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:
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Organization (S): EDF-R & D/MFTT
Handbook of Utilization
U4.4- booklet: Modeling
Document: U4.44.31
Operator DEFI_SPEC_TURB

1 Goal

To define a spectrum of turbulent excitation. Various types of spectra are available:

· for the “beams of tubes under transverse flow”, spectra of the type “length of
correlation ",
· for established uniform flows, parallel with plane or cylindrical structures
circulars, spectra of turbulence of boundary layer,
· spectrum of excitation defined by its decomposition on a family of functions of form in
providing a matrix interspectrale and a list of associated functions of form.
concepts tabl_intsp and function must then be generated upstream,
· preset spectrum of turbulence, identified on model GRAPPE1 or GRAPPE2,
· spectrum of excitation associated with one or more forces and specific moments while providing
a matrix interspectrale of excitations (concept tabl_intsp having to be generated upstream),
the list of the nodes of application of these excitations, the nature of the excitation applied in
each one of these nodes (force or moment) and directions of application of the excitations thus
defined.
Product a concept of the spectrum type.
Handbook of Utilization
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2 Syntax

spe [spectrum] = DEFI_SPEC_TURB (


/SPEC_LONG_COR_1:
_F (





LONG_COR
=
LLC
, [R]





PROF_VITE_FLUI = profv
, [function, formula]






VISC_CINE
=
eps

,
[R]









),

/
SPEC_LONG_COR_2
=
_F (





LONG_COR
=
LLC
, [R]





PROF_VITE_FLUI = profv
, [function, formula]





/FREQ_COUP
= 0.1


[DEFAUT]
PHI0 =
1.5D-3
[DEFAUT]
BETA =
2.7
,
[DEFAUT]
/
FREQ_COUP
=
frc


[R]







PHI0


=
phi0

[R]







BETA


=
beta,

[R]









),


/
SPEC_LONG_COR_3 =
_F (





LONG_COR
=
LLC
, [R]





PROF_VITE_FLUI = profv
, [function, formula]





/FREQ_COUP
=
0.2
[DEFAUT]







PHI0_1

=
5.D-3

[DEFAUT]







BETA_1

=
0.5 [DEFAUT]







PHI0_2

=
4.D-5

[DEFAUT]
BETA_2
=
3.5
,
[DEFAUT]
/
FREQ_COUP
=
frc



[R]







PHI0_1

=
phi01

[R]







BETA_1

=
beta1

[R]







PHI0_2

=
phi02

[R]







BETA_2

=
beta2,

[R]









),


/
SPEC_LONG_COR_4 =
_F (





LONG_COR
=
LLC
, [R]





PROF_VITE_FLUI = profv
, [function, formula]






TAUX_VIDE
=
TV
, [R]





/BETA = 2.
[DEFAUT]







GAMMA

=
4. ,


[DEFAUT]






/BETA


=
beta


[R]







GAMMA

=
gamma,

[R]









),


/
SPEC_CORR_CONV_1:
_F (





LONG_COR_1 = lc1
,
[R]





LONG_COR_2 = lc2

,
[R]





VITE_FLUI
=
vflui
, [R]





FREQ_COUP
=
FC
, [R]





K =/5.8D-3
[DEFAUT]












/K,


[R]





D_FLUI
=
dhyd
,
[R]





RHO_FLUI
=
rho_f
, [R]





COEF_VITE_FLUI_A
=
alpha
, [R]





COEF_VITE_FLUI_O
=
beta
,
[R]





METHOD =/“GENERAL”
[DEFAUT]












/“CORCOS”
/
“AU_YANG”
,









),
Handbook of Utilization
U4.4- booklet: Modeling HT-66/05/004/A

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/
SPEC_CORR_CONV_2 =
_F (





FONCTION
=
fonc
,
[function, formula]





VITE_FLUI
=
vflui
, [R]





FREQ_COUP
=
FC
, [R]





COEF_VITE_FLUI_A
=
alpha
, [R]





COEF_VITE_FLUI_O
=
beta
,
[R]





METHOD =/“GENERAL”
[DEFAUT]
/
“CORCOS”
/
“AU_YANG”
,









),



/
SPEC_FONC_FORME =
_F (





/INTE_SPEC
=
int_spec
,
[tabl_intsp]
FONCTION
=
l_fonc
,
[l_fonction]






/
GRAPPE_1 =/“DEBIT_180”
/
“DEBIT_300”
,






NOEUD
=
No
, [node]






