Upload
nguyenthuy
View
252
Download
0
Embed Size (px)
Citation preview
Archi
ve o
f SID
��� �������� ��� ������� ���� ���
����� ��� �� � ���� ���� ���� ���� �� ��� ���
����� ����� �*!���"#� ����� �**�$%� �&�� �� � !**���%'� �� � �***
�(� '�% ���$)� *�+,�'-!.�/ �01$� 2�3,�'-
�4���,5 -�) ���$)� 2�+,%�67
)����� ���� :�"/�/��$%��&' �()' ���� :�/�/��(
82��+9����� �� �� ��� ��� ������ �������� ���� ��� � ��! "��#� ���$ %�#��& '(��#) � #���* %�+��� ����,����* � -#!�� �#. %& ��� (�#� '/#01� � ��23 4�� �5��� #67�)9(��; 4�1� <& .�0> %� ?�� �� @�) ,���* ,���������;A �B����
��! "��#� (> C���� %�03 ��� � � ��� ���$ <�& %��!�$ �D �&�� �#� .�� �%%���E F#�� �<�&� %�� ��B��#G�� � ���� �� ���&�H;�I���� ��6� �H��J� ���K� ,��� ���B� .� � �B �%C����� L���� � ,� @��) (> ��! %��� � �����& ��! �%�03
��� �; ���$ <&.�� ,��� I���� B�7C���� �M#) ��N��OD#� � �K��� ��! "��#� %> ����J� %+��� � %� ,� %��03 %�� � � �PQ���<& �M %�#�& R�� � 0> <�&�23 ���� � � %� <S2�% %�03 J��%� � <�OD#� ���$��$� ?#) �� ��O�� .���7T0B ���! "��#�
%��� @�) (>%� <S2�� � %%�03 �� ���U� �7V�W <���E %� � ���X �� ?�� � ���� ,���* ���&�� ����� �#;.<02D � ���� �����%��� �%*� R; �� %�03 %� � R�J! �� ��� R�J! ���� %�W <���E ������� � R���N�� �%��� ���� <���E %��W ��� R�J�!
YZ&�� RB�> ���� .�W ��N��! �X%��> � ���� % ��� ��N��OD#� ���$ �; �5���� ,���* ,�#� %��;�<&.
��:;'����#5 : -#!�� ,���* %& ���� %�W �(�#) �� %��� ���! "��#� ��#. ��O�
Experimental Investigations of Supersonic Flow around a Long Axisymmetric Body
M. R. Heidari, M. R. Soltani, M. Taeibi-Rahni, and M. Farahani
Department of Aerospace Engineering, Sharif University of Technology
Agricultural Jihad Engineering Research Center
Abstract: A series of supersonic wind tunnel tests on an ogive-cylinder body were performed to investigate the pressure distribution, the boundary layer profiles, and the flow visualization at various angles of attack. All tests were conducted in the trisonic wind tunnel of the Imam Hossein University. The theoretical shock angle at different model positions compared well with those we obtained via Schilerian results. The static surface pressure results show that the circumferential pressure at different nose sections vary significantly with angle of attack. However, minor changes in the circumferential pressure signatures along
*$+�, -./0' **$ �10' ***$�� 2��� �,
www.SID.irwww.MatlabSite.com | متلب سایت
Archi
ve o
f SID
��� ���������� �� ������ ���� ���
the cylindrical part of the body were observed. The total pressure measurements in the radial direction, perpendicular to the incoming flow, vary significantly both radially and longitudinally (along body length). The boundary layer thickness increases along the body. At the beginnig and at the midle part of the cylinderical portion of the body, the boundary layer thickness increases uniformly with increasing angle of attack. However, this situation differs near the end of the body. Our measurements indicated a turbulent boundary layer along the model, which is probably due to the high turbulence level in the tunnel test section.
Keywords: Supersonic flow field, Pressure distribution, Long axisymmetric body, Three-dimentional boundary layer
���� ���
cdC3�+4-�)5 -6+1' %78��
d�'.�� 9(: +8; ��� -
L/d �.< �=)' >, +8; �:�'.�� 9(: ��� -
1P- .�? @.� A >=; B1C��� �0�
cRe%'+D: A��.�� �?
x�EF�� %�.< .D� -��� �G�� @.' AH ��C
α�6A��E�I
β%='�J K+� ��6A
*δL.���� ��M ���(4
θ%81D� N�6A
<9���=�
�&OP�.� NP'�: �.< Q���R S117C -�T+�� �5 A %O��UP/I
6 VW1&/C�&��)1� HX -�� .�P, �� %&��: SP� 9�WP�
6 �'�: �.< 9�W� Z?�: U/I[��/1�' �=)' L/d %P� HX .P�
]�.[ +: �'�: -6 H��+J �1�1R 6 ��� %��T->�.<)�=)P'
��A +8; �: �.< (�&O�.� %O1���� 6+�X 3�+4 >1EDC -+: -
�PP�E:Q\PP�6 �PP1�T A �PP� .PP]+: - .�PPJ V�O0PP� A
QA�� �M �� 6 H��+J 9��J ZD: �- ��.P< -A+� SP�
�'.^�'�: �T .: �J.C >:�; P; _P1; %P� +: .P� �P��: 6 Q +
+1^.+P11`C �P: +P/�� �P'�: %��P&�' 9P(: H��+J 9��J
%�+��R a.8� +OE�? 3�? �� �T.] .Q6�? �:�A�1' �&O�.�
b�P� �P? A %71P�6 � 6�D� �R �' )c.��P� �PC H6 �P�
V.F (A6+5���, �R�&�?+� S� �1E, �M�-A+� HX �� 6
dE�(� a.8� 6 �'�: -6 : �T.] V6���� ..�e� �P� b+'
�M�%�&� 9�' HX 9��J 6 -A+� �R L�/' 6 �&O�.� %�
�� .��� �&'X %� ��� ��R].[ b+P' S1P17C -+: Sf�8� Q B�
915 6 ���(4 �� 9��J ��� %�1:��M QA�' -A+� -+P1^
HX %:+/C�� .H�P�+J �P1�1R NP7��8� -+P: 9T6\5 S�
�'�: -6 �>�.< -�T P�E�(� V�0���AX >��P� �% QA�P' -+P1^
g8� -6 %O1C��� �0� h�A.C QA�' �U)J -+1^ >PR �0P�
�'�: 6�/� �P� Q�P� L�P/' H��+J H�1� -A�� �i�X 6.
.j�� S� -+:�B����.��J$�P: �'.�P�L/d=15 k�P(�'
Q�� �� .0���AXV�QA�' B1C��P� �0P� hP�A.C -+P1^ -6
�'�: -�T �:�0� ��:�=)' �.< +8; �:+��R� .< �: Q +�)P^
Q�� L�/' .0R A l �] 6 .PJ.� �&'X A %]+: m���' �P� .
