Mark E. Braaten

A STUDY OF RECIRCULATING FLOW COMPUTATION USING BODY-FITTED COORDINATES: CONSISTENCY ASPECTS AND MESH SKEWNESS

A study of the computation of recirculating flows using body-fitted coordinates has been conducted with a numerical algorithm developed previously. Both the consistent treatment of the continuity equation and the effects of the grid skewness on the calculated flow field have been investigated. A more consilient method has been developed that formally satisfies the conservation laws more closely, allowing the mass residual to be driven to lower levels on highly irregular grids. The new method can also be more effective in numerically damping out disturbances in the flow field as the solution progresses. Since the computed flow fields arc found to be quite insensitive to the final level of the residuals, the residuals are not a good indicator of the level of convergence; the kinetic energy of the flow field serves as a useful alternative. It is found that the effects of the excessive local mesh skewness on the overall ac~ curacy of the calculated solution are quite tolerable. This finding demonstrates the d...

Computation of Flow in a Gas Turbine Combustor

Abstract A methodology for computing steady turbulent combusting flow in combustors of complex shape is presented. Included is discussion of fully- or partially-equilibrated chemical kinetic models, the interaction of turbulence and combustion, grid systems, discretization operators and solution procedures for recirculating flows. Examples that demonstrate the influence of these issues are reviewed. A package of three-dimensional codes for grid generation and flow analysis-developed in the course of these studies-is applied to the flow in a sector of a modern annular gas-turbine combustor. Results are compared with available data. The study demonstrates the utility of modern computational methods and indicates directions for future work

Three-dimensional unstructured adaptive multigrid scheme for the Navier-Stokes equations

A solution adaptive multigrid scheme for solving the three-dimensional Navier-Stokes equations on unstructured meshes is presented. The algorithm solves the equations on a fully unstructured mesh of tetrahedral elements, using a multigrid time-marching scheme. The initial unstructured mesh is successively refined based on gradients in the flow solution, with the multigrid levels being determined by the refinement procedure. Important issues related to solving viscous flows on unstructured meshes are discussed. These include calculation of the viscous stress terms in a manner that prevents wiggles, calculation of the time steps to include both inviscid and viscous effects, numerical smoothing considerations, minimization of computer storage requirements, and implementation of the k-e turbulence model. Solutions are presented for several examples of industrial importance that illustrate the potential of the method, including transonic flow about an aircraft engine nacelle, and in both rotating and nonrotating turbomachinery passages.

Semi-structured mesh generation for 3D Navier-Stokes calculations

In the current work a method which builds layers of highly stretched prismatic cells on an existing unstructured surface triangulation is described. The outer surface of this inflated triangulation provides a natural starting point for the advancing front algorithm used to fill the interior with tetrahedra. Care is taken to limit the possibility of a crossed-over mesh in concave geometrical regions. If the mesh does cross over then the offending cells are removed.

A Comparison of Advanced Numerical Techniques to Model Transient Flow in Turbomachinery Blade Rows

Computational predictions of the transient flow in multiple blade row turbomachinery configurations are considered. For cases with unequal numbers of blades/vanes in adjacent rows (“unequal pitch”) a computation over multiple passages is required to ensure that simple periodic boundary conditions can be applied. For typical geometries, a time accurate solution requires computation over a significant portion of the wheel. A number of methods are now available that address the issue of unequal pitch while significantly reducing the required computation time. Considered here are a family of related methods (“Transformation Methods”) which transform the equations, the solution or the boundary conditions in a manner that appropriately recognizes the periodicity of the flow, yet do not require solution of all or a large number of the blades in a given row. This paper will concentrate on comparing and contrasting these numerical treatments. The first method, known as “Profile Transformation”, overcomes the unequal pitch problem by simply scaling the flow profile that is communicated between neighboring blade rows, yet maintains the correct blade geometry and pitch ratio. The next method, known as the “Fourier Transformation” method applies phase shifted boundary conditions. To avoid storing the time history on the periodic boundary, a Fourier series method is used to store information at the blade passing frequency (BPF) and its harmonics. In the final method, a pitch-wise time transformation is performed that ensures that the boundary is truly periodic in the transformed space. This method is referred to as “Time Transformation”. The three methods have recently been added to a commercially-available CFD solver which is pressure based and implicit in formulation. The results are compared and contrasted on two turbine cases of engineering significance: a high pressure power turbine stage and a low pressure aircraft engine turbine stage. The relative convergence rates and solution times are examined together with the effect of non blade passing frequencies in the flow field. Transient solution times are compared with more conventional steady stage analyses, and in addition detailed flow physics such as boundary layer transition location are examined and reported.Copyright

Study of three-dimensional gas-turbine combustor flows

Abstract Both computational and experimental results are presented for studying the three-dimensional flow in an annular gas turbine combustor. The computational approach attempts to strike a reasonable balance to handle the competing aspects of the complicated physical and chemical interactions of the flow, and the requirements in resolving the three-dimensional geometrical constraints of the combustor contours, film cooling slots, and circular dilution holes. The algorithm employs non-orthogonal curvilinear coordinates, second-order accurate discretizations, multigrid iterative solution procedure, the standard k-e turbulence model, and a combustion model comprising of an assumed probability density function and the conserved scalar variable formulation. To assess the performance of the numerical algorithm, three different annular combustor flows with in-house experimental measurements are investigated. Overall, it is found that good theory/data agreement of the characteristic temperature pattern in the exit plane can be obtained. The influence of changing the dilution hole arrangements on the combustor performance is well predicted. The complicated mixing process can be better understood with more detailed information supplied by the numerical simulation. It is concluded that for the normal operating condition where the physical process is likely to be dominant, the performance of a gas turbine combustor can be predicted by the present methodology.

