Inverse BEM Method to Identify Surface Temperatures and Heat Transfer Coefficient Distributions at Inaccessible Surfaces

The purpose of the inverse problem considered in this study is to resolve heat transfer coefficient distributions by solving a steady-state inverse problem. Temperature measurements at interior locations supply the additional information that renders the inverse problem solvable. A regularized quadratic functional is defined to measure the deviation of computed temperatures from the values under current estimates of the heat transfer coefficient distribution at the surface exposed to convective heat transfer. The inverse problem is solved by minimizing this functional using a parallelized genetic algorithm (PGA) as the minimization algorithm and a two-dimensional multi-region boundary element method (BEM) heat conduction code as the field variable solver. Results are presented for a regular rectangular geometry and an irregular geometry representative of a blade trailing edge and demonstrate the success of the approach in retrieving accurate heat transfer coefficient distributions.

Effect of Tip and Pressure Side Coolant Injection on Heat Transfer Distributions for a Plane and Recessed Tip

The present study investigates the effects of coolant injection on adiabatic film effectiveness and heat transfer coefficients from a plane and recessed tip of a HPT first stage rotor blade. Three cases where coolant is injected from (a) five orthogonal holes located along the camber line, (b) seven angled holes located near the blade tip along the pressure side and (c) combination cases when coolant is injected from both tip and pressure side holes were studied. The pressure ratio (inlet total pressure to exit static pressure for the cascade) across the blade row was 1.2, and the experiments were run in a blow-down test rig with a four-blade linear cascade. The Reynolds number based on cascade exit velocity and axial chord length was 8.61×105 and the inlet and exit Mach number were 0.16 and 0.55, respectively. A transient infrared (IR) technique was used to measure adiabatic film effectiveness and heat transfer coefficient simultaneously for three blowing ratios of 1.0, 2.0, and 3.0. For all the cases, gap-to-blade span ratio of 1% was used. The depth-to-blade span ratio of 0.0416 was used for the recessed tip. Pressure measurements on the shroud were also taken to characterize the leakage flow and understand the heat transfer distributions. For tip injection, when blowing ratio increases from 1.0 to 2.0, film effectiveness increases for both plane and recessed tip. At blowing ratio 3.0, lift off is observed for both cases. In case of pressure side coolant injection and for plane tip, lift off is observed at blowing ratio 2.0 and reattachments of jets are observed at blowing ratio 3.0. But, almost no effectiveness is observed for squealer tip at all blowing ratios with pressure side injection. For combination case, very high effectiveness is observed at blowing ratio 3.0 for both plane and recessed blade tip. It appears that for this high blowing ratio, coolant jets from the tip hit the shroud first and then reattach back on to the blade tip. For tip injection, as blowing ratio increases heat transfer coefficient decreases for both plane and recessed tip. In case of pressure side coolant injection and for plane tip, film injection reduced heat transfer coefficient along the pressure side. Minimal effect is observed for recessed tip at all blowing ratios. For combination case, very high heat transfer coefficient is observed at blowing ratio 3.0 for both plane and recessed blade tip. It appears that for this high blowing ratio, coolant jets from the tip hit the shroud first and then reattach back on to the blade tip.

Turbine Airfoil Heat Transfer Predictions Using CFD

Conventional heat transfer design methods for turbine airfoils use 2-D boundary layer codes (BLC) combined with empiricism. While such methods may be applicable in the mid span of an airfoil, they would not be very accurate near the end-walls and airfoil tip where the flow is very three-dimensional (3-D) and complex. In order to obtain accurate heat transfer predictions along the entire span of a turbine airfoil, 3-D computational fluid dynamics (CFD) must be used. This paper describes the development of a CFD based design system to make heat transfer predictions. A 3-D, compressible, Reynolds-averaged Navier-Stokes CFD solver with k-ω turbulence modeling was used. A wall integration approach was used for boundary layer prediction. First, the numerical approach was validated against a series of fundamental airfoil cases with available data. The comparisons were very favorable. Subsequently, it was applied to a real engine airfoil at typical design conditions. A discussion of the features of the airfoil heat transfer distribution is included.

