Numerical study of electrohydrodynamic atomization by openfoam

VIETNAM NATIONAL UNIVERSITY HO CHI MINH CITY HO CHI MINH CITY UNIVERSITY OF TECHNOLOGY MAI NGOC LUAN NUMERICAL STUDY OF ELECTROHYDRODYNAMIC ATOMIZATION BY OPENFOAM Major: AEROSPACE ENGINEERING Major code : 8520120 MASTER’S THESIS HO CHI MINH CITY, July 2023 THIS THESIS IS COMPLETED AT HO CHI MINH CITY UNIVERSITY OF TECHNOLOGY – VNU-HCM Academic Supervisor: Assoc Prof Dr Ngo Khanh Hieu Examiner 1: Assoc Prof Dr Le Tuan Phuong Nam Examiner 2: Dr Pham Minh Vuong This thesis is defended at Ho Chi Minh City University of Technology, VNUHCM on July 15th, 2023 Master's Thesis Committee: Assoc Prof Dr Vu Ngoc Anh Chairman Dr Vuong Thi Hong Nhi Secretary Assoc Prof Dr Le Tuan Phuong Nam Examiner Dr Pham Minh Vuong Examiner Dr Nguyen Song Thanh Thao Member Approval of the Chairman of Master's Thesis Committee and the Dean of Faculty of Transportation Engineering after the thesis being corrected CHAIRMAN OF THESIS COMMITTEE DEAN OF FACULTY OF TRANSPORTATION ENGINEERING VIETNAM NATIONAL UNIVERSITY HO CHI MINH CITY HO CHI MINH CITY UNIVERSITY OF TECHNOLOGY SOCIALIST REPUBLIC OF VIETNAM Independence – Freedom – Happiness MASTER THESIS ASSIGNMENT Student name: MAI NGOC LUAN Student ID: 2170729 Date of birth: 08/11/1997 Place of birth: Ho Chi Minh City Major: Aerospace Engineering Major code: 8520120 I THESIS’S TITLE: Numerical study of electrohydrodynamic atomization by OpenFOAM (Phân tích tượng phun tĩnh điện phương pháp số sử dụng phần mềm OpenFOAM) II THESIS ASSIGNMENT: This thesis aims to develop a electrohydrodynamic solver based on the opensource software OpenFOAM to investigate the single cone-jet mode of electrospray The solver is physically verified and validated with preceding literature and with experiment data under the consideration of liquid’s contact angle condition Additionally, the solver is enhanced to investigate the Taylor cone formulation process under the effects of corona discharge The outcome of this thesis will serve as the basis for future numerical analyses of electrospray III DATE OF ASSIGNMENT: 14/02/2023 IV DATE OF COMPLETION: 09/06/2023 V SUPERVISOR’S FULL NAME: Associate Professor Dr Ngo Khanh Hieu Ho Chi Minh City,……/……./2023 SUPERVISOR (Sign and write full name) HEAD OF DEPARTMENT (Sign and write full name) DEAN OF FACULTY OF TRANSPORTATION ENGINEERING (Sign and write full name) i ACKNOWLEDGEMENT This work is accomplished under a collaboration between VNU-HCM Key Lab for Internal Combustion Engine, Ho Chi Minh City University of Technology, Ho Chi Minh City, Vietnam and School of Engineering and Built Environment, Griffith University, Queensland, Australia I gratefully acknowledge Associate Professor Dr Ngo Khanh Hieu, Dr Dau Thanh Van, Dr Tran Canh Dung, Dr Dinh Xuan Thien, Mr Vu Trung Hieu and Mr Vu Hoai Duc for helping achieve this state of my thesis I would like to thank Dr Nguyen Tan Hoi and CFD team at TechnoStar Vietnam for supporting me during my Master course Additional thanks to Ms Truong Van Ngoc for proofreading and grammatical corrections Ho Chi Minh City, July 2023 Mai Ngoc Luan ii ABSTRACT Electrospray, or Electrohydrodynamic Atomization (EHDA) operates on the principles of electrohydrodynamics which deal with the motion of fluids placed inside an electrical field When a fluid is subjected to an adequately strong electrical field, its surface can be deformed, creating a meniscus from whose apex thin jets is induced Eventually, these jets are destabilized and disintegrated into microscale or nanoscale charged droplets Among the known operating regimes of electrospray, the stable single cone-jet mode is the most desired and applicable because of its stability, controllability, and high yield rate in comparison to other regimes In this thesis, we program an electrohydrodynamic solver to simulate the conejet mode based on the Taylor-Melcher leaky-dielectric model The solution for the electrostatic governing equations is additionally developed, coupling with OpenFOAM’s interFOAM to model incompressible time-dependent multiphase fluid flow The solver is physically