Numerical Analysis of Double Inlet Two-Stage Inertance Pulse Tube Cryocooler

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Numerical Analysis of Double Inlet Two-Stage Inertance Pulse Tube Cryocooler International Journal of Advanced Technology and Engineering Exploration, Vol 8(79) ISSN (Print): 2394-5443 ISSN (Online): 2394-7454 Research Article http://dx.doi.org/10.19101/IJATEE.2021.874108 Numerical analysis of double inlet two-stage inertance pulse tube cryocooler Mahmadrafik Choudhari1*, Bajirao Gawali2, Mohammedadil Momin3, Prateek Malwe1, Nandkishor Deshmukh1 and Rustam Dhalait1 Research Scholar, Walchand College of Engineering, Sangli-416415, India1 Professor, Walchand College of Engineering, Sangli-416415, India2 M.Tech Scholar, Walchand College of Engineering, Sangli-416415, India3 Received: 08-May-2021; Revised: 25-June-2021; Accepted: 27-June-2021 ©2021 Mahmadrafik Choudhari et al. This is an open access article distributed under the Creative Commons Attribution (CC BY) License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract Stirling-type Pulse Tube Cryocoolers (PTC) are designed to meet present and upcoming commercial requirements and needs with durability and low vibrations. Multistaging in Stirling type PTC is one of the major developments reported in recent times for low-temperature achievement, due to improved performance over a period of time. The current study aims to define the methodology for numerical assessment of Double Inlet Two-Stage Pulse Tube Cryocooler (DITSPTC) to achieve cryogenic temperature of 20 K. This paper performs Computational Fluid Dynamics (CFD) simulation of PTC for defining the methodology using the CFD software package and then the same methodology is extended for the analysis of DITSPTC. The system simulations are performed with frequency of 70 Hz and average pressure of 20 bar. The minimum temperatures obtained from simulations are 95 K and 20 K at the first and second stage respectively. Keywords Pulse tube cryocooler, CFD, Cryogenic temperature, Multistaging, Double inlet valve. 1.Introduction Hu et al. [5] done numerical and experimental studies The basic Pulse Tube Cryocoolers (PTC) was invented of DIPTC and IPTC. They determined that optimal by Gifford and Longsworth [1]. A compressor is used phase shift cannot be obtained by the use of an to drive this system which does pressurization and inertance tube only for low cooling power, but can depressurization of working gas to obtain the required provide an optimum phase shift for PTCs with high effect in the system. Continuous analysis and cooling power. Double inlet valve incorporated to subsequent enhancement in the performance of PTC obtain optimal phase shift in case of low cooling has done in the last few decades. Mikulin et al. [2] power PTC. Roy and Kundu [6] done the introduced the orifice type PTC. thermodynamic analysis of basic PTC, OPTC, and DIPTC and shown that the DIPTC gives better cooling The addition of an orifice valve results in Cold End performance than basic PTC, OPTC. Heat Exchanger (CHX) temperature of 105 K using air as the working fluid. Based on phase shift, design Multistaging in Stirling type PTC is one of the major variations were proposed as double inlet Orifice Pulse developments reported in recent times, due to its Tube Cryocooler (OPTC) [3] and Inertance Tube simplicity of operation and improved performance Pulse Tube Cryocooler (IPTC) [4]. They proposed that over a period of time. Multistaging in cryocoolers is the performance of the basic PTC can be enhanced by required to attain much lower temperatures [7]. PTCs adding a phase-shifting mechanism as shown in are thermally coupled in series to form the multistage Figure 1. The setting of a double inlet valve governs PTC. The first stage is employed to precool the second the performance of the cryocooler to a great extent. stage. Matrix with different sizes and materials can be The distribution of the total gas from the compressor employed depending on the operating temperature into the stages is crucial as it mainly depends on the range, resulting in improved efficiency and lower cost. area available through the double inlet valve. Cryocoolers are connected in series to reach the lower Accordingly, the mass flow rate through the valve is temperature region. One stage is used to precool the the governing factor. next stage. Single-stage Stirling type PTC can reach down to a temperature of 40-50 K, while temperatures *Author for correspondence around 20 K could be achieved by two-stage PTC. For 766 International Journal of Advanced Technology and Engineering Exploration, Vol 8(79) below 10 K, three-stage PTC is used [8]. The very first inertance tube and reservoir of the third stage kept in two-stage Stirling type PTC is reported in the literature cryogenic environment instead of ambient, which by Yang et al. [9]. The developed unit has coaxial improves the performance of the system. Jeong and Jin geometry for both stages. Tendolkar et al. [10] done [19] compared two-stage cryocooler and cascade experimental investigations