The NANOGrav collaboration recently reported evidence of a stochastic common-spectrum process which might be interpreted as a stochastic gravitational wave background in the nHz frequency range. One possible explanation for this signal is gravitational waves (GWs) generated at quantum chromodynamic (QCD) scales in the early universe. I will discuss numerical simulations of GWs induced by hydrodynamic and hydromagnetic turbulent sources that might have been present at cosmological QCD phase transitions. For turbulent energies of about 4% of the radiation energy density, the typical scale of such motions may have been a sizable fraction of the Hubble scale at that time. The resulting GWs are found to have an energy fraction of about 10-9 of the critical energy density in the nHz range today. Our finding of shallower GW spectra proportional to the square root of the frequency for nonhelical hydromagnetic turbulence implies more power at low frequencies than for the steeper spectra previously anticipated. The behavior toward higher frequencies depends strongly on the nature of the turbulence. For vortical hydrodynamic and hydromagnetic turbulence, there is a sharp drop of spectral GW energy by up to five orders of magnitude in the presence of helicity, and somewhat less in the absence of helicity. For acoustic hydrodynamic turbulence, the sharp drop is replaced by a power law decay with a rather steep slope. These results support earlier findings of a quadratic scaling of the GW energy with the magnetic energy of the turbulence and an inverse quadratic scaling with the peak frequency, leading to larger GW energies under QCD conditions.