http://kucg.korea.ac.kr kam, hyeong ryeol. abstract introduction related work simulation of...

http://kucg.korea.ac.krhttp://kucg.korea.ac.kr

Kam, Hyeong Ryeol

Feedback Control of Cumuliform Cloud Formation

based on Computational Fluid Dynamics

http://kucg.korea.ac.kr

AbstractIntroductionRelated WorkSimulation of Cumuliform Cloud FormationOur Control Method for Cloud FormationControlling Cloud SimulationResultsDiscussion and Future WorkConclusionAppendix

Contents


Cloud play an important role for creating re-alistic images

The atmospheric fluid dynamics already ex-istsBut difficult to adjust parameters and the ini-

tial statusSo, we focus on

Controlling cumuliform cloud formationThe user specifies the shape of the cloudsAutomatically adjusts parameters to form that

shape

Abstract


Although CFD(Computational fluid dynamics) methods can generate realistic shapes and motion, it is difficult for the user to control the simulation result and impossible to adjust the parameters manually.

In previous methods, the motion of smoke and water such as letters and animals has been calculated.

In this paper, we focus on controlling cloud formation.

1. Introduction


We only focus on cumuliform clouds( 적운 ).Our method generates realistic clouds.The user specifies the contours of the clouds.Previous approach did not produce convinc-

ing results because there are several physical processes: phase transition from water vapor to water

droplets We developed a new method that controls

the physical parameters affecting the cloud formation process.

1. Introduction


Fluid ControlAfter the pioneering work by Treuille et al. [2003]

Control smoke and water by using the adjoint methodMcNamara et al [2004]

Control smoke by adding external forcesFattal and Lischinski [2004]

Calculate the motion of smoke by using a potential field Hong and Kim [2004]

Feedback control mechanism Shi and Yu [2005], Kim et al [2007]

SIMILAR, but NOT directly APPLICABLE to CLOUDSSince physical phenomena involved in cloud formation

is not concerned.

2. Related Work


Fluid ControlMore recently,

Control the motion of water by using control parti-clesThurey et al. [2006]

Make smoke move along a user-specified pathKim et al. [2006]

There are NO methods for controlling the for-mation of clouds based on computational fluid dynamics

2. Related Work


Cloud Simulation1. procedural techniques

Generate the density distribution of clouds using the idea of fractals.Ebert et al [2002]

Modeling without generating 3d density distribu-tionsTrembilski and Brobler [2002], Bouthors and Neyret

[2002], Neyret [1997], Gardner [1985]

Although the cost is very low and it’s possible to generate the desired cloud shapes, a trial and error process is required.

2. Related Work


Cloud Simulation2. physical simulation of formation process

Generate clouds by numerical simulationDobashi et al [2000], Kajiya and Herzen [1984],

Miyazaki et al [2001], Miyazaki et al [2002], Harris et al [2003]

Although these methods have the potential to gen-erate realistic clouds, many physical parameters have to be adjusted to generate convincing results.

Adjusting the parameters MANUALLY is almost impossible.

2. Related Work


The numerical simulation of cumuliform cloud formation

(b) the temperature of the rising air currents de-creases due to adiabatic cooling.

(c) the latent heat is liberated, which creates addi-tional buoyancy forces and promotes further growth of the clouds.

Our method mainly controls the amount of latent heat.

3. Simulation of Cumuliform Cloud Formation


The density of air is assumed to be constant The atmosphere is assumed to be an incom-

pressible and inviscid fluid media.

3.1 Simulation of CCF- Governing Equations


The motion of the atmosphere is expressed by Navier-Stokes equations ,

B : buoyancy force / f : an external forces (such as wind)

T : the temperature / z=(0,0,1) ↑ / kb : the buoyancy coefficient

Tamb : the ambient temperature, inverse-proportion to the height

1st term : proportional to the difference between the temperature of the rising air parcel and the surrounding air

2nd term : the drag force due to the falling water droplets


fBuuu

pt

1)( 0 u

zzB camb

ambb gq

T

TTk


The phase transition between the water vapor and the clouds , ,

Cc : the amount of clouds generated by the phase tran-sition

Sv : the amount of water vapor / α : the phase transi-tion ratio

qs : the saturation vapor content

If Cc < 0 then, the amount of clouds qc is reducedIt means : the evaporation of water droplets


ccc Cqt

q

)(u vcvv SCqt

q

)(u

)( svc qqC ))),/(exp(max( cvs qqCTBAq


The temperature

Γd : the adiabatic lapse rate ω : the z component of the fluid velocityQ : the coefficient of the latent heatST : the heat supplied from the ground

1st term : the advection by the flow field2nd term : the adiabatic cooling of rising air3rd term : the latent heat

The amount of the latent heat is assumed to be propor-tional to the amount of cloud generated by the phase transition


Tcd SQCwTt

)(uT


T0(the initial temperature)=Tamb(the ambient temp)

qv,0(the initial water vapor)Decrease exponentially from the bottom of sim.

spaceThe initial temperature and water vapor

Are constant in the horizontal directionqc,0(the initial cloud density) = zero

u0(the initial velocity) = zeroFor the boundary conditions,

A periodic boundary condition is used in the horizontal

A fixed boundary condition(u=0) is used on the bottom and top of the simulation space

3.2 Simulation of CCF- Initial Status and Boundary Conditions


pink curve = the desired shape

The contour line is projected onto a plane perpendicular to the xy component of the vector connecting the view-point and the center of the simulation space

3d shape(target shape) is generated from the contour line

4. Our Control Method for Cloud Formation


Our method controls the simulation so that the difference between the target shape

and the simulated clouds becomes zeroThe effect of wind is not concerned

Since it doesn’t contribute very much to the ccf

The convection due to the buoyancy force is the main driving force for the cumuliform clouds.



