1. Optimization of Self Activating Bi-Metallic Valve using Thermo –
Structural Coupled FEA
Matin Kagadi1a
, Girish Tembhare1
, Vinaay Patil2b
, Sujay Shelke2
1
Mechanical Engg. Dept, VJTI, Mumbai-400019, India.
2
Vaftsy CAE, Pune-411028, India.
a
matinkagadi@gmail.com, b
vinaay.patil@vaftsycae.com
Keywords: Thermo-Structural coupled FEA, Non linear FEA, Bi-metallic Valve.
Abstract: Besides relying on electronically actuated valves, there is a need to have a mechanically
actuated valve and a warning system as second layer of safety in-case of electronic malfunction.
The specific process for which optimization is carried out, is the process of nitrous oxide generation
from ammonium nitrate. The key challenge in the process was maintaining temperatures below
200ºC, as above this temperature ammonium nitrate becomes explosive and hence safety risks are
involved. The secondary objective was to maintain temperatures above 170ºC, as below this
temperature the reaction does not proceed. In this paper we have tried to fulfill these objectives by
employing a bi-metallic valve and a warning system having bi-metallic strip which will bend at
higher temperatures, thus serving our primary purpose of self-actuation. However the key constraint
in determining the dimensions of the valve and the warning system is a desirable deflection of bi-
metallic strip. To optimize these parameters we have employed non-linear FEA and thermo-
structural coupled FEA, and this paper reflects on the process employed in achieving the same.
Introduction
The primary chemical reaction for which the valve is required is the commercial production of
nitrous oxide by heating of ammonium nitrate. The heating is carried out using superheated steam
[1].
NH4NO3 (solid) → 2 H2O (gas) + N2O (gas). (1)
The chemical reaction is subjected to following thermal considerations.
a. Below 170ºC : No reaction b. 170ºC to 200ºC : Active reaction zone
c. 200ºC to 240ºC : Warning zone d. Above 240ºC : Possible explosion.
Based on the above thermal considerations, the following design requirements are obtained for
the system (refer with: Fig. 1, Fig. 2)
1. The system should remain closed below 200ºC to maintain steam in the vessel
2. 200ºC should trigger opening of the valve (with a warning by a warning system)
3. System should close back when temperature falls to 200ºC.
When the valve opens, the super heated steam will escape, this will result in a pressure drop,
which will translate into reduction of temperature of the steam.
Advanced Materials Research Vols. 622-623 (2013) pp 147-151
© (2013) Trans Tech Publications, Switzerland
doi:10.4028/www.scientific.net/AMR.622-623.147
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2. Figure 1: Thermal Bi-Metallic safety valve Figure 2: Warning system
Background Theory
The main concept that is employed behind a self actuating valve and a warning system is that of a
bi-metallic strip. Bi-Metallic strip is a strip consisting of a film metal bonded to a substrate metal.
The difference between the thermal expansion coefficients ensures that, even though the strip
remains flat at set temperature in cantilever condition, any heating or cooling results in differential
expansion, giving the strip a bend. This bending is directly a function of temperature difference ∆T,
obtained from heating or cooling and is given by the equation [2],
( ) ( )
. (2)
Where, k is curvature (inverse radius, ) of bi-metallic strip,
Ef: Young’s modulus of film metal Es: Young’s modulus of substrate metal
tf: Thickness of film metal ts: Thickness of substrate metal
αf: Thermal expansion coeff. of film αs: Thermal expansion coeff. substrate
If L is length, b is width and t is total thickness of bi-metallic strip then lateral deflection δ(L) of
end tip of flat cantilever bi-metallic strip for gradual temperature change along the length is
given by [3],
δ(L)
( )
. (3)
Figure 3: Deformation state of film and
substrate
Figure 4: Location of the neutral surface
Where, F is a shear force (refer with: Fig. 3) which is given by,
F =
( )
( )
. (4)
148 Manufacturing Science and Technology III

