二维泥沙异重流运动的数学模型王光谦

王光谦　　周建军　　杨本均(,100084)　　关于泥沙异重流研究多采用分析和观测的方法,数学模型计算较少.本文中首先结合流体运动方程和泥沙运动特性,导出平面二维泥沙异重流的运动方程;然后,进行水槽试验模拟异重流运动计算,并与试验测验结果进行对比,验证了数学模型的适用性.,.,,,,,..,[1].,,..,,.,.,,..,,..,,.,,,.,.,.,,.,.,.,.,,,.8120003JOURNALOFBASICSCIENCEANDENGINEERINGVol.8,No.1March20001999-09-08,1999-12-01()..,.,,,.:,,?,?,?,,,,.,.,,.1Fig.1Sketchofdensitycurrentmovement11.,,,,,,.,.1.1[2]h2t+h2u2x+h2v2y=11+s-1s(s-s*)-1vy(1)Xh2u2t+h2u22x+h2u2v2y=11+sfi(u1-u2)-fbu2-1gh2zsx+sgh2zix+h2Dx22u2x2+2u2y2+-2gh22sx+x2u22sx2+2sy2+[-k1xu21vy+u2(s-s*)+h2v2(2)Yh2v2t+h2u2v2x+h2v22y=11+sfi(v1-v2)-fbv2-1gh2zsy+sgh2ziy+h2Dy22v2x2+2v2y2+-2gh22sx+y2v22sx2+2sy2+[-k1yv21vy+v2(s-s*)+h2u2(3)1,2;sNo53.1:,i,b;h,z;u,vxy,.,s,s,s*.fi,fb.DxDyxy,,.=(s-1)/s.vy.1.2h1t+h1u1x+h1v1y=vy(4)Xh1u1t+h1u21x+h1u1v1y=-gh1zsx-11fi(u1-u2)+11h1Dx12u1x2+2u1y2+k1xu2vy+h1v1(5)Yh1v1t+h1u1v1x+h1v21y=-gh1zsx-11fi(u1-u2)+11h1Dx12u1x2+2u1y2+k1xu2vy+h1v1(6)1.3h2st+h2u2sx+h2v2sy=xsxh2sx+ysyh2sy-(s-)(7)zbt=s-sb(8)s*=kU32gh2m(9),.sxsyxy,sb,U2=u22+v22,km.1.4,.,,,;,,,,.,,54Vol.8..,,,[3,4].2,,,.2.11964.,30cm30cm,11m,,,.,.,.,.,11,30cm50cm.,,,,.2.25m5.75m8.75m,.:,,25cm.,,,,,,,,,,.,,,,,.,,..2.2,.,,,:No55.1:..,1997..,1965,,.,.,5cm5cm.,.,,,.,,,,,.,.2.32.3.1Q=0.49l/s,s=50kg/m3.t1=0.1s,t2=ts=0.5s,180min..23,2,3.2Fig.2Depositionprocessofdensitycurrentwithtime,,,,,,:,,,,,0.01mm45%,d50=0.016mm,56Vol.8,.,,.3Fig.3Depositionofdensitycurrentalonglongitudinalprofileatdifferenttime:,,,.2.3.2Q=0.49l/s,s=50kg/m3Q=1.2l/s,s=66kg/m3,.t1=0.1s,t2=0.5s,180min.4(Q=0.49l/s)Fig.4Depthofdensitycurrentvaryingalonglongitudinalprofileatdifferenttime4567.45Q=0.49l/sNo57.1:Q=1.20l/s;67Q=0.49l/sQ=1.20l/s.5(Q=1.20l/s)Fig.5Depthofdensitycurrentvaryingalonglongitudinalprofileatdifferenttime6(Q=0.49l/s)Fig.6Depthofdensitycurrentvaryingwithtimeatdifferentsection,.,,,,,;,,,.58Vol.87(Q=1.20l/s)Fig.7Depthofdensitycurrentvaryingwithtimeatdifferentsection3,:1.,,,,.2.,,.,,,,,,,,,,,,:,,,,,,,,,.3.,;,,,,,.,,,,.No59.1:1...:,19922,..,1996,41(18):171517203,,..,1991,(5):8184,,..,1993,(11):10192-DNumericalModelofSediment-densityCurrentWANGGuangqianZHOUJianjunYANGBenjun(DepartmentofHydraulicEngineering,TsinghuaUniveristy,Beijing100084)AbstractBasedongoverningequationsoffluidflow,adepth-averaagedtwo-dimensionalequationsofsediment-densitycurrenthavebeenderived.Usingthefractional-stepmethodasthediscretescheme,anumericalmodelisbuiltandisusedtocalculateasediment-densitycurrentoccurringinaflume.Thecalculatedresultsaretestedagainstexperimentaldata.Keywords:sediment-densitycurrent,basicequationsandnumericalmodel60Vol.8