INVESTIGATION OF THE THERMAL HYDRAULIC INTERACTION BETWEEN THE BODIES OF A DIFFERENT FORM AND A FLUID

Transcription

1 L I N A S P A U K Š T A I T I S INVESTIGATION OF THE THERMAL HYDRAULIC INTERACTION BETWEEN THE BODIES OF A DIFFERENT FORM AND A FLUID S U M M A R Y O F D O C T O R A L D I S S E R T A T I O N T E C H N O L O G I C A L S C I E N C E S, E N E R G E T I C S A N D P O W E R E N G I N E E R I N G ( 0 6 T ) Kaunas 2015

2 KAUNAS UNIVERSITY OF TECHNOLOGY LITHUANIAN ENERGY INSTITUTE LINAS PAUKŠTAITIS INVESTIGATION OF THE THERMAL HYDRAULIC INTERACTION BETWEEN THE BODIES OF A DIFFERENT FORM AND A FLUID Summary of Doctoral Dissertation Technological Sciences, Energetics and Power Engineering (06T) 2015, Kaunas

3 This doctoral dissertation was prepared in at the Energy Technology Institute of the Kaunas University of Technology Scientific supervisor: Prof. Dr. Habil. Jonas GYLYS (Kaunas University of Technology, Technological Sciences, Energetics and Power Engineering, 06T) Dissertation Defence Board of Energetics and Power Engineering Science Field: Prof. Dr. Habil. Eugenijus UŠPURAS (Lithuanian Energy Institute, Technological Sciences, Energetics and Power Engineering, 06T) Chairman; Dr. Antanas MARKEVIČIUS (Lithuanian Energy Institute, Technological Sciences, Energetics and Power Engineering, 06T). Prof. Dr. Habil. Vytautas MARTINAITIS (Vilnius Gediminas Technical University, Technological Sciences, Energetics and Power Engineering, 06T); Prof. Dr. Liudas PRANEVIČIUS (Vytautas Magnus University Physical Sciences, Physics 02P); Prof. Dr. Habil. Stasys ŠINKŪNAS (Kaunas University of Technology, Technological Sciences, Energetics and Power Engineering, 06T); Official opponents: Prof. Dr. Gvidonas LABECKAS (Aleksandras Stulginskis University, Technological Sciences, Energetics and Power engineering, 06T); Doc. Dr. Egidijus URBONAVIČIUS (Lithuanian Energy Institute, Technological Sciences, Energetics and Power Engineering, 06T). The official defense of the dissertation will be held at 10 a.m. on 30th of April, 2015 at the public meeting of the Board of Energetics and Power Engineering Science Field in the Dissertation Defense Hall at the Central building of the Kaunas University of Technology. Address: K. Donelaičio str , LT Kaunas, Lithuania. Phone (370) , fax. (370) , Summary of dissertation sent out on the 30th of March, Dissertation is available at the libraries of the Kaunas University of Technology (K. Donelaičio g. 20, Kaunas) and the Lithuanian Energy Institute (Breslaujos g. 3, Kaunas).

4 KAUNO TECHNOLOGIJOS UNIVERSITETAS LIETUVOS ENERGETIKOS INSTITUTAS LINAS PAUKŠTAITIS ĮVAIRIOS FORMOS KŪNŲ IR FLUIDO TERMOHIDRODINAMINĖS SĄVEIKOS TYRIMAS Daktaro disertacijos santrauka Technologijos mokslai, Energetika ir termoinžinerija (06T) 2015, Kaunas

5 Disertacija rengta m. Kauno technologijos universiteto Energetikos technologijų institute. Mokslinis vadovas: prof. habil. dr. Jonas Gylys (Kauno technologijos universitetas, technologijos mokslai, energetika ir termoinžinerija - 06T) Energetikos ir termoinžinerijos mokslo krypties disertacijos gynimo taryba: prof. habil. dr. Eugenijus UŠPURAS (Lietuvos energetikos institutas, Technologijos mokslai, Energetika ir termoinžinerija 06T) pirmininkas; dr. Antanas MARKEVIČIUS (Lietuvos energetikos institutas, Technologijos mokslai, Energetika ir termoinžinerija 06T); prof. habil. dr. Vytautas MARTINAITIS (Vilniaus Gedimino technikos universitetas, Technologijos mokslai, Energetika ir termoinžinerija 06T). prof. dr. Liudas PRANEVIČIUS (Vytauto Didžiojo universitetas, Fiziniai mokslai, Fizika 02P) prof. habil. dr. Stasys ŠINKŪNAS (Kauno technologijos universitetas, Technologijos mokslai, Energetika ir termoinžinerija 06T); Oficialieji oponentai: prof. dr. Gvidonas LABECKAS (Aleksandro Stulginskio universitetas, Technologijos mokslai, Energetika ir termoinžinerija 06T); doc. dr. Egidijus URBONAVIČIUS (Lietuvos energetikos institutas, Technologijos mokslai, Energetika ir termoinžinerija 06T). Disertacija bus ginama viešame Energetikos ir termoinžinerijos mokslo krypties tarybos posėdyje 2015 m. balandžio 30 d. 10 val. Kauno technologijos universiteto centrinių rūmų disertacijų gynimo salėje. Adresas: K. Donelaičio g , LT Kaunas, Lietuva Tel. (370) , faksas (370) , el. paštas doktorantura@ktu.lt Disertacijos santrauka išsiųsta 2015 m. kovo 30 d. Su disertacija galima susipažinti Kauno technologijos universiteto (K. Donelaičio g. 20, Kaunas) ir Lietuvos energetikos instituto (Breslaujos g. 3, Kaunas) bibliotekose.

