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**A Study of the Applicability of CFD to Knife Seal Design in the Gas Turbine Industry**

Principal Advisors: Dr. Hasan Akay, IUPUI P. Chakka, PhD., Rolls-Royce T. 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. Peters in Partial Fulfillment of the Degree of Master of Science April 27, 2006

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Note Numerical results, comparisons with test data, conclusions, and other information considered proprietary and/or sensitive have been removed from this presentation.

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**Outline Introduction Objective Numerical Method Computational Grids**

Description of Test Results and Validation Additional Studies Conclusions Acknowledgements References

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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.

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**Introduction (cont.) Typical design practice:**

Semi-empirical codes; interpolate/extrapolate test data. Results are valid inasmuch as new design is similar to tests. Right: Knife seal geometry and parameters assumed in typical seal design codes. Below: (Non)dimensional parameter characterizing mass flow rate thru seal.

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Introduction (cont.) Consequences of seal design error (grossly simplified): Underprediction lower thrust/efficiency Overprediction downstream overheating

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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.

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**Expected Computational Challenges**

Flow 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. Flow is highly compressible at the knife tip and essentially incompressible in the balance of the flow. 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. [Note to trainer: Steps—given in either numbered or bulleted lists—are always shown in yellow text.]

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**Numerical Method Governing Equations Compressible Flow Equations**

Reynolds-Averaged N-S Turbulence Model Discretization Boundary Conditions Solver Method

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**Governing Equations1 Mass conservation: Momentum balance:**

Momentum balance: (1) General form of the mass conservation equation. 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. (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. F also contains other model-dependent source terms such as porous-media and user-defined sources. (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. …stress tensor:

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**Governing Equations Energy conservation: …where:**

…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. Viscous dissipation terms become important in high-Mach-number flows. (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. The first three terms on the right-hand side represent energy transfer due to conduction, species diffusion, and viscous dissipation, respectively. Sh includes the heat of chemical reaction, and any other volumetric heat sources you have defined. Sensible enthalpy h is defined for ideal gases as species j and where Tref is K. …and sensible enthalpy for ideal gasses:

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**Governing Equations in Cylindrical Coordinates (2D)**

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. (2) Axial conservation of momentum (3) Radial conservation of momentum, where Vz is the swirl velocity. (See Section 9.4 for information about modeling axisymmetric swirl.) (3) Is the divergence of velocity. …where:

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**Compressible Flow Physics**

Mach number and speed of sound: Relationship between static and stagnation conditions: Compressible flows can be characterized by the value of the Mach number. Here, c is the speed of sound in the gas. Gamma is the ratio of specific heats. When the Mach number is less than 1.0, the flow is termed subsonic. 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. As the Mach number approaches 1.0 (which is referred to as the transonic flow regime), compressibility effects become important. When the Mach number exceeds 1.0, the flow is termed supersonic, and may contain shocks and expansion fans which can impact the flow pattern significantly. (3,4) Compressible flows are typically characterized by the total pressure and total temperature of the flow. For an ideal gas and constant specific heats, these quantities can be related to the static pressure and temperature. These relationships describe the variation of the static pressure and temperature in the flow as the velocity (Mach number) changes under isentropic conditions. For example, given a pressure ratio from inlet to exit (total to static), Equation can be used to estimate the exit Mach number which would exist in a one-dimensional isentropic flow. For air, Equation predicts a choked flow (Mach number of 1.0) at an isentropic pressure ratio, p/po , of This choked flow condition will be established at the point of minimum flow area (e.g., in the throat of a nozzle). In the subsequent area expansion the flow may either accelerate to a supersonic flow in which the pressure will continue to drop, or return to subsonic flow conditions, decelerating with a pressure rise. If a supersonic flow is exposed to an imposed pressure increase, a shock will occur, with a sudden pressure rise and deceleration accomplished across the shock. (5) For compressible flows, the ideal gas law is written in the form above where Pop is the operating pressure, P is the local static pressure relative to the operating pressure, R is the universal gas constant, and M is the molecular weight. The temperature will be computed from the energy equation. Ideal gas law as implemented in FLUENT:

