Application of the Adjoint Method for Vehicle Aerodynamic Optimization. Dr. Thomas Blacha, Audi AG
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1 Applcaton of the Adjont Method for Vehcle Aerodynamc Optmzaton Dr. Thomas Blacha, Aud AG GoFun, Braunschweg
2 2 AUDI AG, Dr. Thomas Blacha, Applcaton of the Adjont Method for Vehcle Aerodynamc Optmzaton, Outlne Adjont method n theory Necessary smplfcatons Transent vs. steady state RANS => (D)DES Test case: Aud Q5 (bult n 2012) Requred accuracy for prmal soluton Convergence of the adjont method Consstency => accuracy of adjont predctons Results on the Aud Q5 bult n 2012 Conclusons
3 3 AUDI AG, Dr. Thomas Blacha, Applcaton of the Adjont Method for Vehcle Aerodynamc Optmzaton, Adjont method n theory Mnmzaton problem: Lagrange problem: L F d mnmze (u,q) d F Lagrange multplers d F (p, v, ) wth (p, v, ) 0 d ( v)v p (2νD(v)) 0 v 0 Total varaton: δl δβl δvl δpl δ L δ L 0 v p! Senstvty: G L β ν u n t t v n t t Adjont equatons for u & q prmal transport equatons ( v )v p (2νD(v)) convecton pressure dffuson v 0 adjont transport equatons ( v)u u v q (2νD(u)) transpose convecton adjont pressure adjont dffuson u 0 backward convecton Influences sgnfcantly - Convergence behavor - Applcable schemes - Accuracy
4 4 AUDI AG, Dr. Thomas Blacha, Applcaton of the Adjont Method for Vehcle Aerodynamc Optmzaton, Smplfcatons transent Spalart-Allmaras DES tme averagng of p(t) and v(t) p & v p und v RANS* Spalart-Allmaras transport equaton n t *transent adjont method s much too expensve! prmal soluton p, v und n t steady state adjont (frozen turbulence) nterpretaton of senstvtes durng early optmzaton at 1:4 model scale FKFS (no automated morphng)
5 5 AUDI AG, Dr. Thomas Blacha, Applcaton of the Adjont Method for Vehcle Aerodynamc Optmzaton, Test case: Aud Q5 (bult n 2012)
6 6 AUDI AG, Dr. Thomas Blacha, Applcaton of the Adjont Method for Vehcle Aerodynamc Optmzaton, Observatons push nward pull outward Asymmetry s very senstve wth respect to convergence level of n t! unphyscal asymmetry Better convergence qualty of prmal felds v & p necessary?! Longer tme averagng x4 montor pont 1,4 1,2 1 0,8 0,6 0,4 0,2 0 u* base u*[b] base u*[b] x4 u* x4 Sgnfcant dfferences n fnal adjont velocty teratons
7 7 AUDI AG, Dr. Thomas Blacha, Applcaton of the Adjont Method for Vehcle Aerodynamc Optmzaton, Requred accuracy for prmal soluton base x4 Symmetry sgnfcantly mproved
8 8 AUDI AG, Dr. Thomas Blacha, Applcaton of the Adjont Method for Vehcle Aerodynamc Optmzaton, Requred accuracy for prmal soluton p base p x4 p-nterval: 20Pa base RANS-lke??? p-nterval: 100Pa (5% of total range) v-nterval: 0-20m/s x4 Man dfferences n the rear of the car (wake regon) p-nterval: 100Pa (5% of total range) v-nterval: 0-20m/s
9 9 AUDI AG, Dr. Thomas Blacha, Applcaton of the Adjont Method for Vehcle Aerodynamc Optmzaton, Influence of tme averagng perod C * 0,012 0,009 0,006 0, ,003-0,006 C * C ( t) C ("x4") Standard averagng perod suffcent for drag and lft predctons mean(cd) mean(clf) mean(clr) averagng perod / STD averagng perod C d * * C lf * C lr Dfferent treatment of prmal soluton necessary f adjont calculaton s planed! Non-adjont Accurate scale resolvng methods (small tme perod) Adjont Methods, whch resolve only the most mportant turbulent structures
