Improved Accuracy of Computational Fluid Dynamics Calculations

Grid adaptation technique improves the accuracy of engineering predictions regarding air vehicle performance.

December 1, 2006

Understanding how air flows over the surfaces of an air vehicle can help AFRL designers maximize the vehicle's performance and minimize its cost. AFRL scientists recently developed a tool that improves the accuracy of airflow simulations that result from computational fluid dynamics (CFD) calculations. As part of a Small Business Innovation Research effort, AFRL collaborated with Combustion Research and Flow Technology (CRAFT), Inc., to develop the tool for use with unstructured CFD programs. The new tool uses the solver's initial solution to determine where grid points should be added or removed within the CFD mesh, a process which then improves the solver's solution in a second—and any subsequent—iteration. This enhanced accuracy improves AFRL's ability to support the warfighter with lower-cost, higher-value designs.

A comparison of an initial CFD grid and corresponding Mach number predictions, along with the predictions from a subsequent mesh adaptation

CFD programs solve mathematical equations to predict what will happen when a fluid, such as air, flows over or through a structure. These programs solve the equations at each point of a three-dimensional grid of data points— the CFD mesh—located on and around the structure. This grid can be either structured or unstructured. To visualize a structured grid, imagine the grid formed by the lines on a sheet of (Cartesian) graph paper, molded along one edge to conform to the structure, and extending into the third dimension. Incorporating additional sheets of graph paper in this manner, at the same time joining the grid lines between those sheets, produces multiple blocks that cover the entire structure and the space surrounding it. To envision an unstructured grid, first imagine points placed on the structure and throughout the space around it, and then picture lines drawn between these points to form various geometric shapes (e.g., tetrahedrons or prisms). The points at which the CFD program solves the equations can be at the line intersections (for the structured grid) or at the corners of geometric shapes (for the unstructured grid). Alternative solution points may be at the centroids—either of the geometric shapes formed in an unstructured grid or of the hexahedrons formed by a structured grid's lines. While the regularity of a structured grid's pattern simplifies the process of solving the mathematical equations to a predetermined level of accuracy, the corresponding CFD-based mesh development requires an immense amount of time and expertise to design a complex model's optimal block structure. Conversely, the lack of geometric restrictions imposed upon an unstructured grid enables scientists to automate their creation more easily than for structured grids. For example, scientists can generate an unstructured grid for a complex vehicle geometry in days or weeks, versus the weeks or months needed for a comparable structured grid.

Regardless of whether a grid is unstructured or structured, the initial placement of points in the grid is not necessarily optimal, and therefore, the CFD solution may not very accurately model physical reality. AFRL's new CFD tool addresses this shortcoming by using the initial CFD solution to determine where grid points should be located, an approach that improves the accuracy of subsequently executed solutions. To minimize the time required to modify the location of grid points, as well as enable the processing of arbitrarily large problems, the AFRL/CRAFT team focused its enhancement efforts on making the adaptation process run in parallel on multiple processors. To demonstrate the new capability, the scientists modeled a gaseous hydrogen valve with the plug set at a 52% open position (see figure on previous page). The pressure drop across the valve was 2600 psi, a drop that produces an underexpanded, annular jet at the nozzle throat, between the plug and the valve seat. The complex flowpath leads to formation of a large secondary flow and highly turbulent region in the exhaust duct downstream of the valve seat. The figure, which depicts a cross section of the CFD mesh and the resulting CFD Mach number contours, illustrates the improvement in jet definition with mesh adaptation. On the original mesh (image a), these structures are diffused and even exhibit some unsteady character; after two adaptations (image b), five distinct shock cells (displayed in red) are observable in the annular jet.Regardless of whether a grid is unstructured or structured, the initial placement of points in the grid is not necessarily optimal, and therefore, the CFD solution may not very accurately model physical reality. AFRL's new CFD tool addresses this shortcoming by using the initial CFD solution to determine where grid points should be located, an approach that improves the accuracy of subsequently executed solutions. To minimize the time required to modify the location of grid points, as well as enable the processing of arbitrarily large problems, the AFRL/CRAFT team focused its enhancement efforts on making the adaptation process run in parallel on multiple processors. To demonstrate the new capability, the scientists modeled a gaseous hydrogen valve with the plug set at a 52% open position (see figure on previous page). The pressure drop across the valve was 2600 psi, a drop that produces an underexpanded, annular jet at the nozzle throat, between the plug and the valve seat. The complex flowpath leads to formation of a large secondary flow and highly turbulent region in the exhaust duct downstream of the valve seat. The figure, which depicts a cross section of the CFD mesh and the resulting CFD Mach number contours, illustrates the improvement in jet definition with mesh adaptation. On the original mesh (image a), these structures are diffused and even exhibit some unsteady character; after two adaptations (image b), five distinct shock cells (displayed in red) are observable in the annular jet.

As a result of this enhanced capability, scientists can produce more accurate predictions of air vehicle design performance and reduce design options prior to initiating an expensive build and test process. In addition, engineers can use the same technology to assess existing air vehicles, complementing wind tunnel test efforts designed to improve vehicle performance.

Ms. Melissa Withrow (Azimuth Corporation) and Dr. Matt Grismer, of the Air Force Research Laborator y's Air Vehicles Directorate, wrote this article. For more information, visit http://www.afrl.af.mil/techconn_index.asp . Reference document VA-H-06-04.