Supercritical thermodynamic property evaluation via adaptive mesh tabulation

Obtaining accurate computational simulations of fluid flows with a complex thermodynamic behaviour is difficult. This is partly due to the non-linear variation of thermophysical properties in the vicinity of critical point. Supercritical fluid flows are observed in a wide range of applications such as caffeine extraction, supercritical diesel fuel injection, nuclear reactors, and liquid rocket engines. In the near-critical regime, thermodynamic properties are accurately described by a multi-parametric equation of state, but most often using such complex state equations involve expensive computations, thereby consuming a significant portion of the available computational resources. To mitigate this issue, tabulation of state equations stands as an alternative yet they are inefficient due to the strong non-linear property variation in the proximity of critical point. In this thesis a novel tabulation method based on adaptive mesh refinement (AMR) approach is presented, it enabled accurate thermodynamic and physical property evaluation with minimal computational effort. Detailed analyses in the form of error validation, computational cost comparison were performed with reference to the commonly used cubic equations of state. In order to demonstrate the grid scaling effects on total computational cost of a real-fluid CFD simulation, a one dimensional harmonic acoustic wave case was chosen. We show a significant computational cost reduction with the adaptive tabulation approach relative to the cubic state equations (with an underlying iterative root-finding method). It also offered an accurate emulation of the backend equation of state with significantly less computation cost. The developed adaptive tabular equation of state is also integrated into a Computational Fluid Dynamics (CFD) code which has numerical techniques enabling computation of flows with large density gradients. To validate this CFD solver and to observe accurate thermodynamics effects in gasdynamics simulations, the Sod-shock tube and Shu-Osher shock tube problems were solved computationally for both perfect, real fluid thermodynamics. Also the sod-shock tube problem was simulated with three different thermodynamic initial conditions (supercritical, nearcritical, subcritical regions) the nearcritical case has shown a relatively smaller change in temperature, pressure at the shock contact while having a large change in density compared to two other scenarios. It represented the underlying supercritical thermodynamic behaviour that the density increases drastically with a relatively small change in temperature

Numerical Simulation of Compressible Flows with Interfaces

Compressible interfacial flows exist in a variety of applications: reacting fronts, droplet break up, jets and sprays in high speed, shock passage in foams, etc. These flows behave in a complex multi-scale way including interface deformation, wave interface interaction and complex transport phenomena. In the first section, the interaction of a laminar flame with a compression wave is investigated. More precisely, the evolution of the burning interface is investigated and discussion over different compression waves and their effects on the flame geometry and burning rate are made. In the second part, a numeral framework for simulation of compressible multiphase flows using adaptive wavelet collocation method is developed. This study was originally motivated by the desire for a numerical tool capable of simulating the atomization process during start-up conditions in a supersonic combustor. To model such physics, the solver needs to handle high density ratios, transport terms and capillary effects. The multi-scale behaviour of these flows requires a multi-scale approach. Parallel Adaptive Wavelet Collocation Method (PAWCM) makes use of second generation wavelets to dynamically adapt the grid to localized structures in the flow in time and space. This approach allows the solution to be approximated using a subset of the points that would normally be used with a uniform grid scheme. Thus, computation on this subset is efficient and high levels of data compression is achieved

超臨界炭化水素におけるマルチフィジックス熱流動の数値解法

Tohoku University博士（情報科学）thesi

Droplet Dynamics Under Extreme Ambient Conditions

This open access book presents the main results of the Collaborative Research Center SFB-TRR 75, which spanned the period from 2010 to 2022. Scientists from a variety of disciplines, ranging from thermodynamics, fluid mechanics, and electrical engineering to chemistry, mathematics, computer science, and visualization, worked together toward the overarching goal of SFB-TRR 75, to gain a deep physical understanding of fundamental droplet processes, especially those that occur under extreme ambient conditions. These are, for example, near critical thermodynamic conditions, processes at very low temperatures, under the influence of strong electric fields, or in situations with extreme gradients of boundary conditions. The fundamental understanding is a prerequisite for the prediction and optimisation of engineering systems with droplets and sprays, as well as for the prediction of droplet-related phenomena in nature. The book includes results from experimental investigations as well as new analytical and numerical descriptions on different spatial and temporal scales. The contents of the book have been organised according to methodological fundamentals, phenomena associated with free single drops, drop clusters and sprays, and drop and spray phenomena involving wall interactions

Droplet Dynamics Under Extreme Ambient Conditions

This open access book presents the main results of the Collaborative Research Center SFB-TRR 75, which spanned the period from 2010 to 2022. Scientists from a variety of disciplines, ranging from thermodynamics, fluid mechanics, and electrical engineering to chemistry, mathematics, computer science, and visualization, worked together toward the overarching goal of SFB-TRR 75, to gain a deep physical understanding of fundamental droplet processes, especially those that occur under extreme ambient conditions. These are, for example, near critical thermodynamic conditions, processes at very low temperatures, under the influence of strong electric fields, or in situations with extreme gradients of boundary conditions. The fundamental understanding is a prerequisite for the prediction and optimisation of engineering systems with droplets and sprays, as well as for the prediction of droplet-related phenomena in nature. The book includes results from experimental investigations as well as new analytical and numerical descriptions on different spatial and temporal scales. The contents of the book have been organised according to methodological fundamentals, phenomena associated with free single drops, drop clusters and sprays, and drop and spray phenomena involving wall interactions

