Rotational and Shower Head Cooling Hole Effects on Leading-Edge Jet Impingement Heat Transfer

Jet Impingement and shower head cooling are critical cooling techniques used to maintain turbine blades at operational temperatures. Jet impingement is extremely effective at removing large amounts of heat flux from the target surface, the inner blade wall, through stagnation point heat transfer. Shower head cooling produces a cooling film around the exterior of the blade, in return reducing external heat flux. The current work consisted of investigating the jet impingement effectiveness with rotational effects for two different cooling schemes. The analysis was conducted numerically using STAR CCM+ with two different turbulence models, the three equation Lag Elliptic Blending K Epsilon model and the seven equation Elliptic Blending Reynolds Stress Transport (EB RST) model. The EB RST model incorporated the Generalized Gradient Diffusion method. The blade used was NASA/General Electrics E^3 row 1 blade. Two conjugate heat transfer models were developed for just the leading-edge portion of the blade, one with and one without shower head holes. The models consisted of a quarter of the blade-span to reduce computational expense and only one jet was analyzed. A flow field analysis was performed on the free jet region to analyze the potential core velocity and turbulent kinetic energy profiles. Nusselt Number spanwise distribution and external blade temperature profiles were also evaluated. The investigation showed, for both turbulence models, that rotational effects produce turbulent kinetic energy within the jet\u27s potential core, reducing the incoming jet velocity and hence reducing impingement effectiveness. While both turbulence models illustrated an increase in turbulent kinetic energy throughout the structure of the impinging jet, the magnitudes and locations varied significantly. This is due to the well-known underprediction of turbulent dissipation in the K-Epsilon family of turbulence models, as well as the location of applications of the vorticity tensor to the transport equations

Turbulence Closure Models for Computational Fluid Dynamics

The formulation of analytical turbulence closure models for use in computational fluid mechanics is described. The subject of this chapter is the types of models that are used to predict the statistically averaged flow field – commonly known as Reynolds‐averaged Navier–Stokes equations (RANS) modeling. A variety of models are reviewed: these include two‐equation, eddy viscosity transport, and second moment closures. How they are formulated is not the main theme; it enters the discussion but the models are presented largely at an operational level. Several issues related to numerical implementation are discussed. Relative merits of the various formulations are commented on

Investigation of Novel Turbulence Modeling Techniques for Gas Turbines and Aerospace Applications

Standard eddy-viscosity models lack curvature and system rotation sensitized terms in their formulation. Hence they fail to capture the effects of curvature and system rotation on turbulence anisotropy. As part of this effort, an algebraic expression for a characteristic rotation term is developed and tuned with the help of rotating homogeneous shear flow. This formulation is primarily based upon the rotation and curvature sensitized eddy-viscosity coefficient developed by York et al. (2009). A new scalar transport equation loosely based on Durbin’s wall normal turbulent velocity scale (Durbin, 1991) is introduced to account for the modification in turbulence structure due to system rotation and curvature effects. The added transport equation also introduces history effects and stability in the solution with small increase in computational cost. The eddy-viscosity is redefined based on new turbulent velocity scale and hence the effects of rotation and streamline curvature are introduced into the mean momentum equation. A number of canonical test cases with significant curvature and rotation effects along with a cyclone flow, a representative of complex industrial flows, are considered for model validation. Hybrid modeling framework combines the strength of RANS in boundary layers and LES in separated shear layers to alleviate the weaknesses of RANS and limitations of LES model in some complex flows. A recently proposed hybrid RANS-LES modeling framework uses a weighing parameter that dynamically determines the RANS and LES regions based on solution statistics. The hybrid modeling methodology is implemented on a normal jet in crossflow, and a film cooling case for the purpose of model validation and evaluation. The final goal of the proposed effort is to combine advanced RANS modeling capability with LES using the new hybrid modeling framework. Specifically, the curvature and rotation sensitive RANS model developed here is coupled with commonly used LES models to produce a novel model for complex turbulent flows with the potential to improve accuracy of CFD predictions (versus existing RANS models) as well as significantly reduce the computational expense (versus existing LES models). Performance of the model form hence developed is evaluated on a cyclone flow case

ROUGH AIRFOIL SIMULATION FOR WIND TURBINE APPLICATIONS

As a result of insects or other environmental fouling, surface roughness on wind turbine blades can reduce power output significantly. Superhydrophobic surfaces, though possibly a passive, cost-saving, answer to the problem of ice accretion on wind turbine rotors in cold climates, may alter turbulence development in the blade boundary layer similar to environmental roughness. This work uses an equivalent sand grain extension to the Turbulent Potential model to computationally assess the aerodynamic effects of surface roughness on the s809 airfoil, including a representational superhydrophobic surface. Rough surface boundary layer theory, application of the equivalent sand grain method, roughness parameter correlation, and wind turbine aerodynamic computational approaches are discussed. Modifications to the Turbulent Potential model including turbulence Reynolds number dependence are addressed. An altered version of the Turbulent Potential model is proposed using an elliptic damping equation in the pressure strain term. Validation of Turbulent Potential model changes is demonstrated by comparison to multiple direct numerical simulations of Moser et al., the impinging jet of Cooper et. al, and the Ohio State University wind tunnel experiments of the s809 airfoil with both a smooth and rough leading edge