verified and validated with preceding literature as well as with experiment data under the further consideration of liquid’s contact angle condition, followed by analyses on the effects of electrical conductivity, voltage, surface tension, flow rate, and fluid viscosity on spray current and jet diameter Numerical results are in reasonable agreement with experiments and consistent with preceding literature Additional studies on different contact angles are performed, suggesting potentially major impacts of this factor on the cone-jet mode in high voltage and low flow rate circumstances Furthermore, the electrohydrodynamic solver is enhanced to investigate the Taylor cone formulation process under the effects of corona discharge Electrospray-corona simulation and contrasting experiment with high-speed camera show significant improvement of the numerical prediction for Taylor cone formation, implying the crucial role of liquid wetting to the Taylor cone formation in numerical electrospray-corona discharge studies Keywords: capillary nozzle, CFD, cone-jet, corona discharge, electrospray, liquid wetting, OpenFOAM, Taylor cone, … iii TÓM TẮT LUẬN VĂN Công nghệ phun sương lực tĩnh điện sử dụng để tạo sơn khí từ điện áp lớn Công nghệ hoạt động dựa nguyên tắc điện thủy động lực học dùng để giải vấn đề liên quan đến chuyển động lưu chất điện trường Khi chất lỏng đặt trường điện trường đủ lớn, bề mặt bị biến dạng tạo cấu trúc có dạng hình nón từ tạo tia chất lỏng bắn từ đỉnh hình nón Sau tia chất lỏng bị phân tách thành vi hạt mang điện tích Trong chế độ hoạt động công nghệ này, chế độ đơn tia có khả ứng dụng cao tính ổn định, khả điều chỉnh cao phun hiệu Trong luận văn này, tác giả phát triển công cụ mô kết hợp tĩnh điện lưu chất dựa mơ hình Taylor-Melcher leaky-dielectric để nghiên cứu chế độ đơn tia Bộ giải phương trình tĩnh điện phát triển thêm, kết hợp với giải interFoam có sẵn OpenFOAM để mơ dịng chuyển động đa pha, khơng nén, phụ thuộc vào thời gian Độ tin công cụ mô minh chứng cách tái tạo tượng vật lý so sánh với nghiên cứu trước, với thí nghiệm có tính tới ảnh hưởng góc tiếp xúc lưu chất Tiếp đó, ảnh hưởng yếu điện dẫn, điện áp, sức căng bề mặt, lưu lượng, độ nhớt lưu chất lên dịng điện phun đường kính tia phun phân tích Kết mơ cho thấy đồng hợp lý với liệu so sánh Thêm vào đó, phân tích góc tiếp xúc lưu chất khác thể ảnh hưởng lớn yếu tố trường hợp điện áp cao lưu lượng thấp Cuối cùng, công cụ mô cải tiến để xem xét q trình tạo thành nón Taylor ảnh hưởng tượng phóng điện Các kết mô với liệu thực nghiệm cho thấy cải tiến rõ rệt việc dự đốn q trình tạo thành nón Taylor, từ thể vai trị tiềm của tính dính ướt lưu chất mơ hình thành nón Taylor ảnh hưởng tượng phóng điện Từ khóa: ống mao dẫn, phương pháp số động lực học lưu chất, đơn tia, tượng phóng điện, dính ướt lưu chất, OpenFOAM, nón Taylor, … iv THE COMMITMENT I hereby commit that: - This master thesis outline is done by me with guidance from Assoc Prof Ngo Khanh Hieu, Dr Dau Thanh Van, Dr Dinh Xuan Thien, and with the support of Dr Canh-Dung Tran, Mr Vu Trung Hieu and Mr Vu Hoai Duc - Design of the experiment apparatus and supporting experiments are carried out by the research team at the School of Engineering and Built Environment, Griffith University, Australia led by Dr Dau Thanh Van The author’s contributions include program development, all disclosed numerical simulations, data curation and visualization, and scientific discussions presented in this thesis - The data, numbers, results in this work except for specialized experiments are done by me at Ho Chi Minh City University of Technology Any publication or article reusing the content of this work is dominantly authored by me and explicitly declared in the “Publications” section of this thesis - All of the references used in this work are cited fully and clearly in information: name of the author(s), title, date of publication, place of publication with highest precision in my knowledge Author, Mai Ngoc Luan v TABLE OF CONTENTS THESIS ASSIGNMENT i ACKNOWLEDGEMENT ii ABSTRACT iii TÓM TẮT LUẬN VĂN iv THE COMMITMENT v TABLE OF CONTENTS vi List of