:����I +T ./�)J m���' -QA�' -A+� ��M -+1^�WJ %EF�I
%:�1�� �: -+� n� -A6+5 9���AX m���' �&�C ��8�' B� -+:
�'�: -6 ���' �]�[.
o�T +p� A 0���AX S� V�1&C �q 6 �%C�P?�< BP'�:
��D� �:�H-+: V�P7��8� �: %T �=�?CFDQ .P: �P: ��P�
- .< %� ��� S� �R�'.�' A %O� �'.C 9��P�AX -�PT�-+P:
- �? m���' %� +: hJ+� �: �:�0� ]r[���: .m��P�' +Pp� SP�
%� +: �V�0���AX -�&�6 �; -+j' ��1' �� 6%P:+/C �P�
�&'X A h�+� -�T�, �,-+: �P'�: -6 �0� h�A.C �=��D�
%� Q ���� .� .V�?�< �S1�s�T �� �: Q��X �915 %P�1:
6�D�� e^�� Q ���� >:�; ����X �: L X -A+� ��M .
www.SID.irwww.MatlabSite.com | متلب سایت
Archi
ve o
f SID
��� �������� ��� ������� ���� ��t
�'�: -6 �0� h�A.C N=��D� -+: �:�0� -�T �: ��� .�
�9���AX��+j' C ��'�� %'.^�'.^ -�T 6 BPu.R K�0P�G 3�+�
��-+j' 6 N=C+� @.� v�)=' � .J6 V.F c.��� H��+J
.S� ���?��+j' S1��P5 %PE1] NPE�I -�P�6A wP�� �PT
%� �q %�.=; >:�; -�&:.J P�6A �P� A �: %�6 ���T ��PE�I �
%� 9�W� �&�6 S� -�8] �:��]x.[ -�&�6 d74 -+j'
�0� h�A.C N=��D� 9(: .1� y)H��+J �: �05 (�'�:��:
�� �1I�' S� H��+J 9��J >1� .�&P�6 S� �R 2��
-��=� +: S��+^ Q�� �'��M ��� -A+� .D� -�PT %�.P< 6
�� %4+?�- .P< �:P�6A �PR�PE�I +�PF+1G NNP��.� �
�P'�: .PD� +P: .P�? -��P� �?+�)%P4+? �?+P� (
%� �=��D� � ..%=�+P4 �H�P�+J H .P: ���P�X �� L X z+� �:
-�)PP5 -6+PP1' 3�+PP4 H.PP�? �PPDC%PP78���cdCK6 A �
WPR+� >D� 6 - .�? -6+1' HX B�R �: 6 Q�� S117C %���&�
%� �=��D� �0� .� .�P; �P: ��)P:6 ���PR K6 S� �;
N=��D� cdC�� 63�+4 S� 6 {.'�M�L X -A+P�6
����X �� �1): V6���� .�P; �, ��u+T SP� �&P�6 -+P:
N=��D� �0� WR+� >D� 6 - .�? -6+1' 3P���� [��=)' �P��
�� S� � .J6 H��+J 9��J %�;6 �&�6 N=��D� �: �;
�0� h�A.C 9P(: .P1� ���)P1' �P'�: .+P|R �&P�6 -
-+j'cdCA %7:�PC �P&�C %ED� cRe�P� 6N=P��D� -+P:
HX _1; ��: ���: ����' N8�' "��M -A+P� }(0P� +P, �PC
H.�: �7: 6 >=; %I.' -+: ��8�' S� A 3P���� �P�� HX
�=��D� +, ]~[.�5 ��8�' S� QA�' A �P�M ���(P4 -+P1^
+� -A+��'�: �.< +��}1(0C >:�; .: �T.].
S� �_1�DC 1I�' ��u A ���� 6 -A+� ��M �0P�
'�: -6 %O1C����b�P� �P? dE�(� �E�I -��6A "/�
QA�' Q�� -+1^ ��.{.' S� 0P���AX �P: S1P�6 -+P: V�
.0, S1)PI L�P� Q�p0P' Q .j�� �� �: >'.C ){(L�P/'
Q�� �� .�P'�: -6 %O1C��P� �0P� hP�A.C _P�+< A �P1=7C
��� g8� -6 %��&] .� �P� �: Q�P�X P: 6QA�P' �-+P1^
[��=)' NEF�� �C ��� g8� A >R �0� BP� BP�R �: HX A 6
B� �)��.� �]�� V.P�15 -�T(S��P�u b�P� �P? hP�A.C �
QA�' dE�(� NE�I -��6A %�.< �17;.� Q�� -+1^ �P� .
H��+J ��� N7��8� -+:��: -A�� �O�X K6 L�P/' S�+1E1�
6 >P��� @.� >O� 6 ���+^ �P�M v�P�' 6 �PG�� -6 -A+P�
NE�I -��6A ��� dE�(�$�C"b�P� �P? �J "/�
Q�� H����' �� .M.�7� ��E: N'�: �: -�&O�.� �O�� �: �J.C �:
Q 6�D� ��' %�1��5 -+�e5 .'�� -��6A +�01: �&'X -A6+5
Bu.R �E�I�� ._1�DC S� �e��QA�' -�P�6A �&�+1^
NE�IS1q�5��+^ L�/' ���.
>9?���4@ �'A�) �
1ER�0���AX V�V�P�1�DC WPR+� Q .Pj�� �P� �P: >P'.C
S1)I L�� Q�p0' �; B1���� 6+�X){(�P� �P��+^ L�P/' .
�PP� %='�PPJ V�PP'�i�Q �� V �PP=? WPP1' Q�PP� A �PP' :VWPP1&/C
+: �H��+J -A�� �O�XA/D �1� 6+C U�)1� �B� ���P�5 �
%��.� +: � �0� -�T+�.��)'+C �+��.'�� ���] +)OE5�6nP�
Q�p�� �'�� -+:V�?�< KA +5 6 �=� �e] .
>9B9-�� ����
S1)PPI L�PP� Q�p0PP' �PP: >PP'.C){(�PPj�D� �PP7: -
X9���A"/�×"/�×�/�b�P� �P? Q 6�D� �37O� +�� �/��PC
�/�A��.�� �? 6��"��C��"�+�� +: �P� .>P'.C SP�
%P� S�.P: .C .PC.� BP� BP�R �P: %0PO� 6 A�: �� �P'.C
�P� HX - �, h8�� V�� %'M.< 6 �].�O� %'��+J
U�� H��+J dE�(� �/� ��, .+P4�I ��I �eP� >P'.C .,
6 %i1C��P� NP���� 9P� 6 m�P5 ��P� �'M�: - �7C �: W&/�
�%='�PJ K+P� �P�6A 6 �PE�I �P�6A +11`C LW1'�O� �%i1����
�%O1��PPPP�� U�)PPPP1� 6 H�PPPP�+J A�PPPP� �O�X VWPPPP1&/C
Q+1G 6 �0� -�T+�.��)'+C��.>i� )�(SP� n1C���
WPPJ 6 >PP'.C-V�PP?�< ePP] U�)PP1� Q+PP�T �PP: HX H�0PP'
QQ�� ��.
www.SID.irwww.MatlabSite.com | متلب سایت
Archi
ve o
f SID
��� �������� ��� ������� ���� ��r
d�$� �: >'.C N?.�/� n1C�� WJ 6-HX
k$�.�CV�?�< e] U�)1� %'��+J .�' Q+�T �: �0� .)�� B� +
�C/B9� ��DE�' FG' H0I��/-�� ���� J����8K�I� L��' 2�3,�'- 2��M$� �$)O(
Q9>9���
.��J N'�: B� �Q ���� .� ���$ ��E1� �: 6��L/d=15
6(L/d)nose=2.5 �� >O� HX n1C��� �R)�(Q H�0'
Q�PP� �PP� .>OPP� SPP� �S��+PP^ +PP; >PPD� 6 ��PP� �PP7:
�&] .� }(0� W1' �0� -���� Q.��� -6 �yb .�
6 %�.P< ��� B1C��� �0����P17;.� �P� b .P�
QA�' -+: %81D� n1C��� �0� -+1^ Q�� �/� �� .+T
W1' %81D� Q�p�)�����+^ +; b .� ���>i�)�(.
