surface science: physical chemistry of surfaces massimiliano bestetti lesson n° 2 - 11 october 2011

Surface science: physical chemistry of surfaces

Massimiliano Bestetti

Lesson N° 2 - 11 October 2011

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2

Surface topography

1. Parameters

2. Measurements

3. Surface topography modification: examples

4. Standards

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3Example III. Pressure drop in a turbulent pipe flow

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Problem 1

Water is flowing into a pipe of diameter D = 0.1524 m at a flow rate of 0.1262 m3 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.

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1-

22s m 918.6

1524.0

1262.044

D

Qv

63

3

10054.110

101524.0918.6Re

Dv

Reynolds number

Average velocity of water

Turbulent

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fD

e

f Re

51,2

7,3log0,2

1

Friction factor

roughness

(Colebrook – White equation)

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Roughness coefficient e for common materials 8

Surface (m) 10-3

Copper, Lead, Brass, Aluminum (new) 0.001 - 0.002

PVC and Plastic Pipes 0.0015 - 0.007

Stainless steel 0.015Steel commercial pipe 0.045 - 0.09Stretched steel 0.015Weld steel 0.045Galvanized steel 0.15

Rusted steel (corrosion) 0.15 - 4

New cast iron 0.25 - 0.8Worn cast iron 0.8 - 1.5Rusty cast iron 1.5 - 2.5

Sheet or asphalted cast iron 0.01 - 0.015

Smoothed cement 0.3Ordinary concrete 0.3 - 1Coarse concrete 0.3 - 5Well planed wood 0.18 - 0,9Ordinary wood 5

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fD

e

f Re

51,2

7,3log0,2

1

D = 0.1524 m

Re = 1.054·106

e = 5·10-5 m

f =0.01588

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Pressure drop

Pa10493.21524.0

10

2

918.61010588.1

2

1 633

22

D

Lvfp

W 10146.310262.110493.2 426 QpP

Power

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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.

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Re = (15 m/s) (315 mm) (10-3 m/mm ) (1.23 kg/m3) / (1.79 10-5 Ns/m2)

Re = 324679 (kg m/s2)/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

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Using the graphical representation of the Colebrook’s 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 v2 / 2 )

= 0.017 ((10 m) / (0.315 m)) ( (1.23 kg/m3) (15 m/s)2 / 2 )

= 74 Pa (N/m2)

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http://www.efunda.com/formulae/fluids/calc_pipe_friction.cfm#calc

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15Example 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

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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.

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21Example V. Efficiency of centrifugal pumps

Maximum improvement of efficiency for several smoothing steps (estimated by theoretical calculations for medium size pump of 180 m3/h)

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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. ….].

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23

Surface topography: functional filtering

LH

Pow

er

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.

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24Terminology and parameters

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surface science: physical chemistry of surfaces massimiliano bestetti lesson n° 2 - 11 october 2011

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