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Dissertations / Theses on the topic 'Pulse Tube Refrigerator'

Author: Grafiati

Published: 6 September 2023

Last updated: 31 July 2025

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1

Schor, Alisha R. (Alisha Robin). "Design of a single orifice pulse tube refrigerator through the development of a first-order model." Thesis, Massachusetts Institute of Technology, 2007. http://hdl.handle.net/1721.1/40482.

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Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2007.<br>"June 2007."<br>Includes bibliographical references (p. 41).<br>A first order model for the behavior of a linear orifice pulse tube refrigerator (OPTR) was developed as a design tool for construction of actual OPTRs. The model predicts cooling power as well as the pressure/volume relationships for various segments of the refrigerator with minimal computational requirements. The first portion of this document describes the development of this model and its simplifications relative to higher-order num

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2

Emery, Nick. "Cryogenic refrigeration using an acoustic stirling expander." Thesis, University of Canterbury. Mechanical Engineering, 2011. http://hdl.handle.net/10092/5306.

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A single-stage pulse tube cryocooler was designed and fabricated to provide cooling at 50 K for a high temperature superconducting (HTS) magnet, with a nominal electrical input frequency of 50 Hz and a maximum mean helium working gas pressure of 2.5 MPa. Sage software was used for the thermodynamic design of the pulse tube, with an initially predicted 30 W of cooling power at 50 K, and an input indicated power of 1800 W. Sage was found to be a useful tool for the design, and although not perfect, some correlation was established. The fabricated pulse tube was closely coupled to a metallic d

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3

Sultan, Ahmad. "Dynamique dans les fluides quantiques : Etude des excitations collectives dans un liquide de Fermi 2D." Phd thesis, Université de Grenoble, 2012. http://tel.archives-ouvertes.fr/tel-00768021.

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L'4He et l'3He sont des systèmes modèles pour comprendre les propriétés quantiques de la matière fortement corrélée. C'est pour cette raison que plusieurs études ont été consacrées à la compréhension de leur dynamique. A basses températures où les effets quantiques jouent un rôle essentiel, les excitations élémentaires dans l'4He sont décrites par un mode collectif d'excitations: phonon-roton. Par contre pour un système d'3He la description est plus complexe, le spectre d'excitation a deux composantes: un mode collectif (zéro-son) et un continuum d'excitations incohérentes de type particule-tr

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4

Conrad, Theodore Judson. "Miniaturized pulse tube refrigerators." Diss., Georgia Institute of Technology, 2011. http://hdl.handle.net/1853/41108.

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Pulse tube refrigerators (PTR) are robust, rugged cryocoolers that do not have a moving component at their cold ends. They are often employed for cryogenic cooling of high performance electronics in space applications where reliability is paramount. Miniaturizing these refrigerators has been a subject of intense research interest because of the benefits of minimal size and weight for airborne operation and because miniature coolers would be an enabling technology for other applications. Despite much effort, the extent of possible PTR miniaturization is still uncertain. To partially remedy th

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5

Watanabe, Atsuhiko. "Studies of superfluid stirling and pulse tube refrigeration." Thesis, Massachusetts Institute of Technology, 1995. http://hdl.handle.net/1721.1/36051.

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6

David-Calvet, Marc. "Refrigeration par tube a gaz pulse : etude theorique et experimentale." Paris 6, 1992. http://www.theses.fr/1992PA066110.

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Le tube a gaz pulse est un cryogenerateur qui, par sa grande fiabilite (pas de partie mecanique fonctionnant a froid ni orifice a basse temperature), sa relative facilite de construction et son importante capacite de refrigeration, est un candidat potentiel pour, par exemple, les applications embarquees sur satellites. Le principal objectif de cette these est d'expliquer le fonctionnement d'un tube a gaz pulse (t. G. P. ) avec orifice. Un modele analytique du t. G. P. Ideal a ete developpe. Le mecanisme des flux de chaleur aux extremites du tube est explique comme le resultat du cycle d'hyster

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7

Mulcahey, Thomas Ian. "Convective instability of oscillatory flow in pulse tube cryocoolers due to asymmetric gravitational body force." Diss., Georgia Institute of Technology, 2014. http://hdl.handle.net/1853/51808.

