Mechanical Engineering - Theses

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Turbulent flow over spatially varying roughness

Xie, Michael Xinwu ( 2023-03)

Large-scale heterogeneity in surface roughness, such as uneven biofouling on ships, can lead to phenomena such as internal boundary layers (IBLs) and mean secondary flows that increase drag. Contemporary studies in the field often lack near-wall measurements either due to limitations in experimental methods or prohibitive computational costs for direct numerical simulation (DNS). As a result, contemporary studies on heterogeneous roughness model the near-wall flow using the equilibrium log-law without fully accounting for its validity in the presence of spatial heterogeneity. This thesis considers heterogeneities idealised as alternating strips of roughness and uses DNS in conjunction with an immersed-boundary method to resolve the complex surface geometries. This thesis explores two main themes: the equilibrium log-law and flow phenomena associated with heterogeneous roughness. For the former, the equilibrium log-law is found to yield accurate predictions of the wall shear stress when applied to spanwise-heterogeneous roughness. Where velocity measurements are not available, predictions of the skin-friction coefficient can be made in the asymptotic limits of small and large wavelengths of spanwise heterogeneity. The latter theme is explored by perturbing the spanwise heterogeneity through introducing a moving roughness geometry and through introducing an oblique angle to the heterogeneity. The conventional intuition of mean secondary flows as counter-rotating vortex pairs is found to not generalise outside of spanwise-heterogeneous roughness. Finally, IBLs are identified in all obliquely heterogeneous cases where the roughness is not aligned with the flow.
Predicting turbulent heat transfer over rough surfaces

Zhong, Kevin ( 2023-04)

When fluids such as air or water flow over solid surfaces, a transfer of heat between the fluid and solid interface occurs. This heat transfer underpins numerous industrial and natural systems, making routine predictions for heat transfer of paramount interest. In practice this is no easy feat. The fluid flow is often turbulent and the underlying surface is often rough, both of which must be accounted for in accurate predictions. Unfortunately, current state-of-the-art models for this purpose are insufficient, as these models are usually restricted to empirical fits, which admit a diverse set of behaviours in their predictions. To rectify this current ambiguity in rough-wall heat transfer, we have systematically conducted high-fidelity direct numerical simulations (DNSs), aiming to unveil the physical mechanisms governing rough-wall heat transfer. In these comprehensive datasets, we cover a wide array of roughness regimes (controlled by the roughness Reynolds number k+), whilst simultaneously varying the working fluid (dictated by the Prandtl number Pr ). A further dataset is also considered where we vary both k+ and the roughness topography, which we control through the frontal solidity, defined as the frontal projected area divided by the total plan area. These simulations are conducted using the minimal channel framework (MacDonald et al., 2017), which can accurately resolve the near-wall roughness sublayer flow at affordable cost, thus enabling the comprehensive parameter sweep. We examine the disagreements which currently linger regarding the prediction of fully rough (high-k+ ) heat transfer. We focus on the fully rough phenomenologies. Although we find the mean heat transfer favours the scaling of Brutsaert (1975), the Prandtl–Blasius boundary-layer ideas associated with the Reynolds–Chilton–Colburn analogy of Owen & Thomson (1963); Yaglom & Kader (1974) can remain an apt description of the flow locally in regions exposed to high shear. Sheltered regions, meanwhile, violate this behaviour and are instead dominated by reversed flow, where no clear correlation between heat and momentum transfer is evident. The overall picture of fully rough heat transfer is then not encapsulated by one singular mechanism or phenomenology, but rather an ensemble of different behaviours locally. Building on this intuition of distinct heat transfer behaviours locally, we develop a predictive model which idealises the total heat transfer as being comprised of two competing heat transfer mechanisms: exposed heat transfer, which follows a Reynolds–Analogy-like scaling and sheltered heat transfer, which is spatially uniform. The summation of these contributions, each weighted by their individual area fractions yields the total rough-wall heat transfer, and is ultimately dependent on the roughness topography controlled by the frontal solidity. We show that a simple ray-tracing model parameterised solely by a sheltering angle is capable of capturing this sheltered and exposed area partition. Finally, we provide a view to transitionally rough, low-k + heat transfer. Here, we have demonstrated that the virtual-origin framework of Luchini (1996) can provide a valid avenue for the prediction of transitionally rough heat transfer.
Measurements and analysis of turbulent boundary layers subjected to streamwise pressure gradients

