辐射流立方定理的推导及试验研究
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摘要
为了推导辐射流光滑平行板立方定理并研究其适用性,通过理论分析,根据惯性力和黏性力的数量级关系,将水流的分布状态分成黏性区和势流区,在完全处于黏性区的"弱惯性带"中,由N-S方程和Laplace方程推导辐射流立方定理。在水力压强分别为0. 1、0. 2和0. 3 MPa时,对平行板和规则齿进行水力试验,验证平行板实际流量与立方定理吻合程度以及粗糙裂隙面对于立方定理的适用性。结果表明:水力压强为0. 1 MPa时,平行板的流量与立方定理吻合良好;高水头差易产生非线性流,导致流量偏离立方定理;粗糙度的存在会破坏水流的连续性,削弱过流能力,规则齿的试验值比预测值低7. 9%～14. 6%。
This study aimed at deriving the cubic law of radial flow of smooth parallel plates and study its applicability. According to the order of magnitude relationship between the inertial force and the viscous force,the distribution state of the flow was divided into the viscous zone and the potential flow zone. In the "weak inertial band",flow was completely in the viscous zone,the cubic law of radial flow was derived according to the N-S equation and the Laplace equation. In hydraulic testing,hydraulic pressures of parallel plates and regular teeth are 0. 1,0. 2 and 0. 3 MPa,respectively; proving the agreement between the actual flux of the parallel plates and the cubic law and the applicability of rough fracture surface to cubic law. When the hydraulic pressure is 0. 1 MPa,the flux of the parallel plates agrees well with the cubic law. However,high head differences are prone to nonlinear flows,causing flow to deviate from the cubic law. The presence of roughness will destroy the continuity of the water flow and weaken the discharge capability. The test value of the regular teeth is 7. 9%-14. 6% lower than the predicted value.
This study aimed at deriving the cubic law of radial flow of smooth parallel plates and study its applicability. According to the order of magnitude relationship between the inertial force and the viscous force,the distribution state of the flow was divided into the viscous zone and the potential flow zone. In the "weak inertial band",flow was completely in the viscous zone,the cubic law of radial flow was derived according to the N-S equation and the Laplace equation. In hydraulic testing,hydraulic pressures of parallel plates and regular teeth are 0. 1,0. 2 and 0. 3 MPa,respectively; proving the agreement between the actual flux of the parallel plates and the cubic law and the applicability of rough fracture surface to cubic law. When the hydraulic pressure is 0. 1 MPa,the flux of the parallel plates agrees well with the cubic law. However,high head differences are prone to nonlinear flows,causing flow to deviate from the cubic law. The presence of roughness will destroy the continuity of the water flow and weaken the discharge capability. The test value of the regular teeth is 7. 9%-14. 6% lower than the predicted value.
引文
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[15]张春生.混凝土衬砌高压水道的设计准则与岩体高压渗透试验[J].岩石力学与工程学报,2009,28(7):1305-1311.
[16]CAO Cheng,XU Zengguang,CHAI Junrui et al. Mechanical and hydraulic behaviors in a single fracture with asperities crushed during shear[J]. International Journal of Geomechanics,2018,18(11):04018148.
[17]WEINAN E. Boundary Layer Theory and the zero-viscosity limit of the Navier-Stokes Equation[J]. Acta Mathematica Sinica,2000,16(2):207-218.
[18]郭保华,苏承东.多级加载下岩石裂隙渗流分段特性试验研究[J].岩石力学与工程学报,2012,31(S2):3787-3794.
[19]张志昌.水力学(下册)[M].北京:中国水利水电出版社,2011.
[20] KUMAR S,BERGADA J M,WATTON J. Axial piston pump grooved slipper analysis by CFD simulation of three-dimensional NVS equation in cylindrical coordinates[J]. Computers&Fluids,2009,38(3):648-663.
[2]LI Bo,LIU Richeng,JIANG Yujing. Influences of hydraulic gradient,surface roughness,intersecting angle, and scale effect on nonlinear flow behavior at single fracture intersections[J]. Journal of Hydrology,2016,538(538):440-453.
[3]ZHANG Zhenyu,NEMCIK J. Fluid flow regimes and nonlinear flow characteristics in deformable rock fractures[J].Journal of Hydrology,2013,477:139-151.
[4]卢占国,姚军,王殿生,等.平行裂缝中立方定律修正及临界速度计算[J].实验室研究与探索,2010,29(4):14-16+165.
[5]朱红光,易成,谢和平,等.基于立方定律的岩体裂隙非线性流动几何模型[J].煤炭学报,2016,41(4):822-828.
[6]ELKHOURY J E,DETWILER R L,AMELI P. Dissolution and Deformation in Fractured Carbonates Caused by Flow of CO2-Rich Brine[C]//AGU Fall Meeting. AGU Fall Meeting Abstracts,2011.
[7]WANG Lichun,CARDENAS M B,SLOTTKE D T,et al. Modification of the Local Cubic Law of fracture flow for weak inertia,tortuosity,and roughness[J]. Water Resources Research,2015,51(4):2064-2080.
[8]MALLIKAMAS W,RAJARAM H. An improved two-dimensional depth-integrated flow equation for roughwalled fractures[J]. Water Resources Research,2010,46(8):3954-3963.
[9]WANG Lichun,CARDENAS M B. Non-Fickian transport through two-dimensional rough fractures:Assessment and prediction[J]. Water Resources Research,2014,50(2):871-884.
[10]ALYAARUBI A H,PAIN C C,GRATTONI C A,et al.Navier-stokes simulations of fluid flow through a rock fracture[J]. Geophysical Monograph,2013,162:55-64.
[11] MGAYA P,KISHIDA K,HOSODA T. Fluid flow in measured apertures of a single rock fracture:A depth averaged model and the local cubic law simulations[J].Journal of Inclusion Phenomena&Macrocyclic Chemistry,2006,68(1-2):99-108.
[12]MGAYA P,KISHIDA K,HOSODA T,ET AL. Estimation of flow behavior on rock joints using the depth averaged flow model[J]. Journal of Applied Mechanics,2004,7:1013-1021.
[13]KISHIDA K,MGAYA P,OGURA K,et al. Flow on a single rock fracture in the shear process and the validity of the cubic law examined through experimental results and numerical simulations[J]. Soils and Foundations,2009,49(4):597-610.
[14]KISHIDA K,SAWADA A,YASUHARA H,et al. Estimation of fracture flow considering the inhomogeneous structure of single rock fractures[J]. Soils and Foundations,2013,53(1):105-116.
[15]张春生.混凝土衬砌高压水道的设计准则与岩体高压渗透试验[J].岩石力学与工程学报,2009,28(7):1305-1311.
[16]CAO Cheng,XU Zengguang,CHAI Junrui et al. Mechanical and hydraulic behaviors in a single fracture with asperities crushed during shear[J]. International Journal of Geomechanics,2018,18(11):04018148.
[17]WEINAN E. Boundary Layer Theory and the zero-viscosity limit of the Navier-Stokes Equation[J]. Acta Mathematica Sinica,2000,16(2):207-218.
[18]郭保华,苏承东.多级加载下岩石裂隙渗流分段特性试验研究[J].岩石力学与工程学报,2012,31(S2):3787-3794.
[19]张志昌.水力学(下册)[M].北京:中国水利水电出版社,2011.
[20] KUMAR S,BERGADA J M,WATTON J. Axial piston pump grooved slipper analysis by CFD simulation of three-dimensional NVS equation in cylindrical coordinates[J]. Computers&Fluids,2009,38(3):648-663.