Flow Divider Project

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Flow Divider Project

• ME 4232
• Ahmad Jaafar
• Matthew Lueker
• Andrew Quick
• Andrew Tilstra

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Objective

• Create a working Simulink model of a flow divider
  that accurately follows real world behavior.

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How Flow Divider Works?
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Assumptions

• Flow rate through the fixed orifice is equal to
  flow through the variable orifice for one outlet
  path
• Pump delivers constant flow
• Oil density, viscosity, bulk modulus, etc. are
  all constant

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Schematic and Mathematics

• Qa QbQc
• Qb C1(x)SQRT(Pa-Pb)
• Qc C2(x)SQRT(Pa-Pc)
• P1 Pa-(Qb/c1(x))2
• P2 Pa-(Qc/c2(x))2

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Determination of Pa, Qb, Qc

• Newtons Iterative Method Using Jacobian Matrix
• QA - QB - QC 0 (F1)
• QB2 - C12(P1 PB) 0 (F2)
  
• QC2 - C22 (P2 PC) 0 (F3)

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• Initial guess of value for x
• Evaluate f(x)
• Decide if f(x) close to zero
• If so, stop and use x values
• Otherwise iterate again to find new value of x

Then find P1, P2 using values of Pa, Qb, Qc
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Simulink Model
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Simulink Subsystem Model
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M file
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Results
For a constant pressure difference
Plot of pressures
Input and output flows for constant pressure
difference
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For a step change in pressure of one output port
Plot of pressures
Input and output flows for constant pressure
difference
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For a series of step changes in pressure of one
port
Plot of pressures
Input and output flows for constant pressure
difference
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Triangular changes in pressure of one Outlet Port
Plot of pressures
Input and output flows for constant pressure
difference
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Stepped Triangular changes in pressure of one
Outlet Port
Plot of pressures
Input and output flows for constant pressure
difference
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Conclusions

• Newtons method can be used to solve the system
  of nonlinear equations describing the flow
  divider.
• Given an input flowrate and two output pressures,
  our model successfully divides the flow with
  50-50 ratio.
• The flow divider was able to maintain constant
  flow for different types of varying inputs.

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Questions