flower, a model for the analysis of hydraulic networks and processes l. bottura ( ), c. rosso ( )...
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Flower, a Model for the Analysis of Hydraulic
Networks and ProcessesL. Bottura(), C. Rosso()
()CERN, Switzerland
()CryoSoft, France
CHATS, FzK, Karlsruhe, September 2002
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Overview
A bit of history What is Flower today ?
preliminaries on state equation and variable choice
bits and pieces… … of a circuit
What is it good for ? Perspective
the painful bit… Lots of equations !
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A bit of history (the 70’s)
Quench analysis for fusion magnets (70’s)
large stored energy (16 coils, 100 GJ) force-flow cooled cables (CICC’s) issues:
pressure increase (typically > 150 bar) temperature increase (typically <150 K) helium massflow (typically 1 to 10 Kg/s per
coil) safety is critical
radioactive release in case of structural faults
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A bit of history (the 80’s)
1-D (pipe) model of flow and temperature
simple boundary conditions p=const, T=const (infinite reservoir) v=0 (closed valve)
SC cable (T)cooling flow (v,p,T) p=const
T=const
v=0
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A bit of history (the 90’s)
Manifolds direct interconnection between
quenching cables can propagate hydraulically the quench
IEEE Trans. Appl. Sup., 3 (1), 606-609, 1993 see also LHC-String-1 experimental program
must be considered for time scales 10 s
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A bit of history (80’s to 90’s)
First level of improvement simple model for finite inlet/outlet
volumes
SC cable (T)cooling flow (v,p,T) p=f(t)
T=f(t)p=f(t)T=f(t)
0 imtV
mass conservation
qv
hmt
iV i
ii
2
2
energy conservation
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A bit of history (90’s to 00’s)
Second level of improvement describe the external piping circuit, focus
on: buffers/volumes (damp pressure transients) valves (choke the flow, relief lines) pipes (delay lines) heat exchangers (temperature control) pumps/compressors (flow, pressure control)
adopt drastic simplifications in the model
Flower versions 1, 2 and 3
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A bit of history (2002, today)
Evolution add new modeling elements:
heat exchangers turbines
sparse matrix storage technique GMRES iterative solution
Flower version 4
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What is Flower version 4.0?
Objective of the code:
a simplified model of the hydraulic (helium) network that feeds a SC magnet …
… reproducing key features of the (cryogenic) system response …
… allowing consistent simulation of both transient and steady state.
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Vocabulary for an hydraulic network
volume
junction
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Bits and pieces - Preliminaries
pressure p and temperature T as state variables (V. Arp, 1980):
velocity v for flow
dhc
dpc
d22
1
dTCdTCp
di vv
1
Gruneisen parameter =-1 for perfect gas
vast improvement of numerical stability for the flow calculation
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Bits and pieces - 1
Volumes, buffers, manifolds heat
flow p=f(t)T=f(t)
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Bits and pieces - 2
Pipes (compressible flow) heat
flowv=f(x,t)p=f(x,t)T=f(x,t)
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Bits and pieces - 3
Valves as steady state pipes but:
no heat input variable head loss factor :
flowPin,pout=f(t)Tin,Tout=f(t)dm/dt=f(t)
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Bits and pieces - 4
Control valves =f(t,dm/dt,p)
Relief valves =f(p)
Burst disks =f(p(t))
dm/dt
p
p
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Bits and pieces - 5
Volumetric pumps:
Compressors:
flow Pin,pout=f(t)Tin,Tout=f(t)dm/dt=f(t)
-1.5
-1
-0.5
0
0.5
1
1.5
-2 -1 0 1 2p/p0
m/m
0
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Bits and pieces - 6
Isentropic flow (ideal pump):
dS=0
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Bits and pieces - 7
Turbines
Isentropic flow (as for ideal pump):
flow Pin,pout=f(t)Tin,Tout=f(t)dm/dt=f(t)
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Bits and pieces - 8
Heat exchange
Rij
rij rij
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Bits and pieces - Summary
Model is an assembly of: volumes, manifolds, buffers… …1-D flow pipes… …control and check valves… …burst disks… ….ideal volumetric pumps and
compressors… …turbines… …with (possible) heat exchange among
volumes and pipes (HEX)
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Equations as matrices
all equations are in the general form:
non-linear system of ODE’s for each element
elelelelel
el
tQUSA
UM
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The circuit matrices
p1,T1
p2,T2
p3,T3
p1 T1 p2 p3 T3T2
p1
T1
p2
p3
T3
T2
0
0coupling
M1
M2
Sparse matrix storage (SLAP triad)
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System solution
Solution technique
QUSAU
M t
11111
1
nnnn
nnn
tUQUUSUA
UUUM
Iterative solution of algebraic systemincomplete preconditioning GMRES algorithm
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What is it good for ?
Results in the QUELL experiment
Response of a heated helium loop such as the LHC Beam screen
A string of LHC magnets
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QUEnch on Long Length
Cable sample
Current lead
Flow regulation
Cryogenic plant
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QUEnch on Long Length
Cable sample
Equivalent pump
Quench relief valve
Quench relief valve
1 2
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QUEnch on Long Length
1
2
experimental
computed
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A heated helium loop4 pipes
thermally linked L=50 m
D=4.6mmq=0.5…1 W/m
pump dm/dt=7.5 g/s
heat exchanger T0=7 K
relief valve p=5 bar
reservoirV=1000 lT=20 K p=1 bar
1 23
4
t
q
50 1000
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A heated helium loop
Temperature along the pipe
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A heated helium loop
Temperature distribution among the pipesdifferences in friction factor +/- 15 %
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A heated helium loop
oscillations due to the response of the system
oscillations induced by the relief valve
2 3
1
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A string of LHC magnets model of the regular LHC cell: D quadrupole and
lattice correctors 3 dipoles F quadrupole and
lattice correctors 3 dipoles
QV9202SIQV920
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A string of LHC magnets QV9202SI
QV920
MQ1 MB1 MB2 MB3 MQ2 MB4 MB5 MB6
QV920 QV920SI
VR
q
relief valve relief valve
quench heat
cold mass
t
q
0
thermal linkpipe
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Pressure evolution computed pressure OK
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Quench propagation
reasonable match of
quench propagation
MB3-MB2-MB1
quench propagation MB3-
MB4 too fast
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Temperature evolution
by the way… superfluid heat transport is included
computed temperature corresponds to time averaged measured value (no spatial detail)
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Induced flow and discharge valve opening
short flow bursts at quench
initiation
discharge flow
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Summary…
The model in Flower v4.0 has improved: include new features
turbines heat exchangers
take advantage of matrix sparseness reduce memory requirements decrease CPU time
allow solution of larger, more complex systems
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… and perspectives
Towards system solution avoid need for coupling different codes,
describing the assembly of: cryogenic plant proximity cryogenics end-user(s)
a significant improvement is necessary for the next step: single models (turbine, pumps) two-phase thermodynamics and flow