I can$$$$t think it is about material limitations or aerodynamics

• "I cant think it is about material limitations or aerodynamics". It might actually be the main reason: compressor works with temperatures of some 300°C/500°F and speeds of some 500fts/150ms; turbine works with temperatures of some 1300°C/2000°F and speeds of some 1000fts/300ms. Compressor blades (or better, fan blades) are also taller than turbine blades so a higher curvature/twist makes sense for the former. Commented Dec 11, 2022 at 14:51
• Indeed what sophit is saying seems correct. On smaller jet engines which do not have fancy stuff like active blade cooling, the turbine blades look quite similar to the compressor blades. Even the LP turbine blades on modern jet engines look quite similar to the compressor blades, with the exception of the outer ring, which is used to prevent interstage leakage of air, and is exclusive to turbines. Commented Dec 11, 2022 at 23:01
• Also, there's often a single HPT stage driving upto a dozen HPC stages, so it makes sense that the single HPT stage is much more 'agressive' that the HPC stages, since the energy harnessed by the HPT equals the work done by the HPCs plus the losses. Commented Dec 12, 2022 at 1:00

First of all, let's begin with talking about axial compressors and axial turbines1). The short answer is that in both turbines and compressors, the blades are very much streamlined, just the flow regime is different (you can see e.g. the curvature & blade twist in the picture in the post Where can I find detailed dimensions of an aircraft engine compressor blade?)

Compressors

• Low stage load: In a compressor, the problem is that pressure increases in flow direction, and that makes it very much more susceptible to flow detachment around the airfoil, which would lead to a stalling airfoil and subsequently to compressor stall. This limits the pressure ratio achievable per compressor stage, and hence leads to small turning.For the same reason, the target is to have the least flow obstruction possible to minimize flow acceleration (on the suction side).

• Low flow obstruction: Additionally, less flow obstruction means more effective flow area and hence less throttling - more mass flow for a given size of the compressor (or a smaller compressor for a given design mass flow).

Both effects together lead to thin blades with low flow turning per blade (low stage load), and lots of compressor stages for the full compression ratio.

Turbines

• High stage pressure ratio: In turbines stall is no problem because the pressure decreases along flow direction, so pressure ratios per stage can be high. Turbine stage pressure ratios are usually only limited to "below critical pressure ratio", in order to avoid high losses resulting from supersonic flow.

• High flow turning is hence possible and advantageous, because you want high circumferential flow velocity (see Euler turbine equation) for high power per stage.

• Blade thickness: Since the stagnation point on the leading edge shifts with changing velocity triangles, a large leading edge radius makes the blade better adapted to wide range of mass flows. Furthermore, a row of turbine blades is acting as nozzles to convert the pressure upstream to velocity downstream, so some obstruction/thickness is required.

so .. turbine blades end up getting thicker.

The load difference between compressor stages and turbine stages can also be seen that gas turbines have about 4x more compressor stages than turbine stages (eg GE 9HA: 14 compressor stages & 4 turbine stages)

While these are basic aerodynamic considerations, actual blade design is obviously becoming more of a trade-off, with mechanical properties, cooling design, and last not least manufacturability and associated manufacturing cost.

For more theory.. my favorite book on these topics is "Gas Turbine Theory" by Saravanamuttoo, Rogers, Cohen, Straznicky, and Nix.

1) For radial compressors & turbines the points are basically still valid, although less pronounced. In applications like automotive turbo chargers, cheap manufacturing becomes a significant driver compared to e.g. aerodynamic efficiency.