Numerical investigation of Ranque-Hilsch energy separation effect A.S. Noskov 1,a, V.N. Alekhin 1,b, A.V. Khait 1,a

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1 Applied Mechanics and Maerials Online: ISSN: , Vol. 281, pp doi: / Trans Tech Publicaions, Swizerland Numerical invesigaion of Ranque-Hilsch energy separaion effec A.S. Noskov 1,a, V.N. Alekhin 1,b, A.V. Khai 1,a 1 Russian Federaion, Ekaerinburg, Mira sr., 19, Ural Federal Universiy named afer he firs Presiden of Russia B.N. Yelsin a haianaoliy@gmail.com, hai@mail.ru, b referesf@yandex.ru Keywords: Ranque-Hilsch effec, energy separaion, emperaure separaion, vorex ube, compuaional fluid dynamics, numerical simulaion, energy conservaion equaion. Absrac. Some resuls of invesigaion of energy separaion mechanism included in numerical model equaions of air spiral flow appearing in Ranque-Hilsch vorex ube are presened in he aricle. Sandard k-ε urbulence model had been used in he simulaions. I was found ha k-ε urbulence model make possible o predic Ranque-Hilsch energy separaion effec by using special semi empirical erm in energy conservaion equaion which accouns for urbulence hea conduciviy effecs. Inroducion Vorex ube is he device in which he compressed gas (air) is divided ino wo sreams one colder, han iniial sream, and anoher hoer [1, 2]. In simples case vorex ube is a cylindrical or conic pipe ino which he sream of he compressed gas injecs angenially (Fig. 1). As a resul compressed gas sream forms cenrifugal flow. Ouside par of his flow heas up and oules from one side of he ube, he cenral par of he flow is cooled and oules from anoher side of he ube. Energy separaion effec appearing in vorex ube was discovered in 1931 and i is called Ranque- Hilsch effec. Fig. 1. Principle schemaic of vorex ube 1 nozzle inle; 2 energy separaion chamber; 3 cold flow diffuser; 4 unswirler wih hrole orifices; 5 nozzle divergen duc; G1 compressed gas (air) inle; G2 ho flow oule; G3 cold flow oule Since he ime when Ranque-Hilsch effec was discovered grea number of differen heoreical invesigaions was performed o explain he naure of his effec. Some number of differen heoreical simplificaions (hypoheses) was developed. Bu anyway mahemaical model of energy (emperaure) separaion phenomenon are no exis in presen ime. Some resuls of invesigaion of energy separaion mechanism included in numerical model equaions of air spiral flow appearing in Ranque-Hilsch vorex ube are presened in his work. Numerical model Numerical model based on sandard sysem of equaions for viscous compressible fluid dynamics had been used in presen work [3,4,5]. This model includes he following equaions: Reynolds equaion, coninuiy equaion, energy conservaion equaion, equaion of ideal gas sae. All righs reserved. No par of conens of his paper may be reproduced or ransmied in any form or by any means wihou he wrien permission of Trans Tech Publicaions, (ID: , Pennsylvania Sae Universiy, Universiy Park, USA-11/05/16,02:06:22)

2 356 Mechanical Engineering, Maerials and Energy II The sandard semi empirical k-ε urbulence model had been used for closing he equaions sysem. The air had been used as a coninuum and is properies had been accouned for in he model. The main geomery dimensions of considered vorex ube (Fig. 1): energy separaion chamber lengh L =168 [mm]; energy separaion chamber diameer D = 16,8 [mm]; cold flow diffuser diameer d = 9,8 [mm]; conical angel α = 3,5. Numerical soluion of he equaions sysem was carried ou in open source CFD sofware OpenFOAM. RhoCenralFoam solver was used. Kurganov-Tadmor [6] second order cenral numerical schemes are implemened in his solver. The compuaional domain had been meshed by srucured algorihm. Toal number of compuaional cells was The following boundary condiions had been used: - Inle ino he vorex ube (G1, Fig. 1): saic pressure p = 500 [kpa]; saic emperaure T = 300 [К]; k = 0,5 [m 2 /s 2 ]; ε = 0,5 [m 2 /s 3 ]. - Cold (G3) and ho (G2) oules: saic pressure p = 0 [Pa]. - «No slip» and adiabaic wall condiions had been used. Three ypes of energy conservaion equaion had been used: 1. The equaion aking ino accoun molecular and urbulen hea conduciviy (Eq. 1). 2. The equaion aking ino accoun only molecular hea conduciviy (Eq. 1, λ = 0). 3. The equaion wihou molecular and urbulen hea conduciviy (Eq. 1, λ = λ = 0). λ+ λ cp ( ρh) + div( ρvh) div grad( h) p =, (1) H oal enhalpy; h saic enhalpy; V velociy vecor; ρ air densiy; p saic pressure; λ - molecular hea conduciviy coefficien; λ urbulen hea conduciviy coefficien; c p hea capaciy. Sandard k-ε urbulence model accouns for he following funcional dependence for urbulence hea conduciviy: 2 µ C k = ρ, (2) Pr Pr ε λ µ = c p C µ and Pr (urbulen Prandl number) empirical consans of k-ε urbulence model. Numerical simulaion resuls Resuls of numerical simulaions of air spiral flow wih use of all hree ypes of energy conservaion equaion are presened on Fig. 2 and Fig. 3. These figures represens disribuion of saic and oal emperaure in cross-secion of he vorex ube energy separaion chamber which is placed on he disance of one diameer (1D) from he nozzle inle. I is clear from hese figures ha equaion 3 demonsraes he lowes energy separaion effec and equaion 1 demonsraes he highes effec. Toal emperaure disribuion (Fig. 3) for he case of equaions 2 and 3 represens a horizonal curve. I means ha oal emperaure all over he cross-secion have consan value. Bu when he effecs of urbulen hea conduciviy are accouned for oal emperaure has he following disribuion in his energy separaion chamber cross-secion: ouside par of cross-secion has higher emperaure comparing wih cener par. Thus urbulen hea conduciviy effec has more considerable impac on energy separaion in comparison wih molecular hea conduciviy.

