CD-based Modeling of Transort Phenomena for Engineering Problems Maksim Mezhericher Abstract Comutational luid Dynamics is a oular modeling aroach which utilizes numerical methods and comuter simulations to solve and analyze roblems that involve transort henomena in fluid flows. CDbased models demonstrate high versatility and caability of dealing with a wide range of engineering roblems. This article resents two eamles of CD-based comutational modeling successfully alied for different fields of engineering: article engineering by drying rocesses and thermal management of car comartment. Inde Terms car thermal management, comutational fluid dynamics, article engineering, transort henomena M I. INTRODUCTION ANY contemorary engineering roblems involve flows of liquid and/or gas, transort of heat by conduction, convection and radiation mechanisms, mass transfer by diffusion and convection, flows of bubbles, dros or articles, combustion etc. These comle roblems require fundamental understanding that cannot be rovided only by available eerimental techniques, and therefore theoretical and numerical modeling are essential. Recent rogress in comuter industry stimulated fast develoment of comutational aroaches and numerical methods, among them Comutational luid Dynamics (CD). This is a wide sread modeling aroach which utilizes numerical methods and comuter simulations to solve and analyze roblems that involve transort henomena in fluid flows. Lots of commercial and oen comuter codes are imlementing CD technique: ANSYS LUENT, ANSYS CX, LOW-3D, STAR-CD, COMSOL CD, OenOAM, OenVM and many others. This contribution resents two eamles of CD-based comutational modeling successfully alied for different fields of engineering: article engineering by drying rocesses and thermal management of car comartment. In site of aarent differences, these two models have common roots in descrition of transort henomena of the gas hase that resented in the both considered cases. II. PARTICLE ENGINEERING BY DRYING PROCESSES A. Sray Drying Sray drying is a widely alied technology used to transform solutions, emulsions or susensions into dry granules, article agglomerates or owder, by feeding the liquid miture as a sray of drolets into a medium with a hot drying agent. Because sray drying can be used either as a reservation method or simly as a fast drying technique, this rocess is utilized in many industries, such as food manufactures, harmaceutical, chemical and biochemical industries. Sray drying is a raid rocess (u to several seconds) comared to other methods of drying (e.g., ulse combustion drying, drum drying, freeze drying) due to the small sray drolet sizes and their large secific surface areas that maimize rates of heat and mass transfer. Therefore, this technique is the referred drying method for many thermally-sensitive materials. Sray drying also turns a raw material into a dried owder in a single ste, which can be advantageous for rofit maimization and rocess simlification. Along with other drying techniques, sray drying also rovides the advantage of weight and volume reduction. Dyestuffs, aint igments, lastics, resins, catalysts, ceramic materials, washing owders, esticides, fertilizers, organic and inorganic chemicals, skim and whole milk, baby foods, instant coffee and tea, dried fruits, uices, eggs, sices, cereal, enzymes, vitamins, flavors, antibiotics, medical ingredients, additives, animal feeds, biomass this list of the sray-dried roducts is far from being comlete. A tyical sray drying tower includes an atomizer, which transforms the sulied liquid feed into a sray of drolets, and a contact miing zone, where the sray interacts with a hot drying agent. As a result of this interaction, the moisture content of the drying agent increases due to liquid evaoration from the drolets. In turn, due to evaoration, the sray drolets shrink and turn into solid articles. The drying rocess roceeds until the dried articles with the desired moisture content are obtained and then the final roduct is recovered from the drying chamber. Deending on the rocess needs, drolet sizes from 1 to 1000 µm can be achieved; for the most common alications average sray drolet diameters are between 100 to 200 µm. Air under atmosheric ressure, steam and inert gases like nitrogen are oular drying agents used nowadays. It is noted that inert gases are alied for drying flammable, toic or oide-sensitive materials. Manuscrit received March 6, 2012; revised Aril 10, 2012. M. Mezhericher is with the Mechanical Engineering Deartment, Sami Shamoon College of Engineering, Israel (hone: 972-8-647-5075; fa: 972-8-647-5749; e-mail: maksime@sce.ac.il). B. Pneumatic Drying Pneumatic (flash) drying is another eamle of etensively used technology in food, chemical, agricultural
and harmaceutical industries. The main advantages of this rocess are fast elimination of free moisture from rereared feed of wet articles and oeration in continuous mode. Tyically, the feed is introduced into the drying column by a screw via a Venturi ie. The articles dry out in seconds as they are conveyed by hot gas (air) stream. Then, the roduct is searated using cyclones which are usually followed by scrubbers or bag filters for final cleaning of the ehaust gases. In site of its aarent simlicity, the rocess of neumatic drying is a comle multi-scale multi-hase transort henomenon involving turbulent miing of humid gas and multi-comonent wet articles, heat and mass transfer interaction between the drying gas and disersed hase, and internal heat and moisture transort within each conveyed wet article. III. THERMAL MANAGEMENT O CAR COMPARTMENT