Romero, Sylvia ( 2021)

This thesis details the changes in structure between an adverse pressure gradient turbulent boundary layer (APG TBL), zero pressure gradient (ZPG) TBL, and channel flow by means of the mean momentum balance (MMB). In order to understand the effects of a pressure gradient on a turbulent boundary layer, aspects of the physical flow are studied via mean statistics, turbulence measurements, and spectra analysis. This study uses new experimental measurements that are conducted along an APG ramp as well as measurements downstream of the ramp insert to study the flow as it relaxes towards equilibrium. In the present experimental set-up the boundary layer is under modest APG conditions, where the Clauser pressure-gradient parameter $\beta$ is $\leq 1.8$. Well-resolved hot-wire measurements are obtained at the Flow Physics Facility (FPF) at the University of New Hampshire. Comparisons are made with ZPG TBL experimental data at similar Reynolds number and computational data at lower Reynolds number. Present measurements are also compared to existing APG TBL lower Reynolds number experimental and computational data sets. Finally, it is shown how these findings relate to an analytical transformation. The primary takeaways from the MMB analysis presented herein are $(i)$ distance-from-the-wall scaling can result from an assumption of self-similar mean dynamics, and does not require primacy of a single velocity scale, and $(ii)$ distance-from-the-wall scaling does not necessarily imply a logarithmic mean velocity profile; a power-law velocity scale hierarchy along with self-similar mean dynamics simultaneously produces distance-from-the-wall scaling \textit{and} a power law mean velocity profile. The choice to refer to the (potentially) self-similar subdomain as the `inertial sublayer' in the present study (rather than the `log' layer) is therefore deliberate.
Flame Wall Interactions for Flames Diluted by Hot Combustion Products

Jiang, Bin ( 2020)

Flames diluted by combustion products can reduce emissions such as Carbon Monoxide (CO) and Oxides of Nitrogen (NOx) in industrial applications. In applications such as gas turbines, these flames are confined in a combustor and can interact with relatively cold walls. This interaction can quench the flame, producing incomplete combustion products. In this study, Flame-Wall Interaction (FWI) for methane/air flames diluted by hot combustion products was investigated using Direct Numerical Simulation (DNS). One-Dimensional (1D) Head-On Quenching (HOQ) was first simulated to examine operating parameter effects on CO emissions from transient quenching processes. Average CO within the quenching region was used to evaluate these effects, and the species transport budget was used to investigate the dominant terms. At higher dilution levels, the peak average near-wall CO decreases, and the rate of near-wall CO reduction also decreases. At higher wall temperatures, the peak average near-wall CO and its reduction rate increases. The near-wall CO may be modelled under some conditions using only the integrated diffusion term. Then, a two-Dimensional (2D) laminar V-flame was simulated in both steady and forced conditions. The changes in peak near-wall CO due to varying dilution level and wall temperature show similar trends to the 1D results. The exhaust CO is linked directly to the oxidation residence time, which is determined by the flame length. Due to the role of the flame length, the contribution of near-wall CO to the exhaust CO increases as dilution level or the wall temperature is reduced. Premixed flames can extinguish inside the cold-wall thermal boundary layer, which can leave high near-wall CO. This results in disproportionate levels of CO mass flux in the near-wall regions. The near-wall CO features large variations when the local Damkohler number is greater than 0.1. Analysis of the CO transport budget shows that unlike 1D simulation, both convection and diffusion dominate the CO transport in the near-wall region, except for the case with autoignition at the wall. Finally, a three-Dimensional (3D) turbulent V-flame in a channel was simulated with hot and cold walls. A main reaction zone in the central region supported by periodic bulk ignition events changes the position of volumetric reaction zones where CO is formed. Consistent with the 2D results, a lower wall temperature leads to a longer flame, thereby having more contribution to the exhaust CO. Near-wall turbulence-flame interaction creates wrinkled and streaky flame surfaces, and localizes the near-wall CO distribution. The high mean of CO mass fraction locates in the free-stream where the free-stream autoignition happens, while the high RMS of CO mass fraction is present closer to the wall. 1D flame solutions might be sufficient for modelling CO in the free-stream region and some parts of the near-wall region but not closer to be adjacent to the wall. Turbulent mixing and diffusion contribute to this deviation. These results set a benchmark for future near-wall CO modelling.
Sensor and actuator selection for feedback control of fluid flows

