We point out a general framework that encompasses most cases in which quantum effects enable an increase in precision when estimating a parameter (quantum metrology) The typical quantum precision-enhancement is of the order of the square root of the number of times the system is sampled We prove that this is optimal and we point out the different strategies (classical and quantum) that permit to attain this bound

Quantum metrology

The primary focus of this paper is convective heat transfer in axial flow turbines. Research activity involving heat transfer generally separates into two related areas: predictions and measurements. The problems associated with predicting heat transfer are coupled with turbine aerodynamics because proper prediction of vane and blade surface-pressure distribution is essential for predicting the corresponding heat transfer distribution. The experimental community has advanced to the point where time-averaged and time-resolved three-dimensional heat transfer data for the vanes and blades are obtained routinely by those operating full-stage rotating turbines. However, there are relatively few CFD codes capable of generating three-dimensional predictions of the heat transfer distribution, and where these codes have been applied the results suggest that additional work is required. This paper outlines the progression of work done by the heat transfer community over the last several decades as both the measurements and the predictions have improved to current levels. To frame the problem properly, the paper reviews the influence of turbine aerodynamics on heat transfer predictions. This includes a discussion of time-resolved surface-pressure measurements with predictions and the data involved in forcing function measurements. The ability of existing two-dimensional and three-dimensional Navier-Stokes codes to predict the proper trends of the time-averaged and unsteady pressure field for full-stage rotating turbines is demonstrated. Most of the codes do a reasonably good job of predicting the surface-pressure data at vane and blade midspan, but not as well near the hub or the tip region for the blade. In addition, the ability of the codes to predict surface-pressure distribution is significantly better than the corresponding heat transfer distributions. Heat transfer codes are validated against measurements of one type or another. Sometimes the measurements are performed using full rotating rigs, and other times a much simpler geometry is used. In either case, it is important to review the measurement techniques currently used. Heat transfer predictions for engine turbines are very difficult because the boundary conditions are not well known. The conditions at the exit of the combustor are generally not well known and a section of this paper discusses that problem. The majority of the discussion is devoted to external heat transfer with and without cooling, turbulence effects, and internal cooling. As the design community increases the thrust-to-weight ratio and the turbine inlet temperature, there remain many turbine-related heat transfer issues. Included are film cooling modeling, definition of combustor exit conditions, understanding of blade tip distress, definition of hot streak migration, component fatigue, loss mechanisms in the low turbine, and many others. Several suggestions are given herein for research and development areas for which there is potentially high payoff to the industry with relatively small risk.

Convective Heat Transfer and Aerodynamics in Axial Flow Turbines

A methodology for predicting the three-dimensional unsteady aerodynamics of the interaction between two turbomachinery blade rows that are in relative angular motion with one another is described. In this case, the kinematics of the blades introduce a chorochronic (space‐time) periodicity. This periodicity is analyzed in detail, and a mathematically straightforward methodology, based on Fourier series in µ (azimuth) and t (time), is presented for treating the interface between the two rows. These results are implemented in a computational method solving the three-dimensional Favre ‐Reynolds-averaged Navier ‐Stokes equations, with a near-wall wall-normalfree Reynolds-stress model. Only one blade passage per blade row is discretized. At the pitchwise boundaries, phase-lagged periodicity is applied using Fourier series in time. Both the pitchwise boundaries time harmonics and the interface chorochronic tµ harmonics are updated using a low-storage moving-averages technique. Computational results are presented and compared with measurements for a 1 1 -stage turbine, where the two stators have the same number of blades enabling the use of chorochronic periodicity. Sample results are also presented for a transonic inlet guide vane/rotor interaction, illustrating the ability of the interface treatment to handle shock waves.

Analysis and Application of Chorochronic Periodicity in Turbomachinery Rotor/Stator Interaction Computations

A new, computationally-efficient method is presented for processing transient thin-film heat transfer gauge signals. These gauges are widely used in gas turbine heat transfer research, where, historically, the desired experimental heat transfer flux signals, q, are derived from transient measured surface-temperature signals, T, using numerical approximations to the solutions of the linear differential equations relating the two. The new method uses known pairs of exact solutions, such as the T response due to a step in q, to derive a sampled approximation of the impulse response of the gauge system. This impulse response is then used as a finite impulse response digital filter to process the sampled T signal to derive the required sampled q signal. This is computationally efficient because the impulse response need only be derived once for each gauge for a given sample rate, but can be re-used repeatedly, using optimised Matlab filter routines and is highly accurate. The impulse response method can be used for most types of heat flux gauge. In fact, the method is universal for any linear measurement systems which can be described by linear differential equations where theoretical solution pairs exist between input and output. Examples using the new method to process turbomachinery heat flux signals are given.Copyright © 2006 by ASME