CARA_ELEM
=
will cara
,
[cara_elem]






MODELE
=
model
,
[model]









),



/
SPEC_EXCI_POINT =
_F (





/INTE_SPEC
= int_spec
,
[tabl_intsp]
NATURE
=
l_nat
, [l_TXM]
ANGL =
l_theta
,
[l_R]
NOEUD
=
l_no
,
[l_noeud]






/
GRAPPE_2 =/“ASC_CEN”
/
“ASC_EXC”
/
“DES_CEN”
/
“DES_EXC”
,
RHO_FLUI
=
rho_f
, [R]
NOEUD
=
No
, [l_noeud]






CARA_ELEM
=
will cara
,
[cara_elem]






MODELE
=
model
,
[model]









),

TITER = title
, [TXM]









);
Handbook of Utilization
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3 Operands

3.1 Key words
SPEC_LONG_COR_n

The definition of a spectrum of excitation of the type “length of correlation” can be done only by one
only occurrence of one of the key words SPEC_LONG_COR_n factors, corresponding to a zone of the tube
defined beforehand by the function indicated in operand PROF_VITE_FLUI of the command
DEFI_FLUI_STRU [U4.25.01]. Profile speed associated with this zone, pointed out here under the operand
PROF_VITE_FLUI, must be identical to that indicated in DEFI_FLUI_STRU [U4.25.01]. The use
spectra of excitation of the type “length of correlation” is limited to the configuration “beam of
tubes under transverse flow " (key word factor FAISCEAU_TRANS of the operator
DEFI_FLUI_STRU [U4.25.01]).

To carry out a calculation with several zones of excitation, it is necessary to define as many spectra as there is
zones. The contributions of the various spectra can be then added when the excitation is
projected on modal basis by command PROJ_SPEC_BASE [U4.63.14]. However, it is not
possible in this command to combine spectra of the type “length of correlation” with
spectra of another type (SPEC_CORR_CONV_n, SPEC_FONC_FORME or SPEC_EXCI_POINT).

The four spectra of the type “length of correlation” have values defined by defect. The definition
new coefficients is delicate, in particular with regard to the model 3 for which it
exist conditions of connection between the lines determined by the coefficients.

The general analytical form of models 1 to 4 is as follows:

- S

2 - S
S (S
1


1, S, F
2
R) = S (F R) .exp


C

with:


S (S, S, F
interspectre adimensional of turbulence between two points of X-coordinates
1
2

R)
curvilinear S, S
1
2;


S (F
autospectre of turbulence;
R)


- S

2 -

S
exp
1
function of space correlation and C length of correlation.




C



The spectrum is defined according to a reduced frequency Fr (a Strouhal number). For a tube under
transverse flow, the Fr expression is as follows:

F. E
D
F R =

G
V

F is the dimensioned frequency, of the diameter external of the tube and Vg transverse speed
average of the fluid along the structure, which will be recovered in operator PROJ_SPEC_BASE
[U4.63.14] via the concept [melasflu] produced by operator CALC_FLUI_STRU [U4.66.02].
Handbook of Utilization
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3.1.1 Analytical expression of the spectra of the type SPEC_LONG_COR_1

/SPEC_LONG_COR_1

Key word factor corresponding to the first model of spectrum with length of correlation.



LONG_COR = LLC

Length of correlation.



PROF_VITE_FLUI = profv

Name of the profile speed corresponding to the zone where is applied the turbulent excitation.



VISC_CINE
=
eps

Kinematic viscosity of the fluid.


S (F
0
R) =


2


F 2
F 2
R

2
R
1


+ 4
F

F
rc
rc




with: =
0
0 (Re) polynomial of the 5th degree.
= (Re)
= (Re)
F
=
rc
0 2
.

If 1.5.104 < Re 5.104:

4
-
4
-
8
-
2
12
-
3
0 = 13. 10.[2042
.
- 14 10 .Re - 9.8.1 10 .Re + 119
. 7 10
. Re
17
-
4
- 22
5
- 3595
.
10
. Re + 34 69
.
10
. Re]

If Re > 5.104:
0 = 386075
.


If Re 3.5 104
= 0 7
.
= 3
If not if 3.5.104 < Re 5.5 104
= 0 3
.
= 4
If not
= 0 6
.
= 4

3.1.2 Analytical expression of the spectra of the type SPEC_LONG_COR_2

/
SPEC_LONG_COR_2

Key word factor corresponding to the second model of spectrum with length of correlation.

