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Transmission Lines- Unsteady Flow

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Transmission Lines- Unsteady Flow

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    1. Transmission Lines- Unsteady Flow BAE 515 Lecture 7

    2. Transmission Lines - Unsteady Flow Poiseville law, (flow) = (driving force)(resistance) or Where, (hydraulic resistance, laminar) for turbulent flow, Hydraulic Impedance

    3. Transmission Lines - Unsteady Flow Cont.. Force required to accelerate the mass, Where, and since, we have, Simplifying, (driving force) = (inductance)(d/dt flow)

    4. Transmission Lines - Unsteady flow cont.. Hydraulic capacitance- Secant bulk modulus, rearranging, taking the derivative w.r.t time, however, so,

    5. Transmission Lines - Unsteady Flow Cont.. of Gas Oil Mixture Spring rate of fluid column from the definition of secant bulk modulus, rearranging,

    6. Transmission Lines - Unsteady Flow Cont.. Using the universal gas equation and assuming isothermal conditions for gas is found as, Where, Substituting, Therefore,

    7. Transmission Lines - Unsteady Flow Cont.. Radial displacement of a cylinder is described by, Change in volume,

    8. Transmission Lines - Unsteady Flow Cont.. Effective Bulk Modulus of Systems Neglect bulk modulus of accumulator container

    9. Transmission Lines - Unsteady Flow Cont.. System Response By utilizing the concept of impedance and assuming the flow to vary sinusoidally we can write where, is the characteristic tubing impedence which is described by where, If resistance and conductance are ignored,

    10. Transmission Lines - Unsteady Flow Cont.. Pressure waves travel along a line at the speed of sound, = speed of sound The wavelength is described by = wave length = frequency From transmission line theory and for the figure below

    11. Transmission Lines - Unsteady Flow Cont.. The source impedance is related to the line and load impedances as, Open-End line If the transmission line is open to the atmosphere , and the relationship describing becomes Note: input (source) impedance, , is zero for these are conditions of resonance.

    12. Transmission Lines - Unsteady Flow Cont.. Closed End Line- If the power source is driving a closed end line the load impedance, , goes to and the source impedance becomes, Resonance occurs when

    13. Transmission Lines - Unsteady Flow Cont.. Example- A 9 piston pump is coupled to a diesel engine operating at 2100 rpm. MIL-H-5606 fluid at 20.0 Mpa is used in the system. Determine what tubing length causes resonance. 1.14 m and odd multiples of should be avoided

    14. Transmission Lines - Unsteady Flow Cont.. Line With An End Chamber Assume the line terminates in an end chamber, If the chamber has infinite volume the condition is the same as an open end tube If the chamber has zero volume, the condition is the same as for a closed end tube. If the chamber has a cross-sectional area 10 times greater than the line then (resistance) and (inductance) are nearly zero and (capacitance) becomes and

    15. Transmission Lines - Unsteady Flow Cont.. The source impedance becomes Input impedance is zero when or

    16. Transmission Lines - Unsteady Flow Cont.. Comparing to the resonant frequency of a closed end tube, or If we define b as, then R becomes, (See Fig 5.3 in text!)

    17. Transmission Lines - Unsteady Flow Cont.. Comparing to the resonant frequency of a closed end tube, or If we define b as, then R becomes, (See Fig 5.3 in text!) Comparison of resonant frequency of tube to chamber with tube Note: Read and understand 5.7 (line w/fixed orifice) and 5.8 (line w/modulating valve)

    18. Transmission Lines - Unsteady Flow Cont.. Pulse Damping- Attenuation of pressure pulses (pump ripple) is one of the most difficult problems encountered when developing hydraulic systems. Pump ripple can be suppressed by attaching a side branch to the transmission line. Quincke Tube Pressure wave (ripple) cancel when they meet at intersection of tubes 2, 3 and 4 waves out of phase by 1800

    19. Transmission Lines - Unsteady Flow Cont.. Accumulators as Pulse Dampers Closed end line analysis is applicable, Length of accumulator is the important design parameter Determine accumulator length to insure 0 input impedance where, If accumulator has a piston, this must also be taken into account, = mass of piston

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