In our project we discuss a finite element time-relaxation method for high Reynolds number flows. The key idea consists of using local projections on polynomials defined on macro element of each pair of two elements sharing a face. We give the formulation for the scalar convection–diffusion equation and a numerical illustration.

The presence of roughness on a surface subject to high Reynolds number flows promotes the formation of a turbulent boundary layer and the generation of a fluctuating pressure field imposed on the surface. While numerous studies have investigated the wall pressure fluctuations over zero-pressure gradient smooth walls, few studies have examined the effects of surface roughness on the wall pressure field. Additionally, due to the difficulties in obtaining high Reynolds number flows over fully rough surfaces in laboratory settings, an even fewer number of studies have investigated this phenomenon under flow conditions predicted to be fully free of transitional effects that would ensure similarity laws could be observed. This study presents the efforts to scale and describe the wall pressure spectrum of a rough wall, high Reynolds number turbulent boundary layer free of transitional effects. Measurements were taken in the Virginia Tech Stability Wind Tunnel for both smooth and rough walls. A deterministic roughness fetch composed of 3-mm hemispheres arranged in a 16.5-mm square array was used for the rough surface. Smooth and rough wall flows were examined achieving Reynolds numbers up to Re_θ = 68700 and Re_θ = 80200 respectively, with the rough wall flows reaching roughness based Reynolds numbers up to k_g⁺ = 507 with a simultaneous blockage ratio of δ/k_g = 76. A new roughness based inner variable scaling is proposed that provides a much more complete collapse of the rough wall pressure spectra than previous scales had provided over a large range of Reynolds numbers and roughness configurations. This scaling implies the presence of two separate time scales associated with the near wall turbulence structure generation. A clearly defined overlap region was observed for the rough wall surface pressure spectra displaying a frequency dependence of Ï ^-1.33, believed to be a function of the surface roughness configuration and its associated transport of turbulent energy. The rough wall pressure spectra were shown to decay more rapidly, but based on the same function as what defined the smooth wall decay. / Master of Science

In order to protect gas turbine blades from hot gases exiting the combustor, several intricate external and internal cooling concepts are employed. High pressure stage gas turbine blades feature serpentine passages where rib turbulators are installed to enhance heat transfer between the relatively colder air bled off from the compressor and the hot internal walls. Most of the prior studies have been restricted to Reynolds number of 90000 and several studies have been carried out to determine geometrically optimized parameters for achieving high levels of heat transfer in this range of Reynolds number. However, for land-based power generation gas turbines, the Reynolds numbers are significantly high and vary between 105 and 106. Present study is targeted towards these high Reynolds numbers where traditional rib turbulator shapes and prescribed optimum geometrical parameters have been investigated experimentally. A steady-state liquid crystal thermography technique is employed for measurement of detailed heat transfer coefficient. Five different rib configurations, viz., 45 deg., V-shaped, inverse V-shaped, W-shaped and M-shaped have been investigated for Reynolds numbers ranging from 150,000 to 400,000. The ribs were installed on two opposite walls of a straight duct with aspect ratio of unity. For very high Reynolds numbers, the heat transfer enhancement levels for different rib shapes varied between 1.3 and 1.7 and the thermal hydraulic performance was found to be less than unity. / Master of Science

No description available.

Numerous efforts have contributed to the study of phase-change problems for over a century|both analytical and numerical. Among those numerical approximations applied to solve phase-transition problems, phase-field models attract more and more attention because they not only capture two important effects, surface tension and supercooling, but also enable explicitly labeling the solid and liquid phases and the position of the interface. In the research of this dissertation, a phase-field model has been employed to simulate 2-D dendrite growth of pure nickel without a flow, and 2-D ice crystal growth in a high-Reynolds-number lid-driven-cavity flow. In order to obtain the details of ice crystal structures as well as the flow field behavior during freezing for the latter simulation, it is necessary to solve the phase-field model without convection and the equations of motion on two different scales. To accomplish this, a heterogeneous multiscale method is implemented for the phase-field model with convection such that the phase-field model is simulated on a microscopic scale and the equations of motion are solved on a macroscopic scale. Simulations of 2-D dendrite growth of pure nickel provide the validation of the phase-field model and the study of dendrite growth under different conditions, e.g., degree of supercooling, interface thickness, kinetic coefficient, and shape of the initial seed. In addition, simulations of freezing in a lid-driven-cavity flow indicate that the flow field has great effect on the small-scale dendrite structure and the flow eld behavior on the large scale is altered by freezing inside it.

A turbulent channel flow was used to study the scaling of the combined effects of roughness and flow injection on the mean flow and turbulence statistics of turbulent plane Poiseuille flow. It was found that the additional momentum injected through the rough surface acted primarily to enhance the roughness effects and, with respect to the mean flow, blowing produced similar mean flow effects as increasing the roughness height. This was not found to hold for the turbulence statistics, as a departure from Townsend’s hypothesis was seen. Instead, the resulting outer-scaled streamwise Reynolds stress for cases with roughness and blowing deviated significantly from the roughness only condition well throughout the inner and outer layers. Investigation into this phenomena indicated that suppression of the large-scale motions due to blowing may have been contributing to this deviation.

