Flow Characteristic and Natural Convection Heat Transfer Inside …isomase.org/OMAse/Vol.2-1-2015/2-1-12.pdf · 2015-12-25 · Proceeding of Ocean, Mechanical and Aerospace -Science

Proceeding of Ocean, Mechanical and Aerospace -Science and Engineering-, Vol.2:1

November 23, 2015

60 Published by International Society of Ocean, Mechanical and Aerospace Scientists and Engineers

Flow Characteristic and Natural Convection Heat Transfer Inside Refrigeration Cabin

Annisa Wulan Sari,a,* Ary Bachtiar K.P,a, **

a) Departement of Mechanical Engineering, Institut Teknologi Sepuluh Nopember, 60111 Surabaya, Indonesia

*Corresponding author: [email protected],* [email protected],** Paper History Received: 10-October-2015 Received in revised form: 20-November-2015 Accepted: 23-Nevember-2015

ABSTRACT In literature, there are extensive amounts of experimental and numerical studies in refrigeration system, this paper presents natural convection numerically investigated in refrigeration at Difussion Absorption Refrigeration (DAR) system. Object of this study is a 3D model of refrigeration cabin, with source of the cold temperature came from the evaporator that adheres at the back side of the cabin’s wall. The model forms a closed system with no inlet or outlet. Numerical method is finite volume computational fluid dynamics simulations, using the discrete ordinates (DO) laminar model. It is expected to know the flow characteristic and the temperature distribution inside the refrigeration cabin numerically. KEY WORDS: Cabin, DAR, Heat Transfer, Natural Convection, Temperature Distribution NOMENCLATURE

� heat transfer area (��; �) �� specific heat at constant pressure (��/��. ℃; ��/��. �) ∅ pipe diameter (��; �) g gravitational acceleration (�/ �) ��� Grashof number ℎ heat transfer coefficient (�/��℃.; �/��. �)

� height of the cabin (��; �) �/� aspec ratio � thermal conductivity (�/�. ℃; �/�. �) � length of the cabin (��; �) ��� Nusselt number �� Prandtl number � heat transfer rate (�) �" heat flux (�/��) � thermal resistance (℃/�; K/�) �� Rayleigh number ��∗� Rayleigh number based on heat flux �� Reynold number ∆ temperature difference (℃; �) temperature (℃; �) ! ambience temperature (℃; �) " surface temperature (℃; �) �, $, % velocities in &, ', and ( direction � width of the cabin (��; �) &, ', ( Cartesian coordinates ), *, + non-dimensional coordinates Greek symbols , thermal diffusivity (��/ ) - coefficient of thermal expansion (1/�) / energy dissipation rate (��/ 0); emissivity 1 dynamic viscosity (��/� ) v kinematic viscosity (��/ ) 3 density (���40)

1.0 INTRODUCTION Convection heat transfer occurs due to the difference of temperature and velocity. In natural convection heat transfer, there is no velocity, and replaced by Bouyancy that driving Prandtl number (��) and Rayleigh number(��). The absent of

Proceeding of Ocean, Mechanical and Aerospace -Science and Engineering-, Vol.2:1

November 23, 2015

61 Published by International Society of Ocean, Mechanical and Aerospace Scientists and Engineers

Reynold number (��) defines turbulence modelling from ��and Grashof number (��)[1].

Natural convection is experimentally and numerically investigated for various engineering application, such as electrical cooling, thermal energy system, food manufacturing, building design, refrigeration, and so on[2].

Atayilmaz[3] performed an experimental study with bare and concrete horizontal cylinders inside a cabin under transient and steady-state natural convection heat transfer from a heated horizontal concrete cylinder, in the numerical part, CFD package (FLUENT) was used for the 2D heat transfer analysis. Boundary layer was created in the vicinity of the insulation outer surface with finer mesh, and then all boundaries except the upper face of the domain and the outer surface of concrete cylinder were chosen as wall with constant temperature. The standard laminar viscous flow model and surface to surface radiation model were used. For pressure velocity coupling discritization the SIMPLE (Semi-Implicit Method for Pressure Linked Equations) algorithm has been used.

