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Naval Postgraduate School (ifapplicable) 31 Naval Postgraduate School
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Program Element No Project No Task No Work Unit Accession N
UNSTEADY AIRFOIL FLOW SOLUTIONS ON MOVING ZONAL GRIDS
11 Title (include security classification)
2 Personal Author(s) Antonio M. Cricelli
13a Type of Ren -' 13b Time Covered 14 Date ofReport (year, month, day) 15 Page Count
Master's TheSiS From To 1992,December,17 147
6 Supplementary Notation The views expressed in this thesis are those of the author and do not reflect the official policy or position
of the Department of Defense or the U.S. Government.
17 Cosati Codes 18 Subject Terms (continue on reverse ifnecessary and identify by block number)
CFD,Unsteady Flow,Zonal Grids
Field Group Subgroup
19 Abstract (continue on reverse ifnecessary and identify by block number)
Investigation of subsonic and transonic steady and unsteady flowfields over airfoils is an active area
of current computational and experimental research. The performance of rotary wing and fixed wing
aircraft can be enhanced by taking advantage of unsteady phenomena such as dynamic lift. However,
several undesirable effects have prevented designers from taking advantage of these concepts. In the
past few years many advances have been made in algorithm, development for the numerical solution
of the Euler and the Navier Stokes equations. In this study, these new techniques are applied to
body fixed zonal grid approach. This zonal approach is more computationally efficient in solving the
governing equations than previous approaches, and has certain advantages over the standard single
moving grid approach. The zonal grids consists of two grids, one being the inner grid which is fixed
to the airfoil, and the other being the outer grid which extends to the far field or to a specified outer
boundary. The inner grid is allowed to rotate with the body, while the outer grid remains fixed. The
thin—layer Navier—Stokes equations are solved for inner grid, and the Euler equations are solved for
the outer grid. Communication between the two grids is accomplished by interpolated the flow
quantities at the zonal interface. Solutions are obtained for flows at fixed angles of incidence, and for
unsteady flows over pitching and oscillating airfoils. The computed results are in good agreement
with available experimental data.
20 Distribution/Availability of Abstract 21 Abstract Security Classification
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Max F. Platzer (408) 656 - 2058 AA/P1
)D FORM 1473,84 mar 83 APR edition may be used until exhausted security classification of this page
All other editions are obsolete Unclassified
Approved for public release; distribution is unlimited
Unsteady Airfoil Flow Solutions on
Moving Zonal Grids
by
Antonio M. Cricelli
Computer Engineer, NPS
B.S., Penn State University, 1987
Submitted in partial fulfillment of the
requirements for the degree of
MASTER OF SCIENCE IN AERONAUTICAL ENGINEERING
from the
NAVAL POSTGRADUATE SCHOOL
December, 1992
ABSTRACT
Subsonic and transonic steady and unsteady flowfields over airfoils are inves-
tigated with the numerical solution of the governing equations. This study aims to
enhance the performance of rotary wing and fixed wing aircraft by better understand-
ing and by taking advantage of unsteady phenomena such as dynamic lift. In the past
few years many advances have been made in algorithm development for the numerical
solution of the Euler and the Navier Stokes equations. In this study, these new zonal
techniques axe applied. A zonal approach is more computationally efficient in solving
the governing equations than previous approaches, and has certain advantages over
the standard single moving grid approach. The zonal grid consists of two grids, one
being the inner grid which is fixed to the airfoil, and the other being the outer grid
which extends to the far field or to a specified outer boundary. The inner grid is
allowed to rotate with the body, while the outer grid remains fixed. The thin-layer
Navier-Stokes equations are solved for the inner grid, while the Euler equations are
solved for the outer grid. Communication between the two grids is accomplished by
interpolating the flow quantities at the zonal interface. Solutions axe obtained for
flows at fixed angles of incidence, and for unsteady flows over pitching and oscillating
airfoils. The computed results are in good agreement with available experimental
data.
m
TABLE OF CONTENTS
INTRODUCTION
I. 1
BACKGROUND
A.
1
PURPOSE
B. 4
GOVERNING EQUATIONS
II. 6
CONTINUITY EQUATION
A. 6
MOMENTUM EQUATION
B. 6
ENERGY EQUATION
C. 7
TURBULENCE MODEL
D. 9
E. TRANSFORMATION TO GENERALIZED COORDINATES *11
. . .
THIN LAYER NAVTER STOKES EQUATIONS
F. 13
SOLUTION METHODS
III. 15
A. ZONAL GRID GENERATION 15
NUMERICAL SCHEME
B. 16
BOUNDARY CONDITIONS
C. IS
IV. RESULTS AND DISCUSSION 22
STEADY STATE SOLUTIONS
A. 22
1. Inviscid Test Cases 22
a. Case 1. Baseline Grid: 81x40 Inner and 81x22 Outer . . . 22
b. Case 2. Baseline Inner Grid With a 41x22 Outer Grid 25
. .
c. Case 3. Overlap Boundary Set to 1 Chord Length Away
From Body 27
d. Case 4. Overlap Boundary Set to .75 Chord Length Away
From Airfoil 29
iv
