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We present the analysis of physical conditions, chemical composition andkinematic properties of two bow shocks -HH529 II and HH529 III- of the fullyphotoionized Herbig-Haro object HH 529 in the Orion Nebula. The data wereobtained with the Ultraviolet and Visual Echelle Spectrograph at the 8.2m VeryLarge Telescope and 20 years of Hubble Space Telescope imaging. We separate theemission of the high-velocity components of HH529 II and III from the nebularone, determining $n_{\rm e}$ and $T_{\rm e}$ in all components through multiplediagnostics, including some based on recombination lines (RLs). We derive ionicabundances of several ions, based on collisionally excited lines (CELs) andRLs. We find a good agreement between the predictions of the temperaturefluctuation paradigm ($t^2$) and the abundance discrepancy factor (ADF) in themain emission of the Orion Nebula. However, $t^2$ can not account for thehigher ADF found in HH 529 II and III. We estimate a 6% of Fe in the gas-phaseof the Orion Nebula, while this value increases to 14% in HH 529 II and between10% and 25% in HH 529 III. We find that such increase is probably due to thedestruction of dust grains in the bow shocks. We find an overabundance of C, O,Ne, S, Cl and Ar of about 0.1 dex in HH 529 II-III that might be related to theinclusion of H-deficient material from the source of the HH 529 flow. Wedetermine the proper motions of HH 529 finding multiple discrete features. Weestimate a flow angle with respect to the sky plane of $58\pm 4^{\circ}$ for HH529.

Photoionized Herbig-Haro objects in the Orion Nebula through deep high-spectral resolution spectroscopy I: HH529II and III