Mechanical Engineering - Theses

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Blood Flow Dynamics in the Aortic Dissection

WANG, Qingdi ( 2023-08)

Aortic dissection is one of the catastrophic cardiovascular diseases that have high mortality. It refers to an intimal tear in the aortic wall that initiates the formation of a false lumen due to blood flow between the layers of the vessel wall. Decisions about medical management or surgical intervention for long-term dissections are complex and still evolving, depending largely on the individual patient’s condition. In addition to conventional clinical images, the incorporation of more comprehensive physiological data would benefit clinicians in the decision-making process. Recent advancements in four-dimensional phase-contrast magnetic resonance imaging and computational fluid dynamics are promising in providing detailed data on haemodynamic parameters in cardiovascular diseases, including those that are challenging to predict or measure safely in clinical settings. In this work, the robustness and precision of a respiratory-controlled k-space reordering four-dimensional phase-contrast magnetic resonance imaging sequence were evaluated. Imaging data and pressure measurements are used to inform the development of numerical models of dissected aortas. The influence of different inlet boundary conditions on the outcomes of our simulations has also been investigated. The present results indicate that phase-contrast magnetic resonance imaging is valuable for providing patient-specific flow data. The evaluated magnetic resonance imaging sequence is reproducible and accurate in in-vivo flow metrics measurement. Computational fluid dynamics simulations based on multiple imaging modalities hold substantial promise for identifying potential risk factors associated with disease development. To accurately represent physiological haemodynamic parameters in aortic dissection, appropriate inlet boundary conditions and MRI data should be chosen.
Assessing the impact of wall heat transfer on knocking combustion of hydrogen using DNS and LES

Dou, Xinbei ( 2023-06)

Hydrogen has recently received significant attention due to its potential as a clean energy source. However, under some operating conditions, hydrogen is prone to auto-ignition, leading to engine knock and damage to engine components. In order to understand the underlying mechanism of hydrogen knocking combustion, this thesis employs numerical simulations to study the knock mechanism of different intensities. A particular focus is placed on the end-gas auto-ignition behaviour and its impact on pressure oscillations and wall heat transfer. 1D simulations with detailed chemistry are performed to investigate two types of hydrogen end-gas auto-ignition in a confined space: auto-ignition initiated by a hot spot and auto-ignition initiated within a homogeneous mixture. The former configuration explores deflagrative auto-ignition with pressure oscillations of several bars, while the latter investigates developing and developed detonation with pressure oscillations of hundreds of bars. The results show that the hot-spot-induced auto-ignition is mainly influenced by hot spot locations, with negligible impacts from the near-wall temperature gradients. Pressure oscillations are mainly influenced by flame annihilation, and the wall heat flux is mainly influenced by the flame head-on-quenching event, providing insights into understanding the trace knock phenomenon. For auto-ignition initiated within a homogeneous mixture, near-wall temperature gradients have a significant impact on the number of auto-ignition events, their locations, and combustion modes. Especially under lean conditions, with increased near-wall temperature stratification, the auto-ignition location can switch from the near-wall to the near-flame region, and its mode can switch from the developing to the developed detonation. By analysing the temperature and pressure development in the end gas, the generation of auto-ignition is found to have a close relation to pressure fluctuations. Furthermore, near-wall temperature gradients also have an influence on the wall heat flux and pressure oscillations, mainly through their impact on auto-ignition behaviour. For auto-ignition initiated within a homogeneous mixture, pressure oscillations are dominated by the auto-ignition event, and the wall heat flux is influenced by both flame head-on-quenching and the pressure wave hitting the wall. The conclusions in this part help explore the mechanisms of conventional and superknock. In addition to the 1D simulations, this research also explores the occurrence of hydrogen knock using Large Eddy Simulations (LESs) in the Cooperative Research Fuel (CFR) engine, featuring conventional engine knock. Initially, the study evaluates the performance of four commonly-used wall heat transfer models, namely, the Angelberger, Han and Reitz, O'Rourke and Amsden, and GruMO-UniMORE models. The study concludes that while the commonly-used wall heat transfer models perform well in normal combustion, they generate cycles that fall outside the experimental range in knocking combustion, with an increasing number of such out-of-experimental-range (OOR) cycles as the knock intensity increases. Among different wall heat transfer models, the Han and Reitz model is the most suitable model for hydrogen knock modelling as it balances simplicity and accuracy and simulates fewer out-of-range cycles under all conditions. Furthermore, the wall heat transfer characteristics are explored using the Han and Reitz model. For knocking combustion, auto-ignition is prone to occur at locations where the near-wall temperature stratification is most disturbed, which is near the knock meter cavity. The near-wall temperature gradient grows in the burnt area, acting as a barrier and protecting the wall from high wall heat flux. On the contrary, the pressure wave generated by auto-ignition has a significant impact on the wall heat transfer. It influences the wall heat flux through its impact on the flow velocity. As knock intensity increases, the impact of the pressure wave persists for a long time, leading to a higher peak heat transfer rate compared with low-intensity cases.
Data-driven Reynolds-averaged turbulence closures for buoyancy-affected flow

