Statement of Qualfcatons
CFD Modellng by DHI/hkh/hec-ybr/pot/ShortDescrptons 08/10
CFD Modellng by DHI The capablty of understandng and nvestgatng the motons of lquds and gasses n detal s of great mportance n a wde range of engneerng dscplnes and applcatons. Wthn recent years, the use of Computatonal Flud Dynamcs (CFD) methods has expanded and today t s a wdely used tool n the engneerng desgn and the analyss of flud dynamcs. DHI provdes state-of-the-art CFD servces wthn ths feld. We have developed our own CFD code, NS3, and apply ths code together wth the open source system, OpenFOAM, n servces to our clents. Clents are offered fully dynamc as well as steady state CFD analyses of hydrodynamc performance of nternal and external flow problems. A focal pont n the development of our n-house code, NS3, has been the development of an accurate descrpton of the free surface, whch s encountered n many of our proects. Examples of valdaton of NS3 are provded n Mayer et al. (1998), Nelsen & Mayer (2001), Chrstensen (2006) and Bredmose et al. (2006), Nelsen et al. (2008), and Chrstensen et al. (2009). The theoretcal bass of all CFD modellng s the Naver-Stokes equatons, whch are appled to descrbe sngle phase as well as multphase flow condtons. On top of the hydrodynamcs foundaton we have developed advanced facltes, whch nteract wth the basc flow descrpton. These advanced facltes cover for example sedment transport ncludng a morphologcal model and models for transport of conservatve consttuents. DHI manly apples CFD systems, where we have full access to the source code, as ths means that we are able to adapt and extend the code on an as needs bass proect to proect. Characterstc of many of our CFD based servces s that we are applyng a phased approach where the CFD model s used n combnaton wth other DHI software products. Typcally, our leadng MIKE by DHI modellng technology s appled n large-scale models and the results of such coarse grd model are used as boundary condtons for the refned CFD analyses. All CFD codes appled by DHI are able to run on hgh performance computers n 64 bt Wndows or Lnux envronments. DHI s extensvely usng advanced CFD modellng n R&D as well as a drect desgn tool for our clents n a wde range of engneerng dscplnes coverng nternal flow and free surface flow challenges - often n combnaton or as a supplement to physcal model testng. The llustraton shows the wave overtoppng on a sea dke for an oblquely ncdent rregular wave tran durng a possble future clmate scenaro. Page 1
extreme wave loads, flow-nduced vbratons of a rser or operatonal performance of an ndustral process nstallaton. However, there s stll a large number of engneerng desgn processes where physcal modellng s the only relable and accurate optmsaton tool, eg for desgn of rubble mound breakwaters or structures usng concrete armour layers. DHI provdes state-of-the art CFD modellng. Example of flow around a velocty cap, coolng water ntake. Features of a CFD Model CFD modellng s today consdered the most exact numercal modellng toll for the analyss of flow problems. It s recognzed that the role of numercal smulatons n the engneerng desgn process s constantly expandng snce the vrtual test s conducted under controlled envronmental condtons and the amount of nformaton avalable s orders of magntude hgher than any complex physcal model test. Wth the ncreasng computatonal power, CFD modellng s often consdered as an alternatve to physcal laboratory tests. CFD results provde a detaled pcture of the hydrodynamcs. Example of pressure dstrbuton on the wnd turbne foundaton due to a breakng wave A key feature of CFD modellng s that t provdes a complete nsght nto the physcs of the nvestgated problem. Results of the model are not lmted to few measurng ponts but present a complete pcture of the hydrodynamc performance. The complete pcture of the physcs s hghly valuable and can be used to optmse desgns, whether for example for the desgn wnd turbne foundatons exposed to For desgn and optmsaton of