An Examination of Unsteady Flow Predictions for the Chemical Oxygen-Iodine Laser

* Member, AIAA. † Senior member, AIAA. Introduction Theoretical models for chemical lasers depend on a variety of assumptions and empirical data to provide closure and simplify the computationally expensive solution of the governing equations. Among the various assumptions and empirical data built into models for chemical lasers are two assumptions that have direct bearing upon the predicted flow structure: steadiness in the time domain and geometric similarity of the physical domain. Steadiness in the time domain implies that no fluctuations in the flow structure occur due to the amplification of finite disturbances by flow instabilities, and correspondingly that temporal variations of laser gain and power are not large. Geometric similarity of the physical domain, or laser hardware, means that the domain may be reduced to geometrically similar units, or ‘unit-cells’ that contain the essential physics of the large domain and that these physics are identical and symmetric about boundaries separating these units. The two assumptions are related in the sense that geometric similarity may be removed by the presence of flow unsteadiness. An example is a cylinder in crossflow at Reynolds numbers below 280, for which the flow is two-dimensional. An infinite circular cylinder placed in a uniform, steady flow normal to the axis of the cylinder is symmetric about a plane parallel to the flow splitting the circular cross section of the cylinder. However, instabilities in the flow within the wake of the cylinder cause the development of a Karman vortex street, producing spatial and temporal fluctuations in the flow properties about the axis of symmetry. Whereas a time average of the flow at a time scale much greater than those of the fluctuations will be symmetric, samples taken at the time scale of the fluctuations are decidedly nonsymmetric, breaking down the geometric similarity argument. Steady-state 3-D reacting flow Navier-Stokes simulations of chemical oxygen-iodine laser (COIL) flowfields employing unit-cell approximations have been successfully employed by a number of researchers to predict laser gain and laser power and guide the development of laser hardware. COIL simulation provides a good example of the use of these approximations, since COIL flowfields combine complex physics potentially sensitive to the assumptions with geometrically complex hardware. COIL reactant mixing nozzles commonly use transverse jet injection of one of the reactants as a mixing mechanism, with geometric similarity existing in the array of injector orifices. The computational cost of the complex physical models dictates that some reduction in the modeled physical domain be made. Madden and Miller utilized a 3-D, steady-state, unit-cell Navier-Stokes model to predict laser gains at a variety of flow conditions to an accuracy within the error bars of the experiment data. Buggeln et al and Masuda et al have used a steady-state, unit-cell 3-D Navier-Stokes model coupled to a power extraction model to predict laser power and laser gain in efforts to validate and guide hardware development. Thus, it can be safely stated that the steady-state, unit-cell approach is not without merit. Fluid dynamics experiments for jets issuing transverse to a primary flow, known in the literature as the ‘jet in crossflow,’ provide sufficient reason to suspect that the steady-state assumption used in COIL models is not valid. Investigations by Moussa et al, Coelho and Hunt, Fric and Roshko, Blanchard et al, Rivero et al, and Camussi et al in composite provide a picture of the jet in crossflow that is anything but steady. Throughout the Reynolds number range, the jet in crossflow is characterized by a variety of structures that are sources or potential sources for unsteadiness including horseshoe vortices associated with the primary flow boundary layer wrapping around the base of the jet; the counter rotating pair of vortices entrained in the sides of the jet flow that result from the action of shear forces in the primary flow/jet flow interface; jet shear layer type instabilities that occur in 34th AIAA Plasmadynamics and Lasers Conference 23-26 June 2003, Orlando, Florida AIAA 2003-4309