One of the most energy-eensive units in contemorary vehicles is the air conditioning system (ACS). On an average, such systems consume u to 17% of the overall ower roduced by vehicle engines of the world, deending on the cooling regime and environment thermal load [1]. It is remarkable that air-conditioning units in cars and light commercial vehicles burn more than 5% of the vehicle fuel consumed annually throughout the Euroean Union [2]. or instance, the United Kingdom emits about 3 million tones of CO 2 each year simly from owering the air-conditioning systems in vehicles. In South Euroean and Mediterranean countries the roblem of air ollution increase by ACS owering is even more acute. Etensive theoretical and eerimental studies have been erformed throughout the recent years, aimed to reduce the fuel consumtion and environmental ollution due to vehicle air conditioning. Proer thermal management based on the gas dynamics inside the vehicle assenger comartment is crucial for air conditioning and heating systems erformance as well as for the comfort of the assengers. On the other hand, the nature of the flow, namely the velocity field in combination with the temerature distribution, has a strong influence on the human sensation of thermal comfort [3]. In the resent research it is roosed to develo a threedimensional theoretical model of transort henomena in car comartment. This model is based on Eulerian aroach for the gas flow and takes into account thermal energy transfer by simultaneous conduction, convection and radiation mechanisms within the comartment as well as outside the vehicle. The model is able to redict steady-state and transient rofiles of air velocity, density, ressure, temerature and humidity for various regimes of the air conditioning, vehicle driving modes, comartment configurations and ambient conditions. To assess the assenger level of thermal comfort, a methodology based on ublished studies [4,5] might be develoed and the corresonding equations might be couled to the develoed comutational model. Moreover, the effect of the assengers themselves on their thermal comfort (e.g., heat emission by human body, air inhalation and gas miture ehalation etc.) might be considered. The CD-based model of thermal management can be utilized as a tool for the following arametric investigations: enhancement of natural convection within a comartment, influence of thermal insulation and trim materials on the assenger thermal comfort as well as effect of introduction of innovating assive cooling techniques on energy consumtion by ACS. IV. THEORETICAL MODELING A. Sray and Pneumatic Drying Transort henomena in drying rocesses is subdivided into eternal (gas-articles miing) and internal (within disersed drolets/articles). The fluid dynamics of continuous hase of drying gas is treated by an Eulerian aroach and a standard k-ε model is utilized for turbulence descrition. The utilized threedimensional conservation equations of continuity, momentum, energy, secies, turbulent kinetic energy and dissiation rate of turbulence kinetic energy are as follows (i, = 1, 2, 3): - continuity u Sc, (1) t where and u are drying gas density and velocity, and is mass source term. - momentum conservation u u i ui uiu e t i i (2) gi U isc g, where and e are drying gas ressure and effective viscosity, U is article velocity and g is sum of the forces eerted by articles on the gas hase. - energy conservation e h h u h qr Sh, (3) t h where h is secific enthaly, q r and S h are thermal radiation and energy source terms, resectively. - secies conservation e Y v Yv u Yv Sc, (4) t Y where Y v is mass fraction of vaour in humid gas. - turbulence kinetic energy e k k u k Gk Gb t k, (5) where k is turbulent kinetic energy and ε is dissiation rate of turbulent kinetic energy. - dissiation rate of turbulence kinetic energy e u C1G k C2. t (6) k The roduction of turbulence kinetic energy due to mean velocity gradients is equal to: u u i ui Gk T. (7) i S c
The roduction of turbulence kinetic energy due to buoyancy is given by: T T Gb g, (8) where T is gas temerature and is coefficient of gas thermal eansion: T 1 T. (9) The utilized constants are C1 1.44, C2 1.92, and the Prandtl numbers are equal to 0.9 and k h Y T 1.3. The effective viscosity, e, is defined as:, (10) where is turbulent viscosity T In the above eression C 0.09. e T 2 k T C. (11) The constitutive relationshi between air temerature, ressure and density is given by the ideal gas law (such model is sufficient because of small humidity of the gas involved in the considered multihase flow): T, (12) M where is universal gas constant and M is molecular weight of the gas hase. To track the traectories and other valuable arameters of sray of drolets and articles, a Discrete Phase Model (DPM) based on Lagrangian formulation is utilized. The motion of the drolets/articles is described by Newton s Second Law: du dt g. (13) m Here is sum of the forces eerted on given sray drolet/article by the gas hase, by other articles and walls of the sray drying chamber; g is gravity acceleration, and U and m are drolet/article velocity and mass, resectively. In general, the acting forces on sray drolet/article are as follows: where mass force, D B A PG C other, (14) D is drag force, B is buoyancy force, A is added PG is ressure gradient force and C is contact force. The term other reresents other forces, usually imortant for submicron articles and/or at secific conditions, e.g., horetic, Basset, Saffman, Magnus forces etc., and neglected in the resent work for simlicity. The drag force is determined by the eression: 2 d D CD u U u U, (15) 