Oehler, Stephan Friedrich ( 2019)

The present thesis regards linear estimation and control for two fluid flows, with a particular focus on the placement of sensors and actuators. In the first part of the thesis, we study the complex Ginzburg-Landau equation, a simple model for spatially developing flows such as jets, wakes and cavities. (This equation can be seen as a low-dimensional substitute for the Navier-Stokes equations.) The specific focus is on the extent to which estimation and control are (i) fundamentally difficult and (ii) limited by having only a single sensor and a single actuator. To answer these questions, we study three problems. First, we consider the optimal estimation problem in which a single sensor is used to estimate the entire flow field (without any control). Second, we consider the full information control problem in which the whole flow field is known, but only a single actuator is available for control. Third, we consider the overall input-output control problem in which only a single sensor is available for measurements; and only a single actuator is available for control. By considering the optimal sensor placement, optimal actuator placement or both while varying the stability of the system, fundamental placement trade-offs are made clear. We discuss implications for effective feedback control with a single sensor and a single actuator and compare the results to previous placement studies. In the second part of this thesis, we look at an incompressible turbulent channel flow at a friction Reynolds number of Re$_\tau = 2000$. A linear Navier-Stokes operator is formed about the turbulent mean and augmented with an eddy viscosity. Velocity perturbations are then generated by stochastically forcing the linear Navier- Stokes operator. The objective is to estimate and control these perturbations. The estimation and control problems perform best for the largest scales that (i) are high in energy when stochastically forced, (ii) exhibit large transient growth and (iii) are coherent over large wall-normal distances. We determine the locations of sensors and actuators for which estimation and control are most effective by looking at two arrangements: (i) placing them at the wall; and (ii) placing them some distance off the wall. Finally, it is shown that a control arrangement with a well-placed sensor and actuator performs comparably to either measuring the flow everywhere (while actuating it at a single wall height) or actuating it everywhere (while measuring it at a single wall height). In this way, we gain insight (at low computational cost) into how specific scales of turbulence are most effectively estimated and controlled.
Characteristics of energetic motions in turbulent boundary layers

Padinjare Muttikkal, Dileep Chandran ( 2019)

In this dissertation, we present the first measurements of two-dimensional (2-D) energy spectra of the streamwise velocity component (u) in high Reynolds number turbulent boundary layers. The measurements in the logarithmic region of turbulent boundary layers give new evidence supporting the self-similarity arguments that are based on Townsend’s (1976) attached eddy hypothesis. The 2-D spectrum is found to be able to isolate the range of self-similar scales from the broadband turbulence, which is not possible with the measurement of a 1-D energy spectrum alone. High Reynolds number flows are characterized by large separation of scales. Therefore, to obtain converged 2-D statistics while resolving the broad spectrum of length and time scales, a novel experimental technique is required. To this end, we devise a technique employing multiple hot-wire probes to measure the 2-D energy spectra of u. Taylor’s frozen turbulence hypothesis is used to convert temporal-spanwise information into a 2-D spatial spectrum which shows the contribution of streamwise (λx) and spanwise (λy) length scales to the streamwise variance at a given wall height (z). The validation of the measurement technique is performed at low Reynolds number by comparing against the direct numerical simulation (DNS) data of Sillero et al. (2014). Based on these comparisons, a correction is introduced to account for the spatial resolution associated with the initial separation of the hot-wires. The proposed measurement technique is used to measure the 2-D spectra in the logarithmic region for friction Reynolds numbers ranging from 2400 to 26000. At low Reynolds numbers, the shape of the 2-D spectra at a constant energy level shows λy/z ∼ (λx/z)1/2 behaviour at large scales, which is in agreement with the existing literature. However, at high Reynolds numbers, it is observed that the square-root relationship tends towards a linear relationship (λy ∼ λx) as required for self-similarity and predicted by the attached eddy hypothesis. Finally, we present a model for the logarithmic region of turbulent boundary layers, which is based on the attached eddy framework and driven by the scaling of experimental 2-D spectra of u. The conventional attached eddy model (AEM), which comprises self-similar wall-attached eddies (Type A) alone, represent the large scale motions at high Reynolds numbers reasonably well. However, the scales that are not represented by the conventional AEM are observed to carry a significant proportion of the total kinetic energy. Therefore, in the present study we propose an extended AEM, where in addition to Type A eddies, we also incorporate Type CA and Type SS eddies. These represent the self-similar but wall-detached low-Reynolds number features and the non-self-similar wall-attached superstructures, respectively. The extended AEM is observed to predict a greater range of energetic length scales and capture the low- and high-Reynolds number scaling trends in the 2-D spectra of all three velocity components.
Experimental investigation of velocity and vorticity in turbulent wall flows

