Thermodynamic Control Volume

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Thermodynamic Control Volume

• Build a simple model from scratch
• Based on physical principles
• Demonstrate typical model design trade off
• Simplicity vs range of validity
• Simplicity vs numerical robustness
• Dynamic vs static

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Thermodynamic Control Volume

• Control volume First Law for Open Systems

Connector heat transfer
Connector convective flow
M, U
Mass- and Energy Balances
3
Step One Connectors

• Two transported quantities mass energy
• flow variable
• flow variable
• Potential variable for mass flow pressure
• For bi-directional flow specific enthalpy h

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Step One Connectors

• connector SimpleFlow
• SIunits.Pressure p
• SIunits.SpecificEnthalpy h
• flow SIunits.MassFlowRate mdot
• flow SIunits.Power q_conv
• end SimpleFlow

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Thermodynamic Control Volume

• Constitutive Laws Ideal Gas Law

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Ideal Gas Law
partial model PureIdealGas "Ideal Gas Law"
SIunits.SpecificHeatCapacity cv, cp, R
SIunits.SpecificEnergy u SIunits.Temperature
T SIunits.Pressure p SIunits.Volume V
SIunits.Mass M equation pV MRT
cv cp - R u cvT end PureIdealGas
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Thermodynamic Control Volume

• Constitutive Laws physical properties for H2

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Hydrogen Properties

partial model H2cp "cp, for NASA coefficients"
SIunits.SpecificHeatCapacity cp
SIunits.Temperature T(min200, max1000) //
range of validity of polynomial replaceable
IdealGasData data equation cp
data.R(1/(TT)(data.a1
T(data.a2 T(1.data.a3
T(data.a4 T(data.a5 T(data.a6
data.a7T) )))))) end H2cp
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Boundary Conditions

• Given fixed inflow,
• Infinite Reservoir with fixed pressure at outflow

Turbulent pressure drop
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Boundary Conditions I

• model SimpleReservoir
• parameter SIunits.Temperature T0300
• parameter SIunits.Pressure p01.0e5
• parameter SIunits.SpecificHeatCapacity
• cp0H2cp_init(T0)
• FlowA a
• equation
• a.p p0
• a.h cp0T0
• end SimpleReservoir

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Boundary Conditions II
model FlowSource parameter
SIunits.MassFlowRate mdot_fix1.0 parameter
SIunits.Temperature T0300 parameter
SIunits.SpecificHeatCapacity
cp0H2cp_init(T0) FlowB b equation
b.mdot -mdot_fix b.q_conv
-mdot_fixcp0T0 end FlowSource

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Turbulent Flow Resistance
model SimplePressureDrop parameter
SIunits.Pressure dp01.0e3 parameter
SIunits.MassFlowRate mdot00.1 FlowA a
FlowB b protected SIunits.Pressure dp
equation dp a.p - b.p a.mdot if dp
gt 0 then sqrt(dp/dp0)
else -sqrt(-dp/dp0) a.q_conv if dp gt 0
then a.ha.mdot else
b.ha.mdot b.mdot -a.mdot b.q_conv
-a.q_conv end SimplePressureDrop

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Turbulent Flow Resistance

Will this model work for reversing flows?
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Thermodynamic Control Volume

• Control volume First Law for Open Systems

Connector heat transfer
Connector convective flow
M, U
Mass- and Energy Balances
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Thermodynamic Control Volume

• model SimpleControlVolume
• parameter SIunits.Temperature T0300.0
• parameter SIunits.Pressure p01.0e5
• parameter SIunits.Volume V01.0
• extends H2(M(startp0V0/(data.RT0)),T(start
  T0))
• SIunits.InternalEnergy U(startp0V0(H2cp_ini
  t(T0)
• - data.R)/data.R)
• FlowA a FlowB b
• equation
• der(M) a.mdot b.mdot
• der(U) a.q_conv b.q_conv
• U Mu
• V V0
• a.p p b.p p
• a.h cpT b.h a.h
• end SimpleControlVolume1

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The Modelica Model

• 1 to 1 representation of physical model

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How to Structure the Code?

• Reusable Code
• Top level physical objects
• Separate
• Medium specific functions for hydrogen
• Constitutive equations, the ideal gas law
• Mass and energy balances
• Functions or Classes?

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Numerical Considerations

• What kind of equation system do we get?
• Probable difficulties with initial values?
• Numerical robustness guaranteed?

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Numerical Considerations

• Case I
• Internal energy U and mass M are the
  states
• Initial Values for mass and internal energy?

Non-linear equation!
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Numerical Considerations

• Case II
• can we avoid the non-linear system of equations?
• Function cp(T) is causing the problem? Choose T
  as a State instead of U
• Let Dymola do the rewriting ?

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Thermodynamic Control Volume

• model SimpleControlVolume
• parameter SIunits.Temperature T0300.0
• parameter SIunits.Pressure p01.0e5
• parameter SIunits.Volume V01.0
• extends H2(M(startp0V0/(data.RT0)),T(start
  T0))
• SIunits.InternalEnergy U
• Real dT
• FlowA a FlowB b
• equation
• der(M) a.mdot b.mdot
• der(U) a.q_conv b.q_conv
• U Mu
• V V0
• a.p p b.p p
• a.h cpT b.h a.h
• dT der(T)
• end SimpleControlVolume1

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Numerical Considerations

• Case II
• What about initial values?Much easier with T as
  a State than with U!

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Thermodynamic Control Volume

• model SimpleControlVolume
• parameter SIunits.Temperature T0300.0
• parameter SIunits.Pressure p01.0e5
• parameter SIunits.Volume V01.0
• extends H2(p(startp0,fixedtrue),T(startT0,f
  ixedtrue))
• SIunits.InternalEnergy U(fixedfalse)
• Real dp, dT
• FlowA a FlowB b
• equation
• der(M) a.mdot b.mdot
• der(U) a.q_conv b.q_conv
• U Mu
• V V0
• a.p p b.p p
• a.h cpT b.h a.h
• dT der(T) dp der(p)
• end SimpleControlVolume1

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Numerical Considerations

• Case III
• Eliminate the need for extra functions or
  calculations for initial conditions
• Make pressure p and Temperature T the states
• easy initial conditions
• measurements available? System identification
• Let Dymola do the rewriting again

25
Reversing Flows

• Consider this almost trivial system
• Switch of Blower after 1 s
• Control Volumes cools down due to heat loss

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Reversing Flows

• A system that handles reversing flows works
• If the pressure drop is ,
  the system will fail for numerical reasons
• Why? Look at the numerical details

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Reversing Flows Demo

• Open SimpleExamples.mo
• run scripts BackFlow.mos, NoBackFlow.mos
• Important details for start up simulations etc.

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ThermoFlow Library Goals

• Supply basic dynamic flow models
• Take care of initialization
• Consider numerical efficiency
• General numerical robustness important
• Allowing reversing flows a must
• Basic set of physical properties

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Heat exchanger group

• Discuss wanted level of detail
• What types of heat exchangers are needed?
• Identify alternatives, take into account for
  object structure
• Look at examples in Components/Water/HeatExchange
  rs
• Check for available models in PartialComponents
• Start coding geometry parameterization,
  graphical composition, parameter propagation

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Conclusions

• Easy to build physical models with Modelica
• Start with basic conservation equations
• Define connectors
• Numerical aspects important for robustness
• Use model Libraries!