Workshop on Verification and Validation of CFD for Offshore Flows

Transcription

1 Workshop on Verfcaton and Valdaton of CF for Offshore Flows L. Eça (IST), G.Vaz (MARIN) October. Proposed test cases The frst Workshop on Verfcaton and Valdaton of CF for Offshore Flows [] ncluded three test cases: I) A - manufactured soluton for unsteady turbulent flow (ncludng turbulence quanttes of eddy-vscosty models). II) III) The flow around a smooth crcular cylnder. The flow around a straked rser. The goal of the frst exercse s to perform Code Verfcaton,.e. to check that the dscretzaton error tends to zero wth grd refnement and (f possble) demonstrate that the observed order of grd convergence matches the theoretcal order of the code. The objectves of the other two cases were twofold: Check the consstency between error bars obtaned from dfferent numercal solutons of the same mathematcal model,.e. perform Soluton Verfcaton. Apply the V&V Valdaton procedure [] to assess the modelng error. Ths means that experments and smulatons requre the estmaton of ther respectve uncertantes. Ths means that the frst test case s focused on Code Verfcaton, whereas the remanng test cases nclude Soluton Verfcaton and Valdaton.. Partcpants/Presentatons The Workshop ncluded sessons:. Introducton and Code/Soluton Verfcaton.. Soluton Verfcaton.. Soluton Verfcaton/Valdaton.

2 . Valdaton/Overall revew of results.. scusson and future plans.. Introducton and Code/Soluton Verfcaton. Ths sesson ncluded four presentatons: Workshop on Verfcaton and Valdaton of CF for Offshore Flows, L.Eça (IST) and G.Vaz (MARIN). Verfcaton of ReFRESCO wth a URANS Manufactured Soluton, L.Eça (IST), G.Vaz (MARIN) and M.Hoekstra (MARIN). Code Verfcaton of an Unsteady RANS Fnte Element Solver, A.Hay (EPM), Pelleter (EPM), S.Etenne (EPM) and A.Garon (EPM). Verfcaton and Valdaton of VIV-Sm, O.Heynes (MMI Engneerng) and.olan (MMI Engneerng).. Soluton Verfcaton Two presentatons were ncluded n ths sesson followed by a perod of dscusson. CF Calculatons and Soluton Verfcaton for Smooth Fxed Crcular Cylnder n the Range of Hgh Reynolds Numbers, G. Rosett (USP), G.Vaz (MARIN) and A.L.C.Fujarra (USP). Numercal Smulaton of Flow around a Smooth Crcular Cylnder at Re = e to e by Usng k-epslon Turbulence Model, M.Zhang (SJTU), Z.Ln(SJTU), S.Fu (SJTU), Q.Zhou (SJTU) and X.Zhang (SJTU).. Soluton Verfcaton/Valdaton Three presentatons were made n the thrd sesson of the Workshop. Flow past a crcular cylnder: A verfcaton study usng approxmate error scalng I.Celk (WVU), J.Escobar (WVU), J.Posada-Montoya (WVU) and A.Guterrez- Amador (WVU). CF study of the flow over a smooth cylnder and a straked-rser, A.Barbagallo (SBM Offshore).