>9R9S$����'� H0I�� T
S� 6 %PI+< _P1�DC S� V�0���AX L�/' -+: �, U�)1�
%� �Q�� ��]�� hP8�� >P] V.P�15 �P�.� -+P� B� �'.C
�P5 �1)P: %�R+I L�^ �: 9���AX�S1) 6�PI�t/�+P��1E1� (
�F %P�R+I �A�P: 6 ��P� %�.P< .PD� +P: .P�? ND�x�
%E1� �T �R+I +�� .���'+: B� B�R �: B� �R+I 6 �+��,
�'�� -%� L�/' .� .6 3�P' LW1'�PO� �P��X -6 U�)1� S�
�P� H�)O� ��� 6 B� NE�I N�6A e� 6 Q�� �:�� .SP� �P:
��.� �a+< �T6 �P��+^ +; ��� g8� -A.� V.�15 -�?+P�
%P� QA�P' g8� -A.� H��+J �P'+1^ .>OP�)t(�P?.�/� �
WJ �1E, �: U�)1� S� ��� ���'.��+��)P� ��� Q+�T �: V�1
%� H�0' LW1'�O� ���X ���5 -6 Q�� �T .
>9U9���
>O�)�(�C��P� +�6 -�P�' Q ���P� .P� nP� SP�
%P� H�0' V�0���AX �PT .P: �E1P�6 SP� �%C .PF dP�+�
Bu., g8� �: �C Q�� ��]�� 6 %I+< .] �H��+J >:���
-W,+� �'��
www.SID.irwww.MatlabSite.com | متلب سایت
Archi
ve o
f SID
��� �������� ��� ������� ���� ��x
�C/Q9� ��� �����/ 24'��' ��)# � ����0�' ��,� ��:
�C/V9;�0��� �����/ 2�/H0I��$����'� SLA���C� �WX@ � ��� !��� !�'Y *� � ���'4 �- ��� K0�:��#��
S�+��, K�0�G ��R �/� . %I+< �'.^ �: B� �R �� -
%P� ��� -6 ���R +�F �8�' +P8; �P: �PJ.C �P: 6 ��10P'
��.� �TV.�15 -) 6�I�%E1� +P�� (%P� Q H.PC A - +P:
NEF��y/�%E1� +R {6+� ��� g8� -+��QL�P^ �: �R+I �: 6
�Q.(� >] �?+� >1�6+5 ��M QA�P' -A+P� -+P1^ +P, .
B� ��� .� Q � >��� ��P: Q+P� U1P' B� -6 V.�15 N�.�
+8;�6 +��1�'�� "�P'�: %�.P< .PD� -A.P� ND�F ��.�
�� .Q ���� -�&�W1'�i� �1E, �, �� +,� �: LAM S� Q��
9���AX)B� 6 ��1� 6+C ���� (�' �p' w�.C 6 %I+< H�^
Q�� ��]�� �� .
>9Z9��,� ��%����I�'� B[
'+C Q ���� �0� -�T+�.��) SP� Q�P� _P1�DC {.P' A
MPX5100 6MPX5050 �' .S��IQ�P��, �PT V .PF �P:
h�J %� >�? %E4��C 6 Q���, 6 ���, Q 6�PD����� 6y��
%E1� �; �: �:�/�±�F %� �, ���, . %�.p(��5 H��A SP�
www.SID.irwww.MatlabSite.com | متلب سایت
Archi
ve o
f SID
��� �������� ��� ������� ���� ��~
�C/\9,=� ]������ ��� �G'- �@ ��^� 2'�% ��-�� ����
�0P� V+P11`C �P: �T+�.��)'+C � �P7� �%PE1� �P1'�� 6 Q .P:
%J6+] �&'X S1:y/��Cy/���6 ��.�P: �T+�.��)'+C L��C
�P�.� BC +��.'�� n� 6 ��] ��5 B� B�R A >P=; _P1; -
Q�� Q+=1��R V�0���AX L�/' �'.
>9_9� ��DE�' `4'-7 � FG' H0I�� ����'�
C S� +P: n� A �_1�DPCL-818-HG Q�p�P� nP� 6
�'�� -+: Q�P� Q ���P� V�?�< KA +5 6 �=� �e] �P� .
L+' nP� �,+I H��+� �: H��W�T �� �; Q ���� .� W�
+: AA/D �Q V�?�< )'�,+� �: - +: �+P��, >:�; -�&
.< �:�=� 6 e] H��W�T ��, .>i�)�$k( .�' %'�P�+J
P: V�P?�< KA +P5 6 eP] U�)P1� �nPP� +�.�PC Q+P�T
�I �0� ����, H�0'%��T .
>9a9K��#�/ H0I��
-+PP: U�)PP1� A H�PP�+J -A�PP� �O�X S�+1E1PP� Q ���PP�
Q�� �� .U�)1� S� �P, �P�(�� wP�.C �V�P�1�DC WPR+� H
X�Q�PP� ��]�PP� 6 %PPI+< �PP; BPP1���� 6+ nPP� A >i0PP�� �
.� .�,�6+5 +P8; �P: +P7�� NP��X 6 �-A.P� W,+��� .' ��t�
�?+� �: - +=�E1� S1: 6 n� 6 +��1�'���r�1'�� �i?
�� .-+P: V�1F.�P] �P: +�0P1: %���P�X >P'.C ���P� � �P:
: VW1&/C ����+^ �R Q�� N=��D� Q.D' 6 .PJ.� -�T�8]
S� �'.^0���AXhJ+� �: �V� ]�[ .� �7J+� .
R9��'�?���4@ L� �'
_1�DC S� �0���AX V�� .Pj�� �P� �: >'.C %�E�(�
S1)I L�� Q�p0' ){(b�� �? "/�L�P/' �P� .S1P�6
www.SID.irwww.MatlabSite.com | متلب سایت
Archi
ve o
f SID
��� �������� ��� ������� ���� ���
��EI+� NE�I N�6A ���$�����6"�J H.�AX �P�
�0� h�A.C 6�"eP] U�)P1� BP�R �P: ��P� -6 �8�'
Q QA�' �T Q+1]� 6 -+1^��.6 B� 3�' �: ��7: NEI+�
�1%�.P< �17;.� �� HX �: >��� -�&p�E �PE�I -�P�6A 6
c.� �+,e� QA�' ��� o+< >R �0� Q+P1]� m��P�' 6 -+1^
�� .+T 6 �E�I ��6A +T ��%�.< �17;.��Q - +:
6 {6+P� �'�: -6 A [��1; wP�.�� .P< �P:���P: �P8�'
EF���-�T �P'�: g8� A dE�(� 6 L�P/' eP] �P� .�P17;.�
�8�' QA�' -�T �P: BP� �PR+I %�.P< >D� �: �J.C �: -+1^
>O� V6��C +<�]��M .P: V6�P��� -A+P� .�eP� �PR+I
L+' w�.C HX _1; >D� S117C 6 B� Q W� �+P��R - +P:
��6 �0� V�?�< �+1]� �: H��W�T �17;.� �B� >D� WP1'
�=���.A �'�: g8� A B� _1; NEF�� H +R }(0� -+:
+��.1)'��5 B��� _P1; �1): %8] )�P; �P:���/�+P��1E1� (
�� Q ����)QA�' ��� -+1^ +��.1)'��5 S��y�+��1E1� .P:(.