3 Applied Mechanics and Maerials Vol Fig. 2. Saic emperaure disribuion in vorex ube energy separaion chamber cross-secion placed on he one diameer (1D) disance from nozzle inle Fig. 3. Toal emperaure disribuion in vorex ube energy separaion chamber cross-secion placed on he one diameer (1D) disance from nozzle inle I is clear from analysis of saic emperaure disribuion in vorex ube cross-secion (Fig. 2) ha in he case when energy equaion 3 is used he emperaure difference beween ouside and cenral pars of spiral air flow is abou 30 [K] (cenral par of he flow have higher saic emperaure). When molecular and urbulen hea conduciviy were aken ino accoun saic emperaure disribuion become more smooh, in his case he hea energy ransfers from cenral par of he flow ino ouside par. This observaion is in good agreemen wih previous invesigaions resuls [7, 8]. Specific radial hea flow HT (Eq. 3) disribuion in vorex ube cross secion for he case of equaion 1 using is presened on Fig. 4. This hea flow is caused by urbulen and molecular hea conduciviy. The posiive value of HT means hermal energy inflow, negaive value means hea removing. I is clear from Fig. 4 ha here is a border where HT changes is sign sharply, i is placed on he radius abou 5 [mm]. This value of radius also corresponds o he radius of air axial velociy direcion change. Thus he mos acive process of he hea exchange considered in used numerical model arises on radius of direc and reurn sreams separaion. This observaion is also in good agreemen wih [7, 8].

4 358 Mechanical Engineering, Maerials and Energy II λ+ λ h HT =, (3) r cp r r disance from vorex ube cener (radial coordinae). Conclusion Fig. 4. HT hea flow disribuion in vorex ube cross-secion placed on he one diameer disance (1D) from nozzle inle for he case of equaion 1 using As a resul of performed analysis i is possible o conclude ha sandard k ε urbulence model allows o consider he Ranque-Hilsch energy separaion effec by using of special semi empirical erm in energy conservaion equaion which ake ino accoun effecs of urbulen and molecular hea conduciviy. I means ha any inadequacy of k-ε urbulence model in he field of emperaure disribuion wihin vorex ube energy separaion chamber is caused by he incorrec empirical accouning of energy (hermal) ransfer effecs. References [1] A.P. Merkulov. Vorex effec and is applicaion in equipmen. Moscow, Mechanical engineering, p. [2] V.I. Kuznesov. Theory and compuaion of Ranque effec. Omsk, OmGTU, p. [3] J.H. Ferziger. Compuaional mehods for fluid dynamics. Springer, p. [4] D.C. Wilcox. Turbulence modeling for CFD. DCW Indusries, California, p. [5] V. Alekhin, A. Anipin, S. Gorodilov, N. Seinke, S. Erypalov. Calculaing wind sresses and defining wind loads for high-rise building facades and frames in Yekaerinburg-CITY region. 14 h Inernaional conference on compuing in civil and building engineering (14 h ICCCBE). Absrac Volume. Moscow, Publishing House ASV. ISBN P.79. [6] A. Kurganov, E. Tadmor. New high-resoluion cenral schemes for nonlinear conservaion laws and convecion-diffusion equaions. Journal of compuaional physics, 160 (2000). P [7] Kun Chang, Qing Li, Gang Zhou, Qiang Li. Experimenal invesigaion of vorex ube refrigeraor wih a divergen ho ube. Inernaional journal of refrigeraion, 34 (2011), p [8] Sh.A. Piralishvili, V.M. Polyaev, M.N. Sergeev. Vorex effec. Experimen, heory, echnical soluions. Moscow, «Energomash», p.

5 Mechanical Engineering, Maerials and Energy II / Numerical Invesigaion of Ranque-Hilsch Energy Separaion Effec /