6 INTRODUCTION Hydrodynamic and heat transfer problems which occur during the contact of the body of different form and fluid usually are investigated by the experimental methods. However such factors as: complication of the investigations, high price of the experimental equipment, safety related and many other similar problems are the reason why recently higher attention is paid to the development and application of the numerical methods of the investigation. Therefore nowadays are widely used different one-dimensional and two-dimensional numerical methods for modeling processes of the hydrodynamics and heat transfer. Sometimes such methods are not applicable for the modeling of the complicated processes because of the high discrepancy between the results of the modeling and the experimental data. In some cases the mentioned problem can be solved using the 3D numerical cods such as CFX, FLUENT, STAR-CD, Open Foam and others, which are devoted to the numerical investigation of the complicated hydrodynamic and heat transfer processes. Selection of the concrete code depends on the possibility to use the method of the finite elements or the method of the finite volumes. However the main reason which determines the choice of the particular numerical code is the positive result of the validation against the experimental data of the real thermal and hydrodynamic process. This work is devoted to the numerical investigation of the different complicated hydrodynamic and heat transfer processes using the 3D code ANSYS CFX. The results of the numerical investigation are compared with the experimental data obtained by the author and with the results published by the other investigators. Object of investigation thermal hydrodynamic processes between the bodies of a different form and fluid. Aim of the work to justify application of the 3D code ANSYS CFX for the numerical simulation of the thermal hydrodynamic processes which take place between the bodies of a different form and a fluid and to investigate such processes. Tasks of the work Investigate the thermal hydraulic processes between the bodies of a different form and fluid using 3D finite volume simulation. 1. Select necessary models and calculation grids for the modeling of the turbulence and heat transfer processes. 5

7 2. Compose the 3D numerical model of the body of the complex form having the actual parameters and moving in the air and investigate an influence of the velocity on the drag force. 3. Compose the 3D numerical model of the isolation-control valve satisfying the operational parameters and investigate the processes of the water vaporization. 4. Compose the 3D numerical model of the fuel channel of the boiling water reactor satisfying the operational parameters and investigate the thermal hydrodynamic processes inside the channel. 5. Compose the 3D numerical model of the spherical, cylindrical and streamlined bodies and investigate drag force changes induced by the change of the bodies temperature. 6. Experimentally investigate velocity of the spherical and streamlined bodies under the different phases of the water and compare results with the data obtained during the numerical 3D simulation. Novelty of the work Justified application of the 3D ANSYS CFX code for the numerical simulation of the thermal hydrodynamic processes, which take place between the bodies of a different form and a fluid, allows expanding the limits of the 3D finite volume method application for the solving of the complex hydrodynamic, heat and mass transferring scientific problems. Relevance of the work Complicated experimental equipment and relatively high price of it and of research; cases when it is impossible to perform the experimental investigation and many others similar problems restrict an application of the experimental methods for the investigation of the thermal hydrodynamic interaction of the bodies of a different form and fluid. In those cases, in order to solve the occurring problems, it is appropriate to use the numerical methods. The 3D simulation and the results, which are presented in this work, can be applied for the investigation of hydromechanics, heat and mass transfer processes between bodies of a different form and the fluid. Practical importance of the work Methods and results of the investigation of thermal hydrodynamic interaction between the bodies of a different forms and fluid, obtained using ANSYS CFX code, complements and broadens the results, received by the other methods. Recommendations presented in this work can be applied for creation and investigation of the thermal hydrodynamic interaction between the bodies of a different form and fluid. The created numerical models can be investigated 6

8 further by introducing new correlations, especially related to the regularities of the boiling crisis process. Statements of the work 1. The drag force coefficient of the body of complex form with the increase of Mach number from 0.05 to 0.7 initially decreases to 0.34, then stabilizes and after that again increases up to Formation of the water vapor inside the isolation-control valve is influenced by the increasing velocity of the water and by the pressure drop between the valve s main frame and the gates. 3. Irregular heat release inside the technological channel influences on the change of the fluid s pressure and temperature. Local steam generation and steam distribution are influenced by the resistance of the spacer and heat intensification grids. 4. Drag force of the spherical, cylindrical and streamlined bodies can be reduced from 9 to 40%, depending on the body s shape and temperature. 5. Velocity of the spherical and streamlined bodies, covered by the vapor film, increases from 10 to 25%. 6. 3D models, based on the ANSYS CFX code application, are accessible for the numerical investigation of the complex processes, which are going during the contact of the body and fluid. Approbation of the work There were published 6 publications, including 2 publication in the journals from ISI (Institute of Scientific Information) list with citation index; 1 publication in the journal from ISI list without citation index; 3 articles in the Lithuanian Republic and International Conferences proceedings. Scope of the work Dissertation is divided into 3 chapters, conclusions and is presented on 100 pages, including 99 pictures, 15 tables and 93 titles in the reference list. 7

