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This paper aims to describe the physical and numerical modeling of a new computational fluid dynamics solver for hypersonic flows in thermo-chemical non-equilibrium. The code uses a blend of numerical techniques to ensure accuracy and robustness and to provide scalability for advanced hypersonic physics and complex three-dimensional (3D) flows.

The solver is based on an edge-based stabilized finite element method (FEM). The chemical and thermal non-equilibrium systems are loosely-coupled to provide flexibility and ease of implementation. Chemical non-equilibrium is modeled using a laminar finite-rate chemical kinetics model while a two-temperature model is used to account for thermodynamic non-equilibrium. The systems are solved implicitly in time to relax numerical stiffness. Investigations are performed on various canonical hypersonic geometries in two-dimensional and 3D.

The comparisons with numerical and experimental results demonstrate the suitability of the code for hypersonic non-equilibrium flows. Although convergence is shown to suffer to some extent from the loosely-coupled implementation, trading a fully-coupled system for a number of smaller ones improves computational time. Furthermore, the specialized numerical discretization offers a great deal of flexibility in the implementation of numerical flux functions and boundary conditions.

The FEM is often disregarded in hypersonics. This paper demonstrates that this method can be used successfully for these types of flows. The present findings will be built upon in a later paper to demonstrate the powerful numerical ability of this type of solver, particularly with respect to robustness on highly stretched unstructured anisotropic grids.

This work aims to describe the physical and numerical modeling of a CFD solver for hypersonic flows in thermo-chemical non-equilibrium. This paper is the second of a two-part series that concerns the application of the solver introduced in Part I to adaptive unstructured meshes.

The governing equations are discretized with an edge-based stabilized finite element method (FEM). Chemical non-equilibrium is simulated using a laminar finite-rate kinetics, while a two-temperature model is used to account for thermodynamic non-equilibrium. The equations for total quantities, species and vibrational-electronic energy conservation are loosely coupled to provide flexibility and ease of implementation. To accurately perform simulations on unstructured meshes, the non-equilibrium flow solver is coupled with an edge-based anisotropic mesh optimizer driven by the solution Hessian to carry out mesh refinement, coarsening, edge swapping and node movement.

The paper shows, through comparisons with experimental and other numerical results, how FEM + anisotropic mesh optimization are the natural choice to accurately simulate hypersonic non-equilibrium flows on unstructured meshes. Three-dimensional test cases demonstrate how, for high-speed flows, shocks resolution, and not necessarily boundary layers resolution, is the main driver of solution accuracy at walls. Equally distributing the error among all elements in a suitably defined Riemannian space yields highly anisotropic grids that feature well-resolved shock waves. The resulting high level of accuracy in the computation of the enthalpy jump translates into accurate wall heat flux predictions. At the opposite end, in all cases examined, high-quality but isotropic unstructured meshes gave very poor solutions with severely inadequate heat flux distributions not even featuring expected symmetries. The paper unequivocally demonstrates that unstructured anisotropically adapted meshes are the best, and may be the only, way for accurate and cost-effective hypersonic flow solutions.

Although many hypersonic flow solvers are developed for unstructured meshes, few numerical simulations on unstructured meshes are presented in the literature. This work demonstrates that the proposed approach can be used successfully for hypersonic flows on unstructured meshes.

To compute the Navier‐Stokes equations of a non‐equilibrium weakly ionized air flow. This can help to have a better description of the flow‐field and the wall heat transfer in hypersonic conditions.

The numerical approach is based on a multi block finite volume method and using a Riemann's solver based on a MUSCL‐TVD algorithm. In the flux splitting procedure the modified speed of sound, due to the electronic mode, is implemented.

A good description of the shock standoff distance, of the wall heat fluxes and of the peak of electron density number in the shock layer.

The radiative effects are not included in this paper. For the very high Mach numbers, this can modify the shock layer parameters.

The knowledge of the wall heat transfer in the re‐entry body problems.

The building of a robust numerical code in order to well describe hypersonic air flow in high Mach numbers.

The Fay and Riddell (F–R) formula is an empirical equation for estimating the stagnation-point heat flux on noncatalytic and fully catalytic surfaces, based on an assumption of equilibrium. Because of its simplicity, the F–R has been used extensively for reentry flight design as well as ground test facility applications. This study aims to investigate the uncertainties of the F-R formula by considering velocity gradient, chemical species at the boundary layer edge, and the thermochemical nonequilibrium (NEQ) behind the shock layer under various hypersonic NEQ flow environments.

