Turbulence - computational overview and CO2 transfer
Turbulence: a computationaloverview & CO2 transferFabio Fonseca
Overview Turbulent flow ◦ Randomicity vs. Chaos ◦ The Navier-Stokes equation Computational overview ◦ Discretizing and solving the fluid mechanics equations ◦ Sample applications ◦ Understanding the computational problem CO2 transfer at the equatorial Atlantic ocean ◦ CO2 on the oceans ◦ Turbulent transfer ◦ Heat and momentum transfer
Turbulent vs. smooth flow Turbulent flow Smooth flow
Turbulence“Turbulence is composed ofeddies: patches ofzigzagging, often swirlingfluid, moving randomly around theoverall direction of motion.” source: SCIAM Source: McDonnough 2004, 2007
Why study turbulence? What if we could... ◦ Predict the weather? ◦ Simulate the human heart? ◦ Simulate the galaxies flow through the space? ◦ Create air and sea transportation relying only on computer simulations (i.e., not relying on air tunnels)?
Turbulence: The problem“The most important unsolved problem of classical physics.” Richard Feynman “I am an old man now, and when I die and go to heaven there are two matters on which I hope for enlightenment. One is quantum electrodynamics, and the other is the turbulent motion of fluids. And about the former I am rather optimistic.” Sir Horace Lamb (1932)
Turbulence: The problem (as oftoday)source: http//www.claymath.org/millennium
A brief history of turbulence “Observe the motion of the surface of the water, which resembles that of hair, which has two motions, of which one is caused by the weight of the hair, the other by the direction of the curls; thus the water has eddying motions, one part of which is due to the principal current, the other to the random and reverse motion.” - Leonardo da Vinci, circa 1500
A brief history of turbulence The Navier-Stokes equation (Early 19th century): • Believed to embody the physics of all fluid flows (turbulent or otherwise) •Accounts for: The rate of change of momentum at each point in a viscous fluid, u is the fluid velocity field; pressure variations, P is the pressure
A brief history of turbulence This equation cannot be analytically “solved”: ◦ “Two realizations of the flow with infinitesimally different initial conditions may be complete unrelated to each other” – Ecke (2005)
A brief history of turbulence Late 19th century: ◦ In 1987 Boussinesq hypothesis tell us that the turbulent motions are proportional to strains in the flow. ◦ In 1894 Reynolds states that turbulence is far too complicated to permit a detailed understanding and simplifies the problem using an statistical approach, decomposing the flow in its mean and fluctuating parts.
A brief history of turbulence 1960‟s, the onset of the digital computer: ◦ MIT‟s E. Lorenz presented a numerical solution to the Navier-Stokes equation Lorenz‟s model could: ◦ be sensible to variations to the initial conditions ◦ offer „turbulence like‟ structures ◦ be non-repeatable or chaotic ◦ offer a deterministic solution to the N-S equations
Interval: randomicty vs. chaos Lorenz‟s solutions were chaotic
A brief history of turbulence Today: ◦ The statistical approach to the turbulence has become the standard ◦ Experimental studies advanced and helped to define and pinpoint the physical structures of the turbulent flow ◦ Mathematical advances on the solution of the N-S equation ◦ Boom of computational techniques born in the 70‟s and 80‟s
Computational overview What are computers really doing? Simulated fire-plume
Computational overview They‟re solving the N-S equation ◦ At least a specialized, statistically based, version of them ◦ Using simple geometry ◦ Using simplified and/or parameterized physical effects such as chemistry, radiation and others
Estimating the N-S equation The N-S equation is a partial differential equation: ◦ Discretize the partial differential equation by choosing a numerical method ◦ Obtain initial conditions for each variable at every spatial coordinate (and boundary conditions for the simulation) ◦ Choose an adequate time/space grid ◦ Improve it to be feasible to solve at an adequate time (or have a supercomputer and then wait)
Estimating the N-S equation Partial differential equation
Estimating the N-S equation A (very) simple discretization of a partial differential equation Classical explicit method
Estimating the N-S equation Initial condition Boundary condition
Estimating the N-S equation Visualizing the conditions Boundary values given to the problem beforehandThis shape was givento the problem as ainitialcondition Numerical solution to the wave equation – Fonseca (20
Estimating the N-S equation The computational grid Adaptative grid following a shock solution – Fonseca (20
2 sample applications Aircraft engineering Initial conditions: wind velocity & atmospheric disturbances Boundary conditions: the precise airplane shape Grid: The mesh over the airplane Numerical Model: Dependent on the physical properties you want to simulate: drag, lift, momentum, heat diffusion, etc.
