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Select the chair geometry and left-click on the Burning Fuel with Smoke preset from the Phoenix Toolbar.

This will generate an entire setup for you consisting of a Phoenix Simulator, a Phoenix Fire Source, and a Phoenix Particle Shader node used for rendering the Drag Particles produced by the Source.

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Phoenix provides a high-quality GPU Preview directly in the Maya Viewport which should be enabled by default by the Burning Fuel preset.

You may want to disable it if you're working through a Remote Desktop connection or on a machine with integrated graphics.

To do so, go to the Preview rollout → GPU Shade Preview → Enable GPU Preview.

The GPU Preview section of the Preview rollout also contains Lighting controls which only affect the Viewport preview and not the rendering.

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Here's how the simulation looks with the default Burning Fuel preset.

As you can see from the video to the right, there are plenty of issues to address:

1. The emission is uniform - the entire chair is burning instead of only certain sections of it. We will first take care of that by using Maya's Paint 3D Tool to to specify where the emission happens through a Texture map.
   
   
2. The fire is too choppy - we are going for a smoother / calmer look. The noisiness in the fire is caused by the low grid resolution, the Vorticity parameters in the Dynamics rollout of the Simulator, and to a lesser extent - the shading settings set up in the Rendering → Volumetric Options → Fire window. We resolve this by disabling the Vorticity parameters and tweaking the Fire rendering Color and Intensity curve of the volumetric shader.
   
   
3. The fire is moving rather quickly - this would be the desired behavior when simulating a burning flammable fluid but instead we would like to achieve a smoother flame. Think of a campfire - the flames produced by the Burning Fuel preset don't resemble the calm and elongated fire produced by burning wood. We resolve this by slowing down the cached sequence from the Input panel and Re-simulating over the slowed-down cache files with the Time-Bend Resimulation option enabled.

Select the Phoenix Simulator and open the Grid rollout. 

Set the Scene Scale to 1.5 - this will slightly slow down the simulation. 

Set the Cell Size to 0.65 and change the  X / Y / Z dimensions of the grid such that the painted areas of the chair are included in the bounds of the simulator box. This will save some simulation time as those empty voxels will not be calculated in vain. 

The exact position of the Phoenix Simulator is Translate X/Y/Z: (20, 90, -25).

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Set the Adaptive Grid option to Smoke, and the Threshold to 0.02. The Adaptive Grid option allows the container to grow in size once the content of the specified channel near the walls of the simulator reaches the Threshold value. In this case, the container will increase in size when there is smoke near the walls. 

Enable the Expand and Don't Shrink option - because fire simulations tend to be turbulent, it is possible that a certain portion of the container will oscillate between being completely empty and filled with smoke/temperature. This could cause the Adaptive Grid option to constantly resize the bounds of the simulation, producing undesirable results (such as sharply cutting off the fire). 

Enable Manual Adaptation Limits and set the X / Y / Z dimensions according to your needs. In this tutorial, a Phoenix Plain Force is used to add wind blowing from the left so extra space is provided to the right where the fire is expected to go. 

 Set the Extra Margin to 5 - this option allows the Adaptation to keep a number of voxels close to the walls as a buffer zone and expand the grid earlier than usual. This can be especially useful when simulating fast-moving objects or explosions as it allows the simulator to expand before any clipping occurs. 

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Here's how things changed after reducing the Cooling to 0.1.

The flames are now longer - as they should be with this type of burning.

Turning off the Vorticity removed the noisiness in the simulation.

In the next step, we add some detail back into the sim by setting the Conservation Method to Buffered.

To add additional realism to the simulation, we use a Phoenix Plain Force to simulate the effect of wind.

Go to the FX menu set → Phoenix FD → Create and add a Phoenix Plain Force. The Plain Force is a simple directional force.

Rotate it so it points in the positive X direction and set the Strength to 250.

The exact Translate X/Y/Z values are: (-30, 150, -30).

The exact Rotation X/Y/Z values are: (0, 90, 0).

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After adding the Plain Force, the fire is blown to the right instead of going straight up.

Some extra detail in the flames is also revealed.

Now that the animation speed of the scene objects is reduced in half, we need to do the same for the Phoenix Simulation.

Open the Input rollout and set the Play Speed to 0.5.

Set the Blending Method method to Velocity.

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Open the Resimulation rollout and enable Resimulate. Set the Affect drop-down to Both.

Note that when you enable Resimulation, Phoenix will try to read the cache files for preview and rendering from the Resimulation Output Path instead of the 'regular' Output. Don't be alarmed if the Viewport goes blank - you can always go back to the original cache files by simply disabling the Resimulate toggle.

The Grid Resimulation takes care of the Temperature/Smoke/Velocity Grid Channels while the Particle Resimulation will affect the Drag particles emitted by the fire source.

Set the Amplify Resolution to 0. This parameter is used to increase the resolution of the grid for the Resimulation process only (just like the Cell Size in the Grid rollout controls the simulator's resolution). Because we only want to recalculate the cached sequence, we leave the Amplify Resolution at 0.

Enable Use Time Bend Controls and set the Time Bend Method to Slow Down. This option works great when trying to produce a slower version of your base simulation, as is the case with our fire.

Set Wavelet Strength to 0.01. Wavelet Turbulence is used to generate wispy detail in a simulation but we're not looking to add additional details so the Strength is reduced to its lowest possible value.

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Set Simulator → Dynamics → Steps per Frame to 1 so you don't lose detail in the re-simulation process.

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You can use the Amplify Resolution option to add extra detail to the simulation during the Resimulation process.

The Amplify Resolution setting controls the number of voxels that will be used for the grid during resimulation.

Here's the simulation above, resimulated with Amplify Resolution of 1.

The painted Vertex Color on the chair geometry will heavily affect the simulation result.

You can always go back to the Texturing → 3D Paint tool and tweak the emission texture.

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Here is a simulation with the emission pattern from the picture above, with an Amplify Resolution value of 1.0 for the Resimulation.

As mentioned in the beginning, the only illumination source for this scene is the fire itself.

The scene file called 001_start.ma already has the cameras set up for you. However, for reference, here are their properties:

Focal Length: 90

A V-Ray Physical Camera is used for the rendering with the following settings:

F-Number: 2.4

Shutter Speed: 200

ISO: 100

Vignetting: Disabled

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