http://orcid.org/0000-0002-6729-9137
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Abstract
The thermodynamic process parameters such as cooling capacity and percentage Carnot efficiency of an orifice pulse tube refrigerator are maximized using a novel hybrid statistical simulation approach. With the help of a one-dimensional numerical model, the inside gas flow and thermal processes responsible for the production of cooling effect inside the tube have been solved. Subsequently, the thermodynamic process parameters are calculated as a function of input geometrical parameters of the regenerator, pulse tube, and orifice valve. Response surface methodology is thereupon applied to investigate the influence of input factors on outputs. Desirability method is finally adopted to maximize both cooling capacity and percentage Carnot efficiency. A sensitivity investigation has been undertaken to find out the degree of influence of each input on the output. An experimental investigation has been conducted at the optimal set of parameters so as to validate the proposed methodology. The investigation shows that, there exists an almost linear relationship among the geometrical parameters of the pulse tube on outputs, and a nonlinear quadratic relationship among the geometrical parameters of regenerator on outputs. Finally, possible combination of input parameters have been generated by the model at which both the outputs are maximum.
| Nomenclature | ||
| A | = | fluid flow area, m2 |
| As | = | solid/matrix area, m2 |
| AL | = | wetted perimeter, m |
| Cf | = | friction factor |
| cv | = | specific heat at constant volume, J/kg-K |
| CV | = | orifice valve opening coefficient |
| cp | = | specific heat at constant pressure, J/kg-K |
| cs | = | specific heat of solid/matrix, J/kg-K |
| dh | = | characteristic diameter, m |
| f | = | cold head frequency, Hz |
| h | = | heat transfer coefficient, W/m2-K |
| = | cycle average enthalpy flow, J/sec | |
| k | = | fluid thermal conductivity, W/m-K |
| ks | = | solid/matrix thermal conductivity, W/m-K |
| = | mass flow rate, kg/s | |
| P | = | pressure, Pa |
| t | = | time, s |
| T | = | fluid temperature, K |
| TS | = | solid/matrix temperature, K |
| u | = | fluid velocity, m/s |
| V | = | volume, m3 |
| Wc | = | compressor input work, W |
| x | = | axial co-ordinate |
| Greek symbol | ||
| = | density of gas, kg/m3 | |
| τ | = | period, s |
| Subscript | ||
| c | = | compressor |
| o | = | orifice valve |
| res | = | reservoir |
| Acronyms | ||
| ANOVA | = | analysis of variance |
| BBD | = | Box–Benhken design |
| CHX | = | cold heat exchanger |
| COP | = | coefficient of performance |
| DIPTR | = | double inlet pulse tube refrigerator |
| DV | = | double inlet valve |
| GM | = | Gifford–McMahon |
| HHX | = | hot heat exchanger |
| HPV | = | high pressure valve |
| LPV | = | low pressure valve |
| OPTR | = | orifice pulse tube refrigerator |
| OV | = | orifice valve |
| PT | = | pulse tube |
| PTR | = | pulse tube refrigerator |
| REGN | = | regenerator |
| RES | = | reservoir |
| RSM | = | response surface methodology |
| RV | = | rotary valve |
Acknowledgments
Authors are thankful to Mr. Somnath Das for providing some useful suggestions during fabrication of components and leak detection. Mr. Tiga is also acknowledged for providing constructive suggestions during brazing and TIG welding process of components. Mr. S. Pani is acknowledged for his help during assembly.