3 Transent analyss of flow around a smooth cylnder and a straked rser wth a lattce-boltzmann method, M.Mer-Torreclla (AR),.M.Holman (NLT), M. Zurta-Gotor (AR) and J.B. Frandsen (AR).. Valdaton/Overall revew of results Two presentatons were ncluded n ths secton followed by a frst dscusson about the submtted results (focused manly on Code Verfcaton). V&V study on the flow around a straked rser usng URANS supplemented by ES smulatons, M.Manzke (TUHH) and T.Rung (TUHH). ReFRESCO Results for Rser Test-Case of V&V Workshop, G.Vaz (MARIN) and.rjpkema (MARIN).. scusson and future plans The last sesson of the Workshop was dedcated to the comparson of (part of) the submtted data and to dscusson of the plans for the next Workshop (see fnal remarks). Organzaton Insttuto Superor Técnco (IST) Martme Research Insttute Netherlands (MARIN) Flow Solver Mathematcal Test Case Model ReFRESCO URANS Manufactured Soluton École Polytechnque de Montreal (EPM) CAYF URANS Manufactured Soluton SBM Offshore STARCCM URANS Cylnder West Vrgna Unversty (WVU) REAM Naver-Stokes Cylnder West Vrgna Unversty (WVU) FLUENT Naver-Stokes Cylnder Shanga Jaotong Unversty (SJTU) FLUENT URANS Cylnder Unversty of São Paulo (USP)/MARIN ReFRESCO URANS Cylnder MMI Engneerng VIV-Sm URANS Cylnder Abengoa Research SL (AR) XFlow Lattce- Straked Rser Boltzmann MARIN ReFRESCO URANS Straked Rser Hamburg Unversty of Technology FreSCo+ URANS Straked Rser (TUHH) Unversty of Mchgan OpenFoam URANS Cylnder Krylov Shpbuldng Research Insttute ANSYS CFX URANS Cylnder Table : Organzatons, flow solvers, mathematcal models and test cases of submtted results.

4 . Submssons There were groups submttng results for the Workshop coverng all the proposed test cases. The manufactured soluton had the smallest number of submssons (), whereas the largest number of submssons (8) was regstered for the flow around the smooth cylnder. Table presents the name of the organzatons that submtted results, the name of the flow solver, the mathematcal model used and the test cases addressed.. Manufactured soluton There were only two partcpants performng Code Verfcaton wth the proposed Manufactured Soluton. Snce the two exercses presented several alternatves to the proposed manufactured soluton (not exactly equal for the two groups), t was decded to skp the formal submsson of data for ths test case.. Crcular cylnder There were submssons from 7 partcpants whch submtted results at fve dfferent Reynolds numbers wth four dfferent turbulence models. The submtted results are grouped by Reynolds number and turbulence model n table. We have only ncluded n table the submssons that allowed the estmaton of the numercal uncertanty,.e. submssons that ncluded nformaton from more than one grd and tme step. Reynolds Number Turbulence Model Number of Submssons k-ω SST k-ω SST k-ω SST k-ω SST Table : Reynolds and turbulence model of the submssons for the flow around a smooth crcular cylnder.

5 The largest number of submssons wth the same turbulence model () occurred for the SST verson of the k-ω two-equaton model [] for Reynolds numbers of and. There were submssons for three dfferent Reynolds numbers (, and ) that dd not use any turbulence model (dentfed by n table ). Unfortunately, only one submsson was made for the standard two-equaton model [] and the one-equaton model of []. Ths means that for these flow settngs and turbulence model t s not possble to check the consstency of the error bars from dfferent numercal solutons (one of the man goals of the present Soluton Verfcaton exercse).. Straked rser There were dfferent submssons for the calculaton of the flow around a straked rser. Two of them were based on the Reynolds-Averaged Naver-Stokes equatons supplemented by the SST k-ω model [] and one on a Lattce-Boltzmann solver wth a Wall Adaptng Eddy-vscosty model combned wth a LES turbulence closure (as descrbed by the partcpant). One of the presentatons also ncluded results from a ES (etached Eddy-Smulaton) approach based on the k-ω model. However, the results were stll prelmnary.. Uncertanty estmaton for submtted data A procedure based on a power seres representaton of the dscretzaton error wth dfferent contrbutons of the space and tme dscretzaton was appled to the data submtted to the Workshop. The estmated uncertanty reles on a soluton extrapolated to cell sze zero ( h = ) and tme step zero ( τ = ) usng a least squares soluton of px p t τ + α t τ h φ = φo + α x h for monotoncally convergent solutons. Otherwse, the adopted error descrpton s gven by h φ = φ + α o + τ α + α h x t x t h τ h τ τ + α φ stands for any of the flow quanttes requested for the Workshop; φo s the estmate of the exact soluton; h s the typcal cell sze of the space dscretzaton( h corresponds to the fnest grd); τ s the tme step ( τ corresponds to the smallest tme step); px s the observed order of convergence of the space dscretzaton; p s the observed order of convergence of the tme dscretzaton; α x, α t, α x, α t, α x and α t are constants. The detals of the procedure are beyond the scope of ths report. Nevertheless, we exemplfy ts use wth some llustratons of the applcaton to the submtted data. Fgure presents the fts performed to a submsson for the flow around the smooth cylnder at Re = computed wth the SST k-ω eddy-vscosty two-equaton model t.

