<p>For compressible flow simulations involving both shock waves and turbulence, the competing requirements render it challenging to develop high-order numerical methods capable of capturing the discontinuities sharply and resolving the turbulence with high spectral resolution. In this paper, an efficient class of high-order TENO schemes with local adaptive dissipation for compressible flow simulation on unstructured meshes is proposed based on three new concepts: (1) a novel reliable troubled-cell indicator is proposed for the unstructured finite-volume method without case-sensitive parameter to tune; (2) different from the classical shock-capturing schemes for unstructured meshes, which conduct characteristic decomposition at each cell interface, an efficient hybrid weighting strategy is proposed by recasting the high-order linear scheme based on conserved variables for smooth flow scales and invoking the nonlinear TENO weighting process in characteristic space for non-smooth flow scales; (3) noticing that the low-order undivided difference deployed in the calculation of the new indicator is more effective in terms of separating the high-wavenumber fluctuations from the genuine discontinuities than the high-order difference, a new adaptive dissipation control strategy is introduced to combine the good numerical robustness for shock waves with the low-dissipation property for broadband physical fluctuations. Without the necessity of parameter tuning case by case, a set of benchmark simulations reveals that the proposed TENO-E scheme features robust shock-capturing capability and state-of-the-art high-resolution properties for highly compressible flows involving strong shock waves and a wide range of flow scales. Moreover, the proposed scheme is substantially less computationally expensive than the straightforward deployment of classical shock-capturing schemes, and thus is promising for high-fidelity DNS/LES simulation of more complex practical engineering flows.</p>