Turbulent Transport in Pin Fin Arrays: Experimental Data and Predictions

The objective of this research has been to experimentally investigate the fluid dynamics of pin fin arrays in order to clarify the physics of heat transfer enhancement and uncover problems in conventional turbulence models. The fluid dynamics of a staggered pin fin array have been studied using hot wire anemometry with both single and x-wire probes at array Reynolds numbers of 3000; 10,000; and 30,000. Velocity distributions off the endwall and pin surface have been acquired and analyzed to investigate turbulent transport in pin fin arrays. Well resolved 3-D calculations have been performed using a commercial code with conventional two-equation turbulence models. Predictive comparisons have been made with fluid dynamic data. In early rows where turbulence is low, the strength of shedding increases dramatically with increasing in Reynolds numbers. The laminar velocity profiles off the surface of pins show evidence of unsteady separation in early rows. In row three and beyond laminar boundary layers off pins are quite similar. Velocity profiles off endwalls are strongly affected by the proximity of pins and turbulent transport. At the low Reynolds numbers, the turbulent transport and acceleration keep boundary layers thin. Endwall boundary layers at higher Reynolds numbers exhibit very high levels of skin friction enhancement. Well resolved 3-D steady calculations were made with several two-equation turbulence models and compared with experimental fluid mechanic and heat transfer data. The quality of the predictive comparison was substantially affected by the turbulence model and near wall methodology.

Numerical Simulation of Gas Flow and Heat Transfer in Cross-Wavy Primary Surface Channel for Microtubine Recuperators

Three-dimensional numerical simulation was conducted to investigate the flow field and heat transfer performance of the Cross-Wavy Primary Surface (CWPS) recuperators for microturbines. Using high-effective compact recuperators to achieve high thermal efficiency is one of the key techniques in the development of microturbine in recent years. Recuperators need to have minimum volume and weight, high reliability and durability. Most important of all, they need to have high thermal-effectiveness and low pressure-losses so that the gas turbine system can achieve high thermal performances. These requirements have attracted some research efforts in designing and implementing low-cost and compact recuperators for gas turbine engines recently. One of the promising techniques to achieve this goal is the so-called primary surface channels with small hydraulic dimensions. In this paper, we conducted a three-dimensional numerical study of flow and heat transfer for the Cross-Wavy Primary Surface (CWPS) channels with two different geometries. In the CWPS configurations the secondary flow is created by means of curved and interrupted surfaces, which may disturb the thermal boundary layers and thus improve the thermal performances of the channels. To facilitate comparison, we chose the identical hydraulic diameters for the above four CWPS channels. Since our experiments on real recuperators showed that the Reynolds number ranges from 150 to 500 under the operating conditions, we implemented all the simulations under laminar flow situations. By analyzing the correlations of Nusselt numbers and friction factors vs. Reynolds numbers of the four CWPS channels, we found that the CWPS channels have superior and comprehensive thermal performance with high compactness, i.e., high heat transfer area to volume ratio, indicating excellent commercialized application in the compact recuperators.

Studies of Wake-Induced Bypass Transition of a Flat-Plate Boundary Layer: Comparisons Between Two Transition Modes Induced by Small Sphere Wake and Thin Wire Wake

This study aims at deepening the understanding of wake-induced bypass transition process of a flat-plate boundary layer using two types of wake generating objects, which are small spheres and thin wires. Main focus is on emergence of isolated turbulent spots from the influence of the wake passage over the boundary layer. Precursors of the wake-induced turbulent spot, which have not been observed in an explicit manner in any other previous studies, are also of concern in this study. It is expected that wakes from the wires are so weak that an isolated turbulent spot may be induced by the wire wake, while the position of the spot emergence varies randomly along the wire. A multi-channel sensor with 7 hot-wire probes acquires the velocity data of the flow over the flat plate subjected to the wake passage. These velocity data reveal the spot shape and spot generation rate. In addition, the existence of Klebanoff mode in this wake-affected boundary layer is examined.

Towards Defining Objective Criteria for Assessing the Adequacy of Assumed Axisymmetry and Steadiness of Flows in Rotating Cavities

