J. Michael Owen

Uncertainties in transient heat transfer measurements with liquid crystal

Abstract Thermochromic liquid crystal (TLC) is used extensively as an experimental tool to determine heat transfer coefficients. In a transient experiment, if the time at which the TLC changes colour is known, then h , the heat transfer coefficient, can be found from the solution of the so-called semi-infinite-plate problem. If T aw , the adiabatic-wall temperature, is unknown, then two narrow-band TLCs can be used to determine both h and T aw . In this paper, an uncertainty analysis is used to calculate P h , the uncertainty in h , and P T aw , the uncertainty in T aw (when T aw is unknown), in terms of the random uncertainties in the measured temperatures. Computed values, obtained using a Monte Carlo method, are in good agreement with the uncertainties obtained from the analysis. It is also shown how the uncertainties P h and P T aw can be minimised by selecting the appropriate ranges of TLC. Conversely, a poor choice of TLC can result in large values of these uncertainties.

Transient heat transfer measurements using thermochromic liquid crystal. Part 1: An improved technique

Abstract It is common practice to employ thermochromic liquid crystal (TLC) to determine heat transfer coefficients, h , in transient experiments. The method relies on the solution of Fourier’s conduction equation, usually with the boundary condition of a step-change in air temperature. In practice a step-change can be difficult to achieve, and a more general solution to the one-dimensional conduction equation is presented here for a “slow transient,” where the rise in air temperature is represented by an exponential series. An experimental method, based on this technique, requires only a single measurement of surface temperature history, and this has the advantage that narrow-band TLC can be used. As an example, measurements of h are presented from an experiment modelling the internal flow of cooling air inside a gas turbine engine. The measurements are analysed using both the conventional step-change method and the exponential-series technique, and the results show that using the step-change method can give rise to significant errors in the calculated values of h . The new technique should be applicable to many other slow transient heat transfer measurements.

Predictions of effect of swirl on flow and heat transfer in a rotating cavity

Pre-swirl nozzles are used to deliver the cooling air to the rotating turbine blades in the cooling systems of gas turbine engines. This paper considers the case where the cooling air flows radially outward, between two corotating discs, to create a free vortex in the inviscid core between the boundary layers on the discs. A thermodynamic analysis is used to relate the temperature increase of the cooling air to the adiabatic work term (which reduces the air temperature) and to the heat transfer from the discs to the air (which increases the temperature). The Reynolds analogy has been used to determine an expression for the adiabatic-disc temperature and to draw conclusions about the moment coefficient and average Nusselt number. An important parameter is βp, the ratio of the tangential velocity of the pre-swirl air to the speed of the rotating disc, and the Reynolds analogy shows that the moment coefficient is zero when βp=βp,crit, a critical pre-swirl ratio, and that the average Nusselt number is a minimum when βp=βp,opt, an optimal pre-swirl ratio. Computations made using a steady-state axisymmetric elliptic-flow solver, incorporating a low-Reynolds-number k–ϵ turbulence model, are in good agreement with the pressure distribution, adiabatic-disc temperature and local Nusselt numbers predicted by the theoretical models. The computed values of βp,crit agree with the theoretical values, and the computations also confirm the occurrence of a minimum average Nusselt number. For βp βp,opt, whether the temperature decreases or increases depends on the relative magnitude of the adiabatic work term and the heat transfer from the discs.

Experimental Measurements of Ingestion Through Turbine Rim Seals—Part I: Externally Induced Ingress

