The calculation of the performance of gas turbines, turbochargers, compressors and turbines requires the thermodynamic properties of the gases. Tables of properties exist which are effectively exact, but using these tables is tedious and far from practical in computer-based calculations. Representing tabulated results with polynomial approximations is inconvenient and prone to error in implementation. For teaching and simple calculations simple approximations, such as γ = 1.4 for unburned air and γ = 1.3 for combustion products, are sometimes used, but this is far from wholly satisfactory. This paper describes and discusses a simple empirical approach which will give adequate accuracy for many purposes but is simple enough to be used as part of an educational course.

This paper looks at some familiar results, concepts and ideas in a different way, drawing out some common unifying threads. The topics addressed are one, two and three-dimensions; axisymmetry and its breakdown; gaps and leakage paths; and CFD and the limitation of perfection. Certain overlapping issues come up in each of the topic areas.

In the long term the price of fuel will rise and it is now urgent to reduce carbon dioxide emissions to avoid catastrophic climate change. This lecture looks at power plant for electricity generation and aircraft propulsion, considering likely limits and possibilities for improvement. There arc lessons from land-based gas turbines which can be applied to aircraft, notably the small increases in efficiency from further increase in pressure ratio and turbine inlet temperature. Land-based gas turbines also point to the benefit of combining the properties of water with those of air to raise efficiency. Whereas the incentive to raise efficiency and reduce CO(2) will force an increase in complexity of land-based power plant, the opportunities for this with aircraft are more limited. One of the opportunities with aircraft propulsion is to consider the whole aircraft operation and specification. Currently the specification for new aircraft of take-off and climb thrust are not fully consistent with designing the engine for minimum fuel consumption and this will be addressed in some depth in the lecture Preparing for the future entails alerting engineers to important possibilities and limitations associated with gas turbines which will mitigate climate change due to carbon dioxide emissions.

An experimental and computational study of the ramped bleed slot in a compressor cascade is presented. The geometry is a circumferential slot downstream of the stator blade trailing edge, with endwall ramps inside the blade passage, and the paper builds on work previously reported for different bleed off-take geometries [1, 2]. The strong interaction between any bleed slot and the primary flow through the cascade can be strong, thereby causing the levels of loss and blockage in the primary flow leaving the blade passage to be increased at some bleed flow rates. Radial flow into the bleed slot is highly non-uniform because the blade-to-blade pressure field causes flow to enter the bleed slot preferentially where the static pressure is high, and to spill out into the primary flow where the static pressure is low. The mechanism for the ramped bleed slot is different from that described in the earlier papers for other geometries. For the ramped bleed slot a static pressure field, with large variations of static pressure in the circumferential direction, is set up in the slot because the endwall flow entering the slot has higher stagnation pressure downstream of the pressure surface than downstream of the suction surface of the upstream blades. The flow entering the slot with high stagnation pressure is brought to rest in a stagnation point on the downstream surface of the slot, and the consequent variation in static pressure on the rear surface sets tangential and radial components of velocity which are a large fraction of the free-stream velocity. As well as demonstrating the mechanism for the flow behaviour, the paper presents results of experiments and calculations to demonstrate the behaviour and gives guidance for the design of bleed slots by stressing the fundamental features of the flow.

Bleed off-take air pressure and the interaction of the off-take with the primary flow through the blade passage is determined by: (1) the location of the bleed off-take at the endwall relative to the blade passage; (2) the bleed flow rate; and (3) the off-take geometry. In the companion paper (Leishman et al., 2007, ASME J. Turbomach., 129, pp. 645-658) the effect of bleed rate and endwall location was investigated using a circular hole bleed off-take configuration; the circular hole was tested at three endwall locations and for bleed flow rates between 0% and 9% of the primary (core) flow through the blade passage. The effects of bleed off-take geometry are presented in this paper by comparing the aerodynamic behavior of a number of generic bleed off-take configurations. Using results from low-speed cascade experiments and three-dimensional numerical calculations, the off-take configurations are compared with respect to the requirement to maximize bleed off-take air pressure and minimize loss generated within the blade passage. The off-take geometry, and especially the introduction of contoured inlet ramp surfaces to guide flow into the off-take for high bleed pressure, has a strong effect on its aerodynamic behavior because it determines the extent to which flow within the off-take is coupled to the primary flow through the blade passage. In this paper the off-take configurations that give the highest bleed pressure generally cause the highest levels of loss in the blade passage.

In a jet engine bleed off-takes on the hub and casing endwalls, part way through the compressor supply high-pressure air for cooling, sealing, de-icing, and aircraft cabin air applications; bleed also assists compressor operation at part-speed conditions. Two separate issues are of interest: the bleed off-take air pressure and the interaction of the bleed off-take with the primary flow through the blade passage. In this paper the aerodynamic behavior is presented for a circular-hole bleed off-take at three endwall locations within a stationary cascade blade passage: at midpassage; near the blade pressure surface; and near the blade suction surface. Results from low-speed cascade experiments are complemented by three-dimensional numerical calculations using an unstructured mesh-based solver, in which the blade passage and bleed off-take geometry are fully modeled. The bleed off-take location and the magnitude of bleed rate influence the offtake air pressure and the interaction with the primary passage flow. For optimum design at zero and low bleed rates, off-takes near the blade pressure surface give the highest bleed air pressures and minimum loss in the blade passage. For minimum blade passage loss at higher bleed rates, however it is necessary to take bleed near the blade suction surface. The paper discusses the causes for this pattern of behavior.

Averaging non-uniform flow is important for the analysis of measurements in turbomachinery and gas turbines; more recently an important need for averaging arises with results of CFD. In this paper we show that there is a method for averaging which is "correct", in the sense of preserving the essential features of the non-uniform flow, but that the type of averaging which is appropriate depends on the application considered. The crucial feature is the decision to retain or conserve those quantities which are most important in the case considered. Examples are given to demonstrate the appropriate methods to average nonuniform flows in the accounting for turbomachinery blade row performance, production of thrust in a nozzle, and mass flow capacity in a choked turbine. It is also shown that the numerical differences for different types of averaging are, in many cases, remarkably small.

The creation of thrust is the obvious reason for having engines and this chapter looks at how it occurs. This is a simple consequence of Newton's laws of motion applied to a steady flow. It requires the momentum to be higher for the jet leaving the engine than the flow entering it, and this inevitably results in higher kinetic energy for the jet. The higher energy of the jet requires an energy input, which comes from burning the fuel. This gives rise to the definition of propulsive efficiency (considering only the mechanical aspects) and overall efficiency (considering the energy available from the combustion process).