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## Über dieses Buch

The volume provides an exhaustive catalog of common standard day corrections for gas turbine gas path parameters, explores their history, and, most importantly, provides a mathematical framework for the derivation of these important normalization factors. Although use of these corrections is common practice within industry, government, and academia, their genesis, and, in particular, how they can be derived from simple principles, is not general knowledge among many of those who use them on a regular basis. This book elucidates calculation of these important coefficients. Standing as a one-stop source on derivations and a methodology for additional parameter correction refinements, Gas Turbine Parameter Corrections, is ideal as a desk reference for practitioners and researchers, as well as supplemental instruction for university courses on gas turbine performance, control, and DPHM (diagnostics, prognostics and health management).

## Inhaltsverzeichnis

### Chapter 1. Historical Perspective

Abstract
This chapter provides some historical perspective contributing to the use of gas path parameter corrections. It largely involves the use of dimensional analysis and the so-called π theorem due to Edgar Buckingham, an American physicist working at the U.S. National Bureau of Standards in the early twentieth century. This chapter briefly describes the π theorem principle and illustrates the concept with several examples. The reduction in complexity obtained by applying this principle to yield equivalent functional relationships involving new variables (that are rational functions of the fundamental variables) was the driving force that ultimately formed the parameter correction process in common use today.
Allan J. Volponi

### Chapter 2. Mathematical Framework

Abstract
This chapter explores the construction of a mathematical framework to enable the direct derivation of Standard Day corrections for an arbitrary gas path parameter. The fundamental approach is in contrast with the historical methodology of dimensional analysis (briefly) mentioned in Chap. 1. This is accomplished by establishing a formal definition of a corrected parameter along with a short list of properties that corrected parameters are assumed to possess. These collectively form a set of axioms for our mathematical system from which formal derivations can ensue, using only fundamental thermodynamic principles and elementary calculus. This framework will provide the basis for the discussions contained in all subsequent chapters of this book except for Chap. 8, which deals exclusively with the effects of humidity on performance.
Allan J. Volponi

### Chapter 3. Common Corrections

Abstract
This chapter provides the Standard Day corrections for the most common gas path parameters. These corrections are sometimes referred to as classical corrections in that, the θ and δ exponent values that are derived, are the well-recognized values that appear in the literature. The parameters considered include, Rotor Speed, Temperature, Pressure, Air Flow, Fuel Flow, Horsepower, Torque, Acceleration, Thrust, Metal Temperature Rate, Fuel Air Ratio (FAR), and Thrust Specific Fuel Consumption (TSFC). The corrections are derived in detail from the definitions, axioms, and assumptions that were proposed in Chap. 2 along with simple thermodynamic relationships relevant to the parameter under consideration. In order to avoid any circular reasoning, parameters are derived in a particular order, wherein only results from already derived parameters are utilized in a given derivation.
Allan J. Volponi

### Chapter 4. Time Derivative Corrections

Abstract
This chapter provides the Standard Day corrections for the time rate of change, (i.e., time derivative) for the gas path parameters encountered in Chap. 3. The parameters considered include, Acceleration, Temperature, Pressure, Air Flow, Fuel Flow, Horsepower, Torque, Thrust, Fuel Air Ratio (FAR), and Thrust Specific Fuel Consumption (TSFC). As in the previous chapter, corrections are derived in detail from the definitions, axioms, and assumptions that were proposed in Chap. 2 along with simple thermodynamic relationships relevant to the parameter under consideration. In order to avoid any circular reasoning, parameters are derived in a particular order, wherein only results from already derived parameters are utilized in a given derivation.
Allan J. Volponi

Abstract
This chapter provides the Standard Day corrections for several additional parameters not already considered in previous chapters. These include Time Constants, Metal Temperature, and Static Temperature. The derivations proceed as before, employing only the definitions, axioms, assumptions, and derived results from preceding chapters. It should be noted that an additional assumption is employed in the derivation for Metal Temperature, i.e., the conjectured result given in Eq. (4.​50).
Allan J. Volponi

### Chapter 6. Refinements to Common Corrections

Abstract
This chapter provides some refinement to the Standard Day corrections for most of the common gas path parameters considered in Chap. 3. In particular, the parameters considered will include, Rotor Speed, Pressure, Air Flow, Fuel Flow, Horsepower, Torque, and Acceleration. The refinements will stem from the relaxation of our previous assumption that specific heats, cp and cv, are constant and do not change with temperature. Allowing specific heats (and their ratio γ = cp/cv) to vary, as they naturally do, offers theta exponents that are slightly different than the classical values provided in Chap. 3. The derivations follow the same strategy as in Chap. 3 and abide by the constraints imposed by our definitions, axioms, and previous results.
Allan J. Volponi

### Chapter 7. Empirical Methods

Abstract
This chapter considers empirical methodologies to determine (or refine) the θ and δ exponent values for use in Standard Day corrections. The section deviates from all previous chapters in that the corrections are not formally derived from axioms, assumptions and first principles but rather by statistical analysis of available engine data. The only consideration employed from our previous work is that of the form a corrected parameter takes, namely Eq. (2.​3). Hypothetical data is employed to illustrate the techniques.
Allan J. Volponi

### Chapter 8. Humidity Corrections

Abstract
It is well known that humidity levels in ambient air can affect engine performance. The intent of this chapter is to derive correction factors for gas path parameters of interest that will transform them to values that would have been observed had the ambient condition been dry. The strategy employed is to capture the effect of humidity on gas properties, namely, specific heats (cp and cv), their ratio (γ), and the gas constant (R), and extrapolate these levels to changes induced on gas path parameter values. Humidity corrections for Rotor Speed, Air Flow, Δ Temperature, Horsepower, Torque, Acceleration, Fuel Flow, Thrust, Pressure, and Temperature will be considered. Humidity corrections will be applied to Standard Day corrected parameters as an independent correction.
Allan J. Volponi

### Backmatter

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