Scaling and structure of the momentum and scalar fields within a turbulent boundary layer perturbed by an effusion film and its comparison to asymptotic behaviour of pipe flow momentum
File(s)
Author(s)
Burnett, Daniel
Type
Thesis
Abstract
The first part of this thesis presents a new scaling paradigm for the intermediate region of pressure-driven, fully developed turbulent boundary layers. The log law assumption is shown to be invalid for scaling the location of Reynolds shear stress maximum, which predicts $ y^+_{m\tau} \propto Re_{\tau}^{\beta}$ with $\beta = 0.5$. An outer peak in premultiplied production is observed to be further from the wall than the Reynolds shear stress peak, indicating that $\beta > 0.5$. Fitting to high Reynolds number turbulent pipe and channel data produces $\beta = 0.529 \pm 0.005$.
An intermediate velocity scale $\Delta U^+_m \propto Re_{\tau}^{2\beta - 1}$ is derived. The magnitude and location of the outer peak in streamwise velocity variance are shown to scale well with $\Delta U^+_m$. A second-order Taylor expansion about $ y^+_{m\tau}$ is used to predict the location of the outer peak in premultiplied production, which has good agreement with high Reynolds number data.
The second part of this work presents a large-scale experimental study, where a canonical turbulent boundary layer is perturbed by an effusion film - applicable to gas turbine blade cooling. Lower temperature air is injected into the boundary layer through a staggered array of small holes. The injection-freestream velocity ratio ($VR$) is varied from $0.10 < VR < 0.37$. Three-component laser Doppler anemometry and oil film interferometry characterise the momentum field, and simultaneous x-wire and cold-wire characterise the joint momentum-scalar field.
The boundary layer scaling behaviour changes about a critical velocity ratio $VR_c \approx 0.20$, which is attributed to bulk film lift-off. Large spanwise differences in the temperature and momentum fields are observed. Turbulence is significantly enhanced, particularly in the outer region and the near-wall spanwise fluctuations. Neither the local equilibrium hypothesis or Reynolds' analogy are valid.
An intermediate velocity scale $\Delta U^+_m \propto Re_{\tau}^{2\beta - 1}$ is derived. The magnitude and location of the outer peak in streamwise velocity variance are shown to scale well with $\Delta U^+_m$. A second-order Taylor expansion about $ y^+_{m\tau}$ is used to predict the location of the outer peak in premultiplied production, which has good agreement with high Reynolds number data.
The second part of this work presents a large-scale experimental study, where a canonical turbulent boundary layer is perturbed by an effusion film - applicable to gas turbine blade cooling. Lower temperature air is injected into the boundary layer through a staggered array of small holes. The injection-freestream velocity ratio ($VR$) is varied from $0.10 < VR < 0.37$. Three-component laser Doppler anemometry and oil film interferometry characterise the momentum field, and simultaneous x-wire and cold-wire characterise the joint momentum-scalar field.
The boundary layer scaling behaviour changes about a critical velocity ratio $VR_c \approx 0.20$, which is attributed to bulk film lift-off. Large spanwise differences in the temperature and momentum fields are observed. Turbulence is significantly enhanced, particularly in the outer region and the near-wall spanwise fluctuations. Neither the local equilibrium hypothesis or Reynolds' analogy are valid.
Version
Open Access
Date Issued
2024-12-30
Date Awarded
2025-06-01
License URL
Advisor
Morrison, Jonathan
Buxton, Oliver
Sponsor
Engineering and Physical Sciences Research Council
Great Britain. HM Government
Grant Number
EP/P000878
Publisher Department
Department of Aeronautics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)