CAJ | 학술논문

针对环形激波聚焦时产生的高温、高压特性,采用间断有限元方法对环形激波在同轴圆柱形激波管内的聚焦流场进行了数值模拟.为了验证采用方法的有效性,首先对经典激波管问题进行了求解,计算结果与解析解吻合很好.其次,对入射激波马赫效为2.0到5.0的环形激波聚焦流场进行了计算,获得了环形激波在圆柱形激波管内聚焦过程的气动特性.模拟结果表明,采用间断有限元方法能够有效地捕捉激波聚焦过程形成的绕射、反射和聚焦等主要流动特征,而且在聚焦点附近,数值解具有较大的梯度变化,表明该方法对间断解具有较强的捕捉能力.最后比较了网格尺度对聚焦点峰值压力的影响.
침대배형격파취초시산생적고온、고압특성,채용간단유한원방법대배형격파재동축원주형격파관내적취초류장진행료수치모의.위료험증채용방법적유효성,수선대경전격파관문제진행료구해,계산결과여해석해문합흔호.기차,대입사격파마혁효위2.0도5.0적배형격파취초류장진행료계산,획득료배형격파재원주형격파관내취초과정적기동특성.모의결과표명,채용간단유한원방법능구유효지포착격파취초과정형성적요사、반사화취초등주요류동특정,이차재취초점부근,수치해구유교대적제도변화,표명해방법대간단해구유교강적포착능력.최후비교료망격척도대취초점봉치압력적영향.
A numerical simulation of the toroidal shock wave focusing in a co-axial cylindrical shock tube is investigated by using discontinuous Galerkin(DG) finite element method to solve the axisymmetric Euler equations.For validating the numerical method,the shock-tube problem with exact solution is computed,and the computed results agree well with the exact cases.Then,several cases with higher incident Mach numbers varying from 2.0to 5.0 are simulated.Simulation results show that complicated flow-field structures of toroidal shock wave diffraction,reflection,and focusing in a co-axial cylindrical shock tube can be obtained at different incident Mach numbers and the numerical solutions appear steep gradients near the focusing point,which illustrates the DG method has higher accuracy and better resolution near the discontinuous point.Moreover,the focusing peak pressure with different grid scales is compared.