2 sample applications Air pollution Source: http://www.me.jhu.edu/eddy-simulation.htm Initial conditions: Wind velocity, pressure distribution, pollutant source Boundary conditions: The cityscape Grid: The mesh over the cityscape Numerical Model: N coupled types: particle, turbulence, chemistry, etc
Computer simulations: the nitty-gritty What kind of computer can solve the turbulent flow? ANY One dimensional, parameterized Hundred points can Can be intractable even in be solved in 20s in a today‟s supercomputer; Intel‟s CORE 2 quad e.g., DNS
Computer simulations: the nitty- gritty Simulations done by the IAG-USP micrometeorology laboratory ◦ ~ 2003: 3D, serial LES. 8 nodes. 5 days to simulate 1 h using a CRAY supercomputer ◦ ~ 2008: 3D, parallelized LES. 8 nodes. 4 days to simulate 10 h using an Intel cluster ◦ ~ 2009: 3D, parallelized LES. 8 nodes. 1.5 day to simulate 12 h using an Intel cluster ◦ ~ 2011: 3D, parallelized LES. 1024 nodes.Sources: Codato (2008), Marques Filho, (2004); Oliveira et al., (2002); Barbaro (2010) 8 hours to simulate an hour* using an IBM* Personal letter to Barbaro, 2011, SARA: http://www.sara.nl/systems/huygens. The LES model used computed several different physicaleffects, from cloud microphysics to chemistry. In short, a much more complex and superior model than the ones listed before
Computer simulations: the nitty-gritty Why does it take so long to compute? ◦ Each point in the computation grid depends on the calculated values of its neighbors and itself … ◦ … and values for the same points obtained at previous iteration steps ◦ Roughly speaking, the more physical properties you retain, the more “communication” between points and physical parameterizations you have.
Computer simulations: the nitty-gritty Computational gridDiscretization for velocities and viscous stresses around a cell cut by an interface, extracted fromTryggvason G., Scardovelli R. and Zaleski S., Direct Numerical Simulations of Gas-Liquid MultiphaseFlows, Cambrigge University Press, to appear (February 2011) . Source: http://www.lmm.jussieu.fr/~zaleski/drops2.html
Computer simulations: the nitty-gritty In a nutshell ◦ The maths that allow the N-S equations to be discretized at all are crude representations of the complete flow. ◦ The more physical effects you retain in the problem, greater is the effort to compute it. ◦ The more realistic the geometry of the problem, the more intensive is the use of computer resources.
Turbulent CO2 transfer on theequatorial Atlantic ocean Objectives ◦ Investigate the CO2 transfer on the equatorial Atlantic Ocean Gather CO2 and other meteorological data Estimate the heat fluxes Estimate the CO2 flux ◦ Provide a methodology for further studies ◦ Couple the CO2 transfer algorithm to a 1D turbulence model
Turbulent CO2 transfer on the equatorial Atlantic ocean CO2 over the oceans Atmospheric CO2 concentration at Ascension Island (8°S, 14°W) Fonseca (2011)Atmospheric CO2 concentration over the oceans Source: NOAA
Turbulent CO2 transfer on theequatorial Atlantic ocean CO2 transfer on the oceans
Turbulent CO2 transfer on theequatorial Atlantic ocean What is flux? Flux is the amount of “something” passing through a surface http://betterexplained.com/articles/flu x/ Source: http://isites.harvard.edu/icb/icb.do?keyword=k41471&pageid=icb.page194990 Source: wikipedia
Turbulent CO2 transfer on theequatorial Atlantic ocean Why the heat flux? The latent and sensible heat fluxes are estimated by the algorithm and can be used as initial and boundary condition to a turbulence model.Solar radiation powers the Earth systemSource: http://www.answers.com/topic/planetary-boundary-layer
Turbulent CO2 transfer on the equatorial Atlantic ocean Why the heat flux? Values of the flux of Latent and sensible heat and the shortwave and longwave radiation are used by the algorithm to estimate the CO2 transferSource: NASA; The Earth Observer November-December, 2006
Turbulent CO2 transfer on theequatorial Atlantic ocean Wind speed & momentum flux Transfer of wind momentum to the ocean drives the CO2 transfer on the equatorial Atlantic ocean.
Turbulent CO2 transfer on theequatorial Atlantic ocean The CO2 fluxes can be obtained from the heat and momentum fluxes The equatorial Atlantic ocean act as a CO2 source to the atmosphere
Turbulent CO2 transfer on theequatorial Atlantic ocean Implications: ◦ The CO2 transfer algorithm can now be coupled to ocean/atmosphere turbulence models It can act as an upper boundary condition, forcing the water column/atmosphere That, in turn, can force the algorithm, resulting in physically sound estimations of the upper layers of the ocean and the atmosphere.
Summary Turbulent vs. Smooth flow History and theory development Randomicity vs. chaos The N-S equations ◦ Describe all flow state, turbulent or otherwise ◦ Described by a non-linear partial differential equation ◦ Discretized by numerical methods
Summary Numerical methods ◦ Initial and boundary conditions ◦ The numerical grid Sample applications ◦ Aircraft engineering ◦ Air pollution Computer simulations: The nitty-gritty ◦ Dependent on the numerical model and the parameterized physical processes ◦ Dependent on the geometry
Summary Turbulent CO2 transfer ◦ CO2 over the oceans ◦ Flux Heat & Momentum ◦ CO2 over the equatorial Atlantic ocean Gas flux Turbulent mixing ◦ Coupling of the algorithm to a turbulence model