6 []. The data corresponds to the average ( C avg ), root mean squared ( C rms ) and maxmum ( C ) values of the drag coeffcent and to the ampltude of oscllaton ( max C = C C ). The submsson ncludes calculatons usng three grd denstes ( max mn h =, h h =.9 h and h h =. ) and three tme steps ( τ τ =, τ τ = and τ = ). Of the 9 possble combnatons, sx calculatons were performed: τ h h =, τ, h h =.9, τ, h h =.9, τ, h h =., τ, τ = =., τ τ = τ = h =., τ τ = h h and h. τ = τ =.8 C avg.7. C rms h /h τ /τ. h /h τ /τ C max. C... h /h τ /τ. h /h τ /τ Fgure - Flow around a smooth cylnder at Re = computed wth the SST k-ω turbulence model. Fts performed to the average ( C avg ), root mean squared ( C rms ) and maxmum ( C ) values of the drag coeffcent and to the ampltude of oscllaton max ( C = C C ) max mn. Submtted data: red dots. ata ft: blue lnes. The results present a good example of the dffcultes to control and assess numercal uncertantes n ths type of calculatons. All quanttes plotted n fgure were

7 derved from the tme hstory of the same flow quantty. However, the behavour of the convergence wth grd and/or tme step refnement s sgnfcantly dfferent: The average and maxmum values of the drag coeffcent exhbt monotonc convergence, whereas C rms and C present non-monotonc convergence. C avg and C max exhbt second-order convergence n space and frst-order convergence n tme. However, there s a sgnfcant amount of scatter n the C data (the standard devaton of the ft s of the order of the dfference avg between the data), whereas devaton of the ft. C max presents a neglgble value of the standard The two cases wth non-monotonc convergence, C rms and C, do not show the same trend for the space and tme dscretzaton. For the space refnement, the convergence s not monotonc, whereas the convergence wth the tme step (lnes wth constant h h ) shows monotonc convergence. A second example of the error estmaton performed to obtan the numercal uncertanty of the submtted results s presented n fgure. The test case s agan the flow around a smooth cylnder, but n ths case the data s the average value of the drag coeffcent ( C ) obtaned by the same code usng the same turbulence model (k-ω SST avg []) at four dfferent Reynolds numbers ( Re =, Re =, Re = avg Re = ). The number of data ponts and the grd and tme step refnement ratos depend on the selected Reynolds number. Nevertheless, t s clear that the convergence of C s dependent on the selected Reynolds number. There s one case wth nonmonotonc convergence n space and tme ( Re convergence n space and tme ( = ) Re = and Re n space. = = and ) and another wth monotonc Re. For the two hghest Reynolds numbers ( ) the convergence s monotonc n tme and non-monotonc Many more examples could be presented from the data submtted to the Workshop. The ntenton of ths report s not to make an exhaustve demonstraton of the dffcultes to assess and control the numercal uncertanty of complex turbulent flow calculatons. However, we want to emphasze the dfference between the comparson of sngle grd/tme step calculatons and the comparson of numercal solutons wth ther respectve numercal uncertantes. Therefore, n all the comparsons of submtted data we wll nclude the estmated numercal uncertanty. Furthermore, the estmated uncertanty s one of the quanttes requred for the applcaton of the V&V ASME Valdaton procedure []. We must pont out that non-monotonc convergence and/or a sgnfcant amount of scatter n the data (as llustrated n fgures and ) wll lead nevtably to large 7

