Direct Drive Valve Model for Use as an Acoustic Source in a Network Model

Abstract

Direct Drive Valves (DDVs) can be used as acoustic actuators in duct systems when requirements on mechanical or thermal robustness are high, e.g., for the active control of aerodynamic or combustion instabilities. This paper presents a model of a DDV that is used as an active element in an acoustic network model. In acoustic network modelling tools, acoustic sources are often implemented as simple velocity or mass flow boundary conditions. In practice, however, DDVs are not necessarily situated at the boundary of the system and the throughflow depends on the fluctuating pressure drop over the valve. This paper presents an acoustically compact model, based on mass conservation and a time-varying hydraulic resistance. The resistance depends on the fluctuating valve opening. The results are compared to the experiment in terms of acoustic wave transfer function. NOMENCLATURE A Area m 2 C d Discharge coefficient [−] D Transmission coefficient of an acoustic delay [−] L Length [m] M Mach number [−] Q Gas flow rate in norm litre per minute [NLPM] R Reflection coefficient [−] R sys Combined reflection coefficient of an acoustic system [−] Re Reynolds number [−] S Source coefficient [(m/s) /%] S sys Combined source coefficient of an acoustic system [(m/s) /%] T Transmission coefficient [−] V Volume m 3 c Speed of sound [m/s] f Downstream characteristic wave amplitude [m/s] g Upstream characteristic wave amplitude [m/s] p Pressure [Pa] p 0 Total (stagnation) pressure [Pa] r Radius [m] t Time [s] u Velocity [m/s] x, y, z Coordinates [m] x sp Valve (spool) opening [%] ζ Hydraulic loss coefficient [−] ρ Density kg/m 3 • Time-averaged quantity • Perturbation on time-averaged quantitẏ • Rate of change / flow[•/s]