![]() At Mach numbers much less than 1.0 ( 0.1 or so), compressibility effects are negligible and the variation of the gas density with pressure can safely be ignored in your flow modeling. When the Mach number is less than 1.0, the flow is termed subsonic. Here, c is the speed of sound in the gas. Mach number and speed of sound: Relationship between static and stagnation conditions: Compressible flows can be characterized by the value of the Mach number. (See Section 9.4 for information about modeling axisymmetric swirl.) (3) Is the divergence of velocity. (2) Axial conservation of momentum (3) Radial conservation of momentum, where Vz is the swirl velocity. Mass conservation for compressible flow: Momentum balance, axial: Momentum balance, radial: For 2D axisymmetric geometries, (1) the conservation of mass equation where x is the axial coordinate, r is the radial coordinate, Vx is the axial velocity, and Vr is the radial velocity. …and sensible enthalpy for ideal gasses:ġ2 Governing Equations in Cylindrical Coordinates (2D) Sensible enthalpy h is defined for ideal gases as species j and where Tref is K. Sh includes the heat of chemical reaction, and any other volumetric heat sources you have defined. The first three terms on the right-hand side represent energy transfer due to conduction, species diffusion, and viscous dissipation, respectively. (1) FLUENT solves the energy equation in the following form above where Keff = K + Kt is the effective conductivity (Kt is the turbulent thermal conductivity defined according to the turbulence model being used), and Jj is the diffusion flux of species j. Viscous dissipation terms become important in high-Mach-number flows. …where: The energy equation solved by FLUENT correctly incorporates the coupling between the flow velocity and the static temperature, and should be active for compressible flows. …stress tensor:ġ1 Governing Equations Energy conservation: …where: (3) The stress tensor tau where mu is the molecular viscosity, I is the unit tensor, and the second term on the right hand side is the effect of volume dilation. F also contains other model-dependent source terms such as porous-media and user-defined sources. (2) Conservation of momentum in an inertial (non-accelerating) reference frame is where P is the static pressure, tau is the stress tensor (described below), and rhog and F are the gravitational body force and external body forces (e.g., that arise from interaction with the dispersed phase), respectively. The source Sm is the mass added to the continuous phase from the dispersed second phase (e.g., due to vaporization of liquid droplets) and any user-defined sources. Momentum balance: (1) General form of the mass conservation equation. Reynolds-Averaged N-S Turbulence Model Discretization Boundary Conditions Solver Methodġ0 Governing Equations1 Mass conservation: Momentum balance: ĩ Numerical Method Governing Equations Compressible Flow Equations Sharp corners on knife create singularities in flowfield Files you add to the package can include just about anything you want to have along-they don't have to be part of the presentation. Flow is highly compressible at the knife tip and essentially incompressible in the balance of the flow. ![]() Below: (Non)dimensional parameter characterizing mass flow rate thru seal.Ħ Introduction (cont.) Consequences of seal design error (grossly simplified): Underprediction lower thrust/efficiency Overprediction downstream overheatingħ Objective Develop CFD model of a typical (single) knife seal for which test data exists compare results and attempt to infer applicability of CFD to knife seal design.įlow accelerates nearly 2 orders of magnitude in one knife height putting considerable demands on the solver and on the grid, particularly in the region of the knife tip. Right: Knife seal geometry and parameters assumed in typical seal design codes. Results are valid inasmuch as new design is similar to tests. Semi-empirical codes interpolate/extrapolate test data. Peters in Partial Fulfillment of the Degree of Master of Science April 27, 2006Ģ Note Numerical results, comparisons with test data, conclusions, and other information considered proprietary and/or sensitive have been removed from this presentation.ģ Outline Introduction Objective Numerical Method Computational Gridsĭescription of Test Results and Validation Additional Studies Conclusions Acknowledgements ReferencesĤ Introduction Knife/labyrinth seals are non-contact air seals used between rotating and non-rotating components where (air) leakage mass flow must be controlled or minimized.ĥ Introduction (cont.) Typical design practice: Lambert, MS., Rolls-Royce STILL NEED Discretization Finite volume formulation A Presentation to the Faculty of Purdue School of E&T, IUPUI by Joshua M. 1 A Study of the Applicability of CFD to Knife Seal Design in the Gas Turbine Industry
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