Mayank Tyagi

Large Eddy Simulation of Film Cooling Flow From an Inclined Cylindrical Jet

Predictions of turbine blade film cooling have traditionally employed Reynolds-averaged Navier-Stokes solvers and two-equation models for turbulence. Evaluation of several versions of such models have revealed that the existing two-equation models fail to resolve the anisotropy and the dynamics of the highly complex flow field created by the jet-crossflow interaction. A more accurate prediction of the flow field can be obtained from large eddy simulations (LES) where the dynamics of the larger scales in the flow are directly resolved. In the present paper, such an approach has been used, and results are presented for a row of inclined cylindrical holes at blowing ratios of 0.5 and I and Reynolds numbers of 11,100 and 22,200, respectively, based on the jet velocity and hole diameter. Comparison of the time-averaged LES predictions with the flow measurements of Lavrich and Chiappetta (UTRC Report No. 90-04) shows that LES is able to predict the flow field with reasonable accuracy. The unsteady three-dimensional flow field is shown to be dominated by packets of hairpin-shaped vortices. The dynamics of the hairpin vortices in the wake region of the injected jet and their influence on the unsteady wall heat transfer are presented. Generation of hot spots and their migration on the film-cooled surface are associated with the entrainment induced by the hairpin structures. Several geometric properties of a mixing interface around hairpin coherent structures are presented to illustrate and quantify their impact on the entrainment rates and mixing processes in the wake region.

Flow and Heat Transfer Predictions for Film Cooling

Abstract: Film cooling flows are characterized by a row of jets injected at an angle from the blade surface or endwalls into the heated crossflow. The resulting flowfield is quite complex, and accurate predictions of the flow and heat transfer have been difficult to obtain, particularly in the near field of the injected jet. The flowfield is characterized by a spectrum of vortical structures including the dominant kidney vortex, the horse‐shoe vortex, the wake vortices and the shear layer vortices. These anisotropic and unsteady structures are not well represented by empirical or ad‐hoc turbulence models, and lead to inaccurate predictions in the near field of the jet. In this paper, a variety of modeling approaches have been reviewed, and the limitations of these approaches are identified. Recent emergence of Direct Numerical Simulation (DNS) and Large Eddy Simulation (LES) tools allow the resolution of the coherent structure dynamics, and it is shown in this paper, that such approaches provide improved predictions over that obtained with turbulence models.

Large Eddy Simulations of Flow and Heat Transfer in Rotating Ribbed Duct Flows

Large eddy simulations are performed in a periodic domain of a rotating square duct with normal rib turbulators. Both the Coriolis force as well as the centrifugal buoyancy forces are included in this study. A direct approach is presented for the unsteady calculation of the nondimensional temperature field in the periodic domain. The calculations are performed at a Reynolds number (Re) of 12,500, a rotation number (Ro) of 0.12, and an inlet coolant-to-wall density ratio (Δρ/ρ) of 0.13. The predicted time and space-averaged Nusselt numbers are shown to compare satisfactorily with the published experimental data. Time sequences of the vorticity components and the temperature fields are presented to understand the flow physics and the unsteady heat transfer behavior.

A Parallel High-Order Discontinuous Galerkin Shallow Water Model

The depth-integrated shallow water equations are frequently used for simulating geophysical flows, such as storm-surges, tsunamis and river flooding. In this paper a parallel shallow water solver using an unstructured high-order discontinuous Galerkin method is presented. The spatial discretization of the model is based on the Nektar++ spectral/hp library and the model is numerically shown to exhibit the expected exponential convergence. The parallelism of the model has been achieved within the Cactus Framework. The model has so far been executed successfully on up to 128 cores and it is shown that both weak and strong scaling are largely independent of the spatial order of the scheme. Results are also presented for the wave flume interaction with five upright cylinders.

