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

Hypersonic flows around complex geometries with adaptive mesh refinement and immersed boundary method

This thesis develops and validates a computational fluid dynamics numerical method for hypersonic flows; and uses it to conduct two novel investigations. The numerical method involves a novel combination of structured adaptive mesh refinement, ghost-point immersed boundary and artificial dissipation shock-stable Euler flux discretisation. The method is high-order, low dissipation and stable up to Mach numbers $M \lesssim 30$ with stationary or moving complex geometries; it is shown to be suitable for direct numerical simulations of laminar and turbulent flows. The method's performance is assessed through various test cases. Firstly, heat transfer to proximal cylinders in hypersonic flow is investigated to improve understanding of destructive atmospheric entries of meteors, satellites and spacecraft components. Binary bodies and clusters with five bodies are considered. With binary proximal bodies, the heat load and peak heat transfer are augmented for either or both proximal bodies by $+20\%$ to $-90\%$ of an isolated body. Whereas with five bodies, the cluster-averaged heat load varied between $+20\%$ to $-60\%$ of an isolated body. Generally, clusters which are thin in the direction perpendicular to free-stream velocity and long in the direction parallel to the free-stream velocity have their heat load reduced. In contrast, clusters which are thick and thin in directions perpendicular and parallel to the free-stream velocity feel an increased heat load. Secondly, hypersonic ablation patterns are investigated. Ablation patterns form on spacecraft thermal protection systems and meteor surfaces, where their development and interactions with the boundary layer are poorly understood. Initially, a simple subliming sphere case without solid conduction in hypersonic laminar flow is used to validate the numerical method. Where the surface recession is artificially sped-up via the wall Damk\"{o}hler number without introducing significant errors in the shape change. Then, a case with transitional inflow over a backward facing step with a subliming boundary is devised. Differential ablation is observed to generate surface roughness and add vorticity to the boundary layer. A maximum surface recession of $\sim 0.8\times$ and a maximum surface fluctuation of $\sim 0.2\times$ the inflow boundary layer thickness were generated over two flow times.Open Acces

Direct numerical simulation of gas transfer at the air-water interface in a buoyant-convective flow environment