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Pulse tube cryocoolers (PTCs) are among the most attractive choices of refrigerators for applications requiring up to 1 kW of cooling in the temperature range of 4-123 K as a result of the high relative efficiency of the Stirling cycle, the reliability of linear compressors, and the lack of cryogenic moving parts resulting in long life and low vibration signature. Recently, PTCs have been successfully used in applications in the 150 K range, extending the useful range of the device beyond the traditional cryogenic regime. A carefully designed cylindrical cavity referred to as the pulse tube re

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8

Wilson, Kyle B. "The use of Sage simulation software in the design and testing of Sunpower's pulse tube cryocooler." Ohio : Ohio University, 2005. http://www.ohiolink.edu/etd/view.cgi?ohiou1126908659.

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9

Clearman, William M. "Measurement and correlation of directional permeability and Forchheimer's inertial coefficient of micro porous structures used in pulse tube cryocoolers." Thesis, Available online, Georgia Institute of Technology, 2007, 2007. http://etd.gatech.edu/theses/available/etd-07092007-111541/.

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Thesis (M. S.)--Mechanical Engineering, Georgia Institute of Technology, 2008.<br>Kirkconnell, Carl S., Committee Member ; Ghiaasiaan, S. Mostafa, Committee Chair ; Desai, Prateen V., Committee Member ; Jeter, Sheldon M., Committee Member.

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10

Saez, Sébastien. "Magnétomètres - Gradiomètres à capteurs supraconducteurs à haute température critique; Mise en oeuvre dans un cryogénérateur portable à tube pulsé." Phd thesis, Université de Caen, 2000. http://tel.archives-ouvertes.fr/tel-00011006.

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Les SQUID (Superconducting QUantum Interference Device), à haute température critique, permettent la réalisation de magnétomètres directionnels à haute sensibilité, pour des fréquences allant du continu à plusieurs centaines de kHz. Les seuils de détection atteints en chambre blindée autorisent la caractérisation fine du biomagnétisme, dont celui du muscle cardiaque. L'objectif de cette thèse était de réaliser un magnétomètre portable, opérant la détection des signaux cardiaques en milieu magnétiquement non-blindé. La modélisation du signal magnétique cardiaque par un moment magnétique variabl

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11

Cha, Jeesung Jeff. "Hydrodynamic Parameters of Micro Porous Media for Steady and Oscillatory Flow: Application to Cryocooler Regenerators." Diss., Available online, Georgia Institute of Technology, 2007, 2007. http://etd.gatech.edu/theses/available/etd-07092007-194225/.

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Thesis (Ph. D.)--Mechanical Engineering, Georgia Institute of Technology, 2008.<br>Jeremy P. Harvey, Committee Member ; Carl S. Kirkconnell, Committee Member ; Kurt D. Pennell, Committee Member ; S. Mostafa Ghiaasiaan, Committee Chair ; Prateen V. Desai, Committee Member ; Sheldon M. Jeter, Committee Member.

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12

Sun, Ping Wen, and 孫秉文. "Design of Variable Resistence Pulse Tube Refrigerator." Thesis, 1999. http://ndltd.ncl.edu.tw/handle/46618003597028149081.

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碩士<br>國立臺灣大學<br>機械工程學研究所<br>87<br>The main purpose of the research is to discuss replacing a needle valve or an orifice used in an orifice pulse tube refrigerator(OPT) with a variable resistence, and its effects to the performance of a pulse tube refrigerator.From three different types of designs(random-switch variable resistence,synchronous-switch variable resistence,and pressure-controlled-switch variable resistence) of a variable resistence pulse tube refrigerator(VRPT),we can find the optimal operating conditions for a VRPT.From analyses of the flow network theory to the system,

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13

YOU, TZUNG-SHIUN, and 游宗勳. "The Research of Capillary Pulse-Tube Refrigerator." Thesis, 1997. http://ndltd.ncl.edu.tw/handle/72862556081139275873.

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14

Rout, Sachindra Kumar. "Design and Analysis of Pulse Tube Refrigerator." Thesis, 2015. http://ethesis.nitrkl.ac.in/6966/1/2015_Sachindra_Phd_511ME107.pdf.

