Computational study of a novel Knudsen pump design exploiting drilling and 3D printing techniques in low thermal conductivity materials

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The Half-Range Moment Method in Harmonically Oscillating Rarefied Gas Flows

The formulation of the half-range moment method (HRMM), well defined in steady rarefied gas flows, is extended to linear oscillatory rarefied gas flows, driven by oscillating boundaries. The oscillatory Stokes (also known as Stokes second problem) and the oscillatory Couette flows, as representative ones for harmonically oscillating half-space and finite-medium flow setups respectively, are solved. The moment equations are derived from the linearized time-dependent BGK kinetic equation, operating accordingly over the positive and negative halves of the molecular velocity space. Moreover, the boundary conditions of the “positive” and “negative” moment equations are accordingly constructed from the half-range moments of the boundary conditions of the outgoing distribution function, assuming purely diffuse reflection. The oscillatory Stokes flow is characterized by the oscillation parameter, while the oscillatory Couette flow by the oscillation and rarefaction parameters. HRMM results for the amplitude and phase of the velocity and shear stress in a wide range of the flow parameters are presented and compared with corresponding results, obtained by the discrete velocity method (DVM). In the oscillatory Stokes flow the so-called penetration depth is also computed. When the oscillation frequency is lower than the collision frequency excellent agreement is observed, while when it is about the same or larger some differences are present. Overall, it is demonstrated that the HRMM can be applied to linear oscillatory rarefied gas flows, providing accurate results in a very wide range of the involved flow parameters. Since the computational effort is negligible, it is worthwhile to consider the efficient implementation of the HRMM to stationary and transient multidimensional rarefied gas flows

Προχωρημένη ντετερμινιστική και στοχαστική μοντελοποίηση φαινομένων μεταφοράς αερίων στη μικροκλίμακα