The need to make a priori decisions about the level of approximation that can be accepted — and subsequently justified — in flows of industrial complexity is a perennial problem for CFD analysts. This problem is particularly acute in the simulation of rotating cavity flows, where the stiffness of the equation set results in protracted convergence times, making any simplification extremely attractive. For example, it is common practice, in applications where the geometry and boundary conditions are axisymmetric, to assume that the flow solution will also be axisymmetric. It is known, however, that inappropriate imposition of this assumption can lead to significant errors. Similarly, where the geometry or boundary conditions exhibit cyclic symmetry, it is quite common for analysts to constrain the solutions to satisfy this symmetry through boundary condition definition. Examples of inappropriate use of these approximating assumptions are frequently encountered in rotating machinery applications — such as the ventilation of rotating cavities within aero-engines. Objective criteria are required to provide guidance regarding the level of approximation that is appropriate in such applications. In the present work, a study has been carried out into: • The extent to which local 3-D features influence solutions in a generally 2-D problem. Criteria are proposed to aid in decisions about when a 2-D axisymmetric model is likely to deliver an acceptable solution. • The influence of flow features which may have a cyclic symmetry that differs from the bounding geometry or imposed boundary conditions (or indeed have no cyclic symmetry). • The influence of unsteady flow features and the extent to which their effects can be represented by mixing plane or multiple reference frame approximations.

Film Flow Around Bearing Chamber Support Structures

Cooling of aero-engine bearing chamber walls is achieved by the through-flow of thin oil films, which are typically only a few millimeters thick. Support structures and other features disrupt both air and oil motion within such chambers, leading to localized variations in the oil film thickness, causing variation in local heat transfer coefficients. An experimental study has been undertaken to establish the range of conditions under which dry-out occurs upstream and downstream of an obstruction. In addition film thickness measurements around the obstruction have been taken at a set air flow rate for four different liquid flow rates. A regime map of liquid vs. air Reynolds numbers has been created showing where stable and fluctuating type I and II dry-outs occur.

A Numerical Study of 3D Turbulent Cooling Jet Interaction Over a Range of Blowing Ratios, Turbulence Intensity and Turbulent Length Scale

Three-dimensional simulations of an unloaded cooled vane have been conducted for blowing ratios of 0.67, 1.02, and 1.4. For each blowing ratio, three free stream turbulence intensities of 1%, 10%, and 20% have been simulated. A brief investigation into the effects of length scale has also been performed at a turbulence intensity of 10% via a 40% reduction in length scale of. Three rows of cooling holes were simulated for a total of 31 cooling holes. The flow through each hole and the feed plenum were simulated. The first two rows of holes were inclined downward at 60° to the horizon, while the third row exited axially. The cases were run at Mach number 0.23 and Reynolds number based on the blade leading edge diameter, or thickness, of 4.1×104 with a main flow total temperature of 705.6K° and a cooling flow total temperature of 360K°, providing a cold to hot gas density ratio of approximately 2. Surface contours of film cooling effectiveness and static temperature, plots of η vs. s, exit plane static temperature contours, and exit plane plots of mass averaged total temperature are presented along with detailed streamline maps to show the propagation of cooling flows through the passage. The results indicate that cooling effectiveness was greatest for the 1.02 blowing ratio case. Higher blowing ratios resulted in streaks of uncooled blade surface between cooling holes in the showerhead region caused by cooling jet coupling and interactions, and the misplacement of the holes for this condition. These cooling patterns resulted in a cell-like structure of cooling flows in the downstream wake for the lowest turbulence intensity, although this was not observed with higher turbulence. Lastly, cooling flows impacted the lower wall of the passage for all cases. This occurred when cooling flows were either entrained by the corner separation for the two lower blowing ratio cases, or impacted the lower surface before the separation, as observed for high blowing and low turbulence. In the latter case this resulted in suppression of the corner separation in the trailing edge region of the blade.

Analysis of Airfoil Trailing Edge Heat Transfer and Its Significance in Thermal-Mechanical Design and Durability

The trailing edge section of modern high-pressure turbine airfoils is an area that requires a high degree of attention from turbine performance and durability standpoints. Aerodynamic loss near the trailing edge includes expansion waves, normal shocks and wake shedding. Thermal issues associated with trailing edge are also very complex and challenging. To maintain effective cooling ensuring metal temperature below design limit is particularly difficult, as it needs to be implemented in a relatively small area of the airfoil. To date little effort has been devoted to advancing the fundamental understanding of the thermal characteristics in airfoil trailing edge regions. Described in this paper are the procedures leading to closed-form, analytical solutions for temperature profile for four most representative trailing edge configurations. The configurations studied are: (1) solid wedge shape without discharge, (2) wedge with slot discharge, (3) wedge with discrete-hole discharge, and (4) wedge with pressure-side cutback slot discharge. Comparison among these four cases is made primarily in the context of airfoil metal temperature and resulting cooling effectiveness. Further discussed in the paper are the overall and detail design parameters for preferred trailing edge cooling configurations as they affect turbine airfoil performance and durability.