Xu, Xiaowei ( 2021)

Turbulent flow subjected to buoyancy force is ubiquitous in daily life, e.g. in building ventilation, nuclear reactor containment, and geophysical flows. To improve the prediction accuracy of existing turbulence models, this thesis presents the results of the application of an in-house symbolic regression tool, i.e. gene expression programming (GEP), on buoyancy-extended Reynolds-averaged closure models for buoyant flows in a differentially heated vertical planar channel. In the first part of this study, attention is paid to understanding the turbulent Prandtl number's behaviour and improve the predictability of the linear eddy diffusivity models. By comparing the location of mean velocity maxima, there is an infinity anomaly for the eddy viscosity and the turbulent Prandtl number, as both terms are divided by the mean velocity gradient according to the standard definition, in vertical buoyant flow. To predict the quantities of interest, e.g. the Nusselt number, GEP is used with various cost functions, e.g. the mean velocity gradient, with the aid of the latest direct numerical simulation (DNS) dataset for vertical natural and mixed convection. It is found that the new machine-learnt algebraic models, as the reciprocal of $Pr_t$, successfully handle the infinity issue for both vertical natural and mixed convection. Moreover, the proposed models with embedded coordinate frame invariance can be conveniently implemented in the Reynolds-averaged scalar equation and are proven to be robust and accurate in the current parameter space, where the Rayleigh number spans from $10^5$ to $10^9 $ for vertical natural convection and the bulk Richardson number $Ri_b $ is in the range of $ 0$ and $ 0.1$ for vertical mixed convection. However, there are notable errors between the prediction and DNS data when incorporating the algebraic model of turbulent Prandtl number into full Reynolds--averaged Navier--Stokes (RANS) equations. As a result, the turbulence closure is upgraded with buoyancy-extended terms. The second part of this study re-examines the buoyancy-accounting algebraic scalar-flux model proposed by Kenjeres et al., Int. J. Heat Fluid Flow, Vol. 26, pp. 569-586 (2005). Based on a term-by-term analysis on the model with the aid of high-fidelity datasets, it is demonstrated that there are significant discrepancies in the predicted turbulent heat fluxes once the model is combined with the existing algebraic Reynolds stress models. Consequently, it is suggested that the quadratic terms in buoyancy-extended explicit algebraic Reynolds stress models should be included, and such non-linear Reynolds-stress and heat-flux closure models are then developed via GEP. The evaluation of these GEP-based models shows significant improvements in the prediction of mean quantities and second moments in an a-priori stage and in an a-posteriori stage, with the latter being realised by embedding the new models into the elliptic relaxation v^2-f equations, across different Rayleigh number cases. In comparison to passive scalar flow, the complexity of turbulence modelling for natural convection problems is increased as the velocity and scalar fields are strongly coupled by the buoyancy force. The above data-driven turbulence modelling approaches have treated the unclosed terms of the velocity and thermal fields separately, which has lead to inaccurate predictions when handling natural convection problems. Hence, the appropriate Reynolds-averaged closure models for natural convection ought to capture this interaction within the second-moment terms. In the last part of this study, we therefore develop fully coupled buoyancy-extended models by using a novel multi-objective and multi-expression machine-learning framework that is based on CFD-driven training (Zhao et al., J. Comput. Phys., 411, 109413, (2020)).The model candidates obtained from a Gene-Expression Programming approach, and thus available in symbolic form, are evaluated by running RANS solvers for different Rayleigh number cases during the model training process. This novel framework is applied to vertical natural convection, with the emphasis on the importance of coupling the explicit closure model formulations, the choice of cost functions, and the appropriate input flow features (i.e. a generalised flux Richardson number) for developing accurate models. It is shown that the resulting machine-learnt models improve the predictions of quantities of interests, e.g. mean velocity and temperature profiles, for vertical natural convection with Rayleigh numbers in the range of $10^5$ to $10^9$.
A Framework for Multidimensional Analysis and Development of Numerical Schemes