9 1. Methodology Numerical investigation Body s resistance and heat transfer when it is over flown by fluid are one of the essential thermal and hydrodynamic problems. The main task related to those problems is to identify the drag forces and heat transfer intensity appearing at the moment when the bodies are over flown. Complicated and expensive equipment usually is used for the experimental investigation of the hydrodynamic and heat transfer processes, which take place during the contact between the body and fluid flow. Instead of the experimental investigation today wide application obtained the numerical simulation. The ANSYS CFX code, which is based on the finite volume method application, was used in this work. The following equations are included in the ANSYS CFX code: momentum conservation equations: p u wu u S S u ef x C p ; (1.1) p u wv efv SC S pv ; y (1.2) p u ww efw SC S pw, z (1.3) mass continuity equation: energy conservation equation: h t 0 w, (1.4) Uh T : U SE. (1.5) One of the most difficult problems in the turbulence modeling is to ensure accurate simulation results. A number of turbulence models are proposed, some of them are more accurate when speeds are high, the other are meant for modeling the boundary layer, therefore, it is important to choose a turbulence model that allows making the most accurate comparison with experimental data. In computational fluid dynamics (CFD) codes there are introduced various statistical turbulence models. The ANSYS CFX code provides a possibility to use five different turbulence models: k-ε, k-ω, SST, BSL and SSG. There were used two turbulence models in the dissertation work: k-ε turbulence model, which is more applicable for the modeling at the low fluid flow velocity and the SST turbulence model, which is more applicable for the modeling of the wider range and higher flow velocity. 8

10 k-ε turbulence model was applied for the numerical 3D modeling of the isolation and control valve, for the modeling of the technological channel of the RBMK 1500 reactor and for the modeling of the spherical, cylindrical and streamlined bodies. According to the k-ε model, the turbulence viscosity is connected with the kinetic energy of the turbulence and energy dissipation via the following equation: 2 k t C, (1.6) here: C μ constant is equal to k ir ε values are calculated directly from the differential equations of the momentum conservation: k t k t Uk k P P k kb ; (1.7) t U C 1Pk P b C 2 t, (1.8) k where: C ε1, C ε2, σ k - constants (1.44, 1.92 and 1.3 respectively); P k intensity of the turbulence influenced by the viscosity forces. Shear stress transport model (SST) Turbulence over body of complex form has been tested with several turbulence models. These results were compared with the experimental results presented by the other authors. For further research SST model was selected, since it gave the most accurate comparison with experimental data. The Mach number of overflowing air was changed from 0 to 0.7. This turbulence model is based on the k-ω model and allows modeling of the turbulence under the high gradients of the pressure: where: frequency. a k max a, SF 1 v t, (1.9) 1 2 v ir F 2 compound factor; S invariant of the tension t t k-ω model This model spotlights on the influence of the boundary layer for the small Reynolds numbers. According to the k-ω model, the ratio between the kinetic energy of the turbulence and the frequency of the turbulence can be expressed as follows: k t. (1.10) 9

11 Kinetic energy of the turbulence (k) can be obtained solving the equation: k t k t Uk k P P k. (1.11) Frequency of the turbulence (ω) can be obtained from the following equation: k b t k Constants of this model: β = 0.09; α = 5 9; β = 0.075; σ k = 2; σ ω = 2. k 2 t U P P. (1.12) Three-dimensional model of body of complex form was created in the Mechanical Desktop environment and imported into the ANSYS CFX program. After loading the body of complex form model, a numerical finite volume model is generated in the ANSYS CFX software. To create a CFX mesh, tetrahedral finite element type were chosen. The influence of CFX mesh density on the results was rated by changing the quantity of elements from 0.8 to 2.6 million. The difference of the results under 2.5 and 2.6 million elements was insignificant, therefore the quantity of 2.5 million elements was used in further calculations. The body of complex form was developed as having a non-slippery but smooth wall. Overall dimensions of the body of complex form are: diameter 25 mm and length 148 mm. The body was placed inside the channel which simulates a wind tunnel. The outside walls of the wind tunnel are modeled as free slip walls. At the inlet the air velocity is set at Mach and at the exit, the precondition is made that the air static pressure is constant and equal to 0 Pa. The air temperature is 20 C and the reference pressure is Pa. In order to test the turbulent models, the numerical model (cylinder in the channel) was developed. Dimensions of the cylinder: diameter is 0.04 m; length is m. Dimensions of the channel: width is 0.2 m, length is m, and height is 0.5 m. The air flows through the channel, flow velocity is 10 m/s. Fig. 1 demonstrates the calculating grid made by the ANSYS CFX code. kb a) b) Fig. 1. Calculating grid for the test of the turbulence models (a); distribution of the turbulence model test results (b) 10

12 Five points on the surface of cylinder are marked in Fig. 1. Points are located clockwise. Test results are presented at the Table 1. Table 1. The test results of ANSYS CFX code turbulence model Point Experiment k-ε (num-exp)/exp SST (num-exp)/exp BSL (num-exp)/exp SSG (num-exp)/exp As can be seen, turbulence modeling results are fairly good and confirm to the experimental data. k-ε model was selected for the further calculations, as more suitable for modeling turbulent flow at the small flow velocities. The three-dimensional models of the spherical, cylindrical and streamline bodies were established using SOLIDWORKS program. Dimensions of the bodies were as follows: radius of the spherical body 0.02 m; radius of the cylindrical body m, length m; radius of the streamline body 0.02 m, length 0.12 m (Fig. 2). There was selected tetrahedron type mesh for the application of the finite element method. Number of elements was changed from 1 to 4 million. It was selected 1.4 million elements for modeling of the spherical and cylindrical bodies and 3.5 million elements for the modeling of the streamline body. Bodies were placed the channel outside walls of which were modeled as the free surfaces. Water velocity at the inlet to the channel was 0.5 m/s; static pressure at the outlet from the channel is constant and equal to 0 Pa. Temperature of the water was close to the boiling temperature; pressure is equal to Pa. Temperature of the bodies was kept at the 150 C. Fig. 2. Model of the streamlined body Experimental investigation The numerical investigation of the spherical and streamline bodies was complimented by the results of the experimental investigation. For that purpose was designed the experimental set-up (Fig. 3), 11