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After decades of rapid development, the absence of moving parts in the cold head, low vibration, long lifetime and high reliability, pulse tube refrigerators are the most promising cryo-coolers. Because of these momentous advantages, they are widely used in Superconducting Quantum Interference Devices (SQUIDs), cooling of infrared sensors, low noise electronic amplifiers, missiles and military helicopters, superconducting magnets, liquefaction of gases, gamma ray spectrometers, liquefaction of gases, X-ray devices and high temperature superconductors etc. It has also got wide applications in p

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15

Kumar, Pankaj. "Analysis of Pulse Tube Refrigerator using CFD." Thesis, 2019. http://ethesis.nitrkl.ac.in/9845/1/2019_PhD_PKumar_512ME122_Analysis.pdf.

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The present thesis is a detail endeavors of numerical investigation of an Inertance pulse tube refrigerator(IPTR) and Gifford-McMahon (GM) pulse tube followed by corresponding optimization of various geometrical and operating parameters including demonstration of a novel modification in existing GM pulse tube know how by proposing a piston arrangement on the double inlet connecting pipe. To start with, a benchmark IPTR model has been analyzed numerically using 2Daxisymmetric model followed by 3D assembly. Subsequently, the parametric optimizations have been carried out to estimate the opti

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16

Khandual, Abinash. "CFD Analysis of Stirling Type Inertance Tube Pulse Tube Refrigerator." Thesis, 2016. http://ethesis.nitrkl.ac.in/8375/1/2016_MT_214ME5353_AKhandual.pdf.

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Pulse tube cryocooler are generally one dimensional flow fields.By using two stage pulse tube cryocooler one can reach up to very low temperature.In it the compression and expansion of gas inside the pulse tube generates the required temperature.The main advantage of using pulse tube is that it does not have any moving parts inside the pulse tube rather oscillations of gas inside it does the job.All pulse tube cryocooler are of closed cycle type so no mass gets exit during the complete cycle.There is only one moving component named as piston which goes to and fro motion to generate the require

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17

JING-TUN, YOU, and 游鏡涒. "Control of a Variable Resistance Pulse Tube refrigerator." Thesis, 2000. http://ndltd.ncl.edu.tw/handle/42428957093761270512.

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碩士<br>國立臺灣大學<br>機械工程學研究所<br>88<br>The main purpose of this study is to control the cold-end temperature of the VRPT (Variable Resistance Pulse Tube refrigerator) including fixed the cold-end temperature control and increasing the cooling speed in order to apply the VRPT to the CPU cooling in personal computers. The system identification was used in this study to find out the transfer function of the cold-end temperature and the particular input by separating the influence of many inputs of the system. The controller controlled the cold-end temperature in order to achieve a faster c

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18

Yu, Guo Jr, and 余國誌. "Performance Improvement Research of Orifice Pulse Tube Refrigerator." Thesis, 1997. http://ndltd.ncl.edu.tw/handle/22036507454385782063.

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19

Rawat, Vivek Kumar. "Theoretical and Experimental Studies on Pulse Tube Refrigerator." Thesis, 2009. http://ethesis.nitrkl.ac.in/287/1/PTR_thesis.pdf.

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The absence of moving components at low temperature end gives the pulse tube refrigerator (PTR) a great leverage over other cryo-coolers like Stirling and GM refrigerators that are conventionally in use for several decades. PTR has greater reliability; no electric motors to cause electromagnetic interference, no sources of mechanical vibration in the cold head and no clearance seal between piston and cylinder. Moreover, it is a relatively low cost device with a simple yet compact design. The objectives of the present work are to 1) understand the basic phenomena responsible for the production

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20

Banjare, Yamuna Prasad. "Theoretical and Experimental Studies on Pulse Tube Refrigerator." Thesis, 2009. http://ethesis.nitrkl.ac.in/2757/1/YP_Banjar_thesis.pdf.

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The pulse tube refrigerator (PTR) is a cryocooler which is capable of reaching temperature of a few tens of Kelvin in a single stage and a few Kelvin in two stages. Unlike ordinary refrigeration cycles which utilize the vapor compression cycle, a PTR implements the oscillatory compression and expansion of gas within a closed volume to achieve the desired refrigeration. Pulse tube refrigerator has the advantages of long–life operation, high reliability and low vibration over the conventional cryocoolers, such as G-M and Stirling coolers because of the absence of moving parts at their low temp

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21

Dalai, Sisir Kumar. "Numerical analysis of diaphragm type pulse tube refrigerator." Thesis, 2013. http://ethesis.nitrkl.ac.in/5426/1/211ME3187.pdf.

