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We present an analysis of the effects of heating, suction, and compressibility on the stability characteristics of boundary-layer flows within the framework of a complete nonparallel, linear, spatial stability theory. Included in the theory are disturbances due to velocity, Pressure, temperature, density, and transport properties as well as 'variations of the fluid properties with temperature. The method of multiple scales is used to account for the nonparallelism of the mean flow and equations are derived for the evolution of the disturbance amplitude and wave number vector. / Ph. D.

Boundary-layer flows near leading edges of generally curved obstacles have been studied for a long time. Apart from having many practical applications, the theory and approaches prevailing in this area stimulate development of a variety of computational tools and form a ground for testing them. The specific aim of this work is to study two-dimensional laminar boundary layer flows near the leading edges of airfoils and other elongated bodies, and to explore geometries for which boundary layer separation can be avoided. This class of problems is relevant to optimal design of wings, aircraft and projectile noses, laminar flow control methods and adaptive wing technology. One of the findings of this work suggests that local modifications to parabolic wing noses can yield up to 11% increase in the unseparated angle of attack. Another result obtained here is the set of shortest possible generalised elliptic noses of long symmetric bodies which allow unseparated flow. Methods adopted in this work are based on the combined use of numerically solved Prandtl equations written in Gortler variables, and inviscid solutions obtained semi-analytically by the conformal mapping method. The resulting technique being reliable, fast and computationally inexpensive, can complement or test the results obtained using a comprehensive CFD approach. / Thesis (Ph.D.)--School of Mathematical Sciences, 2002.

In this thesis, a new turbulence model developed previously for channel and flat plate flows is evaluated for flat plate flows with pressure gradient. For this purpose a flow solver, which uses boundary layer equations as the governing equations and Von Karman momentum integral equation for the calculation of skin friction, is developed. It is shown that the error of the new turbulence model, in predicting the velocity profile, is less than 5 % for the flat plate flows without pressure gradient and less than 10 % for the flat plate flows with favorable pressure gradient. It is also shown that results with an error in the order of 20 % can be achieved for the flat plate flows with adverse pressure gradient.

Boundary-layer flows near leading edges of generally curved obstacles have been studied for a long time. Apart from having many practical applications, the theory and approaches prevailing in this area stimulate development of a variety of computational tools and form a ground for testing them. The specific aim of this work is to study two-dimensional laminar boundary layer flows near the leading edges of airfoils and other elongated bodies, and to explore geometries for which boundary layer separation can be avoided. This class of problems is relevant to optimal design of wings, aircraft and projectile noses, laminar flow control methods and adaptive wing technology. One of the findings of this work suggests that local modifications to parabolic wing noses can yield up to 11% increase in the unseparated angle of attack. Another result obtained here is the set of shortest possible generalised elliptic noses of long symmetric bodies which allow unseparated flow. Methods adopted in this work are based on the combined use of numerically solved Prandtl equations written in Gortler variables, and inviscid solutions obtained semi-analytically by the conformal mapping method. The resulting technique being reliable, fast and computationally inexpensive, can complement or test the results obtained using a comprehensive CFD approach. / Thesis (Ph.D.)--School of Mathematical Sciences, 2002.

