I want to calculate lift and drag coefficient of a airfoil at multiple using CFD simulation. I am using steady state simulation to run analysis. However I am worried about results. Does steady state simulation captures the vortex shedding effect on lift and drag coefficients?
The steady state solver consider that the solution should converge to a steady state. Let's consider for example (and for simplicity) to be in a finite volume solver. What the algorithm is trying to do is to send the residual (generated by the flux assembly) of your Navier-Stokes discretized system to 0.
In the particular case of unsteady phenomena (like the vortex shedding) the residual is related to the time and in your steady problem you are not considering the time dependence (or better it is hidden, if you are interested in it, see the last part of the answer). This would mean that what you will get as a result will be an oscillating field of your states (velocity, density and energy in case of compressible solver) but it is only your solver that is trying to converge to a steady state, with no real physical meaning (at least it depends on the type of the time discretizationa and the way of solving the equation, but this is more a philosophical discussionbut). Furthermore you have to pay attention that you are converging to the correct result. As I told you the phenomenon is unsteady, hence it is not given that the oscillating residual will converge to your tolerance and to the physical admissible solution. For more information have a look at this discussion.
To simplify it imagine that for each iteration your unsteady solver is doing the same, it converge to a steady state and later it advances. Collecting all the steady states at the different time, will give you the history and will allow you to collect the history of your field evolving through time and allowing you to extract the unsteady phenomenon features (e.g the oscillation frequency and the Strouhal Number).
Not to forget, another method to analyse the vortex shedding is to decompose what you obtain from the steady flow simulation in different mode, hence to do a singular value decomposition of your field (very similar to the POD technique).