Tugas 1 Metnum Dani

Considering the complex heat transfer process in the actual filling process, some assumptions have been made for the filling process of hydrogen storage cylinders. The contents are as follows: 1. At the initial injection stage, the temperature in the high-pressure hydrogen storage cylinder is consistent with the ambient temperature.

2. Heat transfer characteristics of various materials are regarded as isotropic.

3. Ignoring the gravity effect, a two-dimensional (2D) axisymmetric model is used for numerical simulation.

4. The energy exchange between hydrogen and the pipeline installed at the connection between the hydrogen storage tank and the cylinder is ignored.

Based on the above assumptions, a CFD model, including heat transfer, turbulence, and real gas properties, was established. The control equations are described as follows. The mass conservation equation can be expressed in the following form.

(1) The momentum transport equation under the 2D axisymmetric inertial reference system is described as follows. ∂ ∂ � ( � � ) + 1 � ∂ ∂ � ( � � � � ) + 1 � ∂ ∂ � ( � � � � ) = − ∂ � ∂ � + 1 � ∂ ∂ � [ � ( � + � � ) ( 2 ∂ � ∂ � − 2 3 ( ∇ · � → ) ) ] + 1 � ∂ ∂ � [ � ( � + � � ) ( 2 ∂ � ∂ � + ∂ � ∂ � ) ] (2) A modified standard k–ε model for transport based on the turbulent kinetic energy k and dissipation rate ε is proposed. Compared with the standard k–ε model, � 1 �

changes from 1.44 to 1.52, which makes the correlation between permeability and momentum, time, and density more accurate [23]. The turbulent kinetic energy k and its dissipation rate ε are obtained using the following transport equation.

∂ ∂ � ( � � ) + ∂ ∂ � ( � � � ) = ∂ ∂ � [ ( � + � � � � ) ∂ � ∂ � ] + � � − � � − � � (3) ∂ ∂ � ( � � ) + ∂ ∂ � ( � � � ) = ∂ ∂ � [ ( � + � � � � ) ∂ � ∂ � ] + � 1 � � � � � − � 2 � � � 2 � (4) In the above two equations, � �

represents the turbulent kinetic energy generated by the average velocity gradient.

� � = − � � ′ � ′ ¯ ∂ � ∂ � (5) � �

represents the contribution of pulsating expansion in compressible turbulence to the total dissipation rate, and its calculation expression is shown in Equation (6).

� � = 2 � � � � 2 (6) In this form, � �

is a turbulent Mach number, defined as the following.

� � = � � 2 (7) The turbulent viscosity � �

can be obtained from the combined expressions of k and ε. The specific definitions are as follows.