Model-Based Predictive Control System in a Transonic Aerodynamic Test Facility

Mathematical Modeling of Wind-Tunnel Thermal Behavior

“…(8) and (9), k i are the total pressure loss factors in the n sections of the wind tunnel defined by the mechanical energy or "head loss" equation:…”

“…M ATHEMATICAL models for the behavior of wind tunnels and test facilities have been developed for a variety of reasons [1][2][3][4][5][6][7][8]. For example, in [1], a mathematical model of a new wind tunnel was developed to ensure that the facility would achieve its target test envelope.…”

“…Alternatively, basic equations describing the facility behavior can be used to provide feedforward predictions of the facility response to control inputs [6]. In more advanced applications, mathematical models are used to not only facilitate changes in tunnel operating conditions between steady-state set points, but also to maintain close control over the way in which the tunnel transitions between those set points [7,8]. This kind of "fly the mission" control could be used to simulate transient flight conditions, such as would occur, for example, during simulation of a pitch-up maneuver by the test model.…”

“…Mathematical models are typically developed from basic fluidmechanic equations; however, the fundamental purpose of the models described in [1][2][3][4][5][6][7][8] is to provide rapid time-accurate predictions for the response of the full wind tunnel to changes in test conditions or control settings. As such, approximations or simplifications to the basic equations are incorporated to handle the large physical scale of the problem with satisfactory computational expense.…”

“…These approximations typically introduce empirical parameters into the model that must themselves be simulated over the operating envelope of the wind tunnel to ensure the accuracy of the overall model. Examples of these parameters include total pressure loss factors, heat transfer coefficients, or valve flow coefficients [8]. The behavior of these parameters can vary in complicated ways with the local Reynolds number or with other factors, making it difficult to accurately predict their values using theoretical or computational methods.…”