波浪力学第四章 小尺度结构物上的波浪力

{{{{{{{4.1{4.2z4.2.1Morisonz4.2.2z4.2.3z4.2.4z4.2.5{4.3{4.4OFFSHORESTRUCTURES™••••™™4.1™•••••{4.1.1™™™‰‰‰{4.1.1™‰‰‰56310Re3.510×≤×{4.1.1™‰™‰ρ—‰—‰‰—δ{4.1.2Re55Re40≤40Re150≤150Re300≤5300Re310≤×56310Re3.510×≤×Re105.36×{4.1.2{4.1.20vDfS=)2cos(v2120ftDCfLLπρ=)4cos(v2120ftDCfDDπρ′=′{4.1.2StrouhalSRe{4.1.3‰‰‰{4.1.3‰‰{4.1.3‰‰:{4.2z4.2.1Morisonz4.2.2z4.2.3z4.2.4z4.2.5{4.2.1dxzoczdzfHfH™f——‰‰xxDDuAuCfρ=21{4.2.1dxzoczdzfHfH™f——dtduVCdtduVfxmxI00ρ+ρ=dtduVCxM0ρ={4.2.1dxzoczdzfHIDHfff+=dtduVCdtduVuAuCxmxxxD0021ρ+ρ+ρ=dtduVCuAuCxMxxD021ρ+ρ={4.2.1dxzoczdzfHdtduDCuDuCfxMxxDH4212πρ+ρ=tuDCuDuCfxMxxDH∂∂πρ+ρ=4212{4.2.1xuxuDCfxxDH&&−−ρ=)(21dxzoczfHx)(4422xtuDCtuDxmx&&−∂∂πρ+∂∂πρ+xuxuDCfxxDH&&−−ρ=)(21xDCtuDCmxM&&4422πρ−∂∂πρ+{4.2.2dxzoczdzfHdztuDCdzuDuCdzfdFxMxxDHH∂∂πρ+ρ==4212{4.2.2dxzoczdzfH∫=21zzHHdzfF∫∫∂∂πρ+ρ=21214212zzxMzzxxDdztuDCdzuDuC{4.2.2∫η+=dHHdzfF0dxzoczdzfH∫∫η+η+∂∂πρ+ρ=dxMdxxDdztuDCdzuDuC020421{4.2.2∫η+=dHHdzzfM0dxzoczdzfH∫∫η+η+∂∂πρ+ρ=dxMdxxDzdztuDCzdzuDuC020421{4.2.2∫∫η+η+∂∂πρ+ρ=dxMdxxDHdztuDCdzuDuCF020421{4.2.2——∫∫η+η+∂∂πρ+ρ=dxMdxxDHdztuDCdzuDuCF020421)cos(tkxaω−=η)cos(sh)(chtkxkddzkTHuxω−+π=)sin(sh)(ch222tkxkddzkTHtuxω−+π=∂∂{4.2.2dztuDCdzuDuCdzfdFxMxxDHH∂∂πρ+ρ==4212dzkdkzTHDCdzkdkzTHDCdzfdFMDHHθππρ+θθ⎟⎠⎞⎜⎝⎛πρ==sinshch24coscosshch212222{4.2.2∫=21zzHHdzfF∫∫θππρ+θθ⎟⎠⎞⎜⎝⎛πρ=2121sinshch24coscosshch212222zzMzzDdzkdkzTHDCdzkdkzTHDCθγπ+θθγ=sin8coscos22212KHDCKDHCMDkdkzkzzzkK2sh82sh2sh)(212121−+−=kdkzkzKchshsh122−={4.2.2∫η+=dHHdzfF0θγπ+θθγ=sin8coscos22212KHDCKDHCMDkddkdkK2sh8)(2sh)(21η++η+=kddkKch)(sh2η+={4.2.2——‰η‰ηηkdHdkHdkKK2sh8)2(2sh)2(211+++==′kdkdKKchsh22==′θ′γπ+θθ′γ=sin8coscos22212KHDCKDHCFMDHkddkdkK2sh8)(2sh)(21η++η+=kddkKch)(sh2η+=θγπθθγsin8coscos22212KHDCKDHCFMDH+={4.2.2——θ′γπ+θθ′γ=sin8coscos22212KHDCKDHCFMDHFHDmaxFHImaxθ+θθ=sincoscosmaxmaxHIHDHFFF{4.2.2dxzocfH∫−=21)(1zzHHdzfzzMθγ+θθπγ=sin16coscos24232KHLDCKLDHCMD{4.2.2∫−=21)(1zzHHdzfzzMθγ+θθπγ=sin16coscos24232KHLDCKLDHCMD[])2ch2(ch2sh)(2)(22sh3211221221223kzkzkzzzkzzkkdK−−−+−=[])ch(chsh)(2ch1122124kzkzkzzzkkdK−−−={4.2.2∫η+=dHHdzzfM0∫∫η+η+∂∂πρ+ρ=dxMdxxDzdztuDCzdzuDuC020421θγ+θθπγ=sin16coscos24232KHLDCKLDHCMD[]1)(2ch)(2sh)(2)(22sh321223+η+−η+η++η+=dkdkdkdkkdK[]1)(ch)(sh)(2ch14+η+−η+η+=dkdkdkkdK{4.2.2——θ′γ+θθ′πγ=sin16coscos24232KHLDCKLDHCMMDHMHDmaxMHImaxθ+θθ=sincoscosmaxmaxHIHDHMMM{4.2.2θ+θθ=sincoscosmaxmaxHIHDHFFFθ+θθ−=θcossincos2maxmaxHIHDHFFddFmaxmaxsin2cosHIHDFF+θ−θ=θFHDmaxθFHImaxFHImaxFHDmax{4.2.2θ+θθ=sincoscosmaxmaxHIHDHFFFθFHDmaxθFHImaxFHImaxFHDmaxFHImaxFHDmaxθFHmaxFHImaxFHImaxFHDmaxθθFHImaxFHDmax⎟⎟⎠⎞⎜⎜⎝⎛=θxmaHDHIFF2arcsinmax⎥⎥⎦⎤⎢⎢⎣⎡⎟⎟⎠⎞⎜⎜⎝⎛+=2max411xmaHDHIxmaHDxmaHFFFF{d=20mD=1mH=0.6mT10s{4.2.3————{4.2.340Re150≤{4.2.340Re150≤ν=DumReDTuKCm={4.2.3mvuDfS=wvrfff=Tfw1=KCfSr={4.2.3™™)cos(2112∑=θ+ωρ=NnnnLmLtnCDuf•Um,D——•ω——•θn——n•CLn——nKC{4.2.3™)cos(2112∑=θ+ωρ=NnnnLmLtnCDuf•CLn——n1….54.14•CL2——4.14•——•)(2cos212tkxKDHCFLLω−γ={4.2.4{4.2.4dxzocIIIπ=φ2LlI+IIθ0θ+θθ=sincoscosmaxmaxHIHDHFFF{4.2.4xy(i,j))sin()cos()cos(maxmaxtkxFtkxtkxFFijijHIijijijHDHijω−+ω−ω−=∑∑=ijHijHFF{4.2.4™dxzo{4.2.4™c{4.2.4™c{4.2.4∑∑=ijHijijHFKFl/D2341.51.2510.70.81.0{4.2.6—CDCMCL™——™),Re,,(1TtDKCfCDδ=),Re,,(2TtDKCfCMδ=),Re,,(3TtDKCfCLδ={4.2.6—CDCMCL™{})Re,,(DKCfCCCiLMDδ=™TDKCν==β2Re{}),,(DKCfCCCiLMDδβ={4.2.6—CDCMCL™APIDNVCCSStokesStokesCD0.61.00.51.21.2CM1.52.02.02.0{4.3{4.3ux{4.3.1™nMnnDDCDCUUUf&4212πρ+ρ=xyzoeφϕUn⎪⎭⎪⎬⎫⎪⎩⎪⎨⎧+⎪⎭⎪⎬⎫⎪⎩⎪⎨⎧=⎪⎭⎪⎬⎫⎪⎩⎪⎨⎧zyxMzyxnDUUUDCUUUDC&&&4212πρρUfffzyx{4.3.1xyzoeφϕUn™kejeiezyx++=e™Un)(een××=•kujuiuzyx++=•xkuiuzx+=sincosxeϕφ=sinsinyeϕφ=coszeϕ=⎪⎭⎪⎬⎫⎪⎩⎪⎨⎧+⎪⎭⎪⎬⎫⎪⎩⎪⎨⎧=⎪⎭⎪⎬⎫⎪⎩⎪⎨⎧zyxMzyxnDUUUDCUUUDC&&&4212πρρUfffzyx{4.3.1xyzoeφϕUn™Un)(een××=uUkUjUiUzyxn++=U[]zzxxxxzxzxxxueueeueeueuU−=−−=)1(2[]zzxxyyzzyxxyueueeeeueeuU−=−−=[]zzxxzzzzzxxzueueeueueeuU−=−+−=)1(2[][]2/12222/1222zzxxzxzyxnueueuuUUUU−+=++=⎪⎭⎪⎬⎫⎪⎩⎪⎨⎧+⎪⎭⎪⎬⎫⎪⎩⎪⎨⎧=⎪⎭⎪⎬⎫⎪⎩⎪⎨⎧zyxMzyxnDUUUDCUUUDC&&&4212πρρUfffzyx{4.3.1™xyzoeφϕUntueetueUzxzxxx∂∂−∂∂−=)1(2&tueetueeUzyzxyxy∂∂−∂∂−=&tuetueeUzzxzxz∂∂−+∂∂−=)1(2&⎪⎭⎪⎬⎫⎪⎩⎪⎨⎧+⎪⎭⎪⎬⎫⎪⎩⎪⎨⎧=⎪⎭⎪⎬⎫⎪⎩⎪⎨⎧zyxMzyxnDUUUDCUUUDC&&&4212πρρUfffzyx{4.3.1™xyzoeφϕUniukujuiuxzyx=++=)(een××=uU])1[(2keejeeieuzxyxxxn−−−=U21xxneu−=UdsDCdFnnDDUUρ=21{4.3.1™xyzoeφϕUn()dsueDCdFxxDDx332121−ρ=dsueeeDCdFxyxxDDy22121−ρ−=dsueeeDCdFxzxxDDz22121−ρ−={4.3.1™xyzoeφϕUn()dsueDCdFxxDDx332121−ρ=dsueeeDCdFxyxxDDy22121−ρ−=dsueeeDCdFxzxxDDz22121−ρ−=xyzoeϕUn‰xozφ0ex=sinϕ,ey=0,ez=cosϕdsuDCdFxDDx23cos21ϕρ=dzDuCxDϕρ=22cos21dsDuCdFxDDzϕϕρ−=sincos2122dzDuCxDϕϕρ−=sincos212{4.3.1™xyzoeφϕUn()dsueDCdFxxDDx332121−ρ=dsueeeDCdFxyxxDDy22121−ρ−=dsueeeDCdFxzxxDDz22121−ρ−=‰yozφ90ex=0,ey=sinϕ,ez=cosϕxyzoeϕdsDuCdFxDDx221ρ=0==DzDydFdF{4.3.1™xyzoeφϕUn()dsueDCdFxxDDx332121−ρ=dsueeeDCdFxyxxDDy22121−ρ−=dsueeeDCdFxzxxDDz22121−ρ−=‰ϕ90ex=cosφ,ey=sinφ,ez=0dsDuCdFxDDxφρ=22sin21dsDuCdFxDDyφφρ−=cossin21220=DzdF{4.3.1™xyzoeφϕUn‰ϕ90ex=cosφ,ey=sinφ,ez=0‰(a)φ=0,ex=1,ey=ez=0;dsDuCdFxDDxφρ=22sin21dsDuCdFxDDyφφρ−=cossin21220=DzdFXeyzo0===DzDyDxdFdFdF{4.3.1™xyzoeφϕUn‰ϕ90ex=cosφ,ey=sinφ,ez=0‰(a)φ=90,ex=0,ey=1ez=0;dsDuCdFxDDxφρ=22sin21dsDuCdFxDDyφφρ−=cossin21220=DzdFXeyzo0==DzDydFdFdsDuCdFxDDx221ρ={4.3.2™™™z{4.3.2™‰‰™{4.3.2™znnDDCUUfρ=21eern××=uUcruuu+=ccDDCuu)u(