Images Constructed from Computed Flowfields

A method for constructing interferograms, schlieren, and shadowgraphs from ideal- and real-gas, two- and three-dimensional computed flowfields is described. The computational grids can be structured or unstructured, and multiple grids are an option. The constructed images are compared with experimental images for several types of flow, including a ramp, a blunt body, a nozzle, and a reacting flow. The constructed images simulate the features observed in the experimental images. They are sensitive to errors in the flowfield solutions and can be used to identify solution errors. In addition, techniques for obtaining phase shifts from experimental finite fringe interferograms and for removing experimentally induced phase-shift errors are discussed. Both the constructed images and calculated phase shifts can be used for validation of computational fluid dynamics (CFD) codes. OR decades experimental interferograms, schlieren, and shad- owgraphs have been used for quantitative and qualitative flow- field studies. These three images are created by passing light through the flowfield, and the recorded intensity patterns are func- tions of the phase shift and angular deflection of the light. In infinite and finite fringe interferograms, the recorded inten- sity patterns (fringes) are caused by phase shifts (optical path length differences). These phase shifts result from variations in the flowfield density and are proportional to path integrals of the refractive index. The path of integration is the path that the light follows through the flowfield. For two-dimensional and axisymmetric flowfields, point infor- mation can be extracted from interferograms and compared with computational results. The first step in extracting this information is to calculate the phase shifts from the interferogram's fringe pat- terns. These phase shifts can be obtained from either infinite or finite fringe interferograms. However, in flowfield regions where there are only small changes in the density and, hence, fractions of fringe shifts, calculating the phase shifts from finite fringe inter- ferograms will give more accurate results. Several methods for calculating the phase shifts from finite fringe interferograms exist. These methods involve either tracing individual fringes,1'2 fitting sinusoidal functions to intensity varia- tions in a single interferogram,3 or using multiple interferograms and phase-stepping techniques.4 After the phase shifts are found, a transformation is applied, and the refractive index (as well as den- sity for nonreacting flows) at every point in the flowfield is obtained. This point information can then be compared with flow- field solutions. For three-dimensional flows, the transformation from the exper- imental phase shifts to point information cannot be made, and other methods of comparison must be used. For example, Strike et al.5 presented theoretical interferograms over 15 years ago, Wat- kins6 used path-averaged density contours to compare flowfield solutions with experimental infinite fringe interferograms, and Havener and Obergefell7 tracked individual fringes through flow- field solutions and compared these results with experimental finite fringe interferograms. These methods do allow for comparison of computed and experimental flowfields but not necessarily on a one-to-one basis. A graphics package that was developed by Tamura and Fujii8 and is available in Japan does have the capabil-