No description available.

No description available.

This thesis explores the effects of favourable pressure gradient on the structure of turbulent boundary layers (TBL). In this context, the structure of three types of boundary layers namely a zero-pressure-gradient boundary layer, equilibrium boundary layers under favourable pressure gradient and relaminarising boundary layers is investigated mostly from the point of view of large-scale dynamics. This covers a whole range of flows on the so-called Reynolds number - pressure gradient diagram - from turbulent zero pressure gradient flows to relaminarising flows at relatively low Reynolds numbers. The study of turbulent and relaminarising boundary layers is carried out primarily using direct numerical analyses and some limited experiments in this thesis. The direct numerical simulations (DNS) of a zero-pressure-gradient turbulent boundary layer (ZPG TBL) is validated against the experimental and DNS data available in the literature. Furthermore, the important question of time-averaged signature of a large scale vortex structure and its relation with the two-point correlations in the context of ZPG TBL is addressed. In this context, a synthetic flow consisting of hairpin vortex structures is generated. The two-point correlations in the synthetic TBL and a real TBL are found to be qualitatively similar. This shows that the vortex structure leaves a time-averaged footprint in the form of correlations of velocity and vorticity. A study of two-point correlations in a real TBL shows that the structure angle deduced from two-point correlations varies with wall-normal location. The structure angle is small near the wall and increases away from the wall in agreement with the previous studies. The small angle close to the wall signifies the presence of streamwise structure. Away from the wall, this streamwise coherence is lost and the correlation contours become more isotropic. The presence of the wall and the mean shear affects smaller scales making them anisotropic close to the wall. Towards the edge of the boundary layer, smaller scales tend to become isotropic leading to -5/3 law in the energy spectrum. Further, a relation between a passive scalar in a flow and vorticity is explored. It is found that the scalar product of vorticity and scalar gradient is conserved in a non-diffusive situation. This assertion is demonstrated under various flow conditions. Despite the differences in Schmidt numbers, the structures observed in the outer layer are similar in both numerical and experimental flow visualisations. Further, the equilibrium turbulent boundary layers under favourable pressure gradient are studied. The numerical simulations of equilibrium sink flow TBL are validated against the experimental results of Dixit (2010). A study of two-point correlations reveals that the near-wall structure angle decreases with a favourable pressure gradient in sink flow TBLs. In the outer region, the loss of streamwise coherence occurs at a wall-normal location closer to the wall than in an ZPG TBL. Edge intermittency study reveals that the flow is non-turbulent beyond y/δ = 0.8 inside the mean boundary layer edge. The variation of the ratio of pressure gradient to Reynolds shear stress gradient shows that this ratio is very large (> 50) beyond y/δ = 0.8. The dominance of pressure gradient makes this part of sink flow TBL to behave like a Euler-region. Small scales in sink flow TBL tend to be isotropic near the edge of the boundary layer and spectra shows -5/3 law akin to ZPG TBL, albeit at lower Reynolds numbers. The concept of equilibrium is extended to flows with wall transpiration. The sink flow TBL is a special case of more generalised equilibrium TBLs with wall transpiration. Conditions required for the flow with wall transpiration are derived. It is observed that there is a systematic variation of various statistical properties with wall velocity. Further, it is observed that the motion in these equilibrium flows is purely active like in sink flow TBL. In equilibrium TBL, the Reynolds shear stress is directly related to mean velocity. So we have at our disposal an exact relation between the Reynolds shear stress and the mean velocity gradient without the need to do any ad-hoc modelling for the sink flow. This is an interesting observation from the point of view of modelling TBLs using eddy-viscosity. Eddy-viscosity model derived from sink flow TBL data is found to predict the mean velocity profiles in flows with wall transpiration with a sufficient accuracy. Similarly, it is plausible that any general non-equilibrium flow may be treated as a departure from equilibrium. With suitable modifications, eddy viscosity obtained from equilibrium TBL may be used to model them without invoking ad-hoc assumptions. Finally, the effect of initial Reynolds number on the process of relaminarisation is studied numerically and experimentally. ZPG TBLs with two different initial Reynolds number are subjected to different degrees of acceleration. However, the pressure gradient history is same in both the cases. It is observed that the flow with a higher initial Reynolds number relaminarises at a lower pressure gradient value than the flow with a lower initial Reynolds number. Assessment of different parameter criteria reveals that the criterion proposed by Narasimha & Sreenivasan (1973) is appropriate for the prediction of the onset of relaminarisation. Further, the structures in relaminarising flows are studied. The near-wall structure angle is found to decrease with the increasing FPG and the streamwise length of the structure also increases. The low and high speed streaks in the near-wall region are found to become longer and less undulating with an increase in the spanwise spacing. A stabilisation mechanism of near-wall streaks is also presented which suggests that the kinematic effect of mean vertical velocity directed towards the wall is responsible for the stabilisation of streaks.

