Browsing by Subject "Boundary layers"

Now showing 1 - 3 of 3
  • Thumbnail Image
    Item
    Experimental verification of a heat/mass transfer analogy in two dimensional laminar and turbulent boundary layers.
    (2008-07) Kulkarni, Kaustubh Shankar
    Heat and mass transfer from a solid surface into a fluid stream both are diffusion driven processes. Their mathematical model equations are identical for identical flow and boundary conditions. Problems with engineering applications are transformed from one domain to another for practical and economical advantages. A mass transfer technique using naphthalene sublimation is faster, of higher resolution, economical and more accurate than a direct heat transfer measurement. The diffusion rates of heat transfer in air and naphthalene in air are quantitatively different. Hence, the advantages of naphthalene sublimation technique are justified when the heat/mass transfer analogy is experimentally verified and an analogy factor (F = Nu/Sh ) is determined. Heat/mass transfer analogy is experimentally verified for two dimensional laminar and turbulent boundary layer flows. Thermal boundary layer technique is used to measure local heat transfer coefficient ( Nu ) and naphthalene sublimation technique is used to measure local mass transfer coefficient ( Sh ) for two identical plates subjected to identical boundary layer flows. The accuracy of the thermal boundary layer technique is determined using a constant heat flux plate made of steel shim subjected to constant electrical power. The convective heat flux is determined using this electrical power after correcting for conduction and radiation effects. These results are compared to the heat flux values determined using the thermal boundary layer technique and are found to agree within 2%. The effect of conduction within the thermocouple wires is studied with a numerical model using fin analysis and a variable convective heat transfer load. The equilibrium thermocouple temperature is solved for various locations of the thermocouple probe within the boundary layer to simulate an equivalent experiment for an analytically calculated laminar boundary layer flow. The predictions of the model agree within 1% of the experimental measurements and are used to correct them for laminar case. The heat/mass transfer analogy factor is calculated using the corrected Nu and Sh. It is found to agree with the analytical prediction of 0.677 within 2% for the laminar case and is found to be a constant of 0.667 for the turbulent case.
  • Thumbnail Image
    Item
    Modal and nonmodal stability analysis of shock-wave/boundary-layer interactions
    (2019-04) Hildebrand, Nathaniel
    This dissertation is about the modal and nonmodal stability of an oblique shock wave impinging on a Mach 5.92 laminar boundary layer at a transitional Reynolds number. The adverse pressure gradient of the oblique shock wave causes the laminar boundary layer to separate from the wall, resulting in the formation of a recirculation bubble. For sufficiently large oblique shock angles, the recirculation bubble is unstable to three-dimensional perturbations, and the flow bifurcates from its original laminar state. We use direct numerical simulation (DNS) and global stability analysis (GSA) to show that this first occurs at a critical oblique shock angle of 12.9 degrees. The least-stable global mode is stationary at bifurcation, and it takes place at a nondimensional spanwise wavenumber of 0.25, in good agreement with the DNS results. Examination of the critical global mode reveals that it originates from an interaction between small spanwise corrugations at the incident shock base, streamwise vortices inside the recirculation bubble, and spanwise modulation of the bubble strength. Furthermore, the global mode drives the formation of long streamwise streaks downstream of the bubble. This stationary three-dimensional instability is similar to other mechanisms observed in laminar recirculation bubbles. We show that centrifugal instability plays no role in the self-sustaining mechanism of the stationary global mode. Further, we employ an adjoint solver to corroborate our physical interpretations by showing that the critical global mode is most sensitive to base flow modifications that are entirely contained inside the recirculation bubble. We also perform a parametric study to determine the effect of freestream Mach number on shock-wave/boundary-layer interaction (SWBLI) instability. Along with DNS and GSA, we investigate the physical mechanisms responsible for transient growth in an SWBLI using a power iteration method. This approach lets perturbations propagate upstream and downstream, which allows us to capture the complex physics associated with the recirculation bubble and understand how it amplifies fluctuations. For a Mach 5.92 boundary layer with no oblique shock wave, we demonstrate that the transient response arises from the inviscid Orr mechanism, the Landahl lift-up effect, and first-mode instability. The optimal transient growth for this spatially-developing boundary layer with a nondimensional streamwise domain length of 235 is G=1.69x10^3 and occurs at a spanwise wavenumber of 0.6. This corresponds to an amplification of 4.11x10^1, which is similar to that seen in a variety of parallel boundary layer flows. We compute the optimal transient growth of an SWBLI at the exact same conditions as the spatially-developing boundary layer. The presence of an oblique shock wave changes the optimal transient response such that G=1.36x10^7 at a spanwise wavenumber of 0.6. Hence, the transient growth in an SWBLI is four orders of magnitude larger than the transient growth in a spatially-developing boundary layer. The nondimensional spanwise wavenumber of the optimal transient response also increases from 0.6 to 2.6. Moreover, the corresponding optimal spanwise wavelength for the SWBLI is on the order of twice the boundary-layer thickness, agreeing with SWBLI experiments. These changes are attributed to the sudden change in the streamline curvature in the upstream region of the flow field. Furthermore, the optimal initial condition for the SWBLI consists of elongated streaks in the upstream boundary layer. As this initial condition evolves to its final state, we observe the formation of streamwise streaks in the recirculation bubble (that are further amplified in the downstream boundary layer) along with a large perturbation that comes off of the bubble apex and convects downstream. Our results demonstrate large transient growth in a Mach 5.92 SWBLI and suggest that inevitable imperfections in a hypersonic wind tunnel would play an important role in the early stages of transition to turbulence.
