Nome relatore 3 Example III. Pressure drop in a turbulent pipe flow
Nome relatore 4 Example III. Pressure drop in a turbulent pipe flow Problem 1 Water is flowing into a pipe of diameter D = 0.1524 m at a flow rate of 0.1262 m 3 s -1. Is the flow turbulent or laminar? Estimate the pressure drop along a distance of 1000 m for different wall roughnesses. Calculate the power needed to keep the water flow in stationary conditions.
Nome relatore 5 Example III. Pressure drop in a turbulent pipe flow Reynolds number Average velocity of water Turbulent
Nome relatore 6 Example III. Pressure drop in a turbulent pipe flow Friction factor roughness (Colebrook – White equation)
Nome relatore 7 Example III. Pressure drop in a turbulent pipe flow
Nome relatore 9 Example III. Pressure drop in a turbulent pipe flow D = 0.1524 m Re = 1.054·10 6 e = 5·10 -5 m
Nome relatore 10 Example III. Pressure drop in a turbulent pipe flow Pressure drop Power
Nome relatore 11 Example III. Pressure drop in a turbulent pipe flow Problem 2 Air at 0°C is flowing in a galvanized duct, having a diameter of 315 mm diameter, with velocity 15 m s -1. Estimate the Reynolds number and pressure drop along a distance of 10 m when ε - for galvanized steel is 0.15 mm.
Nome relatore 12 Example III. Pressure drop in a turbulent pipe flow Re = (15 m/s) (315 mm) (10 -3 m/mm ) (1.23 kg/m 3 ) / (1.79 10 -5 Ns/m 2 ) Re = 324679 (kg m/s 2 )/N Re = 324679 ~ Turbulent flow With roughness - ε - for galvanized steel 0.15 mm, the roughness ratio can be calculated: Roughness Ratio = ε / D = (0.15 mm) / (315 mm) = 4.76 10 -4
Nome relatore 13 Example III. Pressure drop in a turbulent pipe flow Using the graphical representation of the Colebrooks equation - the Moody Diagram - the friction coefficient - f - can be determined to: f = 0.017 The pressure drop for the 10 m duct can be calculated Δp = f ( l / D) ( ρ v 2 / 2 ) = 0.017 ((10 m) / (0.315 m)) ( (1.23 kg/m 3 ) (15 m/s) 2 / 2 ) = 74 Pa (N/m 2 )
Nome relatore 14 Example III. Pressure drop in a turbulent pipe flow http://www.efunda.com/formulae/fluids/calc_pipe_friction.cfm#calc
Nome relatore 15 Example IV. Turbine blade aerodynamics Improvement of the aerodynamic design of modern turbines for heavy duty gas turbines Way of major performance improvements: improve the overall engine cycle efficiency (higher hot gas temperatures at the turbine inlet and higher pressure ratios). Use of thermal barrier coatings sprayed on blading surfaces of turbine front stages (hot gas temperatures). Changes in surface quality: 1) the spraying process itself 2) erosion of the coatings under operating conditions Typically the surface roughness increases due to the coating process. It is of interest to understand the impact of surface roughness on blade aerodynamic losses
Nome relatore 16 Example IV. Turbine blade aerodynamics
Nome relatore 17 Example IV. Turbine blade aerodynamics
Nome relatore 18 Example IV. Turbine blade aerodynamics
Nome relatore 19 Example IV. Turbine blade aerodynamics
Nome relatore 20 Example IV. Turbine blade aerodynamics An experimental test series is presented which was carried out to understand the impact of surface roughness on turbine blade aerodynamics. Measurements of the total pressure losses of the test profiles and total pressure loss differences between profiles or profile sections of different surface finish. The Reynolds number dependency was measured. It was found that maximum loss increase due to surface roughness occurs at the highest Reynolds number tested. Maximum loss increase due to the highest surface roughness analysed is 40% at nominal flow conditions compared to a hydraulically smooth reference blade.
Nome relatore 21 Example V. Efficiency of centrifugal pumps Maximum improvement of efficiency for several smoothing steps (estimated by theoretical calculations for medium size pump of 180 m 3 /h)
Nome relatore 22 Surface topography 1.None of the conventional parameters is an intrinsic property of a surface. 2.All surface parameters vary with the scale over which they are measured. 3.To apply a surface measurement to an engineering problem it is essential that the scale of the problem and the scale of the measurement are related. [Imagine to take a 1:50000 geographic map and progressively enlarging it by linear factor of 10. The smallest feature we could resolve would be 100 m across. After one enlargement the topography starts to have an engineering effect; height variations with a wavelength of 10 m will cause vibrations in the suspension of an aircraft as it lands. After another enlargement to 1 m a similar effect will be produced on the suspension of road and rail vehicles. Amplitudes on this scale may vary from 10 to 100 m. ….].
Nome relatore 23 Surface topography: functional filtering L H Power 1 / Wavelenght Functional filtering: to obtain finite numerical values for surface paraneters it is necessary to reject certain portions of the spectrum at both its short-wavlength and its long wavelength measured.