Suspensions and their applications can be found in many engineering, environmental or medical fields. Considering the special field of dilute suspensions, possible applications are cement paste or procedural processes in the production of medication or food. While the homogenized behavior of these applications is well understood, contributions in the field of pore-scale fully resolved numerical simulations with non-spherical particles are rare. Using Smoothed Particle Hydrodynamics as a simulation framework we therefore present a model for Direct Numerical Simulations of single-phase fluid containing non-spherically formed solid aggregates. Notable and discussed model specifications are the surface-coupled fluid-solid interaction forces as well as the contact forces between solid aggregates. Moreover we simulate and analyze the behavior of dilute non-colloidal suspensions of non-spherical solid particles in Newtonian fluids. The focus of this contribution is the numerical model for suspensions and its implementation in SPH. Therefore shown numerical examples present application examples for a first numerical analysis of influence factors in suspension flow. Results show that direct numerical simulations reproduce known phenomena like shear induced migration very well. Moreover the present investigation exemplifies the influence of concentration and form of particles on the flow processes in greater detail.