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Papers by Owen Williams

The aim of the current experimental program is to use PIV to measure turbulent statistics within ... more The aim of the current experimental program is to use PIV to measure turbulent statistics within a smooth surface boundary layer at Mach 7.4. It has been shown that the high shear present in a hypersonic boundary layer can lead to an error called peak locking, known to have a significant impact on first order statistics. To limit its effects, particle image displacements must be increased, leading to correspondingly larger interrogation window sizes. The variation of velocity across each window can be significant, testing the limits of many PIV algorithms. Four cross-correlation codes (MatPIV, ISSI, WIDIM and DaVis) are examined at two scales, paying particular attention to their behavior of turbulence in the near wall region and the extent of peak locking generated by shear. High quality seeding is required to ensure an accurate comparison. A successful method for the preparation of TiO 2 particles and their introduction into flow using a fluidized bed seeder is described. The current results show great promise for the resolution of hypersonic turbulence with PIV, as the majority of algorithms showed mean velocity profiles that lay on a clearly defined log-law, as well as streamwise turbulent intensities clustering near the DNS profile of Priebe and Martin (2011) at the same Mach number. The greatest differences between algorithms were in the near wall region. It is shown that for the purposes of the current study, DaVis 8.0 produced the highest quality results, with no peak locking, deviation below the log-law towards the transition region and giving a clear peak in streamwise turbulence near the wall. MatPIV also produced similar results, however significant peak locking was experienced, as would be expected from a code with no method of shear compensation. The ISSI code allowed a comparison between square and rectangular windowing. It was demonstrated to have significant peak locking in conditions when vectors were over half the size of the interrogation window. Additionally, the rectangular windows reduced the extent of peak locking, but showed significant scatter in streamwise turbulent intensity in the outer layer. For WIDIM results, while no peak locking was observed, the mean velocity profile showed significant dependence on the choice of windowing overlap. Differences were amplified in the near wall region. Significantly, mean velocity profiles resulting from calculations using the recommended offset of 75% displayed the greatest deviation from all other results. Near wall turbulence also appeared to be filtered. Wall-normal turbulence statistics were shown to be about half the expected magnitude, and were not influenced appreciably by the choice of PIV algorithm. This may be due to particle lag (although this is considered unlikely) or insufficient boundary layer development length.

The effect of varying three-dimensional, cylindrical post-type trip size on the mean and turbulen... more The effect of varying three-dimensional, cylindrical post-type trip size on the mean and turbulent velocity profiles of a Mach 7.6 turbulent boundary layer is examined using particle image velocimetry. It is shown that the effect of under-and overtripping is to amplify the wake component of the mean velocity profile and outer-layer turbulence intensity, confirming trends from incompressible flow. Such results indicate that overly aggressive tripping introduces artificial large-scale turbulence that requires longer downstream distances to decay. For the current experiment, adequate tripping was obtained for trip sizes between 1.7 and 2.3 times the laminar boundary-layer displacement thickness at the trip, δ tr , with the optimum size approximately 2.3 δ tr. The wake strength for the optimally tripped cases followed the correlation of Fernholz and Finley (AGARDograph 253, Neuilly sur Seine, France, 1980) at the same Reynolds number, providing a good indicator for under- or overtripping. These results confirm that compressible boundary layers mimic incompressible trends but require larger trip sizes and have increased sensitivity, making a boundary layer free from initial conditions harder to achieve.

The effects of stable thermal stratification on turbulent boundary layers are experimentally inve... more The effects of stable thermal stratification on turbulent boundary layers are experimentally investigated for smooth and rough walls. For weak to moderate stability, the turbulent stresses are seen to scale with the wall shear stress, compensating for changes in fluid density in the same manner as done for compressible flows. This suggests little change in turbulent structure within this regime. At higher levels of stratification turbulence no longer scales with the wall shear stress and turbulent production by mean shear collapses, but without the preferential damping of near-wall motions observed in previous studies. We suggest that the weakly stable and strongly stable (collapsed) regimes are delineated by the point where the turbulence no longer scales with the local wall shear stress, a significant departure from previous definitions. The critical stratification separating these two regimes closely follows the linear stability analysis of Schlichting (Z. Angew. Math. Mech., vol. 15 (6), 1935, pp. 313–338) for both smooth and rough surfaces, indicating that a good predictor of critical stratification is the gradient Richardson number evaluated at the wall. Wall-normal and shear stresses follow atmospheric trends in the local gradient Richardson number scaling of Sorbjan (Q.), suggesting that much can be learned about stratified atmospheric flows from the study of laboratory scale boundary layers at relatively low Reynolds numbers.

The response of an initially neutral rough-wall turbulent boundary layer to a change in wall temp... more The response of an initially neutral rough-wall turbulent boundary layer to a change in wall temperature is investigated experimentally. The change causes a localized peak in stable stratification that diffuses and moves away from the wall with downstream distance. The streamwise and wall-normal components of turbulent velocity fluctuations are damped at similar rates, even though the stratification only directly impacts the wall-normal component. The Reynolds shear profiles reveal the growth of an internal layer that scales approximately with the bulk Brunt–Väisälä frequency.

A new method for measuring turbulent heat fluxes using a combination of particle image velocimetr... more A new method for measuring turbulent heat fluxes using a combination of particle image velocimetry and a nanoscale fast-response cold-wire is tested by examining a rough-wall turbulent boundary layer subject to weakly stable stratification. The method has the advantages of simple calibration and setup, as well as providing spatial correlations of velocity and temperature and their associated integral length scales. The accuracy of using Taylor’s hypothesis when employing a large field of view is investigated. Heat flux, velocity–temperature correlation coefficients and turbulent Prandtl number profiles, as well as spatial velocity and temperature correlations, are presented.

