Transient response of a compressible fluid in a rapidly rotating circular pipe

The transient adjustment process of a compressible fluid in a rapidly rotat ing pipe is studied. The system Ekman number E is small, and the assumption s of small Mach number and the heavy-gas limit (gamma = 1.0) are invoked. F luid motion is generated by imposing a step-change perturbation in the temp erature at the pipe wall T-w. Comprehensive analytical solutions are obtain ed by deploying the matched asymptotic technique with proper timescales O(E -1/2) and O(E-1). These analytical solutions are shown to be consistent wit h corresponding full numerical solutions. The detailed profiles of major va riables are delineated, and evolution of velocity and temperature fields is portrayed. At moderate times, the entire flow field can be divided into tw o regions. In the inner inviscid region, thermo-acoustic compression takes place, and the process is isothermal-isentropic with the angular momentum b eing conserved. In the outer viscous region, diffusion of angular momentum occurs. The principal dynamic mechanisms are discussed, and physical ration alizations are offered. The essential differences between the responses of a compressible and an incompressible fluid are highlighted. The issue of stability of the analytically obtained flow is addressed by un dertaking a formal stability analysis. It is illustrated that, within the r ange of parameters of present concern, the flow is stable when epsilon simi lar to O(E).