  • Thumbnail Image
    Item
    Studies in wall turbulence using dual plane particle image velocimetry and direct numerical simulation data.
    (2010-02) Saikrishnan, Neelakantan
    Wall-bounded turbulent flows play a critical role in a variety of engineering applications. A detailed understanding of the fundamental processes underlying these flows is crucial to the accurate modeling and design of efficient and practical systems. The present studies are directed towards demonstrating the utility of experimental and numerical approaches in tandem to elucidate the structure and dynamics of wall-bounded turbulent flows over a range of Reynolds numbers. The first part of this thesis deals with the use of Dual Plane Particle Image Velocimetry (DPPIV) to understand the organization of vortex structures in the logarithmic region of turbulent boundary layer and channel flows. DPPIV provides the full velocity gradient tensor in a plane parallel to the wall and was used to calculate the projection angles of vortex structures with the three coordinate directions. In order to validate the experimental technique for identification of vortex cores, Direct Numerical Simulation (DNS) data at a comparable Reynolds number and higher resolution were used. The DNS data were averaged to the resolution of the DPPIV data and a vortex core identification routine was implemented to compare the raw DNS, averaged DNS and DPPIV data. It was observed that results from the DPPIV data match those from the raw and averaged DNS data very well. This confirms that DPPIV is a robust technique for calculating vortex core statistics, and the resolution of the measurements is sufficient to adequately resolve these structures. The second part of the thesis examines the effect of Reynolds number on the scale energy budget in wall-bounded turbulent flows. An understanding of the distribution of turbulent kinetic energy across the momentum deficit region in wall-bounded turbulent flows is critical to the complete understanding of the energy dynamics in these flows. The scale energy budget provides a tool to simultaneously assess the influence of spatial location and scales in the flow on the distribution of turbulent energy. This analysis was conducted using three DNS data sets across a range of Reynolds numbers, and results from these data were compared to results from an earlier study at a smaller Reynolds number. It is observed that the previous low Reynolds number study did not sufficiently resolve all the quantities of the energy budget in the near-wall region, primarily due of the lack of a distinct logarithmic region in the low Reynolds number simulation. Close to the wall, no effects of Reynolds number were observed on the terms of the scale energy analysis across the datasets studied. Upon moving away from the wall, the turbulent production term did not display any effects of Reynolds number, while the scale transfer term increased with increasing Reynolds number. As a result the cross-over scale, a quantity related to the shear scale in turbulent flows, increased with increasing Reynolds numbers for all datasets. The shear scale provides the scale at which the change from an isotropy-recovering range to an anisotropic region is observed, while the cross-over scale provides a transition between a transfer dominated range to a production dominated range of scales. The plot of cross-over scale versus wall-normal location revealed that the slope of the best fit lines increased with increasing Reynolds number. Further, the slope of the best fit line decreased with increasing wall-normal location. DPPIV data were also used to conduct the same analysis in turbulent boundary layers across a range of Reynolds numbers. The aim of using DPPIV data was to quantify the effects of Reynolds number on the scale energy analysis, using larger Reynolds number experimental data. The effects of resolution and Reynolds number on the DPPIV data were assessed and described in detail. The effect of resolution was most dominant on the wall-normal gradients of the streamwise and spanwise velocities, and hence the transfer of energy in physical space and the transfer of energy in scale space were overestimated in the lower resolution data. The effect of resolution was smallest on the turbulent production term, since it does not contain of any fluctuating velocity gradients. With increasing Reynolds numbers, the production term did not change significantly in the logarithmic layer, while the scale transfer term increased, resulting in a larger range of transfer-dominated scales. The value of the cross-over scale between the effective production and scale transfer term increased with increasing Reynolds number, suggesting a larger range of isotropic-type transfer dominated scales. In conclusion, it was demonstrated that DPPIV in tandem with DNS can be used to reliably assess the scale energy budget in wall-bounded turbulent flows. i