8 where d is drolet/article diameter and u is velocity of gas hase. The drag coefficient, C D, is calculated according to well-known emirical correlations for sherical articles. The buoyancy force ooses gravity and in the resent study it is much smaller than the latter, because the densities of sray drolets and drying gas differ more than thousand times. or this reason the buoyancy of drolets/articles is currently neglected. The added mass ( virtual-mass ) force, required to accelerate the gas surrounding the drolet/article, is given by: 3 d d A u U. (16) 12 dt or flow in dryers, this force may be imortant in the drolets/articles entrance region, where the velocities of inected disersed hase and drying gas are substantially different and their intensive miing leads to high change rates of the relative velocities. The ressure gradient in the gas hase additionally accelerates drolets/articles and results in the following force: GP 3 d. (17) 6 This force can be essential and worth consideration in the dryer regions with fast ressure changes like inlet, outlet and swirling zones of the gas hase. The contact force arises from collision interactions between the given drolet/article with other drolets/ articles or walls of the drying chamber. At the current ste these interactions are not considered and corresondingly the contact force is neglected, because the focus of this work was on imlementation of reviously develoed descrition of internal transort henomena in the disersed hase. In the resent work the internal transort henomena within each drolet/ article are described with the hel of reviously develoed and validated two-stage drying kinetics model, see [6]. The drying rocess of drolet containing solids is divided in two drying stages. In the first stage of drying, an ecess of moisture forms a liquid enveloe around the drolet solid fraction, and unhindered drying similar to ure liquid drolet evaoration results in the shrinkage of the drolet diameter. At a certain moment, the moisture ecess is comletely evaorated, drolet turns into a wet article and the second stage of a hindered drying begins. In this second drying stage, two regions of wet article can be identified: layer of dry orous crust and internal wet core. The drying rate is controlled by the rate of moisture diffusion from the article wet core through the crust ores towards the article outer surface. As a result of the hindered drying, the article wet core shrinks and the thickness of the crust region increases. The article outer diameter is assumed to remain unchanged during the second drying stage. After the oint when the article moisture content decreases to a minimal ossible value (determined either as an equilibrium moisture content or as a bounded moisture that cannot be removed by drying), the article is treated as a dry non-evaorating solid shere. It is worth noting that all drolets and articles are assumed to be sherical and a full radial symmetry of inter-drolet hysical
drolet temerature Proceedings of the World Congress on Engineering 2012 Vol III arameters (temerature, moisture content etc.) is believed. The concet of two-stage drolet drying kinetics is illustrated by ig. 1. D D i 3 4 mean drolet diameter is assumed to be 70.5 μm, the sread arameter is set at 2.09, and the corresonding minimum and maimum drolet diameters are taken as 10.0 μm and 138.0 μm, resectively. The overall sray mass flow rate is equal to 0.0139 kg/s (50 kg/hr). The walls of drying chamber are assumed to be made of 2-mm stainless steel, and the coefficient of heat transfer through the walls is set to zero as though there is a erfect thermal insulation of the chamber. inally, the gage air ressure in the outlet ie of the drying chamber is set to -100 Pa. 1 2 0 1-st stage 2-nd stage final sensible heating D 0 drying time ig. 1. Concet of two-stage drolet drying kinetics [6]. B. Thermal Management of Car Comartment The conservation equations of the above 3D model of transort henomena in article engineering rocesses can also be alied to describe the gas flow and heat and mass transfer within a car assenger comartment and in its surroundings. Particularly, in the resent study 3D comressible Reynolds Averaged Navier-Stokes (RANS) equations including k-ε turbulence formulation (1)-(12) are utilized to redict flow atterns of the gas miture (air, vaor, CO 2 ) inside a assenger comartment and air flow outside the cabin. These equations are solved by alying a inite Volumes Method (VM). The comutational model formulated in such way is caable of redicting air velocity, temerature and secies flow atterns inside the comartment under different ambient conditions. Moreover, the model can be used to rognosticate energy consumtion of ACS that is necessary for roviding assengers comfort at given outside thermal load. In addition, numerical simulations with this 3D model may facilitate revealing weak oints and otimization of eisting/newly designed car air conditioning systems. A. Sray Drying V. NUMERICAL SIMULATIONS A cylinder-on-cone sray dryer with co-current flow of drying air and sray of drolets (ig. 2) is adoted from the literature [6]. A centrifugal ressure nozzle atomizer is located at the to of the drying chamber and the drying air enters the to of the chamber through an annulus without swirling at angle of 35 with resect to the vertical ais. Preheated atmosheric air at temerature 468 K and absolute humidity of 0.009 kg H 2 O/kg dry air is sulied into the drying chamber through a central round inlet of the flat horizontal ceiling. The air inlet velocity is 9.08 m/s, whereas its turbulence kinetic energy is equal