流体动力学定常与非定常流动中的热力学第一定律
The first law of thermodynamics in hydrodynamic steady and unsteady flows
AI总结：
该研究以理想气体平面可压缩流动为非平衡模型，证明定常与非定常状态下内能均可表示为非平衡熵、体积和粒子数的状态函数，并满足热力学第一定律。
摘要：
我们研究理想气体的平面可压缩流动，将其作为非平衡热力学系统的模型。我们证明，此类系统在定常和非定常状态下的内能 $U(S^{*},V,N)$ 仅为三个状态参数的函数，即非平衡熵 $S^{*}$、体积 $V$ 和系统中的粒子数 $N$。在不同状态之间转变时，系统遵循热力学第一定律，即 $dU=T^{*}dS^{*}-p^{*}dV+μ^{*}dN$，其中 $U=3/2 NRT^{*}$ 且 $p^{*}V=NRT^{*}$。将圆柱置于通道内，我们发现 U 仅通过状态参数依赖于圆柱位置 $y_{c}$，即在 V=const 时为 $U(S^{*}(y_{c}),V,N(y_{c}))$。此外，当绕圆柱流动变得不稳定，且速度、压力和密度开始作为时间 t 的函数振荡时，U 仅通过状态参数依赖于 t，即在 V=const 时为 $U(S^{*}(t),V,N(t))$。这些例子表明，这种形式的内能具有稳健性，即使在非定常流动中也不依赖于特定的边界条件。
英文摘要：
We studied planar compressible flows of ideal gas as models of a non-equilibrium thermodynamic system. We demonstrate that internal energy $U(S^{*},V,N)$ of such systems in stationary and non-stationary states is the function of only three parameters of state, i.e. non-equilibrium entropy $S^{*}$, volume $V$ and number of particles $N$ in the system. Upon transition between different states, the system obeys the first thermodynamic law, i.e. $dU=T^{*}dS^{*}-p^{*}dV+μ^{*}dN$, where $U=3/2 NRT^{*}$ and $p^{*}V=NRT^{*}$. Placing a cylinder inside the channel, we find that U depends on the location of the cylinder $y_{c}$ only via the parameters of state, i.e. $U(S^{*}(y_{c}),V,N(y_{c}))$ at V=const. Moreover, when the flow around the cylinder becomes unstable, and velocity, pressure, and density start to oscillate as a function of time, t, U depends on t only via the parameters of state, i.e. $U(S^{*}(t),V,N(t))$ for V=const. These examples show that such a form of internal energy is robust and does not depend on the particular boundary conditions even in the unsteady flow.
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