Mechanical Engineering - Theses
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ItemReduced-order modeling for membrane wings at low Reynolds numbers( 2019)The present work develops reduced-order models for the fluid-structure interaction of two-dimensional membrane wings at low Reynolds numbers. The fluid-structure interaction models are obtained from the coupling between a linear unsteady aerodynamic model and a structural membrane model. The linear aerodynamic model is derived from high-fidelity simulations at low Reynolds numbers using a system identification procedure. It is able to model the unsteady aerodynamic loads generated by a deflection of the wing, decomposed into its rigid and flexible degrees of freedom. The rigid degrees of freedom are represented by pitching and plunging, while the flexible degrees of freedom are decomposed into Fourier modes. The aerodynamic model is presented in state-space form, hence it is compatible with modern feedback control frameworks. Feedback control techniques are employed to investigate the performance of the individual degrees of freedom of the wing in tracking a reference lift and rejecting external disturbances. A one-dimensional nonlinear equation is adopted to model the structural dynamics of the membrane wing. From the nonlinear model, two lower-order approximations are derived by means of a truncated Taylor expansion: a quasi-linear model and a linear model. From the coupling with the linear aerodynamic model, a nonlinear, a quasi-linear and a linear fluid-structure interaction model are obtained. These models are adopted to investigate the static aeroelastic response and the stability of the membrane wing at different Reynolds numbers. Using Harmonic Balance methods, the forced aeroelastic response to pitching and the autonomous response of linearly unstable cases are also studied. Finally, an adjoint-based optimization procedure is employed to optimize the aerodynamic response of the membrane to an external disturbance in the form of a convective vortex. The results are compared against high-fidelity Direct Numerical Simulation to validate the predictive capabilities of the models and to discuss their range of applicability.
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ItemAnalysis of resolvent method for turbulence inflow generation( 2018)High-fidelity simulations of turbulent flows aim to accurately reproduce the statistical and structural properties of real-life turbulence. Such simulations rely on accurate inflow boundary conditions. A novel turbulent inflow generation method for high-fidelity DNS/LES has been developed which utilizes reduced order modelling (ROM) and evolutionary algorithms. The core idea behind this method is the classical view of turbulence which represents it as a collection of coherent structures. A low-rank approximation approach known as the resolvent analysis, developed by McKeon and Sharma [Journal of Fluid Mechanics, Vol. 658, 336-382 (2010)], is used to represent the governing equations as a linear input-output system. The non-linearities in the governing Navier-Stokes equations are the driving force behind the ow. This forcing of the linear system produces a response which represent the velocity perturbations. The resolvent analysis is performed at different wavenumber-frequency combinations which are selected in a manner to represent a variety of energetic coherent structures like the near-wall longitudinal streaks, hairpin vortices, Large Scale Motions (LSMs) and Very Large Scale Motions (VLSMs). A Singular Value Decomposition (SVD) of the linear operator in the input-output system is performed to generate a set of orthonormal basis functions for the forcing and response fields. A major advantage of the resolvent analysis is its reduced dependence on external data. It requires only the mean statistical quantities as an input which are readily available for various ow problems or can be easily obtained from cost-effective RANS simulations. The amplitudes of the selected modes were linearly scaled such that the turbulence kinetic energy (TKE) of the resolvent modes is equal to the target TKE. This technique successfully resulted in a fully developed turbulent field, although with a large development length. A further improvement of this method is obtained by optimizing the amplitude of each resolvent mode, which represents the energy content of the associated coherent structure. A genetic algorithm approach has been used to optimize the resolvent modes to represent the target Reynolds stress profiles. This modified process results in a significantly improved development length.
