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Ohr, Young-Gie,Eu, Byung-Chan Korean Chemical Society 1986 Bulletin of the Korean Chemical Society Vol.7 No.3
It is shown that the linear stability coincides with the thermodynamic stability in the case of stress tensor evolution for simple dense fluids even if the constitutive (evolution) equation for the stress tensor is nolinear. The domain of coincidence can be defined in the space of parameters appearing in the constitutive equation and we find the domain is confined in an elliptical cone in a three-dimensional parameter space. The corresponding state theory in rheology of simple dense fluids is also further examined. The validity of the idea is strengthened by the examination.
오영기 배재대학교 자연과학연구소 2013 自然科學論文集 Vol.24 No.1
Strong shock waves are non-equilibrium phenomena far out of equilibrium, which can not be interpreted by the near equilibrium linear thermodynamic theories. One of the obvious problems remained to be answered in this subject is the temperature profile, although many efforts have been done to extend the limit of linear theories. The temperature profile obtained by existing theories and computer experiments of Monte Carlo simulations overshoots in the shock layer. The overshoot does evidently violate the second law of thermodynamics, however, it has not yet been resolved. The problem seems to be arisen by the improper use of heat capacity of gases, which defines the local temperature by the relation (internal energy–heat capacity-temperature). In this study, we use the relation (heat flux-heat conductivity-temperature gradient) to introduce the local temperature. In order to obtain the temperature profile, the iterative method for the solution of Boltzmann equation has been employed. The results of the first iteration gives a temperature profile which does not overshoot in the shock layer, i.e., the result which is consistent with the thermodynamic law. Also the obtained temperature profile shows correct limiting property for weak shocks. The theory provides formulas for transport coefficients in the shock layer, however, the limiting properties of weak shock transport coefficients do not consistent with the linear theory, which should be reexamined in the future study.
반복적 Cumulant 모멘트 방법에 의한 Boltzmann 방정식의 해법과 충격파구조에 관한 연구
오영기,Ohr, Young Gie 대한화학회 1998 대한화학회지 Vol.42 No.4
Boltzmann 방정식의 비선형 해법으로서 cumulant 모멘트 방법을 연구하였으며, Maxwell 분자모형 단원자분자 기체계의 정상충격파 문제에 대하여 적용하였다. 모멘트 방정식의 해는 Maxwell-Ikenberry-Truesdell(MIT) 반복법을 사용하였다. 원래의 MIT 반복법은 초기값을 평형분포함수로부터 구하지만, 본 연구에서는 반복계산의 초기값을 Mott-Smith의 두방식(bimodal)함수로부터 구하였다. 모멘트 계산은 2차 반복단계까지 수행하였으며, 강한 충격파에 대한 밀도, 온도, stress, heat flux 등의 윤곽과 충격파의 두께, 그리고 마하수 1.4 미만의 약한 충격파의 두께를 계산하였다. 1차 반복계산에서 충격파 윤곽에 대한 간단한 형태의 해석적 표현을 얻었으며, 이로부터 도출한 약한 충격파 두께에 대한 극한법칙은 Navier-Stokes 이론과 정확히 일치한다. 2차 반복계산에 의한 결과는 강한 충격파의 윤곽곡선 및 충격파 두께가 Monte Carlo 문헌값과 정량적으로 일치함을 보인다. For non-linear solution of the Boltzmann equation, the cumulant moment method has been studied. To apply the method to the normal shock wave problem, we restricted ourselves to the monatomic Maxwell molecular gases. The method is based on the iterative approach developed by Maxwell-Ikenberry-Truesdell (MIT). The original MIT approach employs the equilibrium distribution function for the initial values in beginning the iteration. In the present work, we use the Mott-Smith bimodal distribution function to calculate the initial values and follow the MIT iteration procedure. Calculations have been carried out up to the second iteration for the profiles of density, temperature, stress, heat flux, and shock thickness of strong shocks, including the weak shock thickness of Mach range less than 1.4. The first iteration gives a simple analytic expression for the shock profile, and the weak shock thickness limiting law which is in exact accord with the Navier-Stokes theory. The second iteration shows that the calculated strong shock profiles are consistent with the Monte Carlo values quantitatively.
정상 평면충격파에 대한 Navier-Stokes 방정식의 적용한계에 관한 열역학적 연구
오영기,Ohr, Young Gie 대한화학회 1996 대한화학회지 Vol.40 No.6
선형 비평형 열역학의 최소 엔트로피 생성원리를 사용하여 정상 평면충격파 형상에 대한 Navier-Stokes 유체방정식의 적용한계를 연구하였다. 해석적 결과를 얻기 위하여 평형상태에 가까운 하류 위치에서 방정식을 선형화 하였다. 하류 극한의 경계조건을 충족하는 Navier-Stokes 방정식의 해를 충격파 진행속도의 마하수 M=1 근처에서 급수전개하였을 때, 일차항까지는 열역학의 요구조건과 부합하였다. The limit of applicability of Navier-Stokes equation to stationary plane shock-waves is examined by using the principle of minimum entropy production of linear irreversible thermodynamics. In order to obtain analytic results, the equation is linearized near the equilibrium of downstream. Results show that the solution of Navier-Stokes equation which fits the boundary condition of far downstream flow is consistent with the thermodynamic requirement within the first order when the solution is expanded around the M=1, where M is the Mach number of upstream speed.