rubble mound breakwaters physcal model testng s the only relable and accurate tool. Applcaton Areas DHI has developed and appled advanced CFD smulaton tools for more than two decades. Our comprehensve record of experence covers areas such as: wave and current-nduced desgn loads on varous type of structures wave run-up and green water effects wave overtoppng sedmentaton n waves and currents wave breakng and assocated sedment transport n the surf zone self-nduced vbratons of free spannng ppelnes n currents and wave-nduced flow free-surface waves around pers flow over spllways CSO structures mult-phase flow problems dam-breaks and other transent problems movng bodes n flow felds assessment of structural flow resstance A number of selected proects where we appled CFD are llustrated and dscussed n the followng. Page 2
Wave Run-up on a Wnd Turbne Foundaton Durng recent years, numerous offshore wnd farms have been constructed. One of these s located at Horns Rev, a reef n the Dansh sector of the North Sea. Observatons and measurements from the wnd farm have clearly shown that the wave run-up on the turbne tower shaft can be qute sgnfcant, and the obectve of the proect was to evaluate the mpact of wave run-up under extreme wave condtons. Especally the state of breakng may have a large nfluence on the run-up. The n-house CFD software, NS3, was appled to study the run-up on the structure for a number of layouts. CFD smulaton of a large labyrnth wer The labyrnth wer was modelled n DHI s threedmensonal CFD model, NS3. Two sectons of the wer were ncluded n the set-up. The approach flow upstream of the dam/wer was modelled by the MIKE 21 HD model and the results of the MIKE 21 model were appled as boundary condtons for the CFD model. CFD smulaton of wave run-up on offshore wnd turbne. The scour protecton enhances the wave run-up. The CFD smulatons revealed enhanced run-up, especally for short waves. The run-up was found to be much larger than found from conventonal potental dffracton theores. Labyrnth Wer One of the man obectves of ths study was to nvestgate the performance of a proposed labyrnth wer connected to a spllway on a planned dam n Ecuador. The space avalable for a wer at the ste was lmted, and n order to ncrease the flow capacty a labyrnth wer was appled. The purpose of the model was to verfy whether the theoretcal expresson developed by Tulls s applcable for the wer. The formula developed by Tulls s a sememprcal model developed on the bass of a large seres of model tests. Free surface flow over one tooth of the labyrnth wer CFD smulaton results are very close to the Tulls expresson and demonstrated that ths formula s vald and applcable for the actual wer. Comparson of the CFD smulated flow over one tooth of the labyrnth wer wth theoretcal formula developed by Tulls. Page 3
CFD Modellng of Artfcal Surfng Reefs Durng the last decade there has been a growng nterest n multpurpose reefs as a soluton to provde coastal protecton whle also creatng favourable surfng condtons at the same tme. Assessng the surfng qualty of a submerged reef requres hghly detaled nformaton on the wave breakng characterstcs such as the shape of the overturnng wave and the propagaton velocty of the movng breakpont. In addton the powerful and hghly nonunform wave breakng condtons across the reef nduce strong return currents and areas of hgh local veloctes, both of whch strongly affect the wave breakng characterstcs and represents crucal reef desgn parameters, when assessng structural stablty, nduced eroson ssues and adacent beach safety. NS3 can be coupled wth DHI s MIKE 21 BW wave model to provde the 3D offshore boundary condtons hence effectvely decreasng the necessary NS3 model doman sze and allowng the representaton of regonal effects such as nonunform refracton around adacent headlands and offshore focusng generated by offshore bathymetrcal features. Couplng of MIKE 21 BW and NS3 Boussnesq wave models have been ncreasngly popular for coastal engneerng applcatons durng