��.� @A�' �1): B� -�T 6 �'EF1=�P� UR �&'X �.S�+:�P�: �
6 �17;.� QA�' ��� ^-+1 ��Q�: 3)��� >PD� %P7;6 @.P'
��.� -�P8] - BP� -�T %,�P' �P: +P:+: �PR �P� y/�±
+��1E1� 6+:Q�� ��.
U9b��c0� �d'�' � e �
9(: �� _1�DC S� m���' :hP�A.C �H�P�+J -A�� �O�X
6 ��� -6 �0� QA�' -+1^ %P� �Pq -A+P� ��M .P�.SP�
X -+� S���u >F�I m���' 9��P�A �P� SP� A %Pi� �P,
.P� VM�PI �P1E, -+P: >'.C H��+J H .: ����X �V�0���AX
���+^ +; �1q�C 6 %:��A �� .
U9B9��� �4����C/@
-A�P� �O�X -+P: �_P1�DC S� A ��P� �.PI H�P�+J
S�+1E1� U�)1� Q�� Q ���� �� .V+11`C �: ��):6 K6 S�
P: .PT - �)O' }]�� +P11`C >P1� �%��Ppu -+P: 6 �P�
+11`C �R M�: -�&�?+� ��� +C���� %��pu VH6+P� +: �R
]�.[ >O� )y(PG�� -6 H�P�+J -A�P� �O�X m���' N
9���AX .� ��� Q�P� Q H�0' +�F NE�I N�6A �P� .
S� �>i� >��� @.� H ����)%<6+(� (�6A 6�HX�=)P'
�, �'�: �:}(0� [���� .:���D' {�7� >1� -�.� ��G��
�G�� -6 ��1�]� �EPF�� +P; �P'�: A �PJ 6 S1P7� -
���+^ �� .H��+J ��1I�' S� �.P� �05 ���PR %0P]+u
>i0� [��=)' HX >I 6 Q .:�� .L+' B�R �: W�CAD �6A �
@.� [ 6�I >������J QA�' �� -+1^ ��' �: �Rm�-+Pj'
)��/r�(%'.(�T %:.] �1): . .PJ.� BPu.R o��]
%� ��G�� �]�� -�8] �: v.:+� �'.C �6A��HX @.P' >iP�
.��J�G�� QA�' K6 �� 6���: ��6A -+1^ .S� m���'-+j'
�, Q�� l+(�� %<6+(� �.� �6�J A .P< �: �P: %P71=<
-6 �.� m���'�G�� �R .��J -�T V6��C % .-A+� ��M
�G�� -6 @A�' W1' ��6 >:�; +�.�C S� �� .
>O� )"(+�.�C S�+1E1� �6A �E�I �"H�0P' �J
Q�� Q �� .�P: >OP� S� �.� %�D�� H ��C L�? >P1�
�6A .J6�E�I o��] A6+: 6 ��� N6 M�P: @.P� NP�6A
�G�� S1��5 3J.� �, �� 9T�P, ��)P; �.P� V �P;
%� �?+� %=)' 9�W� 6 ��� %�M�: .� .�i7��:�9P(:
��6� 6��)H��+J �: 6 �1I�'(Q�� +C ��A �.� V �; ����
%� H��+J �?+� 9T�, Z?�: �, .� .S1P: �?+P� o��P]
�P/� ZP?�: WP1' ��P� S�+�A 6 %�M�: -�&��); nP� H�P�+J
%4+?�� �1�.C [��/1�' 6+1' +: -6%� .� .%C .F ��6A �,
�E�I �I A ̂ W: %�17� +� .� ���P� %'�P;.� g8P� A H��+J
P: �P: +^ 6 6 Q�P� �J �%P� .PJ6 V�P;6 3PEG �P, 6X
%� %0]+u H��� �/� Z?�: 6 Q .: H �����' .� .
>O�)�(A+��T v.8] b�� �? ��P� �P: >PI A Q�P�X
9���AX .� ��� -+: - �?%� H�0' �T �P�6A HX �R
�7: b�� �? V+11`C ��G�� @.� A 6 @.� l.P� <�)P=' %
�'�: -��: Q�� }(0� ��._1�DC S� - �? m���' �1E,
L+' -+J A W�MBTLNS �1=P� �P: �; �, �- �P? -A�P�
c.��� H��+J ����T -6 ����X V.F H �P�C -�PT �P: - .PD�
www.SID.irwww.MatlabSite.com | متلب سایت
Archi
ve o
f SID
��� �������� ��� ������� ���� ���
�C/f9/@�4����+W� �#�� ���'4 �- �g��- h�� ��� �'��� ��-
�C/i9�#�� ���'4 �- �g��- h�� ��� �'��� �4����C/@ _��-
X
Y
0 0.5 1 1.5 2 2.5
0
0.5
1
1.5
2
�C/ j94'0�% k�"G �g��- ��� �X�38 )4' ���� b��0��-�D �� (��- W� �#�� ���'4 �-
www.SID.irwww.MatlabSite.com | متلب سایت
Archi
ve o
f SID
��� �������� ��� ������� ���� ���
��M VM �7� A Q ���� +�6�' �A�'$�i=� 6 �,.�� -�T �P�u
��� %,.E:�� �:Q��X �']�[.
U9>9��� ��� ��,� l�4��
NE�I -��6A �nu., �0P� h�A.C %p�)P:6 %i1C��P�
�: -+��, A��.�� �? .V�� �+p� V �=? �: �P? +1��PC
�0� h�A.C -6 A��.�� �: ��):6��(0� 9��PJ -�T �P�M
-A+��� ]~[.V+11`C �, �/'X AA�6�E�I � _P1�DC S�
��� nu., �E�I -��6A � 6�D� �0P� h�A.C %i1C��P�
��� %81D� .1� L�? +p'�0' ��� 9��J -A+P� �P�M
�� .�&�C �S�+:��: %� +: �:P�6A V+P��hP�A.C -6 �PE�I
�0�Q�� ��] +5 ��.
>O� )�( �0P� hP�A.C - �? 6 %:+/C m���' n1C��P�
-6 �'�: H��+J �&J ��6A 6+�PF NPE�I Q H�0P'
Q�� �� .��); >O� S� S1��5 �17;.� � �0P� -�&] .P�
��� �'�: -6 n1C��� }(0�%���, .1ER �-�T .�'
�8] NE1� � �0� h�A.C�y P1ER N=P��D� �: � .PJ.� -�PT�8]
QA�' Q�� U� �]�� 6 -+1^ �P� .H�P�T �P, �P'.^ Q�P�
%� A - �P? 6 %P:+/C m��P�' .P�x / d 0=�PC x / d 12=
�' +p��i� �: %:.] [��=)' _:�8C .o��P] Q�P� Q�T�0P�
��� -�&�')x / d 12>([M���I H�P�+J 9��PJ >1� �:�P� �
�:+4 l.� .]+: Q .P� A %P��' - >P'.C -�PT)P:�>P1�
Q .� g8� %��F�'(�:+4 l.� 2�i7' �� �+P: �PG�� .EJ -
��� g8� -6 )Q .� �: .]+: A �5(��� ���=' V+� �� �
%P=1R+C �� 6 ��� -�&�' �0� 9�W� [��/1�' 6 -A+� ��M +:
�&'X A��.�: LAM ��- 6 -6 V.PF+�A H��+J �R ��
D�FN�(C �C��� �0� >1� �: �D�F -�&�' %O1 +� ���='
%� 9�W� �:��]�[.
