Vegetation is commonly modelled as emergent arrays of rigid, circular cylinders. However, the drag coefficient (CD) of real stems or trunks is closer to that of cylinders with a square cross-section. In this thesis, vegetation has been idealised as square cylinders in laboratory experiments with a turbulence intensity of the order of 10% which is similar to that of typical river flows. These cylinders may also represent other obstacles such as architectural structures. This research has determined CD of an isolated cylinder and cylinder pairs as a function of position as well as the average drag coefficient (CDv) of larger arrays. A strain gauge was used to measure CD whilst CDv was computed with a momentum balance which was validated by strain gauge measurements for a regularly spaced array. The velocity and turbulence intensity surrounding a pair of cylinders arranged one behind the other with respect to mean flow (in tandem) were also measured with an Acoustic Doppler Velocimeter. The isolated cylinder CD was found to be 2.11 in close agreement with other researchers. Under fixed flow conditions CD for a cylinder in a pair was found to be as low as -0.40 and as high as 3.46 depending on their relative positioning. For arrays, CDv was influenced more by the distribution of cylinders than the flow conditions over the range of conditions tested. Mean values of CDv for each array were found to be between 1.52 and 3.06. This new insight therefore suggests that CDv for vegetation in bulk may actually be much higher than the typical value of 1 which is often assumed to apply in practice. If little other information is available, a crude estimate of CDv = 2 would be reasonable for many practical applications. The validity of a 2D realizable k-epsilon turbulence model for predicting the flow around square cylinders was evaluated. The model was successful in predicting CD for an isolated cylinder. In this regard the model performed as well as Large Eddy Simulations by other authors with a significant increase in computational efficiency. However, the numerical model underestimates CD of downstream cylinders in tandem pairs and overestimates velocities in their wake. This suggests it may be necessary to expand the model to three-dimensions when attempting to simulate the flow around two or more bluff obstacles with sharp edges.

This thesis is concerned with studies on spatially developing high speed mixing layers with twin objectives: (a) to provide enhanced and detailed understanding of spatial development of two-dimensional mixing layer emanating from splitter plate through large eddy simulation (LES, from now on) technique and (b) to evolve a consistent strategy for Unsteady Reynolds Averaged Navier-Stokes (URANS) approach to mixing layer calculations. The inspiration for this work arose out of the explanations that were being developed for the reduction in the mixing layer thickness with compressibility (measured by a parameter called convective Mach number, Mc). The reasons centered around increased stability, increase in compressible dissipation that was later discounted in favor of reduction in production and pressure-strain terms (with Mc, of course). These were obtained with direct numerical simulations (DNS) or LES techniques with homogeneous shear flow or temporal mixing layer. As apart, there was also a wide held view that using RANS (steady) techniques did not capture the compressibility effects when used in a way described above and so classical industrial codes for computing mixing- layer-embedded flows are unsuitable for such applications. Other important aspects that come out of the examination of literature are: the mixing layer growth is controlled in the initial stages by the double- boundary layer profile over the splitter plate and results in the mixing layer growth that is somewhat irregular due to doubling and merging of vertical structures. The view point of a smooth growth of the mixing layer is a theo- retical approximation arising out of the use of a smooth tan-hyperbolic profile that results at larger distances from the splitter plate. For all practical applications, it is inferred that the initial development is what is important because the processes of ignition and stable combustion occur close to the splitter plate. For these reasons, it was thought that understanding the development of the mixing layer is best dealt with using accurate spatial simulation with the appropriate initial profile. The LES technique used here is drawn from an OpenFOAM approach for dissimilar gases and uses one-equation Eddy Model for SGS stresses. The temporal discretization is second order accurate backward Euler and spatial discretization is fourth order least squares; the algorithm used for solving the equations is PISO and the parallelized code uses domain decomposition approach to cover large spatial domain. The calculations are performed with boundary layer profiles over the splitter plate and an initial velocity field with white noise-like fluctuations to simulate the turbulence as in the experiments. Grid independence studies are performed and several experimental cases are considered for comparison with measured data on the velocity and temperature fields as well as turbulent statistics. These comparisons are excellent for the mean field behavior and moderately acceptable for turbulent kinetic energy and shear stress. To further benefit from the LES approach, the details of the mixing layer are calculated as a function of four independent parameters on which the growth depends: convective Mach number (Mc = (U1 -U2)/ (a1 +a2)), stream speed ratio (r = U2=U1), stream density ratio (s = p2/p1) and the average velocity of the two streams ((U1+U2)=2) and examine the various terms in the equations to enable answering the questions discussed earlier. It is uncovered that r has significant influence on the attainment of self similarity (which also implies on the rate of removal of velocity defect in the double-boundary layer profile) and other parameters have a very weak influence. The minimum velocity variation with distance from the splitter plate has the 1/paxial distance behavior like in wakes; however, after a distance, departure to linear rise occurs and the distance it takes for this to appear is delayed with Mc. Other features such as the coherent structures, their merger or break up, the area of the structures, convective velocity information extraction from the coherent structures, the behavior of the pressure field in the mixing layer through the field are elucidated in detail; the behavior of the correlations between parameters (like pressure, velocity etc) at