Adaptive Unstructured 2D Navier-Stokes Solutions on Mixed Quadrilateral/Triangular Meshes

This paper presents a solution adaptive scheme for solving the Navier-Stokes equations on an unstructured mixed grid of triangles and quadrilaterals. The solution procedure uses an explicit Runge-Kutta finite volume time marching scheme with an adaptive blend of second and fourth order smoothing. The governing equations are solved in a 2D, axisymmetric or quasi-3D form.In viscous regions quadrilateral elements are used to facilitate the one dimensional refinement required for the efficient resolution of boundary layers and wakes. The effect of turbulence is incorporated through using either a Baldwin-Lomax or k-e turbulence model.Solutions are presented for several examples that illustrate the capability of the algorithm to predict viscous phenomena accurately. The examples are a transonic turbine, a nozzle and a combustor diffuser.© 1993 ASME

Application of the SAS Turbulence Model to Buoyancy Driven Cavity Flows

The SST-SAS model has been applied to compute variable-density flow and heat transfer in cavities subjected to intensive rotation. To validate the model, a benchmark test case was simulated first and numerical solutions were compared with the measurements at different mass flow rates and rotation rates. A fairly good agreement with the experiment is demonstrated compared with the characteristic flow features observed in the experiments (e.g., two counter-rotating vortices of global circulation and a radial arm flow) as well as for the trends in disk heat transfer. This justified the application of the model to a rotor cavity of a real aircraft engine. The simulations performed indicate that the SST-SAS model captures the large-scale vortical structures developing in the cavity and predicts measured temperature difference between the cavity inlet and outlet within the experimental uncertainty limits. For both considered flows, a grid sensitivity study has been performed confirming a sufficient accuracy of the numerical solutions obtained on the baseline grids.Copyright

Experimental and Computational Investigation of Heat Transfer Effectiveness and Pressure Distribution of a Shrouded Blade Tip Section

An experimental and computational investigation was conducted to study the detailed distribution of heat transfer effectiveness and pressure on an attached tip-shroud of a turbine blade. Temperatures and pressures were measured on the airfoil-side and gap-side surfaces of the shrouded tip in a three-airfoil stationary cascade. The instrumented center airfoil and the two slave airfoils modeled the aerodynamic tip section of a blade and have the capability to vary tip clearance. The experiments were run at gaps varying of 0.25% to 1.67% of blade span and at an airfoil exit Reynolds number of 1.26×106 and Mach number of 0.95. The effect of coolant flow through the radial-cooled airfoil was also studied. The experimental results are compared with a computational model using the commercially available code, CFX. This unique study presents the influence of gap and coolant flow on the pressure distribution and heat transfer effectiveness of an attached tip-shroud surface.Copyright

Combustor Flow Computations in General Coordinates with a Multigrid Method

. -A computational approach has been developed and applied to calculate the single phase combusting turbulent flowfields. The approach attempts to strike a reasonable balance to handle two competing aspects of the modeling work, namely, the complicated physical and chemical interactions of the flow, and the requirements in resolving the threedimensional geometrical constraints of the combustor contours, film cooling slots, and circular dilution holes. The algorithm employs the non-orthogonal curvilinear coordinates, the second-order accurate discretizations, a multigrid iterative solution procedure, the standard k-E turbulence model, and a combustion model comprising of an assumed probability density function and the conserved scalar variable formulation. This paper gives an account of the overall computational approach, including recent advances in the solution procedure of the coupled pressure and velocity variables, the 3-D grid generation algorithm, 2-D adaptive grid method applied to recirculating turbulent reacting flows, and theory/data assessments for 3-D combusting flows in a modern annular gas-turbine combustor. Such a numerical approach can be useful in aiding combustor design. Two of the significant ways in which the performance level of aircraft turbine engine have been improved are by use of higher pressure ratio compressors and higher turbine inlet temperatures. While these approaches have the potential of improving the engine performance, they have also resulted in an increasingly hostile environment for the engine combustor and turbine components [I]. The rapidly escalating cost of cut-and-try component development testing efforts directed towards improving hot section durability and aerothermal performance has necessitiated the development o f sophisticated and more fundamentally based combustor analysis methods. This has included the development of turbulent reacting flow models and suitable numerical algorithms, as assessed in Ref. [2]. Recent rapid advances in computer technology have permitted the extension of these computational models to fully 3-D elliptic form suitable for detailed analytical simulation of the internal aerothermal flowfield of conventional