Part I of this two-part paper presented experimental results for externally-induced (EI) ingress, where the ingestion of hot gas through the rim seal into the wheel-space of a gas turbine is controlled by the circumferential variation of pressure in the external annulus. In Part II, experimental results are presented for rotationally-induced (RI) ingress, where the ingestion is controlled by the pressure generated by the rotating fluid in the wheel-space. Although EI ingress is the common form of ingestion through turbine rim seals, RI ingress or combined ingress (where EI and RI ingress are both significant) is particularly important for double seals, where the pressure asymmetries are attenuated in the annular space between the inner and outer seals. In this paper, the sealing effectiveness was determined from concentration measurements, and the variation of effectiveness with sealing flow rate was compared with theoretical curves for RI ingress obtained from an orifice model. Using a nondimensional sealing parameter phio the data could be collapsed onto a single curve, and the theoretical variation of effectiveness with phio was in very good agreement with the data for a wide range of flow rates and rotational speeds. It was shown that the sealing flow required to prevent RI ingress was much less than that needed for EI ingress, and it was also shown that the effectiveness of a radial-clearance seal is significantly better than that for an axial-clearance seal for both EI and RI ingress.

Fluid Dynamics of a Pre-Swirl Rotor-Stator System

In a direct-transfer pre-swirl supply system, cooling air flows axially across the wheel-space from stationary pre-swirl nozzles to receiver holes located at a similar radius in the rotating turbine disc. This paper describes a combined computational and experimental study of the fluid dynamics of such a system. Measurements of total and static pressures have been made using a purpose-built rotor-stator rig, with 24 pre-swirl nozzles on the stator and 60 receiver holes in the rotor. The number of pre-swirl nozzles could be reduced, and it was possible to calculate C D , the discharge coefficient of the receiver holes. Information on the flowfield was also obtained from three-dimensional, incompressible steady turbulent flow computations. The measurements showed that there was a significant loss of total pressure between the outlet from the pre-swirl nozzles and the rotating core of fluid in the wheel-space. This loss increased as the pre-swirl flow-rate and inlet swirl ratio increased, and as the number of nozzles decreased. C D increased as the swirl ratio at the receiver hole radius approached unity; also C D decreased as the number of nozzles decreased. Computed pressures and tangential velocities were in mainly good agreement with the measurements. The computations help to explain the reasons for the significant losses in total pressure and for the relatively low values of C D in this pre-swirl system.

Transient heat transfer measurements using thermochromic liquid crystal. Part 2: Experimental uncertainties

Abstract In Part 1 of this two-part paper, an “exponential-series technique” was used to calculate heat transfer coefficient, h , for the so-called slow transient case where it is not possible to generate a step-change in the air temperature. Small uncertainties in the measured temperatures can, however, create large uncertainties in the calculated value of h , and the amplification parameter, Φ h , is defined as the ratio of the relative uncertainty in h to the relative uncertainties in the temperatures. Using an uncertainty analysis, theoretical expressions for Φ h are found for the slow transient case, and these expressions are in excellent agreement with values computed using a Monte Carlo method. The results provide guidance in the selection of design parameters for an experiment and for the calculation and minimisation of the uncertainty in h .

Prediction of Ingestion Through Turbine Rim Seals—Part I: Rotationally Induced Ingress

The mainstream flow past the stationary nozzle guide vanes and rotating turbine blades in a gas turbine creates an unsteady nonaxisymmetric variation in pressure in the annulus, radially outward of the rim seal. The ingress and egress occur through those parts of the seal clearance where the external pressure is higher and lower, respectively, than that in the wheel-space; this nonaxisymmetric type of ingestion is referred to here as externally induced (EI) ingress. Another cause of ingress is that the rotating air inside the wheel-space creates a radial gradient of pressure so that the pressure inside the wheel-space can be less than that outside; this creates rotationally induced (RI) ingress, which—unlike EI ingress—can occur, even if the flow in the annulus is axisymmetric. Although the EI ingress is usually dominant in a turbine, there are conditions under which both EI and RI ingress are significant, these cases are referred to as combined ingress. In Part I of this two-part paper, the so-called orifice equations are derived for compressible and incompressible swirling flows, and the incompressible equations are solved analytically for the RI ingress. The resulting algebraic expressions show how the nondimensional ingress and egress vary with Θ0, which is the ratio of the flow rate of sealing air to the flow rate necessary to prevent ingress. It is shown that e, the sealing effectiveness, depends principally on Θ0, and the predicted values of e are in mainly in good agreement with the available experimental data.