Tables ix List of Figures x Nomenclature xiv Chapter Thesis introduction 1.1 Motivation 1.2 Objective(s) of the study 1.3 Investigation subject and scope of study 1.4 Literature review Chapter 2.1 Background theories .14 Electrostatics 14 2.1.1 Electric charge and electric field 14 2.1.2 Coulomb’s law 15 2.1.3 Gauss’s law .16 2.1.4 Conservation of charge 17 2.1.5 Electrostatic force density .18 2.2 Computational Fluid Dynamics 18 2.2.1 Navier-Stokes equations 18 vi 2.2.2 OpenFOAM 19 2.2.3 InterFOAM solver 20 2.2.3.1 Pressure-velocity coupling 20 2.2.3.2 Volume of Fluid interface tracking method .25 2.2.3.3 Contact angle correction .28 Chapter 3.1 Electrohydrodynamic coupling procedure .30 The Taylor-Melcher leaky-dielectric model 30 3.1.1 Fluidic field .32 3.1.2 Electrostatic field 32 3.1.3 Corona discharge 33 3.2 Structure and solving process of interElectroFoam .34 Chapter 4.1 Results and discussion 36 Code validation .36 4.1.1 Physical verification of interElectroFoam 36 4.1.2 Validation with previous literature 41 4.1.3 Validation with experiment results 47 4.2 Dimensionless analyses 53 4.3 Contact angle effects on Taylor cone .60 4.4 Simulation of corona discharge effects in electrospray 63 4.4.1 Corona discharge condition assumptions .64 4.4.2 Simulation results on Taylor cone formulation 64 Chapter Conclusion and prospective future research 71 Publications 73 Reference 74 vii Appendix A Experimental apparatus 83 Appendix B Additional experiment results 85 Appendix C Contact angle correction formulation .87 Appendix D Additional simulation results 90 VITA .92 viii [53] [54] [55] [56] [57] [58] [59] [60] [61] [62] [63] [64] [65] [66] [67] [68] J Roche, "Introducing electric fields," Physics Education, vol 51, no 5, p 055005, 2016 E Britannica (2022, 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Pham, and V T Dau, "Jet flow in a circulatory miniaturized system using ion wind," Mechatronics, vol 47, pp 126-133, 2017 82 Appendix A Experimental apparatus The numerical simulation for the jet formation at the nozzle tip is investigated and evaluated by experiment using the nozzle-to-ring configuration whose schema is described in Fig A1 Liquid is fed to the tip of a nozzle, where its interface is deformed by an applied electric field before elongating into a jet The system consists of a steel nozzle, a metal ring with an outer diameter of 10 mm and an inner diameter of 4.8 mm, a high-voltage power source, and a syringe pump Two types of nozzles, Nozzle (N1) and Nozzle (N2), are employed for the experiment, with N1 featuring outer diameter (o.d) and inner diameter (i.d) of 0.3 and 0.15 mm (G29 nozzle), respectively, and N2 featuring o.d and i.d of 0.7 and 0.4 mm (G22 nozzle), respectively The distance between nozzle and ring ( rE ) is adjusted at mm for N1 and mm for N2 to establish sufficient electric field A high-speed camera (HHC X9 Pro, Mega Speed, USA) and a microscope camera (AM 4113, Dino-Lite, Australia) are used to capture the formation of Taylor cone and its development into fluid jet and droplets at the nozzle tip The used liquid is polyethylene glycol with molecular weight of 200 (PEG-200 - Merck, Australia) The objective of this experiment is to observe the formation of Taylor cones, jet elongation, and propagation of liquid using both high-speed and microscope camera To achieve a stable Taylor cone and jet, the applied voltage is fixed at 3400 and 5400 V for N1 and N2, respectively Meanwhile, a voltage of 5600 V is applied to capture the formation process of a Taylor cone with the high-speed camera The flow rate is fixed at 0.75 ml/h, which is determined by the approximation of the minimum flow rate required for a stable Taylor cone Q   r  /  e These experimental conditions allow for the observation and analysis of the physical phenomena of interest Moreover, the contact angle of PEG-200 is determined by capturing the droplet on a stainless-steel plate with a digital camera (HHC X9 Pro, Mega Speed, USA) The measurements on are performed using the ImageJ software 83 (NIH) Here, similar material with the metal nozzles is employed to