Tan, Yiyun Raynold ( 2020)

Partial differential equations are found throughout engineering and sciences. Under the constraint of complex initial and boundary conditions, most of these complex equations do not have analytical solutions, and therefore require solution by numerical methods. In the context of this thesis, the goal is to examine the governing equations of fluid mechanics (Euler and Navier Stokes) which require both spatial and temporal discretization. Under the effects of numerical differencing, the numerical solution is subjected to both dispersion and dissipation error. These error can be identified and analyzed through spectral analysis method. The analysis of numerical schemes under a coupled spatial temporal framework in one dimensional wavespace is well understood. However, the extension of these methods to multidimensional wavespace and the spectral properties of a hybrid finite difference/Fourier spectral spatial discretization method in multidimensional space is not well understood. Furthermore, the extension of this multidimensional analysis framework to non-linear shock capturing schemes is not done before. This dissertation introduces a generic method for the spectral analysis of linear and non linear finite difference schemes in multidimensional wavenumber space. The aim is to understand the properties of the coupled system for a series of representative spatial and temporal schemes. Theoretical predictions are then compared with numerical solutions based on model equations such as the advection, linearized Euler and linearized Navier Stokes equations. Finally, this framework is used to develop a spectrally optimized hybrid shock capturing scheme which switches between a linear and non linear scheme. Various canonical numerical examples were conducted in order to compare the spectral properties of the new scheme with existing numerical schemes. For the one dimensional linearized Euler equation, it was shown that the dispersion relation belonging to the largest eigenvalue provides the limiting criteria for the stability limit as well as the onset of dispersion error. When the linear spectral analysis method is extended to the two dimensional wavespace, the dispersion and dissipation properties of the coupled schemes become a function of both the reduced wavenumber and the wave propagation angle. When the two dimensional linear spectral analysis method is extended to the two dimensional linearized Compressible Navier Stokes equations (LCNSE), viscous and acoustic effects are taken into account in addition to the convection effects. The addition of the acoustic term to the dispersion relation leads to a coupling of the resolution characteristic such that the group velocities in either spatial direction become a function of the wavenumber in both spatial directions. The two dimensional spectral analysis method was extended to non linear finite difference schemes based on a quasi-linear assumption. In this assumption, the contribution of the harmonic modes (as a result of the non linear differentiation) are neglected during the calculation of the modified wavenumber of the spatial scheme. Using the semi-discretized dispersion relation of the two dimensional advection and linearized Euler equations, the dispersion and dissipation property of a non linear scheme in two dimensional wavespace can be quantified. Using this framework, a non linear scheme, HYB-MDCD-TENO6 was developed based on the principle that the linear part of the scheme can be optimized for minimum dispersion and dissipation error. Furthermore, the non linear part of the scheme is only activated in the vicinity of a sharp gradient. Through a series of numerical experiments, it was found that the hybrid scheme optimized based on the linearized Euler equation tend to give slightly better results than the one optimized based on the advection equation in some of the numerical experiments. In all cases, it was found that the HYB-MDCD-TENO6 scheme provides better resolution than existing baseline TENO and WENO-JS schemes for the same grid size considered.
Turbulence Model Development and Implementation for Low Pressure Turbines using a Machine Learning Approach