the last decade, wth consderable mprovement of lnear and non-lnear accuracy. Overturnng waves, splash zone dynamcs and extreme run-up on structures, however, are beyond the capabltes of ths model class. A relable descrpton of such phenomena requres a more flexble treatment of the free surface such as a fully non-lnear Naver-Stokes solver wth VOF (Volume of Flud). DHI s MIKE 21 BW s used for calculaton of the far-feld waves for offshore wnd farms and other offshore renewable systems In Chrstensen et al (2009), the Boussnesq model s used for the far-feld waves, whle the nner regon surroundng the structure s modelled by the Naver- Stokes solver. The nner soluton handles wave breakng as well as the loads on the structure. The combned model s appled to wave loads on offshore wnd turbne foundatons. Vsual comparson between model results and camcorder recordngs of the wave breakng characterstcs at three dfferent locatons along the reef The NS3 model was used to reproduce the wave transformaton processes captured n a large-scale physcal model of an artfcal surfng reef presented n Henrquez (2004). Calculatons of the wave breakng heght and wave pealng velocty along the reef were n excellent agreement wth physcal model measurements. A vsual comparson between the numercal model predctons and physcal model vdeo records of the surfng wave shape and breakng characterstcs also demonstrated excellent agreement. Wave pressure and flow feld around a gravty based foundaton of an offshore wnd turbne. The transfer of waves from the Boussnesq model to the Naver-Stokes solver requres specfcaton of the free surface elevaton and the velocty feld over the entre couplng boundary. Page 4
Numercal Smulaton), but such an approach would requre a very detaled computatonal mesh and very fne temporal dscretsaton. From a practcal pont, ths s only possble for low Reynolds numbers. Sequence of horzontal force and overturnng moment from the rregular waves: - - Wheeler stretchng + Morson equaton, ----- BW+ Morson, CFD In many applcatons, the man nterest s to gan nformaton about the average performance of the turbulent flow. Ths s accomplshed by averagng the basc equatons to flter out the many scales of the turbulent flow and selectng a turbulent closure model that models the effect of turbulence on the mean flow. A common averagng method s the ensemble averagng leadng to the Reynolds Average Naver- Stokes equatons (RANS): u x x u t 0 uu x u ( t ) x g u x p x Comparson of maxmum overturnng moments found from zero-crossng analyses. Model Equatons The basc equatons of all CFD models are the threedmensonal Naver-Stokes equatons. The Naver-Stokes equatons for a one phase ncompressble flow are gven by: u x u t x 0 uu x u x u x g p x where u are the three average velocty components, g the gravtatonal acceleraton, p the average pressure, and t the dynamcal eddy vscosty. The result of ths approach s that n the momentum equaton averaged scales appear as the Reynolds stress tensor. The eddy vscosty hypothess relates the turbulent stresses to the velocty gradents of the mean flow. The modellng s then reduced to the specfcaton of the eddy or turbulent vscosty (exchange coeffcent for momentum) n terms of the local turbulence n the flow. Several dfferent models of the turbulent vscosty have been developed. Where u are the three velocty components, g the gravtatonal acceleraton, p the pressure, the flud densty, and the dynamcal vscosty. The frst of two equatons s the contnuty equaton, whle the second equaton s the momentum equaton. Most flows encountered n engneerng practce are turbulent. In prncple the Naver-Stokes equaton can be appled drectly on a turbulent flow (Drect RANS model of the turbulent energy n an nector pump Page 5