Reynolds Stress Transport Model Predictions and Large Eddy Simulations for Film Coolant Jet in Crossflow

Predictions of a film coolant jet in a crossflow for turbine blade cooling applications have traditionally employed k-e and k-ω closure models of turbulence. An evaluation of several such models (Hoda and Acharya, 1999) revealed that the existing two equation models fail to resolve the highly complex flow field in the vicinity of the jet created by the jet-crossflow interaction. The eddy viscosity approximation used to obtain closure for the Reynolds stress terms in the time-averaged Navier Stokes equation is unable to represent the anisotropy of the flow and does not model the wake region created behind the jet adequately. A more accurate prediction of the stress field can be obtained by the Reynolds stress transport (RST) equations, which represent a higher level of closure for the turbulent stresses. In this paper, two formulations of the RST model have been employed to predict the flow behind a row of jets discharging normally into a crossflow. The flow field predictions and turbulent statistics are compared with the experimental data of Ajersch et al. (1995) and with k-e predictions using the model of Lam and Bremhorst (1981). Predictions using Large Eddy Simulations (LES) are also presented to show the predictive capability of LES.© 2000 ASME

Closed Form Control Gains for Zero Assignment in the Time Delayed System

Control of the vibrating structures is desirable in various engineering applications for preventing fatigue and failure. It can be achieved by passive means using dynamic absorbers or by active means using sensors and actuators. In some cases, it is also not practical to apply a desirable control force in those locations at which the dynamics of the structure are to be controlled. In recent years, dynamic absorption schemes are investigated in which control strategies that absorb a steady state motion of a desired location in the structure have been developed. Such a vibration control strategy is termed as zero assignment. Unlike conventional full-state feedback control, which requires all the states of the system to be measured, zero assignment requires least numbers of sensors and actuators (depending on the number of dynamic absorption points) for estimating the control gains and, hence, it may provide economical engineering solution. However, while applying control strategy by active zero assignment, small time delay from the sensors and actuators in the feedback loop is unavoidable and they influence the control gains as well as the stability of the system. In this paper, we have developed vibration control strategy by active zero assignment and obtained closed form control gains for systems with and without time delays by using truncated and full Taylor series expansion. Some examples related to conservative and nonconservative systems as well as realistic distributed parameter systems are presented to demonstrate the active dynamic absorption and the effects of time delay on control gains. The effect of delay in the stability of the controlled system is also summarized.

Large Eddy Simulations of Rectangular Jets in Crossflow: Effect of Hole Aspect Ratio

Large eddy simulations of rectangular jets in crossflow are performed to study the effect of hole geometry on the penetration and spread of the coolant jet. Three different holes of aspect ratio 0.5, 1.0 and 2.0 are studied. In the present study, the jet to crossflow blowing ratio is 0.5 and the jet Reynolds number is approximately 4,700.

A Computational Fluid Dynamics Approach to Predict Pressure Drop and Flow Behavior in the Near Wellbore Region of a Frac-Packed Gas Well

Well completion plays a key role in reservoir production as it serves as a pathway that connects the hydrocarbon bearing rock with the wellbore, allowing formation fluids (e.g. oil, gas, water) to flow into the well and then up to production facilities on the surface. Frac-packing completion (F&P) is a well stimulation technique that vastly increases the fluid transport capability of the near wellbore region in comparison with the original formation capacity by filling fractures and perforation tunnels with high-permeability proppant, thus enabling higher production rates for the same pressure drop. Hence, it is of interest for the production engineer to have an accurate description of the actual and predicted production performance in terms of pressure drop and flowrate after the F&P completion process is done. However, in developing a mathematical model of this scenario two critical challenges should be faced: (a) as fluid flows at high flowrates it begins to deviate from linear behavior, i.e. Darcy’s law is no longer valid, (b) compressible fluid flow behavior in the near wellbore region cannot be intuitively predicted due to the geometrical complexity introduced by the well completion (e.g. perforation tunnels and fractures). Additionally, this kind of mathematical model must take into account the existence of three different domains: reservoir (porous, low permeability), completion region (porous, high permeability), and free flow region.In view of these complications, this study presents a computational approach to model and characterize the near wellbore region with F&P completion using computational fluid dynamics (CFD) modeling, combining a non-linear (non-Darcy or Forchheimer) real gas flow in porous media with a turbulence model for the free flow region. This study is classified into three parts: 1) verification case, 2) Darcy vs. non-Darcy flow, and 3) erosion analysis. All simulation cases are assumed to be isothermal, steady state gas flow. Streamlines are implemented to identify the possible kinds of flow regimes, or patterns, in the near wellbore region and it is shown that gas flow pattern can be high unpredictable. Turbulence production and erosional velocity limit are also analyzed. Finally, mathematical correlations for well completion performance of this particular case study are derived using data curve fitting.In conclusion, the CFD approach has proven to be a powerful yet flexible computational tool that can help the production and/or reservoir engineer to predict flow behavior as well as production performance for a gas producing well with F&P completion, while providing an insightful graphical description of pressure and velocity distribution in the near wellbore region.Copyright