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**Governing Equations Reworked: RANS**

Variables decomposed into mean and fluctuating components: Resulting Reynolds averaged Navier-Stokes equations (interpreted, for compressible flows, as Favre-averaged): In Reynolds averaging, the solution variables in the instantaneous (exact) Navier-Stokes equations are decomposed into the mean (ensemble-averaged or time-averaged) and fluctuating components. For the velocity components where ui_bar and ui’ are the mean and fluctuating velocity components (i=1,2 in 2D planar model). (2) For pressure and other scalar quantities, where phii denotes a scalar such as pressure, energy, or species concentration. Substituting expressions of this form for the flow variables into the instantaneous conservation of mass and momentum equations and taking a time (or ensemble) average (and dropping the overbar on the mean velocity, u_bar) yields the ensemble-averaged momentum equations. They can be written in Cartesian tensor form as: (3,4) Reynolds-averaged Navier-Stokes (RANS) equations. They have the same general form as the instantaneous Navier-Stokes equations, with the velocities and other solution variables now representing ensemble-averaged (or time-averaged) values. Additional terms now appear that represent the effects of turbulence. These Reynolds stresses, -RhoU’U’, must be modeled in order to close Equation For variable-density flows, Equations and can be interpreted as Favre-averaged Navier-Stokes equations [ 131], with the velocities representing mass-averaged values. As such, Equations and can be applied to density-varying flows.

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**Turbulence Model Spalart-Allmaras (1-Equation): Boussinesq hypothesis:**

The Spalart-Allmaras model is a relatively simple one-equation model that solves a modeled transport equation for the kinematic eddy (turbulent) viscosity. This embodies a relatively new class of one-equation models in which it is not necessary to calculate a length scale related to the local shear layer thickness. The Spalart-Allmaras model was designed specifically for aerospace applications involving wall-bounded flows and has been shown to give good results for boundary layers subjected to adverse pressure gradients. It is also gaining popularity for turbomachinery applications. In its original form, the Spalart-Allmaras model is effectively a low-Reynolds-number model, requiring the viscous-affected region of the boundary layer to be properly resolved. In FLUENT, however, the Spalart-Allmaras model has been implemented to use wall functions when the mesh resolution is not sufficiently fine. This might make it the best choice for relatively crude simulations on coarse meshes where accurate turbulent flow computations are not critical. Furthermore, the near-wall gradients of the transported variable in the model are much smaller than the gradients of the transported variables in the k-e or k-w models. This might make the model less sensitive to numerical error when non-layered meshes are used near walls. See Section for further discussion of numerical error. On a cautionary note, however, the Spalart-Allmaras model is still relatively new, and no claim is made regarding its suitability to all types of complex engineering flows. For instance, it cannot be relied on to predict the decay of homogeneous, isotropic turbulence. Furthermore, one-equation models are often criticized for their inability to rapidly accommodate changes in length scale, such as might be necessary when the flow changes abruptly from a wall-bounded to a free shear flow. (2) The Reynolds-averaged approach to turbulence modeling requires that the Reynolds stresses be appropriately modeled. A common method employs the Boussinesq hypothesis to relate the Reynolds stresses to the mean velocity gradients. The Boussinesq hypothesis is used in the Spalart-Allmaras model (as well as the k-e models and k-w models). The advantage of this approach is the relatively low computational cost associated with the computation of the turbulent viscosity, mut. (mut is the primitive variable in S-A but divided by rho.) In the case of the Spalart-Allmaras model, only one additional transport equation, representing turbulent viscosity, is solved. The disadvantage of the Boussinesq hypothesis as presented is that it assumes mut is an isotropic scalar quantity, which is not strictly true. In many cases, models based on the Boussinesq hypothesis perform very well, and the additional computational expense of the Reynolds stress model (RSM) is not justified. (However, the RSM is clearly superior for situations in which the anisotropy of turbulence has a dominant effect on the mean flow. Such cases include highly swirling flows and stress-driven secondary flows.)

