This was my engineering viva question and I couldn't think of any example, for I am totally convinced that there cannot be drag in a inviscid flow. It also bothers me whether it is possible, a tricky scenario in fluid mechanics or gas dynamics.
[Physics] Example of inviscid flow with drag
dragfluid dynamics
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Based on your sketch, the block is always moving along it's long axis, in other words, the velocity is always along the direction of your red vector. This means in the picture on the left, there is only vertical velocity while in the picture on the right, there is both vertical and horizontal velocity. This is what you have described, I am only summarizing to make sure the rest of my answer makes sense and is consistent with this understanding.
Now, you claim the drag coefficient of the case on the left is known yet the drag coefficient for the case on the right is unknown. To clarify a point, the drag coefficient is a scalar, not a vector as you claimed it to be. And in this case, the drag coefficient is actually the same in both cases if the block is moving along the vectors shown. Why is this the case?
Consider the area vector of each face to be the area of the face times the surface normal, ie.:
$$\vec{A} = A\cdot\hat{n}$$
In your example on the left, the area normal is in the $\hat{j}$ or Y-normal direction and so is the velocity. This gives you the drag coefficient you cite.
In your example on the right, you now have a component of the area vector in the $\hat{i}$ direction and a component in the $\hat{j}$ direction. But your velocity also has components in both those directions.
You are correct to say that the area increases in the $\hat{j}$ direction -- you now have both a portion of the short side and a portion of the long side exposed to the Y-direction. However, the block is still moving normal to the short side along the red vector, which means the area vector for the long sides are perpendicular to the red vector and that area does not contribute to the so called "frontal area" of the block.
The answer depends on your definition of "steady". A flow is called turbulent when small oscillations are no longer damped, but instead excited. Therefore when looking at the fluid on a microscopic scale, a turbulent flow is not steady.
However, turbulence can be modeled on a macroscopic scale (cf. https://en.wikipedia.org/wiki/Turbulence_modeling), effectively encapsulating the local non-steadiness. Thus on a macroscopic scale, turbulent flow can be steady.
An example for a (macroscopic) partially turbulent steady flow is the flow around an airfoil. At the nose, the flow is laminar. At some point (the transition point) at both upper and lower surface, the flow becomes turbulent. (The location of the transition point for a dedicated airfoils is depending on flow velocity and the angle of attack.)
Best Answer
Horseshoe vortex system in three dimension is a very good example for drag in a inviscid flow. See this