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AutoPIPE Wiki 01. How to apply Kanti Mahajan theory of Vortex Shedding
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            • 01. How to apply Kanti Mahajan theory of Vortex Shedding
            • 02. How to apply Henry Bednar theory of Vortex Shedding
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    01. How to apply Kanti Mahajan theory of Vortex Shedding

    Wind induced vibrations on tall vessels are a concern and AutoPIPE Vessel currentley has two methods to address this design consideration.

    1. Obtain first the natural frequency ‘f’ of your vessel
    2. Check for vibration possibility

     

    If W/LDr2 <=20, issue message in report “Vibration analysis necessary to be performed as W/LDr2 <=20”

    vibration analysis must be performed and proceed to step 3

     

    where W= corroded wt. in lb, L=length in ft., Dr=average internal diameter of top half of the structure in ft.

     

    If W/LDr2 >20, issue message in report “Vibration analysis not necessary to be performed as W/LDr2 >20”

     

    1. Perform stability investigation,

     

    Calculate damping factor DF=Wδ/LDr2

     

    Default value of δ = 0.03 (Table 3)

     

    If DF <= 0.75, issue message in report “system is unstable and vortex shedding vibration analysis is required as DF <= 0.75”, proceed to step 4

     

    If DF > 0.75, issue message in report “Vortex shedding vibration analysis not necessary to be performed as DF > 0.75”

     

    1. Calculate critical wind velocity being where S = 0.226 (Strouhal number)

     

    Justification: In the book this formula appears as   in mph, but Dr is introduced in feet, f in Hz, so the number of Strouhal is affected by a conversion factor from feet to miles and hours to seconds. To reverse this change and work in consistent units we have to divide by 1.466 (1mph = 5280/3600 = 1.466 ft/s). And to place S in the denominator, we inverse the coefficient:

     

    1. Calculate maximum wind velocity at top of the structure (H = 10m or 30ft)

    Vw =Vb(L/H)0.143

    Where Vb = wind velocity at H

     

    1. Apply gust factor, 1.3 to obtain maximum gust velocity = 1.3Vw

     

    1. If Vc <=maximum gust velocity, perform amplitude calculations go to step 8.

     

    If Vc > maximum gust velocity, issue message in report “Vibration amplitude no need to be calculated as Vc > maximum gust velocity”.

     

    1. Calculate amplitude of maximum dynamic deflection, Z=L5VC2/W δ Dr (10)-6 (0.00243) in.

     

    1. Check if Z < Maximum Deflection input by user, issue message in report “structure is safe:amplitude of maximum dynamic deflection < maximum allowable deflection”

     

    If Z> Maximum Deflection input by user, issue message in report “structure is unsafe:amplitude of maximum dynamic deflection exceeds maximum allowable deflection, please modify design”

     

    Reference: Kanti Mahajan, PE. (1979). Design of Process Equipment. Tulsa, OK: Pressure Vessel Handbook Publishing.

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