(october 1969) - nasa · summary of progress in 1972-1973 and proposed research for 1973-1971* a...
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NASA NOTICE FOR HANDLING PROPOSALS
(October 1969)
This proposal shall be used, or duplicated, only for NASA
evaluation purposes and this notice shall be applied to any
reproduction or abstract thereof*
Disclosure of this proposal outside the Government for NASA
evaluation purposes shall not be made unless the policy and
procedures prescribed by NASA Procurement Regulation 1.304-2(f),
including the requirements for approval and for an arrangement
with the outside evaluator prior to disclosure, are followed.
The restrictions contained in this notice do not apply to
technical data or business information obtained from another
source without restriction.
RESEARCH PROPOSAL SUBMITTED TO THE
NATIONAL AERONAUTICS AND SPACE ADMINISTRATION
BY
NEW YORK UNIVERSITY
COURANT INSTITUTE OF MATHEMATICAL SCIENCES
251 MERCER STREET
NEW YORK, NEW YORK 10012
NUMERICAL DESIGN OF TRANSONIC SHOCKLESS AIRFOILS
Principal Investigator
Name: Paul R. Garabedian
Title: Professor
Social Security # 565-^4-9568
Renewal of NGR-33-016-167 (NYU ACCT. # 0-57^3-0^0)
Starting Date:Sept. 1, 1973 Duration:12 Mos. Amount Requested:$100,000
Residual funds expected to be on hand -0- as of August 31» 1973
Other support - None
Approval Signatures:
Principal Investigator Director
Name: Paul R. Garabedian Peter D. Lax
Title: Professor
Signat ure:
Telephone: 460-7359 460-7421
March 26, 1973 March 26, 1973
Continuation of Grant NGR-33-016-167
Proposed Budget
September 1, 1973 to August 31. 1971*
SALARIES:
Professor Paul R. Garabedlan
(Principal Investigator)10058 1 Summer Month $ 3,889
Associate Professor Samuel Burstein
10035 2 Summer Months it,020
Antony Jameson
Sr. Research Scientist
66-2/358 12 Months 16,333
David Korn
Research Scientist
30$ 12 Months 6,000
Prances Bauer
Research Scientist ^
5056 12 Months 8,750<
1 Research Assistant
10058 12 Months . " - 5,000
1 Secretary
2558 12 Months —2,750
TOTAL SALARIES $ 46,7*2
OVERHEAD (6656 of salaries) 30,850*
FRINGE BENEFITS (1M.5* of salaries) 6,778
COMPUTER TIME 12,000
TRAVEL 2,000
PUBLICATIONS . 1,500
MISCELLANEOUS (Communications, supplies, etc.) 130
TOTAL " $ 100,000
*The above overhead rate does not include k% of cost sharingor $1,870 representing the university's contribution.
NUMERICAL DESIGN OP TRANSONIC SHOCKLESS AIRFOILS
Summary of Progress in 1972-1973
and
Proposed Research for 1973-1971*
A numerical method for the analysis of three-dimensional
transonic flow past a skew supercritical wing has been devel
oped and programmed. It is based on a parabolic coordinate
system in plane sections perpendicular to the span and on a
rotated finite difference scheme that generates appropriate
artificial viscosity. Comparisons with experiment Indicate
that lift-drag ratios computed by this method are physically
realistic.
During the next year we plan to make improvements in the
accuracy and effectiveness of our three-dimensional program.
For calculations with supersonic free streams the present
first order accurate difference scheme can only give good
accuracy with a fine mesh. We wish to investigate the possi
bility of constructing difference schemes with second order
accuracy, or at least reduced truncation errors. It is also
desirable to achieve a sharper representation of the weak
shock waves on the wing, perhaps by the use of special differ
encing procedures near the shock waves. Better resolution is
needed at t*?e tips. Better resolution of the Kutta condition
is also needed when the trailing edge does not coincide with
a mesh point, so that the effects of twist can be reliably
assessed. It should be possible to use the program to make
comparisons of the merits of various shockless airfoils
- 1 -
developed by our design method, to be discussed below.
It would be desirable to move forward from the model of
a skew wing to that of a swept wing or of a wing-body combina
tion. As a preliminary step in that direction, a method for
the analysis of yawed flow past an axially symmetric body
would be desirable. In this connection there has been colla
boration with South at Langley on computations of axially
symmetric transonic flow. In the current proposal a signi- •
ficant request for purchase of computer time has been included
because of the long runs required for the study of the three-
dimensional scheme.
