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Chapter2. Theory 9 address this matter. Only if those quanitities agree for both model and full-scale experiment, can the two can be considered having equal flow properties. This means, that the values of specific geometrical and physical quantities have to be equal for each flow point [31]. The relevant dimensionless quantities for this work are the Mach number Ma, the Reynolds number Re and the Strouhal number St. These quantities are derived from dimension analysis, either by applying the Buckingham π theorem or us- ing the matrix method [27, 31]. The Mach number is the dimensionless relation between the local air velocity c and the speed of sound a, see Eq. 2.8. Ma = ac where a = γRT (2.8) For an ideal gas, the speed of sound is dependent on the local static tempera- ture T, the individual gas constant of air R and the adiabatic index for diatomic gases γ [27]. Since it holds that the latter two values are constants, hence the √ speed of sound is proportional to the temperature a ∼ sound is much higher in the hot jet of a turbofan engine, the outlet flow does not reach supersonic speed. The dimensionless Reynolds number Re can be interpreted as the ratio of mo- mentum forces to viscous forces of a specific flow condition, Eq. 2.9. Re = c · l (2.9) ν The momentum forces equate to the speed of the fluid c and a characteristic length l, which is typically lower for the experiment model. The viscous forces are represented by the kinematic viscosity ν. The Reynolds number is the paramount dimensionless quantity in fluid mechanics, as the flow condition of two geomet- rically similar bodies of different scale are considered comparable, provided that Re is equal for both cases. This can be achieved by varying the flow speed c or by using a fluid with different kinematic viscosity ν [31]. The Strouhal number St, also called dimensionless frequency, is the ratio of the path l that a particle travels with speed c to the frequency f of a transient pro- cess, e.g. the frequency of vortex shedding due to air flow around an object, Eq. 2.10 [31]. St = l · f (2.10) c T. Because the speed ofPDF Image | Investigation of wing installation effects on the sound field of a model jet engine
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