Verification and Validation of LAD2D Hydrocodes for Multi-material Compressible Flows

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1 8 Ieaoal Cofeece o Physcs Maheacs Sascs Modellg ad Sulao (PMSMS 8) ISBN: Vefcao ad Valdao of ADD Hydocodes fo Mul-aeal Copessle Flows Ru-l WANG * ad Xao IANG Isue of Appled Physcs ad Copuaoal Maheacs Bejg 94 Cha Shadog Uvesy of Scece ad Techology Qgdao 6659 Cha * Coespodg auho Keywods: ADD Hydocodes Copessle flows Vefcao ad valdao SOD pole Cylde es. Asac. agaga Hydocodes s he a sulao ool ul-aeal copessle flows of hgh epeaue ad hgh pessue. The poa poles we ae up agas ae how e should cofdece odelg ad sulao e ccally assessed. The vefcao ad valdao (V&V) of copuaoal sulaos ae he pay ehods fo uldg ad quafyg hs cofdece. Vefcao s he assesse of he accuacy of he soluo o a copuaoal odel y copaso wh ow soluos. Valdao s he assesse of he accuacy of a copuaoal sulao y copaso wh epeeal daa. I hs pape The vefcao ad valdao (V&V) of agaga Hydocodes of ul-aeal copessle flows was pese. Vefcao of he ADD Sofwae was pleeed y he Sod pole. Valdao of he ADD Sofwae was pleeed y he cylde es. Ioduco agaga Hydocodes s he a sulao ool ul-aeal copessle flows of hgh epeaue ad hgh pessue. The poa poles we ae up agas ae how we should cofdece odelg ad sulao e ccally assessed. The vefcao ad valdao (V&V) of copuaoal sulaos ae he pay ehods fo uldg ad quafyg hs cofdece. Befly vefcao s he assesse of he accuacy of he soluo o a copuaoal odel y copaso wh ow soluos. Valdao s he assesse of he accuacy of a copuaoal sulao y copaso wh epeeal daa []. The Copuaoal Model Goveg Equaos We cosde he followg se of equaos fo a wo-desoal ul-aeal copessle flud syse wh elasc ad plasc es we agaga foals: V V ε ε y ε () du Σ T T ν d () dv T Σ Σ Σ ν d (3) de Σ ε Σ ε Σ ε T γ d (4)

2 whee ad ae space coodaes. I wo desoal plaa s he level deco s he pepedcula deco; fo wo desoal cylde syey s aal syey deco s pepedcula deco. u v e ad P ae he velocy copoes desy eal eegy ad pessue especvely. The uppe a s he devave espec o e V s he capacy ao ε ε ε ae posve sa ao γ s he shea sa ao ν s geoey coeffce ν epeses wo deso plaa ν s fo wo deso cylde syey. I ode o ac he dscouy ea he shoc we oduce afcal vscosy ad wll e u o oly whe he sa ao s egave. We ae o e he lea coao of adshoff Vscosy ad Vo Neua-Rchye vscosy he Vo Neua-Rchye vscosy s he followg fo: V l NR < V qnr V (5) V whee l NR has legh deso l a A ; a Vo Neua-Rchye vscosy coeffce; A s NR NR NR he aea of he cell adshoff vscosy s gve y: V l < c V q V V whee l has legh deso l a A ; a adshoff vscosy coeffce. The Joes-Wls-ee (JW) equao of sae (EOS) s used fo he eaced ad u-eaced gases he eplosve egos. The EOS of he pessue-depede JW ype s foud o e (6) ω R V ω R V ωe PEOS A e B e RV R V (7) V whee P EOS s he pessue V s elave specfc volue V E s he deoao eegy pe u volue E e ad A B R R ad ω ae cosas o e calaed. The calculaed pessue of he shoc wave y usg JW paaees deeed y he uecal ehod agees wh epeeal esuls. To accou fo he effec of couso o deoao dyacs he pessue he hgh eplosve egos s copued y usg P PEOS F. (8) The u faco F ha cool he elease of checal eegy s copued y F [ a( F F )] (9) whee F deoes o ug; < F < deoes ug; F deoes ug fshed. Wls fuco F s defed as: ( V V )/( V V ) F J V V V > V > V V V C-J u fuco F s defed as: J J ()

