An efficient preconditioning scheme for real-fluid mixtures using primitive pressure–temperature variables

An improved preconditioning scheme incorporating a unified treatment of general fluid thermodynamics is developed for treating fluid flows over the entire regime of fluid thermodynamic states at all speeds. All of the thermodynamic and numerical properties (such as eigenvalues and Jacobian matrices) are derived directly from fundamental thermodynamics theories, rendering a self-consistent and robust algorithm. Further efficiency is obtained by employing temperature instead of enthalpy as the primary dependent variable in the preconditioned energy equation. No iterative solution of a real-fluid equation of state is required. This approach, combined with the use of explicit treatments of temporal and spatial derivatives, results in a scheme for which load balance is much easier to achieve in a distributed computing environment. A numerical stability analysis is performed to assess the effectiveness of the scheme at various fluid thermodynamic states. Sample calculations are also carried out. These include injection and mixing of cryogenic fluids and flame dynamics of coaxial jets of liquid oxygen and methane under supercritical conditions. The robustness and efficiency of the present work are demonstrated over a wide range of thermodynamic and flow conditions.     

A numerical study of fluid injection and mixing under near-critical conditions

Nitrogen injection under conditions close vicinity of the liquid-gas critical point is studied numerically.The fluid thermodynamic and transport properties vary drastically and exhibit anomalies in the near-critical regime.These anomalies can cause distinctive effects on heat-transfer and fluid-flow characteristics.To focus on the influence of thermodynamics on the flow field,a relatively low injection Reynolds number of 1 750 is adopted.For comparisons,a reference case with the same configuration and Reynolds number is simulated in the ideal gas regime.The model accommodates full conservation laws,real-fluid thermodynamic and transport phenomena.Results reveal that the flow features of the near-critical fluid jet are significantly different from their counterpart.The near-critical fluid jet spreads faster and mixes more efficiently with the ambient fluid along with a more rapidly development of the vortex pairing process.Detailed analysis at different streamwise locations including both the flat shear-layer region and fully developed vortex region reveals the important effect of volume dilatation and baroclinic torque in the near-critical fluid case.The former disturbs the shear layer and makes it more unstable.The volume dilatation and baroclinic effects strengthen the vorticity and stimulate the vortex rolling up and pairing process.     

A Consistent Characteristic Boundary Condition for General Fluid Mixture and Its Implementation in a Preconditioning Scheme

Characteristic boundary conditions that are capable of handling general fluid mixtures flow at all flow speeds are developed. The formulation is based on fundamental thermodynamics theories incorporated into an efficient preconditioning scheme in a unified manner. Local one-dimensional inviscid (LODI) relations compatible to the preconditioning system are proposed to obtain information carried by incoming characteristic waves at boundaries accurately. The approach has been validated against a variety of sample problems at a broad range of fluid states and flow speeds. Both acoustic waves and hydrodynamic flow features can pass through the boundaries of computational domain transparently without any unphysical reflection or spurious distortion. The approach can be reliably applied to fluid flows at extensive thermodynamic states and flow speeds in numerical simulations. Moreover, the use of the boundary condition shows to improve the computational efficiency.