe sections and preprocesses the force time histories to be used in the dynamical module of the pipe stress program.
11. A spectrum breakdown of force time histories is available. The analyst can see the natural frequencies of the fluid response that tend to excite the piping system.
12. Both Metric (SI) and English Units can be selected.

Typical analyses using BOS Fluids include: water transmission and distribution systems, main cooling water systems for chemical plants, sewage water systems, combined power and drinking water cycle power stations, oil product transport lines, tanker loading and unloading systems and dynamical behavior of chemical liquid transport lines. Acoustic analyses for compressors and pumps.

Leonard@thill.biz

http://www.thill.biz

 

[masaflu]

Hi Tremolo,
Thank you for the insights into the solution for this issue.
I would like to send you all the formulas that I'm using. I certainly will appreciate if you could check them for me.
Is it possible to have your e-mail?
Mehdi

 

[Tremolo]

masaflu,

You can e-mail me at elicson@fauske.com.

I thought you posted your equations in a separate thread, but now I canb't seem to find the thread.

In any case, I would be happy to review your equations. Please contact me.

Tremolo.