Hello again,
I have some doubts regarding DLF generator.
Both the questions are interrelated.
1)You have answered this doubt once, but I was not able to understand. So I am asking again: When we feed the force v/s time to generate, whether that same time will be considered as a load duration. That is, If I give 100ms time as input for DLF generotion, whether this same time (100ms) will be considered as duration of impulse due to slug/water hammer.
Also if my time history is as below
Time force
0 1500
100 1500
101 0
1000 0
What will be be duration of impulse ?whether it will be 100 ms and then will be zero upto 1000 or it will be 1000.

2)For slug analysis , what should be the time history to be given? that is only the time for which slug is in contact with elbow or along with this,time upto which next slug will come in contact with elbow.
For example, suppose slug duration is 100 ms and next slug will hit the elbow after 1000ms then which is correct method out of those shown below:
Option 1. Time Force
0 1500
100 1500
or option 2. Time Force
0 1500
100 1500
101 0
1000 0

Dear Piyush,
Here I give a sample Force Time History for slug flow problems:

Solution to slug flow problems can be obtained by first carrying out the two-phase flow(thermal) analysis and then pipe stress (dynamic) analysis.
In two-phase flow analysis , the flow pattern may be predicted from the correlations proposed by Baker[Oil Gas J.,53-12,185-190,192,195(1954)] as shown in fig. 1 . These flow regimes can be obtained by generating Baker Charts for all the piping segments. Further two-phase flow analysis is carried out only for the segments where slug formation is predicted by Baker chart.
Two-phase flow analysis must further be extended to get liquid slug length, gas length and liquid slug velocity.
Unbalanced force due to Slug impact is equal to change in momentum with respect to time. It can be calculated by the formula :
F = dp/dt = rho. sq.V . A [(1- COS theta)/2]1/2
Where rho– Fluid Density
V – Slug Flow Velocity
A – C/S Area
theta– Bend Angle
Duration of loading(TL) can be obtained by dividing the liquid slug length by liquid slug velocity.
Rise time(TR) and fall time(TF) are difficult to calculate and are generally assumed.
These parameters would be sufficient to get the Force-Time History for single occurance. In order to include the second occurrence of slug loading calculate the periodicity of slug.
Periodicity of slug(TP) can be calculated by dividing the “length of liquid slug + gas length” by slug velocity.
A sample time History is given here for proper understanding of the subject.

SAMPLE TIME HISTORY :

LIQUID SLUG LENGTH = 0.072 m
GAS LENGTH = 0.072 * 90/10 = .648 m
DURATION OF LIQ SLUG = 0.072/13.75 = 0.0052 Sec=5.2ms
PERIODICITY OF SLUG=(0.072+0.648) /13.75=0.052 Sec=52 ms

TIME (ms) FORCE

0 (0) 0
0.52(0.52) F
5.72(0.52+5.2) F
6.22(0.52+5.2+0.52) 0
52 0
52.52 F
57.72 F
58.24 0

Navendu Shrivastava
navendu@klgsystel.com

In a time history analysis, the pulse duration is <em>not</em> the same as the load duration. The pulse duration is the last time value specified in the pulse table. The load duration is specified on the Control Parameters Dialog, and is the length of time the analysis runs. For realistic results, the load duration should be greater than the pulse duration.

Once you take your pulse back to zero, you do not need to extend it (at zero magnitude) to the load duration time. CAESAR II will assume this for you. So, in your "item 2" above, for option 1, CAESAR II will assume a pulse magnitude of 1500 from 100 milliseconds through the load duration. For option 2, CAESAR II will use a pulse magnitude of 0 from 101 milliseconds through the load duration. Your last entry "1000 0" is not necessary.

A <font color="#0000ff"><em>really excellent</em></font> article on setting up time history input can be found in the June 1994 issue of our <em>Mechanical Engineering News</em>, beginning on page 8. If you don't have this newsletter, you can view it from this web site at: http://www.coade.com/newsletters/menlist.htm . I highly recommend this article.