The theoretical and computational investigation of non-equilibrium transport phenomena in rarefied gases is one of the most interesting and challenging fields in engineering and physics. In recent years, this topic is gaining constantly increasing attention mainly due to its implementation in a wide range of technological applications, ranging from small scale devices like accelerometers and micro gas analyzers up to large scale gas distribution systems in fusion reactors and particle accelerators. The behavior of gasses in rarefied conditions cannot be captured by conventional fluid dynamic approaches, based on the Navier-Stokes-Fourier equations, due to the limited number of intermolecular collisions leading to a departure from local equilibrium. Modeling must be based on kinetic theory of gases on the basis of the Boltzmann equation, which unavoidably is associated with increased complexity and computational cost. In the present work, advanced kinetic modeling is conducted using the well-established deterministic Discrete Velocity (DVM) and stochastic Direct Simulation Monte Carlo (DSMC) methods. Novel numerical additions are developed for both methodologies and their validity and effectiveness is demonstrated by solving prototype problems in rarefied gas dynamics. Then, these new approaches are implemented to investigate and understand the underlying physics of unexpected transport phenomena observed in gas flows and heat transfer configurations far from local equilibrium. Furthermore, based on computationally efficient and advanced modeling, certain flow and heat transfer configurations, encountered in the design of various devices with miniaturized sizes and/or operating under low pressure conditions, are simulated. The computational advancements in conjunction with the Discrete Velocity Method include the development and implementation of a) a semi-analytical-numerical methodology based on the method of characteristics to simulate kinetic equations with external force terms, b) a marching DVM algorithm on unstructured meshes approximating complex geometries and c) a half-range synthetic acceleration scheme to speed-up the convergence rate of the DVM including the bulk quantities at the boundaries. The computational advancement in conjunction with the DSMC method includes the decomposition of the solution into its ballistic and collision parts, by accordingly tagging the simulation particles. Τopics concerning the application of kinetic theory and modeling in the design process of devices operating under rarefied conditions are addressed. The range of validity of the so-called implicit boundary conditions in pressure driven flows with respect to the flow parameters is specified. Also, a detailed parametric investigation is conducted for various geometrical configurations encountered in thermally driven micropumps. Finally, an uncertainty propagation analysis is performed for typical gas flow and heat transfer configurations.Η θεωρητική και υπολογιστική μελέτη φαινομένων μεταφοράς μακριά από τη θερμοδυναμική ισορροπία σε καταστάσεις υψηλής αραιοποίησης είναι ένας από τους πιο ενδιαφέροντες και απαιτητικούς κλάδους της μηχανικής και της φυσικής. Αυτό το πεδίο έρευνας αποκτά όλο και περισσότερη προσοχή τα τελευταία χρόνια, καθώς τέτοιες καταστάσεις απαντώνται σε ένα μεγάλο εύρος εφαρμογών, από μικροδιατάξεις όπως επιταχυνσιόμετρα και μικρό χρωματογράφους έως μεγάλης κλίμακας δίκτυα μεταφοράς αερίων σε αντιδραστήρες σύντηξης και επιταχυντές σωματιδίων. Η συμπεριφορά των αερίων σε καταστάσεις υψηλής αραιοποίησης δεν μπορεί να περιγραφεί από τις συμβατικές προσεγγίσεις της ρευστοδυναμικής που βασίζονται στις εξισώσεις Navier-Stokes-Fourier λόγω του περιορισμένου αριθμού των συγκρούσεων μεταξύ των μορίων του αερίου που οδηγεί σε μεγάλες αποκλίσεις από την θερμοδυναμική ισορροπία. Η μοντελοποίηση φαινομένων σε τέτοιες συνθήκες βασίζεται στην κινητική θεωρία των αερίων μέσω της εξίσωσης Boltzmann. Αυτό αυξάνει σημαντικά την πολυπλοκότητα και το υπολογιστικό κόστος αυτών των προσομοιώσεων. Στην παρούσα διατριβή, οι κινητικές προσομοιώσεις γίνονται χρησιμοποιώντας τις, πλέον καθιερωμένες ντετερμινιστικές και στοχαστικές μεθόδους, αυτές των διακριτών ταχυτήτων (DVM) και της απευθείας προσομοίωσης Monte Carlo (DSMC). Καινοτόμες επεκτάσεις εισάγονται και για τις δύο αυτές μεθοδολογίες και η ακρίβεια και αποδοτικότητά τους παρουσιάζονται λύνοντας κάποια πρότυπα προβλήματα του κλάδου της αραιοποιημένης θερμορευστοδυναμικής. Στη συνέχεια οι προσεγγίσεις αυτές εφαρμόζονται για την μελέτη και κατανόηση της φυσικής πίσω από κάποια απρόσμενα και παράδοξα φαινόμενα που παρατηρούνται σε διατάξεις ροής και μεταφοράς θερμότητας σε καταστάσεις υψηλής αραιοποίησης. Επιπλέον, κάνοντας χρήση αποδοτικών και πρωτοπόρων υπολογιστικών προσεγγίσεων γίνεται υπολογιστική μελέτη ροής και μεταφοράς θερμότητας σε διατάξεις που απαντώνται σε μικροηλεκτρομηχανολογικά εξαρτήματα και σε συσκευές που λειτουργούν σε περιβάλλον χαμηλής πίεσης. Οι καινοτομίες στις αριθμητικές μεθοδολογίες που χρησιμοποιούνται σε συνδυασμό με τη μέθοδο διακριτών ταχυτήτων περιλαμβάνουν την ανάπτυξη και εφαρμογή α) ενός ημι-αναλυτικού αριθμητικού σχήματος που βασίζεται στην μέθοδο των χαρακτηριστικών για την επίλυση των κινητικών εξισώσεων υπό την επίδραση εξωτερικών πεδίων δυνάμεων, β) ενός σχήματος προέλασης για την επίλυση των κινητικών εξισώσεων σε αδόμητα πλέγματα και περίπλοκες γεωμετρίες, γ) και ενός αριθμητικού σχήματος επιτάχυνσης της σύγκλισης της μεθόδου διακριτών ταχυτήτων που επιδρά και στους οριακούς κόμβους και βασίζεται σε ημιάπειρες ροπές. Η καινοτομία σε συνδυασμό με την μέθοδο απευθείας προσομοίωσης Monte Carlo περιλαμβάνει τη διάσπαση της λύσης σε δύο επιμέρους τμήματα που αντιστοιχούν στα σωματίδια που φτάνουν σε κάποιο σημείο του πεδίου με και χωρίς ενδομοριακές αλληλεπιδράσεις. Γίνεται εφαρμογή της κινητικής θεωρίας στον σχεδιασμό συσκευών και διατάξεων που λειτουργούν σε συνθήκες υψηλής αραιοποίησης. Βρίσκεται το εύρος εφαρμογής, σε σχέση με τις παραμέτρους της ροής, των λεγόμενων πεπλεγμένων οριακών συνθηκών σε ροές λόγω κλίσης πίεσης. Γίνεται, επίσης, μία λεπτομερής παραμετρική ανάλυση διαφόρων διατάξεων που απαντώνται στον σχεδιασμό μικρο-αντλιών χωρίς κινούμενα μέρη. Τέλος, γίνεται ανάλυση αβεβαιότητας σε τυπικές διατάξεις ροής και μεταφοράς θερμότητας

Pressure and temperature driven fully-developed rarefied gas flow in a channel with uniform injection/suction through its permeable walls

The pressure and temperature driven fully-developed rarefied gas flow between two parallel permeable plates, with uniform gas injection and suction from the bottom and top plates respectively, is investigated, based on the linearized Shakhov (S) model and the linearized Boltzmann equation (BE). Both flow configurations are characterized by the gas rarefaction parameter and the injection/suction velocity magnitude. Computational results for the so-called kinetic coefficients, as well as for the macroscopic quantities are provided in a wide range of the two parameters. The Onsager-Casimir reciprocity relation between the mechanocaloric and thermal creep coefficients has been proven to hold for arbitrary values of the injection velocity and has been used to validate the accuracy of the obtained results. It is shown that, the kinetic coefficients and macroscopic quantities are significantly affected as the injection velocity is increased. In addition, the kinetic results properly recover the corresponding analytical solutions in the free molecular and slip regimes. The examined prototype rarefied injection/suction flows may be useful to the investigation of more complex and realistic flow configurations in channels of various cross-sections with permeable walls where the injection velocity is not constant in the whole flow domain