The most common models relate the eddy vscosty to two scalars whch are representatve of the turbulence n the flow. These scalars are normally the turbulent knetc energy and ts dsspaton or specfc dsspaton. For each of the addtonal two scalars, an addtonal transport equaton s solved n whch further modellng assumptons are ncorporated. The k-ε model s an example of a two-equaton model. Ths model has been appled wth success n many dfferent smulatons, but t has some dsadvantages. The most serous one s perhaps the lack of senstvty to adverse pressure gradents. Flow wth a free surface s a class of flows wth movng boundares. The poston of the boundary s only known ntally, and the soluton must track the poston of the free surface. In NS3, trackng of the surface s based on the VOF method. The poston of the free surface s calculated by solvng a transport equaton of the vod fracton, f: f t + (u f) = 0 x Another two-equaton model s the k- model. Ths model performs better than the k-ε model under adverse pressure gradent condtons, but the model depends on the free stream values that are specfed for the specfc turbulent dsspaton rate,. Another method s the Shear Stress Transport (SST) k- model, whch s a conglomeraton of the k-ε and k- model. In ths model, the k- model s appled n the near wall regon, whle the k-ε model s appled n the far-feld. Turbulent flows contan typcally a wde range of tme and length scales. The turbulent large-scale motons contan generally much more energy than the small scales, whch are utlsed n the so-called Large Eddy Smulaton method (LES). In the LES method, the small-scale turbulence s fltered out of the Naver-Stokes equaton, and a set of equatons whch s very smlar to the Reynolds Average Naver-Stokes equatons s obtaned. Closure of the LES model requres a model of the sub-grd scale Reynolds Stress. Detals of the LES model are for example gven n Chrstensen (2006). At the boundares, approprate condtons for the flow feld as well as the varables of the turbulence model must be specfed. Smulaton of the boundary layer requres a very fne mesh resoluton and ths together wth the fact that many turbulence models are not able to predct flow n the boundary layer correctly causes that a wall functon s often appled n ths zone. Wth the wall functon approach, flow and turbulence n the boundary layer are predcted on the bass of assumptons, for example a logarthmc velocty profle, and the Naver-Stokes equaton together wth the turbulence model are matched to the wall functon a certan dstance above the fxed boundary. F=0.5 track the free surface n a CFD model of supercrtcal flow n a rver where f=1 n the flud and f=0 n the ar. The poston of the free surface s defned by f=0.5. The knematc and dynamc boundary condtons are mposed along the free surface. The knematc condton constrants flud partcles at the free surface to follow the local flud velocty, and the dynamc boundary condton expresses the equlbrum of stresses across the free surface. In general, DNS and LES requre a fne resoluton and the CPU-tme for such calculatons s rather excessve. Ths n combnaton wth the fact that nformaton about average performance of the turbulent flow s often adequate, causes that the RANS approach s appled n most applcatons. Numercal Methods The numercal schemes of the CFD solvers are based on the fnte volume approach. NS3 requres dscretsaton of doman n a structured mult-block mesh, whle OpenFOAM supports unstructured as well as structured mesh. Space Integraton The spatal doman s dscretsed by subdvson of the contnuum nto non-overlappng cells. Each cell s bounded by a set of flat faces, and each face s shared wth only one neghbourng cell. Flow Page 6