We examine the effects of compressibility, slip, and fluid inertia on the frequency response of p... more We examine the effects of compressibility, slip, and fluid inertia on the frequency response of particle-based velocimetry techniques for supersonic and hypersonic flows by solving the quasi-steady drag equation for solid, spherical particles. We demonstrate that non-continuum and fluid inertial effects significantly affect the particle response under all typical supersonic flow conditions. In particular, the particle frequency response obtained from a shock response test depends on the strength of the shock, decreasing with shock strength as non-continuum effects become more prominent. For weak disturbances, such as those typical of turbulence, the actual particle frequency response can therefore be much lower than that obtained from a typical shock response. The greatest variability in the response was found to occur at low supersonic Mach numbers. The results were found to be typical of solid particles used for velocimetry under a wide range of wind tunnel conditions, and so, previous particle frequency response analyses based solely on shock response tests may well have overestimated the response to turbulence.

Thesis Chapters by Owen Williams

his dissertation examines the e↵ects of density gradients on turbulent boundary layer statistics ... more his dissertation examines the e↵ects of density gradients on turbulent boundary layer statistics and structure using Particle Image Velocimetry (PIV). Two distinct cases were examined: the thermally stable atmospheric surface layer characteristic of nocturnal or po- lar conditions, and the hypersonic bounder layer characteristic of high speed aircraft and reentering spacecraft.
Previous experimental studies examining the e↵ects of stability on turbulent boundary layers identified two regimes, weak and strong stability, separated by a critical bulk stratifi- cation with a collapse of near-wall turbulence thought to be intrinsic to the strongly stable regime. To examine the characteristics of these two regimes, PIV measurements were ob- tained in conjunction with the mean temperature profile in a low Reynolds number facility over smooth and rough surfaces. The turbulent stresses were found to scale with the wall shear stress in the weakly stable regime prior relaminarization at a critical stratification. Changes in profile shape were shown to correlate with the local stratification profile, and as a result, the collapse of near-wall turbulence is not intrinsic to the strongly stable regime. The critical bulk stratification was found to be sensitive to surface roughness and potentially Reynolds number, and not constant as previously thought. Further investigations examined turbulent boundary layer structure and changes to the motions that contribute to turbulent production.
To study the characteristics of a hypersonic turbulent boundary layer at Mach 8, sig- nificant improvements were required to the implementation and error characterization of PIV. Limited resolution or dynamic range e↵ects were minimized and the e↵ects of high shear on cross-correlation routines were examined. Significantly, an examination of parti- cle dynamics, subject to fluid inertia,compressibility and non-continuum e↵ects, revealed that particle frequency responses to turbulence can be up to an order of magnitude smaller than estimates made using a standard shock response test. The e↵ect of over-large tripping
devices was also found to increase the wake strength of the mean velocity profile as well as freestream turbulence. A final assessment of the data reveals that Morkovin scaling col- lapses the streamwise turbulence profiles with DNS at the same Mach number. Wall-normal turbulence measurements remain compromised by limited particle frequency response.

The objective of this thesis is to simulate the thermo-fluid interaction of a Solar Updraft Tower... more The objective of this thesis is to simulate the thermo-fluid interaction of a Solar Updraft Tower (collector, tower and turbine) using a one-dimensional numerical analysis. The aim is to develop a tool for the accurate prediction of the performance of a Solar Updraft Tower of any dimension in a timely and accurate manner. An additional objective is the preliminary analysis of the three dimensional flow under the solar collector.
The one-dimensional simulation is transient and compressible. The simulation was centred on the flow equations by solving the complete continuity, momentum and energy equations using finite volumes and the SIMPLE method. Models of frictional, inlet and exit losses as well as losses in the transition section between the collector and tower were included in the flow simulation. Adjacent to the flow, the heat storage in the ground was accomplished by solving the heat equation over a set of one-dimensional domains. A simple model of the collector roof was incorporated into the simulation to allow for additional heat transfer at the upper surface.
The ground, flow, and cover are all linked via a set of heat fluxes, evaluated using an energy balance developed from appropriate convective coefficients and radiative exchange between the ground and collector cover. This simulation was validated using data from the pilot plant at Manzanares.
The three dimensional analysis uses a commercial CFD code, Cfx5, to model a section of the solar collector. This investigation focused on identifying local flow regimes and their effect on convective heat transfer rates from the upper and lower surface. This knowledge was then applied to the heat transfer correlations used in the one-dimension simulation in order to increase their accuracy.
As a result of this analysis, a set of mixed convective heat transfer correlations were developed to improve the perceived deficiencies. Using these correlations, the simulation was validated and found to produce a maximum daily output of 47.6kW with an error of 0.6%. The addition of the new heat transfer correlations was essential to the accuracy of the simulation as those for purely forced convection did not even approach the correct output and underestimated the temperature rise in the collector.
A sensitivity analysis was conducted to evaluate the effect of different types of boundary conditions on the solution; both constant and time varying. It was concluded that the remaining discrepancies between the simulation and the pilot plant were a result of differences between the boundary conditions of the simulation and those of the pilot plant. Further increase in accuracy could be gained through incorporation of time varying inlet and outlet temperatures and pressures.
The simulation was determined to be a success, demonstrating the benefits solving the complete flow equations in conjunction with a high fidelity ground model. Further benefits include the accurate modelling of the adiabatic lapse rate, compressible chimney flow and incorporation of losses. As a result, this simulation can be applied to the prediction of a full scale solar updraft tower with confidence in the accuracy of the result.