We are preparing a report describing a number of shockless
airfoils of interest to industry which will include extensive
off-design analyses. We have found that drag creep presents
a significant problem with some of the airfoils we developed
in the past. We intend to make available a new improved
series of profiles that will give better evidence of what
our hodograph method is able to provide. In this connection
we hope to receive visitors from industry interested in learn
ing how to make effective use of the design method. Finally,
in this report we will give an updated version of the design
and analysis programs which include a number of improvements
that have arisen in practice. An effort will be made to speed
up the program and make it more understandable.
We have developed a version of the two-dimensional
analysis program that exploits the best features of two
versions prepared earlier by Korn and Jameson. The new
version incorporates a straightforward boundary layer correc-
tion. This seems to handle boundary layer-shock wave inter
action with some success. However, there is a distinct
difficulty in formulating a correct model of the flow at the
tail for a heavily aft-loaded supercritical wing section*
While progress on this problem has already been made, we
anticipate that a significant amount of further work will
be necessary to bring the program to a satisfactory final
state. In particular, it will have a semi-empirical feature
that requires comparison with experimental data. We hope
for assistance in this respect from current testing being
planned at Langley by Whitcomb.
Research will continue on time-dependent transonic flow
studies. Progress has been made on a numerical method in
corporating the effect of entropy change across a shock
wave. However, the work has been slowed down by difficulties
with the boundary conditions, especially in the region near
the tail. We plan now to use new coordinates based on the
parabolic system that has proved to be successful in our
three-dimensional work. Also, there is the possibility of
looking into a simpler formulation of the problem based on
a potential equation in which the effects of entropy varia
tion are neglected.
- 3 -
Curriculum Vitae
Prances Bauer
BORN: July 5, 1923 .New York City, New York * . * .
EDUCATION - • .. , '
A.B. 19^3 Brooklyn CollegeSc.M. 19^5 in Applied Math, Brown UniversityPh.D. 1948 in Applied Math, Brown University
POSITIONS: . • •
Research Associate, Brown University, 19^5-48
Research Associate, Polytechnic Institute of Brooklyn,
19^9-50
Senior Mathematician, Reeves Instrument Corporation,
1950-51, 1952-61Mathematician, Bureau of Standards, contract with
American University, 1951-52.
. Research Scientist, Courant Institute of Mathematical
Sciences, New York University, 196l-present
MEMBERSHIPS: '
Sigma Xi, AMS, ACM
HONORS:
Rockefeller Foundation Fellowship, 1943-45
PUBLICATIONS: -.. •
• •• , and Reiss, E. L., On the Numerical Determination of
Shrinkage Stresses, J. Appl.-Mech. 37 (1970), pp. 123-127.
., and Reiss, E. L., Stresses in Cantilever Plates, Int.
J, of Computers and Structures 3^ (1972). '
• , Garabedian, P. R., and K6rn5 D. G., A Theory of
Supercritical Wing Sections, with Computer Programs and Examples,
Lecture Notes in Economics and Mathematical Systems, 66, Springer-
Verlag, 1972. ~
Curriculum Vitae
' Samuel Z. Burstein
BORN: October 4, 1935
Brooklyn, New York < . .
EDUCATION:
B.M.E. 1957 Polytechnic Institute of Brooklyn
M.M.E. 1958 Polytechnic Institute of Brooklyn
Ph.D. 1962 Polytechnic Institute of Brooklyn
POSITIONS:
Instructor, Polytechnic Institute of Brooklyn, 1957-62
Research Scientist, Courant Institute of Mathematical
Sciences, 1962-65
Assistant Professor, Courant Institute of Mathematical
Sciences, 1965-68
Associate Professor, Courant Institute of Mathematical
Sciences, 1968-present
HONORS:
Graduate Cum Laude •
PI TAU SIGMA
TAU BETA PI
SIGMA XI •
PROFESSIONAL ' • .
MEMBERSHIPS:
SIAM o
Assoc. Editor, Journal of Computational Physics
PUBLICATIONS: • .
, and Youdin, M., "Mathematical analysis of model for
measuring distribution of XENON-133 in the adult human brain,"
Biomedical Engineering Society, 1972.
