The Reynolds number is varied from 78000 to 3900000 (1 m/s to 50 m/s). It is found that, for a parachute without a vent at the top, as the Reynolds number is increased from 78000 to 800000, the drag coefficient is decreased from about 2.5 to 1.4, and then as the Reynolds number is increased to 1500000, the drag coefficient increased to about 1.62 and it stayed constant for higher Reynolds number up to 3900000.
The Reynolds number is affected by the velocity of the parachute, but also by its scale.
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Measured Drag Coefficients for Small Test Parachutes
The Cd obtained from tests are higher than for those for full-scale parachutes
As an example: flat circular, Cd of 1.3 for small scale, and 0.78 for full scale.
Perhaps we can say that the drag coefficient decreases when the speed increases, but also when the scale increases, up to a point of stabilization.