Computational Investigation of Impingement Cooling for Regeneratively Cooled Rocket Nozzles

Jet impingement cooling is an internal cooling configuration used in the thermal management of temperature sensitive systems. With rocket engine combustion temperatures rising as high as 3600 K, it is essential for a cooling method to be applied to ensure that the nozzle integrity can be maintained. Therefore, a novel heat transfer study is conducted to investigate if jet impingement cooling is feasible for a regenerative cooling rocket nozzle application. Regenerative cooling for liquid propellant rockets has been widely studied. However, to the best of the author’s knowledge, there is currently no literature describing this method in conjunction with impingement cooling techniques. In this study, a literary empirical model my Martin (1977) is compared to a computational fluid dynamics (CFD) model designed for single and round nozzle (SRN) jet impingement with conjugate heat transfer (CHT) analysis. The CHT analysis is utilized to investigate the resulting surface temperatures in the presence of convection and lateral conduction effects while investigating the Nusselt number (Nu) and temperature profiles of the impingement configuration. Heat transfer data is first extracted for air impinging onto a heated flat plate, whose results are used as the benchmarking model. The model is then altered to assess its application feasibility for a regeneratively cooled rocket nozzle throat similar to that of the Space Shuttle Main Engine (SSME) with LOX/LH2 propellants. A 1-D thermal analysis of supercritical LH2 coolant at 52.4 K and 24.8 MPa for the SSME with various nozzle wall materials, such as Stainless Steel 304 (SS 304), Inconel x-750, copper and ABS plastic, is conducted. The material selections were chosen to cover a range of thermal conductivities. It was found that none of the selected materials are feasible with impingement cooling alone due to the extremely high heat transfer rates within the throat. With material temperature limitations below 200 K. the materials cannot withstand the high stresses acting on the nozzle even with alterations to the benchmark model. Therefore, it is concluded that an additional cooling method is required to increase the hot-side thermal resistance. To ease the thermal stresses on the remaining metals, an average film cooling effectiveness (n) of 0.5 was assumed, to stimulate the benefit of film cooling. Having been incorporated into the hot gas side calculations, it decreased the adiabatic wall temperature from 3561 K to 1667.3 K, allowing the materials to be properly cooled on the inner side of the nozzle. Even with this assisted cooling method added, it is concluded that only SS 304 and Inconel x-750, with their low material resistance and high temperature capabilities, were capable of withstanding the rocket nozzle temperatures. CFD simulations for these two materials are studied for their feasibility of a SSME-like nozzle throat region. It was concluded that film cooling cannot be eliminated from the system with the SSME parameters studied. Additionally, with minimal differences between the 1-D analysis and CFD simulations, lateral conduction effects are minimal, which proves 1-D analysis is sufficient for future analysis

Thermal enhancement strategies for fluid jets impinging on a heated surface

This research investigation examines the thermal behaviour of single and arrays of fluid jets impinging at heated surfaces, and formulates enhancement schemes for the jet impingement heat transfer processes for high-intensity cooling applications. The proposed techniques are numerically modelled and analysed over a wide parametric range to identify flow characteristics leading to thermal enhancement and optimum performance. The first scheme applies to a single fluid jet and incorporates a protruding object at the impingement surface to improve heat transfer. In this, a conical protrusion of high thermal conductivity is attached to the heated surface directly beneath the jet. Three different aspect ratios of 0.5, 1 and 2 are investigated for the protrusion while the inclusion of a fillet at the base of the cone is also studied. Jet Reynolds numbers between 100 and 30,000 are modelled. The observed thermal performance is compared with a reference case having no surface attachment. With this arrangement, the heat transfer rate typically varies between 10 and 40 percent above the reference case although depending on certain parametric combinations, the heat transfer may increase above or decrease below the reference performance. The highest indicated increase in heat transfer is about 90 percent while 15 percent below is the lowest. Careful selection of cone surface profile creates potential for further thermal enhancement.The second scheme applies to a single fluid jet and incorporates a recess in the impingement surface to improve heat transfer. In this, a cylindrical cavity is introduced to the surface beneath the jet into which the fluid jet impinges. The effects of the cavity on heat transfer are examined for a number of different cavity diameters, cavity depths and jet discharge heights wherein a surface without a cavity is taken as the reference surface. Cavity diameters of 2, 3 and 4 times the jet diameter are investigated at cavity depths between zero and 4 times the jet diameter. Jet discharge heights range between 2 jet diameters above the reference surface to 2 jet diameters below the reference surface. The jet Reynolds number is varied between 100 and 30,000. With this enhancement technique, increases in heat transfer rates of up to 45 percent are observed when compared to the reference performance. The thermal performance of fluid jet arrays is examined by altering square or hexagonal array configurations to identify flow characteristics leading to optimal heat transfer rates. For this, the jet to jet spacing is varied between 1.5 and 7 times the jet diameter while the jet to surface height is varied between 2 and 6 times the jet diameter. Jet Reynolds numbers between 100 and 30,000 are investigated. For each configuration, a critical jet-to-jet spacing is identified below which the heat transfer is observed to reduce significantly. Correlations for the expected heat transfer for a square or hexagonal array are presented in terms of the jet to jet spacing, jet height and jet Reynolds number