Effect of nozzle geometry on the efficiency of compressed air nozzles

Papers presented to the 11th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, South Africa, 20-23 July 2015.This paper evaluates the performance of different nozzle geometries which are all used in industrial blowing applications. Five different geometries were selected: a converging nozzle, a stepped nozzle, a straight pipe, a converging-diverging nozzle and an energy-efficient nozzle. The flow field of the various nozzles was calculated using CFD simulations. The compressible RANS equations were solved using the SST k-omega turbulence model. Different properties, like the total impact force, the impact pressure and the entrainment rate were obtained from the simulations to compare the nozzles with each other. For each of these properties, the most efficient nozzle was the one for which the mass flow rate of compressed air was the lowest. All nozzles showed comparable mass flow rates for the same impact force and the difference was in the order of 5% better than a straight pipe geometry. Only the energy saving nozzle used around 10% less mass flow and is the best solution to reduce compressed air consumption without losing performance.The authors gratefully acknowledge the funding of this study by the Agency for Innovation by Science and Technology (IWT) through the TETRA project nr. 130223.am201

First Stages of a Viscous Finite Element Solver for Non-Inertial and Aeroelastic Problems

This thesis concentrates on expansion of the Euler equations to full Navier-Stokes equations for laminar cases. The study develops the needed terms to adapt the equations, implements the equations in Fortran code, and then finishes by verifying and validating the code. Several viscous test cases were used varying across the subsonic, transonic, and supersonic regimes. Test cases include Blasius solution, circular cylinder, and several airfoil solutions. After verification and validation, the solver was found to work well for test cases in the subsonic, transonic, and supersonic laminar solutions; but the solver does not possess a turbulence model, and therefore cannot properly predict separation or properties in a transitional or turbulent boundary layer.Mechanical & Aerospace Engineerin

Riemann solvers with non-ideal thermodynamics: exact, approximate, and machine learning solutions

The Riemann problem is an important topic in the numerical simulation of compressible flows, aiding the design and verification of numerical codes. A limitation of many of the existing studies is the perfect gas assumption. Over the past century, flow technology has tended toward higher pressures and temperatures such that non-ideal state equations are required along with specific heats, enthalpy, and speed of sound dependent on the full thermodynamic state. The complexity of the resulting physics has compelled researchers to compromise on rigour in favour of computational efficiency when studying non-ideal shock and expansion waves. This thesis proposes exact, approximate, and machine learning approaches that balance accuracy and computational efficiency to varying degrees when solving the Riemann problem with non-ideal thermodynamics. A longstanding challenge in the study of trans- and supercritical flows is that numerical simulations are often validated against prior numerical simulations or inappropriate ideal-gas shock tube test cases. The lack of suitable experimental data or adequate reference solutions means that existing studies face difficulties distinguishing numerical inaccuracies from the physics of the problem itself. To address these shortcomings, a novel derivation of exact solutions to shock and expansion waves with arbitrary equation of state is performed. The derivation leverages a domain mapping from space-time coordinates to characteristic wave coordinates. The solutions may be integrated into a suitable Riemann solution algorithm to produce exact reference solutions that do not require numerical integration. The study of wave structures is also pertinent to the development of practical Riemann solvers for finite volume codes, which must be computationally simple yet entropy-stable. Using the earlier derivations, the idea of structurally complete approximate Riemann solvers (StARS) is proposed. StARS provides an efficient means for analytically restoring the isentropic expansion wave to pre-existing three-wave solvers with arbitrary thermodynamics. The StARS modification is applied to a Roe scheme and shown to have improved accuracy but comparable computational speed to the popular Harten-Hyman entropy fix. Four test cases are examined: a transcritical shock tube, a shock tube with periodic bounds that produce interfering waves, a two-dimensional Riemann problem, and a gradient Riemann problem---a variant on the traditional Riemann problem featuring an initial gradient of varying slope rather than an initial step function. Additionally, a scaling analysis shows that entropy violations are most prevalent and yield the greatest errors in trans- and supercritical flows with large gradients. The final area of inquiry focuses on FluxNets, that is, learning-based Riemann solvers whose accuracy and efficiency fall in between those of exact and approximate solvers. Various approaches to the design and training of fully connected neural networks are assessed. By comparing data-driven versus physics-informed loss functions, as well as neural networks of varying size, the results show that order-of-magnitude reductions in error compared to the Roe solver can be achieved with relatively compact architectures. Numerical validation on a transcritical shock tube test case and two-dimensional Riemann problem further reveal that a physics-informed approach is critical to ensuring smoothness, generalizability, and physical consistency of the resulting numerical solutions. Additionally, parallelization can be leveraged to accelerate inference such that the significant gains in accuracy are achieved at one quarter the runtime of exact solvers. The trade-off in accuracy versus efficiency may be justified in the case of non-ideal flows where even minor errors can result in spurious oscillations and destabilized solutions