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In present study a new modeling approach for the performance of a pulse tube refrigerator is proposed. A single stage Stirling type diaphragm type pulse tube refrigerator is considered for CFD simulation using Fluent software. The two-dimensional geometry is taken for simulation. In this simulation the physical dimensions of all the components are kept constant and pressure input is generated from the different UDF (User Defined Function) for compressor and diaphragm. Generally, DC gas flow in pulse tube refrigerator created a crucial problem at the time of application, which will affect the c

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22

Panda, Samarendra. "Numerical Analysis of Double Inlet Pulse Tube Refrigerator." Thesis, 2015. http://ethesis.nitrkl.ac.in/7921/1/2015_MT_NUmerical_Panda.pdf.

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Pulse Tube cryocooler or Pulse Tube Refrigerator (PTR) is a compact refrigerator which is capable of attaining a cryogenic temperature below 123 K (-150 K). As there are no moving components at low temperature side of PTR, it attracts the attention of various researchers. The advantages are mainly its simplicity, low vibration at cold end side, low cost, long life span and ease of manufacturing. With the tremendous development in the performance of PTR and due to its compactness, PTR has a wide range of applications like infrared sensors, aerospace, night vision equipments, communication, micr

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23

Kujur, Anjuni. "CFD Simulation of Inertance-Tube Pulse Tube Refrigerator with Variable Cross Section of Regenerator and Pulse Tube." Thesis, 2016. http://ethesis.nitrkl.ac.in/8376/1/2016_MT_214ME5328_AKujur.pdf.

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The computational fluid dynamics simulation of inertance tube pulse tube refrigerator with linear cross section and variable cross section of regenerator and pulse tube are presented in this paper. Volume of regenerator and pulse tube were kept same as linear cross section of regenerator and pulse tube for all cases. Five models with different cone angles and variable length of the convergent or divergent type regenerator and pulse tube were designed for each case. To optimize the cone angle where the performance of the inheritance tube pulse tube refrigerator is maximized, two models were int

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24

Ashwin, T. R. "CFD Studies Of Pulse Tube Refrigerators." Thesis, 2010. https://etd.iisc.ac.in/handle/2005/1849.

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The performance evaluation and parametric studies of an Inertance Tube Pulse Tube Refrigerator (IPTR) are performed for different length-to-diameter ratios, with the Computational Fluid Dynamics (CFD) package FLUENT. The integrated model consists of individual models of the components, namely, the compressor, compressor cooler, regenerator, cold heat exchanger, pulse tube, warm heat exchanger, inertance tube and the reservoir. The formulation consists of the governing equations expressing the conservation of mass, momentum and energy with axi-symmetry assumption and relations for the variable

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25

Ashwin, T. R. "CFD Studies Of Pulse Tube Refrigerators." Thesis, 2010. http://etd.iisc.ernet.in/handle/2005/1849.

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The performance evaluation and parametric studies of an Inertance Tube Pulse Tube Refrigerator (IPTR) are performed for different length-to-diameter ratios, with the Computational Fluid Dynamics (CFD) package FLUENT. The integrated model consists of individual models of the components, namely, the compressor, compressor cooler, regenerator, cold heat exchanger, pulse tube, warm heat exchanger, inertance tube and the reservoir. The formulation consists of the governing equations expressing the conservation of mass, momentum and energy with axi-symmetry assumption and relations for the variable

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26

Wang, Liang-Yun, and 王良耘. "Variable Duty Cycle Orifice Pulse Tube Refrigerator System Design." Thesis, 1999. http://ndltd.ncl.edu.tw/handle/98282681919666979990.

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碩士<br>國立臺灣大學<br>機械工程學研究所<br>87<br>The concept of using electro-magnetic valves to adjust the pressure waveform in an orifice pulse tube refrigerator (OPT) is experimentally and theoretically investigated. The objective of this thesis is to build an OPT system using a modified commercial refrigerant compressor and a pair of solenoid valves. A linear flow network model was developed for the system analysis of this refrigerator. The experiment results show that adjusting the duty cycle of input pressure may improve the cooling power of an OPT up to 20%, but the flow network model is no

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27

Kumar, M. "Phasor analysis of GM-type double Inlet pulse tube refrigerator." Thesis, 2014. http://ethesis.nitrkl.ac.in/6157/1/E-57.pdf.