The work reported in this thesis is an experimental and theoretical investigation of the so-called sink flow boundary layers. These are two-dimensional (in the mean), favourable-pressure-gradient (FPG) boundary layer flows where the boundary layers experience stream-wise acceleration inside a two-dimensional convergent channel with smooth and plane walls. The boundary layers studied are mainly turbulent with few cases that may be identified as reverse-transitional. The sink flow turbulent boundary layers (TBLs) are the only smooth-walled layers that are in ‘perfect equilibrium’ or ‘exact self-preservation’ in the sense of Townsend (1976) and Rotta (1962). The present boundary layer experiments were conducted in an open-return low-speed wind tunnel. The sink flow conditions were established on the test-plate by using a contoured test-section ceiling for creating a convergent channel with smooth and plane walls. The strength of the streamwise FPG was varied by changing the freestream speed in the test-section. Few zero-pressure-gradient (ZPG) turbulent boundary layers were also measured in the same tunnel for which the contoured ceiling was replaced by a straight one. The velocity measurement techniques used include conventional Pitot-tubes for mean flow measurements and hotwire/crosswire probes for turbulence measurements. For measurement of skin friction in ZPG flows, Preston-tube was used while for the sink flows the so-called surface hotwire method was employed. Static pressures were measured on the test-surface using an alcohol-based projection manometer. Boundary layers were tripped at the beginning of the test-plate to ensure quick transition to turbulence. The mean velocity scaling in sink flow TBLs in the presence of strong FPG has been studied systematically, especially in view of the apparent pressure-gradient-dependence of the logarithmic laws reported in the literature (Spalart & Leonard, 1986; Nickels, 2004; Chauhan et al., 2007). The experimental study of sink flow TBLs carried out over a wide range of streamwise FPGs has shown that the mean velocity profiles (in inner coordinates) exhibit systematic departures from the universal logarithmic law as the pressure gradient parameter ∆p is varied. Even so, each of these profiles exhibits a logarithmic region, albeit non-universal, whose constants are functions of the pressure gradient. Systematic dependence of these constants on the pressure gradient parameter ∆p is observed. Moreover, the wake region is uniformly absent in all these profiles. In other words, each profile looks like a ‘pure wall-flow’, in the sense of Coles (1957), only if it is viewed in relation to its own non-universal logarithmic law. To support the experimental observation of the pressure-gradient-dependence of logarithmic laws in sink flow TBLs, a theory based on the method of matched asymptotic expansions has been applied to sink flow TBLs and this theory reveals a systematic dependence of inner and outer logarithmic laws on the pressure gradient parameter ∆p. This dependence is essentially a higher-order effect and therefore becomes significant only in the presence of relatively strong pressure gradients. Comparison of the theory with the experimental data demonstrates that the disappearance of the universal logarithmic law in strong FPG situations does not necessarily imply the absence of classical inner-outer overlap region. The overlap may still manifest itself as a logarithmic functional form with constants that are strongly influenced by the magnitude of the FPG. An immediate use of the non-universal log laws is towards the estimation skin friction in strong-pressure-gradient equilibrium and near-equilibrium TBL flows and this issue has been studied in some detail. It is shown that the conventional Clauser-chart method for estimation of skin friction (which gives fairly accurate results for ZPG or mild-pressure-gradient flows), originally proposed by Clauser (1954), can be modified to deal with the situations involving strong streamwise pressure gradients, provided that the equilibrium or near-equilibrium TBL under consideration is not very close to relaminarization or separation. In such cases, the overlap layer manifests itself in the form of non-universal logarithmic laws that are dependent on the local strength of the pressure gradient. Using these non-universal log laws in conjunction with the measured pressure distribution (necessary for obtaining the acceleration parameter K) and a measured mean velocity profile, it is possible to obtain the local skin friction coefficient to an accuracy which is typical of skin friction measurements. This modified Clauser-chart method (MCCM) employs a two-fold iterative procedure (one iteration on Cf and the other on ∆p) in contrast to the conventional method that involves only one iteration (on Cf alone). As a by-product of this MCCM, one obtains the local pressure gradient parameter ∆p and the slope 1/κ and intercept C of the non-universal log law for that profile. It is also demonstrated that the arm´MCCM is quite robust to the changes in the universal values of K´arman constant κ0 and intercept C0 for the ZPG turbulent boundary layer. Various aspects of the large-scale structure in turbulent and reverse-transitional sink flow boundary layers subjected to streamwise FPGs have also been investigated. The use of sink flow configuration allows systematic characterization of the large-scale structure with the strength of the FPG as a parameter where the characterization is not contaminated by the upstream history effects. The large-scale structure is identified by cross-correlating the wall-shear stress fluctuation with the streamwise velocity fluctuation. The structure orientation is found to be linear over a large wall-normal extent typically extending from y/δ of 0.1 to 0.6. Beyond y/δ =0.6, the correlation under consideration becomes very weak to allow any conclusive results. The average structure inclination angle αavg is found to decrease systematically with increase in the streamwise FPG. This result is important and has implications towards modeling of the near-wall region. Further it is found that the structure gets elongated considerably as the FPG is increased, i.e. the streamwise spatial extent of the structure increases. Taken together, it is observed that the structure becomes flatter and longer with the increase in FPG. Structural models are proposed for sink flow TBLs in the form of either the shape of individual hairpin vortices or the possible structural self-organization. These models are then discussed in the light of present experimental results. It is also shown that the process of relaminarization of a TBL by strong FPG may be better appreciated by appealing to these structural models. The validity of Taylor’s hypothesis for structure angle measurements in the present study has been established experimentally. This exercise is important since the flows under consideration are highly accelerated and sometimes even reverse-transitional. In most of the previous work on the validity of Taylor’s hypothesis, at least for the measurements similar to the present work, the emphasis has been on ZPG turbulent boundary layers. The present exercise is therefore crucial for accelerating flows. Possible reasons for the observed validity of Taylor’s hypothesis have also been identified − specifically it is seen that the condition ∆xp/L << 1 needs to be met for Taylor’s hypothesis to be valid in pressure gradient flows. Investigation of the structure convection velocity from the space-time correlations has revealed that the convection velocity of a typical structure in the present sink flow boundary layers is almost equal to the local mean velocity (more than 90%). This implies that the structure gets convected downstream almost along with the mean flow. Near-wall ‘active’ and ‘inactive’ motions in sink flow TBLs have been studied, discussed and compared with the corresponding results for ZPG turbulent boundary layers from five different aspects: (i) turbulent diffusion of TKE, (ii) quadrant statistics, (iii) profiles of the streamwise turbulence intensity, (iv) event correlation length scales obtained from conditional sampling on the instantaneous flux signal and (v) profiles of the Townsend parameter Tp =(−uv) /u2. Near-wall inactive motion is seen to be related to the strength of the large-eddy structure in the outer region of TBL flow. For APG flows the near-wall inactive motion is known to be more intense (Bradshaw, 1967b) than the ZPG flows, say at the same K´arman number δ+. This observation is consistent with a stronger large-eddy structure that may be perceived from the stronger wake component in the mean velocity variation and the larger mean entrainment in an APG turbulent boundary layer as compared to the ZPG flow at same δ+. In sink flow TBLs, the large-eddy structure is much weaker in comparison to the ZPG flow at same δ+ which is consistent with the absence of wake component in the mean velocity profile as well as the zero mean entrainment into the layer. A sink flow TBL represents, a state of weakest large-eddy structure and hence minimum intensity of inactive motion compared to any other equilibrium or near-equilibrium TBL flow having the same K´arman number δ+. All the analysis of the relevant experimental data seems to support this.

