Exercises in Combustion Technology

Transcription

1 Exercises in Combustion Technology Exercise 4: Turbulent Premixed Flames Turbulent Flow: Task 1: Estimation of Turbulence Quantities Borghi-Peters diagram for premixed combustion Task 2: Derivation of the straight line equations for Re t, Da, Ka Task 3: Regimes of the Flamelet-approach Task 4: Working point regimes of a gas turbine, an internal combustion engine and a PSR-burner 4/1

2 Task 1: Turbulence quantities a) Give quantities to describe a turbulent flow and a certain eddy! 4/2

3 Task 1: Turbulence quantities b) Describe Kolmogorov s eddy-cascade! Dissipation Integral length scale (Macro length scale) Kolmogorov length scale (Micro length scale) Inertial region: - eddies are formed by mean flow velocity - energy transfer from large scale eddies to small scale eddies - viscosity effects play a minor role only energy transfer, no dissipative energy loss viscous region: - very small eddies - viscosity effects become dominant -(molecular diffusion is faster than turbulent diffusion) - conversion of turbulent kinetic energy into molecular heat fluctuation -> only energy dissipation (of k) rate of energy transfer (turbulence formation) ε 1 = rate of energy dissipation ε 2 Excited energy = dissipated Energy 4/3

4 Task 1: Turbulence quantities Estimate the characteristic turbulence quantities (l c, τ c, u c of the kolmogorov cascade) for a turbulent flow inside a pipe (D = 50 mm, U = 10 m/s, ν = 1,6*10-5 m 2 /s) containing a coarse turbulence grid (d = 10 mm, Tu = 10 %)! inertial region L x = u = τ t = k 1 = ε 1 = viscous region η = u η = τ η = k 2 = ε 2 = 4/4

5 Task 1: Turbulence quantities inertial region L x =10 mm u = 1 m/s τ t = 10 ms k 1 = 1,5 m 2 /s 2 ε 1 = 150 m 2 /s 3 viscous region η = 80 µm u η = 0,2 m/s τ η = 0,4 ms k 2 = 0,06 m 2 /s 2 ε 2 = 150 m 2 /s 3 4/5

6 Flame regimes In premixed flames combustion is strongly influenced by interactions between turbulent flow and reaction There are several regimes of turbulent premixed flames with different mechanisms: Borghi-Peters diagram to distinguish between the regimes of turbulent premixed combustion 4/6

7 Borghi-Peters diagram turbulent flow parameters are compared to laminar flame parameters s L laminar flame speed δ L laminar flame front thickness laminar flame parameters are experimentally easier accessible than turbulent ones logarithmical construction for linear characteristics of Damköhler-, Karlovitz- and Reynolds-numbers non-dimensional numbers: Re t = u L v x Da τ t = τ c Ka L = 2 δ η 4/7

8 Task 2: Da, Re t and Ka Task 2: Derive the straight line equations for Da, Re t and Ka! 4/8

9 Task 3: Flamelet-approach In which regime is the Flamelet-approach valid? What is its meaning? Flame front is infinitely thin (δ L < 1 mm) Thin reaction zone = infinitely fast chemistry compared to turbulent mixing Thin layers = laminar flamelets (1d) valid for Ka < 1, Da >> 1 Contours of reaction progress variable 4/9

10 Task 4: Working points in Borghi diagram In which region (regime) lie these working points of a Gas turbine, an internal combustion engine (Otto-engine) and a PSR-burner? For which points is the flamelet approach valid? Can we plot working points of Diesel IC engines in the Borghi-diagram? Otto-engine (p = 40 bar, T =700 K) Gas turbine (ABB Burner, T VH = 650 K, λ = 2, p = 1 bar) PSR-Burner (80%H 2 /CH 4 /Air, λ = 3.33, p = 4 bar) L x 2 mm 5 mm 5 mm δ L mm 0.1 mm 1 mm u 1.63 m/s 10 m/s 300 m/s s L 0.6 m/s 0.5 m/s 2.0 m/s L x / δ L u / s L Flamelet? 4/10

11 Working points in Borghi-Peters diagram Task 4: In which region (regime) lie these working points of a Gas turbine, an internal combustion engine (Otto-engine) and a PSR-burner? For which points is the flamelet approach valid? Can we plot working points of Diesel IC engines in the Borghi-diagram? Otto-engine (p = 40 bar, T =700 K) Gas turbine (ABB Burner, T VH = 650 K, λ = 2, p = 1 bar) PSR-Burner (80%H 2 /CH 4 /Air, λ = 3.33, p = 4 bar) L x 2 mm 5 mm 5 mm δ L mm 0.1 mm 1 mm u 1.63 m/s 10 m/s 300 m/s s L 0.6 m/s 0.5 m/s 2.0 m/s L x / δ L u / s L Flamelet? Y N N Working points of Diesel IC engines can not be plotted in the Borghi-diagram: Characteristic flame parameter s T (s L ) is not defined for non-premixed flames! 4/11