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Turbomachinery Class 11

Configuration Selection & Multidisciplinary Decisions Turbomachinery Design Requires Balance Between: Performance Weight Cost

Turbomachinery Design Several Aspects to "Cost" as seen by customer First Cost - Price Operating Cost - Fuel & Maintenance Efficiency Weight No. of Parts Complexity Manufacturing Materials Life; Stress & Temperature

Turbomachinery Design Consider Turbine Efficiency & Stress Performance - Smith Correlation for simplicity "A Simple Correlation of Turbine Efficiency" S. F. Smith, Journal of Royal Aeronautical Society, Vol 69, July 1965 Correlation of Rolls Royce data for 70 Turbines Shows shape of velocity diagram is important for turbine efficiency Correlation conditions - Cx approximately constant - Mach number - low enough - Reaction - high enough - Zero swirl at nozzle inlet - "Good" airfoil shapes - Corrected to zero clearance

Note: The sign of E should be negative Increasing  Note: The sign of E should be negative

Dixon This is E

Turbomachinery Design Efficiency Variation on Smith Curve Increasing E from 1.33 to 2.4 [more negative] (at Cx/U=0.6): Higher turning increasing profile loss faster than work. Raising Cx/U from 0.76 to 1.13 (at E=1.2): Higher velocity causes higher profile loss with no additional work Remember - Mach number will also matter!

Secondary Air Systems Hot air at the top rotating shaft is at the bottom, not visible here

Turbomachinery Design Structural Considerations Centrifugal stresses in rotating components Rotor airfoil stresses Centrifugal due to blade rotation [cent] Rim web thickness Rotating airfoil inserted into solid annulus (disk rim). Airfoil hub tensile stress smeared out over rim Disk stress [disk] Torsional: Tangential disk stress required to transfer shaft horsepower to the airfoils Thermal: Stresses arising from radial thermal gradients Cyclic effect called low-cycle fatigue (LCF)

Turbomachinery Design Structural Considerations Airfoil Centrifugal Stress Blade of constant cross section has mass:

Turbomachinery Design Structural Considerations Centrifugal stress is limited by blade material properties Aan

Turbomachinery Design Structural Considerations For centrifugal stress of 40,000 lbf/in2, AanN2 = 790,000 x 40,000=3.16 x 1010 Design practice for AN2 is from (2.5-3.5) x 1010 Since N is fixed, this places upper limit on annulus area In another, more basic form: Where: Ut Blade Tip Speed,ft/sec m Metal Density, lbm/in3 cent Centrifugal Stress, lbf/in2 l hub/tip radius ratio From chart 11 

Typical Centrifugal Stress Values

Typical Centrifugal Stress Values

Typical Centrifugal Stress Values Need to determine if blade with this stress level will last 1000hr to rupture

Turbomachinery Design Structural Considerations Centrifugal stresses due to torsional disk stresses The force from the change in angular momentum of gas in the tangential direction which produces useful torque. Mw = bending moment about axial direction Ma=gas bending moment about tangential direction [If Cx constant, pressure force produced in axial direction] Mw is largest bending moment Approximate form for bending stress Design blade with centroids of cross section slightly off-center gas bending moment is of opposite sign to centrifugal bending moment

Turbomachinery Design Structural Considerations Disk & Blade Stress considerations influence selection of work and flow coefficients – from above Selection of work and flow coefficients greatly effects blade cross sections Following chart from former Pratt&Whitney turbine designers illustrate blade shape variation Their meanline doesn’t exactly match Smith data

Turbomachinery Design Structural Considerations Allowable stress levels are set by material properties, material temperature, time of operation and cycles of strain Stress level measures Ultimate stress: part fails if this level is reached 1000 hrs rupture life: part fails after 1000 hrs at a given temperature 1000 hrs creep life: part will stretch a certain percentage (0.1 - 0.2%) at a given temperature

S R S R

Turbomachinery Design Structural Considerations Blade pitch [s] at Rmean chosen for performance s/b, h/b values Need to check if [s] too small for disc rim attachment number of blades have an upper limit Fir tree holds blade from radial movement, cover plates for axial slight movement allowed to damp unwanted vibrations manufacturing tolerances critical in fir tree region

