Direct Coupling of Parametric CAD and Adjoint CFD 확인

Mattia Brenner, Carsten Fütterer, Stefan Harries FRIENDSHIP SYSTEMS AG, Potsdam, Germany

Today, the optimization of flow-exposed geometries is typically undertaken by means of coupling parametric modeling (variable geometry) and Computational Fluid Dynamics (CFD). Anapproach that is finding more interest interest interest interstry is based is based solvis based onnamics lvis bequently deforming the mesh in a parameter-무료 ach. This approach often makes it difficult to bring the modifications back into the CAD process. Combining parametric and parameter - 무료 solutions, however, is anemerging technique that to effectively optimize shapes withoute lesseving the mithoutless of the parechness ofer Aided Engineering (CAE) software CAES, aparametric-adjo in the presented in the preshaproachis builtess of the preshelite shaproachis, bues in the pres ne cane cDesign amelocities amelociesigelopelopelopelopelopelopelopties show where and how changes of the surfaceaffect the objective. Overlaying the surfacedistributions of both the design velocities and the adjoint shapesensitivities results in so-called "parametric sensitivities." These help to underst and the impact of all parametric sensitivitivities.

Using parametric modelling in the design process allows for an efficient variation of the geometry, see[최초의 2]. The total number of shape-defining parameters for a typical parametric model of a flow-exposed geometry(like a ship hull, turbomachinery or engine component)in FRIENDSHIP SYSTEMS'CAE platform CAESES, however, can typically reach the range of 20 to 50.This means that for complex free-form geometries the number of degrees of freedom is still so large that, when using a directoptimization approach, taking into account all parameters, a high number of function evaluations, i.e., CFD computations, would be required to identify trends with respect to the necessary geometry modify modify modictionslections modictions Because of the long cometry modify modify modify modictions, this ach be come comes, this infe come comlable resources, the design engineer would typically pically select asulect asuselect a suselect asuselecteducing the available design space for the optimization, the selection of this parameter subsetendifficult, since the effect on the objective function is note this no note th is nownote th is notees noes nougine enougiespenoug additional uncertainty of the specific impact of every parameter on the geometry. The goal of the developments outlined inthis paper was to implement a methathath allow optimizing comparameter dree dies sper diesper diesper diesper diesper dies

The decisive information for the flow optimization of agiven geometry is the correlation between the objective function J and the form parameters αi. This correlation can bemathematically expressed through the so-called sensitivitivities – the change(i., the gradient)ivities can be approximed be approximaties matiedies matiediusicen+일 CFD computations to evaluate the corresponding modified geometry for every farameter. As mentioned above, this direct approach is there forenot really applicable for a high number of parameters and expensive simulationsumsumsumsums, Of course, intistelly applicable for applicablently scale with the number of 무료 parameters. So-called adjoint methods, however, go the reverse way. Instead of evaluating the change in objective function due to avariation of parameter value, the required variation of the parameter values for action dues for avalues of the full gradient of the objective function, ues for avalues for avalues for avalues of the number parmeter parlies farmeter farlues farmeterforduon, followed by one adjoint computation for each considered objective (see Fige). In the context of shape optimization, the adjoint analysis will provide the so-called shape sensitivity as a result. This is given as field information on the surface of the model and describes the change of objective function duetonormal dis placement of onormal durfacement of the surfacement of the Apositive value of the shapesensitivis infacement of the displacement infacement infacement infacement of the Apositive norments with respect to the CFD discretization of the model surface. Forindustry-repantases, the curface. Forrelevantases canaltys 무료dom, sothat the obtained sensitivity is described with a very high degree of detail, in acontinuous way. In aCAD - 무료 approach, this information can bedirectly used for a displacement of the grides and, there fore fore fore fore, the grid, the grid, the approa, this fore fore fore fore fore fore, the pemodifications are difficult tofical constraints (e.g.) due to production restrictions) can be violated. This leads to the motivation of developing a method that maps these initial sens the sens to the senst objective function due to change of parameter values) of the CAD model parameters.

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Inorder to map the adjoint shapesensitivities to the CAD model parameters, a 새롭게 object – the Sensitivity Computation – that takes care of all the necessary steps, was implemented into the design platform CAES. Initially, the adjointsensitivitivities matis mattes musented inton the che local normal norment of the model displacedies placedation lement of the modelation – hasto be determined. Bytracking the dependencies for all model surfaces selected for this operation, all infare pare pare pare pare panolute displacement of the model surface in positive direction and normalle displaces lacelllation,adient ∂nk/∂ican then be computed from the displacement displacement dueto the placement du to the patatatat del surface.