LONG_COR = LLC

Length of correlation.
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PROF_VITE_FLUI
=
profv

Name of the profile speed corresponding to the zone where is applied the turbulent excitation.

/FREQ_COUP
=
frc

Reduced frequency of cut.

PHI0
=
phi0
BETA
=
beta

Coefficients of the spectrum.

Note:

If the user informs one of these operands, it must obligatorily
to inform the two others, in order to have coherent values.
If the user does not inform any of the three operands, the default values
are used.


S (F
0
R) =
F
R
1+ F
rc

The values of the default settings are:
- 3

F
0 = 15
. 10, = 2 7
. , rc = 01.

3.1.3 Analytical expression of the spectra of the type SPEC_LONG_COR_3

/
SPEC_LONG_COR_3

Key word factor corresponding to the third model of spectrum with length of correlation.

LONG_COR
=
LLC

Length of correlation.

PROF_VITE_FLUI
=
profv

Name of the profile speed corresponding to the zone where is applied the turbulent excitation.

/FREQ_COUP
=
frc

Reduced frequency of cut.

PHI0_1
=
phi01
BETA_1
=
beta1
PHI0_2
=
phi02
BETA_2
=
beta2

Coefficients of the spectrum.

Note:

The five operands must be used simultaneously. If one is
informed, the others must be it also.
The default values are used when the user did not inform any
of the five operands.
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0
0
= F
S (F
0
rc
R)
()
=


F
with
=
where
= 0 2
.
R

(frc)
frc

If F F
- 3
R
rc
0 = 5 10
= 05.
If not

5
0 =
-
4 10
= 35.

3.1.4 Analytical expression of the spectra of the type SPEC_LONG_COR_4

/
SPEC_LONG_COR_4

Key word factor corresponding to the fourth model of spectrum with length of correlation.

LONG_COR = LLC

Length of correlation.

PROF_VITE_FLUI = profv

Name of the profile speed corresponding to the zone where is applied the turbulent excitation.

TAUX_VIDE
=
TV

Rate of vacuum (diphasic flow).

/BETA
=
beta


GAMMA = gamma

Coefficients of the spectrum.

Note:

If the user informs one of these two operands, it must obligatorily
to inform the other.
If none of the two operands is indicated, values by
defect are used.



1

10
=
S (F
0
- 2

6 8
. 1
0
R) =
0
(with

F

R) (v)
0 5
.
1 5
.
2 5
.
3 5

=.
To v -.
B v + C. v -.
D. v

v the rate of vacuum indicates;
To = 24 042
.
; B = - 50 421
.
; C = 63 483
.
; D = 33 284
.
.

The default values of the exhibitors are = 2 and = 4.

NR F E (xi)

=

v is the volume throughput: v
m ×V =
×V
NR N
i= NR D
where V indicates the speed of the fluid for which the study of interaction
fluid-structure was carried out and NR N the number of points taken into account on
the excited length. The speed of the fluid will be recovered in the operator
PROJ_SPEC_BASE [U4.63.14] via the concept [melasflu] produced by
operator CALC_FLUI_STRU [U4.66.02].
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3.2 Key words
SPEC_CORR_CONV_n

The key words factors SPEC_CORR_CONV_1 and SPEC_CORR_CONV_2 make it possible to define
respectively spectra of turbulence of boundary layer and a function of the frequency
unspecified.

Theoretical precise details:

· In the case of a plane structure subjected to a parallel turbulent flow, which one wishes
to know the spectral response to this excitation, the model of correlation of CORCOS introduces one
function of correlation between two items X and X on the plane structure, of the type

(

-

-
-
, X, X)
X X
y y
(X X)
R
= exp -
×
-





exp
*
1




cos
2

×

U.a.



1


1 =
ave
C K L = 0 1
, ×

K L
U.a.
In the basic model of CORCOS, one has

1


2 = with kT = 0.5,5×


kT
U.a.

X is the axis parallel with the flow.
y is the axis perpendicular to the flow.

U.a. is the convective speed of the swirls. It is allowed that it represents between 60 and 70% of
speed of the fluid. By defect, one takes it equal to 65% speed of the fluid.

· In the case of a circular cylindrical structure subjected to an axial flow, the model of
correlation of AU_YANG introduces a function of correlation between two points defined by:

(

-
-

-
-
, X, X)
X X
(X X)
R
R (
)
R
= exp -
-



cos
× exp
cos

×




U.a.