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The simplicity and varied application of a pulse tube refrigerator has always gained the attention of many scientist and researchers towards itself. It is because of this very reason that various different types of pulse tube refrigerator has come up with time. A GM type double inlet pulse tube refrigerator (DIPTR) is one of the many configuration of the pulse tube that has come up with time. Although the configuration of a DIPTR seems to be quite simple but its working principle is a bit complicated. The aim of the present work is to study the working principle behind a DIPTR and develop a MA

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28

K, Prakash. "Numerical Investigation on Single Stage Co-Axial Pulse Tube Refrigerator." Thesis, 2017. http://ethesis.nitrkl.ac.in/9054/1/2017_MT_KPrakash.pdf.

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Pulse tube cryocooler is the best medium to attain very low temperatures. These Cryocoolers have practical applications everywhere ranging from Space Rockets to house hold refrigeration, like in Industrial Field, the industrial gases liquid oxygen and liquid nitrogen produced from air are very important assets. They account for about one-third of all cryogenic activity (nearly about $4 billion) in sales per year in the U.S., In Space Application they are used to produce Vacuum Chambers at high altitude for testing and also provide cooling of Cryogenic engines with liquid helium to sustain the

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29

Kumar, B. M. "Numerical investigation on the performance of inertance tube pulse tube refrigerator varying compressor frequency." Thesis, 2014. http://ethesis.nitrkl.ac.in/6274/1/E-92.pdf.

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Numerical studies of Pulse Tube Refrigeration are performed in the present dissertation to investigate the influence compressor frequency on the performance of Stirling type single stage Inertance Tube Pulse Tube Refrigerator (ITPTR). The entire inertance tube pulse tube refrigerator (ITPTR) operating under a specified boundary conditions are modelled using Finite Volume Method (FVM) with commercial software package ANSYS with Dynamic Meshing and User Defined Function. It is found that the performance of the ITPTR and the cooling rate is strongly dependent on the frequency of the compressor. T

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30

Pulagam, Madhu Kalyan Reddy. "Numerical Analysis of a High Pressure Helical Coil Tube in Tube Heat Exchanger for a Pulse Tube Refrigerator." Thesis, 2018. http://ethesis.nitrkl.ac.in/9758/1/2018_MT_216ME5407_MKRPulagam_Numerical.pdf.

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In the field of cryogenics heat exchangers always play an important role in bringing down the temperature or maintaining the temperature of a fluid. There are many types of heat exchangers being used worldwide for many different applications. One such application is the Pulse tube cryocooler. These pulse tube cryocoolers work on Stirling cycle and can bring the temperature down to 4K with the proper equipment and they are bound to have a heat exchanger at one of the pulse tube ends. Generally, a shell and tube heat exchangers are used because of it availability in the market but a helical c

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31

Gautam, C. K. "Numerical investigation on the performance of inertance tube pulse tube refrigerator by varying compressor amplitude." Thesis, 2014. http://ethesis.nitrkl.ac.in/6275/1/E-91.pdf.

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A numerical study has been made for the predication of the performance of inertance tube pulse tube refrigerator (ITPTR). Here basically the effect of amplitude of the piston in compressor on the performance of ITPTR has been investigated. At first, a specific geometry of ITPTR with a particular compressor-amplitude (from Cha et al., 2006) has been numerically modelled and studied and the results has been compared (with Cha et al., 2006) for the validation purpose. Then another one geometry of ITPTR has been considered and the amplitudes of this ITPTR compressor piston has been varied in two d

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32

Pagidipalli, Bhanu Chandar. "Numerical Analysis of Pulse Tube Refrigerator using Mixture of Gases as the Working Fluid." Thesis, 2018. http://ethesis.nitrkl.ac.in/9757/1/2018_MT_216ME5404_BCPagidipalli_Numerical.pdf.

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In the present project, numerical simulations are carri ed out for Inertance tube Pulse-Tube-Refrigerator (ITPTR) using pure He and gas mixture of helium and nitrogen (80% He and 20% N2in v/v basis). Pulse Tube Refrigerators are complex systems which require high amount of time and money for performing analysis through experimental study. A two dimensional(2D)axi-symmetric model of ITPTR is designed using the commercial CFD software: FLUENT.Simulation results of single stage ITPTR using helium gas and a mixture of helium and nitrogen gas are presented in this dissertation. The detail study

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33

Manoj, K. N. Sai. "Experimental Studies Towards Development of a Single Stage High Refrigerating Capacity G-M Type Pulse Tube Refrigerator." Thesis, 2016. http://ethesis.nitrkl.ac.in/8488/1/2016_MT_K._N.S_Manoj_614ME1004.pdf.