10 10 AUDI AG, Dr. Thomas Blacha, Applcaton of the Adjont Method for Vehcle Aerodynamc Optmzaton, Consstency Tme averaged DES values and RANS turbulent vscosty v, p & n t Input values for RANS adjont solver contnuty (mass conservaton s lnear) momentum (hghly non-lnear) RANS turbulent vscosty can only represent sotropc turbulence. X base x4 Resdual of RANS momentum equaton RANS momentum resdual falls
11 11 AUDI AG, Dr. Thomas Blacha, Applcaton of the Adjont Method for Vehcle Aerodynamc Optmzaton, Consstency Predctons by means of tme averaged transent prmal (e.g. PANS, DES, etc.) and steady state adjont. Prmal nput values: v, p und n t How to obtan n t? v! (v )v p (2νD(v)) 0 nfluence on adjont (v )u u v q (2νD(u)) Defnton/Meanng of n=n m + n t?! n t s pure turbulent RANS vscosty => calculated usng RANS turbulence model Velocty feld of prmal has to fulfll eddy vscosty law v ' v j v ' n t x Only sotropc turbulence can be represented n t s closure value of any meanng j v x j 2 k j 3 Can be chosen n order to mnmze the resdual. (Does not necessarly requre to solve a n t transport equaton) Not necessarly of scalar type => tensoral vscosty also possble
12 12 AUDI AG, Dr. Thomas Blacha, Applcaton of the Adjont Method for Vehcle Aerodynamc Optmzaton, Results on Aud Q5 (bult n 2012) push nward pull outward DCd Measure CFD 1:4 Exp. FKFS 1: Lateral knk wth bgger radus 2: More materal at bottom of front wndow near A-pllar 3: More materal n front of sde vew mrror 4: Extenson of mrror base by 110mm 5: Sharper tralng edge on D-pllar 6: Outward pullng wth sharp tralng edge on rear shoulder 7: Outward pullng before rear wheel 8: Mountng of a small horzontal plane below rear wndow (also 1:1)
13 13 AUDI AG, Dr. Thomas Blacha, Applcaton of the Adjont Method for Vehcle Aerodynamc Optmzaton, Conclusons Greatest challenges for the applcaton of the adjont method n vehcle aerodynamcs are Convergence (fnal convergence, numercal nose) Accuracy (scheme order, nfluence from prmal soluton, dscretzaton of ATC, lmtng) Computatonal cost for transent adjont method stll too hgh Strateges necessary whch rely on steady state adjont If tme averaged flow felds are used as nput values for a steady state adjont solver, consstency cannot be guaranteed. In partcular, the relablty of predcted senstvty maps sgnfcantly depends on the choce of tme averagng wndow. The requred mnmum tme averagng perod s n general sgnfcantly larger than for regular drag and lft predctons. Adjont and Non-Adjont setup necessary for prmal soluton! Alternatve calculaton of n t n order to mprove consstency (There are lmts!)? Nevertheless stable results were obtaned even on an automatcally generated unstructured grd. The predcted nfluence of dfferent measures on drag s n good agreement wth measurements at 1:4 model scale and wth tme averaged DES calculatons.
14 14 AUDI AG, Dr. Thomas Blacha, Applcaton of the Adjont Method for Vehcle Aerodynamc Optmzaton, References Blacha, T., Gregersen, M.M., Islam, M. and Bensler, H., Aerodynamc Vehcle Optmzatons Usng the Contnuous Adjont Method, Proceedngs of the 10th FKFS-Conference, 2015 Blacha, T., Gregersen, M., Islam, M., and Bensler, H., "Applcaton of the Adjont Method for Vehcle Aerodynamc Optmzaton," SAE Techncal Paper , 2016, do: / Othmer, C. A contnuous adjont formulaton for the computaton of topologcal and surface senstvtes of ducted flows. Int. J. Num. Meth. Fluds 58, 861 (2008). Thank you! Questons?
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