8 estmated uncertantes. However, the am of the comparsons of the next secton s not to dscuss the uncertanty estmaton procedure (the same procedure was appled to all submssons). Our goal s to check f submssons usng the same flow settngs and the same mathematcal model lead to overlappng error bars. If not, somethng s wrong n the numercal predctons (or the estmated uncertantes are under conservatve). =. =.. C avg. C avg.... h /h τ /τ. h /h τ /τ = =. C avg C avg...8 h /h τ /τ. h /h 7 8 τ /τ Fgure - Flow around a smooth cylnder at Re =, Re =, Re = Re = computed wth the SST k-ω turbulence model. Fts performed to the average ( C ) value of the drag coeffcent. Submtted data: red dots. ata ft: blue lnes. avg. Comparson of data. Manufactured solutons As we mentoned above, the two groups that performed Code Verfcaton usng the Method of Manufactured Solutons (MMS) [] have not followed exactly the proposed Manufactured Soluton (MS). Therefore, we do not present any comparson of submtted data. Nevertheless, we would lke to gve one example of the capabltes of the MMS and ts mportance to assess the convergence propertes of RANS solvers. and 8

9 Fgures and presents the grd convergence propertes obtaned for the ν of the calculatons of horzontal velocty component ( ) x u and for the eddy-vscosty ( ) three two-dmensonal, steady, ncompressble manufactured solutons (MS, MS and MS) [7] performed wth two RANS solvers usng the one-equaton model []. e(l (u x )) TM TML TM MS p=. MS p=. MS p=. MS p=. MS p=. MS p=. MS MS p=. h /h Fgure Convergence of the L norm of the dscretzaton error of the horzontal velocty component for three steady, two-dmensonal, manufactured solutons (MS, MS and MS). Results obtaned wth the PARNASSOS and ReFRESCO RANS solvers usng the one-equaton model of. fferent schemes n the dscretzaton of the convectve terms the turbulence model transport equaton: TM Second-order upwnd wthout lmters; TML Second-order upwnd wth lmters; TM Frst-order upwnd. The plots ncluded n fgures and present the L norm of the dscretzaton error as a functon of the typcal cell sze n logarthmc scales. The two flow solvers use sgnfcantly dfferent dscretzaton technques: fnte-dfferences for non-orthogonal structured curvlnear grds (PARNASSOS) and faced based fnte-volume for cells of arbtrary shape (ReFRESCO). The calculatons were performed wth at least secondorder accurate dscretzaton schemes for the contnuty and momentum equatons n sets of geometrcally smlar Cartesan grds. However, dfferent schemes were tested n the dscretzaton of the convectve terms of the turbulence model transport equaton: frstorder upwnd (TM); second-order upwnd wth (TML) and wthout (TM) lmters. The convergence propertes exhbt several nterestng features: t MS p=. MS p=. MS p=. MS p=. 8 9

10 e(l (ν t /ν)) MS MS p=. MS MS MS p=. p=. MS p=. MS p=. MS MS MS p=. p=. p=. MS MS p=. p= TM TML TM h /h 8 Fgure Convergence of the L norm of the dscretzaton error of the eddy-vscosty for three steady, two-dmensonal, manufactured solutons (MS, MS and MS). Results obtaned wth the PARNASSOS and ReFRESCO RANS solvers usng the one-equaton model of. fferent schemes n the dscretzaton of the convectve terms the turbulence model transport equaton: TM Second-order upwnd wthout lmters; TML Second-order upwnd wth lmters; TM Frst-order upwnd. As expected, second-order grd convergence s obtaned for the TM scheme n both codes. Naturally, a frst-order scheme used n the turbulence model transport equatons (TM) makes the order of grd convergence of the eddy-vscosty ( ν t ) drop to for both codes. However, the same effect s observed for the mean flow horzontal u. velocty component ( ) x The effect of the lmter n the second-order convecton scheme (TML) s much stronger n the fnte-dfference code (PARNASSOS) than n the fnte-volume solver (ReFRESCO). In PARNASSOS, the dscretzaton error s shftng from the TM to the TM soluton wth grd refnement. Such type of convergence propertes would be extremely hard to dscuss n the context of practcal complex flows.

