You should track fuel density in the tube along the axis, or better just track from the downstream to the location, where your fuel is more than 99% burnt out, or its density has become less than 1% of the initial value. Plot that location in time and you can get location of flame front and location of onset of detonation and further slope will give you flame speed and once slope is constant, you can assume detonation has been achieved depending on the velocity you get from slope (Must be of the order of 1000 m/s or more).

Thanks for replying @Sunil Bassi, I was thinking whether I can compare the maximum velocity achieved in the tube with the CJ velocity ? Can this thing tell about the onset of detonation velocity?

The temperature average I am getting is around 4000K but I used 1500K as the burnt temperature value to ignite the unburnt component at 300K. Is this fine or my temperature value is quite large ?

CJ values are theoretical values. You can compare the value of your flame velocity when slope of the plot discussed above becomes constant to theoretical values.

Mostly temperatures are in range of 2600-2800 K, but what fuels do you consider? And what equivalence ratios? And what initial pressure and temperatures?

There is a very good website called NASA/CEA or NASA/Thermobuild, you can get you theoretical CJ values at your given initial conditions on the tool given in this website.

I have used 1bar, 300k for unburned and 1bar, 1500k for burned mixture. Equivalence ratio is 1. Fuel is RP 1 and O2.

Then 4000 K is highly unlikely. You can check NASA thermobuild to get theoretical values. I think they have RP 1 fuel in database. If not available, you can see for other fuels like Jet A, JP 10 etc. All these have similar properties.