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

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

Principal Advisors: Dr. Hasan Akay, IUPUIP. Chakka, PhD., Rolls-RoyceT. Lambert, MS., Rolls-Royce

Note

Numerical results, comparisons with test data, conclusions, and other information considered proprietary and/or sensitive

have been removed from this presentation.

Outline

• Introduction

• Objective

• Numerical Method

• Computational Grids

• Description of Test

• Results and Validation

• Additional Studies

• Conclusions

• Acknowledgements

• References

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.

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.

tU

U

AP

TW

U

tU

T

APW

Introduction (cont.)

Consequences of seal design error (grossly simplified):

• Underprediction lower thrust/efficiency

• Overprediction downstream overheating

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.

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

Numerical Method

Governing EquationsCompressible Flow Equations

Reynolds-Averaged N-STurbulence Model

DiscretizationBoundary Conditions

Solver Method

Governing Equations1

Mass conservation:

Momentum balance:

…stress tensor:

0

0 00

0

Governing Equations

Energy conservation:

…where:

…and sensible enthalpy for ideal gasses:

000

Governing Equations in Cylindrical Coordinates (2D)

Mass conservation for compressible flow:

Momentum balance, axial:

…where:

Momentum balance, radial:

0

0

0

0

0

0

0 0

Compressible Flow Physics

Mach number and speed of sound:

Relationship between static and stagnation conditions:

Ideal gas law as implemented in FLUENT:

Governing Equations Reworked: RANS

Resulting Reynolds averaged Navier-Stokes equations (interpreted, for compressible flows, as Favre-averaged):

Variables decomposed into mean and fluctuating components:

Turbulence Model

Spalart-Allmaras (1-Equation):

Boussinesq hypothesis:

Discretization

A conservation equation for an arbitrary CV:

Discretized:

Linearized: …where:

Segregated Solver Method (FLUENT)

P*, rhou*, rhov*

rho, u , v, P

rhou* , rhov*

…+ T*, v*, …

P*, rhou*, rhov*

Boundary ConditionsOperating 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)

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

Boundary Conditions (cont.)

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.

Turbulence intensity at inlet estimated by:

Computational Grids

“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

“Primary Grid” (zoom)

Above: Knife tip zoom. Maximum aspect ratio around 5.

“Secondary Grid”

Below: Computational domain

Left: Zoom on center region

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.

“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.

Description of Test

2D Seal Rig (performed c.1970)

Left: Labyrinth Seal Test Rig

Below: Representative Single Knife Test

(Removed. See slide #2, “Notes.”)

(Removed. See slide #2, “Notes.”)

Rig Instrumentation

Below: Labyrinth Seal Test Rig Instrumentation

(Removed. See slide #2, “Notes.”)

Results and Validation

2D Planar Models vs. 2D Planar Test DataAxisymmetric Models vs. Semi-Empirical CodesRepresentative Residuals, Vectors, and Contour

Plots

FLENT Model vs. Test – 2D Planar

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.’

tU

U

AP

TW

(Removed. See slide #2, “Notes.”)

Model vs. Semi-Empirical Codes – Axisymmetric

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

(Removed. See slide #2, “Notes.”)

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.”)

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.

Velocity Vectors

Velocity Vectors (zoom)

Mach Number

Left: Mach # Contours (nearly converged)

Below: Mach # plot, inlet (black), outlet (red)

Total Temperature

Static Temperature

Entropy

Enthalpy

Internal Energy

Total Energy

Total Pressure

Above: Ptmin at knife tip: 11.14psia

Right: Regions of “Pt creation” >.004psi

Static Pressure

Modified Turbulent Viscosity

Left: mtv contours

Below mtv at inlet and outlet

Wall y+

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

Additional Studies

Viscous heating impact on WTurbulence model impact on W

Discretization order impact on WNo-slip rotor impact on W

Grid impact on WSolver Formulations

Parallel speed-up

Selected Additional Studies

Turbulence model impact on flow parameter (PR=3.0):

Viscous heating impact on flow parameter (PR=2.5):

No-slip rotor impact on flow parameter (PR=2.0):

(Removed. See slide #2, “Notes.”)

(Removed. See slide #2, “Notes.”)

(Removed. See slide #2, “Notes.”)

Additional Studies

Discretization order impact on flow parameter (PR=2.0):

Solver formulations:

(Removed. See slide #2, “Notes.”)

(Removed. See slide #2, “Notes.”)

Additional Studies

Grid impact on flow parameter (PR=3.0):

Parallel Processing:

Two processors:

Three processors

Three processors after load balancing

(Removed. See slide #2, “Notes.”)

Conclusions

Conclusions

On applicability of CFD to knife seal design (KN=1):

(Removed. See slide #2, “Notes.”)

Next Step

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

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

Acknowledgements

IUPUI• Dr. Hasan Akay

• 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

References and Resources

Papers Studied or Referenced

* 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.

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)

• [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)

• Stanford CFD Class Lecture Notes (G.Iaccarino)

• AVIDD Cluster Primer (RATS, IU)

• Getting Started on AVIDD-I (RATS, IU)

• PBS Manual