11 . Crcular cylnder There were results submtted for fve dfferent Reynolds numbers (see table ): (,,, and ). In ths secton, we present the comparson between the dfferent submssons ncludng the estmated uncertantes. Ths means that submssons that dd not nclude enough data ponts to estmate the numercal uncertanty wll not be ncluded. Although the man goal of ths test case s Soluton Verfcaton,.e. assessng the qualty of numercal solutons, we wll nclude the avalable expermental data n the plots of the followng sectons. Unfortunately, we do not have the expermental uncertanty. Nevertheless, for some flow condtons there s more than one measurement... rag coeffcent, C Fgure presents the drag coeffcent data. The requested data ncluded the average ( C avg ), root mean squared ( C rms ) and maxmum ( C max ) values of the drag coeffcent and the ampltude of oscllaton ( C = Cmax C mn ). Expermental data s only avalable for the average drag coeffcent.. k-ω SST Experments. k-ω SST C avg. C rms... = = = = = = = = = = k-ω SST. k-ω SST. C max. C... = = Fgure - Submtted data for the flow around a smooth cylnder. Average ( C avg ), root mean squared ( C rms ) and maxmum ( C max ) values of the drag coeffcent ampltude of C = C C. oscllaton ( ) = max = mn = = = = = =

12 Most of the estmated uncertantes are too large. As mentoned above, ths s mostly a consequence of the sgnfcant amount of scatter n some of the submssons and/or non monotonc convergence n space and/or tme for the grd refnement and tme step levels used n the calculatons. Nevertheless, there are several examples of calculatons performed wth the same turbulence model that do not exhbt overlappng error bars. Furthermore, predctons that show consstent error bars for one feature of the drag tme hstory do not show t for others. The comparson of the numercal predctons wth the expermental C avg suffers from the absence of the expermental uncertanty. Nevertheless, as mentoned above, there are two expermental ponts for four of the fve Reynolds numbers ncluded n fgure 8. Surprsngly, the dscrepances between the predctons and the experments are largest for the two smallest Reynolds numbers... Lft coeffcent, C L The submtted data for the lft coeffcent ( C L ) s presented n fgure. In ths case, there s expermental data for C Lrms at two of the selected Reynolds numbers and the expected average value should be zero. Some of the submssons dd not report the average value of C and so the plot wth C contans less entres than the other three plots.. L. k-ω SST.. Lavg k-ω SST. Experments C Lavg -. C Lrms k-ω SST. k-ω SST.. C Lmax.. C L.. Fgure - Submtted data for the flow around a smooth cylnder. Average ( C mean squared ( C Lrms ) and maxmum ( C Lmax ) values of the lft coeffcent ampltude of oscllaton ( CL = C Lmax CLmn ). Lavg ), root

13 k-ω SST -. - k-ω SST. (Cp b ) avg -. - (Cp b ) rms = = = = = = = = = = Fgure 7 - Submtted data for the flow around a smooth cylnder. Average ( Cp b ) avg and root mean squared ( Cp values of the base pressure coeffcent. ) rms b In general, the estmated uncertantes are even hgher than for the drag coeffcent and the trends are smlar to those observed n the drag coeffcent data... Base pressure coeffcent, Cp b The results submtted for the base pressure coeffcent ( Cp b ) ncluded some awkward numbers there are most lkely due to a msnterpretaton of the nstructons. Therefore, fgure 7 presents only the average ( Cp values. ) avg b Cp and root mean squared ( b ) rms Although there are a few submssons wth an acceptable estmated uncertanty, the range of values obtaned for the base pressure coeffcent s agan mpressve. Therefore, the results renforce the man trends observed n the drag and lft coeffcents: the dffculty to control (and assess) the numercal uncertanty of the predctons and the exstence of nconsstences n predctons performed wth the same mathematcal model... Locaton of the separaton pont, θ sep Not all the partcpants reported the values of the locaton of the flow separaton pont. Furthermore, n some cases dfferent technques have been used to determne ts locaton. Therefore, the data avalable s not as complete as for the prevous flow quanttes and so we do not present any results n ths comparson. Nevertheless, we must emphasze that the trends observed n the data are smlar to those dscussed above for the other flow quanttes... Strouhal number, St The last selected flow quantty s the Strouhal number St whch was supposed to be determned from the frst harmonc of the lft coeffcent tme hstory. Although there