Effects of Stress-Dependent Hydraulic Properties of Proppant Packs on the Productivity Indices of the Hydraulically Fractured Gas Reservoirs

Hydraulic fracturing stimulates wells and has enabled exploitation of the vast unconventional hydrocarbon resources in the US and globally. Proppants, which are granular materials that prevent fractures from closing, must provide high fracture conductivities and withstand closure stresses without getting crushed. Advances in imaging technologies and high-performance computing enable calculation of transport and mechanical properties of pore-scale images. Imagebased mechanical and flow simulations can rapidly and accurately estimate the transport properties of proppant packs in fractures at different closure stresses, providing a credible alternative to difficult and expensive physical experiments. This study examines transport properties of a ceramic proppant pack with confining stresses from zero to 20,000 psi. The images of this packing show rearrangement of the packing structure, embedding of the grains at the rock wall, and crushing of individual proppant particles. Lattice Boltzmann (LB) simulation results of this proppant pack indicate that the permeability and inertial flow parameter are sensitive to stress at high stresses (which crush the proppant particles) compared to lower stresses. Predicted stress-dependent permeability and non-Darcy factors corresponding to the effective stress fields around the hydraulic fractured completions are included in a two-dimensional gas reservoir simulator to calculate the productivity indices. Productivity indices with permeability and non-Darcy factors kept constant at initial effective stress (6000 psi) are ca. 0.03 percent higher than those with stress-dependent permeability and non-Darcy factors for a gas rate of 20 MMscf/D.Hydraulic fracturing stimulates wells and has enabled exploitation of the vast unconventional hydrocarbon resources in the US and globally. Proppants, which are granular materials that prevent fractures from closing, must provide high fracture conductivities and withstand closure stresses without getting crushed. Advances in imaging technologies and high-performance computing enable calculation of transport and mechanical properties of pore-scale images. Imagebased mechanical and flow simulations can rapidly and accurately estimate the transport properties of proppant packs in fractures at different closure stresses, providing a credible alternative to difficult and expensive physical experiments. This study examines transport properties of a ceramic proppant pack with confining stresses from zero to 20,000 psi. The images of this packing show rearrangement of the packing structure, embedding of the grains at the rock wall, and crushing of individual proppant particles. Lattice Boltzmann (LB) simulation results of this proppant pack indicate that the permeability and inertial flow parameter are sensitive to stress at high stresses (which crush the proppant particles) compared to lower stresses. Predicted stress-dependent permeability and non-Darcy factors corresponding to the effective stress fields around the hydraulic fractured completions are included in a two-dimensional gas reservoir simulator to calculate the productivity indices. Productivity indices with permeability and non-Darcy factors kept constant at initial effective stress (6000 psi) are ca. 0.03 percent higher than those with stress-dependent permeability and non-Darcy factors for a gas rate of 20 MMscf/D.

Zero Assignment in Vibration: With and Without Time Delay

Control of the vibrating structures is desirable in various engineering applications for preventing fatigue and failure. It can be achieved by passive means using dynamic absorbers or by active means using sensors and actuators. In some cases, it is also not practical to apply a desirable control force in those locations at which dynamics of the structure to be controlled. In recent years, nodal control or dynamic absorption schemes are investigated in which control strategies to absorb a steady state motion of a desired location in the structure have been developed. Unlike conventional full-state feedback control which requires all the states of the system to be measured, nodal control strategy requires least numbers of sensors and actuators (depending upon the number of dynamic absorption points) for estimating the control gains and hence it may provide economical engineering solution. Nodal control problems are essentially a zero assignment problems in which a desired control is achieved by assigning zeroes to the prescribed locations in the structure. However while applying nodal control strategy by active means, small time delay from the sensors and actuators in the feedback loop is unavoidable and they influence the control gains as well as the stability of the system. In this paper we have developed nodal control strategy and obtained control gains for systems with and without time delays. Some examples related to conservative and nonconservative systems as well as realistic distributed parameter systems are presented to demonstrate the nodal control strategy and the effects of time delay on control gains.Copyright