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University LondonThe gas transfer process across the air-water interface in a buoyant-convective environment has been investigated by Direct Numerical Simulation (DNS) to gain improved understanding of the mechanisms that control the process. The process is controlled by a combination of molecular diffusion and turbulent transport by natural convection. The convection when a water surface is cooled is combination of the Rayleigh-B´enard convection and the Rayleigh-Taylor instability. It is therefore necessary to accurately resolve the flow field as well as the molecular diffusion and the turbulent transport which contribute to the total flux. One of the challenges from a numerical point of view is to handle the very different levels of diffusion when solving the convection-diffusion equation. The temperature diffusion in water is relatively high whereas the molecular diffusion for most environmentally important gases is very low. This low molecular diffusion leads to steep gradients in the gas concentration, especially near the interface. Resolving the steep gradients is the limiting factor for an accurate resolution of the gas concentration field. Therefore a detailed study has been carried out to find the limits of an accurate resolution of the transport for a low diffusivity scalar. This problem of diffusive scalar transport was studied in numerous 1D, 2D and 3D numerical simulations. A fifth-order weighted non-oscillatory scheme (WENO) was deployed to solve the convection of the scalars, in this case gas concentration and temperature. The WENO-scheme was modified and tested in 1D scalar transport to work on non-uniform meshes. To solve the 2D and 3D velocity field the incompressible Navier-Stokes equations were solved on a staggered mesh. The convective terms were solved using a fourth-order accurate kinetic energy conserving discretization while the diffusive terms were solved using a fourth-order central method. The diffusive terms were discretized using a fourth-order central finite difference method for the second derivative. For the time-integration of the velocity field a second-order Adams-Bashworth method was employed. The Boussinesq approximation was employed to model the buoyancy due to temperature differences in the water. A linear relationship between temperature and density was assumed. A mesh sensitivity study found that the velocity field is fully resolved on a relatively coarse mesh as the level of turbulence is relatively low. However a finer mesh for the gas concentration field is required to fully capture the steep gradients that occur because of its low diffusivity. A combined dual meshing approach was used where the velocity field was solved on a coarser mesh and the scalar field (gas concentration and temperature) was solved on an overlaying finer submesh. The velocities were interpolated by a second-order method onto the finer sub-mesh. A mesh sensitivity study identified a minimum mesh size required for an accurate solution of the scalar field for a range of Schmidt numbers from Sc = 20 to Sc = 500. Initially the Rayleigh-B´enard convection leads to very fine plumes of cold liquid of high gas concentration that penetrate the deeper regions. High concentration areas remain in fine tubes that are fed from the surface. The temperature however diffuses much stronger and faster over time and the results show that temperature alone is not a good identifier for detailed high concentration areas when the gas transfer is investigated experimentally. For large timescales the temperature field becomes much more homogeneous whereas the concentration field stays more heterogeneous. However, the temperature can be used to estimate the overall transfer velocity KL. If the temperature behaves like a passive scalar a relation between Schmidt or Prandtl number and KL is evident. A qualitative comparison of the numerical results from this work to existing experiments was also carried out. Laser Induced Fluorescence (LIF) images of the oxygen concentration field and Schlieren photography has been compared to the results from the 3D simulations, which were found to be in good agreement. A detailed quantitative analysis of the process was carried out. A study of the horizontally averaged convective and diffusive mass flux enabled the calculation of transfer velocity KL at the interface. With KL known the renewal rate r for the so called surface renewal model could be determined. It was found that the renewal rates are higher than in experiments in a grid stirred tank. The horizontally averaged mean and fluctuating concentration profiles were analysed and from that the boundary layer thickness could be accurately monitored over time. A lot of this new DNS data obtained in this research might be inaccessible in experiments and reveal previously unknown details of the gas transfer at the air water interface.Isambard Scholarshi

Computational science of turbulent mixing and combustion

Implicit Large Eddy Simulation (ILES) with high-resolution and high-order computational modelling has been applied to flows with turbulent mixing and combustion. Due to the turbulent nature, mixing of fuel and air and the subsequent combustion still remain challenging for computational fluid dynamics. However, recently ILES, an advanced numerical approach in Large Eddy Simulation methods, has shown encouraging results in prediction of turbulent flows. In this thesis the governing equations for single phase compressible flow were solved with an ILES approach using a finite volume Godunov-type method without explicit modelling of the subgrid scales. Up to ninth-order limiters were used to achieve high order spatial accuracy. When simulating non chemical reactive flows, the mean flow of a fuel burner was compared with the experimental results and showed good agreement in regions of strong turbulence and recirculation. The one dimensional kinetic energy spectrum was also examined and an ideal k−5/ 3 decay of energy could be seen in a certain range, which increased with grid resolution and order of the limiter. The cut-off wavenumbers are larger than the estimated maximum wavenumbers on the grid, therefore, the numerical dissipation sufficiently accounted for the energy transportation between large and small eddies. The effect of density differences between fuel and air was investigated for a wide range of Atwood number. The mean flow showed that when fuel momentum fluxes are identical the flow structure and the velocity fields were unchanged by Atwood number except for near fuel jet regions. The results also show that the effects of Atwood number on the flow structure can be described with a mixing parameter. In combustion flows simulation, a non filtered Arrhenius model was applied for the chemical source term, which corresponds to the case of the large chemical time scale compared to the turbulent time scale. A methane and air shear flow simulation was performed and the methane reaction rate showed non zero values against all temperature ranges. Small reaction rates were observed in the low temperature range due to the lack of subgrid scale modelling of the chemical source term. Simulation was also performed with fast chemistry approach representing the case of the large turbulent time scale compared to the chemical time scale. The mean flow of burner flames were compared with experimental data and a fair agreement was observed