13 which consisted from the vertical experimental channel, samples of the bodies, light source, digital camera, heat source and computer. Channel s dimensions: height 1.55 m; square cross section (0.1x0.1) m 2 ; water level in the channel 1.5 m. Dimensions of the experimental samples of the bodies correspond to the dimensions, which were used for the numerical investigation: radius of the spherical body 0.02 m; radius of the streamline body 0.02 m, length 0.12 m (Fig. 3). Fig. 3. Experimental stand-up: 1 channel, 2 - liquid, 3 body, 4 heat source, 5- computer, 6 camera, 7 heat source Results and discussion Body of complex form Results of the simulation of an air flow around body of complex form are presented in the Fig.4 Fig. 7. Fig. 4 shows the distribution of the force that is acting on the surface of body towards X axis. The actual drag force is the sum of drag forces in every mesh node. When the Mach number of an air flow is 0.65, the actual drag force is 6.11 N. Fig. 4. Drag force distribution according to X-axis when the Mach number of the airflow is

14 Fig. 5 shows full air pressure (a) and density (b) distribution around the body of complex form at the Mach number It can be seen that the bottom is influenced by the pressure of the opposite direction. a) b) Fig. 5. Full pressure distribution (a) and air density distribution (b) at the moment the air overflows the body when the Mach number of the airflow is 0.65 Fig. 6 indicates air density distribution on the body surface (Mach number was 0.65). Maximum density is received at the body front. The air at the body back thins out. The plot of an air flow velocity along X axis is shown in Fig. 6a. Fig. 6b demonstrates velocity streamlines under an air flow at the Mach number a) b) Fig. 6. Distribution of airflow velocity (a) and velocity streamlines (b) at the Mach number of the airflow 0.65 In Fig. 7a is shown the dependence of drag force for the body of complex form on the Mach number of the overflowing air. Together with the increasing air speed the force influencing the body s surface increases. As long as the air speed is not high, the force influencing the body of complex form is not strong. With increasing speed of the overflowing air, the drag force non-linearly increases. The drag force values obtained during the simulation and values measured during the experimental study differ by no more than 3 percent. 13

15 F d, N Experiment Numerical Mach number Re a) b) Fig. 7. Dependence of the drag force (a) and drag coefficient (b) of the body that is overflown upon the Mach number when the air temperature is 20 C Fig. 7b represents the body of complex form drag coefficient dependence on the Reynolds number. While the Reynolds number is low, about and is approaching to 0, the drag coefficient is the highest and increases. When friction drag forces prevail the drag coefficient is the most volatile. When the speed of the overflowing air is increasing, the body s drag coefficient reduces, stabilizes, and again starts to increase from the Reynolds number Isolation-control valve Augmentation of the fluid flow velocity and reduction of the pressure inside the isolation and control valve initiate steam generation, which disturbs fluid flow in the valve and reduces cooling intensity of the technological channel. Steam generation inside the isolation and control valve of the boiling water reactor influenced on the fluid flow rate and on the reduction of the cooling rate of the fuel channel. Comparison the results of the numerical modeling with the experimental data showed its good agreement, discrepancy was less than 5%. The results of the numerical investigation showed the increase of the pressure gradient in the initial part of the valve (Fig. 8). Slight difference of the pressure can be noticed at the inlet to the valve and at the outlet. The results of the modeling by Cosmos-Floworks code and by the ANSYS CFX code were analogues for the same initial conditions (Fig. 8 and Fig. 9). C d a) b) Fig. 8. Variation of the fluid pressure (a) and velocity (b) inside the valve (Cosmos- Floworks code) 14

16 a) b) Fig. 9. Variation of the fluid pressure (a) and velocity (b) inside the valve (ANSYS CFX code) Fig. 10 demonstrates steam generation inside the valve. The most intensive steam formation was noticed at the initial part of the valve. This phenomenon influenced on the increase of the resistance and on the reduction of the flow rate. Fig. 10. Variation of the steam mass fraction inside the valve for the flow rate: a) - 20m 3 /h; and b) 11 m 3 /h Comparison between the results of the numerical investigation and the experimental data (Fig. 11) demonstrated its quite good agreement. Deviation is not exceeded 5%. 15

17 DP, MPa mm CFX 6 mm CFX 8 mm CFX 10 mm CFX 12 mm CFX 16 mm CFX 4 mm eksp. exp 6 mm eksp. exp 8 mm eksp. exp 10 mm eksp. exp 12 mm eksp. exp 16 mm eksp exp Q, m 3 /h Fig. 11. Flow rate influence on the pressure drop for the different opening of the valve Numerical investigation indicated design shortages of the valve. In order to reduce valve resistance and increase flow rate it is advisable decrease number of the sealing and make rounder the edge of the first sealing of the valve Fuel channel 3D model of the fuel channel of the boiling water reactor allowed investigating the thermal hydrodynamic processes inside the channel. Irregular heat release inside the fuel channel influenced on the change of the fluid s pressure and temperature. Due to the resistance of the distance grids the local steam generation occurred. Inequalities of the pressure and temperature changes inside the fuel channels were influenced by the nonlinear power distribution along the height of the reactor core. Steam generation was determined by the pressure drop in the distance grids of the fuel elements. Thermal hydrodynamic processes in the numerical model were estimated at the 13 points of the fuel channel cross section (Fig. 12) 16

