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Page 1: Figure A fully threedimensional sim - ITUnas/images/tezintamami/a01_4_2.pdf · Figure A fully threedimensional sim ulation of the in teraction of nine equal sized bubbles Time progresses

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Figure ����� A fully three�dimensional simulation of the interaction of nine equal

sized bubbles� Time progresses from left to right� top to bottom� The

nondimensional time� t�� is equal to ��� �� ��� �� �� �� Thenondimensional time is scaled by a�Ur and velocity is scaled by reference

velocity� Ur� Computational domain size is x�a � �� y�a � � and

z�a � ������

Page 2: Figure A fully threedimensional sim - ITUnas/images/tezintamami/a01_4_2.pdf · Figure A fully threedimensional sim ulation of the in teraction of nine equal sized bubbles Time progresses

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Figure ����� Velocity �eld for selected frames from the fully three dimensional sim�

ulation of nine�bubble interaction� The velocity �eld is shown at every

other grid point in the middle plane of the computational box in y di�

rection� Time progresses from left to right� The nondimensional time�

t�� is equal to ��� �� ��� �� �� �� The nondimensional

time is scaled by a�Ur and velocity is scaled by reference velocity� Ur�

Computational domain size is x�a � �� y�a � � and z�a � ������

Page 3: Figure A fully threedimensional sim - ITUnas/images/tezintamami/a01_4_2.pdf · Figure A fully threedimensional sim ulation of the in teraction of nine equal sized bubbles Time progresses

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Figure ����� Velocity �eld for selected frames from the fully three dimensional sim�

ulation of nine�bubble interaction� The velocity �eld is shown at every

other grid point in the middle plane of the computational box in x di�

rection� Time progresses from left to right� The nondimensional time�

t�� is equal to �� �� �� �� �� ��� The nondimensional

time is scaled by a�Ur and velocity is scaled by reference velocity� Ur�

Computational domain size is x�a � �� y�a � � and z�a � � � �

Page 4: Figure A fully threedimensional sim - ITUnas/images/tezintamami/a01_4_2.pdf · Figure A fully threedimensional sim ulation of the in teraction of nine equal sized bubbles Time progresses

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Page 5: Figure A fully threedimensional sim - ITUnas/images/tezintamami/a01_4_2.pdf · Figure A fully threedimensional sim ulation of the in teraction of nine equal sized bubbles Time progresses

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Figure ����� Temperature contours for selected frames from the fully three dimen�

sional simulation of nine�bubble interaction� �� equally spaced contours

are shown in the middle plane of the computational box in x direction�

Time progresses from left to right� The nondimensional time t� is equalto �� � �� � �� ��� The nondimensional time is scaled by

a�Ur and temperature is scaled after subtracting a reference tempera�

ture by arT�� Computational domain size is x�a � � y�a � �and z�a � ������

Page 6: Figure A fully threedimensional sim - ITUnas/images/tezintamami/a01_4_2.pdf · Figure A fully threedimensional sim ulation of the in teraction of nine equal sized bubbles Time progresses

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