Impulse Response Processing of Transient Heat Transfer Gauge Signals

DNS of separating, low Reynolds number flow in a turbine cascade with incoming wakes

The paper focuses on the unsteady pressure field measured around the rotor mid-span profile of the VKI Brite transonic turbine stage. The understanding of the complex unsteady flow field is supported by a quasi-3D unsteady Navier-Stokes computation using a k-? turbulence model and a modified version of the Abu-Ghannam and Shaw correlation for the onset of transition.The agreement between computational and experimental results is satisfactory. They both reveal the dominance of the vane-shock in the interaction. For this reason, it is difficult to identify the influence of vane-wake ingestion in the rotor passage from the experimental data. However, the computations allow to draw some useful conclusions in this respect.The effect of the variation of the rotational speed, the stator-rotor spacing and the stator trailing edge coolant flow ejection is investigated and the unsteady blade force pattern is analyzed.Copyright © 2000 by ASME

Investigation of the Unsteady Rotor Aerodynamics in a Transonic Turbine Stage

The growing interest for unsteady flows in turbomachines over the last two decades has led to an intensive development of fast response measurement techniques, capable of resolving with high frequency phenomena related to inlet distortion, rotating stall and blade row interference effects with blade passing frequencies ranging from 3 to 30 kHz. This development was favoured by major advances in sensor technology and data acquisition systems. The paper reviews the progress in fast response measurement techniques for high speed turbomachinery and application with emphasis on fast response pressure and temperature probes and blade surface sensors including pressure, heat transfer and shear stress determination.

Measurement techniques for unsteady flows in turbomachines

In high-pressure turbines, a small amount of cold flow is ejected at the hub from the cavity that exists between the stator and the rotor disk. This prevents the ingestion of hot gases into the wheel-space cavity, thus avoiding possible damage. This paper analyses the interaction between the hub-endwall cavity flow and the mainstream in a high-pressure transonic turbine stage. Several cooling flow ratios are investigated under engine representative conditions. Both time-averaged and time-resolved data are presented. The experimental data is successfully compared with the results of a 3D steady Navier-Stokes computation. Despite the small amount of gas ejected, the hub-endwall cavity flow has a significant influence on the mainstream flow. The Navier-Stokes predictions show how the ejected cold flow is entrained by the rotor hub vortex. The time-resolved static pressure field around the rotor is greatly affected when traversing the non-uniform vane exit flow field. When the cavity flow rate is increased, the unsteady forces on the rotor airfoil are reduced. This is linked to the decrease of vane exit Mach number caused by the blockage of the ejected flow.Copyright © 2004 by ASME

Effect of the Hub Endwall Cavity Flow on the Flow-Field of a Transonic High-Pressure Turbine

A transonic turbine stage is computed by means of an unsteady Navier-Stokes solver. A two-equation turbulence model is coupled to a transition model based on integral parameters and an extra transport equation. The transonic stage is modeled in two dimensions with a variable span height for the rotor row. The analysis of the transonic turbine stage with stator trailing edge coolant ejection is carried out to compute the unsteady pressure and heat transfer distribution on the rotor blade under variable operating conditions. The stator coolant ejection allows the total pressure losses to be reduced, although no significant effects on the rotor heat transfer are found both in the computer simulation and the measurements. The results compare favorable with experiments in terms of both pressure distribution and heat transfer around the rotor blade.

Unsteady heat transfer in stator-rotor interaction by two-equation turbulence model

A trailing edge cooled low aspect ratio transonic turbine guide vane is investigated in the VKI Compression Tube Cascade Facility at an outlet Mach number {bar M}{sub 2,is} = 1.05 and a coolant flow rate {dot m}c/{dot m}g = 3 percent. The outlet flow field is surveyed by combined total-directional pressure probes and temperature probes. Special emphasis is put on the development of low blockage probes. Additional information is provided by oil flow visualizations and numerical flow visualizations with a three-dimensional Navier-Stokes code. The test results describe the strong differences in the axial evolution of the hub and tip endwall and secondary flows and demonstrate the self-similarity of the midspan wake profiles. According to the total pressure and temperature profiles, the wake mixing appears to be very fast in the near-wake but very slow in the far-wake region. The total pressure wake profile appears to be little affected by the coolant flow ejection.

R. Dénos

Papers

Investigation of the Unsteady Rotor Aerodynamics in a Transonic Turbine Stage

Measurement techniques for unsteady flows in turbomachines

Effect of the Hub Endwall Cavity Flow on the Flow-Field of a Transonic High-Pressure Turbine

Unsteady heat transfer in stator-rotor interaction by two-equation turbulence model

Investigation of the flow field downstream of a turbine trailing edge cooled nozzle guide vane