, and Mirin, A., "Difference methods for hyperbolic
equations using space and time split difference operators of
third order accuracy," Springer-Verlag Lecture Notes in Physics
#8, Jan. 1971.
, and Mirin, A., "Third older difference methods fur
hyperbolic equations," Journal of Computational Physics, Vol. 5,
No.'3, June 19 70. > ^
, "Difference methods for the inviscid and viscous
equations of a compressible gas," Journal of Computational
Physics- 2, pp. 457-470 (1968),
S. Z. BURSTEIN
PUBLICATIONS:
""Nonlinear combustion instability in liquid propellantrocket engines - the transverse mode," National Aeronautic
and Space Administration TR 32 - 1111, Sept. 1967.
•...•..., "High order accurate difference methods in hydro
dynamics, nonlinear partial differential equations," a
symposium ed. by W. F. Ames, Academic Press, pp. 279-290,
1967.
, "High order accurate difference methods in hydro
dynamics," symposium on nonlinear partial differential
equations, University of Delaware, Dec. 1965, published by
Academic Press, 1967.
• •••.•••, 'Finite difference calculations for hydrodynamic
flows containing discontinuities,*" AEC Research and Development
Report, NYO-1480-33, Sept. 1965, Journal of Computational
Physics, pp. 198-222 (1966).
, "Numerical methods in multidimensional shocked
flows," AIAA Journal, Vol. 2, No. 12, pp. 2111-2117, Dec. 1964.
........, "Numerical calculations of multidimensional shocked
flows," Courant Institute Research and Development Report
NYO-10, 433, Nov. 1963.
, "Spray combustion model with droplet breakup:
analytical and experimental results," Vol. 6, Progress in
astronautics and rocketry, detonation and two-phase flow,
Academic Press, New York, 1962.
, "A Spray combustion model with droplet breakup:
including gas dynamic coupling,"PRL 61-12, AFOSR 433, June
1961. m '
^ .., "A spray combustion model with droplet breakup,
analytical and experimental results," ARS Preprint No.
1719-61, April 1961.
■
, "Evaporation and breakup of fuel droplets in one-
dimensional gas flow in a combustion chamber," PRL No. 60-7,
AFOSR Doc. No. Tn 60-229, Jan. 1960.
, "A spray combustion model with droplet breakup,
Proceeding of the first conference - kinetics, equilibria,
and performance of high temperature systems,""Edited by
G. S. Bahn and E. E. Zukoski, Butterworth and Co., Ltd.,
Nov. 1959. ' •■• *
, "Nonlinear theory of combustion instability:
liquid propellant rocket motors," Astia No. 209-491,
PRL 58-1, AFOSR Doc. No. 59-60, Dae. 1958.
■y
Curriculum Vitae
. ■ •
BORN:
EDUCATION:
POSITIONS:
Paul R.
August 2, 1927
Cincinnati, Ohio
A.B.
A.M.
Ph.D: • •1948
Garabedian
•
Brown
Harvard
Harvard
National Research Council Fellow, 1948-49Assistant Professor - Math, University of California,
1949-50Assistant Professor - Math, Stanford University
1950-52
Associate Professor - Math, Stanford University,
1952-56Professor - Math, Stanford University, 1956-59Professor - Math, Courant Institute of Mathematical
Sciences, New York University, 1959-present;
Director, AEC Computing & Applied Mathematics
Center, Courant Institute of Mathematical Sciences,
New York University, 1972-present.
HONORS:
American Academy of Arts & Sciences
Sloan Foundation Fellowship; 1961-63Guggenheim Fellowship, 1966
PROFESSIONAL SOCIETIES ' : ■MEMBERSHIPS:
American Math Society
Society for Industrial and Applied Math
RECENT PUBLICATIONS: ...4
......... Bauer, P., and Korn, D. G., ffA theory of supercritical
wing sections, with computer programs and examples," Lecture
Notes \n Economics and Mathematical Systems, 66, Springer-Verlag,
1972,• .
v , and Korn, D. G., "Numerical design of shockless
transonic airfoils," Actes du Congres International des
Mathematiciens, Vol. 3, pp. 95-97 (1971).
,'and Korn, D. G., "Analysis of transonic airfoils,"
Comm. Pure Appl. Math., Vol. 24, pp. 811-851 (1971).
•P. R. Garabedian ' * ' . • • " .'.
