Unified theoretical foundations of lift and drag in viscous and compressible external flows

168 Pages·2018·4.075 MB·English

by  Liu, Luo-Qin

Springer Theses
Recognizing Outstanding Ph.D. Research
Luo-Qin Liu

Unified Theoretical
Foundations of Lift
and Drag in Viscous
and Compressible
External Flows
Springer Theses
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Luo-Qin Liu
fi
Uni ed Theoretical
Foundations of Lift and Drag
in Viscous and Compressible
External Flows
Doctoral Thesis accepted by
Peking University, Beijing, China
123
Author Supervisors
Dr. Luo-Qin Liu Prof. Jie-Zhi Wu
Collegeof Engineering DepartmentofAeronauticsandAstronautics
PekingUniversity PekingUniversity
Beijing Beijing
China China
Prof. Wei-Dong Su
Department ofMechanics andEngineering
Science
PekingUniversity
Beijing
China
ISSN 2190-5053 ISSN 2190-5061 (electronic)
SpringerTheses
ISBN978-981-10-6222-3 ISBN978-981-10-6223-0 (eBook)
https://doi.org/10.1007/978-981-10-6223-0
LibraryofCongressControlNumber:2017952526
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To my mother,
who gave me blood and flesh;
To my wife,
who gives me love and soul;
and finally
To my supervisors,
who give me wisdom and truth.
’
Supervisors Foreword
This book represents a significant contribution of Dr. Luoqin Liu to the very
foundation of modern theoretical aerodynamics. To help understand its achieve-
ment,itisnecessarytofirstbrieflyrecallthehistoryofaerodynamicforcetheoryfor
steady external flow.
The birth and development of classic theory for incompressible, steady, and
external-flow aerodynamics were achieved by two mutually enriched and alterna-
tive approaches at the fundamental level: far-field and near-field approaches. The
formerusesfar-fieldlinearizedequationstoderiveaerodynamicforceformulasthat
still hold exactly true in near field. It was pioneered by Joukowski in 1906 in the
proof of the well-known Kutta–Joukowski’s circulation theorem for lift, L¼qUC
intwo-dimensionalinviscidflow(KJtheoremforshort),andbyFilonin1926inhis
derivationoftheviscousdragformulaD¼qUQ(acounterpartoftheKJtheorem),
where Q is the inflow, a contour integral of rotational stream function. Then,
Goldsteinin1931openedanavenuetoextendtheKJtheoremandFilon’sformula
tothreedimensions,whichwasneverfullycompletedyet.Bynature,thesefar-field
resultsarealluniversallyvalidforanyincompressibleandsteadyflowoverabody
of arbitrary geometry, but leave some key quantities to be determined by the
near-field approach, such as circulation C and inflow Q. Contrary to the far-field
approach, the near-field approach works on the fully nonlinear equations under
specificboundaryconditions.ItwaspioneeredbyPrandtlin1918whoprovedthat
the aerodynamic force in three-dimensional flow simply equals the integral of the
Lambvector,knownasthevortexforce,ofwhichtheKJtheoremisaspecialcase
and the famous lifting-line theory is a simplified approximation with the KJ the-
orem built in as an indispensable ingredient. Since this approach enables deter-
mination of aerodynamic forces for specific bodies, it has since become the
mainstreamoftheoreticalaerodynamics.Theextensionofthevortex-forcetheoryto
include effects of viscosity and unsteadiness has been done since 1920s and
completed now.
vii
viii Supervisors’Foreword
Asone’sfocusshiftedtohigh-speedaerodynamicssince1940–1950s,however,
the situation changed. Far-field approach stopped because classic inviscid
high-speed theory, suitable for simple attached flow only, does not permit the
existence of linear far field in transonic and supersonic speed. High-speed aero-
dynamics has been developed almost solely by near-field approach, without any
universal force laws to serve as the benchmark reference and test. In particular,
today’smodernaerodynamicsisfacingvariouscomplexseparatedflowscontaining
vortices, shocks, and entropy increments, which is far beyond the reach of entire
classic near-field theories that are still taught in every textbook. Consequently,
theoretical aerodynamics is fading away from the development of modern aero-
dynamics and yields its position to powerful computational fluid dynamics
(CFD) and advanced experimental aerodynamics (EFD). This situation implies the
loss of a planform that can refine and condense the extremely rich flow data from
CFD and EFD to quantitative physical laws, against which all results of CFD and
EFD should be tested. Therefore, for truly healthy advances of modern aerody-
namics, a set of exact aerodynamic theories based on the same full Navier-Stokes
equations as CFD uses are urgently needed.
Dr.Liu’spresentbookprovidespreciselythedesiredtheoriestofillthelongtime