A wind tunnel investigation of an axisymmetric bluff body, known as a Goldschmied propulsor, was completed. This model conceptually combines boundary layer control and boundary layer ingestion into a single complementary system that is intended to use energy to reduce the axial force on the body by eliminating separation and increasing the pressure recovery aft of the body’s maximum thickness. The goal of the current project was to design, fabricate, and fully document the performance of a wind tunnel model incorporating the Goldschmied propulsor concept and complete an examination of its aerodynamic performance. The investigation took place at California Polytechnic State University, San Luis Obispo in the Aerospace Engineering Department’s subsonic 3ft by 4ft wind tunnel. The model is 38.5 inches in length and 13.5 inches in diameter with a discrete suction slot at 85% of the body length and an embedded propulsor that provides the suction flow, expelling it out of the model’s aft end. The experiment included measurements of surface pressure, total axial force, suction mass flow rate, fan thrust, fan torque, fan speed, and input fan power. The size of the suction slot and amount of input fan power were the main test variables in the 54 data point test matrix that was completed at a length Reynolds number of 1.34 million and a tunnel speed of 66 ft/s (20 m/s). The model was able to achieve fully attached flow on the aftbody with as little as 100W of input power and a net positive (forward) axial force coefficient of 0.12 with as little as 200W of input power. The model was also able to achieve a peak axial pressure force coefficient of 0.005 in the forward direction with an input power of 500W and a slot gap of 1.6% of the body length. A slightly lower axial pressure force coefficient of 0.0045 was achieved with only 200W of input power and a slot gap of 0.7% of the body length. The peak axial pressure force for most tested slot gaps occurred at about 200W of input power, and a slot gap of 0.7% of the body length resulted in the best overall performance for most input power settings. Two different suction slot configurations, a simple gap and a cusp, were tested, and no significant performance differences were seen between them. The pressure coefficient data showed similar trends as test data from 1956 of a similar model at higher Reynolds number, but it did not show complete agreement. Despite these positive aspects of the investigation, a simple power based comparison between the collected data and a conventional non-integrated propulsor does not show a performance improvement for the Goldschmied propulsor.

published_or_final_version / Mechanical Engineering / Doctoral / Doctor of Philosophy

published_or_final_version / Mechanical Engineering / Master / Master of Science in Engineering

published_or_final_version / Mechanical Engineering / Master / Master of Philosophy

No description available.

The evolution of the large scale structures and the mean field were investigated in axisymmetric and plane mixing layers. Some aspects of the linear instability of an axisymmetric jet have been demonstrated. The axisymmetric geometry admits two additional length scales with relation to the two-dimensional shear layer: the radius of the jet column and the azimuthal wavelength. The importance of these two length scales in governing the instability of an axisymmetric jet was explored. The special case of a thin axisymmetric shear layer was analyzed and the results stressing the evolution of different azimuthal modes were compared with some phase-locked data which was produced by subjecting the jet to axisymmetric and helical excitation. The importance of the initial spectral distribution in a natural jet was demonstrated when it is used as an input to the amplification curve obtained from linear stability theory to predict a measured spectral distribution at a further downstream location. The inclusion of the nonlinear terms in the stability analysis reveals two main interactions: mean flow-wave interaction and wave-wave interaction. The modification of the mean flow of an axisymmetric jet was examined by exciting two azimuthal modes simultaneously. The interaction resulted in an azimuthal modulation of the mean velocity profile having a cosine shape. Effectively, the geometry of the jet was modified without changing the geometry of the nozzle. The coupling between an excited periodic disturbance and the mean flow was analyzed and the spatial evolution of both were compared with experimental results obtained in a plane mixing layer. The behavior of the concommittant Reynolds stresses is discussed in detail. The conditions under which one disturbance will transfer energy to another were derived and demonstrated in an axisymmetric jet. The interaction between a large amplitude plane wave with a weak subharmonic component was shown to enhance the amplification rate of the subharmonic. It was further shown that the nonlinear interaction between two azimuthal modes can produce a third azimuthal mode which was not initially present in the flow. The coupling between a fundamental wave and its subharmonic in a parallel plane mixing layer was demonstrated numerically.

This thesis focuses on secondary instability mechanisms of high-speed boundary layers over cones with a circular cross section. Hypersonic transition investigations at Mach 8 are performed using Direct Numerical Simulations (DNS). At wind-tunnel conditions, these simulations allow for comparison with experimental measurements to verify fundamental stability characteristics.To better understand geometrical influences, flat-plate and cylindrical geometries are studied using after-shock conditions of the conical investigations. This allows for a direct comparison with the results of the sharp cone to evaluate the influence of the spanwise curvature and the cone opening angle. The ratio of the boundary-layer thickness to the spanwise radius is used to determine the importance of spanwise curvature effects. When advancing in the downstream direction the radius increaseslinearly while the boundary-layer thickness stays almost constant. Hence, spanwise curvature effects are strongest close to the nose and decrease in downstream direction. Their influences on the secondary instability mechanisms provide some rudimentary guidance in the design of future high-speed air vehicles.In experiments, blunting of the nose tip of the circular cone results in an increase in critical Reynolds number (c.f. Stetson et al. (1984)). However, once a certain threshold of the nose radius is exceeded, the critical Reynolds number decreases even to lower values than for the sharp cone. So far, conclusive explanations for this behavior could not be derived based on the available experimental data. Therefore, here DNS is used to study the effect of nose bluntness on secondary instability mechanisms in order to shed light on the underlying flow physics. To this end, three different nose tip radii are considered-the sharp cone, a small nose radius and a large nose radius. A small nose radius moves the transition on-set downstream, while for a large nose radius the so-called transition reversal is observed. Experimentalists hold influences of the entropy layer responsible but detailed numerical studies may lead to alternateconclusions.