to 0.027 m 2 /s 2 and turbulence energy dissiation rate is 0.37 m 2 /s 3. The sray of liquid drolets is obtained by atomizing the liquid feed in the nozzle. The sray cone angle is assumed to be 76, the drolet velocities at the nozzle eit are assigned to 59 m/s, and the temerature of the feed is set at 300 K. The distribution of drolet diameters in the sray is assumed to obey the Rosin-Rammler distribution function, where the ig. 2. Sray dryer setu used in the study. Left icture - isometric view, right icture - sketch of the adoted chamber geometry. The numerical solution of the model equations and comutational simulations have been erformed by utilizing a 3D ressure-based solver incororated in CD ackage ANSYS LUENT 13. The solver is based on the finite volumes technique and enables two-way couled Euler- DPM algorithm for treatment of the continuous and discrete hases. The chamber geometry has been meshed by 619,711 unstructured grid cells of tetrahedral and olyhedral shae with the various mesh sizes. Particularly smaller mesh volumes are located in the regions of high concentration of the discrete hase in the downstream direction of the sray inection, where large gradients of momentum, heat and mass transfer are eected to occur. Corresondingly, grid cells of the larger sizes are located near the to and side walls of the chamber. The 3D sray from ressure nozzle is modeled by 20 satial drolet streams. In turn, each drolet stream is reresented by 10 inections of different drolet diameters: minimum and maimum diameters are 10.0 μm and 138.0 μm, whereas the intermediate drolet sizes are calculated by alying Rosin-Rammler distribution function with 70.5 µm of drolet average size. In this way, totally 200 different drolet inections have been introduced into the comutational domain. All the numerical simulations of sray drying rocess have been erformed in steady-state two-way couling mode of calculations. or continuous hase, the satial discretization was erformed by uwind scheme of second order for all conservation equations (ecet ressure solved by PRESTO! rocedure) and SIMPLE scheme was used for couling between the ressure and velocity. or the disersed hase, the tracking scheme was automatically selected between low order imlicit and high order traezoidal schemes based on the solution stability. DPM sources were udated every iteration of the continuous
hase. The overall steady-state numerical formulation was of the second order of accuracy. The comutation of internal transort henomena for the discrete hase was accomlished using the concet of user defined functions (UD). In this way, the first drying stage and the final heating of non-evaorating dry articles were simulated using the ANSYS LUENT built-in functions resonsible for evaoration and sensible heating of drolets. or the second drying stage, the set of corresonding equations was solved for each wet article using the original numerical algorithm described in details by Mezhericher [6]. This numerical solution was imlemented as a subroutine and linked to the ANSYS LUENT solver via a set of the original UDs. The decision whether the built-in functions or the UDs of the second drying stage should be used for the secific sray article at the given calculation ste was made automatically by the solver based on the current article moisture content. ig. 3. low fields of air velocity (m/s): frontal (left), side (middle) and isometric (right) cuts. ig. 4. low atterns of air temerature (Kelvin): frontal (left), side (middle) and isometric (right) cuts. ig. 6. Particle traectories colored by article law inde: frontal (left), side (middle) and isometric (right) views. Here 0 means drolet initial heating, 1 corresonds to drolet evaoration, 2 indicates second drying stage (wet article drying) and 3 designates article final sensible heating. B. Pneumatic Drying or the uroses of the theoretical study the geometry of Baeyens et al. [7] eerimental set-u is adoted. Hot dry air and wet articles are sulied to the bottom of vertical neumatic dryer with 1.25 m internal diameter and 25 m height (see ig. 1). The develoed theoretical model was numerically solved with the hel of inite Volume Method and 3D simulations of neumatic drying were erformed using the CD ackage LUENT. or these uroses, the 3D numerical grid with 9078 distributed heahedral/wedge cell volumes was generated in GAMBIT 2.2.30 using the Cooer scheme. The flow of wet articles in the neumatic dryer was simulated through 89 inections of sherical articles. Each inection began on the bottom of the dryer at the centroid of one of the 89 bottom lane mesh elements. The article inections were normal to the dryer bottom lane and arallel to each other. The numerical simulations were erformed in the following way. irst, the flow of drying air was simulated without the discrete hase until converged solution. At the net ste, wet articles were inected into the domain and two-way couled simulations were erformed until convergence. The convergence of the numerical simulations was monitored by means of residuals of the transort equations. Particularly, the converged values of the scaled residuals were ensured to be lower than 10-6 for the energy equation and 10-3 for the rest of equations. The convergence was also verified by negligibly small values of the global mass and energy imbalances. ehaust gas dry articles 25 m Ø 1.25 m ig. 5. Particle traectories colored by article surface temerature (Kelvin): frontal (left), side (middle) and isometric (right) views. wet articles air ig. 7. Schematic sketch of neumatic dryer setu [7] (left) and utilized numerical grid (right).