18 Fig. 12. Position of the check points in the cross section of the channel There were clarified the changes of the flow velocity, pressure and temperature, steam fraction. Modeling results are presented in the Fig. 13 Fig. 16. a) b) Fig. 13. Temperature distribution at the height of the channel mm: a) 1 5 points; b) 6 9 points; c) points Fig. 13 presents the dependence of the fluid temperature on the height of the fuel channel. It was stated that the starting point of the boiling depended on the c) 17

19 channel power and on the particular place of the cross section of the channel. Boiling started from the middle part of the cross section, and at all the check points boiling started at the height less than 2.0 m. a) b) c) Fig. 14. Steam fraction changes at the height of the channel mm: a) 1 5 points; b) 6-9 points; c) points Fig. 14 shows the influence of the height of the fuel channel on the steam fraction. Formation of the steam started in zone where fluid temperature was higher (middle part of the cross section). a) b) Fig. 15. Flow velocity (a) and pressure (b) distribution at the mm height of the channel (1 5 points) 18

20 Height, mm Height, mm Fig. 15 presents the alternation of the flow velocity and pressure. Peaks in the figure can be explained by the fact that the fuel assembly of the RBMK reactor consists of two bundles, which has the same height. There are no fuel elements between both bundles therefore fluid velocity and fluid pressure experience drastically changes there Mass fraction 0 a) b) Vidutinė Average galia Minimali Minimum galia Maksimali Maximum galia Velocity, m/s Vidutinė Average galia Minimali Minimum galia Maksimali Maximum galia 19

21 Height, mm Height, mm Vidutinė Average galia Minimali Minimum galia Maksimali Maximum galia Absolute pressure, MPa Vidutinė Average Minimali Minimum Maksimali Maximum Fig. 16. Influence of the channel height on the distribution of the steam fraction (a), fluid velocity (b), fluid pressure (c) and fluid temperature (d) Fig. 16 presents the influence of the channel height on the changes of the steam fraction (a), fluid velocity (b), fluid pressure (c) and fluid temperature. Numerical investigation identified (Fig. 16) the following height of the starting point of the steam generation: 1050 mm for the channel of the maximal power; 1750 mm for the channel of the average power; 2450 mm for the channel of the minimal power. c) Temperature, C d) 20

22 Table 2. Comparison results of the numerical investigation with the exploitation data Parameters Exploitation data Results of the numerical investigation Channel s power, MW 2,53 2,53 Steam quality at the exit from the channel, % Coolant temperature at the inlet to channel, C Water steam mixture temperature at the outlet, C ,7 Pressure drop in the channel, MPa 0,5 0,533 Coolant velocity at the outlet from the channel, m/s Numerical investigation of boiling water reactor was generalized by next equation: k m n x Re Pr Nu A 1 (3.1) here: A 0.026; x =0 0.5; k 0.23; m 0.8; n The first time was established 3D numerical model of the boiling water reactor fuel channel. Comparison results of the numerical investigation with the experimental data showed its good agreement (Table 2). Spherical, cylindrical and streamlined bodies During the movement of the body in the fluid (liquid or gas) a drag force occurs, which effects on the stability of the movement and on the energy consumption necessary for body s motion. The drag force depends on the fluid characteristics, on the body cross-sectional area (shape) and etc. Particularly, the drag force is influenced by fluid density the lower density, the lower drag force. In addition, drag force is as bigger, as much the body velocity is higher. As a result, it is necessary to reduce the drag force, which effects the body movement. The resistance to the body movement in a liquid can be reduced not only by changing the shape, but also by reducing density of the environment (liquid), in which the body moves. In addition, there is no need to reduce the density of total fluid volume, it is sufficient to cover up the moving body with less density layer of liquid or gas. Thus, the frontal and friction resistance will be reduced accordingly. The lower density of the environment (gas) layer around the moving body can be created in many different ways. For example, it can be made by using special holes, fitted in the front part of the moving body, let/feed gas, which can cover the moving body by gas (air, combustions products) envelope. Another way is to use a super cavitation effect. A super cavitation can be created on the bodies, which has a specific geometry. The front surface of such bodies is flat 21

23 with sharp prominence sideways. Then the body moves in a liquid at a high velocity, a fluid is compressed on a flat front of the body. Behind that surface the pressure falls down suddenly. Due to the big difference of the pressures a gas pillow occurs at the body surface. Super cavitation effect is possible only at high velocities of the body (approximately 180 km/h and more). At the low velocities gas pillow generates slowly, thus the drag force changes a little only. In order to increase and stabilize this process, the combustion products are injected to the liquid. Another method, which helps to form a gas (steam) envelope, is based on the second order boiling crisis fact. On the surface of a body, heated to the high temperatures, usually can be formed an integral gas (steam) film, which surrounds the moving body and reduces the drag force also. The conditions of the fluid and the gas layer change then the fluid flows around the heated surface of the body. If the temperature of fluid grows, the density of it reduces and the phase transformation may occur. The aim of this investigation is to model the drag force reduction for the case, when one-phase (water) flow turns to the twophase flow on the heated surface of the moving body. There were used three bodies with a different shape: sphere, cylinder and streamline body. Cylindrical body Figures 17 and 18 show the drag force changes at the surface of the cold cylindrical body. It can be noticed that the highest velocity was at the front part of the edges of the body where water flow is forced to rebound. The highest force was at the front and at the tail of the body. Total drag force, which influences the motion of the body, was N. Due to the vortex beyond the cylindrical body, the drag force at the tail part became negative. a) b) Fig. 17. Velocity distribution around the cold cylindrical body (a); drag force changes for the cold cylindrical body (b) Fig. 18 shows water velocity change nearby the hot body. One can see in Fig. 17a and Fig. 18a a significant difference of the velocity on the front zone where the flow abruption appears. Fig. 18b represents the distribution of the flow density. Sharp decrease in density appears nearby the hot cylindrical surface. 22