Akolekar, Harshal Deepak ( 2019)

The design of the gas turbine, which is the work horse of the aviation industry, has reached a high degree of maturity; given that the first gas turbine flew in the late 1930s. Despite this, the industrial sector is looking towards harnessing even incremental points of efficiency with novel methods, which can translate to millions of dollars of savings and large reductions in carbon emissions. Current gas turbine design is primarily carried out using low-fidelity simulations due to their low cost and user-friendliness. However, these simulations lack the accuracy of high-fidelity simulations, largely due to the use of a linear stress-strain relation – the Boussinesq approximation. With the increase in the power of computing, high-fidelity simulations are becoming increasingly commonplace but are still not feasible as an iterative industrial design tool. In order to bridge the gap between high and low-fidelity simulations, certain high-fidelity data sets can be harvested to extract meaningful physics-based insights with machine learning processes to improve the accuracy of iterative low-fidelity calculations. This thesis focuses on improving low-fidelity modelling strategies (Reynolds–Averaged Navier–Stokes (RANS)) for low pressure turbine (LPT) flows, by harnessing meaningful physics-based information from high-fidelity data using a machine learning approach – gene expression programming (GEP). Improvement in the accuracy of the existing linear stress-strain closure relations is sought by developing machine-learnt explicit algebraic Reynolds stress models (EARSM). Of the many physical phenomena that occur in an LPT, designers are very interested in being able to accurately model the wake mixing using RANS, as this phenomenon governs the stagnation pressure loss in a turbine and also because existing RANS-based turbulence models fail to accurately predict this phenomenon. Therefore, the goal of this thesis is to develop and implement non-linear EARSMs to enhance the wake mixing in LPTs using GEP and high-fidelity data sets at realistic engine operating conditions. Firstly, an extensive analysis of the existing RANS-based turbulence models for LPTs with steady inflow conditions was conducted. None of these RANS models were able to accurately reproduce wake loss profiles based on high-fidelity data. However, the recently proposed k-v2-omega transition model was found to produce the best agreement with high-fidelity data in terms of blade loading and boundary layer behaviour and was thus selected as the baseline model for turbulence closure development. Using different training regions for model development, the resulting closures were extensively analysed in an a priori sense (without running any CFD) and also while running CFD calculations. Importantly, to assess their robustness, the trained models were tested both on the cases they were trained for and on testing, i.e. previously not seen, cases with different flow features. The developed models improved prediction of the Reynolds stress, TKE production, wake loss profiles and wake maturity across all cases. The existing GEP framework was extended to include RANS feedback during the model development process. It was found that the models generated via this method allow greater flexibility to the user in terms of selecting metrics of direct interest. The models returned offer a higher degree of numerical stability and robustness across different flow conditions and even geometries. Models developed on the LPT were tested on a high pressure turbine case and vice-versa and some of the models were able to reduce the peak wake loss error by up to 90% over the Boussinesq approximation in this cross-validation study. A zonal based model development approach was proposed with an aim to enhance the wake mixing prediction of unsteady RANS calculations for LPTs with unsteady inflow conditions. High-fidelity time-averaged and phase-lock averaged data at a realistic isentropic Reynolds number and two reduced frequencies, i.e. with discrete incoming wakes and with wake ‘fogging’, were used as reference data. This is the first known study to develop machine learning based turbulence models for unsteady flows, and also the first study to use phase-lock averaged data for the same. Models developed via phase-lock averaged data were able to capture the effect of certain prominent physical phenomena in LPTs such as wake-wake interactions, whereas models based on the time-averaged data could not. Correlations with the flow physics led to a set of models that can effectively enhance the wake mixing prediction across the entire LPT domain for both cases. Based on a newly developed error metric, the developed models have reduced the a priori error over the Boussinesq approximation on average by 45%. Based on the analysis conducted in this work, a few best practice guidelines have been proposed which can offer future designers an insight into the GEP-based model development process. Overall, this study showcases that GEP is a promising avenue for future RANS-based turbulence model development.
Numerical methods and turbulence modelling for large-eddy simulations