To measure the difference, we use the height ratio R of the top of the simulated clouds to the top of the target shape.


),...,1 ;,...,1(

),,(/),(),(

yx

targetc

NjNi

jiHjiHjiR


Key features in our control method1. Feedback control

adjusts the vertical extent of the clouds

2. Geometric potential fieldadjusts the horizontal extent of the clouds



1. Feedback controllerPromotes the cloud growth until the clouds

reach the top of the target shape (R(i,j)=1.0)2. Geometric potential field

When the target shape is not a height field, the clouds may grow outside of the target shapeSo, geometric potential field is used

External forces preventing the clouds from growing outside

We use only the horizontal components of the external forces.



1. Feedback controllerCloud growth is promoted by controlling the la-

tent heat and by supplying additional water va-por2 functions

The latent heat controller controls the coefficient for the latent heat Q (old : constant). - updates Qc(i,j) that was for the grid point (i,j,0) as a control

variable - the coefficient for latent heat for grid point (i,j,k) = Qc(i,j)

The water vapor supplier adds water vapor where clouds does not reach the top of the

target shape (old: at the bottom of the simulation space + top of the clouds)

- determines the amount of water vapor, Sv,c(i,j), to be supplied

There are Nx*Ny*2 control variablesTo adjust these parameters, we employ PID controller

PID=proportional-integral-derivative



2. Geometric potential fieldis generated in a preprocessing step so that the

potential value becomes large inside the target shape

The external forces are generated in propor-tion to the gradient of the potential field.

As a result, the external forces prevent clouds from growing outside the target shape.



How our control mechanism works?1. Compute the height ratio R(i,j)

Ratio is sent to latent heat controller, the water va-por supplier

2. the water vapor supplier determines the amount of the water vapor, Sv,c

and adds this at the grid points corresponding to the top of the simulated clouds.

Promotes the phase transition from water vapor to clouds.



How our control mechanism works?3. the latent heat controller

Increases Qc where the clouds have not reached the top of the target shape (R(i,j)<1.0)

Qc increases the temperature when the clouds are generated due to the phase transition

The increase in temperature results in an increase in the buoyancy force

This promotes the cloud growth to higher regions.4. During cloud growth

The external forces due to the geometric potential field push clouds inwards the inside the target shape



How our control mechanism works?5. As the clouds approach the top of the target

shapeThe water vapor supplier decreases the amount of

additional water vapor . The latent heat controller also stops increasing the

latent heat coefficient6. So, user-specified clouds are generated au-

tomatically

The simulation is terminated manually by the userAfter done, the details might be reduced because

the control forces could prevent vortices and detail from developing



1. The generation of the target shape2. The geometric potential field3. The feedback control of the simulation4. The water vapor supplier

5. Controlling Cloud Simulation


The target shape is generated from the user specified contours of the desired cloud shape.1. the user specifies the generating region

The center of the simulation space is placed at the center of the specified region

2. the user draws the contours on the screen3. the contours are projected onto a plane4. the target shape is generated

Thickens the 2d sketch by extracting its medial axis5. a bounding box of the target shape is gener-

ated and is subdivided into a 3d gridGrid is used to compute the geometric potential

field and to simulate the cloud formation process

5.1 Controlling Cloud Simulation- Generation of Target Shape


1. An initial potential field is generated1 : inside grid points0 : outside grid points

2. Applying a 3d Gaussian filter to the initial field in order to create a smooth and continu-ous potential fieldThe result field is the geometric potential field.

5.2 Controlling Cloud Simulation- Geometric Potential Field


During simulation,F, the external force due to the geometric po-

tential filed is calculated at each grid pointBecause of using only the horizontal compo-

nent of F,

qc : the density of clouds / ψ : the potential fieldSince the external force is proportional to the gra-

dient of the potential field, it only works near the boundary of the target shape.