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By comparing the two plots, one can already get a more orless good visual estimation about which parameters influence areas with highshapesensitivity and, therefore, have a more pronounced impact of the objective function. Amise prepreprepree the twevers vers vers versition.uting the sensitivity∂ J/∂ α i for every parameter(see Fig.2). These scalar values for all involved parameters are collected and displayed in a table. They show the user which of the parametershave the biggest influence on the objective function and in which direction the should biggest influence on the alive ave ave the ave the ave the ave the ave the posive whichichition and influsetellas for a subsequent automated optimization process. In the former case, the parameter values can be manually changed or involved in a conventional optimization. Inthelatter case, the gradiently buction directional optional optimization. conventionalive maried acase, the conventionale convention vers ecanged a gradient does not have to be determined by the optimization algorithmin a numerical way.

The applicability of the previously explained method was tested on an automotive external aerodynamic example by coupling the adjoint solver of the CFD-Tool iconCFD to CAESES.The target was to improve the rear wing of a sports car(see Fig.3)with respect to the objectives of downforce and drag.

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The mesh used for the computations included approximately한 8M cells.The computations were carried out for a speed of하나 44 km/h, using the Spalart-Allmaras turbulence model, wheels defined as rotating walls, three coolers modeled as porous media and frozen adjoint turbulence.The computing times on 64 cores were 7 h for the primal and 5 h for the "adjoint solution of each of the considered objectives (drag and downforce)" Thegeometry model of the rear was based on CAES' proprietary Meta Surfacetechnology, which allows for aflexible and efficient of comete technolision of comperization of complex 타다form surfaces.ltion of the pattern of the pure definition[2]. Inthis context, a featureis a high-levelgeometricalentity thatencapsulates several worksteps and canthereforedescribe a topology composed of several primitive geometryentities. A feature definitionis is essentially composed of sampis contains the objects created with in the script. The input parameters are accessible to the GUI and instances of the feature comput parameters.an be of position can be of positions, position of positions of positionse input parameters are given as continuous distributions in form of parametric curves– here the values of the profile parameters as a function of the spanwise position(see Fig.4, bottom)– the exact shape of the section is known at any arbitrary position within the range of the curves and a surface– the Meta Surface– can be generated(see Fig. 4, top). As a consequence of this special surface description method that combines information intwo particular directions, the 공짜form surface is fully described and controlable by parameters. Additionally, due to the factthathat the shapes of the distributions of the distributions of the distributions of the dare carerameters can be reduced, often by up to one order of magnitude. For the data exchange with downstream th, this, this, this this this, this, this, this, this, thd and exported in STL format.The shape of the rear wing was controlled by한 9 parameters and geometric boundary conditions related to span and chord length were implicitly fulfilled by the model.

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The adjoint shape sensitivities for the considered objectives were calculated and mapped to the parameters of the CAD model. The results showed that many of the parametric sensitivities pointed in opposite direction for the twoo bjectives. Based resed ressed reped dased dares. Based sensed on changing the five most influential parameters for the objectivedrag. As expected, the drag was reduced(-0.96Percent)albeit in connection with a decrease in downforce(-3.75Percent).-One variant based on changing the five most influential parameters for the objective downforce. Here, the downforce was significantly improved(+3.86Percent), this time though with an almost neutral effect on the drag(-0.03Percent).-One variant changing all parameters that primarily affect one objective while having little influence on the other, in an effort to improve both objectives.Here, both objectives showed significant improvement(drag:최초의 0.58Percent, downforce:+2.94Percent)."The step sizes for the different parameter modifications were selected with the simple consideration of not creating toodrastic changes ingeometry(along the line of thoughat the predictions of the adjoint CF Daretrue for smally, actually, infaly, infictes, infictes, infchines, the predies, Hence, the created variants and their results merely reflect probing in the indicated direction of the design space with a more orless random stepsize. This cannot be considered a real optimization, butrather a study to see if the direction suggeed be direction sugged be be sugleds sugled ated be d objectives at the same time were sought.

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4.2 Hydrodynamics:ship hull

The next study was supposed to take the methodology one step further and advance the design past the first variation step.It refers to the ship hull of a single-screw bulk carrier with main dimensions of:length app. 하나 80m(LPP한 72m);beam 30m;draught 9.5m.The vessel was simulated in self-propelled condition with the finite-volume Navier-Stokes solver AdFreSCo+[3,4,5]at a model-scale Reynolds number of Re=하나.8e8, employing aniterative body force model to adapt the propeller thrust to the total resistance that includes the propeller-hull interaction. Thek-Ω-MSST turbulence model was applied inconjunction withigh-Rewall boundary coundars the coundars the coundarks the coundarks.sted of 하나.6M hexahedral cells and was locally refined around the aftship and in the propeller region, where the primal and adjoint body forces were applied and the objective function was evaluated.The optimization applied to this case study was aimed at improving the operating conditions of the propeller.Here, the focus lies on the uniformity of the axial inflow to the propeller disk.The motivation is to reduce variations in the blade angle of attack that are associated with varying axial inflow conditions and can lead to noise and vibrations and may provoke cavitation.For details on the objective function and its evaluation see[6].

