Numerical simulations of a hot turbulent jet are performed on full unstructured grids with the aim to compute the noise generated in the far field. The jet flow is computed with the Onera CEDRE code using the LES (Large Eddy Simulation) approach and provide the unsteady inputs to the Onera KIM acoustic solver, based on the integral surface FW-H (Ffowcs Williams and Hawkings) approach which is used to reconstruct the acoustic far field. Several unstructured grids of increasing resolution are considered and the results obtained for both the computed jet flow and far field acoustics are compared to measurements carried out in the Onera CEPRA19 anechoic wind tunnel and to previous computations with the same codes but based on structured grids. Results show that unstructured grids allow a better grid tailoring work with an evident ease of construction, compared to the structured grid approach. Very good results are obtained and compare well with available measurements with an unstructured grid of roughly 130 millions cells. These results open the way to the use of unstructured grids in more complex geometries such as those encountered in real life configurations dealing with noise reduction devices or installation effects.