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**Discretization A conservation equation for an arbitrary CV:**

Discretized: Discretization FLUENT uses a control-volume-based technique to convert the governing equations to algebraic equations that can be solved numerically. This control volume technique consists of integrating the governing equations about each control volume, yielding discrete equations that conserve each quantity on a control-volume basis. Discretization of the governing equations can be illustrated most easily by considering the steady-state conservation equation for transport of a scalar quantity phi. This is demonstrated by the following equation written in integral form for an arbitrary control volume V as in the first eqn, for density rho, velocity vector v, surface area vector A, diffusion coefficient gamma for gradient del(phi) of the transported scalar quantity and source S unit volume. The first equation is applied to each control volume, or cell, in the computational domain. The 2D, triangular cell shown is an example of such a control volume. Discretization of the first Equation on a given cell yields the second equation where N faces enclosing cell, phif is value of phi convected through face f, mass flux rhoAv through the face, area A of face, and del(phi)n is magnitude of phi gradient normal to face. The equations solved by FLUENT take the same general form as the one given above and apply readily to multi-dimensional, unstructured meshes composed of arbitrary polyhedra. Figure is the Control Volume Used to Illustrate Discretization of a Scalar Transport Equation By default, FLUENT stores discrete values of the scalar phi at the cell centers C0 and C1. However, face values phif are required for the convection terms in the 2nd Equation and must be interpolated from the cell center values. This is accomplished using an upwind scheme. Upwinding means that the face value phif is derived from quantities in the cell upstream, or "upwind,'' relative to the direction of the normal velocity vn in 2nd Equation. FLUENT allows you to choose from several upwind schemes: first-order upwind, second-order upwind, power law, and QUICK. These schemes are described in Sections The diffusion terms in 2nd Equation are central-differenced and are always second-order accurate. Linearized Form of the Discrete Equation The discretized scalar transport equation (Equation ) contains the unknown scalar variable at the cell center as well as the unknown values in surrounding neighbor cells. This equation will, in general, be non-linear with respect to these variables. A linearized form of Equation can be written as (3), where the subscript nb refers to neighbor cells, and AP and Anb are the linearized coefficients for phi and phinb. The number of neighbors for each cell depends on the grid topology, but will typically equal the number of faces enclosing the cell (boundary cells being the exception). Similar equations can be written for each cell in the grid. This results in a set of algebraic equations with a sparse coefficient matrix. For scalar equations, FLUENT solves this linear system for the dependent variable phi in each cell using a point implicit (Gauss-Seidel) linear equation solver in conjunction with an algebraic multigrid (AMG) method which is described in Section For example, the x-momentum equation is linearized to produce a system of equations in which velocity u is the unknown. Simultaneous solution of this equation system (using the scalar AMG solver) yields an updated x-velocity field. The source term b is the net flow rate into the cell. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 26.1 Overview of Numerical Schemes FLUENT allows you to choose either of two numerical methods: segregated solver, coupled solver. Using either method, FLUENT will solve the governing integral equations for the conservation of mass and momentum, and (when appropriate) for energy and other scalars such as turbulence and chemical species. In both cases a control-volume-based technique is used that consists of: Division of the domain into discrete control volumes using a computational grid. Integration of the governing equations on the individual control volumes to construct algebraic equations for the discrete dependent variables ("unknowns'') such as velocities, pressure, temperature, and conserved scalars. Linearization of the discretized equations and solution of the resultant linear equation system to yield updated values of the dependent variables. The two numerical methods employ a similar discretization process (finite-volume), but the approach used to linearize and solve the discretized equations is different. Linearized: …where:

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**Segregated Solver Method (FLUENT)**