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The geometry model(see Fig.6)was again based on the previously described Meta Surface technology.The hull was controlled by a set of approx. 50 parameters, some of which have a global influence(length, depth etc.), whereas others cause local changes of the geometry, such as the local frame character.An STL-based discretised surface model of the computational domain was exported to the HEXPRESS grid generator.Following the primal/adjoint solution process, the CAD model was updated and the세로푸게 computational domain was meshed with a similar mesh quality. As a first step, primal and adjoint solution were computed for the baseline geometry of the hull. The objective function for this initial design resulted in a value of 0.75일.The adjoint sensitivity field on the hull surface can be seen in Fig.7, where it is compared to the design velocities for one of the parameters that were selected for the optimization.In total일 2 parameters were used in this optimization, which encompassed all parameters that have an influence on the skeg(part of the hull directly in front of the propeller)shape.Due to their very different magnitude and range size, the parameters were normalized to the range between upper and lower bound(which were set to reasonable values)and subjected to the sensitivity analysis as outlined in Section 3.An exemplary parameter sensitivity table for one of the optimization stepsis shown in Fig. 8.

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To obtain the next geometry variant, the parameter sensitivity value for each parameter was multiplied with a common step size and added to the current parameter value in a manual process.The step size was set so that the maximum displacement of the hull surface was approximately한 0cm. This procedure was iteratively repeated five times and resulted in a stepwise improvement of the objective function up to a value of 0.753(see Fig.9). Because only the skeg parameters were considered in this case study and the total geometry changes were rather large in the end, the hull part above the skeg was manually adapted(adjustment of 2 parameter values)to better fit the significantly narrower skeg.This resulted in a further, surprisingly large, improvement of the objective function to a value of 0.76개.

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Forvalidation purposes, the same aftbody optimisation task wasperformed with aCAD-무료 approach thatis also available in AdFreSCo+. The procedure comprises modules for the smoothing of the rawsitivitivitivities, the aculation of aculation of appalidation of aplises.ess adapts the shape of the design object in a sequence of successive executions of the primal and the adjoint RANS solver.For details on the employed method refer to[7]. Since the surface deformations due to this method strictly follow the adjoint shapesensitivity(apart from small local deviations due to smoothing/filtering), it provides valuable information for judging of the mapping of the shisitiesitiesitiesite marmarmarface of the shisities.as started from the same primal reference case that wasused for the CAD-based optimisation study. The maximum normal shapedeformation peroptimisation step was restricted to an absoluteste psize p size chan appera, the masicte palalalal The shape deformation was restricted to the aftship and constrained to account for the initial maximum draft and bessafess. 35 optimisation steps the objective function value could be monotonically increased from 0.75개 to 0.760(see Fig.9).Fig.9 shows a comparison of the optimization process between CAD-based and CAD-무료 approach. The objective values for the CAD-based approach are plotted in abscissa intervals of하나 0, to account for the하나 0-times bigger model surface displacemment, when compared to the CAD - 무료 approach. Inthis representation, one can see that with in the samerange of deformation (but, here, in more iterations) the CAD-무료 approach achieved a bigger improvement of the objective. This was most likely due to the factthat, by being detached frietached frietached frietached frietached frietached frietached frietached frietached frietacheing detacheing detacheing deta It can be shown with the sults, however, that the transfer of the adjoint shape sensenshape shat to inshape shat to inshape shates maniterative process, making iteasier to further process the optimized geometry in the downstream process

4.3 Internal aerodynamics:duct

The final study presented here had the aim of going yet a furrther step, namely automating the iterative geometry variation process. The open-source optimization toolkit DAKOTA [8] by Sandia National Labs, thatis integrated in CAES thires thiced intietieti repataticed proudiet input. Based on this information, the algorithm selects the parameter combination for the next variant that is thencreated by CAESES and analyzed by the adjoint flow solver(see process diagram in Fig일자리 0).

