System Simulation of an Elastocaloric Heating and Cooling Device Based on SMA

Abstract

Elastocaloric (EC) cooling uses solid-state NiTi-based shape memory alloy (SMA) as a non-volatile cooling medium and enables a novel environment-friendly cooling technology. Due to the high specific latent heats activated by mechanical loading/unloading, substantial temperature changes are generated in the material. Accompanied by a small required work input, a high coefficient of performance is achievable.
Recently, a fully functional and illustrative continuous operating elastocaloric air cooling system based on SMA was developed and realized. To assist the design process of an optimized device with given performance and efficiency requirements, a fully coupled thermo-mechanical system-level model of the multi-wire cooling unit was developed and implemented in MATLAB. The resulting compact simulation tool is qualified for massively parallel computation, which allows fast and comprehensive parameter studies.
In this work, the influence of different SMA diameters, rotation frequencies, and airflow rates is investigated. The results are analyzed to find the suited parameter for high efficiency (COP) and temperature span.

Full text

SYSTEM SIMULATION OF AN ELASTOCALORIC HEATING AND COOLING DEVICE BASED ON SMA
Felix Welsch1, Susanne-Marie Kirsch1, Nicolas Michaelis3, Michele Mandolino1, Andreas Schütze3, Stefan
Seelecke1,2, Paul Motzki2, Gianluca Rizzello1
1Intelligent Material Systems Lab, Saarland University, Saarbruecken, Germany
2Intelligent Material Systems Lab, ZeMA gGmbH, Saarbruecken, Germany
3Lab for Measurement Technology, Saarland University, Saarbruecken, Germany
ABSTRACT
Elastocaloric (EC) cooling uses solid-state NiTi-based
shape memory alloy (SMA) as a non-volatile cooling medium
and enables a novel environment-friendly cooling technology.
Due to the high specific latent heats activated by mechanical
loading/unloading, substantial temperature changes are
generated in the material. Accompanied by a small required
work input, a high coefficient of performance is achievable.
Recently, a fully functional and illustrative continuous
operating elastocaloric air cooling system based on SMA was
developed and realized. To assist the design process of an
optimized device with given performance and efficiency
requirements, a fully coupled thermo-mechanical system-level
model of the multi-wire cooling unit was developed and
implemented in MATLAB. The resulting compact simulation tool
is qualified for massively parallel computation, which allows fast
and comprehensive parameter studies.
In this work, the influence of different SMA diameters,
rotation frequencies, and airflow rates is investigated. The
results are analyzed to find the suited parameter for high
efficiency (COP) and temperature span.
  

1. INTRODUCTION
         



        

        


       


      
        

  
        
        

        
     
   




       

         


         


      
        
      
     
       
        
    



2. REALIZED EC-DEVICE
      

       

           
 

Proceedings of the ASME 2020 Conference on Smart Materials,
Adaptive Structures and Intelligent Systems
SMASIS2020
September 15, 2020, Virtual, Online
SMASIS2020-2262
1
Copyright © 2020 ASME
Attendee Read-Only Copy

FIGURE 1:    
   





       
      
     

         



          
         

          
          

     




       

  
         

    
  
  
3. DEVICE SIMULATION TOOL


        

         

         


FIGURE 2:    

3.1. Device model
The load profile represents the central component of the
mechanics, governing the elastocaloric cycle and is modeled as
a piecewise function depending on the rotation angle of the SMA
arrangement.  function is adaptable to different
thermodynamic cycles to optimize the performance of the
device.[5]         


   
        The
fluid transport and temperature evolution in the ducts on the hot
and cold side are implemented as one-dimensional flow with
homogeneous radial and axial temperature distribution. The
outlet temperatures are calculated with the inlet temperatures and
flow velocities by solving the advection-diffusion partial
differential equation for the fluid temperature. The heat
exchange coefficient strongly depends on the SMA wire
diameter, as well as flow velocity and is calculated with the
Churchill-Bernstein Equation [26].
  coupling of the individual loaded
SMA elements is covered by the multiple copies of an SMA
model. The current material composition between martensite and
austenite is calculated with the Mueller-Achenbach-Seelecke
model using Boltzmann statistics on a multi-well free energy
function.[27] The temperature of each SMA element is
calculated by the energy balance in the SMA material, which
links the temperature rate with the heat exchange to the
surrounding fluid and the production or absorption of latent heats
due to phase transformations.
Rot. Frequency
Cam geometry
Inlet temperatures
Flow rate
Channel geometry
Torque
Mechanical power
Efficiency (COP)
Thermal power
Outlet temperatures
Elastocaloric Device
Me chanics
SMA arrangement Fluid
SMA Model
SMA Model
SMA Mode l
SMA Model
SMA

