Adaptation of Pressure Based CFD Solvers for Mesoscale Atmospheric Problems. May 2009.

Átírás

1 Adaptation of Pressure Based CFD Solvers for Mesoscale Atmospheric Problems Gergely Kristóf Ph.D., Miklós Balogh,, Norbert Rácz 4-th May 2009.

2 Advantages of a CFD based model Meso scale model CFD (with some changes) CFD model conversion interface The bidirectional interface is a source of numerical errors eg. it can cause partial reflection. Gravity waves?? grid refinement Better geometrical description More general turbulence models Easy customization Advanced pre- and post processing Thermal convection (UHIC)??

3 Methodology Incompressible CFD model (FLUENT) + transformation system + customized source terms

4 Mathematical description ( T ~ ) ~ ρ = ρ ρ β 0 0 T0 ~ v = 0 ( ρ ~ 0v ) + ( ρ ~ v ~ 0 v) = p~ + τ + ( ~ ρ ρ0 ) g + F t ( ρ ) ( ) pt ~ ~ pt ~ ( t T ~ 0c + v ρ 0 c = K ) + ST t ( ) ( ~ µ ) t ρ0 k + ρ0 v k = k Gk + Gb + Sk t + ρ0 ε σ k 2 µ + ε ρ ε + ρ ~ ε = t 0 0 v ε ρ0 C1 S ε ρ0 C2 t σε k + ν ε ε ~ ρ,t ~ + C1ε C3ε Gb + S, p~, ~ v,z ~ k ( ) ( ) + Transformed variables Customized volume sources ε

5 Transformation expressions T = T ~ T + 0 T p = ρ ρ 0 p~ + p = e ζz p~ + p ρ = ρ~ ρ0 + ρ z = 1 ζ Ln 1 ( ζ z~ ) w = ρ ρ 0 ζ z = e w ~ w ~

6 Equilibrium profiles for proper elimination of the hydrostatic pressure gradients T = T0 γ z p = p 0 T 0 γ z T 0 g R γ ρ = ρ0 e ζ z T 0 = K p0 = Pa ρ0 = 1.225kg / m 3 γ = 0.65 C/100m g /(Rγ) = ζ = 10 4 m 1 Standard ISA profile (up to 11km) Approximate profile Error bound is within 0.4% below 4000 m.

7 Summary of source terms S u = ρ 0 fv ρ 0 S v = ρ w~ ST = J SΘ ρ0 cp Γ γ In momentum equation: S w = ρ In the energy equation: In the transport equation of turbulent kinetic energy In turbulent dissipation equation: Stratification + adiabatic heating Coriolis force Compressiblilty l w~ ( 2 )( 1 ( ) ) 1 ( 2 p~ ) T ~ J lu J + β T g + ρ lu J + ζ J ρ S k Sε = C1ε C3ε C Γ γ = m J fu w ~ ( )J µ = β g t Pr ε β g k µ t Pr t t ( Γ γ ) ( Γ γ ) l = 2Ω cosφ f = 2Ω sinφ J ( 1 ζ ) 1 = z~

8 Related publications [1] Kristóf G, Rácz N, Balogh M: Adaptation of Pressure Based CFD Solvers for Mesoscale Atmospheric Problems, Boundary-Layer Meteorol, [2] N.Rácz, G.Kristóf, T.Weidinger, M.Balogh: Simulation of gravity waves and model validation to laboratory experiments, CD, Urban Air Quality Conf. Cyprus, [3] G.Kristóf, N.Rácz, M.Balogh: Adaptation of pressure based CFD solvers to urban heat island convection problems, CD, Urban Air Quality Conf. Cyprus, [4] G.Kristóf, N.Rácz, Tamás Bányai, Norbert Rácz: Development of computational model for urban heat island convection using general purpose CFD solver, ICUC6, 6-th Int.Conf.on Urban Climate, Göteborg, pp , [5] G. Kristóf, T. Weidinger, T. Bányai, N. Rácz, T.Gál, J.Unger: A városi hısziget által generált konvekció modellezése általános célú áramlástani szoftverrel - példaként egy szegedi alkalmazással, III. Magyar Földrajzi Konferencia, Budapest, 2006., Bp, CD [6] Kristóf G., Rácz N., Bányai T., Gál T., Unger J., Weidinger T.: A városi hısziget által generált konvekció modellezése általános célú áramlástani szoftverrel összehasonlítás kisminta kísérletekkel A 32. Meteorológiai Tudományos Napok elıadásai. Országos Meteorológiai Szolgálat, Bp., 2006 [7] Dr. Lajos T., Dr. Kristóf G., Dr. Goricsán I., Rácz N.: Városklíma vizsgálatok a BME Áramlástan Tanszékén, hısziget numerikus szimulációja VAHAVA projekt (A globális klímaváltozás: hazai hatások és válaszok) zárókonferenciája Bp. CD, 2006 [8] Rácz N. és Kristóf G.: Hısziget cirkuláció kisminta méréseinek összehasonlítása saját fejlesztéső LES modellel Egyetemi Meteorológiai Füzetek No. 20 ELTE Meteorológiai Tanszék, Bp , [9] M. Balogh, G. Kristóf:Automated Grid Generation for Atmospheric Dispersion Simulations, pp.1-6., MICROCAD konferencia, Miskolc, 2007.

9 Model validation 1. analytical solutions 2. laboratory experiments 3. a standard test case 4. a full scale event

10 Gravity waves Gyüre, B. and Jánosi, I.M., Stratified flow over asymmetric and double bell-shaped obstacles. Dynamics of Atmospheres and Oceans 37, U/Nh = 1.4 U/Nh = 0.3

11 Thermal convection (UHIC) A.Cenedese, P.Monti: Interaction between an Inland Urban Heat Island and a Sea-Breeze Flow: A Laboratory Study, CFD results T(z) profiles are also in line with the measured data. PIV results (Cenedese & Monti 2003)

12 Cold bubble: -15 C Down-burst test case Straka et al.1990, Reinert 2007 Θ u w

13 Results Compressible version Simplified (incompressible) Θ u w

14 Down-slope windstorm Boulder 1972 jan. Measured velocity field Measured potential temperature 60 m/s

15 Velocity field Results Potential temperature For idealized topography: For realistic topography: After a longer period of time:

16 Two application examples - Dispersion of pollutants - Analyses of instabilities

17 Meso scale atmospheric dispersion Orography of Pilis mountain Evolution of surface concentration

18 Micro-scale atmospheric dispersion Streamlines colored by temperature Chimney height 180 m Standard (stable) temperature profile Wind speed: 3m/s Injection velocity: 5 m/s

19 Von KármánK vortices behind a volcanic island Satellite image about Guadalupe island First CFD results

20 Investigation of instabilities Kelvin-Helmholtz instability Comp. domain: 25 km x 5.5 km Temperature difference 20 C Cloud formation:

21 Conclusions An easy to implement method has been developed for taking into account: stratification effects, adiabatic heat, Coriolis force, compressibility. The model has been validated against: some analytic solutions, laboratory experiments, reference calculations, in field measurements. Further effort is necessary for including: moisture transport and phase changes, porous drag models, radiation heat transfer, surface energy balance. Foreseeable applications: local convections (e.g. UHIC, see breeze, valley breeze), dispersion of pollutants (e.g. due to traffic, industry, chemical vapors), meteorological research (e.g. gravity waves, cloud formation), assessment of the wind power potential, simulation of catastrophes (e.g. large fires, volcanism).