on an integral- cryocooler on the thermal performance basis and it is configuration Stirling-type Two-Stage Pulse Tube observed that cascading performs better when the Cryocooler (TSPTC). A double inlet valve is temperature ratio is large. incorporated to the second stage with an inertance tube for the enhancement in the performance of the system. For the design and optimization of PTC, there are Dietrich and Thummes [11] developed a TSPTC for a different models accessible in the literature with cooling load of 12.9W at 25K. The specialty of this certain benefits and some limitations. The system is the use of cold head instead of the cold end experimental assessment of PTC is tremendously heat exchanger in the first stage as no cooling is demanding and expensive, while analytical is a time- required at intermediate temperature. Wu et al. [12] requiring assessment method. Most of the researchers achieved 15K with a cooling load of 0.3W. developed different numerical models for analysis due to the accurate prediction of results. Isothermal model Recent advancements in the multistaging of IPTC are [20–22], adiabatic model [10, 23], energy equation the addition of step displacer as a phase shifter [13– model [24], and Computational Fluid Dynamics 16], Stirling/Pulse Tube Hybrid Cryocooler (SPC) (CFD) model [25–27]. The isothermal model and [17], cryogenic phase-shifting mechanism [18], and adiabatic model are extensively used due to their cascading of cryocoolers [19]. Pang et al. [13, 14] simplicity. These models can give broad clarification added step displacer in two-stage PTC to enhance the by considering the real process occurring in the system performance. Integral structure type step displacer to some extent. At lower cold end temperatures, it is improved efficiency by 5.42%. Step displacer found that the energy equation model can anticipate implements two functions, one is to distribute work the cooling power performance of the PTC system between two stages and the second is to control phase sensibly well. CFD model can give detailed shift. In the second stage of step displacer Two-Stage clarification about the real process occurring in the Inertance Pulse Tube Cryocooler (TSIPTC), the cyclic system and it predicts much more accurate results. steady temperature of 16.9 K is attained at CHX Researchers have done CFD analysis of PTC for experimentally [15, 16]. Raytheon Company different geometrical and operational parameters with developed an innovative SPC in 1999. SPC is made 2D axisymmetric [25, 26] and 3D plane-symmetric with a combination of Stirling cryocooler and PTC in models [27, 28]. For optimization of PTC, CFD the first and second stage respectively. SPC has the models [29] and various artificial intelligence methods collective advantage of high efficiency and reliability like ANN, PSO-ANN, and ANFIS method are used to from Stirling cryocooler and PTC respectively. That’s attain maximum refrigeration and Coefficient of the reason why SPC is suitable for space application. Performance (COP) by giving an optimum range of Liu et al. [17] developed SPC with cooling capacity of inputs [30–32]. Panda et al. [32] revealed that 1.16W at 35K and 7.25W at 85K. Dang et al. [18] used refrigerating capacity and COP increased by 10.8% a cryogenic phase-shifting approach instead of an and 0.76% respectively. external precooling approach to avoid complexity in multistaging. In the case of the three-stage PTC, Figure 1 Inertance pulse tube cryocooler system 767 Mahmadrafik Choudhari et al. Exhaustive literature is available about single-stage default settings. FLUENT offers the user-defined configurations. However, very scanty data are function option for defining such conditions. available about the double inlet valve with multistage configurations in the literature. As per the author’s 2.1Governing equations knowledge, three-dimensional CFD modeling of The continuity, momentum, and energy equation are multistaging with double inlet valve is not available in the main governing equations employed. When fluid the literature. So, we get motivated and developed the flows in the PTC, these Equations 1, 2 and 3 must be methodology for the numerical investigation of satisfied. Conservation equations based on the multistaging PTC with the double inlet valve. The continuum can be used throughout the PTC system. objective of the current study is to design a Double The mean free path of a gas molecule is often Inlet Two-Stage Pulse Tube Cryocooler (DITSPTC) significantly less than the characteristic dimension of for 20K cryogenic temperatures. the PTC components. 휕휌 + 훻 ∙ (휌푣⃗) = 0 (1) 휕푡 This paper performs CFD simulations of IPTC for 휕 (휌푣⃗) + 훻 ∙ (휌푣⃗푣⃗) = − 훻푝 + 훻 ∙ (휏̿) (2) defining the methodology using the CFD software 휕푡 package and then the same methodology is extended 휕 (휌퐸) + 훻 ∙ (푣⃗(휌퐸 + 푝)) = 훻 ∙ (푘푒푓푓훻푇 + (휏푒푓푓̿ ∙ 푣⃗)) to the analysis of DITSPTC. For the assessment of 휕푡 (3) DITSPTC and CFD was used as a numerical tool. Cha et al. [26] PTC model and Tendolkar et al.
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