Boundary layer calculations are performed around an airfoil and its wake. Smith-van Ingen transition prediction method is employed to find the transition from laminar to turbulent flow. First, potential flow around the airfoil is solved with the Hess-Smith panel method. The resulting velocity distribution is input to the boundary layer equations in order to find a so called blowing velocity distribution. The output of the boundary layer equations are also used to compute the location of onset of transition using the Smith-van Ingen en transition prediction method. The obtained blowing velocity distribution is fed back to the panel method to find a velocity distribution which includes the effects of viscosity. The procedure described is repeated until convergence is observed. A computer program is developed using the theory. Results obtained are in good accord with measurements

The linear instability of laterally diverging/converging flows is an important aspect towards understanding the laminar-transition process in many viscous flows. In this work the linear instability of constant pressure laterally diverging/converging flow has been investigated. The laminar velocity field for laterally diverging/converging flows, under the source/sink approximation, has been reduced to two-dimensional flows. This reduction is alternative to the Mangier transformation used earlier. For a constant pressure laterally strained flow, the laminar velocity is found to be governed by the Blasius equation for flow over a flat plate. The non-parallel linear instability of constant pressure laterally strained flows has been examined. The instability equation is found to be same as that for the Blasius flow. This implies that the stability is same as that for the Blasius flow. A lateral divergence/convergence is shown to alter the Reynolds number from that in a two-dimensional flow. The instability of a laterally converging/diverging flow thus can be obtained from the available results for the Blasius flow by scaling the Reynolds numbers. This leads to the result that while a diverging flow is more unstable than the Blasius flow, a converging flow is more stable. Some additional relevant results are also presented.