 



 


2
Copyright © 2020 ASME

The interacting modules, enable the calculation of the
coefficient of performance (COP) by dividing the transported
heat from the cold to the hot through the mechanical input
energy. These energies are calculated by integrating the thermal
and mechanical power over the time interval of one rotation after
reaching a stationary temperature distribution in the fluid ducts.
The simulation tool is fully implemented in MATLAB and
solved using a standard ode113 solver, allowing fast and
accurate computation. The short computation time, due to the
 vectorization,
as well as massively parallel computation on multi-core
computers, enables economic comprehensive parameter studies.
      
        



3.2. Parameter study
    
  and 

.Device parameters like mass of SMA material, wire
diameter, rotation frequency, airflow rate represent degrees of
freedom during the design process to reach the best COP. 
          
     

    
 

4. SIMULATION SETUP AND RESULTS

       
         
     
           
       
  
TABLE 1: PARAMETER SWEEP
SMA diameter
(μm)
Rotation
frequency (Hz)
Airflow rate
(m3/h)
50
0.25
25
100
0.5
50
200
1.0
100
500
2.0
150
4.0
4 steps
5 steps
4 steps
80 simulations
      
     
          
         

TABLE 2: MATERIAL PARAMETERS OF NITICO#3
Parameter
Value
Unit
Description
EA
53.8
GPa

EM
22.6
GPa

T
0.0246
-
Transformation strain

6317
kg/m3
Mass density
c
463
J/kg/K
Specific heat capacity
H
15.6
J/g
Latent heat
h

W/m2/K
Convection coefficient,
depending on air velocity
T0
295.15
K
Reference temperature
(T0)
542.5
MPa

(T0)
423.3
MPa


7
MPa/K
Temperature dependency
of transformation stress
VLE
510-23
m3
Volume element size
x
0.001
s
Phase transition time constant
        
 
 
 
        
         
           
   
        

            
            



         
         

       
 
        



         
         

        





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 
 
FIGURE 3:     


 
 
FIGURE 4:    
    
    
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
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 
FIGURE 5: 




        
 
       
        
       


        
 
     


The presented parameter study imposingly illustrates the
advantages of small wire diameter and high flow rates like high
COP at high frequencies, large thermal power, and high
temperature span. However, for the given machine configuration
with 24 bundles of 30 individual wires, a change to 50
wires, while maintaining the mass of SMA material, leads to
480 wires per bundle. For practical reasons, a compromise
between manufacturing effort and high performance is often
found at slightly thicker wire diameters.
5. CONCLUSION




         
        
     

       
        

ACKNOWLEDGMENT
       
    
      



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
Sci.
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

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Technol. Built Environ.
      
 
  
   

 
       
   Int. J. Refrig.  

 et al.
       
Energy Technol.     

  
     
     
    
      
  Thermag VII    

          
     

ASM Int. - Int. Conf. Shape Mem. Superelastic Technol.
SMST 2019
 et al.

    ASME 2019
Conference on Smart Materials, Adaptive Structures and
Intelligent Systems
  
  
     Refrigeration
Science and Technology    

 

     Thermag VII

 
    
   ASM Int. - Int. Conf. Shape
Mem. Superelastic Technol. SMST 2019  

  
     
     Int. J.
Refrig.
         
     
    Contin.
Mech. Thermodyn.
 
      
    
  Int. J. Solids Struct.    

        

Acta Mater.
   et al.   
     
     
Contin. Mech. Thermodyn.      

  
     
  
   Refrigeration Science and
Technology
  
     
     
    
Thermag
VII
          
     
     
ASM Int. - Int. Conf. Shape Mem. Superelastic Technol.
SMST 2019
        
     
     
ASME
2019 Conference on Smart Materials, Adaptive
Structures and Intelligent Systems
 et al.
ASME 2018 Conference
on Smart Materials, Adaptive Structures and Intelligent
Systems
       
   
  

       
   
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
        
      
        J. Heat
Transfer
       
     
Mater. Sci. Eng. A

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