3 ( ) F < < / () whee ( ) / γ γv V J deoes CJ volue; V deoes al volue; γ deoes he ao of specfc heas fo a; s acual e; s he e fo a zoe o sa ug; / J D R R s cell wdh; J D s he deoao velocy; γ s he ao of specfc heas; ad γ ae adjusale paaees. The sffeed gas equao of sae whee he pessue P ad soud speed s c ae gve es of he desy ad he specfc eal eegy e y ( ) ( ) e c P γ () ( ) ( )e c c s γ γ γ γ. (3) agaga Fe Volue Foulao The copuaoal ehod s agaga fe volue o aaly polygoal gd. To each ode e.g. Fgue we defe he cool volue o e coeced y he cee of eghog cells ad he cee of edges suoudg he ode whee... ae odes aoud... ae he cell cee of he suoudg cell... ae he coespodg cee of he edges. Fgue. Cool volue Ω of oeu equao The dscesao foulao of velocy s gve hough dsceo of he oeu equao he followg: ( ) ( ) ( ) ( ) {[ ] ( ) ( ) ( ) ( ) [ ]} ( ) ( ) ( ) ( ) {[ ] ( ) ( ) ( ) ( ) [ ]} G T T B v v F B u u ν ν Σ Σ Τ Τ Σ Σ (4) wh l A B ( ) Τ M A F π ( ). A G M π Σ Σ (5) Usg he ew velocy ode we ge he ew poso of ode fo he e e sep:

4 u. v The dscezao of he ohe equaos s gve he followg seco. (6) Fo eaple he eal eegy equao has he followg fo: ( p q V V ( s ε s ε s ε τ γ ). (7) e ) We ca dscee (7) o cell ad use he followg sequece o copue sep y sep S ( ) ( S S ) (8) ( Z ) ( s ε s ε s ε τ γ ) (9) ( P q ) ( Z ) ~ e e () ~ P e ( ~ ) P () fally we ge ( P ) P e ~ ~ e wh () ( e ) P P. (3) agaga Adapve Hydodyacs Code Two Desoal Space ADD (see Fgue ) s he aevao fo agaga adapve hydodyacs code wo desoal space whch s a self-developed copuaoal sofwae ad as a sudyg deoao flud dyacal syse wh elasc-plascy sucue [3]. Vefcao ad Valdao of he ADD Sofwae Vefcao of he ADD Sofwae The fudaeals of vefcao ae o defy easue ad educe eos he copuaoal odel ad s uecal ehod. Thee ae wo ypes of vefcao. Oe ype s soluo vefcao aohe s code vefcao. Soluo vefcao s o quaavely evaluae he uecal pecso of dscezao ehods fo ouday ad al codos ad dscee soluos of PDEs [4]. The Sod pole (Sod 978) s a esseally oe-desoal flow dscouy pole whch povdes a good es of a copessle code s aly o capue shocs ad coac dscoues wh a sall ue of zoes ad o poduce he coec desy pofle a aefaco. I also ess a code s aly o coecly sasfy he Rae-Hugoo shoc jup codos [5]. The flud s ally a es o ehe sde of he eface ad he desy ad pessue jups ae chose so ha all hee ypes of flow dscouy (shoc coac ad aefaco) develop. To he lef ad gh of he eface we have:

5 u p... R u.5 R. p. R > (4) Fgue. Sucue of he ADD sofwae.

6 The equao of sae of gas s used wh P ( γ ) e he adaac cosa γ s chose o e.4 o oh sdes of he eface. Fgue 3 shows he esul of ug he Sod pole wh ADD o a wo-desoal gd wh he aalycal soluo show fo copaso..8 Nuecal soluo Aalycal soluo.8 Nuecal soluo Aalycal soluo.8 desy.6.4 pessue.6.4 velocy.6.4 Nuecal soluo Aalycal soluo Fgue 3. Copaso of uecal soluos ad aalycal soluos o Sod pole A. hee dffee olea waves ae pese: a aefaco ewee. 6 ad. a coac dscouy a. 45 ad a shoc a. 86. Nea he coac dscouy ad he aefaco we fd sall eos of aou % he desy ad specfc eal eegy wh sla eos he velocy sde he aefaco. Elsewhee he uecal soluo s eac; o oscllao s pese. Valdao of he ADD Sofwae Valdao s a pocess of deeg he degee o whch a odel s a accuae epeseao of he eal wold fo he pespecve of he eded uses of he odel. I s he pocess of deeg he degee o whch copuaoal sulao esuls agee wh epeeal daa ad eal wold. The fudaeal ehod of valdao volves defyg ad quafyg he eo ad uceay he physcal ad copuaoal odels [67] quafyg he uecal eo he copuaoal soluo esag he epeeal uceay ad he copag he copuaoal esuls wh epeeal daa. Cylde es s o pu he deoao o a coppe ue of equal hcess whch s deoaed fo oe sde ad easued y a hgh-speed oag caea. Ths d of ess s a sadadzed es o deee he deoao JW sae equaos ad evaluae he eaco pocess. The scheac daga of cylde es s aaged as Fgue 4. Fgue 4. Scheac daga of cylde es fo deoao The copuaoal doa s show Fgue 5 Paaees values used fo Wls ae law descg JOB93 eplosve ae 3.79 D CJ s. 84 g 3 Coeffce of c