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ItemDirect numerical simulation of turbulent natural convection bounded by differentially heated vertical walls( 2013)Using new, high-resolution direct numerical simulation (DNS) data, this study appraises the different scaling laws found in literature for turbulent natural convection of air in a differentially heated vertical channel. The present data is validated using past DNS studies, and covers the Rayleigh number (Ra) range between 5.4 × 10^5 to 1.0 × 10^8. This is followed by an appraisal of various scaling laws proposed by four studies: Versteegh and Nieuwstadt (77), Holling and Herwig (34), Shiri and George (63) and George and Capp (23). These scaling laws are appraised with the profiles of the mean temperature defect, mean streamwise velocity, normal velocity fluctuations, temperature fluctuations and Reynolds shear stress. Based on the arguments of an inner (near-wall) and outer (channel-centre) region, the DNS data is found to support a −1/3 power law for the mean temperature in an overlap region. Using the inner and outer temperature profiles, an implicit heat transfer equation is obtained and a correction term in the equation is shown to be not negligible for the present Ra range when compared with explicit equations found in literature. In addition, I determined that the mean streamwise velocity and normal velocity fluctuations collapse in the inner region when using the outer velocity scale. A similar collapse is noted in the profiles of temperature fluctuations with increasing Ra when normalised with inner temperature and length scale. Lastly, I show evidence of an incipient proportional relationship between friction velocity and the outer velocity scale with increasing Ra. The study is extended to the spectrum of turbulent kinetic energy and temperature fluctuations of the flow. The one-dimensional streamwise spectra collapse onto the −5/3 slope, coinciding with the standard Kolmogorov form of the power spectra reported in literature. This collapse is found to occur in the outer region of the flow in the bounds between the peaks of the mean streamwise velocity. In spectrogram form, I find evidence that the spectral peaks correspond to energetic velocity structures in the channel — the structures of streamwise velocity fluctuations appear to stretch half of the streamwise domain and occur at a quarter intervals in the spanwise direction. From 2-dimensional autocorrelations, the structures of spanwise velocity fluctuations are found to be organised in a hatched pattern in an inner location (z^× i ≈ 7) and at the channel-centre. The respective pattern angles are \theta_ i ≈ 54◦ and \theta_ o ≈ 48◦, both measured from the horizontal. For the temperature spectrum, the −5/3 collapse is also observed in the same bounds as the velocity spectrum. In pre-multiplied form, the spectral peak is found to occur at the wall-normal location which coincides with the peak temperature fluctuations in the channel. With increasing Ra, the wall-parallel isocontours of temperature are found to show standard features of turbulent pressure driven boundary layers — streaks with spanwise length of 100+ units.
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ItemDirect numerical simulations of flow past a rotating sphere and droplet( 2011)The transport of a spherical particle or droplet has been subjected to intensive research for centuries as the hydrodynamic forces acting on the spherical particle or droplet are known to affect its flight path. Typical engineering applications of the transport of a particle or droplet can be found in areas such as internal engine combustion, inkjet printing, drug and chemical delivery where the particle or droplet's trajectory is usually predicted using the standard drag coefficient correlation for a stationary sphere. The objective of this study is focused on the flow past a solid rotating sphere at small to moderate Reynolds numbers at different rotation axis angles. The deformation of the droplet on the total hydrodynamic forces is also investigated. At moderate Reynolds numbers, $\Rey = 100$, $250$ and $300$, a parametric study on the effect of rotation axis angles was performed. The goal was to identify the change in behaviour for the flow past a rotating sphere over a range of rotation axis angles, $\alpha = 0$, $\pi/6$, $\pi/3$ and $\pi/2$. The sphere was rotated at dimensionless rotation rates, $\varOmega^* = 0.05$, $0.20$, $0.50$ and $1.00$. For $\Rey = 100$, the flow is steady and the effect of rotation axis angles on both near wake flow fields and forces are insignificant at $\varOmega^* = 0.05$. The effect of rotation axis angles becomes more pronounced with increasing $\varOmega^*$. For $\Rey = 250$ and $300$, the dynamic behaviours of both wake structures and forces are highly correlated to the rotation axis angle, $\alpha$, and rotation rate, $\varOmega^*$. The flow was classified into five different regimes for all parameters considered at $\Rey = 250$ and $300$, the hydrodynamic forces acting on the sphere are closely related to the corresponding flow regime. The changes to the time-averaged flow