EO� -�&)�$d� 6k( �0P� %81D� h�A.C n1C��P�
x / d 3=6x / d 6=U� �)P���� - �P? >I m���' �: 6
�Q��� .�6 Q�p�)P� )x / d 3=(- �P? >PI m��P�' �P:
m���' %'.P(�T %:+/C %:.P] [��=)P' �0P� hP�A.C %P�6 �
�)1' H ���� ���R %:+/C .L�? S� %P� H ��C +<�P] �P: �P'.C
�6A�H��+J �� >'.C -�8] ��� �]�� A %��' �- �O�+C �P:
Q�p�� %�.�7� ���: .S1P�s�T �P�E: �-�P8] -6 ��P� H .P:
3�' - .< %� +1��C e^ ] S�+�Ou.R �: �R �8 nP� -6+P1'
6 o+D' Z?�: 6 �/� %='�J �� A N�6Aβ%P� H��+J .P� .
>'.C S� - �, h8�� H��+J �1�1, �, �� +,� �: LAM
QA�' [�=; dE�(� b�� �? %,�PI �EPF�I m���' 6 Q�� -+1^
- �, h8�� H��+J ��' o+D' A�� ]��[.h�A.C m���'
L6 Q�p�)� �0�)x / d 6=(�P� �6 Q�p�)� �:�0� W1'�
>i�)�$k(.
>O� )��( %�.< �0� h�A.C -��6A NE�I$�PC "
�J Q�� U� �� .>1� �:�H ������ H .: %�z+P� H.C
+, �,Q �P�6A -�T �I �PE $ �PJ 0θ =��P: � �P7
w�+PP�PP�6A��PPE�I�PPJ � 180θ =��PP� >OPP�
)��$d� .( �0� -�&] .� Q�� �1=7C �17;.� 0θ =��P:
�6A 9�W����P� �E�I .P1� �P'�: %P� +P; 6 �P'+1^
�&'X A %��' %i1C��� �0� S�+:��: %� 9T�R �:�� .SP� �P��
�J.C >:�; �G�� -6 �&�C 9T�R Q .P: �'.�P� 9P(: 6-
�'�:)F.�(� ��� -�&�' %�.I [� (%� +��R .�.Q���5 S�
��P� NG�� �+�F+1G NE�I -��6A �, �� 3E8� S� ����
�'�: H ��C -�T +P: -6+P1' UPj? ��); - .D��P1�.C
%� ��,]~[.+4 �, �/'X A3� �0� -6 �'.�P� 9P(: -
A6-�� NE�I �nu., U,�PE�I NP�6A A +1��PC Q .P: 6 �1)P:
+�F �: B� W' ��� - .�? -6+1' HX A >F�I �PJ.C >P:�;
'6 Q .= S� Q���5 : �'�: �0� WR+� H�� B� W' Z?�: �-.P�
�E�I -��6A �G�� %� .� .�'�: -�&�' � �0P� n1C��P�
+PT -+: %,�P' �PE�I �P�6A 6 9�WP� �P���� �P��>iP�
)��$d� .(�E�I -��6A �6�$ �0P� hP�A.C WP1' �PJ
�PE�I �P�6A m��P�' �P: �:�0P� dE�(� -�&T�p�)� %81D�
+�F�-�&Ei� )�$d� 6k(�P� Q 6X �P���� SP� �P,
'Q�0 ��.
>O� )��$k(6A 6 -+: �0� 3�+4 %�.< h�A.C��
www.SID.irwww.MatlabSite.com | متلب سایت
Archi
ve o
f SID
��� �������� ��� ������� ���� ���
�C/m9� b��0� �I��=� ���� ��� ��,� l�4�� �-�D � ��
d� $�17;.� x / d 3=k$�17;.� x / d 6=
�C/T9� l�4�� �-�D � �� � b��0� �I��=� �"� � ��,��- W� �#�� ���'4 �-
�E�I�6"Q H�0' �J Q�� �� .H��T SP� �P, .<
�&Ei� %� Q�T�0� .��W� 9��J 6 -�6A �ZP?�: �E�I
+11`CV-6 %Ou.R ��=)' CpQ�� 6+11`C S� V NPG��
�� +�01: �'�: .>i� �: �)���� )��$d� (�P�6A 9�WP� �
I?�: �E�Z9�W� |Cp|�PG�� �.P< 9�WP� SP� 6 Q�P�
+: -6+1' �0�%� �/� -+�01: -%��I ���, hP�A.C �P,
�'.�� N'�: �.< n1C��� �0� %�.)PD� +P11`C >iP� -
Q +i' ���-�&Ei� )��$k 6 d� (.
>O� )��(%81D� h�A.CCpA -+: -��6 NPE�I �6"
�J � U� Q�6V+11`C �'6 �: �:�0� ��6A %E=; -�T���
>i� )�$k 6 d� .(�6A 9�W� �:�%P� �Pj�' �E�I �PR 6
��P0� 3�+4 �P � 1: �'�: +�AP0P .� +�.4.� S� P {.
www.SID.irwww.MatlabSite.com | متلب سایت
Archi
ve o
f SID
��� �������� ��� ������� ���� ���
d�-�E�I ��6A 2,2α = −�J
k-�E�I ��6A 4,6α =�J
�C/Bn9�X�� ��,� l�4�� ��� ����
EOPP�-�& )��$l 6 dPP� (L.PP� 6 �6 Q�p�)PP� %PP�7� >PP:�;
Q�T�0��� .�: �� A �6A ��E�I ��: +^ %��T Q �P: [�=; �,
Q g14.C �&'X >1i0C �P� A NP1I�' �P: 6 Q�P� �PJ �PG��
%� K+�)^ �'�: -�&�' ��� :����.H.u S��: +^ �T� �: >P1
_1; H ��C L�?H �����' �'�: 6 H��+J �0� h�A.C H ��C ��'
9(: .1� �'�:: �%� UT ��'A�-�&Ei�)��6��(]x[.�P:
�+p�' %81D� -�T �0� h�A.C -+1^ %� W1' H.C -6+1' 3�+4
%ED� - .�? �=��D� +,.
U9R924'��' �4� ��o ��:
���(4 V+11`C��M+�%�.< �&J -A ��� -��6A
dE�(� NE�I .� _1�DC S� W1' %� +:���+^ +; �� .
www.SID.irwww.MatlabSite.com | متلب سایت
Archi
ve o
f SID
��� �������� ��� ������� ���� ���
��� -���� x / d 3=
k-�17;.� x / d 6=
l-�17;.� x / d 11.5=
�C/ <<9��,� l�4�� �"� � �#�� ���'�4 �- ���� ���\�i�-�
www.SID.irwww.MatlabSite.com | متلب سایت
Archi
ve o
f SID
��� �������� ��� ������� ���� ��t
A dPE�(� >F.� B� NE1�6 �: >R �0� � .j�� S� -+:
QA�' �'�: g8� Q�� -+1^ 6+: hP�A.C HX 2�� b�P� �P?
