The flow in rod bundles is of key importance in a variety of engineering fields. It is representative, for instance, of the flow in a nuclear reactor core and the flow in a tube and shell heat exchanger. For particularly tight rod bundles (pitch to diameter ratio lower than 1.1 in hexagonal arrays) the flow is subject to a Kelvin-Helmholtz instability that is present in both laminar and turbulent flows and is likely to influence transition. Such instability has been proven to exist in bare bundles and even in bundles containing spacing devices. In fact, rod bundles are typically separated by devices designed to keep the rods (or tubes) in place and avoid vibrations. Simple spacer designs, such as honeycomb arrays with dimples, do not remove the instability. The present paper discusses a procedure to investigate the effect of spacing devices have on the most unstable mode of turbulence. A linear stability analysis of the laminar flow for several spacing device configurations has been performed by using adjoint methods. The results show the effect of the spacing on the formation of large scale coherent structures and help lay the ground for a theory of turbulence control in tight rod bundles.