×

U.a.


- and correspond to the angular positions of the two points of the cylinder to correlate,
-
X and X indicate the dimensions of the points to be correlated,
-
R is the radius of the cylinder,
- U.a. is the axial convective speed of the swirls: it is equal to the product of the coefficient of
axial speed by the speed of the fluid,
- U.a. is convective speed orthoradiale swirls: it is equal to the product of
coefficient speed orthoradiale by the speed of the fluid,
-
and are the lengths of correlation according to the axis and the direction orthoradiale
respectively.

· Correlation GENERALE is a function of the type

X - X
X - X
R (, X, X) = exp -



cos

×




U.a.


-
X and X are the vectors locating the positions of the two points to be correlated,
- U.a. is the convective speed of the swirls,
-
is the length of correlation.
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3.2.1 Definition of a spectrum of turbulence of boundary layer

/
SPEC_CORR_CONV_1

Key word factor corresponding to the first model of spectrum of pressure with length of
correlation and speed of convection of the swirls in the fluid.

LONG_COR_1 = lc1

First length of correlation (along the axis parallel with the flow) for the method
AU-YANG. Length of correlation of method GENERALE.

LONG_COR_2 = lc2

Second length of correlation for the method of AU_YANG.

VITE_FLUI
=
vflui

Speed of the fluid skirting the studied structure.

FREQ_COUP
=
FC

Cut-off frequency of the spectrum. In the case of the method of CORCOS, one uses
U
value F C = 10
(see notations below) by defect.
D

K = K

Constant giving the amplitude of the spectrum of pressure.
By defect, K is worth 5,8 10­3 in units IF.

D_FLUI = dhyd

Hydraulic diameter entering the expression of the amplitude of the spectrum of pressure.

RHO_FLUI = rho_f

Density of the fluid.

COEF_VITE_FLUI_A
=
alpha

Coefficient the convective speed of the swirls in the axial direction (direction of
the flow) for the methods of CORCOS, AU_YANG.

COEF_VITE_FLUI_O
=
beta

Coefficient the convective speed of the swirls in the direction orthoradiale with
roll, for the method of AU_YANG.

METHODE
=
“GENERALE” or “CORCOS” or “AU_YANG”

Method of correlation determined by the type of the structure which one wants to study them
vibrations generated by turbulence.
By defect, method GENERALE is used.

Note:

In the case of the method of CORCOS, one uses for LONG_COR_1 and LONG_COR_2 the lengths
of correlation of the basic model (see [§3.2]).
The spectrum of pressure used is of the type S
2
2
2
3
p () = K (U) D if F F C and 0 for F > F C.
K indicates the constant of the model, well informed under the operand K. Pour the model of CORCOS, K
is in experiments given and is worth K =
-
5 8 10 3 s1 2 m3 2
,
;
is the density of the fluid, well informed under operand RHO_FLUI;
U is the speed of the fluid, well informed under operand VITE_FLUI;
D is the hydraulic diameter, well informed under operand D_FLUI.
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3.2.2 Definition of a spectrum of turbulence of a function of the frequency
unspecified

/
SPEC_CORR_CONV_2

Key word factor allowing to define a spectrum of unspecified pressure function of
frequency.

FONCTION
=
fonc

Concept of the function type defining the spectrum of pressure according to
frequency, produced by one of operators DEFI_FONCTION [U4.31.02], CALC_FONCTION
[U4.32.04] or CALC_FONC_INTERP [U4.32.01].

VITE_FLUI
=
vflui

Speed of the fluid skirting the studied structure.

FREQ_COUP
=
FC

Frequency cut-off beyond which the function defining the spectrum of pressure
is regarded as null.

COEF_VITE_FLUI_A = alpha

Coefficient the convective speed of the swirls in the axial direction (direction of
the flow).

METHODE
=
“CORCOS”

Method of correlation for the structures of the type plates. Lengths of correlation
reserves are the lengths of the model of CORCOS per defect (see [§3.2]).

3.3 Key word
SPEC_FONC_FORME

/
SPEC_FONC_FORME

Key word factor allowing to define a spectrum of excitation by its decomposition on one
family of functions of form.

/INTE_SPEC
=
int_spec

Concept of the tabl_intsp type defining a matrix interspectrale excitation. It
concept can be produced by operator LIRE_INTE_SPEC [U4.36.01] after reading
matrix interspectrale on external file.



