a study of the applicability of cfd to knife seal design in the gas turbine industry a presentation...
TRANSCRIPT
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