P*, rhou*, rhov* rho, u , v, P rhou* , rhov* P*, rhou*, rhov* Idea: enforce and iterate on momentum starting with guesses and extract better guesses by mass imbalance. The segregated solver is the solution algorithm previously used by FLUENT 4. Using this approach, the governing equations are solved sequentially (i.e., segregated from one another). Because the governing equations are non-linear (and coupled), several iterations of the solution loop must be performed before a converged solution is obtained. Each iteration consists of the steps illustrated in Figure and outlined below: 1. Fluid properties are updated, based on the current solution. (If the calculation has just begun, the fluid properties will be updated based on the initialized solution.) 2. The u, v, w momentum equations are each solved in turn using current values for pressure and face mass fluxes, in order to update the velocity field. 3. Since the velocities obtained in Step 2 may not satisfy the conservation of mass equation locally, a "Poisson-type'' equation for the pressure correction is derived from the conservation of mass equation and the linearized momentum equations. This pressure correction equation is then solved to obtain the necessary corrections to the pressure and velocity fields and the face mass fluxes such that continuity is satisfied. 4. Where appropriate, equations for scalars such as turbulence, energy, species, and radiation are solved using the previously updated values of the other variables. 6.A check for convergence of the equation set is made. (iterate) In summary, the segregated approach solves for a single variable field (e.g., x-momenum) by considering all cells at the same time. It then solves for the next variable field by again considering all cells at the same time, and so on. There is no explicit option for the segregated solver. …+ T*, v*, …

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**Boundary Conditions Operating Conditions: Pop=14.698psia**

Inlet: Total pressure (gauge; varied to control pressure ratio), total temperature (533R), hydraulic diameter and turbulence intensity (solution-based iterations) Outlet: Static pressure (gauge; fixed at 0 for all models), recirculation total temperature (533R) and modified turbulent viscosity (solution-based iterations) -Think of Pop as the absolute static pressure at a point in the flow where you will define the gauge pressure P to be zero. -Choose a well-posed boundary condition combination that is appropriate for the flow regime. Recall that all inputs for pressure (total or static) must be relative to the operating pressure, and the temperature inputs at inlets should be total (stagnation) temperatures, not static temperatures. -Well-posed inlet and exit boundary conditions for compressible flow: For flow inlets: Pressure inlet: Inlet total temperature and total pressure and, for supersonic inlets, static pressure Mass flow inlet: Inlet mass flow and total temperature For flow exits: Pressure outlet: Exit static pressure (ignored if flow is supersonic at the exit. All the information travels downstream in a supersonic region, hence the pressure at the outlet can be computed by directly extrapolating from the adjacent cell center [ 132]. Therefore, it is not meaningful to use the exit static pressure prescribed in the boundary conditions panel, and the exit static pressure is ignored).

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**Boundary Conditions (cont.)**

Stator (top): No-slip Knife/Disk: No-slip Rotor: No-slip or inviscid (<1% ΔW) Near-wall velocity profile: standard wall functions -Think of Pop as the absolute static pressure at a point in the flow where you will define the gauge pressure P to be zero. -Choose a well-posed boundary condition combination that is appropriate for the flow regime. Recall that all inputs for pressure (total or static) must be relative to the operating pressure, and the temperature inputs at inlets should be total (stagnation) temperatures, not static temperatures. -Well-posed inlet and exit boundary conditions for compressible flow: For flow inlets: Pressure inlet: Inlet total temperature and total pressure and, for supersonic inlets, static pressure Mass flow inlet: Inlet mass flow and total temperature For flow exits: Pressure outlet: Exit static pressure (ignored if flow is supersonic at the exit. All the information travels downstream in a supersonic region, hence the pressure at the outlet can be computed by directly extrapolating from the adjacent cell center [ 132]. Therefore, it is not meaningful to use the exit static pressure prescribed in the boundary conditions panel, and the exit static pressure is ignored).

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**Boundary Conditions (cont.)**