Q�� �=��D� Q�p�)� +T �� . -�&'��+J L��C c.��P� V.PF
-.EJ +T V.�15 ��.� �:+4 l.� n� %P� ���5 - .�? - �P�X .
�S�+:��: b�� �? ���: %ED� �:Ca�PF �17;6 S� �: �J.
6�=��D� +, . 9��P�AX ��� -6 H��+J -A�� �i�X m���'
-�&EiPP�)x6~( �PP/� +p'�0PP' PP��:+PP4 l. - .PP�? -
l.P� �P: �PG�� A %�, �EF�� �, �� �'�: -.EJ ��);
%� >��=C >��� .� .-+: o6+P7� �P8: A >PR �0P� �=��D�
%E� V.�15 ��.��" ]��[Q�� Q ���� �P� .N=P��D� -+P:1P
)%E� V.�15 ��.� �8: A�1' .� %O1C��� �0�(: ��M�P: >1�
�M 3�+�C H��+J A��.�� �? H .:�-A+� : @A�' ��P�� �PR
��]��[.
H��T �, .< ��.� �� Q �� UPT V.�15 -�T -��P� ��P�
���)T . �S�+:��: +TA�6�E�I ���&'X W1' AX H��+J �: H��T
��6A %�+1^'�.6 �1746 o��] QA�P' -�8] SP� -+P1^
��.� �6A �C �T��E�I �-+P: %P�6 ��P� z�P�G >:�; �J
���: +�^ W: -��6Am���' a�F +, ]�[.
>i� )��(Q ��P� 6 H���P1u �1�1, �P�.� - eP^ -�PT
H�0' n� V.�15 Q�� Q�� .H��T >iP� SP� �P, .<
%P� Q�� Q ��P� V.P�15 �P�.� wP�6 k+P5 � .P�)�(S�+P�&:
QA�' �P�.� SP� �,+I +�A ��� �'�: -6 -A+� ��M +1^
��� .D� +: .�? -��� [��1; �E�I -��6A %���C�� .
S�+:��:�QA�' �?+� [��/1�' 6 �0� P�.� S� w�.C Q�� -+1^ �
�P� Q�p�)P� H��T -A+� ��M H6 �?+� h�A.C o+7� .
���:�J ���.� +��� %��J QA�' �?+� 6 Q .=' %?�7� �T -+P1^
-A+� ��M �?+� _1; V+11`C +p'�0' Q�� �)P1' A�P1' 6
V�I�F �:.
>i� )��(QA�P' -A+P� �P�M >P1�6+5 �Q�P� -+P1^
n� %8�6 k+5 �� w�.C)�.��V.P�15 -�PT~6�6�(
Q�� Q H�0' +�F �E�I ��6A �� .�?+� V+11`C �:
�� ��.� A Q��X -�T~6�H�)Pi� [���, �P' +p'�0P' �P,
QA�' >D� H��+J H ��C +�PF �E�I ��6A Q�� -+1^
�� �J .
-�&EOPP�)���PPC �"(�PP&�C �PPq �PP: wPP�6 k+PP5 m��PP�'
%� ��'A +5 �� -�&EO�)���C(��.� N�T m���' V.P�15 -�PT
A+P��T v.8] V .F �: %P� H�0P' �P�T .>OP� )��(�
�6 Q�p�)� {��C 3)I +: b�� �? V+11`C)NEPF�����
�PG�� @.' A -+��1E1� (V6�P��� NPE�I -�P�6A �$�PC ~
�J Q�� U� �� .�>iP� S� %P� �PjI�� �P: �PR .P�
� �6A 9�W����(4 �E�I ��M %� 9�W� -A+� �P:�� .�P�
N=� b�� �?��M -A+� �� Q�P� a.P46 �P: �&EOP� SP�
%� .� .�, .� �J.C b�� �? -A+� ��M N8�' S� A �?
+�01: W1' AX H��+J b��Q�� �� .�: +11`C S� >P1� 9�WP�
%�+J %: 6��M �?+� 9T�R �A -�T S�+�� .V �=? �:
�+p� RH�� U �?+� S�+P�A 9P(:M-A+P� �P� 3PJ.�
9T�, %�+J %: - .=? AQ�P� 9(: S� �P: 9T�PR SP� 6
�?+� 9�W�n� W' �M N=� �%� H+=J -A+� .�.�)P���� A
-�&Ei�)��$k 6 d� (%� Q�T�0� �P�6A 9�WP� �: �, .�
� +�01: W1' -A+� ��M ���(4 ��E�IQ���.
�:�0� %��&1�D�� >O�)�r(>OP� )�y(Q�p�)P� -+P:
L6 )x / d 5.75=(Q�PP� Q H�0PP' �PP� .�PP&1�D�� SPP� �
���(4��M -A+� �6 Q�p�)� -�&E1�6+5 �: �=)':�V .F
�jI�� >:�; -����� 9�W� �� .�S1�s�T P� 9�WP�P�?+
=���P�M P� P-A+ SP� Q�p�)P� 0PuP1p�PP� +C+PQ��P��
Ei� -�& )�y$k 6 d� .(
>O� )�"(�QA�P' m���' Q�P� -+P1^ L.P� Q�p�)P�
)x / d 11.25=(Q 6XQ�� �� .���(4 �, .� �J.C �P�M
-A+� -+�01: �� Q�p�)� S� ������� . U&� ��i' ���
A �P: �, �� HX Q�p�)� S� �PE�I �P�6A �P� �PJ 6 �PC�
9�W� ���(4����� 6HX A �P5 %P� 9T�PR �P:��.+P�A ��P:
�6A 9�W���E�I � -.�EI �: +^ ��J n� �PG�� @.P'
6 �/� I�'P1���� -�&�'A(:P� 9P .1 �J �'�: Q�P�
61`C -A+� ��M >1�6+5P� +1P%�T ]�t.[ o+< Ap� P�+�:
www.SID.irwww.MatlabSite.com | متلب سایت
Archi
ve o
f SID
��� �������� ��� ������� ���� ��r
�� ���J�� �G�/ ������8 p���
d�$Q ��� V.�15 �
k$Q ��� V.�15 ~l$Q ��� V.�15 �
�C/BV9W� �#�� ���'4 �- �4� ��o ����7 ��-
www.SID.irwww.MatlabSite.com | متلب سایت
Archi
ve o
f SID
��� �������� ��� ������� ���� ��x
d� $�E�I -��6A 2,0,2α = −�J k$�E�I -��6A 4,6α =�J
/�CBU9�4� ��o ����7 ��' 2�30I�' �-
d� $�E�I -��6A 2,0,2α = −�J k$�E�I -��6A 4,6α =�J
�C/BZ9L�- 2�30I�' �- �4� ��o ����7
www.SID.irwww.MatlabSite.com | متلب سایت
Archi
ve o
f SID
��� �������� ��� ������� ���� ��~
d�$�E�I -��6A 2,0,2α = −�J k$�E�I -��6A 4,6α =�J
�C/B_9��o ����7 �4� �-L�� 2�30I�'
�E�I ��6A 9�W� , [�/� �C -A+� ��M �=� �?+� U%P� .P� .
