Surface Heat Transfer In Quenching Operations

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Surface Heat Transfer In Quenching Operations
Research Team Kalyana C. Gummadam
gummkal_at_iit.edu T Calvin
Tszeng
tszeng_at_iit.edu
Thermal Processing Technology Center Department
of Mechanical, Materials and Aerospace Engineering
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Outline

• OBJECTIVES STRATEGY
• OVERVIEW OF QUENCHING BACKGROUND
• FEM MODEL
• EFFECT OF T/C LOCATION TIMESTEP SIZE
• STABILITY ACCURACY
• EFFECT OF NOISE
• TIME LAGGING
• CONCLUDING REMARKS/ FUTURE RESEARCH

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OBJECTIVES

• To develop a module for calculating the
  surface heat transfer coefficient (HTC) which is
  to be used in the FEM modeling of components in
  the quenching operations of industrial heat
  treating processes.
• To develop the reliable methodology for
  determining the surface heat transfer
  coefficients from measured temperature profiles
  in quenched specimens.
• To develop an efficient temperature sensing
  strategy and experimental method, and to measure
  the temperature profiles in quenched specimens.

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STRATEGY

• Perform extensive study on the inverse heat
  transfer module in the 2D modeling system
  HOTPOINT. Determine the influence of various
  factors on the solution behavior
• Develop an efficient and reliable
  technique of temperature measurement that
  provides the data for determining the surface
  heat transfer coefficients.
• Establish a neural network model for
  predicting the surface heat transfer coefficients
  in a broad range of quenching operations

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OVERVIEW OF QUENCHING
Wetting process on the surface of a 1040 steel
Adopted form     George E. Totten, Maurice A.H.
Howes, Steel Heat Treatment Handbook, 1997
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BACKGROUND

• Inverse Heat Transfer
• Fourier law for heat flux through the surface
  ---
• Determination of the boundary conditions (heat
  transfer coefficients) that aaproduce a
  specified, or measured , internal temperature
  distribution.
• Underlying mathematical problem is ill-posed
• Solution does not depend continuously on the
  data
• Small errors in the data may cause large errors
  in the solution
• Various Approaches
• Conjugate Gradient method( Huang, 1999)
• Time Variable number of future temperatures (
  Blanc, G 1997)
• Space Marching Algorithm( Al-Khalidy, 1998)
• Sequential Methods( Reinhardt, 1993)
• Function Specification method ( Beck, 1985)

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INVERSE CALCULATION

• 2D FEM MODEL HOTPOINT 1.0 ( T Calvin Tszeng,
  IIT)

Mesh the Object
Specify HTC at object surfaces
Location of T/Cs
Perform Direct Simulation
Generate Cooling curves
Perform Inverse Calculation
Generate Surface HTC
Error Analysis
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VALIDATION

• The inverse heat transfer module can offer
  generally good results of surface heat transfer
  coefficients by using the simulated cooling
  curves.
• Time step size that is greater than the sampling
  rate of cooling curves can reduce instability in
  the results.
• The oscillation in the solution can be reduced by
  using a regulating parameter which is
  incorporated in the residual error function.

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EFFECT OF SENSOR LOCATION
1D Axi Symmetric Initial temperature 1200
C Quenching time 40 s
Insulated
dx
Heat Transfer
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EFFECT OF SENSOR LOCATION
Time step size 0.4s Regulating parameter of
0.75

• Good accuracy until a depth of 5mm
• Deviation from the true solution at higher depths

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EFFECT OF TIMESTEP SIZE
dx 10mm Regulating parameter 0.75

• Better accuracy at larger time step size under
  2s
• Bad solution at much higher time step size due
  to insufficient data
• Time lag reduces the accuracy at smaller time
  step size

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STABILITY AND ACCURACY (1/3)
Symbolic Mathematical Model F A ?B Error
Equation A (dT)2 -- Temperature Error (
Stochastic) B (dh)2 -- Solution Error (
Deterministic) ? Regulating Parameter (
Numerical Const)
Insulated

• 1D Case Considered
• Axi-symmetric geometry.

h(T)
Heat Transfer
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STABILITY AND ACCURACY (2/3)

• Varying regulating parameter (0.01-100) after
  different times Initial regulating parameter
  value of 0.75
• Accuracy decreases with increase in regulating
  parameter
• Accuracy and stability both decrease with
  further increase in regulation parameter value

After 2.5s
Stability
2
After 7.5s
Stability
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STABILITY AND ACCURACY (3/3)
OD- 1.5 Length - 6 h heat transfer
co-efficient

• 2D Case
• Axi-symmetric geometry.

l
0.01

• After 2.5 s
• Similar results as compared
• to 1D case
• Good Stability for all ?
• values
• Accuracy decreases as ?
• increases

0.008
2
2
5
5
0.006
100
0.004
20
20
0.002
0
0
2
4
6
8
10
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EFFECT OF NOISE

• Constant Boundary condition
• 10 peak to peak noise induced
• Sequential Digital filter algorithm used to
  smooth data
• Smoothed data provides better results

with 10 noisy data
with smooth data
theoretical solution
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TIME LAGGING (1/4)
Temperature Calculations




T

, t

, x

• Constant Heat flux applied to semi infinite body
• T -- Dimensionless Temperature
• t -- Dimensionless time
• x -- Dimensionless distance

Adopted from Beck,J.V 1992
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TIME LAGGING (2/4)
10 mm
15 mm
20 mm
25 mm

• Normalized Second derivative of the Temperature
  Vs Time
• Obtain points of inflection for increasing dx
  (T)
• Time lag increases with distance

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TIME LAGGING (3/4)
surf
Reference line
1000

• The deviation from the cooling curve for a
  change in the boundary condition can be
  distinctly seen
• Time lag increases with distance
• Time lag beyond 5mm is substantial

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TIME LAGGING (4/4)

• Linear relation between Theoretical and
  Calculated time lag
• For 1D case the calculated time lag can be
  estimated from this plot
• The time lag could specify the min time step
  size to be used
• A closed form solution for the theoretical case
  will

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SUMMARY ( 1/2)

• Sensor Location
• Deviation from the true solution at higher
  depths
• Good accuracy for Sensor location until a depth
  of 5mm
• Time step size
• Bad solution at much higher time step size due
  to insufficient data
• Instability arises at very small time step size
• The choice of time step size depends on the
  location of sensor
• Regulating Parameter
• Solution accuracy and stability become poorer
  for higher values of aaregulation
  parameter.
• Lower regulating parameter leads to better
  accuracy and stability

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SUMMARY ( 2/2)

• Noise
• More the noise, more inaccurate and unstable the
  solution
• Sequential Digital Filter Algorithm used to
  smooth the data
• Time Lag
• Poor accuracy at small time step size due to
  time Time lag
• Time lag increases with distance and is
  substantial beyond 5mm
• Time lag Provides an estimate of minimum time
  step size to be aaused to obtain a better
  solution
• Future Research

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NEXT STEPS(1/2)
Experimentation
Material - 1045 Cold Rolled Geometry -
Solid Rounds Furnace - IIT Samples
- Diameter Length 1 8,6,4,2,1,0.5 2 12,
8,6,4,2,1,0.5 - 12 TCs (max) on each
sample. -Measure cooling curves at different
locations on the surface - Perform Inverse
calculation to obtain HTCs
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NEXT STEPS(2/2)