24 a) b) Fig. 18. Velocity distribution around the hot cylindrical body (a); density changes for the hot cylindrical body (b) Fig. 19 indicates a distribution of the vapor mass fraction on the surface of the body. Maximum vapor generation was noticed at the front part of the cylinder immediately behind the flow abruption point. Average vapor mass fraction on the surface was Further (going to the tail) more water was contacted with the body s surface and cooling became more intensive, therefore vapor was destroyed by the colder water. At the end part of the cylinder, where the vortex occurred and velocity decreased, cooling went down, and the amount of vapor increased. Figures 4 and 8 reflect the difference between the drag forces. The second phase (vapor) generation in the water impacted on the drag force. Changes can be seen at a front part of the cylindrical body. The total drag force for the heated body was N. These figures show only half of the cylindrical surface of the body. a) b) Fig. 19. Vapor mass fraction changes on the surface of the hot cylindrical body (a) and hot cylindrical body s drag force distribution on the surface (b) Fig. 20 shows flow velocity distribution for the cold and for the hot cylindrical body. Cylinder is seen from the front side. The changes of the 23

25 velocity can be noticed at the edge of the frontal part of the cylindrical body. Here the cylindrical body is shown from the front side as a black circle. Fig. 20. Cold and hot cylindrical body s velocity distribution According to the experimental tests estimated factor of the drag force was for the case of one-phase flow (water and body s temperatures were 98 o C). In accordance to the numerical calculations drag force was equal to The calculation error was about 2 %. As it can be seen, even if there was a small amount of the vapor, the drag forces decreased sufficiently (about 9%). Spherical body Spherical body was modeled analogically like the cylindrical body. Fig. 21 shows velocity distribution for the cold and hot bodies. In the case of the cold body was noticed the decrease of the flow velocity at the front part of the body. a) b) Fig. 21. Velocity distribution: for the cold spherical body (a); for the hot spherical body (b) 24

26 Fig. 22 represents the flow density and steam mass fraction distribution for the hot spherical body. The most intensive generation of the steam occurred at the tail part of the body due to the lower flow velocity. Minimal flow density was noticed at the tail part of the body also. a) b) Fig. 22. Flow density (a) and steam mass fraction (b) distribution for the hot spherical body Fig. 23 indicates drag force distribution for the spherical body. In this case of the cold body the drag force is equal to N. When the spherical body is heated, the total drag force is equal to N. Mass fraction of the generated steam on the surface of the spherical body was Even for such small amount of the vapor the drag force was reduced about 25%. a) b) Fig. 23. Drag force distribution on the surface of the spherical body: cold body (a); hot body (b) Fig. 24 gives the distribution of the velocity of the streaming flow, for cold and hot spherical body. In this figure, the spherical body is seen from the front side. The change of the velocity is observed at the biggest cross-section of the spherical body. Here a spherical body is presented from the front side as a black circle. 25

27 Fig. 24. Flow velocity distribution for the cold and hot spherical body For the spherical body, moving in the one-phase water flow at a given velocity, experimentally estimated coefficient of the drag force is equal to Numerical investigation showed a value equal to Calculation error is 3%. The drag force coefficient of the hot spherical body decreases to (or 25%). Streamline body Modeling of the streamline body was prosecuted under the same conditions like the spherical and cylindrical bodies. Body s surface temperature was set equal to 150ºC, water temperature was 98 o C, and velocity was 0.5 m/s. Distribution of liquid density and mass fraction around the streamline body during the heating process is shown in the Fig. 25. The minimal density was noticed at the back part of the body and after it was falling. Velocity of the liquid phase was maximal at the point where the mass fraction began to rise. a) b) Fig. 25. Density (a) and liquid fraction (b) distribution around the body during the heating process 26

28 Drag coefficient dependence on the body s velocity is presented in the Fig. 26. Numerical modeling was applied for two cases: body moving in the onephase liquid (water) and gas (air). Drag coefficient C d Series1 Water Series2 Air Velocity, m/s Fig. 26. Drag coefficient dependence on the body s velocity Fig. 27 indicates the distribution of the overflow velocity for the cold and hot body. Water flow at the frontal part and at the tail of the streamline hot body was blocked less than in the case of the cold body due to the steam formation. Therefore fluid flow was abrupt nearby the body s head and near the tail also. As a result of that less drag force of the hot body in comparison with the cold body (Fig. 28). a) b) Fig. 27. Water flow velocity: a) cold body; b) hot body 27

29 Drag force distribution for the cold and for the hot streamline bodies is shown in the Fig. 28. It can be seen that the area of the cold body s surface, influenced by the drag force was, larger than in the case of the hot body. The total drag force was equal to N for the hot body, and to N for the cold body. Steam formation reduced the drag fore similar like in the case of the spherical or cylindrical bodies. a) b) Fig. 28. Drag force distribution for the cold (a) and for the hot (b) streamline body During the numerical investigation was obtained that the drag coefficient reduction was about 32% (from for the cold body to for the hot body) at the body s velocity equal to 0.5 m/s. Experimental investigation Analyzing the spherical and cylindrical bodies, a small temperature difference between the surface and the fluid was chosen because of the limitations of the ANSYS CFX code, there are still no possibilities to model the processes, with high temperature alteration. In the case of high temperature alteration, a vapor film would emerge at the surface of the body, and would reduce the drag force even more. In order to find more precise influence of the two-phase flow on the drag force and on the drag coefficient it is necessary to execute the additional experimental investigations, and new obtained results could supplement another more precise numerical models. The results of the experimental investigation of the spherical and streamline bodies are presented in the Fig. 29 Fig. 36. Fig. 29 shows the spherical body falling down in the cold water. Initial temperature of the water was 15ºC, body s temperature was 300ºC. Under such conditions steam film on the body s surface was formed very quickly, however this film disappeared very soon also. Duration of the steam formation was 0.15 seconds only. Main reason of that was low water temperature (much lower than the saturation temperature) and high heat capacity of the water. Due to the low velocity of the body in the upper part of the experimental channel the difference between the velocity of the hot and cold body was insignificant. 28