Turbulence intensity at inlet estimated by: Preliminary solutions were run with an estimated value; final solutions were obtained by iterating on density and velocity and updating turbulence intensity. Iterations were performed for modified turbulent viscosity at the outlet. The turbulence intensity, I, is defined as the ratio of the root-mean-square of the velocity fluctuations, u’, to the mean flow velocity, uavg. A turbulence intensity of 1% or less is generally considered low and turbulence intensities greater than 10% are considered high. Ideally, you will have a good estimate of the turbulence intensity at the inlet boundary from external, measured data. For example, if you are simulating a wind-tunnel experiment, the turbulence intensity in the free stream is usually available from the tunnel characteristics. In modern low-turbulence wind tunnels, the free-stream turbulence intensity may be as low as 0.05%. For internal flows, the turbulence intensity at the inlets is totally dependent on the upstream history of the flow. If the flow upstream is under-developed and undisturbed, you can use a low turbulence intensity. If the flow is fully developed, the turbulence intensity may be as high as a few percent. The equation above is for turbulence intensity at the core of a fully-developed duct flow derived from an empirical correlation for pipe flows. At a Reynolds number of 50,000, for example, the turbulence intensity will be 4%, according to this formula. Turbulence Length Scale and Hydraulic Diameter The turbulence length scale, , is a physical quantity related to the size of the large eddies that contain the energy in turbulent flows. In fully-developed duct flows, is restricted by the size of the duct, since the turbulent eddies cannot be larger than the duct. An approximate relationship between and the physical size of the duct is (7.2-2) where is the relevant dimension of the duct. The factor of 0.07 is based on the maximum value of the mixing length in fully-developed turbulent pipe flow, where is the diameter of the pipe. In a channel of non-circular cross-section, you can base on the hydraulic diameter. If the turbulence derives its characteristic length from an obstacle in the flow, such as a perforated plate, it is more appropriate to base the turbulence length scale on the characteristic length of the obstacle rather than on the duct size. It should be noted that the relationship of Equation 7.2-2, which relates a physical dimension ( ) to the turbulence length scale ( ), is not necessarily applicable to all situations. For most cases, however, it is a suitable approximation. For fully-developed internal flows, choose the Intensity and Hydraulic Diameter specification method and specify the hydraulic diameter in the Hydraulic Diameter field.

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Computational Grids

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**“Primary Grid” Characteristics: Quad, 26k cells, 40x50 at knife tip.**

Advantages: Reduced cell count, reduced aspect ratios near knife tip. Disadvantages: Slight increase in skewness near knife tip; non-stream-aligned faces. Below: Domain Left: Zoom on knife

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“Primary Grid” (zoom) Above: Knife tip zoom. Maximum aspect ratio around 5.

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“Secondary Grid” Characteristics: Quad BL, triangle 22k cells, 40x40 at knife tip Advantages: High resolution, locally-refined at knife tip, and extended outlet (hence smoothed outlet flow) improved convergence. Disadvantages: High aspect ratio and high skew in cells near knife tip. High resolution downstream of knife caused trouble for coupled solvers. Below: Computational domain Left: Zoom on center region

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**“Secondary Grid” (zoom)**

Above: Zoom on knife tip. 25% cell count reduction relative to “Primary Grid.” Mach number gradient based grid adaption applied, degrading already-poor convergence characteristics. Adaption not used in results presented.

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Description of Test

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**2D Seal Rig (performed c.1970)**

(Removed. See slide #2, “Notes.”) Left: Labyrinth Seal Test Rig Below: Representative Single Knife Test (Removed. See slide #2, “Notes.”) While sounds and movies in your slide show may work perfectly on your own machine, they might be surprisingly, and frustratingly, absent when you play the presentation from a different computer.

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**(Removed. See slide #2, “Notes.”)**

Rig Instrumentation Below: Labyrinth Seal Test Rig Instrumentation (Removed. See slide #2, “Notes.”) While sounds and movies in your slide show may work perfectly on your own machine, they might be surprisingly, and frustratingly, absent when you play the presentation from a different computer.

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**Results and Validation**

2D Planar Models vs. 2D Planar Test Data Axisymmetric Models vs. Semi-Empirical Codes Representative Residuals, Vectors, and Contour Plots Upstream: shielded iron-constantan (I.C.) thermocouples.

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**FLENT Model vs. Test – 2D Planar**

(Removed. See slide #2, “Notes.”) Seven FLUENT models (planar) run at increasing pressure ratios: mass flow rate (W) in terms of the flow parameter Φ plotted versus pressure ratio. Grid independence check @PR=2.0 using ‘Grid 3.’ While sounds and movies in your slide show may work perfectly on your own machine, they might be surprisingly, and frustratingly, absent when you play the presentation from a different computer.

