Improved Simulation of Hydraulic System Pressure Transients Using EASY5

1
Improved Simulation of Hydraulic System Pressure
Transients Using EASY5

• Dr. Arun K. Trikha
• Associate Technical Fellow
• The Boeing Company
• [phone]
• Presented at the 2000 EASY5 User Conference
• May 17, 2000

2
Presentation Overview

• Alternate approaches to simulating Hydraulic Line
  Dynamics
• Comparison of Models and Simulation Results using
  the alternate approaches
• Conclusions and Recommendations

3
Alternate Approaches to Simulating Hydraulic
System Line Dynamics

• Approach 1 (Lumped Line Model Approach)
• Divide a line into many sections, each of which
  can be assumed to have a uniform pressure within
  it.
• Use continuity equation to calculate rate of
  change of pressure within each section
• Use momentum equation to calculate the rate of
  change of flow from one section to the next
  section.
• This approach results in solution of ordinary
  differential equations and is the
• approach used in EASY5 Hydraulic Library
  components PW and PX.
• Approach 2 (Continuous Line Model Approach)
• Work directly with the continuous line model
  which represents the continuity and the momentum
  equations as partial differential equations.
• Use Method of Characteristics for solving partial
  differential equations
• The implementation of this inherently more
  accurate approach by using
• standard EASY5 components is discussed in this
  presentation.

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One-Dimensional Model of Hydraulic Line Dynamics

• The Continuity Equation is
• (1/K) . ?p / ?t ?v / ?x 0
• and the Momentum equation is
• ?p / ?x ? . ?v / ?t f(t) 0
• where
• x coordinate in axial direction of the line
• t time
• p pressure
• v fluid velocity
• f(t) pressure drop per unit length (including
  frequency-dependent
• friction effects)
• ? fluid density
• K bulk modulus of fluid
• With proper selection of f(t), the above
  equations are equivalent to linearized
  two-dimensional Navier-Stokes equations.

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Equivalent Differential Equations UsingMethod of
Characteristics(1 / c) . dp/dt ? . dv/dt
f(t) 0valid on the characteristic given by
dx / dt cand- (1 / c) . dp/dt ? . dv/dt
f(t) 0valid on the characteristic given by
dx / dt -cwhere c velocity of sound in
fluid (K / ?) 0.5

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Characteristic Lines in the x- t Plane
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First Order Finite Difference Approximations to
Differential Equations along Characteristic
Lines (1 / c).(pN - pR) ?. (vN - vR) 0.5
(fN fR) . ?t 0.xN - xR c (tN - tR) - (1
/ c).(pN - pS) ?. (vN - vS) 0.5 (fN fS) .
?t 0. xS - xN c (tN - tS) Note that if
point N is at the current time, points R and S
are at time ? t in the past. The continuous time
delay component CD (in EASY5) can be used to
keep track of the variable values in the past.
8
Comparison of Models and Results
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EASY5 Model Using Component PW
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EASY5 Model Using Continuous Line Model Approach
11
Details of New Submodel for Line Dynamics
12
Data Used for Simulations
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Pressure Transients Using Component PW

• Normalized
• Pressure
• Downstream
• of Valve
• Normalized
• Pressure
• Upstream
• of Valve

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Pressure Transients Using Component Time Delays

• Normalized
• Pressure
• Downstream
• of Valve
• Normalized
• Pressure
• Upstream
• of Valve

15
Comparison of Results

• When using component PW, there are significant
  high frequency pressure ripples superimposed on
  the primary pressure transients. The frequencies
  of these extraneous pressure ripples are
  proportional to the no. of pipe sections and
  their amplitudes are inversely proportional to
  the same.
• With the continuous line model approach using
  time delays, there are no significant high
  frequency pressure ripples superimposed on the
  primary pressure transients. The no. of sections
  affects only the accuracy of the pressure drop.
• The calculated pressure wave amplitude and period
  are significantly closer to the closed form
  solution when using the time delay approach.
• For the simulated system, the computation time
  using the time delays approach was only 10
  percent of that required when using component PW.

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Conclusions and Recommendations

• Working directly with the continuous line model
  for hydraulic line dynamics, by using appropriate
  time delays, provides significantly better
  results than the lumped line model implemented
  in component PW.
• It is recommended that the hydraulic line
  submodel presented here be packaged as a new
  EASY5 component for ease of use.
• Note This recommendation is being implemented.