14 are a few cases wth too large estmated uncertantes, the Strouhal number s the varable wth the most consstent set of results.. k-ω SST. Experments. St.. = = = = = Fgure - Submtted data for the flow around a smooth cylnder. Strouhal number St.. Straked rser Only three groups submtted results for the straked rser test case and n some cases only prelmnary calculatons were performed up to the date of the Workshop. Therefore, we wll restrct the comparson of the results to table that contans the average and root mean squared drag coeffcent, C avg and C rms, the root mean squared of the lft coeffcent, C Lrms, and the Strouhal number, St. It should be mentoned that submssons I and Ia are statstcally steady flow calculatons. The table ncludes two submssons wth the same code (I and Ia), whch dffer only n the sze of the computatonal doman. One was performed wth the recommended dmensons of the computatonal doman and the other wth an nlet boundary moved upstream. These prelmnary results suggest that the recommended sze of the computatonal doman (locaton of the nlet boundary) has to be checked. Naturally, the present submssons are not suffcent to obtan a relable estmate of the numercal uncertanty and so we cannot apply the V&V ASME Valdaton procedure []. Nevertheless, the present submssons already lead to nterestng dscussons and suggestons for future mprovement.

15 Submssons I Ia II III C avg C rms C....9 Lrms St Table Submtted results of the flow around a straked rser. Average and root mean squared drag coeffcent, C avg and C rms, root mean squared lft coeffcent C Lrms and Strouhal number St.. Fnal remarks Ths frst edton of the Workshop on Verfcaton and Valdaton of CF for Workshop flows showed the dffcultes and advantages n assessng separately numercal (Verfcaton) and modelng (Valdaton) errors n complex turbulent flows. Ths report presents a bref overvew of the data submtted to ths frst edton. It represents a startng pont for what we beleve to be the most promsng way to mprove the accuracy of our numercal solutons, understand the lmts of our present turbulence models and mprove the qualty of the mathematcal models behnd our CF smulatons. We must emphasze that all sessons of the Workshop lead to very nterestng and frutful dscussons. Therefore, we would lke to thank to all the groups that submtted results to the Workshop (ncludng those that have not attended the sessons) and to all the partcpants of the OMAE Conference that attended the sessons of ths Workshop. Snce we beleve that ths type of events promotes the qualty of CF applcatons n the Offshore Industry, a second edton of ths Workshop s proposed for the forthcomng OMAE Conference that wll be held n June n Nantes. The same three test cases wll be retaned for the next edton of the Workshop ncludng Code Verfcaton, Soluton Verfcaton and Valdaton exercses. However, there are some small changes n the proposed exercses: the flow around the crcular cylnder wll be dvded n two dfferent exercses: Soluton Verfcaton for Reynolds numbers away from drag crss; Valdaton for Reynolds numbers n the regon of drag crss. For the

16 flow around the straked rser t s recommended to the partcpants to check the nfluence of the nlet boundary on ther predctons. References [] Eça L., Vaz G, Workshop on Verfcaton and Valdaton of CF for Offshore Flows, OMAE -8, Ro de Janero, Brazl, July. [] ASME Commttee PTC : ANSI Standard V&V : Gude on Verfcaton and Valdaton n Computatonal Flud ynamcs and Heat Transfer, 9. [] Menter F.R., Two-Equaton Eddy-Vscosty Turbulence Models for Engneerng Applcatons, AIAA Journal, Vol., August 99, pp [] Launder B.E., Spaldng, The numercal computaton of turbulent flows, Computer Methods n Appled Mechancs and Engneerng, Vol., 97, pp [] Spalart P.R., Allmaras S.R., A One-Equaton Turbulence Model for Aerodynamc Flows, AIAA th Aerospace Scences Meetng, Reno, U.S.A., 99. [] Roache P.J, Code Verfcaton by the Method of the Manufactured Solutons, ASME Journal of Fluds Engneerng, Vol., March, pp. -. [7] Eça L., Hoekstra M., Vaz G., Manufactured solutons for steady-flow Reynoldsaveraged Naver Stokes solvers, Internatonal Journal of CF, Vol. :,, pp--. [8] Kok J.C., Resolvng the ependence on Free-stream values for the k-ω Turbulence Model, NLR-TP-999, 999.