No external forces are generated at the grid points where no clouds exist since F is also proportional to qc

5.2 Controlling Cloud Simulation- Geometric Potential Field

000

010

001

),( cc qqF


updates the coefficient for the latent heat, Qc(i,j)Using PID control mechanism -> PI control

∆H(i,j) : the normalized height difference between the top of the clouds and the target shape

5.3 Controlling Cloud Simulation- Latent Heat Controller

D

HIHPc djijiKjijiKjiQ0

),,(),( ),(),(),(

j)(i,H

j)(i,Hj)(i,HjiRji

target

ctargetH

),(0.1),(


1st term : proportional controller

KP : proportional gainWhen only using this, small gaps between the simu-

lated clouds and the target shape are left (So, 2nd term is needed)Not counting when clouds grow near the top of the

target shape, Because ∆H becomes very small

2nd term : integral controller Contributes when the accumulated difference be-

comes largeD : Duration for the accumulation / KI : integral

gainRemoves the gaps and updates Qc until ∆H be-

comes zero


D

HIHPc djijiKjijiKjiQ0

),,(),( ),(),(),(


The control parameters need to be specified.We determine KP and KI experimentally

It is difficult to determine all these parameterFrom experiments, we found that larger values are re-

quired for KP and KI where the top of the target shape is highBecause the cloud growth in such regions has to be pro-

moted further than the regions where the top of the target shape is low.

We assume that KP and KI are proportional to the height of the target shape.

кP,кI : proportionality coefficientsĤtarget : the height of the target shape divided by the height

of the simulation space.

As a result, кP,кI are specified by the user.


),(),( & ),(),( argarg jiHjiKjiHjiK ettIIettPP

C

PICP T85.0

,45.0


Adds water vapor if

Indicates that the water vapor is supplied at the grid points where the ratio R(i,j) < the average of the ratios

The water vapor supplier tries to make the ratio of the cloud growth the same for all grid points The top of the cloud at all grid point reaches the top

of the target shape almost simultaneously.The amount of additional water vapor

Cv : a control parameter for the water vapor supplier,

specified by the user / qv,0 : the initial water vapor at the beginning

(i,j,ktop) : the grid point corresponding to the top of the clouds

5.4 Controlling Cloud Simulation- Water Vapor Supplier

x yN

n

N

myx

mlRNN

jiR1 1

),(1

),(

),,(),( 0,, topvvcv kjiqcjiS


Intel Core2 Extreme X9650 with nVidia GeForce 8800 GTX

The simulation space : 320 * 80 * 100 gridThe average computation time for each time

step of the simulation : 7 secondsThe additional computational cost due to con-

trol mechanism is very low and is less than one percent of the total computation cost

6. Results


кP=4.95, кI=0.6, cv=0.5cv is from process of trial and errorOnce the appropriate values for these parame-

ters have been found, we can generate various shapes of clouds

6. Results


Comparing to Fattal’s method

In Fattal’s method, clouds are generated where they should not be

Our method can generate realistic clouds while their shapes closely match the target shapes.

6. Results


Case that is not the height field

6. Results


The target shapes are completely different from height fields.

6. Results


Generating clouds resembling real clouds in a photo

6. Results


Our control mechanism is fairly indirect.Feedback controllers cannot guarantee that the

clouds will completely form the desired shape.The indirect control makes it possible to pro-

mote the cloud growth as naturally as possible (realistic-looking)

The indirect control allows the user to specify the rough shape of the clouds and finally gen-erate the realistic clouds.

7. Discussion and Future Work


Our method controls the cloud motion in the vertical directionThe horizontal movement of the clouds is not

controlledSince the forces due to cloud formation work

only in the vertical directionIt is difficult to control the horizontal move-

ment by controlling the cloud formation process

The previous fluid control methods might be suitable for horizontal control it is expected that the combination of methods to

control the cloud motion in both vertical and hori-zontal directions.



Our method can handle a desired shape that is not a height field.However, it is still difficult to handle a shape

that is very different from a height field the cumuliform cloud formation process affects

the vertical movement of the cloudsHorizontal external forces are required

Our goal for generating realistic clouds form-ing the desired shape has been achieved.Extending the method to handling multiple tar-

get shapes is our next important research di-rection



The user specifies the shape of clouds viewed from only a single direction. solution : to specify the multiple target

shapes viewed from multiple viewpoints.Ziegler-Nichols method doesn’t always pro-

vide ‘good’ parameters. A trial and error process is still required.

Extension of our method to other types of clouds such as stratus is also an interesting area for future work



Controlling cumuliform cloud simulationOur method can generate clouds with desired

shapes Controlled by our feedback controller and ex-

ternal forces calculated by the geometric po-tential field.

For feedback control, we developed a latent heat controller and a water vapor supplier.

By controlling the amounts of latent heat and additional water vapor, clouds grow naturally and converge into the desired shape

Our method provides a simple way to gener-ate realistic clouds with desire shapes

8. Conclusion


We determine кP,кI based on this method1. Experimental simulations are carried out several

times with the proportional controller only.2. Carried out with increasing кC and the controller

tries to make the clouds reach a target heightIn experiment, the target height is set to 80% of space

When кC is small, the clouds cannot reachAs кC increases, the clouds can reach

At a certain value of кC, the cloud growth exhibits period-ical oscillations Clouds repeatedly exceed and fall below the target height

2. TC : the period of the oscillation

Appendix A.Ziegler-Nichols Method

C

PICP T85.0

,45.0


Any questions?

THANK YOU

http://kucg.korea.ac.kr kam, hyeong ryeol. abstract introduction related work simulation of...

Documents

controlling cloud formation

cloud formation process

formation of clouds

control smoke

cloud simulation1

cloud simulation2

cumuliform clouds

realistic clouds