Validation of the Chemistry Module for the Euler Solver in Unified Flow Solver

In the world of computational fluid dynamics (CFD), three main types of flow regimes exist: continuum, rarified, and free molecular. Of these regimes, the rarified regime is the most difficult to model because the continuum equations don\u27t apply and using the Boltzmann equation is too computationally expensive to use. The Unified Flow Solver (UFS) is currently being developed to solve this problem by using the kinetic continuum Euler equations where valid, and only using the Boltzmann equation where necessary, thus reducing the computational cost. The use of the kinetic Euler equations helps to aid in the coupling of the Euler equations with the Boltzmann equation. This work compares UFS with a common nonequilibrium solver, LeMANS, to attempt to validate the thermo-chemical Euler solver available in UFS. Three types of simulations were run to validate the Euler solver: perfect gas, thermal nonequilibrium, and thermo-chemical nonequilibrium. The perfect gas simulation was run using both a monatomic and two species diatomic gas. The thermal nonequilibrium simulation was run using a 2 species gas, while the thermo-chemical nonequilibrium simulation was run using a 2 and 11 species gas. The results of the simulations show that UFS matches closely for both the monatomic and 2 species perfect gas simulations as well as the thermal nonequilibrium simulation. The thermo-chemical nonequilibrium simulations do not show the correct vibrational temperature, which causes the species concentrations to be incorrect. All of the simulations show that UFS is much slower than LeMANS in number of cpu hours. This means that UFS not a practical choice for a CFD solver and cannot be fully validated in its current state

Unified gas-kinetic wave-particle methods VII: diatomic gas with rotational and vibrational nonequilibrium

Hypersonic flow around a vehicle in near space flight is associated with multiscale non-equilibrium physics at a large variation of local Knudsen number from the leading edge highly compressible flow to the trailing edge particle free transport. To accurately capture the solution in all flow regimes from the continuum Navier-Stokes solution to the rarefied gas dynamics in a single computation requires genuinely multiscale method. The unified gas-kinetic wave-particle (UGKWP) method targets on the simulation of such a multicale transport. Due to the wave-particle decomposition, the dynamics in the Navier-Stokes wave and kinetic particle transport has been unified systematically and efficiently under the unified gas-kinetic scheme (UGKS) framework. In this study, the UGKWP method with the non-equilibrium among translation, rotation and vibration modes, is developed based on a multiple temperature relaxation model. The real gas effect for high speed flow in different flow regimes has been properly captured. Numerical tests, including Sod tube, normal shock structure, hypersonic flow around two-dimensional cylinder and three-dimensional flow around a sphere and space vehicle, have been conducted to validate the UGKWP method. In comparison with the discrete velocity method (DVM)-based Boltzmann solver and particle-based direct simulation Monte Carlo (DSMC) method, the UGKWP method shows remarkable advantages in terms of computational efficiency, memory reduction, and automatic recovering of multiscale solution

Modeling and simulation in supersonic three-temperature carbon dioxide turbulent channel flow

This paper pioneers the direct numerical simulation (DNS) and physical analysis in supersonic three-temperature carbon dioxide (CO2) turbulent channel flow. CO2 is a linear and symmetric triatomic molecular, with the thermal non-equilibrium three-temperature effects arising from the interactions among translational, rotational and vibrational modes under room temperature. Thus, the rotational and vibrational modes of CO2 are addressed. Thermal non-equilibrium effect of CO2 has been modeled in an extended three-temperature BGK-type model, with the calibrated translational, rotational and vibrational relaxation time. To solve the extended BGK-type equation accurately and robustly, non-equilibrium high-accuracy gas-kinetic scheme is proposed within the well-established two-stage fourth-order framework. Compared with the one-temperature supersonic turbulent channel flow, supersonic three-temperature CO2 turbulence enlarges the ensemble heat transfer of the wall by approximate 20%, and slightly decreases the ensemble frictional force. The ensemble density and temperature fields are greatly affected, and there is little change in Van Driest transformation of streamwise velocity. The thermal non-equilibrium three-temperature effects of CO2 also suppress the peak of normalized root-mean-square of density and temperature, normalized turbulent intensities and Reynolds stress. The vibrational modes of CO2 behave quite differently with rotational and translational modes. Compared with the vibrational temperature fields, the rotational temperature fields have the higher similarity with translational temperature fields, especially in temperature amplitude. Current thermal non-equilibrium models, high-accuracy DNS and physical analysis in supersonic CO2 turbulent flow can act as the benchmark for the long-term applicability of compressible CO2 turbulence.Comment: Carbon dioxide flow, Vibrational modes, Three-temperature effects, Supersonic turbulent channel flow