Probably the most difficult dynamic analysis to attempt with CAESAR II is a slug analysis. The difficulty is in determining (actually guessing) the slug size and corresponding force. Since you really don't know whether the slug encompasses the entire cross section, or how long it is, the best thing to do is assume a small slug and a large slug. This way, you envelope that actual slug and the true response of the system.


------------------
Regards,
Richard Ay (COADE, Inc.)


[This message has been edited by rich_ay (edited May 05, 2000).]

Sorry, but I forgot to mention this yesterday.

There is a <font color="#0000ff"><em>really great</em></font> article on the DLF generator in another issue of <em>Mechanical Engineering News</em>. See the November 1994 issue, starting with page 9.


------------------
Regards,
Richard Ay (COADE, Inc.)

Thanks Navendu and ray for the prompt reply. But Ray,I think, my question is little bit misinterpreted. In clear words, I wanted to know whether whatever navendu is saying, is correct or not. That is can we feed two impulse in the DLF generator to take care of periodic nature of slug ?.

In TIME HISTORY analysis also, as told by you, load will be applied for the time specified in history with load. For the rest of the duration , it will be zero. Now
can we give the two impulse to take care of periodic force due to slug. Giving an example, if slug is hitting elbow after every 1000ms and stay with it for 100 ms. can we feed time history as follow
0 F
100 F
101 0
1000 0
1001 F
1101 F
and continuing in this manner uptill say 20 cycles to take care of periodic nature. (Offcourse, load duration in control parameter should be greater than time for 20 cycles.

For Response Spectrum Analysis, yes you can feed multiple impulses into the DLF generator. Note that the resulting DLF will contain values greater than 2.0, which is the limit for a <em>single</em> impulse.

You can see the resulting DLF graphically if you're running Version 4.20. This version plots the DLF next to the DLF table values.

For Time History Analysis, you can define any (multiple shaped) pulse you want.


------------------
Regards,
Richard Ay (COADE, Inc.)

Throwing my hat in the ring, my advice is to use time history for this analysis and use spectral analysis only as a measuring stick.
Spectral analysis considers maximum responses of modes only, independent of timing issues, summing them as best we can. Even with a single impulse, we have an approximation that is more accurately evaluated by time history analysis. Attempting to sum multiple impulse events based only on their maximum modal responses becomes less accurate.
We usually say 'use spectral analysis for slugs' because we have a poor approximation of the problem, therefore, why bother deriving an accurate solution? The answer is: "Because we have a timing issue."
Even if we can combine contributions of multiple DLF curves in CAESAR, the summation is independent of timing, which is what this problem is all about - Spectral analysis becomes limited in its validity.
My advice is to predict the force time profiles that are anticipated and perform a time history analysis.
The article Rich Ay (ray) refers to is very instructive, and is very helpful in terms of how to input the data; I recommend that you refer to it.
As far as input goes, it is helpful to manually plot the graph, then input the data corresponding to the plot.
In my opinion, the timing issue is about strain energy.
Using a simple loop as an example, if a slug hits one of two elbows in the far end of an expansion loop, and the loop moves, what happens when the slug hits the second elbow depends entirely on timing. If the energy from the first elbow impact is putting energy into the system, then the effect of the impact on the next elbow will be additive. If it the system is moving the other way when the impact hits, it will offset the load.

One issue to keep in mind is that CAESAR evaluates the force-time input differently for time-history than it does for spectral analysis input.
In time history, although the input prompts for force(lb) input, you should input a factor, such as 1.0 for full force, 0.5 for half. The Spectral analysis will give you the correct DLF curve whether you input the actual load or not, but the time history requires that you enter the force in either the force time input, or the force spectrum input. If you put it in both, they will be multiplied.
The article Rich mentioned will assist you in this also.
Hope this helps.

The cyclic nature of slug load can be considered in the following way;

1)Do time history analysis just for one
impulse
2)Get peak stress
3)Calculate the stress intensity
4)Estimate cycle number for life time
5)Compare stress intensity with ASME code
fatigue curve.

Regards

Alvin Zhu