There have been very few studies investigating the rough wall pressure spectra under fully rough flows, which are relevant to many common engineering applications operating within this regime. This investigation uses the Virginia Tech Stability Wind Tunnel to perform experiments on a series of high Reynolds number zero pressure gradient turbulent boundary layers formed over rough walls in an effort to better understand and characterize the behavior of the rough wall pressure spectrum. The boundary layers were fully rough, and the boundary layer height remained sufficiently larger than the height of the roughness elements. Two rough surfaces were tested. One consisted of an array of 1-mm ordered hemispherical elements spaced 5.5-mm apart, and the other contained 3-mm hemispherical elements randomly spaced, but with the same element density as 1/3 of the 1-mm ordered roughness. The wall pressure spectrum and its scaling were then studied in detail, and it was found that the rough wall turbulent pressure spectrum at vehicle relevant conditions is defined by three scaling regions. One of which is a newly discovered high frequency scaling defined by viscosity, but controlled by the friction velocity adjusted to exclude the pressure drag on the roughness elements. Based on these three scaling regions an empirical model describing the wall pressure spectra for hydraulically smooth, traditionally rough, and fully rough flows was explored. Two point wall pressure fluctuations were also analyzed for each surface condition, and it was found that the roughness inhibits the convective velocities within the inner portions of the boundary layer. / Master of Science

A new version of the Deforming-Spatial-Domain/Stabilized Space--Time (DSD/SST) formulation of incompressible flows has been introduced recently to have additional subgrid-scale representation features. This is the space--time version of the residual-based variational multiscale (VMS) method. The new version is called DSD/SST-VMST (i.e. the version with the VMS turbulence model) and also Space--Time VMS (ST-VMS). The thesis starts with a brief overview of the ST-VMS method. It continues with a comprehensive set of test computations with 3D airfoil geometries at high Reynolds numbers and comparison with experimental data. The thesis shows that the test computations signal a promising future for the ST-VMS method.

A new version of the Deforming-Spatial-Domain/Stabilized Space--Time (DSD/SST) formulation of incompressible flows has been introduced recently to have additional subgrid-scale representation features. This is the space--time version of the residual-based variational multiscale (VMS) method. The new version is called DSD/SST-VMST (i.e. the version with the VMS turbulence model) and also Space--Time VMS (ST-VMS). The thesis starts with a brief overview of the ST-VMS method. It continues with a comprehensive set of test computations with 3D airfoil geometries at high Reynolds numbers and comparison with experimental data. The thesis shows that the test computations signal a promising future for the ST-VMS method.

Solid propellant gas generators that have high gas capacity are used for fast pressurization of inflatable devices or elastic shells. However, many applications such as control surface actuation, air bottle pressurization in rocket engines and safety systems of automobiles (airbags) require exit gases at near ambient temperature. A scheme suitable for short duration applications is passive cooling of gas generator gases by using a packed bed as compact heat exchanger. A study indicated that the mass flow rates of solid propellant gas generators for applications such as air bottle pressurization and control system actuators were of the order of 1 kg/s. Since pressure and enthalpy drop correlations for packed beds with mass flow rates (~1 kg/s) and packing sphere based Reynolds number (Red) ~ 9X104 were unavailable in open literature, an experimental investigation was deemed necessary. The objectives of the present study were (a) characterization of packed beds for pressure and enthalpy drop, (b) develop Euler and Nusselt number correlations at Red~105 and (c) evolve an engineering procedure for estimation of packed bed pressure and enthalpy drop. An experimental test facility with a hydrogen-air combustor was designed and fabricated for this purpose to characterize a variety of packed beds for pressure drop and heat transfer. Flow through separate packed beds consisting of 9.5mm and 5mm steel spheres and lengths ~200mm and ~300mm were studied in the sphere based Reynolds numbers (Red) range of 0.4X104 to 8.5X104. The average porosity (є) of the randomly packed beds was ~0.4. The ratios of packed bed diameter to packing diameter for 9.5mm and 5mm sphere packing were ~ 9.5 and 18 respectively. The inlet flow temperature was unsteady and a suitable arrangement using mesh of spheres was used at either ends to eliminate flow entrance and exit effects. Stagnation pressures were measured at entry and exit of the packed beds. The pressure drop factor fpd, (ratio of Euler number (Eu) to packed bed dimensions) for packed bed with 9.5mm spheres exhibited an asymptotically decreasing trend with increasing Reynolds number, and a correlation for the pressure drop factor is proposed as, fpd=Eu/ [6(1-є) (L/dp)] =125.3 Red-0.4; 0.8X104 < Red < 8.5X104 (9.5mm sphere packing). However, for packed beds with 5mm spheres the pressure drop factor fpd, was observed to increase in the investigated Reynolds number range. The correlation based for pressure drop factor is proposed as, fpd= Eu/ [6(1-є) (L/dp)] =0.0479 Red0.37; 0.4X104 < Red < 3.9X104 (5mm sphere packing). The pressure drop factor was observed to be independent of the inlet flow temperature. Gas temperatures were measured at the entry, exit and at three axial locations along centerline in the packed beds. The solid packing temperature was measured at three axial locations in the packed bed. At Red~104, the influence of gas phase and solid phase thermal conductivity on heat transfer coefficient was found to be negligible based on order of magnitude analysis and solid packing temperature data obtained from the experiments. Evaluation of sphere based Nusselt number (Nud) at axial locations in the packed bed indicated a length effect on the heat transfer coefficient, which was a function of Reynolds number and size of spheres used in packing. The arithmetic average of Nusselt numbers at different axial locations in the packed bed were correlated as Nud=3.85 Red0.5; 0.5X104 < Red < 8.5X104. The Nusselt numbers obtained in the experiments were consistent with corresponding literature data available at lower Reynolds numbers. In this experimental study Euler number correlations for pressure drop and Nusselt number correlations for heat transfer were obtained for packed beds at Red~105. An engineering model for estimation of packed bed pressure and enthalpy drop was evolved, which is useful for sizing of packed bed heat exchanger in solid propellant gas generation systems.