�U���.P� �P�M ���(P4 �P� 3=P� �: +� S� [M���I*δ6 �
A�1' .� %�+J %: .=? [��/1�'�� .
>O� )��(1�D�� -�&��M -A+� ��� -6 )�P� +PT
�6A Q�p�)��NPE�I"�PJ ( WP� L+P' BP�R �P: CAD
l+(�� Q�� �� .���(4 z+� �:��M +�F -A+� �.P'
�G�� �Q�P� Q�' e^ %�D�� B� �8�' �&u S� A +p'�0P' �P,
�� �P�M �PC �PG�� @.P' A -A+P� x / d 11.25=�P� .�P:
���(P4 �P� �P'6 6 �&1�D�� %� +: �P�M -A+P� %P� H.PC
��� QA�P' v�P�' 6 �PE�I -��6A L��C H��+J �, �-+P1^
Q�� ����X�� ����' 6[�P=�+�C ����X �: L X A H��+J A >P=;
Q�p�)� S1�6��EF�� A +��, -����PG�� @.' A +��1E1� �
Q b �� .H +R �15 -+: >D� _1; S� �P� LAM ��P��'
H�P�+J �PR PC �PG�� @.P' A�x=110 mm .P< �P: >P��,
-A�� �O�X+, �,P�6A V+P� �V .F S� �-6 �PE�I
0� W1' ����' >D� %� .& .� .�P, �P�u +TA 6-�P� NPE�I
Bu.R:�J �%��J �jI�� >:�; ��P��' >PD� -)+P11`C �P:
�E�I ��6A (:�%�' .J6 ��X %�6 �915 %P� %P�1: �P, .P� �P:
�6A 9�W�� �E�I ��P� .P1���PG�� �P: ��P��' NP8�'
��� 6 +�O� W'��6� 6)H�P�+J �: 6 ( 6 �PG�� A +PC
.�]�r.[
>O� )��(A+��T v.8] �0� )@.� �05 - .P�?(�
QA�' A Q�� -+1^�t�.�NV.�15 �P�6A 3P1C+C �:�NPE�I
6 +�PPF"�PPJ �6 Q�p�)PP� )x / d 2.75=(Q H�0PP'
Q�� �� .���(4��M -A+� �6A �>P1� �P: �+�PF NPE�I
H .: Bu.R��:�Q .P=' �P�� >P:�; a.46 P�6A %P�6 �"
�J a.46 �:}(0� Q�� �P� .H�P�T Q�T�0P� �P, .P<
%� ��� H.�+15 H��+J H ��C L�? � .� �E�I ��6A~�J
�: �=)' �J +�F �� +�01:.C L�? S�: [M���I H �� �>1�
��P� H �P�C L�? %,�')�]�P� �P; L�P? A %P��' (�P� 6
Q �: W1' [�=; �, �� - �, h8�� >] H��+J ��6A o+D'
�� ZD: HX ]��[.
www.SID.irwww.MatlabSite.com | متلب سایت
Archi
ve o
f SID
��� �������� ��� ������� ���� ���
�C/Ba9���� ��� �- �4� ��o �'��q� �$ $� �#�� ���'4 �-_��-
d�$A�6��E�I 0α =�J k$A�6��E�I 6α =�J
�C/Br94'0�% k�"G �s ��,� )��� t�� u,7 �'(�- ���� v'�' x 2.75d=
�C/BT94'0�% k�"G �s ��,� )��� t�� u,7 �'(v'�' �- ���� �#�� ���'4_��- ��-x 5.75d=
www.SID.irwww.MatlabSite.com | متلب سایت
Archi
ve o
f SID
��� �������� ��� ������� ���� ���
d�$A�6��E�I 4α =�J k$A�6��E�I 6α =�J
�C/>[94'0�% k�"G �s ��,�)��� t�� u,7 �'(�- ���� v'�' x 11.25d=
d�$A�6N�E�I 6=α�J 675.5=dx
k$A�6N�E�I 4α =�J 6x 11.25d=l$6A ���E�I 6α =�J 6
x 11.25d=
�C/>B–4'0�% k�"G���� v'�' x�� -�D
www.SID.irwww.MatlabSite.com | متلب سایت
Archi
ve o
f SID
��� �������� ��� ������� ���� ���
�C/>>94'0�% k�"G�- ���� v'�' x�� -�D �#�� ���'4_��-x 11.25d=
>O� )��(!A+��T v.8] �M�: �:�0� L6 Q�p�)� -+:
�6A �NE�I "�J Q�� U� �� .�, .� �J.C >P1� �P:
9�W�x/d����(4 ��M Q�P� +�0P1: -A+� �P� .�S1P�s�T
L�? H��+J H ��C P: ��P� %Pi� W' >iP� SP� �3PC+�
1: >iP� A +�0 )��(�P� H �P�C L�P? 9�WP� HX >P1� �P,
�: +^ Q�p�)� S� -.�EI -�T) .,eP� >P�M +P: Q6�P? (
��.
>OP�)�(�A+P��T v.P8] P�6A �0P��NPPE�I �6"
�J -+: L.� Q�p�)� %� H�0' �T .+PT H�P�+J H ��C
6 %,�' ��6A �� ����� .=&: .%� �jI�� .P� �PR >1i0PC
�: +^ �'�: -6 -.�EI -�T��6A NE�I r{6+P� �PJ 6
�6A �"%� >��, �J .��>i� )�$k.(>P1� �: ���=�
Q v��' UR ��=)' �7C �]�� ��A NEF�� 6 - +: BP� -�PT
�+p��O� A�: +^ �T���R -6+� ���)1' .�S1P�s�T >OP�
)�$k(H ��C L�?+^�: �TQ�� %P� .P� �P��� [ �P/� �P,
�� %E=; ZI�=� .
>O� )�$d� (A+��T v.8] �Q�p�)P� b�P� �?
�6A 6 L6 ��E�I "�J Q�� Q H�0' �� .WP1' >OP� S�
�:�0� >O�)��(��' H ��� �� +j' �: 6%��, �� -A+� ��M
��� �� H��+J %,�' A +��1(4 -A+� ��M �P� �Pu �
�� .EO�-�&)�$l 6 k(A+P��T v.8] b�P� �P?
L.� Q�p�)�6A-��6 NE�I�6"%P� H�0P' �PJ �PT .
>O� )�$k(>O� ��'�� W1' )��(� -M�:�: +^ -6 -�T
1I�' B� �'�:��?+�+5 )�P: M�P: >PR �0P� (%P� Q�P� .P� .
s�T1��S�6A �NE�I "��J 1I�' B��:�?+P�+5 BP� �
6 S1:Q�� >1i0C -.�EI N: +^ �� .
>O� )(v.P8] �P: � �P7� ��?+P� A+��T v.8] �
�0� A+��T >O� )�(�Q�� U� %P� H�0P' �, �PT H�P�+J
H.�+15 H �P�C A �'�: [��=)P' �P� .P]+: %:.P] .SP�
>O��+1)P� �P: +^ -�PT >1i0PC -6 Q�P� : �P'�: +P�& Q�P�
%� .�.S� >1O0C �: +^ �TPC��6 6+P1' -6 %&J.PC >P:�; +1
6��0^ -�T �+P��R a.8P� 6 �P'�: %O1��P�� 6+�X ��P� 6
%���&� -�&�6 +� �: � �7� �&'X +��6A��PE�I k.)PD�
%� ���, ]�x[.
