The shock absorber from LABEIN

mesfet [1]
Sara Casado (LABEIN)

The system under consideration has 27 equations and 27 unknowns with several parameters whose value is only known approximately. Two kind of unknowns are considered: The total degree of the equations is equal to one or two. These come from two different physical conditions: flow equilibrium in the different components of the electric-hydraulic circuit and pressure value in every node of such a diagram. The flow equilibrium equations are:
q1=q2
q2=q3+q7
q3=q4
q4=q5
q5=q6
q7=q8
q8=q9+q13
q13=q14
q14=q15
q9=q10
q6+q10=q11
q11=q12
and the pressure equations are:
P2-P1 =
q12
r
2
k
 
cont
S1-S2
S13
P3-P2 =
q22
r
2
[k
 
exp
(S3-S2)3
S22S32
+k
 
gr
1
S22
]
P4-P3 =
q32
r
2
k
 
cont
S3-S4
S33
P5-P4 =
q42
r
2
k
 
exp
(S5-S4)2
S52S42
P6-P5 =
q5 A
nr
d4
P10-P6 =
q62
r
2
[k
 
exp
(S10-S6)3
S62S102
+k
 
gr
1
S62
]
P7-P3 =
q72
r
2
[k
 
cont
S3-S7
S33
+k
 
gr
1
S32
]
P8-P7 =
q8 A
nr
d4
P9-P8 =
q92
r
2
[k
 
cont
S8-S9
S83
+k
 
gr
1
S82
]
P10-P9 =
q102
r
2
[k
 
exp
(S10-S9)2
S92S102
+k
 
gr
1
S92
]
P11-P10 =
q112
r
2
[k
 
cont
S10-S11
S103
+k
 
gr
1
S102
]
P14-P11 =
q122
r
2
k
 
exp
(S14-S11)2
S142S112
P12-P8 =
q132
r
2
[k
 
cont
S8-S12
S83
+k
 
gr
1
S82
]
P13-P12 =
q142
r
2
[k
 
exp
(S13-S12)2
S122S132
+k
 
gr
1
S122
]
P14-P13 =
q152
r
2
k
 
exp
(S14-S13)2
S142S132
The initial data is given by the knowledge of the pressure and flow at the entry node:
q1=Q,   P1=0
In this case, only real solutions are required.

Characteristics:



Example 1:
params := [kcont, kexp, kgr,r,Anrd,
           S1 S2,S3,S4,S5,S6,S7,S8,S9,S10,S11,S12,S13,S14, Q];
[q1-q2, q2-(q3+q7), q3-q4, q4-q5, q5-q6, q7-q8, q8-(q9+q13), q13-q14,
q14-q15, q9-q10, q6+q10-q11, q11-q12, 
P2-P1-q1^2*(r/2)*kcont*(S1-S2)/(S1^3),
P3-P2-q2^2*(r/2)*(kexp*(((S3-S2)^3)/(S2^2*S3^2))+kgr*(1/(S2^2))),
P4-P3-q3^2*(r/2)*kcont*((S3-S4)/(S3^3)),
P5-P4-q4^2*(r/2)*kexp*(((S5-S4)^2)/(S5^2*S4^2)), 
P6-P5-q5*Anrd,
P10-P6-q6^2*(r/2)*(kexp*(((S10-S6)^3)/(S6^2*S10^2))+kgr*(1/(S6^2))), 
P7-P3-q7^2*(r/2)*(kcont*((S3-S7)/(S3^3))+kgr*(1/(S3^2))), 
P8-P7-q8*Anrd,
P9-P8-q9^2*(r/2)*(kcont*((S8-S9)/(S8^3))+kgr*(1/(S8^2))),
P10-P9-q10^2*(r/2)*(kexp*(((S10-S9)^2)/(S9^2*S10^2))+kgr*(1/(S9^2))),
P11-P10-q11^2*(r/2)*(kcont*((S10-S11)/(S10^3))+kgr*(1/(S10^2))),
P14-P11-q12^2*(r/2)*kexp*(((S14-S11)^2)/(S14^2*S11^2)),
P12-P8 -q13^2*(r/2)*(kcont*((S8-S12)/(S8^3))+kgr*(1/(S8^2))),
P13-P12-q14^2*(r/2)*(kexp*(((S13-S12)^2)/(S12^2*S13^2))+kgr*(1/(S12^2))), 
P14-P13-q15^2*(r/2)*kexp*(((S14-S13)^2)/(S14^2*S13^2)),
q1-Q,P1
];

References

[1]
D. Bini and B. Mourrain. Polynomial test suite. 1996.
This document was translated from LATEX by HEVEA.