Prediction of Ingress Through Turbine Rim Seals—Part I: Externally Induced Ingress

Rotationally induced (RI) ingress is caused by the negative pressure (relative to the external air) inside the wheel-space of a gas turbine; this negative pressure, which is created by the rotating flow in the wheel-space, drives the ingestion of hot gas through the rim seals. Externally induced (EI) ingress is caused by the circumferential distribution of pressure created by the blades and vanes in the turbine annulus: Ingress occurs in those regions where the external pressure is higher than that in the wheel-space, and egress occurs where it is lower. Although EI ingress is the dominant mechanism for hot-gas ingestion in engines, there are some conditions in which RI ingress has an influence: This is referred to as combined ingress (CI). In Part I of this two-part paper, values of the sealing effectiveness (obtained using the incompressible orifice equations developed for EI ingress in an earlier paper) are compared with published experimental data and with the results obtained using 3D steady compressible computational fluid dynamics (CFD). Acceptable limits of the incompressible-flow assumption are quantified for the orifice model; For the CFD, even though the Mach number in the annulus reaches approximately 0.65, it is shown that the incompressible orifice equations are still valid. The results confirm that EI ingress is caused predominantly by the magnitude of the peak-to-trough circumferential difference of pressure in the annulus; the shape of the pressure distribution is of secondary importance for the prediction of ingress. A simple equation, derived from the orifice model, provides a very good correlation of the computed values of effectiveness. Using this correlation, it is possible to estimate the minimum sealing flow rate to prevent ingress without the need to know anything about the pressure distribution in the annulus; this makes the orifice model a powerful tool for rim-seal design.

Effect of Ingestion on Temperature of Turbine Disks

This paper describes experimental results from a research facility which experimentally models hot-gas ingress into the wheel-space of an axial turbine stage with an axial-clearance rim seal. Thermochromic liquid crystal (TLC) was used to determine the effect of ingestion on heat transfer to the rotating disk; as far as the authors are aware, this is the first time that the measured effects of ingestion on adiabatic temperature have been published. An adiabatic effectiveness for the rotor was defined, and this definition was used to determine when the effect of ingress was first experienced by the rotor. Concentration measurements on the stator were used to determine the sealing effectiveness of the rim seal, and transient heat transfer tests with heated sealing air were used to determine the adiabatic effectiveness of the rotor. The thermal buffer ratio, which is defined as the ratio of the sealing flow rate when ingress first occurs to that when it is first experienced by the rotor, was shown to depend on the turbulent flow parameter. The local Nusselt numbers, Nu, which were measured on the rotor, were significantly smaller than those for a free disk; they decreased as the sealing flow rate decreased and as the ingress correspondingly increased. The values of Nu and adiabatic effectiveness obtained in these experiments provide data for the validation of CFD codes but caution is needed if they (particularly the values of Nu) are to be extrapolated to engine conditions.

Influence of Fluid-Dynamics on Heat Transfer in a Pre-Swirl Rotating-Disc System

Modern gas turbines are cooled using air diverted from the compressor. In a “direct-transfer” pre-swirl system, this cooling air flows axially across the wheel-space from stationary pre-swirl nozzles to receiver holes located in the rotating turbine disc. The distribution of the local Nusselt number, Nu, on the rotating disc is governed by three non-dimensional fluid-dynamic parameters: pre-swirl ratio, βp , rotational Reynolds number, Reφ, and turbulent flow parameter, λT . This paper describes heat transfer measurements obtained from a scaled model of a gas turbine rotor-stator cavity, where the flow structure is representative of that found in the engine. The experiments reveal that Nu on the rotating disc is axisymmetric except in the region of the receiver holes, where significant two-dimensional variations have been measured. At the higher coolant flow rates studied, there is a peak in heat transfer at the radius of the pre-swirl nozzles, associated with the impinging jets from the pre-swirl nozzles. At lower coolant flow rates, the heat transfer is dominated by viscous effects. The Nusselt number is observed to increase as either Reφ or λT increases.Copyright