Zimmerman, Spencer James ( 2019)

This thesis details the results of a research effort both to acquire sufficiently-resolved velocity and vorticity vector time-series in turbulent wall-bounded flows, as well as to use the acquired data to juxtapose two canonical wall-bounded flows: the zero-pressure-gradient boundary layer and the fully-developed pipe. Towards these ends, a novel configuration of measurement sensors has been designed, evaluated, and deployed in three of the largest canonical wall-flow facilities in existence: the Flow Physics Facility (FPF) at the University of New Hampshire, the High Reynolds Number Boundary Layer Wind Tunnel (HRNBLWT) at the University of Melbourne, and the Centre for International Cooperation in Long Pipe Experiments (CICLoPE) at the University of Bologna. The datasets presented herein are the first to contain simultaneously-acquired velocity and vorticity statistics in both pipe and boundary layer flows under matched conditions. The capacity of the measurement probe to resolve the velocity and vorticity vectors under idealised conditions is evaluated via `synthetic experiments', whereby the response of the probe to a simulated turbulent flow is modeled, and the resulting aggregate statistics compared to those of the known input. The synthetic experimental results are then compared to statistics obtained from physical experiments, and show close agreement for most quantities despite differences in Reynolds number. Disagreement between the physical and synthetic experimental results in several quantities is used to diagnose a limitation of the present sensor system. An awareness of the measurement capabilities (and limitations) afforded by the comparison between the synthetic and physical experiments pervades the ensuing analysis and discussion of additional physical experimental results. Normalised statistical moments (up to the kurtosis) of velocity and vorticity are presented for both pipe and boundary layer cases. The two flows are shown to exhibit virtually no differences from one another wallward of the wake region aside from the transverse velocity component variances. The boundary layer wake is characterised by higher turbulence enstrophy and turbulence kinetic energy (TKE) than the pipe, despite containing both turbulent and non-turbulent states. Although there is no `free-stream' in the fully-developed pipe, a significant time-fraction of the flow can be described as `quasi-irrotational' near the centreline. This results in a departure of the velocity and vorticity kurtosis (and, when not identically zero, skewness) from Gaussian behaviour in the outer region of the pipe, as is known to occur in the boundary layer (owing to turbulent/non-turbulent intermittency). Spectral properties of the velocity and vorticity signals acquired in both flows are examined, both for their own content as well as to compare the two flows. Despite very little difference in the observed streamwise turbulence kinetic energy, the contributions to the total differ considerably by scale between the two flows. The pipe is observed to contain more streamwise TKE than the boundary layer in scales longer than 10 times the outer length scale $\delta$, while the opposite is true for scales shorter than $10\delta$. This `crossover' scale also applies to the spectra of the transverse velocity components and Reynolds shear stress. The measured enstrophy spectrum is shown to be approximately invariant under Kolmogorov normalisation for wall-distances greater than about 200 viscous-lengths. Finally, local isotropy and axisymmetry in the velocity components are evaluated. Local isotropy is observed to be satisfied over a range of scales for which the characteristic timescale of inertial energy transfer is expected to be small relative to the timescale of the mean strain rate. The relationship between the transverse velocities and the streamwise velocity, however, does not appear to approach isotropy along the pipe centreline, suggesting that the bounding wall also plays a role in imposing a sense of direction on the turbulence. Indeed, the aforementioned timescale criterion is shown to identify a cutoff scale that increases proportionally with wall-distance, confounding a conclusive statement regarding the primary source of anisotropy away from the centreline.
Structure of mean dynamics and spanwise vorticity in turbulent boundary layers

Morrill-Winter, Caleb ( 2016)