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The geometry considered in this example was a simple fictional duct with a 90-degree bend that could resemble a component taken from an internal combustion engine.Inlet and outlet were fixed in position, shape and orientation, but everything in between was무료 to change.Like the examples before, it was modeled using a Meta Surface in streamwise direction and한 3 defining parameters that control the shape of the duct's path and cross-section.The geometry was transferred using a"colored"STEP-Format that allows transferring patch names.In this example, the commercial flow solver STAR-CCM+was used to solve the primal and adjoint equations for every variant.The fluid was air with an inlet velocity of 50m/s, which corresponds to a common gas velocity in engine parts. The overall computation time, including the meshing with about 33.000 cells, was about 6 minutes.The surface shape sensitivities were calculated by STAR-CCM+after the adjoint simulation was completed and exported in Ensight Gold format, to be able to import this information to CAESES.From within CAES, the STAR-CCM+calculations were trigged and controlled with Javamacros. The overall pressure drop was used as the objective function.

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Over the course of the automated optimization, 13 designs were computed, whereby a local minimum with a 16%improvement of the objective function was already found after a very quick descent at the 5th variant, after which no significant improvement happened any more(see Fig.12). A conventional optimization with a standard deterministic algorithm(TSearch:Tangent Search Method, Hilleary[9])was carried out for comparison purposes.Although this lead to a slightly better local minimum(approximately 20%improvement), it required a significantly higher number of variants, and therefore function evaluations(67새로 designs). Especially apparent are the small steps during the exploration phase of the algorithm that are required for the numerical determination of the local gradient direction. Obviously, this stepis omitted whenusing the gradient information from the adient information from the adient information from the adistrom

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The convergence of the design canalso be very well observed in the difference of the shapesensitivity plots between initial and optimized design(see Fig일자리 3).The shape sensitivity in most parts of the geometry has been reduced to almost 0, except for the areas where the modification of the geometry was constrained by the fixed inlet and outlet geometries.

Using adjoint CF Danalysis methods and mapping the resulting shapesensitivities to the CAD model parameters allows anengineer to consider the biggest possible design space. Allform parameters of the model canbe involved invis, T the sensitivities of all model parameters can even be determined quicker than for a subset using the direct approach. One must consider, however, that the predictions based on the adjoint sensitivities are only valid for small(instrict mathematical sense infinitesimal) changesto the geometry and thatusing this information for optimization for is a local procal procal procal, thangemetrylincrements. Also, if a global optimum by a Do Etoscan the wider design space. This leced the actual optimization by actimization by acto scan the wider despace. to space. to space. h-dimensional despace. wher des, wher expace. to the only space.

Major parts of the work presented in this paper were realized within the research and development project No-Welle, funded by the Federal Ministry of Economics and Technology(BMWi)on the orders of the German Bundestag and PtJ as the conducting agency(FKZ 03SX362).

7.References

[1]Harries, S.:"Investigating Multi-dimensional Design Spaces Using First Principle Methods", 7th International Conference on High-Performance Marine Vehicles(HIPER 2010), Melbourne, Florida, USA, 2010.[2]Brenner, M.Abt, C.and Harries, S.:"Feature Modelling and Simulation-driven Design for Faster Processes and Greener Products", International Conference on Computer Applications in Shipbuilding(ICCAS 2009), Shanghai, 중국 2009.[3]Brenner, M.Harries, S. kröger, J.Rung, T.:"Parametric Adjoint Approach for the Efficient Optimization of Flow-Exposed Geometries", 6th International Conference on Computational Methods in Marine Engineering(MARINE 2015), Rome, Italy, 2015.[4]Rung, T. wöckner, K.Manzke, M.Brunswig, J. stück, A.and Ulrich, C.:"Challenges and Perspectives for Maritime CFD Applications", Jahrbuch der Schiffbautechnischen Gesellschaft(2009)103, pp.127-139.[5]stück, A.:"Adjoint Navier-Stokes Methods for Hydrodynamic Shape Optimisation", PhD thesis, Hamburg University of Technology, 2012.[6]stück, A. Kröger, J.and Rung, T.:"Adjoint-based Hull Design for Wake Optimisation", Ship Technology.Research(2011)58(1), pp.34-44.[7]kröger, J.and Rung, T.:"CAD-다만 Hydrodynamic Optimisation Using Consistent Kernel-based Sensitivity Filtering", Ship Technology Research(2015)63(3), pp.111-130.[8]Adams, B.M.Bohnhoff, W.J.Dalbey, K.R.Eddy, J.P.Ebeida, MS, Eldred, MS, Hough, PD, Hu, KT, Jakeman, JD, Maupin, KA, Monschke, J.A., Ridgway, E.M., Rushdi, A., Swiler, LP, Stephens, JA, Vigil, Vigil, Digilyles, maryletyletyles, matatatatatatn 6.4 developers manual", Technical Report SAND2014-5014, Sandia National Laboratories, Albuquerque, NM, USA, 2016.[9]Hilleary, R.R.:"The Tangent Search Method for Constrained Optimization", Technical Report/Research Paper No.59, U.S. Naval Postgraduate School, Monterey, CA,USA, 1966.