Propulsion and Power

D1 Gas Properties and Standard Atmosphere We show how the gas properties gas constant, specific heat, enthalpy and entropy function for a half-ideal gas, are derived from basic thermodynamics. GasTurb reads gas properties from tables calculated with the NASA program CEA. Environmental conditions are defined by the International Standard Atmosphere (ISA), which derives ambient pressure and temperature from the altitude.

D2 Spreadsheet Calculations We first summarize the equations used for describing component performance, including non-dimensional parameters, such as corrected mass flow, Mach number total/static ratios. The isentropic and polytropic efficiency definitions for compressors and turbines, are compared. We then follow with a detailed hand-calculation through the cycle of a turbojet engine in-flight. We cover each component from the inlet to the nozzle and evaluate the differences caused by using the mean specific heat rather than the entropy function (as used in GasTurb).

D3 Non-Dimensional Performance We illustrate that if the velocity triangles for a compressor, run to two different conditions, have the same angles and Mach numbers, then the non-dimensional parameters (speed, pressure ratio, temperature ratio, etc.) will also be the same. Without resorting to higher mathematics, this method is extended to cover whole engine parameters such as fuel flow, thrust and power. We show how to correct the non-dimensional parameters to standard conditions using exponents for δ (P/PISA) and Θ (T/TISA) and the use of the cycle model to derive the exponent values for each parameter including humidity and “real engine” effects.

D4 Reynolds Number Corrections We explain why the ratio of inertia to friction forces, as characterized by the Reynolds number, influence gas turbine performance. We describe how the use of the Reynolds Number Index can simplify performance calculations. How to correlate Reynolds number corrections to real data is illustrated through use of a pipe flow analogy and Moody charts.

D5 Turbine Efficiency Starting from a single stage un-cooled turbine, we extend the definition of turbine efficiency to cover both cooled and multi-stage turbines. The consideration of secondary effects such as pumping work, windage and sealing flows is discussed and the concepts of chargeable and non-chargeable flows are introduced. It is shown that there are many options and that performance models typically use a control volume to derive an equivalent single stage definition. The pros and cons of various approaches are discussed, and the calculated values are compared to “thermodynamic efficiency”, the ratio of actual power delivered to the cumulative power potential of each individual flow. The chapter concludes with a numerical evaluation of the efficiency loss due to cooling in a real engine.

D6 Secondary Air System In this Chapter we show how the very complex secondary air system in a modern gas turbine may be greatly simplified and integrated into a cycle model without compromising the quality of overall performance results. Calculation examples from single and multi-stage turbines are given which describe in detail how to account for interstage bleed flows and their re-introduction into the main gas path.

D7 Mathematics In this chapter we explain why off-design performance calculations require an iterative approach to maintain continuity in mass and energy flows in component matching. We start with a simple example of a turboshaft engine with a free power turbine and show how the number of iteration variables increases as the engine architecture becomes more complex. We demonstrate how the use of the Newton-Raphson algorithm may be extended to any number of variables as well as dynamic engine simulations. We conclude the chapter with some examples of problems that may occur when setting up iteration schemes and give practical advice on how to resolve them.

D8 Optimization In chapter we show how to use optimization to evaluate design studies with many variables. The two numerical optimization methods available in GasTurb (using gradient or random search algorithms) are described, with clear illustrations of the difference between local and global optima. Advice is given on the use of constraints and on the definition of the figure of merit when a study has multiple objectives.

D9 Monte Carlo Simulations The Monte Carlo method is a powerful and simple tool for generating statistical information. Typical examples of its gas turbine applications are in the uncertainty analysis of measurements, the probability of achieving an engine design target and production tolerance estimates. Engine tests evaluate much more than overall characteristics in terms of thrust and specific fuel consumption; the main objective of performance testing is the efficiency of the engine components. Both random and systematic measurement errors affect the accuracy of the analysis result. When a new engine is designed, there is always uncertainty about the component performances achievable. That transfers to an uncertainty in the overall engine performance. For example, even though the design target in specific fuel consumption is met ostensibly, the cycle or guaranteed value may need to be modified to improve the level of confidence. If we simulate a batch of engines with randomly distributed properties, as the result of component manufacturing tolerances, we can predict the effects of various combinations of these on thrust or shaft power, efficiency and specific fuel consumption. The influence of variations in internal air systems can also be accounted for. GasTurb makes Monte Carlo simulations easy, both for cycle design and off-design applications.