RECENT PUBLICATIONS:
•......., Kacprzynski, J. J., Ohman, L. HI and Korn, D. G.,
"Analysis of the flow past a shockless lifting airfoil in design
and off-design conditions," N.R.C. of Canada Aeronautical Report
LR-554, Ottawa, 1971.
•......., and Korn, D. G., "Numerical design of transonic airfoils",
pp. 253-269 in: Numerical Solution of Partial DifferentialEquations - II, ed. by B. Hubbard, Academic Press, 1971. .
, and Bloch, Eugene, "Solution of free boundary problems
by the method of steepest descent", p. C5-1 and C5-2 in: Proc.
of the APS Topical Conference of Numerical Simulation of Plasma,
Los Alamos, 1968. Los Alamos Report LA 3990, 1968.
, "Computer experiments with the Bieberbach conjecture,"
pp, 627-628 in: Proc. Intfl. Congress of Math., Moscow, 1966-Moscow, IZD, "MIR" 1968. . . . . •
, "The local maximum theorem for the coefficients of
univalent functions," Archive for Rational Mech. and Anal.
26:1-31 (1967).
, "An extension of Grunskyfs inequalities bearing on
the Bieberbach conjecture", Journal dfAnalyse Math., 18:81-97
(1967).
..•••••.., "Conference on Education in Applied Mathematics,"
Aspen, Colorado, 1966, Proc. of a conference sponsored bySociety for Industrial and Applied Mathematics. SIAM Review
9:289:415 (1967). . -
• • , "General solutions in the complex domain as an answer
to problems of mechanics", pp. 7-12 in v.2 of: Int'l. Symposium
on Applications and the Theory of Functions in Continuum Mechanics,
Tbilisi, 1963, Proceedings, Moscow 1965.
.. , "Asymptotic description of a free boundary at the point
of separation", pp. 111-117 in: Proc. Symposia in App..Math. App.
of non-linear partial,differential equations in mathematicalphysics Proc, Providence, R.I., American Math. Society, 1964,
p. 234. •
, "Partial differential equations", N.Y., Wiley, 1964",
;672 pp.
I........ "Proof of uniqueness by symmetrization", pp. 126-127in: Studies in Mathematical Analysis and Related Topics. Essays
in honor of George P'olya Stanford University Press, 1962, 447 pp.
, "Transonic flow behind a detached shock wave", pp. 110-
111 in: Intfl. Union of Theoretical and Applied Mechanics,
Symposium Transonicum, Aachen, September 3-7, 1962. Ed. by Klaus
Oswatitsch, Berlin, Springer, 1964, .490 pp. •
Curriculum Vitae
Antony Jameson
BORN:
POSITIONS:
HONORS:
November 20, 193^Gillingham, Kent, England
EDUCATION: B.A. )
M.A. )Ph.D.)
1955/1963 Cambridge University, England
Research Fellow, Trinity Hall, Cambridge," 1960-63Chief Mathematician and Staff Consultant, Hawker
Siddeley Dynamics Missile Division, Coventry,
1963-66Project Leader/Engineer, Grumman Aerospace, 1966-72Adjunct Associate Professor; Sr. Research Scientist,
Courant Institute of Mathematical Sciences, New
York University, 1972-present
M.A. in Engineering (first class honors)Alfred P. Sloan Foreign Post Doctoral Fellow, 1962
SELECTED PUBLICATIONS: . ■ .' . ' ■'
Articles • •" >
. Generation of Alfven Waves, J. Fluid Mechanics, Vol. 19, Part
4, pp. 513-527, 1964
Solution of the Equation AX + XB = C by Inversion of an M x M
or N x N Katrix, SIAM J. on Appl. Math., Vol. lb, No. 5, PP.
'1020-1023, 196« '■ .
The Analysis of Propeller Wing Flow Interaction, Analytic
Methods in Aircraft Aerodynamics, NASA Symposium, Proceedings
SP-228, pp. 721-71*0, October 1969 •
Comparison of Four Numerical Algorithms for Solving the Liapunoy
Matrix Equation, Int. J. of Control, Vol. II, No. 2, pp. ltil-19ti
1970 '(co-author)
*
Optimization of Linear Systems of Constrained Configuration;
Int. J, of Control, Vol." II, .No. 3, pp. 409-421, 1970
Design of a Single Input System for Specified Roots Using: Output
Feedback, IEEE Trans, on Automatic Control, Vol. AC-15, No. 3,
1970
Antony Jameson " T
, 'SELECTED PUBLICATIONS! . •qS ... ^
Articles •
' A Direct Approach to the Design of Asymptotically Optimal
Controllers, Int. J. Control, Vol. 13, No. 6, pp. 1041-1050,
1971 (co-author)
On Criteria for Closed Loop Sensitivity Reduction, J. Math.