blank. On the one hand, he fully inherited the precious heritage of Joukowski,
Filon, and Goldstein and found that as long as the viscosity is introduced, the
far-field approach can well be applied to steady compressible flow, by which the
KJ-Filon-Goldstein lift-drag theorem can be rigorously proved as universally and
exactlyvalidallthewayfromsubsonictoatleastsupersonicregimes.Insodoing,
Luoqin has gone even further to lay down a general foundation for far-field
approaches, by a zonal structure for various flow models used in aerodynamics:
incompressible-flow model, steady-flow model, and inviscid-flow model, in terms
oftherespectivedecayratesofphysicalquantitiesineverymodels.Thistheoretical
developmentispurelyanalytical,unabletobeobtainedbyCFDorEFDbuthasgot
strong support from CFD.
On the other hand, the exploiting of modern fully nonlinear near-field theories,
LuoqinalsoinheritedthepreciousheritageofPrandtlandextendedthevortex-force
theory to a longitudinal-transverse theory for the force and moment exerted on an
arbitrary moving-deforming body in viscous and compressible flow, steady or
unsteady. An innovative theoretical foundation of modern external-flow aerody-
namics is thereby at its dawn. Either one of the above far-field and near-field
developmentsalreadyrepresents averygoodprogressandbothhavebeenfulfilled
and expounded in this book.
Fiveyears’closecooperationwithLuoqinwasourverypleasantexperience.We
found him the very best graduate student we have ever supervised in our entire
academic careers. His outstanding mathematical-physical basis, sharp insight into
thecoreofproblems,fluentskillofperformingnumericalsimulations,andveryfast
workingpacemadehimthe“schooltyrant”recognizedbyallteachersandgraduate
students at the college of Engineering, Peking University. He is also a very
hard-workingyoungman,willingtocomeupwithalotoftimegnawingonabone.
Supervisors’Foreword ix
Atmeantime,heisaveryeasy-goingpersonandgoodteam-member,alwaysliketo
do whatever he can for others. It is our great pleasure to recommend this book to
wider readers, especially those interested in theoretical aerodynamics, applied
mathematics, and general physics and mechanics.
Beijing, China Prof. J.Z. Wu
June 2017 Prof. W.D. Su
Preface
Great advances in the theory of aerodynamics have been made in the first
half-century since the Wright brothers successfully flew the first powered, con-
trolled,heavier-than-airairplanein1903.But,althoughhumanbeingshaverealized
their dream offlying, even at supersonic and hypersonic speeds, it seems that the
theoretical aerodynamics has stopped at its classic content as today still being
taught in every aerodynamic book. This embarrassment is mainly due to the fol-
lowingtworeasons.Ontheonehand,classicaerodynamicscanonlyhandlesimple
flows, where the flow fields are solved as analytically as possible. This, however,
can hardly be done in modern days since we are facing various complex flows
involving boundary-layer separations, vortices and shocks, as well as their evolu-
tions and interactions. On the other hand, owing to the rapid development of
computational fluid dynamics (CFD), it has now been routine work to find
numerical solutions for complex flows. Since the classic aerodynamics theory is
mainlybasedontheEulerequations,however,itisoflittlehelpforreadingoffthe
precisekeyphysicsfromCFDdataandunabletoguidetheadvancementofCFD.It
is our belief that theoretical aerodynamics has to be developed hand in hand with
but can never been replaced by CFD since “ideas and concepts come out of the
mind, not out of computers or wind tunnels” (Küchemann 1978).
Aiming at developing modern theoretical aerodynamics based on exactly the
sameNavier-StokesequationsasusedinmodernCFDforviscousandcompressible
externalflows,this bookconsists ofthree innovative breakthroughs inthefar-field
and near-field theories. First, we construct a universal zonal structure of aerody-
namicfarfield,inwhichalldisturbanceflowquantitiesmustdecayexponentiallyif
andonlyiftheflowisviscous,unsteady,andcompressible.Threecommonlyused
simplified flow models, being inviscid, steady, or incompressible, only work in
their respective true subspaces of the free space. Second, we prove rigorously a
universal and exact total-force formula as direct extension of and with the same
formastheclassicliftanddragformulasduetoKutta,Joukowski,andFilon,along
with its far-field asymptotic in terms of physically testable variables. Third, we
derive a general near-field theory for aerodynamic force and moment, steady or
unsteady, which permits detailed complex-flow diagnosis including the
xi