ig. 8. 3D air flow atterns for PVC drying in neumatic dryer (adiabatic flow). Left velocity magnitude, m/s, right temerature, K. ig. 12. Simulated contours of air velocity in car comartment (m/s, reresentative vertical cut). C. Air low Patterns in Car Passenger Comartment A simlified model of conventional car assenger comartment was adoted for numerical simulations. The original car model was created in 3D Studio Ma software whereas the etracted comartment geometry was rocessed in ANSYS ICEM CD rogram and meshed with 518,705 olyhedral (3-6 faces) grid cells. Then, steady state 3D numerical simulations using ANSYS LUENT code were erformed. ig. 9. Car model in 3D Studio Ma software (left) and etracted comartment geometry (right). ig. 10. Numerical grid used in the flow simulations igures 11-13 demonstrates the results of numercal simulations of air flow atterns in the comartment. our air inlets with velocity 1 m/s and temerature 12 ºC and two air outlets with -150 Pa gage ressure were assumed. The ambient temerature was taken 37 ºC and heat transfer coefficient was set to 10 W/(m 2 K), assuming arked car. ig. 11. Simulated streamlines of steady-state air velocity in car comartment. ig. 13. Simulated contours of air temerature in car comartment (ºC, reresentative vertical cut). VI. CONCLUSION Comutational CD-based modelling is a owerful tool for descrition, simulation and analysis of variety of engineering roblems involving macroscoic transort henomena (fluid/gas dynamics, turbulence, heat transfer and mass transfer). CD-based models demonstrate high versatility and caability of dealing with a wide range of engineering roblems. Numerical simulations utilizing CD-based models can substantially reduce amount of necessary eeriments, time and overall cost of solution of many engineering and scientific roblems. Basic knowledge in CD-based modelling and ability to work with CD software are becoming to be necessary skills for contemorary engineers and researchers. REERENCES [1] M.A. Lambert, and B.J. Jones, Automotive Adsortion Air Conditioner Powered by Ehaust Heat. Part 1: Concetual and Embodiment Design, J. Automobile Engineering, vol. 220, no. 7,. 959-972, 2006. [2] Sortion Energy Seeking to Commercialize Waste Heat-Driven Adsortion Heat Pum Technology for Vehicle Air Conditioning. Green Car Congress htt://www.greencarcongress.com, 24 Aril 2010. [3] Alication Briefs from LUENT. EX170. Vehicle Ventilation System. htt://www.fluent.com/solutions/automotive/e170_vehicle_ventilati on_system.df [4] L. Huang and T.A. Han, Case Study of Occuant Thermal Comfort in a Cabin Using Virtual Thermal Comfort Engineering, in Proc. EACC 2005-2nd Euroean Automotive CD Conference, rankfurt, Germany, 29-30 June 2005. [5] G. Lombardi, M. Maganzi,. Cannizzo and G. Solinas, The Use of CD to Imrove the Thermal Comfort in the Automotive ield, in Proc. EACC 2007-3nd Euroean Automotive CD Conference, rankfurt, Germany, 5-6 July 2007. [6] M. Mezhericher, Theoretical modeling of sray drying rocesses. Volume 1. Drying kinetics, two and three dimensional CD modeling. LAP Lambert Academic Publishing, Saarbrücken, Germany, 2011. ISBN 978-3-8443-9959-2. [7] J. Baeyens, D. van Gauwbergen and I. Vinckier, Pneumatic drying: the use of large-scale eerimental data in a design rocedure, Powder Technology, vol. 83,. 139 148, 1995.