* >Analysis and Applications (to be published, co-author)
Inverse Problem of Optimal Control, SIAM J. Control (to bepublished, co-author) " ~ . • .
Reports . . " ■ •
Radiation Patterns of Cylindrical Aerials
Hawker Siddeley Dynamics Tech. Memorandum R22il, 1966
. -Effectiveness of a Large Salvo
Hawker Siddeley Dynamics Tech. Memorandum R225, 1966
. Shocks and Kinks In Strings
Hawker Siddeley Dynamics Tech. Memorandum R226, 1966
Lift of a Body of Circular Section with Three or More Wings
tiawker Siddeley Dynamics Tech. Memorandum R227, 1966
•- • Reaction Time and the Sequential Interception of Multiple
targets, Hawker Siddeley Dynamics Tech. Memorandum R22b, 1966
. -...Optimization of Linear Systems • •
Grumman Aerodynamics Report 393-68-2, 1968
Preliminary Analysis of the Lift of a Wing; In an Elliptic
Slipstream, Grumman Aerodynamics Report 393-68-6,
Application of Optimization Techniques to the Lateral Control
of the E-2A, Grumman Report ADN 06-05-69-1, 1969 (co-author)
Some New Methods of Solving the Equation AX > XB = C With the
Aid of Similarity Transformation, Grumman Tech. Memo ENG FS
MGR 70-4, 1970 " .
On the Design of a Compensator with Dynamic Elements to Realize
»the Optimal Control and Reduce Sensitivity to Parameter Variations
Grumman Tech Memo ENG FS MGR 70-5, 1970
On the Use of Cross Product Terms in the Performance Index to
Eliminate Specified Feedbacks From a Linear Optimal Control
Grumman Tech Memo ENG FS MGR 70-6, 1970
Analysis of Wing Slipstream Flow Interaction
NASA* C.R. 1632, 1970* \
Curriculum Vltae
David G. Korn
BORN: August 28, 19*13 * •Brooklyn, New York '
EDUCATION:
B.S.. 1965 Mathematics, Rensseiaer PolytechnicInstitute
Ph.D.. 1969 Mathematics, New York University
POSITIONS:
Research Assistant, Courant Institute of. Mathematical
Sciences, 1965-69Associate Research Scientist, Courant Institute of
Mathematical Sciences, 1969-70; Research Scientist,
1970-present; Adjunct Assistant Professor, 1972-
present
HONORS: . . ; .Graduated Cum Laude * ■
Nominated to PI MU EPSILON Math Honorary
National Science Foundation Fellowship
PROFESSIONAL • •
MEMBERSHIPS:
SIAM ' •
PUBLICATIONS: . . . " ' . "
., Bauer, F., and Garabedian, P. R., ffA Theory of Super
critical Wing Sections, with Computer Programs and Examples,"
Lecture Notes in Economics and Mathematical Systems, 66, Springer-
Verlag, 1972.
, and Garabedian, P. R., "Numerical design of shockless
transonic airfoils," Actes du Congres International des
Mathfematiciens, Vol. 3, pp. 95-97 (1971). \ .
, and Garabedian, P. R., "Analysis of transonic airfoils,"
Comm. Pure Appl. Math., Vol. 21, pp.-! 841-851 (1971).
.'•/• , Kacprzynski, J. J., Ohman, L. H. and Garabedian, P. R.,ffAnalysis of the flow past a shockless lifting airfoil indesign and off-design conditions," N.R.C. of Canada Aeronautical
Report LR-554, Ottawa, 1971.
••• , and Garabedian, P. R., "Numerical design of transonicairfoils", pp. 253-269 in: Numerical Solution of PartialDifferential Equations - II, ed. by B. Hubbard, Academic Press, 1971,
• ,-"Computation of shock-free-transonic flows for airfoil
design", NYO Report NYO-1480-125.
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