The overall aim of this research is to develop a refined scaling analysis for the two-dimensional mean momentum balance (MMB) for the zero-pressure gradient turbulent boundary layer (TBL), and to describe the mean and fluctuating spanwise vorticity structure in a context consistent with the mean dynamical scaling. Towards this aim, a custom multi-element hot-wire sensing array was used to measure spanwise vorticity fluctuations and Reynolds shear stress time series in turbulent boundary layers. Smooth wall boundary layer profiles, with very good spatial and temporal resolution, were acquired over a K\'arm\'an number range of $2,400-16,400$ at the Melbourne Wind Tunnel at the University of Melbourne, and in the University of New Hampshire's Flow Physics Facility (FPF). These data represent the most highly resolved measurements over this Reynolds number range available to date. For canonical boundary layers the mean inertia, which is a function of the wall-normal distance, appears instead of the constant mean pressure gradient force in the MMB for pipes and channels. The constancy of the pressure gradient has led to theoretical treatments for pipes/channels, that are more precise than for the TBL. Elements of these analyses include the logarithmic behaviour of the mean velocity, specification of the Reynolds shear stress peak location, the square-root Reynolds number scaling for the log layer onset, and a well-defined layer structure based on the balance of terms in the MMB. The present analyses evidence that similarly well-founded results also hold for turbulent boundary layers. This follows from transforming the mean inertia term in the MMB into a form that resembles that in pipes/channels, and is constant across the outer inertial region of the TBL. The present measurements support these analytical developments. Congruent with the self-similar structure admitted by the transformed mean governing equations, a description of the mean and fluctuating vorticity structure in turbulent boundary layers is presented. Due to the decreasing mean value of vorticity with increasing wall distance and Reynolds number, the fluctuating enstrophy approaches that of the instantaneous enstrophy on the inertial outer domain. Furthermore, this underlies an emerging self-similarity between the mean and standard deviation of vorticity over the same subdomain where the mean velocity profile is logarithmic. The accompanying data analysis includes a detailed description of the spanwise vorticity statistical structure. For flat plate boundary layers the spanwise vorticity is the only component that fluctuates about a non-zero mean, and hence was selected for this study. Empirical support for the proposed similarity structure is also provided.
The quiescent core of turbulent channel and pipe flows

Kwon, Yongseok ( 2016)

A new conceptual view of turbulent channel and pipe flows is presented via the proposition of the `quiescent core', which is analogous to the free-stream in turbulent boundary layers. The quiescent core is detected as a zone of roughly uniform streamwise momentum, which happens to be relatively quiescent compared to the rest of flow, residing in the central region of channel and pipe flows. It occupies a large proportion of the flow and oscillates with the large-scale wavelengths in a predominantly anti-symmetric manner. Within the intermittent region of wall-turbulence, it is observed that the oscillation of the turbulent/non-turbulent interface or quiescent core can contaminate the fluctuating velocity components under the traditional Reynolds decomposition. A new method of decomposing the total velocity is proposed to remove this contamination. The use of this new decomposition method, along with the zone-averaging technique, enables the examination of `true' turbulent structure and scale purely inside the `turbulent shear flow' region (below the free-stream or outside the quiescent core) of both internal (channel and pipe) and external (boundary layer) flows. The results are compared in internal and external flows to reveal that the structure and scale of turbulence in those flows are indeed much more similar than previous studies have concluded. It is shown that the geometry of the pipe core can be well-represented by a few dominant azimuthal Fourier modes. The dominant azimuthal modes of the pipe core are associated with streamwise streaks and roll-modes in axisymmetric arrangements and they often maintain a high degree of spatial coherence along the streamwise direction (for over a pipe radius). The investigation of temporal progression of the pipe core reveals that it simply convects downstream without azimuthal rotation and rapid evolution. The most energetic modes of channel flow are extracted and investigated by means of proper orthogonal decomposition. It is observed that the large-scale wall-normal eigenfunctions appear in pairs which carry comparable amounts of turbulent kinetic energy and Reynolds shear stress. The turbulent kinetic energy and Reynolds shear stress are mostly concentrated in the large-scale modes (with the first 20 modes carrying about a half of these quantities). The most energetic modes represent the large-scale inclined flow structures with symmetric or anti-symmetric arrangements between the top and bottom channel walls, which can efficiently replicate the associated large-scale geometry of the channel core.
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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