Turbomachinery Design Structural Considerations External load due to: airfoil, attachment & platform pull disk lug side plates, seals, etc. Inertial loads due to: centrifugal force from bore to live rim

Turbo Design - Structural Considerations Airfoils inserted into slots of otherwise solid annulus [rim] Airfoil tensile stress is treated as ‘smeared out’ over rim Disk supports rim and connects to shaft

Turbo Design - Structural Considerations Tangential disk stresses: forces on itself due to rotation + external (blade pull ) forces Average Tangential Stress Consider radial inertia load on disk element: Noting that , an element of area in the disk cross section: X dr

Turbomachinery Design Structural Considerations is the polar moment of inertia of disk cross section about the center line. The total radial force becomes: Design disk for constant stress… as r decreases, increase thickness x Force normal to any given diameter is needed for average tangential force:

Turbomachinery Design Structural Considerations note that FR Fv q Fv/2

Turbomachinery Design Structural Considerations The average tangential stress due to inertia then is: The contribution of the external force to the average tangential stress is so that the total average tangential stress becomes:

Turbomachinery Design Structural Considerations For the same speed and pull, the average tangential stress can be reduced by: increasing disk cross sectional area decreasing disk polar moment of inertia - moving mass to ID of disk

Turbomachinery Design Structural Considerations Rim Stress - Consider a thin ring. Neglecting the external force, the rim inertial tangential force is: dr X r

Turbomachinery Design Structural Considerations Important Thoughts About Tangential Stress in a Ring Wheel Speed Drives Stress, not RPM ! Hoop Stress Low at Low Wheel Speed Ring Cannot Support Itself at High Speeds (needs a bore!) Hoop Stress Equation Has form of Dynamic Head, a Pressure Term

Turbomachinery Design Structural Considerations Average Tangential Stress in HPT disks is Increasing

Turbomachinery Design Structural Considerations Conclusions: Disk Stress Driven by Wheel Speed & Radius Ratio. Mass at Bore Strengthens Disks Mass at Rim Difficult to Carry At Some Thickness, Bore is Impractical Direct Relation Between Flow & Work Coefficients & Disk Stress

Turbomachinery Design Structural Considerations Stress and major flow design parameters (, E) relate directly to achievable  Recalling from Dimensional Analysis: Higher stress () at constant N and Dmean occurs on longer blades and lower flow coefficient ()

Turbomachinery Design Structural Considerations Also : Flow, Density & Work are set by cycle requirements Stress (P/A) capability is set by material, temperature, & blade configuration Parametric effects increased N  increased  (to first order), decreased E (to 2nd order) increased D  decreased  (to first order), decreased E (to 2nd order)

Plot shows effect of +20% change in N, D & stress on Cx/U, E, and Efficiency. Stress changes allowable blade height or annulus area.

Turbomachinery Gaspath Design Problem Objective: to illustrate interaction of several design parameters , stress level (cent), x, cost, weight flowpath dimensions Design a baseline turbine and 3 alternative configurations Dmean or weight and cost on  Aan or Cx or weight on  Stress level on  All turbine designs have the following conditions

Turbomachinery Gaspath Design Problem Design: fill in the missing blanks in the table below Account for tip clearance losses as a 2% debit in efficiency Remember cent  AanN2 and cost  blade count (nb)

Turbomachinery Gaspath Design Problem Base Case: Assume only for this case M1=0.8 is given.

Turbomachinery Gaspath Design Problem Base Case: Assume only for this case M1=0.8 is given.

Turbomachinery Gaspath Design Problem Base Case:

Turbomachinery Gaspath Design Problem Base Case:

Turbomachinery Gaspath Design Problem Baseline Design: Account for tip clearance losses as a 2% debit in efficiency Remember cent  AanN2 and cost  blade count (nb)

Turbomachinery Gaspath Design Problem Alternate Design 1: Given N, Aan1N2, Dmean1

Turbomachinery Gaspath Design Problem Alternate Design 1:

Turbomachinery Gaspath Design Problem Alternate Design 1:

Turbomachinery Gaspath Design Problem Summary