different points is used to elucidate the coherence of their fluctuating field. The effects of the parameters on the energy spectra have expected trends. An examination of the kinetic energy budget terms reveals that • the production term is the main source of the xx turbulence stress, whereas it is not significant in the yy component. • A substantial portion of this is carried by the pressure-velocity coupling from the xx direction to the yy direction, which becomes the main source term in the yy component. • Both, the production term as well as the pressure-velocity term show a clear decrease with increase in Mc. The high point of the thesis is related to using the understanding derived from an analysis of various source terms in the kinetic energy balance to evolve an unsteady Reynolds Averaged Navier Stokes (URANS) model for calculating high speed mixing layers, a subject that has eluded international research till now. It recognizes that the key feature affected by ompressibility is related to the anisotropy of the stress tensor. The relationship between stress component (_Txy) and the velocity gradient (Sxy) as obtained from LES is set out in the form of a simple relationship accounting for the effects of other parameters obtained earlier in this thesis. A minor influence due to _Tyy is extracted by describing its dependence on Sxy again as gleaned from LES studies. The needed variation of Prandtl and Schmidt numbers through the field is extracted. While the detailed variations can in fact be taken into account in URANS simulations, a simple assumption of these values being around 0.3 is chosen for the present simulations of URANS. Introduction of these features into the momentum equation gives the much expected variation of the reduction in the growth rate of the mixing layer with convective Mach number as in experiments. The relationships that can be used in high speed mixing layers are Introduction of these features into the momentum equation gives the much expected variation of the reduction in the growth rate of the mixing layer with convective Mach number as in experiments. This is then a suggested new approach to solve high speed mixing layers. While it can be thought that the principal contributions of the thesis are complete here, an additional segment is presented related to entropy view of the mixing layer. This study that considers the mixing layer with two different species expresses various terms involved in the entropy conservation equation and obtains the contribution of various terms on the entropy change for various Mc. It is first verified that the entropy derived from the conservation equation matches with those calculated from fluid properties, entropy being a state variable. It is shown that irreversible diffusion comes down the most with convective Mach number. Left: This image shows pictorially the flow of source of turbulent stress from the axial to the cross wise turbulent stress. Production (Σ) of turbulence happens mainly in the xx direction, a part of it is carried by the pressure-velocity correlation to the yy direction, which itself has a low production. With increasing Mc, both the production as well as the pressure-velocity correlation decrease. Right: This image shows the growth rate obtained from simulations scaled with the incompressible growth rate, of LES and RANS in the background of experiments (others). As is clear, the growth rate obtained is well within the band of experimental results.

Syngas consisting mainly of a mixture of carbon monoxide, hydrogen and other diluents, is an important fuel for power generation applications since it can be obtained from both biomass and coal gasification. Clean coal technologies require stable and efficient operation of syngas-fired gas turbines. The trapped vortex combustor (TVC) is a relatively new gas turbine combustor concept which shows tremendous potential in achieving stable combustion under wide operating conditions with low emissions. In the present work, combustion of low calorific value syngas in a TVC has been studied using in-situ laser diagnostic techniques and numerical modeling. Specifically, this work reports in-situ measurements of mixture fraction, OH radical concentration and velocity in a single cavity TVC, using state-of-the art laser diagnostic techniques such as Planar Laser-induced Fluorescence (PLIF) and Particle Image Velocimetry (PIV). Numerical simulations using the unsteady Reynolds-averaged Navier-Stokes (URANS) and Large Eddy Simulation (LES) approaches have also been carried out to complement the experimental measurements. The fuel-air momentum flux ratio (MFR), where the air momentum corresponds to that entering the cavity through a specially-incorporated flow guide vane, is used to characterize the mixing. Acetone PLIF experiments show that at high MFRs, the fuel-air mixing in the cavity is very minimal and is enhanced as the MFR reduces, due to a favourable vortex formation in the cavity, which is corroborated by PIV measurements. Reacting flow PIV measurements which differ substantially from the non-reacting cases primarily because of the gas expansion due to heat release show that the vortex is displaced from the centre of the cavity towards the guide vane. The MFR was hence identified as the controlling parameter for mixing in the cavity. Quantitative OH concentration contours showed that at higher MFRs 4.5, the fuel jet and the air jet stream are separated and a flame front is formed at the interface. As the MFR is lowered to 0.3, the fuel air mixing increases and a flame front is formed at the bottom and downstream edge of the cavity where a stratified charge is present. A flame stabilization mechanism has been proposed which accounts for the wide MFRs and premixing in the mainstream as well. LES simulations using a flamelet-based combustion model were conducted to predict mean OH radical concentration and velocity along with URANS simulations using a modified Eddy dissipation concept model. The LES predictions were observed to agree closely with experimental data, and were clearly superior to the URANS predictions as expected. Performance characteristics in the form of exhaust temperature pattern factor and pollutant emissions were also measured. The NOx emissions were found to be less than 2 ppm, CO emissions below 0.2% and HC emissions below 700 ppm across various conditions. Overall, the in-situ experimental data coupled with insight from simulations and the exhaust measurements have confirmed the advantages of using the TVC as a gas turbine combustor and provided guidelines for stable and efficient operation of the combustor with syngas fuel.