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**Model vs. Semi-Empirical Codes – Axisymmetric**

(Removed. See slide #2, “Notes.”) Nine FLUENT models (axisymmetric) run at increasing pressure ratios: mass flow rate (W) in terms of the flow parameter Φ plotted versus pressure ratio. Turbulence models compared at PR=3.0 While sounds and movies in your slide show may work perfectly on your own machine, they might be surprisingly, and frustratingly, absent when you play the presentation from a different computer.

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**Model vs. Semi-Empirical Codes – Axisymmetric**

Data from FLUENT (leading to plots). Iterative solution procedure: Density, velocity, and modified turbulent viscosity were obtained in solutions; turbulence intensity and modified turbulent viscosity were input as boundary conditions leading to new solutions and updated boundary conditions... (Removed. See slide #2, “Notes.”) While sounds and movies in your slide show may work perfectly on your own machine, they might be surprisingly, and frustratingly, absent when you play the presentation from a different computer.

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**Typical Residuals and W Convergence at PR=2.00**

Right: Scaled residuals thru 9000 iterations Below: Mass flow rate convergence inlet) thru 9000 iterations Discussion: Sources of convergence trouble and probable fixes. While sounds and movies in your slide show may work perfectly on your own machine, they might be surprisingly, and frustratingly, absent when you play the presentation from a different computer.

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Velocity Vectors While sounds and movies in your slide show may work perfectly on your own machine, they might be surprisingly, and frustratingly, absent when you play the presentation from a different computer.

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**Velocity Vectors (zoom)**

While sounds and movies in your slide show may work perfectly on your own machine, they might be surprisingly, and frustratingly, absent when you play the presentation from a different computer.

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**Mach Number Left: Mach # Contours (nearly converged)**

Below: Mach # plot, inlet (black), outlet (red) While sounds and movies in your slide show may work perfectly on your own machine, they might be surprisingly, and frustratingly, absent when you play the presentation from a different computer.

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Total Temperature U, v, rho, T, P.

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Static Temperature While sounds and movies in your slide show may work perfectly on your own machine, they might be surprisingly, and frustratingly, absent when you play the presentation from a different computer.

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Entropy While sounds and movies in your slide show may work perfectly on your own machine, they might be surprisingly, and frustratingly, absent when you play the presentation from a different computer.

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Enthalpy While sounds and movies in your slide show may work perfectly on your own machine, they might be surprisingly, and frustratingly, absent when you play the presentation from a different computer.

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Internal Energy While sounds and movies in your slide show may work perfectly on your own machine, they might be surprisingly, and frustratingly, absent when you play the presentation from a different computer.

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Total Energy While sounds and movies in your slide show may work perfectly on your own machine, they might be surprisingly, and frustratingly, absent when you play the presentation from a different computer.

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**Total Pressure Above: Ptmin at knife tip: 11.14psia**

While sounds and movies in your slide show may work perfectly on your own machine, they might be surprisingly, and frustratingly, absent when you play the presentation from a different computer. Above: Ptmin at knife tip: 11.14psia Right: Regions of “Pt creation” >.004psi

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Static Pressure While sounds and movies in your slide show may work perfectly on your own machine, they might be surprisingly, and frustratingly, absent when you play the presentation from a different computer.

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**Modified Turbulent Viscosity**

Left: mtv contours Below mtv at inlet and outlet While sounds and movies in your slide show may work perfectly on your own machine, they might be surprisingly, and frustratingly, absent when you play the presentation from a different computer.

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**Wall y+ Right: Wall y+ values along knife (black) and stator (red)**

While sounds and movies in your slide show may work perfectly on your own machine, they might be surprisingly, and frustratingly, absent when you play the presentation from a different computer.