Design Guidelines for Thermally Driven Micropumps of Different Architectures Based on Target Applications via Kinetic Modeling and Simulations

The manufacturing process and architecture of three Knudsen type micropumps are discussed and the associated flow performance characteristics are investigated. The proposed fabrication process, based on the deposition of successive dry film photoresist layers with low thermal conductivity, is easy to implement, adaptive to specific applications, cost-effective, and significantly improves thermal management. Three target application designs, requiring high mass flow rates (pump A), high pressure differences (pump B), and relatively high mass flow rates and pressure differences (pump C), are proposed. Computations are performed based on kinetic modeling via the infinite capillary theory, taking into account all foreseen manufacturing and operation constraints. The performance characteristics of the three pump designs in terms of geometry (number of parallel microchannels per stage and number of stages) and inlet pressure are obtained. It is found that pumps A and B operate more efficiently at pressures higher than 5 kPa and lower than 20 kPa, respectively, while the optimum operation range of pump C is at inlet pressures between 1 kPa and 20 kPa. In all cases, it is advisable to have the maximum number of stages as well as of parallel microchannels per stage that can be technologically realized

Pumping effect due to temperature gradients imposed in a multistage assembly consisting of long tapered orthogonal channels

International audienceThe temperature driven rarefied gas flow and the associated pressure difference in a multistage assembly consisting of a series of channels with linearly diverging or converging rectangular cross sections are computationally investigated. Each stage of the multistage assembly is consisting of one converging and one diverging channel. The net mass flow rate and the induced pressure difference between the inlet and outlet of the multistage assembly are parametrized in terms of the geometrical and operational data, paying specific attention to the diode effect and to the number of stages. The flow may be in the whole range of the Knudsen number and therefore modeling is based on kinetic theory, while the channels are taken efficiently long in order to justify the implemented infinite capillary methodology. Various flow setups are investigated to obtain the characteristic curves of the net mass flow rate versus the pressure difference in terms of channel geometry, input pressure, imposed temperature ratio and number of stages. The present work provides a powerful modeling tool in the manufacturing of a multistage Knudsen pump meeting certain pumping specifications

Proposal of a novel Knudsen pump design benefitting from drilling and 3D printing techniques in low conductivity materials

International audienceOver the past two decades a large number of MEMS and micro-devices have been developed. These miniaturized systems, such as lab-on-chip sensors, gas chromatography analyzers, etc., require micro-pumps for air sampling through the testing stages of the device. Additionally, some microscale components such as radio frequency switches, microscopic vacuum tubes and other parts that depend on electron or ion optics, require certain vacuum environment for proper operation. Simply sealing the devices is not sufficient because leaks and outgassing are excessively detrimental in vacuum devices at microscale level. Accordingly, such components may need vacuum pumping to maintain proper functionality. The thermal transpiration phenomenon has been extensively investigated; however, functional prototypes based on this phenomenon have been only recently developed. The Knudsen pump, which is one of the devices exploiting this well-known phenomenon, is able to generate a macroscopic gas flow by solely exploiting a tangential temperature gradient along a surface without requiring any external pressure gradient [1]. Specific geometrical and operational configurations have been investigated to optimize the efficiency of the pump in terms of generated mass flow rate and pressure difference, so analytical and numerical solutions for different configurations have been provided [2] and experimental measurements for thermal transpiration flow through channels have been reported [3]. Still, fabricating a Knudsen pump is not a trivial task mainly due to microfabrication difficulties and constraints linked to the control of local thermal gradients [4, 5]

Pumping effect due to temperature gradients imposed in a multistage assembly consisting of long tapered orthogonal channels

International audienceThe temperature driven rarefied gas flow and the associated pressure difference in a multistage assembly consisting of a series of channels with linearly diverging or converging rectangular cross sections are computationally investigated. Each stage of the multistage assembly is consisting of one converging and one diverging channel. The net mass flow rate and the induced pressure difference between the inlet and outlet of the multistage assembly are parametrized in terms of the geometrical and operational data, paying specific attention to the diode effect and to the number of stages. The flow may be in the whole range of the Knudsen number and therefore modeling is based on kinetic theory, while the channels are taken efficiently long in order to justify the implemented infinite capillary methodology. Various flow setups are investigated to obtain the characteristic curves of the net mass flow rate versus the pressure difference in terms of channel geometry, input pressure, imposed temperature ratio and number of stages. The present work provides a powerful modeling tool in the manufacturing of a multistage Knudsen pump meeting certain pumping specifications

Computational study of a novel Knudsen pump design exploiting drilling and 3D printing techniques in low thermal conductivity materials

International audienc