varables, u and p, are cell-centred. The Fnte Volume method s based on the Naver-Stokes equatons n an ntegral form, where the ntegraton s carred over each cell volume: Model Input The necessary nput data to run a CFD model can be derved nto the followng groups: tt t tt t tt t u x dvdt 0 u dv t p dvdt x uu x tt t dvdt x u x t t t u x g dvdt dvdt Usng the Gauss theorem on these equatons results n relaton between the cell and face-centred values of u and p. Fnally, applyng dfferencng schemes to express the face-centred values as a functon of the varables n the neghbourng cells results n a large set of equatons, whch express the relaton between p and u throughout the doman. Doman and tme parameters - Computatonal grd - Smulaton length and tme steps Equatons, dscretsaton and solutons technque - Turbulence model - Numercal scheme - Wall functon - Transport models (sedment) - Soluton technques Intal condtons - Cold start (ntal values of flow varables) - Hot start Parameters - Models parameters (for example turbulence model parameters) - Body forces Boundary condtons - External doman boundary condtons (nflow, outflow, symmetry, perodc) - Fxed wall boundary condtons Computatonal mesh of an eector pump Tme Integraton The tme ntegraton s based on a fractonal step approach. Frstly, a propagaton step s performed calculatng an approxmaton soluton to the velocty feld, u, by solvng the momentum equaton. Secondly, applyng the contnuty equaton on the approxmated velocty feld results n an equaton whch s used to predct the pressure feld s new tme step and the new pressure feld s appled to correct the velocty feld. The propagaton n tme can be carred out by dfferent schemes such as an mplct Euler scheme, explct Euler scheme, etc. Provdng a CFD model wth a sutable grd s essental for obtanng relable results from the model. Settng up the mesh ncludes approprate selecton of the flow doman, adequate model resoluton and specfcaton of boundary condtons. It s often possble to take advantage of symmetrcal condtons and hereby reduce the computatonal doman. Selecton of approprate numercal schemes s an mportant part of the model set-up. Selecton of these schemes s often a trade off between stablty consderatons versus accuracy. For example an upwnd scheme s typcally more stable than a central dfference scheme but, on the other hand, anupwnd scheme tends to ntroduce numercal dffuson n the soluton. Selecton of an approprate turbulence model s also mportant. The selected model must be able to catch mportant features of the flow. Page 7
Model Output At each mesh pont and for each tme step, the followng type of nput s saved n an NS3 smulaton: Veloctes Pressure Turbulence model varables Effectve vscosty F (vod fracton) of the mpact of a fxed lnk between Denmark and Germany. Results of a CFD smulaton can be presented n dfferent ways such as: Contour plots Vector plots Tracer plots Anmatons Output from CFD smulatons s often postprocessed usng dfferent tools. The post-processng ncludes several varous analyss tools such as ntegraton of pressure felds over surfaces n order to calculate forces and momentum, creatons of tme seres plots of a flow varable at a sngle pont, ntegraton of fluxes over surfaces n tmes, etc. Valdaton The NS3 model has successfully been appled to a number of basc test cases where the results can be compared wth analytcal solutons, expermental tests or nformaton from lterature. These tests cover basc hydraulc aspects such as: Standng waves Travellng waves Shoalng Wave-current nteractons Smulaton of boundary layer flow Detals of the above can be obtaned from the references lsted n the secton Reference on Basc Tests. Use of Purpose-bult Software Tools based on the Open-source Lbrary, OpenFOAM The OpenFOAM system has been valdated n numerous PhD theses and papers for a range of physcal models and cases. Ths ncludes anythng from flud flow, free surface, mult-phase, DNS/LES, turbulence modellng to stress analyss, and sold-flud nteracton. An example of the use at DHI s gven below. It shows the generaton of an nternal wave n a flud wth varyng salnty. The analyss s a part of hydrographc servces for Femern Bælt A/S n the envronmental nvestgaton Internal wave between layers wth dfferent salnty generated by the presence of a future brdge per. References Bredmose, H, Skourup, J, Hansen, EA, Chrstensen, ED, Pedersen, LM, and Mtzlaft, A (2006): Numercal reproducton of extreme wave loads on a gravty wnd turbne foundaton. Proc. of OMAE 25 th Int. Conf. on Offshore Mechancs and Arctc Eng., 4-9 June 2006, Hamburg, Germany. Buxbom, IP, Fredsøe, J, Sumer, BM, Conley, DC, and