Sidebottom, William Thomas ( 2015)

Turbulence is of interest in many engineering applications, ranging from aerospace design to naval architecture. The inherent complexities of turbulence make it difficult to measure experimentally, and, to simulate numerically. The focus of this dissertation is the simulation of turbulent flow with the computational methodology known as large-eddy simulation (LES). LES uses a filter to partition a flow-field into large- (or resolved) and small- (or subgrid) scales and solves only for the large-scales. This method provides more accuracy when compared to other computational methods, such as those based on the Reynolds-averaged Navier--Stokes equations. The increased accuracy, however, comes with an associated increase in computational cost. Indeed, the computational cost of LES can often be prohibitive, especially for cases involving wall-bounded flow over complex geometries at high Reynolds numbers. This high computational expense is one of the primary limitations of LES. Methods to reduce the cost of LES form the focus of this dissertation. The high cost of LES is in great part due to the near-wall resolution requirement. To accurately represent a flow-field with LES, it is necessary to sufficiently resolve all of the dynamically important scales of motion. This is relatively inexpensive in free-shear flows, where the large-scales are the most energetic, but it is more difficult in wall-bounded flows, where the energy-containing scales get increasingly small near a wall. These near-wall small-scales make it impractical to resolve all of the energy containing scales. Therefore, models that mimic the effect of the near-wall turbulent structures on the wall and on the core of the flow are often used. These models are known as wall-models, and, if accurate, they are able to significantly reduce the computational cost of a large-eddy simulation. At present there is no wall-modelling approach that has been shown to be apposite in a broad range of applications. In particular, current wall-models are often inaccurate when applied to separating wall-bounded flow and are limited by their inability to predict fluctuations of wall-shear-stress and the near-wall velocity. Because of this, a key focus of this dissertation is the proposal and investigation of a new wall-model that aims to overcome these two limitations. In addition, the new model aims to reduce the computational cost of LES by significantly reducing the near-wall resolution requirement. Before introducing this new wall-model, flow over a circular cylinder is investigated in order to gain familiarity with the large-eddy simulation methodology and to assess the effect of some key computational parameters in LES. In this investigation, the effects of mesh resolution, discretisation schemes, SGS-models, and wall-models on prediction of the flow-field are assessed. One of the primary outcomes of this study is the finding that `standard' wall-models are inadequate for turbulent separating flows. This motivated the investigation of the new wall-model. The new wall-model is able to predict the fluctuating wall-shear-stress from a large-scale velocity input. The model is based on the spectral structure of the turbulent boundary layer and the interaction between large-scale events in the logarithmic layer and small-scale events near the wall. Importantly, the model includes many important parameters that are able to preserve the structure of the boundary layer while remaining relatively straightforward to implement in a solver. Further, the model does not increase the computational cost of a simulation compared to current wall-modelling approaches. The model is implemented in large-eddy simulations of channel flow to assess its efficacy compared to a standard wall-model. The influence of two subgrid-scale models on the large-scale velocity input is also investigated. Results show that the new wall-model is able to resolve more of the wall-shear-stress variance when compared to a standard wall-model, and it has a small effect in the outer-regions of the boundary layer.

Mechanical Engineering - Theses

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