An Investigation of Shock Wave Physics via Hybrid CFD-BGK Solution Methods for Nonequilibrium Flows

The Unified Flow Solver, a hybrid continuum-rarefied code, is used to investigate the internal structure of a normal shock wave for a Mach range of 1.55 to 9.0 for Argon, and 1.53 to 3.8 for diatomic Nitrogen. Reciprocal shock thickness, density, temperature, heat flux, and the velocity distribution function are calculated for a one-dimensional shock wave and compared with experimental data from Alsmeyer and DSMC results from Bird. Using the Euler, Navier-Stokes, BGK model, and Three-Temperature BGK model schemes, results from UFS compare well with experiment and DSMC. The Euler scheme shows atypical results, possibly resulting from modifications made to include internal energies. An entropy spot is introduced into a two-dimensional domain to investigate entropy-shock interactions over a range of Knudsen numbers (Kn=0.01, 0.1, and 1.0) for Mach 2.0 in Argon. Previous work on entropy-shock interactions has only been performed using an Euler scheme. Here, results are presented in Argon using coupled BGK and Navier-Stokes solvers. Density, pressure, and temperature profiles, as well as the profiles of their gradients, are reported at certain times after the entropy spot convects through the shock

Rotational and Vibrational Nonequilibrium in a Low Diffusion Particle Method for Continuum Flow Simulation

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/77353/1/AIAA-2009-3743-194.pd

Shock interactions in continuum and rarefied conditions employing a novel gas-kinetic scheme

Shock interactions can have a significant impact on heating rates and aerodynamic performance of hypersonic vehicles. The study presents different shock interactions in partially rarefied hypersonic flows predicted employing a recently developed gas-kinetic scheme for diatomic gases with rotational degrees of freedom. The new gas-kinetic schemes will be presented along with shock/wave boundary interactions as well as Edney Type IV shock–shock interactions. Various levels of rarefaction have been considered to highlight the effect of thermal relaxation between the translational and rotational modes. In addition, for the Edney test case, the imposed wall temperature on the shock-generating wedge and the cylinder surface has been varied, to evaluate the importance of the boundary layer thickness in the interaction region

Kinetic modelling of rarefied gas flows with radiation

Two kinetic models are proposed for high-temperature rarefied (or non-equilibrium) gas flows with radiation. One of the models uses the Boltzmann collision operator to model the translational motion of gas molecules, which has the ability to capture the influence of intermolecular potentials, while the other adopts the relaxation time approximations, which has higher computational efficiency. In the kinetic modelling, not only the transport coefficients such as the shear/bulk viscosity and thermal conductivity but also their fundamental relaxation processes are recovered. Also, the non-equilibrium dynamics of gas flow and radiation are coupled in a self-consistent manner. The two proposed kinetic models are first validated by the direct simulation Monte Carlo method in several non-radiative rarefied gas flows, including the normal shock wave, Fourier flow, Couette flow, and the creep flow driven by the Maxwell demon. Then, the rarefied gas flows with strong radiation are investigated, not only in the above one-dimensional gas flows, but also in the two-dimensional radiative hypersonic flow passing cylinder. In addition to the Knudsen number of gas flow, the influence of the photon Knudsen number and relative radiation strength is scrutinised. It is found that the radiation can make a profound contribution to the total heat transfer on obstacle surface.Comment: 34 pages, 15 figures. arXiv admin note: substantial text overlap with arXiv:2201.0685