Symmetrical flow past a uniformly accelerated circular cylinder

Abstract

The flow normal to an infinite circular cylinder which is uniformly accelerated from rest in a viscous fluid is considered. The flow is assumed to remain symmetrical about the direction of motion of the cylinder. Two types of solution are presented. In the first an expansion in powers of the time from the start of the motion is given which extends the results of boundary-layer theory by taking into account corrections for finite Reynolds numbers. Physical properties of the flow for small times and finite but large Reynolds numbers are calculated from this expansion. In the second method of solution the Navier-Stokes equations are integrated by an accurate procedure which is a logical extension of the solution in powers of the time. Results are obtained forR²= 97·5, 5850, 122 × 10³and ∞, whereRis the Reynolds number. This is defined asR= 2a(ab)^½/v, whereais the radius of the cylinder,bthe uniform acceleration andvthe kinematic viscosity of the fluid. The methods are in good agreement for small times.The numerical method of integration has been carried to moderate times and various flow properties have been calculated. The growth of the length of the separated wake behind the cylinder forR²= 97·5, 5850 and 122 × 10³is compared with the results of recent experimental measurements. The agreement is only moderate forR²= 97·5 but it improves greatly asRincreases. The numerical integrations were continued in each case until the implicit method of integration failed to converge, which terminated the procedure. A secondary vortex appeared on the surface of the cylinder for the caseR²= 122 × 10³.