7 JW-EOS s A B R. 397 R.6 w.48 [89]. The sulao ad es esuls ae copaed Fgue 6 whch s copaso wh each ohe vefyg he effecveess of hs paaee calao appoach. Fgue 5. Scheac daga of copuaoal doa. 3.8 R_Poso(c) The Resuls of Epee The Resuls of ADD R_Velocy(c/us) The Resuls of Epee The Resuls of ADD Te(us) Te(us) Fgue 6. Copaso of he sulao esuls ad he epeeal daa (ef: Radal wall poso; Rgh: Radal wall velocy) Radal wall po s dsace fo he deoao. Suay The cedly of he sulao esul o pedco esul he egeeg uecal sofwae has a poa fluece o decso-ag. Egeeg applcao sofwae V&V s a ccal ehod used fo evaluag he cedly of he sofwae ad sulao esul. we poposed he V&V ehods of agaga Hydocodes of ul-aeal copessle flows. The pape efes o hee a aspecs cludg coecess vefcao sofwae aheacal heoy adapaly valdao physcal odelg ad uceay quafcao odel. Evaluag he cedly of physcal odel s a pocess whch paly use he epee daa fo dffee heachcal valdao epee o evaluae s adapaly ad quafy s uceay. The asc faewo of he odule vefcao ehods ad he fuco valdao ehod wee poposed coposg he deoao flud dyacs odel V&V ehods of ADD. The dea of V&V saegy ca e also appled ohe physcal odel flud dyacs ad ohe sofwae cople egeeg. Acowledgee Ths wo was suppoed y Scece Challege Pojec No. TZ8 ad Naoal Naue Scece Foudao of Cha [Ga Nos ] ad he Defese Idusal Techology Develope Poga (C5).

8 Refeeces [] W.. Oeapf C. J. Roy Vefcao ad valdao scefc copug New Yo: Cadge Uvesy Pess. [] R. Wag X. ag Z. ADD: A copue code fo deoao flud dyacs pole wh lage dsoo ad eal slp[j] Defec ad Dffuso Fou 7 Vol. 379 pp (.48 / [3] WANG Rul IN Zhog WEN Wazh. Develope ad applcao of adapve ul-eda agaga flud dyacs sofwae ADD[J] Copue Aded Egeeg 4 3():-7. ( Chese) [4] P.J. Roache Vefcao of codes ad calculaos AIAA J : [5] G.A. Sod. Revew a suvey of seveal fe dffeece ehod of syse of olea hypeolc cosevao laws. J. Copu. Phys ():-3. [6] Wag R Jag S. Maheacal ehods fo uceay quafcao olea ul-physcs syses ad he uecal sulaos[j]. Sc S Mah 5 45: do:.36/n4-5. ( Chese). [7] ag Xao Wag Ru-. Sesvy aalyss ad valdao of deoao copuaoal flud dyacs odel[j] Aca Physca Sca (7) DOI:.7498/aps ( Chese) [8] Wag Ya-Fe u Je Zhag Xu JW equao of sae of ueaced JOB-93 eplosve[j] Chese Joual of Hgh Pessue Physcs 6 3(5): ( Chese) [9] Hu Ba-y Ha Chag-sheg u Da- The coposo aalys s he deoao poducs y TNT ad JOB-93[J] The Joual of Eplosves ad Popellas 3: ( Chese).