The stagnation-point heat flux calculated with the F–R formula was evaluated by comparison with thermochemical NEQ calculations and existing flight experimental values.

The comparisons showed that the F–R underestimated the noncatalytic heat flux, because of the chemical composition at the surface. However, for fully catalytic heat flux, the F–R results were similar to values of surface heat flux from thermochemical NEQ calculations, because the F–R formula overestimates the diffusive heat flux. When compared with the surface heat flux results obtained from flight experimental data, the F–R overestimated the fully catalytic heat flux. The error was 50% at most.

The results provided guidelines for the F–R calculations under hypersonic flight conditions and for determining the approximate error range for noncatalytic and fully catalytic surfaces.

A finite difference method for solving the quasi one‐dimensional non‐equilibrium hypersonic flow equations in a diverging nozzle is presented and discussed. In chemically reacting flows the system of equations to be solved is very stiff. Some reactions may be several orders of magnitude faster than others and generally, they are much faster than the convective process except for very high Ma numbers. For this reason the development of a numerical scheme whose stability is independent of the chemical reaction rates is of importance. The main advantage of this scheme is the conservation of each chemical component, the positivity of densities and vibrational energies, as well as its relative simplicity, which results in a fast computer code.

This study aims to perform flow simulations inside the acinus with fine alveolar pores (Kohn pores) using hexagonal cells and bottom-up geometric modeling, which enabled the elimination of invalid voids using previous top-bottom methods and spherical or circular cells.

Regular hexagonal cells were used to construct alveoli with no gaps via tessellation. Some hexagonal cells were fused to eliminate the inner boundaries to represent the structure of the bronchial tree. For the remaining hexagonal cells, the side lengths of the shared walls were adjusted to construct alveolar pores. Periodic moving boundaries with the same phase were set for all walls to describe synchronous contraction and expansion of the bronchi and alveoli.

More realistic flow characteristics in the distal lung were obtained. The effects of pore size and the mechanism of auxiliary ventilation of alveolar pores were revealed.

To the best of the authors’ knowledge, this is the first numerical simulation study on the function of multiple alveolar pores at the level of pulmonary acini, which will be helpful for simulating the dynamic process of cough and sputum excretion in the future.

The purpose of this paper is to study the mechanism of efficient sputum excretion from the distal lung by using a tessellationally distal lung model with alveolar pores.

First, a two-dimensional tessellational composite structure of the bronchus, alveoli and alveolar pores (Kohn pore) is constructed with the tessellational splitting and fusion of regular hexagonal elements. Then, the level set method is used to study the effects of alveolar pores and their sizes, expiratory cycles and respiratory intensity.

The existence of alveolar pores is the prerequisite for sputum excretion, and there is an optimal size of alveolar pores for sputum excretion. Strong asymmetric respiration can break the reversibility of the flow at a low Reynolds number and causes significant net displacement of sputum. The expiratory cycle is negatively correlated with the net displacement of sputum. The respiratory intensity is positively correlated with the net displacement of sputum.

This research is helpful for understanding the complex sputum excretion process in diseases, such as pneumonia, and developing corresponding adjuvant therapy.

A finite volume, semi‐implicit scheme, is proposed and discussed, which solves the two‐dimensional Euler equations for the hypersonic flow of a mixture of chemically reactive specie. The present scheme can be applied on a general, unstructured grid. The first order version guarantees non negativity of the densities and of the vibrational energies for arbitrarily large time steps. The semi‐implicit time discretization of advective terms and the fully implicit discretization of the highly nonlinear terms yield a simple and efficient computer algorithm. Numerical tests show that shocks are well captured and the correct profiles for the chemical specie are reproduced at low computational cost.

The purpose of this paper is to study numerically the steady thermal convection in a chamber filled with a nanoliquid affected by a chemical reaction using the single-phase nanofluid approximation.

Water was considered as a host fluid while nanoparticles are aluminum oxide. Homogeneous reactions are analyzed. The nonlinear partial differential equations describing the considered problem are simulated using the finite difference technique.

The results of streamlines, isotherms, isoconcentrations, nanofluid flow rate, mean Nusselt and Sherwood numbers are discussed. The data demonstrate that the mean Sherwood number increases with the homogeneous reaction rate. Further, nanofluid flow rate can be increased with nanoparticles concentration for high Rayleigh numbers owing to the homogeneous chemical reaction inside the cavity.

Searching the existent references illustrates that the homogeneous-heterogeneous reactions influence on the nanoliquid motion and energy transport within enclosures has not been investigated before. The results of this paper are completely original and the numerical results of the present paper were never published by any researcher.