Bring out an icosphere and subdivide it up into level 3. Then go to edit mode and delete half of it. This is gonna be the flow object that emit the particle which create the shape of the explosion.

To give the surface of the icosphere more randomize, add a displacement modifier at the modifier panel.

Click new on the texture, then go to the texture panel and switch the type into clouds. Then you can play with the size so you can get your desired shape. After done playing with the shape, scale down the icosphere.

To create the particle system, go to the particle properties panel and click the plus sign to create one. Then we need to change some settings.

My setting:

-Number of particle - 6000

-Frame start - 10

-End -15 (so the particle system last for 5 frame)

-Lifetime - 5

In the velocity segment :

-Normal - 3

-Z direction (which is up) - 7

-Randomize - 0.5

You also can add more particle system to make the explosion look more interesting. To do that, just copy the icosphere and rotate and position it around. After that  go to the texture panel, create a new texture and change the size to give some different variation from the previous one. You also need to change the some setting in the particle system. Before that, duplicate the particle system so it dosen't change the previous one.

My setting :

-Start frame - 11

-End - 16

In the velocity segment :

-Normal - 4

-Z direction - 6

-Randomize - 0.9

If you want them to collide with something add a mesh plane and resize it. Make sure the flow object is above the plane. Go to the physics panel and select collison. Then we need to change some settings.

My setting :

-Damping - 0.7 (to control the bounciness of the particle)

-Randomize - 2.5

-Friction - 0.7

-Randomize - 0.5

Lets set up the flow object. Go to the physics tab, click fluid, and set the type to flow. Change the flow type into Fire + Smoke. For the flow behavior change into inflow.

Other setting :

-Sampling substeps - 7

Flow source :

-Change to the particle system that we just created.

-And for the particle system, select the one on the menu.

Enable initial velocity

-Source - 3

Do it manually for the other flow object

Lets say I want this one to be an initial explosion and the the another explosion after that around 60 frame later. We can achive this by selecting all the flow object and then copy it. But before that add all the flow object of the first explosion in to one folder by hitting M on the keyboard. Do the same thing to the flow object of the second explosion.

After that we just need to change the frame start and the end frame of the flow object. Don't forget to duplicate the particle system for every flow object that you copied. You also can change the rotation and the direction also their particle settings of the new flow object to give more variation of the explosion.

My setting :

-Icosphere 1 :

 - Frame start - 70

 - End - 75

-Icosphere 2 :

 - Frame start - 71

 - End - 76

Lastly, we need to bake all the particle system by going to the particle properties and find the cache segment. Then click on bake all dynamics.

Before bake in the smoke simulation, we need to add a domain. To do that add the cube mesh and resize it. make sure it is the same height as the plane and all the particle system aare inside the domain object. Then go to the physics panel, click fluid and change the type to domain. Then we need to play with some setting.

My setting :

-Resolution - 128

-Enable bottom in border collision.

-Enable adaptive domain.

-Gas -> Vorticity - 0.05

-Enable noise in the gas setting.

-Fire -> Reaction speed - 0.4

-Cache -> End frame - 120

-Change the type into all (so we can bake everything all at once)

Start bake the simulation. 

Now lets set up the materials. Go to the shader editor and play with some nodes to add texture on the fire.

Add a couple more assets like changing the plane into a desert and add so texture to the sky to make the scene look more interesting.