reflect equivalent conditions with the liquid on nozzles Figure A1 Schema of experiment installation Figure A2 (a) The experiment setup (1) Power supply, (2) Voltmeter, (3) Amplifier, (4) Electrospray device, (5) Microscope camera, (6) Ammeter; (b) Close-up image of the Electrospray device (7) Nozzle, (8) Ring electrode, (9) Syringe pump; (c) High-speed camera (HHC X9 Pro, Mega Speed, USA); (d) Microscope camera (AM 4113, Dino-Lite, Australia) Our experiment setup is shown in Fig A2(a),(b) which each device’s annotation listed in the caption Meanwhile, Fig A2(c),(d) include the images of the used highspeed camera and the microscope camera used for capturing Taylor cone’s shape and formation 84 Appendix B Additional experiment results Figure B1 provides close-up images of the nozzle’s tip used in experiments and of the geometric model used in simulations As observed, empirical nozzle is relatively filleted and rounded at the outer edge, therefore, the simulation model is also prepared with rounded edge to maintain conformity with experiments Figure B1 Close-up capture of (a) The tip of empirical nozzle N2; and (b) The tip of simulation nozzle N2 Figure B2 shows an unannotated capture of PEG-200 on a stainless-steel plate in addition to the image included in the main content Figure B2 Unannotated capture of PEG-200 droplet situated on a stainless-steel plate Figure B3 Overall view of experimental capture of (a) N1 configuration; and (b) N2 configuration Since experimental Taylor cones in the main content are not clear and may cause confusion due to the slight inclined jet of the N1 configuration We include an 85 overall view of the experiment results in Fig B3, showing that the incline angle is negligibly small, and the cone-jet mode is still steady and produces relatively straight and stable spray in both cases, therefore, we consider the achieved cone-jet is acceptably symmetric Figure B4 Additional long exposure captures of ionized glowing region adjacent to the nozzle’s outer edge Glowing region indicates strong electric field and source of corona discharge In addition to Fig 4-32 in the main content, we provide more photographs of the ionized glowing region nearby the nozzle’s outer edge in Fig B4 This is in support for our discharge source assumption and our electric field contour in Fig 4-31(a) Figure B5 Image of (a) A PEG-200 droplet on Teflon; (b) Electrospray of PEG-200 with a Teflon nozzle Figure B5(a) shows high contact angle created by a droplet of PEG-200 on a Teflon surface; and Fig B5(b) shows the PEG-200’s Taylor cone attaching on the inner edge of the nozzle’s wall These results support the claims on the contact angle effects in section 4.3 In this case, special treatments on voltage application must be performed since Teflon is a plastic-type and not electrically conductive Subsequently, there is no corona discharge from the Teflon nozzle edges, hence, the behaviors of the liquid’s interface not contradict with the findings in section 4.4 86 Appendix C Contact angle correction formulation This section provides the formulation of the Eq (2.38) in the main content which calculates the contact angle correction coefficients a and b The formulation in this section is derived by the author by dissecting the OpenFOAM’s source code Eq (2.38) writes a cos   cos  cos(   ) ,  cos  02 cos(   )  cos  cos  b ,  cos  02 (C.1) Firstly, some definitions have to be clarified Figure C1 Illustration of the vectors and angles in contact angle correction of OpenFOAM Annotations are (i) The uncorrected liquid interface forming an uncorrected contact angle (  ) with the solid surface; (ii) The corrected liquid interface forming a desired contact angle (θ) with the solid surface t and t w are the tangential vectors at liquid-solid contact position of interface (i) and (ii), respectively Contact angle cos   t c  t w  n c  n w and cos   t  t w  n  n w n0 : The uncorrected interface normal vector calculated from   in which the   is taken from either initial condition or the previous time step nc : The corrected interface normal vector which is the final result of