Chrstensen, ED (2003): Large eddy smulaton of turbulent wave boundary layer subect to constant ventlaton. In Coastal Sedments 03, 18-23 May 2003. Sheraton Sand Key Resort, Clearwater Beach, Florda, USA. Chrstensen, ED, Bredmose, H, and Hansen, EA (2009): Transfer of Boussnesq waves to a Naver- Stokes solver. Applcaton to wave loads on an offshore wnd turbne foundaton. In Proceedngs of the ASME 28 th Internatonal Conference on Offshore Mechancs and Arctc Engneerng (10 pages). Honolulu, Hawa: ASME. Chrstensen, ED (2006): Large eddy smulaton of spllng and plungng breakers, Coastal Engneerng, Volume 53, Issues 5-6, Aprl 2006, Pages 463-485. Chrstensen, ED, Bredmose, H, and Hansen, EA (2005a): Extreme wave forces and wave run-up on offshore wnd-turbne foundatons, In Proc. of Copenhagen Offshore Wnd Conference, 10 pages. Page 8
Chrstensen, ED, and Hansen, EA (2005b): Extreme wave run-up on offshore wnd-turbne foundatons, In Proc. of Int. Conf. on Computatonal Methods n Marne Engneerng (MARINE 2005), Oslo, Norway, 27-29 June 2005, pp 293-302. Chrstensen, ED, Zanuttgh, B and Zyserman, J (2003): Valdaton of numercal models aganst laboratory measurements of waves and currents around low-crested structures. In Coastal Structures 03, 26-29 August 2003, Portland, Oregon, USA. Chrstensen, ED, D-J Waltra and N Emerat (2002): Vertcal varaton of the flow across the surf zone, Coastal Engneerng, Vol 45, No 3-4, pp 169-198. Chrstensen, ED, Jensen, JH, and Mayer, S (2000): Sedment transport under breakng waves. Proc. 27th, ICCE00, Sydney, Australa. Emarat, N, Chrstensen, ED, Forehand, DIM and Mayer, S (2000): "A study of plungng breaker mechancs by PIV measurements and a Naver- Stokes solver", In Proc. of the 27 th Int. Conf. Coastal Eng., ASCE, Vol 1, pp 891-901, Sydney, Australa. Hansen, EA and Meyer, S (2001): A numercal model for current-nduced vbratons of multple rsers. In Proc. of the 20 th Conference on Offshore Mechancs and Artc Engneerng, OMAE 01, Ro de Janero, Brazl. Hansen, EA, Bryndum, M, Mørk, K, Verley, R, Sortland, L, and Nes, H: Vbratons of a free spannng ppelne located n the vcnty of a trench. In Proc. of the 20 th Conference on Offshore Mechancs and Artc Engneerng, OMAE 01, Ro de Janero, Brazl. Kawamura T, Mayer, S, Garapon, A, Sørensen, LS (2001): Large Eddy Smulaton of the Flow past a free-surface percng crcular Cylnder. In: Transactons of the ASME. Journal of Fluds Engneerng, Vol 124, Issue 1, pp 91-101. Mayer, S, Nelsen, KB, and Hansen, EA (2005): Numercal predcton of wave mpact loads on multple rectangular beams, Coastal Engneerng Journal, Vol 45, No 1, pp 41-65. Mayer, S, Garapon, A and Sørensen, LS (1998): A fractonal step method for unsteady free-surface flow wth applcaton to non-lnear wave dynamcs. Intl. Journal for Numercal Methods n Fluds, Vol 28, No 2, pp 293-315. Nelsen, KB, and Mayer, S (2004): Numercal predcton of green water ncdents, Ocean Engneerng, Vol 31, pp 363-399. Nelsen KB and Mayer, S (2001a): VOF smulatons of green water load problems. 4 th Numercal Towng Tank Symposum, September 2001, Hamburg, Germany. Nelsen, KB, Mayer, S (2001b): Numercal smulaton of tank sloshng, SRI-TUHH mn- Workshop on Numercal Smulaton of Two-Phase Flows, Tokyo, Japan. Tulls, JP, Amanan, N, and Waldron, D (1995): Desgn of labyrnth spllways, Journal of Hydraulc Engneerng, Vol 121, No 3, pp 247-255. Jensen, JH and Fredsøe, J (2001): Sedment transport and Backfllng of Trenches n oscllatory Flow. Journal of Waterway, Port, Coastal and Ocean Engneerng, ASCE, Sep-Oct 2001, pp 272-281. Jensen, JH, Madsen, EØ, and Fredsøe, J (1999): Oblque flow over dredged channels. II: Sedment Transport and Morphology. J. Hyd. Engrg, ASCE, 125(11), pp 1190-1198. Jensen, JH, Madsen, EØ, and Fredsøe, J (1999a): Oblque flow over dredged channels. Part I: Flow Descrpton. Journal of Hydraulc Engneerng, ASCE, 125(11), pp 1181-1189. Page 9
Agern Allé 5 Tel: +45 4516 9200 DK-2970 Hørsholm Fax: +45 4516 9292 Denmark E-mal: Web: dh@dhgroup.com www.dhgroup.com Page 10