fields as a result of increasing Reynolds numbers are less pronounced. The flow past a rotating sphere was also numerically simulated at a higher Reynolds number, $\Rey = 500$ and $1,\!000$ for streamwise and transverse rotation only. The non-dimensional rotation rates, $\varOmega^*$, were considered over the range of $0.00$ and $1.20$. For streamwise rotation at $\Rey = 500$, a dimensionless parameter was defined to differentiate the transition of the flow structures from rotating vortex shedding to spiral structures. For $\Rey = 1,\!000$, a reverse rotation is observed due to small-scale eddies release mechanism. The phase diagram $\left( C_{Ly}, C_{Lx} \right)$ no longer forms a closed curve for the reverse rotation flow regime. For transverse rotation, a newly observed flow regime is calculated for $\Rey = 500$ and $\varOmega^* = 1.00$; and $\Rey = 1,\!000$ and $\varOmega^* \geq 0.80$. At this flow regime, stable foci are formed in the near wake increasing the hydrodynamic forces oscillation amplitude. The deformation and dynamic behaviours of a droplet rotating in streamwise and transverse directions, released into a free stream were studied at initial Reynolds number, $\Rey_i = 40$, for different initial Weber numbers, $We_i$, viscosity ratios, density ratios and dimensionless rotation rates $\left( \varOmega^* \leq 1.00 \right)$. The upper limit of $\varOmega^*$ is chosen to be unity to avoid droplet breakup. For large $We_i$, the droplet shape pancakes along the free stream as a result of streamwise rotation. Hence, its frontal area increases and leads to an increase in the total drag coefficients. But a decrease in $We_i$ shows a negative total drag coefficient. For a transversely rotating sphere, the deformation is divided into along the free stream direction and along the rotating axis. The different deformation leads to two distinctively different droplet dynamic behaviours.
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ItemNumerical study of internal wall-bounded turbulent flows( 2011)Direct numerical simulation (DNS) of turbulent pipe flow has been performed at Reynolds numbers ranging from Reτ ≈ 170 to 2000. A literature review highlights a need for higher Reynolds number pipe flow DNS data. There have been many numerical studies for internal geometry (pipe and channel) wall-bounded turbulent flows. Many of the numerical data for both pipe and channel flows, which are now readily accessible are at lower Reynolds numbers. At higher Reynolds numbers, there is a lack of pipe flow DNS data as compared to channel flow DNS data. As the highest Reynolds numbers in numerical simulations are starting to overlap the lower region of experiments, validation of both experimental and numerical results is now possible. Moreover, numerical simulations are extremely useful in complementing experimental results in the near-wall region where accurate experimental data are often difficult to obtain. However, available DNS data of internal wall-bounded turbulent flows are performed with different grid resolutions and computational domain sizes, making it difficult to directly compare between them. An undertaking of this thesis involves a systematic study (using constant grid resolutions) of the domain length effect on the convergence of turbulence statistics. Investigations carried out using numerical data from fully developed pipe flow simulations indicate a recommended computational length of 8π pipe radius or half channel height for turbulence statistics to converge. It is hoped that this will serve as a benchmark computational domain length for future numerical simulations performed. A study is also carried out to better understand the similarities and differences of the flow physics between turbulent channel and pipe flows. This is performed using the newly obtained pipe flow DNS data and channel flow DNS data of del ´ Alamo et al. (2004) at a comparable Reynolds number of Reτ ≈ 1000. Different turbulence statistics investigated including mean flow, turbulence intensities, correlations and energy spectra. Comparison of both wall-bounded channel and pipe flows shows little discrepancies in the near-wall region but differences are observed in the outer-region. Although there is abundant literature for both experimental and numerical wall bounded turbulent flows, further analysis reveals discrepancies in the open literature. One of the primary contributing factors that plagues reported results are spatial resolution issues. In this thesis, the numerical data is used to investigate the effects of insufficient spatial resolution in wall-bounded turbulence by averaging the streamwise velocity component in the spanwise direction. A correction scheme is proposed to correct experimental results suffering from insufficient spatial resolution. The correction scheme is applied to attenuated experimental results such as streamwise turbulence intensity and one-dimensional energy spectra and is shown to be effective. The method of using DNS data to analysis and correct experimental results can be extended to other experimental techniques such as particle image velocimetry and laser doppler velocimetry.