A Second-Order Finite Volume Method for Field-Scale Reservoir Simulation

Subsurface reservoirs are large complex systems. Reservoir flow models are defined on complex grids that follow geology with relatively large block sizes to make consistent simulations feasible. Reservoir engineers rely on established reservoir simulation software to model fluid flow. Nevertheless, fluid front position inaccuracies and front smearing on large grids may cause significant errors and make it hard to predict hydrocarbon production efficiency. We investigate higher-order methods that reduce these undesired effects without refining the grid, thus making reservoir simulation more accurate and robust. For this paper, we implemented a second-order finite volume method with linear programming (LP) reconstruction in the open-source industry-grade reservoir simulator OPM Flow (part of the open porous media initiative, OPM). We benchmark it against the first-order method on full-scale cases with standard coarse and refined grids. We prepared open refined-grid models of a synthetic reservoir with an unstructured grid and refined Norne field example. Our results confirm that the LP method predicts front positions as accurately as the first-order method on the refined grid for problems dominated by transport. These include the water alternating gas scenario on the synthetic reservoir and piston-type injection on the Norne field. Moreover, we study the gains from the LP method for CO2 injection problems on the Norne field with full multi-phase complexity beyond transport. We observe the relevant difference between the first- and the second-order methods in these cases. However, in some configurations, the reservoir complexity overshadows the gains from the second-order methods.publishedVersio

A computational approach to flame hole dynamics

Turbulent diffusion flames at low strain rates sustain a spatially continuous flame surface. However, at high strains, which may be localized in a flow or not, the flame can be quenched due to the increased heat loss away from the reaction zone. These quenched regions are sometimes called flame holes. Flame holes reduce the efficiency of combustion, can increase the production of certain pollutants (e.g. carbon monoxide, soot) as well as limit the overall stability of the flame. We present a numerical algorithm for the calculation of the dynamics of flame holes in diffusion flames. The key element is the solution of an evolution equation defined on a general moving surface. The low-dimensional manifold (the surface) can evolve in time and it is defined implicitly as an iso-level set of an associated Cartesian scalar field. An important property of the method described here is that the surface coordinates or parameterization does not need to be determined explicitly; instead, the numerical method employs an embedding technique where the evolution equation is extended to the Cartesian space, where well-known and efficient numerical methods can be used. In our application of this method, the field defined on the surface represents the chemical activity state of a turbulent diffusion flame. We present a formulation that describes the formation, propagation, and growth of flames holes using edge-flame modeling in laminar and turbulent diffusion flames. This problem is solved using a high-order finite-volume WENO method and a new extension algorithm defined in terms of propagation PDEs. The complete algorithm is demonstrated by tracking the dynamics of flame holes in a turbulent reacting shear layer. The method is also implemented in a generalized unstructured low-Mach number fluid solver (Sandia's SIERRA low Mach Module ``Nalu") and applied to simulate local extinction in a piloted jet diffusion flame configuration