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**Additional Studies Viscous heating impact on W**

Turbulence model impact on W Discretization order impact on W No-slip rotor impact on W Grid impact on W Solver Formulations Parallel speed-up

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**Selected Additional Studies**

Viscous heating impact on flow parameter (PR=2.5): (Removed. See slide #2, “Notes.”) Turbulence model impact on flow parameter (PR=3.0): (Removed. See slide #2, “Notes.”) While sounds and movies in your slide show may work perfectly on your own machine, they might be surprisingly, and frustratingly, absent when you play the presentation from a different computer. No-slip rotor impact on flow parameter (PR=2.0): (Removed. See slide #2, “Notes.”)

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Additional Studies Discretization order impact on flow parameter (PR=2.0): (Removed. See slide #2, “Notes.”) Solver formulations: While sounds and movies in your slide show may work perfectly on your own machine, they might be surprisingly, and frustratingly, absent when you play the presentation from a different computer. (Removed. See slide #2, “Notes.”)

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**(Removed. See slide #2, “Notes.”)**

Additional Studies Grid impact on flow parameter (PR=3.0): (Removed. See slide #2, “Notes.”) Parallel Processing: Two processors: Three processors Three processors after load balancing 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. [Note to trainer: Steps—given in either numbered or bulleted lists—are always shown in yellow text.]

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Conclusions

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**(Removed. See slide #2, “Notes.”)**

Conclusions On applicability of CFD to knife seal design (KN=1): (Removed. See slide #2, “Notes.”)

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**Next Step 3D Knife Seal Model with Honeycomb Land and Rub-Groove**

While sounds and movies in your slide show may work perfectly on your own machine, they might be surprisingly, and frustratingly, absent when you play the presentation from a different computer.

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**Knowledge/Skills/Tools Acquired**

CFD principles, methods, experience Grid theory, experience Compressible flow theory Labyrinth seal theory Parallel processing Experimental tools, methods UNIX, LINUX, GAMBIT, FLUENT 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. [Note to trainer: Steps—given in either numbered or bulleted lists—are always shown in yellow text.]

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**Acknowledgements IUPUI Rolls-Royce Dr. Hasan Akay Pitchaiah Chakka**

Dr. Akin Ecer Dr. Erdol Yilmaz Dr. Nishant Nayan Hsiao Tung Rolls-Royce Pitchaiah Chakka Tony Lambert Eugene Clemens Ed Turner Ron Hall Steve Gegg Tiffany Brown and the Co-Op Department

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**References and Resources**

Papers Studied or Referenced Stanford CFD Class Lecture Notes (G.Iaccarino) AVIDD Cluster Primer (RATS, IU) Getting Started on AVIDD-I (RATS, IU) PBS Manual [1] FLUENT Doc. & Theoretical Manuals Grid Generation: State of the Art (Nick Wyman) Introduction to Gambit (Fluent.com) Gambit Specifications (wwwsupercomputing.it) Introduction to Computational Fluid Dynamics (T.Xing, F.Stern, IIHR) Introduction to CFD for Compressible Flow at High Mach Numbers (H.Deconinck, Von Karman Institute for Fluid Dynamics) Solver Methodology (Ballute, Australian National University) Flow Over an Obstruction (S.C.Rasipuram Shape Optimization of a Labyrinth Seal Applying the Simmulated Annealing Method (V.Schramm, J.Denecke, S.Kim, S.Wittig) Tutorials Performed or Referenced Flat Plate with Heat Transfer (Fluent, Inc.) Lid-Driven Cavity (Fluent, Inc.) 2D Airfoil (Fluent, Inc.) 3D Annulus (Fluent, Inc.) Axisymmetric Nozzle Flow (Cornell) 2D Airfoil (Cimbala, PSU) Axisymmetric Inlet Flow (Cimbala, PSU) When a file is linked, that means it is not an actual part of your presentation and won’t automatically copy over when you copy the presentation file. So, when you try to play the video or sound file you’re expecting, you’ll get a ringing silence. About sound files: All sound files except for some .wav files are automatically inserted in the presentation as linked, rather than embedded, files. A .wav file that is more than 100 kilobytes (KB) will, by default, be inserted as a linked file. * AVIDD-B and AVIDD-I are twin PentiumIV Linux clusters in Bloomington and Indianapolis for use by IU faculty and their sponsored staff and graduate students.

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