30 Fig. 29. Spherical body falling in the cold water Fig. 30 demonstrates the spherical body falling down in the hot water (water temperature was 99ºC). In this case the steam film existed about 3 minutes. The turn of the film boiling regime to the bubble boiling regime was accompanied by steam explosion. Differently from the sphere fall in the cold water there was no bubbles trace following the falling body. Fig. 30. Spherical body falling in the hot water Fig. 31 presents the influence of the body s temperature on the body s falling velocity. Temperature of the water was constant and equal to 15ºC; temperature of the body varied from 15 up to 700ºC. It was noticed that the maximal velocity corresponded to the diapason of the temperatures from 300 to 400ºC. Falling velocity of the hot body was higher than the velocity of the cold body by about 25%. 29

31 Velocity, m/s Greitis v, m/s 2,3 2,2 2,1 2 1,9 1,8 1,7 1,6 1, Temperatūra, C Temperature, C Fig. 31. Falling body s velocity dependence on the body s temperature Fig. 32 displays the image of the jumping spherical body. The buoyancy of the body, covered by the steam layer (film boiling regime), was higher than that of the body alone. Therefore the Archimedes force lifted the body up. But soon, just then the steam bubble separated from the body, the body fall down on the bottom of the channel. After that the jumping process was repeated again until the body s temperature dropped and film boiling regime occurred. Approaching to the point when the film boiling reversed to the boiling regime the jumping height decreased, but the jumping frequency increased. Fig. 32. Jumping sphere at the bottom of the channel 30

32 Velocity, m/s Fig. 33 represents the influence of the falling time on the body s velocity. Continuous lines show the velocity obtained by the numerical modeling (blue line velocity in the air, black line velocity in the water at the temperature equal to 15ºC). Black dots matter the experimental data for the water at the cold body, red dots express the experimental data for the water at the hot body (initial temperature of the body was equal to 410ºC). Velocity of the hot body was about 20% higher than that for the cold body. Correlation between the modeling results and the experimental data was quite good Šalto Air kūno kritimas ore. Sakitinis tyrimas Šalto Water kūno kritimas vandenyje. Skaitinis tyrimas Šalto Cold kūno kritimas vandenyje. Eksperimentas Karšto Hot kūno kritimas vandenyje. Eksperimentas Falling time, s Fig. 33. Falling time influence on the body s velocity Fig. 34 gives the image of the streamline body falling at the different positions in the experimental channel. It can be seen intensive steam generation at the tail part of the body. Front part of the body was cooled faster due to its temporary contact with the flow of the cold water. As a result generation here occurred only during the first phase of the contact between the streamline body and water. The rest part of the body contacted with the water, which temperature was higher. Therefore the steam generation here was more intensive and continued longer. Fig. 35 demonstrates how the film boiling regime changes to the bubble boiling regime. Initial temperature of the streamline body was 410ºC; water temperature was 99ºC (close to the saturation temperature). Film boiling shift to the bubble boiling began from the head of the body due to the better cooling by the colder water flow. 31

33 Fig. 34. Streamline body falling at the different positions of the experimental channel Fig. 35. Film boiling regime change to the bubble boiling regime Dynamics of the cooling process of the streamline body falling inside the cold water is shown in the Fig. 36. Body was cooled down from the temperature equal to 410ºC till the temperature of 100ºC during 25 seconds. Film boiling regime was fully changed by the bubble boiling regime after 9 seconds only. 32

34 Temperature, ºC Time, s CONCLUSIONS Fig. 36. Dynamics of the cooling process of the streamline body Dissertation is devoted to the numerical simulation using 3D code ANSYS CFX and to the experimental investigation of the complex hydrodynamic and heat transfer processes going during the interaction between the body of different form and fluid flow. During numerical and experimental investigation: 1. The tetrahedral finite volumes mesh, k-ε and SST turbulence models and homogenous heat transfer model were chosen for the numerical 3D simulation. 2. The numerical model of the body of a complex form over flown by air was created. This model showed that the drag coefficient decreases from 0.47 to 0.35 when Mach number changes from 0.05 to 0.2; is constant (around 0.34) when Mach number changes from 0.2 to 0.6 and increases from 0.34 to 0.39 when Mach number changes from 0.6 to 0.7. Comparison of the results of the numerical modeling and the experimental data showed its good agreement; discrepancy was less than 5%. 3. The numerical model with real parameters of the isolation-control valve of the boiling water reactor was created. Simulation showed that in normal operation conditions steam did not generate inside the gap between the hull of the valve and the valve itself. Steam was generated in the case when flow of coolant exceeds operational limits. Comparison the 33