FONCTION = l_fonc

List concepts of the function type defining the family of functions of form
associated.


/GRAPPE_1 = “DEBIT_180” or “DEBIT_300”

Two possible choices corresponding to the flows for which excitation GRAPPE1
was identified.

NOEUD
=
No

Node of application of the excitation.
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CARA_ELEM
=
will cara

Concept of the cara_elem type produces by operator AFFE_CARA_ELEM [U4.42.01], defines
geometrical characteristics assigned to the elements of the structure.
The geometrical characteristics are necessary to the estimate of the diameter
hydraulics. Moreover, the concept of the cara_elem type brings relative information
with the orientations of the elements.

MODELE = model

Concept of the model type produced by operator AFFE_MODELE [U4.41.01], defines them
types of elements assigned to the meshs of the structure.

Note:

1) The length of application L is characterized in an intrinsic way by
field of definition of the functions of form associated with the excitation. The zone
of application is centered around the node of application.
2) The turbulent excitation being able to be developed in a way correlated in both
orthogonal directions with the axis of the telegraphic structure (axis X), functions of form
are a priori vectors with two components (according to y and Z).
One will thus inform, by convention, these functions about the interval (0; 2L), them
fields (0; L) and (L; 2L) being respectively associated with the directions y and Z.

3.4 Key word
SPEC_EXCI_POINT

/
SPEC_EXCI_POINT

Key word factor allowing to define a spectrum of excitation associated with one or more forces
and specific moments.

/INTE_SPEC
=
int_spec

Concept of the tabl_intsp type defining a matrix interspectrale excitations
specific. This concept can be produced by operator LIRE_INTE_SPEC
[U4.56.01] after reading of the matrix interspectrale on external file.

NATURE
=
l_nat

List arguments of the text type defining the nature of the excitation of each one of
nodes of application. The licit arguments are “FORCE” or “MOMENT”.

ANGL
=
l_theta

List angles defining the directions of the vectors forces and moments in
each node of application (see diagram).
Z
P
RF

y
Node of application
X (neutral fiber)


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The vector force is directed in the plan P orthogonal with neutral fiber. In this plan,
the azimuth gives the direction of the vector. The angles must be given in degrees.

NOEUD
=
l_no

List nodes of application of the specific excitations.

Note:

The matrix interspectrale has as a dimension the number of forces and moments
specific applied. The diagonal terms of this matrix characterize them
autospectres of these excitations.
Lists defining the nodes of application, the nature and the direction of
imposed excitations must thus be ordered in accordance with the structure
matrix interspectrale of excitations.

/
GRAPPE_2
=
“ASC_CEN” or “ASC_EXC” or “DES_CEN” or “DES_EXC”

Four possible choices corresponding to the various experimental configurations
for which excitation GRAPPE2 was identified:

· flow ASCendant stem of CENtrée command,
· flow ASCendant stem of EXCentrée command,
· flow DEScendant stem of CENtrée command,
· flow DEScendant stem of EXCentrée command.

Excitation GRAPPE2 is characterized by a specific force and a moment
applied in the same node, in a homogeneous way in the two directions
orthogonal with the axis of the telegraphic structure.

RHO_FLUI
=
rho_f

Density of the fluid surrounding the structure.

NOEUD
=
No

Node of application of excitation GRAPPE2.

Note:

When one resorts to a preset spectrum GRAPPE2, the list of nodes
waited under operand NOEUD is reduced to only one element (only one node
of application).

CARA_ELEM
=
will cara

Concept of the cara_elem type produces by operator AFFE_CARA_ELEM [U4.42.01],
defines the affected geometrical characteristics in the elements of the structure.
The geometrical characteristics are necessary to the estimate of the diameter
hydraulics. Moreover, the concept of the cara_elem type brings information
relating to the orientations of the elements.

MODELE = model

Concept of the model type produced by operator AFFE_MODELE [U4.41.01], defines them
types of elements assigned to the meshs of the structure.

4 Bibliography

[1]
NR. GAY, T. FRIOU: Resorption of software FLUSTRU in Aster HT-32/93/002/B
[2]
L. PEROTIN, Mr. LAINET: Integration of a general model of turbulent excitation in
Code_Aster: specifications HT-32/96/003/A
Handbook of Utilization
U4.4- booklet: Modeling HT-66/05/004/A

Outline document