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The absence of moving components at low temperature end gives the pulse tube refrigerator(PTR)a great leverage over other cryocoolers like Stirling and G-M refrigerators that are conventionally in use for several decades.PTR has greater reliability;no electric motors to cause electromagnetic interference,no sources of mechanical vibration in the cold head and no clearance seal between piston and cylinder.Moreover,it is a relatively low cost device with a simple yet compact design.The objectives of the present work is to design,fabricate and test a single stage G-M type pulse tube refrigerator

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34

Kumar, Kranthi J. R. A. "Studies on Single and Two Stage Stirling Type Pulse Tube Coolers of Low and Medium Capacities including Performance Enhancement of Pressure Wave GeneratoI and a Novel Helium Recondensation System." Thesis, 2017. http://etd.iisc.ac.in/handle/2005/4224.

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Cryocoolers are mechanical devices that produce cold at temperatures below -150oC. Work required to produce the cold is supplied by a Pressure Wave Generator (PWG). This thesis is concerned with the development and analysis of Stirling type pulse tube cooler (PTC) systems of low and medium capacities along with performance improvement of PWG and design of a novel oil free and low maintenance helium recondensation system based on Stirling type pulse tube coolers and Joule-Thomson expansion. Pressure Wave Generator is a crucial part of pulse tube cooler system. Performance of PWG depends on m

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35

Yuan, Jie. "A study of pulse tube refrigerators." 1998. http://catalog.hathitrust.org/api/volumes/oclc/42641342.html.

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36

V, Venkatesh, and Chandru R. "Experimental Study of Pulse Tube Refrigerators." Thesis, 2007. http://ethesis.nitrkl.ac.in/116/1/10303008.pdf.

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The working fluid for the pulse tube refrigerator is Helium, which is non-toxic to humans and harmless to the environment. The Pulse Tube Refrigeration unit offers a viable alternative to units that currently require CFC and HCFC working fluids. Pulse Tube Refrigerators can be operated over wide range of temperatures. These units can be used in numerous space and commercial applications, including food freezers freeze dryers. It can also be used to cool detectors and electronic devices. The design of Pulse Tube Refrigeration Unit was based on Orifice Pulse Tube Concept. First the gas is compr

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37

Shi, Jinglei. "Optimization of single and multi-stage pulse tube refrigerators /." 2008. http://www.library.wisc.edu/databases/connect/dissertations.html.

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38

Koustubh, Bhosarkar. "Numerical Simulation of 3 Buffer type Pulse tube Cryocooler." Thesis, 2018. http://ethesis.nitrkl.ac.in/9753/1/2018_MT_216EE5397_BKoustubh_Numerical.pdf.

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The pulse tube refrigerator (PTR) is one of the cryocoolers which are used to produce very low temperatures. Since there are no moving parts (only moving part is piston which induces periodic motion to the working fluid), pulse tube refrigerator is therefore highly reliable and has long life -span than other cryocoolers. So, pulse tube refrigerator has been popularly used in various applications over other cryocoolers. To design the pulse tube refrigerator accurate model is required to predict its performance, such models are available in literature with their own limitati

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39

Lee, Cheng-Chung, and 李正忠. "Study on the Titanium Tube Condenser for Refrigeration System of Purse Seiner." Thesis, 2011. http://ndltd.ncl.edu.tw/handle/05317943638643962774.

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碩士<br>國立高雄海洋科技大學<br>輪機工程研究所<br>99<br>The purse seiner is one of the fishing vessels with lots of capital and technology in fishery industries. In west Pacific Ocean, there are 205 American Purse Seiner vessels, of which 88 vessels belong to Taiwan ship-owners (34 vessels are registered in Taiwan others are convenience flag ships). It almost occupies approximately 43 percents. The annual catching of these 34 Taiwan vessels is about two hundred thousand tons, and this is the largest amount in Taiwan deep-sea fishery. The most influential effect of the fish price depends on its fresh condition wh

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