3. The distances of neutral surface (refer with: Fig 4) and is given by
= t . (5)
=
( )
( )
. (6)
and are the moment of inertia of film and substrate and can be obtained using parallel-axis
theorem as
= + ( ) . (7)
= + ( ) . (8)
Finite Element Analysis
Key characteristics of the finite element analysis (FEA) performed in ANSYS mechanical
workbench are:
1. Type: Thermo – Structural coupled FEA (refer with: Fig. 5)
2. Elements: 2nd
Order hexahedron elements (refer with: Fig. 6, Fig. 7)
3. Non linearity: Material non linearity (refer with: Fig. 8, Fig. 9),
Contact non linearity (refer with: Fig. 10, Fig. 11), Geometric
non linearity (change in response due to large deformations). .
Figure 5: Flow of Thermo-Structural Coupled FEA
Meshing: The system of interest is first discretized into elements; in this case, the elements are
second order hex dominant. The corner vertices and mid side vertices of these hexahedron elements
are called “nodes” and are the discrete points where the value of interest is solved.
Thermal
FEA
Thermal B.C
(Temperature)
Material Input
(Conductivity Kxx)
Output
Temperature Distribution
Thermal Load
Thermal Expansion
Coefficient
Structural
FEA
Structural B.C
(Support)
Material Input (Young’s
Modulus, Poissons ratio))
Advanced Materials Research Vols. 622-623 149

4. Figure 6: Meshing of a strip and flow casing Figure 7: 2nd
Order Hexahedron Element
Material non-linearity: Non linear material properties such as conductivity K, Young’s
modulus of elasticity E of the film metal (CZ-1400-E) and the substrate metal (IN-4082-SP) as
shown in graphs (refer with: Fig. 8, Fig. 9) are used in analysis.
Figure 8: Conductivity as a function of T Figure 9: Modulus of elasticity as a function
of T
Similarly, poison’s ratio and non linear thermal coefficient of expansion of the film metal (CZ-
1400-E) and the substrate metal (IN-4082-SP) as a function of temperature are used [4].
Contact between film and substrate metal is defined as a bonded contact (refer with: Fig. 10).
Accuracy achieved using multiple sub steps.
Figure 10: Bonded contact Figure 11: No separation contact
Boundary Conditions: Thermal boundary conditions for analysis of the thermal safety valve
and the warning system are applied as shown (refer with: Fig. 12, Fig.13).
Figure 12: BCs. for the thermal safety valve Figure 13: BCs. for the warning system
150
200
250
300
350
400
450
500
-50 50 150 250
CZ-1400-E
IN-4082-SP
T (deg.C)
K
(W/
mC)
0,00E+00
5,00E+10
1,00E+11
1,50E+11
2,00E+11
-50 50 150 250
CZ-1400-E
IN-4082-SP
T (deg. C)
E
in
Pa
150 Manufacturing Science and Technology III

5. Results and discussion
Equation 10 is an optimizing equation for a cantilever bi-metallic strip of a warning system (refer
with: Fig. 14) with a dimensions b = 3mm, tf = ts = 4mm,
y = 0.104x 3.540. (10)
Figure 14: Graph of end tip deflection Vs length Figure 15: Deflection(m) of strip
The main focus of analysis is on opening and closing position of the valve and the warning
system with respect to change in temperature of superheated steam inside the process vessel (refer
with: Fig. 15, Fig. 16). The curved cantilever strip with initial curved radius of 20mm, width 30mm
and thickness of film and substrate metal is 1.4mm each, we got the desirable deflection of 4.36mm.
Figure 16: Deflection(m) of curved bimetallic strip of a safety valve
Conclusion
Usage of non linear FEA alters the results significantly, hence for realistic determination of
performance non linear FEA is recommended.
Using a cantilever arrangement for a warning system, under which both the materials are
exposed to the heat, is more effective in giving a range bound mechanism.
References
[1] Information on http://en.wikipedia.org/wiki/Nitrous_oxide.
[2] S. Timoshenko, “Analysis of Bi-metal Thermostats,” J. Opt. Soc. Am.,11(1925) 233.
[3] J. W. Eischen and J. S. Everett, “Thermal Stress Analysis of a Bimaterial Strip Subject to an
Axial Temperature Gradient,” Vol. 111 ,Journals of Electronic Packaging (1989).
[4] Moduluc Control Systems, USA: “Objective and outline document no 234221.”
y = 0,1044x - 3,5405
0
2
4
6
8
50 60 70 80 90 100
Theorotical Linear FEA Non linear FEA
Length in mm
δ in
mm
Advanced Materials Research Vols. 622-623 151