Z9� �0� ��:
_1�DC S��H��+J b�P� �? �: ����X V.F c.���~/�
�'�: B� -6 6�� <>P�. �PE�I -�P�6A �$�PC ~�PJ
6 �P�+^ +P; %� +: .� P: X �H�P�+J -A�P� �O� K6 �P:
S�+1E1� >O� ���6A 6dPE�(� NPE�I -��6A �G�� @.�
QA�' m���' �: 6 -+1^-+j' �)���� �P� .o+P< A +Pp� ��P�M
www.SID.irwww.MatlabSite.com | متلب سایت
Archi
ve o
f SID
��� �������� ��� ������� ���� ���
W1' @.� A �7: H��+J H�1� 6 -A+�w�.C A�� �O�X 9���'
Q ��.s�TS1� ��� g8� -6 %O1C��� �0� h�A.C ��"
�PPE�I -�PP�6A �PP8�'$�PPC "��PPJ L�PP^ �PP:�PPJ �
QA�' Q�� -+1^ �� .m���' _1�DC +p'�0' �E�I N�6A UR +1��C
�6A 6�θ)%81D�(�P�6A � 6�D� �9��P�AX .P� �PE�I �
�0� 3�+4 -6 �.< 9P(: �'.�P� �P� �P'�: - .�P�
C-+P11`C �E�I ��6A �: 3����� ��� �G�� -6 �0� h�A.
%� 2.)D� ��R.
PP�M� 6 V6�PP��� %�.PP< Q�p�)PP� �PP� H�PP�+J -A+PP�
NE�I -��6Ac.� +,e�QA�' �>1�6+5 6 �� -+1^��M 6 -A+P�
A+��T v.8] b�� �? 6 >R �0�H.�+15 �P�X �� �: ��� .
%� H�0' m���' � �: �R �T �6A 9�W��.< -6+015 6 �E�I
�'�:����(4 ��M %P� 9�W� -A+� �P:�� .A P�6��PE�I ~
�J ��: +^ -6 -�T �P'�: ��P� -�P&�' %P� Q�P� .P� .
V+11`C -�&1�D�� �?+� �P�M -A+P� �P��� H .P: ���P�X
H��+J Q�p�)� �� +T QA�' -+1^�� .H��+J -A�� �O�X
A %0(: �G�� -��: %P� H�0P' ��)P; SP� �PR �PT
�� L X H��+J .�S�+:��:%��P�M ��P��' �PR A 2�PI H.C
%P� �=|� �0� H�� +^ �R %��J ��G�� -�&�' -A+� .P��
�� Q ��� c��C.
��'-��Y � C,�
�� �1E, A H�^�' �p' H �, �' ���� 6+�X WR+� P1 �P; B
)I L�� Q�p0' S1){(>1� �:6 H6+P� -�&P��C - �PO�T
�'�/� L�/' V�0���AX S� 6WP1' AV�?�)P� 6 �P���I
%: - 6�P�� 6 9T6\P5 �KA.�X �'6�7� �� h���PF H��A�P�
���.T A [����&' 66 d�+� %�7�F Q�p0' V�P�1�DC �'6�7�
%'�=1�0P5 >P1� �: -+;�: �1&� h���F PT-�%��P� _P1�DC SP�
��1�F%� +i0C 6 - Wp���� �' �,��.
���� 2;'�
1- Schilerian 2- computational fluid dynamic 3- test case 4- SOSE (second order shock expansion) 5- leeward 6- transition
7- Rake 8- multi-pelexer 9- traversing 10-transducer 11-potentiometer 12-curved shock
13-windward 14-cross flow 15-error bar 16-Rayleigh pitot tube 17-boundary layer edge
l'�
1. Fleeman, E.L., Tactial Missile Design, AIAA, 2001. 2. Cebeci, T., “Three Dimensional Boundary Layer on
Missiles,” Tactical Missile Aerodynamics, Vol. 104, pp. 723-777, 1986.
3. Loposer, J.D., “Average Skin Friction Coefficients from Boundary Layer Measurements on an Ogive-Cylinder Body in Flight at Supersonic Speeds,” NACA-RM L52K28a, 1953.
r.%'�8EPPP��L. .�%EPPP4���a.��PPP1'�T+��k.�6- 6 �{.�
”�.P��C BP��: 6 BP1���� 6+�X ��� %:+/C �7��8�“��+0P'
%�E?$����� %0T6\5 ��� ��Q ��� �������.
5. Moore, F.G., “Approximation Methods for Weapon Aerodynamics, ” AIAA, Vol. 186, 2000.
6. Perkins, E.W., and Jorgensen, L.H., “Comparison of Experimental and Theoretical Normal-Force Distributions (Including Reynolds Number Effects) on Ogive-Cylinder Body at Mach Number 1.98,” NACA-TN 3716, 1975.
�.%'�T+� - �:XA+:�L.�”H�P1� %P:+/C �7��8� c.��P� H�P�+J
>P�.< 6�P� �P'�: BP� �.PI V.F�“%P���&� Q�O0P'
�d�+P� %�7�PF Q�p0' ����.T �P� %P���� �R ���P� �
���.
www.SID.irwww.MatlabSite.com | متلب سایت
Archi
ve o
f SID
��� �������r�� ��������� �t�r ���
8. Pope, A., High Speed Wind Tunnel Testing , John Wiley and Sons Inc., 1966.
�.- �1I�L.�%�1j?�{.�6%=1< %�T �L.�”�1=� H��+J -A��
c.��� ���X V.F �: 6�� L�)J �.I ��0P5 �P1I�' L���'
%;�P=8'+1G %,.PE: A+P� 6 %,.E:�P�u �i=P� A Q ���� �:�“
��+0' %�E? $6\5T%0���.T 6 n1'�i� ��EJ�Q ��P� ���
+� ���r.
��.- ����L.�” �: >'.C - �R h8�� H��+J �1�1R %� +:
S1)I L�� Q�p0' ){(�“H���5 ��� %���� �, ���' Q�O0'
�d�+� %�7�F Q�p0' ����.T %���&����� .
11. Anderson, J.D., Fundamentals of Aerodynamics,McGraw-Hill, 2nd Ed., Singapore, 1991.
12. White, F.M., Viscous Fluid Flow, McGraw-Hill, 2nd
Ed., Singapore, 1991. 13. Soltani, M.R., Taiebi-Rahni M., Heidari, M.R., and
Farahani, M., “Flow Measurements Around a Long Axisymmetric Body with Varying Cross Section,” AIAA Paper 2005-50.
14. Carros, R.J., “Effect of Mach Number on Boundary-Layer Transition in The Presence of Pressure Rise and Surface Roughness on an Ogive-Cylinder Body with Cold Wall Conditions,” NACA RM A56B15, 1956.
15. Mendenhall, M.R., and Perkins, S.C., “Vortex Cloud Model for Body Vortex Shedding and Tracking,” Tactical Missile Design, Vol. 104, pp. 519-571, 1986.
www.SID.irwww.MatlabSite.com | متلب سایت