LES of Jets and Sprays Injected into Crossflow

The objective of this thesis is to numerically simulate a fluid jet injected into a crossflow of the same or another fluid, respectively. Such flows are encountered in many engineering applications in which cooling or mixing plays an important role, e.g. gas turbine combustors. The jet in crossflow (JICF) is used both for cooling and for injecting liquid fuel into the air stream prior to combustion. The numerical simulations regard three space dimensions and track also the flow dynamics by integrating the governing equations in time. The spatial and the temporal resolution are such that the large-scale flow structures are resolved. Such an approach is referred to as large eddy simulations (LES). The motion of the fuel droplets is treated by Lagrangian particle tracking (LPT) with the stochastic parcel method, along with submodels for evaporation, collision, breakup, and a novel submodel for aerodynamic four-way coupling: The particle drag is corrected depending on relative positions of the particles. Mixture fraction and temperature transport equations are solved to enable the modeling of droplet evaporation and the mixing of the gaseous fuel with ambient air. In the simulations of multiphase JICF, several computed results are shown to be inconsistent with the underlying assumptions of the LPT approach: The magnitude of the Weber numbers indicates that droplets are not spherical in large portions of the flow field in wide ranges of parameters which are relevant for gas turbine operation. The magnitude of the droplet spacing suggests that aerodynamic interaction (indirect four-way coupling) among droplets may be important. The LES with aerodynamic four-way coupling reveals significant effects compared to two-way coupling for monodisperse particles in a dense multiphase flow. For single-phase JICF, the impact of nozzle shape on the large-scale coherent structures and the mixing is studied. Effects of circular, square, and elliptic nozzles and their orientation are considered. It is demonstrated that square and elliptic nozzles with blunt orientation raise turbulence levels significantly. The scalar distribution in a cross-sectional plane is found to be single-peaked for these nozzles whereas circular and the nozzles with pointed orientation show double-peaked scalar distribution. It is the nozzles with a single-peaked distribution which are the better mixers. The differences and similarities of single- and multiphase JICF are compared, and it is demonstrated that the flow field solution for multiphase flow approaches the flow field solution of single-phase flow in the limit of small Stokes numbers

Reactive Flows in Deformable, Complex Media

Many processes of highest actuality in the real life are described through systems of equations posed in complex domains. Of particular interest is the situation when the domain is variable, undergoing deformations that depend on the unknown quantities of the model. Such kind of problems are encountered as mathematical models in the subsurface, or biological systems. Such models include various processes at different scales, and the key issue is to integrate the domain deformation in the multi-scale context. Having this as the background theme, this workshop focused on novel techniques and ideas in the analysis, the numerical discretization and the upscaling of such problems, as well as on applications of major societal relevance today

Accelerating large-eddy simulations of clouds with Tensor Processing Units

Clouds, especially low clouds, are crucial for regulating Earth's energy balance and mediating the response of the climate system to changes in greenhouse gas concentrations. Despite their importance for climate, they remain relatively poorly understood and are inaccurately represented in climate models. A principal reason is that the high computational expense of simulating them with large-eddy simulations (LES) has inhibited broad and systematic numerical experimentation and the generation of large datasets for training parametrization schemes for climate models. Here we demonstrate LES of low clouds on Tensor Processing Units (TPUs), application-specific integrated circuits that were originally developed for machine learning applications. We show that TPUs in conjunction with tailored software implementations can be used to simulate computationally challenging stratocumulus clouds in conditions observed during the Dynamics and Chemistry of Marine Stratocumulus (DYCOMS) field study. The TPU-based LES code successfully reproduces clouds during DYCOMS and opens up the large computational resources available on TPUs to cloud simulations. The code enables unprecedented weak and strong scaling of LES, making it possible, for example, to simulate stratocumulus with $10\times$ speedup over real-time evolution in domains with a $34.7~\mathrm{km} \times 53.8~\mathrm{km}$ horizontal cross section. The results open up new avenues for computational experiments and for substantially enlarging the sample of LES available to train parameterizations of low clouds

An explicit primitive conservative solver for the Euler equations with arbitrary equation of state

This work presents a procedure to solve the Euler equations by explicitly updating, in a conservative manner, a generic thermodynamic variable such as temperature, pressure or entropy instead of the total energy. The presented procedure is valid for any equation of state and spatial discretization. When using complex equations of state such as Span–Wagner, choosing the temperature as the generic thermodynamic variable yields great reductions in the computational costs associated to thermodynamic evaluations. Results computed with a state of the art thermodynamic model are presented, and computational times are analyzed. Particular attention is dedicated to the conservation of total energy, the propagation speed of shock waves and jump conditions. The procedure is thoroughly tested using the Span–Wagner equation of state through the CoolProp thermodynamic library and the Van der Waals equation of state, both in the ideal and non-ideal compressible fluid-dynamics regimes, by comparing it to the standard total energy update and analytical solutions where available