the contact angle correction nw : The wall normal vector which is calculated from computational mesh 87  : The desired contact angle which is declared in boundary conditions (   20  or any predeclared angle) and used to control by the formula cos   n c  n w  : The uncorrected contact angle which is calculated from cos   n  n w The illustration of the involved vectors and angles are shown in Fig C1 The calculations of contact angle must satisfy two criteria Firstly, the resulted contact angle must be planar with both wall normal vector nw and the uncorrected interface normal vector n0 , therefore n c  a n w  bn , (C.2) where a and b are correction coefficients Secondly, the value of nc must satisfy cos   n c  n w , (C.3) where  is the desired contact angle At this point, nw is known from the mesh geometry and n0 can be calculated from the initial/previous condition, so the problem is to find the correction coefficients a and b so nc can be calculated This procedure commences by deriving a system of equations by dot product of the two sides of Eq (C.2) with nw and n0 simultaneously cos   a  b cos 0 cos   a  b cos 0   nc  n0  a cos 0  b cos(0   )  a cos 0  b (C.4) a  cos  b cos0 (i)  cos(0   )  a cos 0  b (ii) where    is the angle between the corrected and uncorrected interface normal vector, and cos(   )  n c  n (i) a  cos   b cos   (ii) cos(   )   cos   b cos   cos   b  cos(   )   cos  cos   b cos  02   b with  cos(   )  cos  cos   b 1  cos   0 b cos(   )  cos  cos  (iii)  cos  02 88 replacing (iii) in (i) obtains a cos   cos  cos(   ) ,  cos  02 (C.5) and nc can be calculated Eventually, the new nc is used to evaluate the new  field and will modify the VOF calculation, the direction of the surface tension force by     correcting the curvature       , and ultimately affect the r.h.s of the  momentum equation 89 Appendix D Additional simulation results Figure D1 includes the space charge density contour for cases with two different electric conductivities (  e   10 5 S/m and  e   10 4 S/m ), while Fig D2 shows the cone and jet 3D render from phase fraction for these same two conductivities As can be seen, the charge density is considerably larger in the case of higher conductivity, especially in the cone-to-jet transition region, inducing larger jet velocity As discussed in the main content, larger jet velocity and mass conservation are responsible for a reduction in jet diameter which can be observed in Fig D2 Figure D1 Volumetric charge density contour in cases (a)  e   10 5 S/m and (b)  e   10 4 S/m Figure D2 3D cone and jet render in cases (a)  e   10 5 S/m and (b)  e   10 4 S/m 90 Additionally, Fig D3 includes a set of results for cases with different applied voltages (   3600 V and   4000 V ), Fig D3 (a),(b) contrast the jet velocity and Fig D4 (c),(d) compare the jet diameter in these two cases Here, the velocity of the larger voltage is mildly higher than the other case, whilst jet diameter experiences an opposite tendency This relationship causes a relatively unchanged spray current discussed in the main content Figure D3 Jet velocity contour in cases (a)   3600 V and (b)   4000 V ; 3D jet render in cases (c)   3600 V and (d)   4000 V Figure D4 additionally provides the contour the corona charge cloud in different discharge currents from I d  0.1  A to I d  1.5  A The width of the charge cloud can be explicitly seen more expanded due to higher currents, which is in support of the discussion surrounding Fig 4-34 in the main content Figure D4 Corona charge cloud coverage for different discharge currents 91 VITA Name: Mai Ngoc Luan Date of birth: 08/11/1997 Place of birth: Ho Chi Minh City Address: 153/64 Le Hoang Phai, Ward 17, Go Vap District, Ho Chi Minh City EDUCATIONAL BACKGROUND Time Educational background 6/2015 – 6/2019 Ho Chi Minh City University of Technology, Bachelor of Engineering in Aerospace Engineering 2/2022 – 7/2023 Ho Chi Minh City University of Technology, Master of Engineering (Research-based) in Aerospace Engineering EMPLOYMENT HISTORY Time 6/2019 – current Employment history Representative Office of TechnoStar Co Ltd in HCMC 92