35 34 results of the numerical modeling with the experimental data showed its good agreement, discrepancy was less than 4%. 4. The numerical model of the boiling water reactor fuel channel with the real parameters was created. The simulation showed that the temperature and pressure distribution in the channels of the different power were influenced by the nonlinear power distribution along the height of the reactor core. Steam generation was determined by the pressure drop in the distance and intensification grids of the fuel elements. Numerical investigation showed the following height of the start point of the steam generation: mm for the channel of the maximal power; mm for the channel of the average power; mm for the channel of the minimal power. Comparison of the results of the numerical modeling with the operational data showed good agreement; discrepancy was less than 15%. 5. Numerical models of the spherical, cylindrical and streamline bodies were created. Simulation showed that drag force depends on bodies and water temperature. When body temperature is 150ºC, and water temperature is near the saturation temperature the drag force is reduced by: 25% - for the spherical body; 9% for the cylinder; 32% - for the streamline body. 6. Experimentally was determined that the velocity of the spherical and streamline bodies, covered by vapor film, increased by 10-30%. Maximal velocity was reached at the initial temperature of the body equal to ºC.

36 ABOUT THE AUTHOR Linas Paukštaitis was born on the 17 of September in 1982 in Marijampolė, Lithuania. In 2001 graduated Marijampolė s 5th school in Marijampolė. From 2001 till 2005 studied at the Kaunas University of Technology, Faculty of Mechanical Engineering and Mechatronics, Bachelor s degree in Nuclear engineering. From 2005 to 2007 studied at the Obninsk State Technical University for Nuclear Power Engineering, Obninsk, Russia, Department of Nuclear Power Plant Equipment and Operation and in 2007 graduated Master s degree in Nuclear power plant engineering. In 2007 started to work at the Energy Technology Institute, Kaunas University of Technology as engineer : Doctoral studies at the Energy Technology Institute, Kaunas University of Technology (Technological sciences, Energetics and Power Engineering, 06T). Contact linas.paukstaitis@ktu.lt 35

37 PUBLICATIONS LIST ON DOCTORAL DISSERTACION THEME Articles in journals from ISI (Institute of Scientific Information) list with citation index 1. Gylys, Jonas; Paukštaitis, Linas; Skvorčinskienė, Raminta. Numerical investigation of the drag force reduction induced by the two-phase flow generating on the solid body surface // International Journal of Heat and Mass Transfer. Oxford : Pergamon-Elsevier Science Ltd. ISSN , Vol. 55, iss , p [Science Citation Index Expanded (Web of Science); CAB Abstracts; COMPENDEX; INSPEC; Science Direct; 0,333]. [Indėlis grupėje: 0,333] 2. Fedaravičius, Algimantas; Jonevičius, Vaclovas; Kilikevičius, Sigitas; Paukštaitis, Linas; Šaulys, Povilas. Estimation of the drag coefficient of mine imitator in longitudinal air flow using numerical methods // Transport : research journal of Vilnius Gediminas Technical University and Lithuanian Academy of Sciences. Vilnius : Technika, Taylor&Francis. ISSN , Vol. 26, no. 2, p [Science Citation Index Expanded (Web of Science); COMPENDEX; ICONDA; SCOPUS; PaperChem; Mechanical and Transportation Engineering Abstracts; CSA Technology Research Database; CSA/ASCE Civil Engineering Abstracts; Aerospace & High Technology Database; Earthquake Engineering Abstracts; 0,346]. 3. Gylys, Jonas; Skvorčinskienė, Raminta; Paukštaitis, Linas. Peculiarities of the Leidenfrost effect application for drag force reduction // Mechanika / Kauno technologijos universitetas, Lietuvos mokslų akademija, Vilniaus Gedimino technikos universitetas. Kaunas : KTU. ISSN , Vol. 20, no. 3, p [Science Citation Index Expanded (Web of Science); INSPEC; Compendex; Academic Search Complete; FLUIDEX; Scopus]. [0,333]. [Indėlis grupėje: 0,680] Articles referred in Lithuania Science Council approved list of international databases Articles in Lithuanian republics and International Conference Proceedings 1. Žiedelis, Stanislovas; Paukštaitis, Linas. Kai kurie reguliuojančioizoliuojančio vožtuvo modeliavimo rezultatai // Šilumos energetika ir technologijos : konferencijos pranešimų medžiaga, 2009 m. vasario 5, 6 d. / Kauno technologijos universitetas, Lietuvos energetikos institutas, Lietuvos šiluminės technikos inžinierių asociacija; redakcinė kolegija: Stasys Šinkūnas (atsakingas redaktorius)... [et al.]. Kaunas : Technologija, ISBN p [0,500] 36

38 2. Žilinskas, Danielius; Adomavičius, Arvydas; Paukštaitis, Linas. Branduolinio reaktoriaus RBMK-1500 kuro rinklės šilumos mainų skaitinis tyrimas // Šilumos energetika ir technologijos : konferencijos pranešimų medžiaga, 2012, vasario 2, 3 d. / Kauno technologijos universitetas, Lietuvos energetikos institutas, Lietuvos šiluminės technikos inžinierių asociacija, Branduolinės energetikos asociacija. Kaunas : Technologija. ISSN , p [0,333] 3. Gylys, Jonas; Paukštaitis, Linas; Skvorčinskienė, Raminta. Leidenfrosto efekto įtaka skystyje judančio kūno energijos sąnaudoms // Šilumos energetika ir technologijos : konferencijos pranešimų medžiaga, 2013 sausio31, vasario 1 d. / Kauno technologijos universitetas, Lietuvos energetikos institutas, Lietuvos šiluminės technikos inžinierių asociacija, Branduolinės energetikos asociacija. Kaunas : Technologija. ISSN , p [0,333] [Indėlis grupėje: 1,750] 37