Moraga et al[4] in their work reported a study of the heat and mass transfer during the freezing of a block of beef in the freezer compartment of a household refrigerator. It takes into account the natural convection in air coupled to the heat conduction and water diffusion in the meat. The nonlinear partial differential equations describing mass conservation, linear momentum, energy, and species concentration in 2Dwere solved with the SIMPLE algorithm and the finite volumes method. Smolka[5] presented the shape optimisation of a natural air circulation heating oven based on an experimentally validated 3D simplification CFD model. The discrete ordinates (DO) model was selected from three different radiation models based on the model validation of the baking process in an electric oven. Turbulence modelling was first-order upwinds of the � 5 / and � 5 6 models.

TaridanMehrtash[6] numerically investigated the steady-state natural convection from heat sinks with parallel arrangement of rectangular cross section vertical plate fins on a vertical base in order to obtain a validated model that was used for investigating inclined orientations of a heat sink. Natural convection and radiation heat transfer rates from the fronts of the heat sinks heated from the back with a heater were obtained from finite volume computational fluid dynamics simulations. Steady state solutions were obtained by using the zero-equation turbulence model with no slip boundary condition was used for all surfaces.

Dehghan[7] presented a numerical study of 3D buoyancy-driven flow in a half-scale model of a two-floor building model. The model consisted of an upper compartment and a lower compartment with a stairway connecting the two floors. Numerical method was Large Eddy Simulation (LES) with the dynamic kinetic energy transport subgrid model. Radiation exchange was modelled using the discrete ordinates (DO) radiation model. The thermal boundary conditions on the model walls were set as heat flux. Turbulence modelling was � 5 /, the measured wall temperatures were set as boundary conditions, which removes the dependency on initial temperature. There is no study yet to investigate flow characteristic and the temperature distribution at Difussion Absorption Refrigeration (DAR) system to our knowledge, and thus, this paper presents natural convection heat transfer numerically investigated inside refrigeration cabin at DAR system using program ANSYS 12.1

FLUENT Solver. In the DAR function of compressor is, replaced by bubble-pump, and it can be operates without any use of electrical or mechanical energy. Main characteristic of DAR is having no moving parts and is driven by heat [8]. 2.0 MATHEMATICAL MODEL

To plot model of cabin, SolidWorks 2014 was used. Object (Fig.1) of this study is a 3D model of refrigeration cabin, with source of the cold temperature came from the evaporator that adheres at the backside of the cabin’s wall. The model forms a closed system with no inlet or outlet. Dimension of the cabin and evaporator’s pipe, present at Table 1

The three-dimensional equations governing the conservation of mass, momentum, and energy at every point in the enclosure express in eq.1-5

78

79:

7;

7<:

7=

7>? 0 (1)

A�

AB: �

A�

A&: $

A�

A': %

A�

A(? 5

13A�A&

:$ C7D879D :7D87<D :

7D87>DE (2)

A$AB : �

A$A& : $

A$A' : %

A$A( ? 513

A�A'

:$ C7D;79D :7D;7<D :

7D;7>DE (3)

A%AB : �

A%A& : $

A%A' : %

A%A( ? 513

A�A(

:$ C7D=79D :7D=7<D :

7D=7>DE (4)

7F7G : �

7F79 : $

7F7< :%

7F7> ? , C7DF79D :

7DF7<D :

7DF79DE (5)

a b

Figure 1:Cabin of DAR System (a) From Outside Drawn with SolidWorks 2014

(b) Actual from Inside (Back Cover Opened)

Proceeding of Ocean, Mechanical and Aerospace -Science and Engineering-, Vol.2:1

November 23, 2015

62 Published by International Society of Ocean, Mechanical and Aerospace Scientists and Engineers

Cabin of DAR system is enclosure, with dimensionless equations like Prandtl number can calculate with eq.6[9]

�� ?

;

H (6)

as for Grashof number can be use eq.7-8[10]

�� ?IJ∆F�K

;D (7)

�� ? LMNO (8)

then, for calculating Nusselt number, the Rayleigh number must be defined. It can be find based on dimension and type of enclosure. Cabin of DAR system is enclosure with the type is tall enclosure, because aspect ratio, �/� P 1 (Fig.2). Thus,��can calculate with eq.9[1] for isothermal wall, eq.10[1] for uniform heat flux wall.

��� ? IJ�K∆FH; (9)

��∗� ? IJ�QR"H;S (10)

and then, we obtain �� fromeq.11[1].

��� ? 0,34. ��∗��/V C�WEX/V

(11)

Type of fluid flow for tall enclosure, can be find with

condition at eq.12[1]. ��~10V��~10V��Z [10

40 \ �� \ 100] (12)

if the value is less than the condition, then flow is Laminar. If the other way, value is higher than the condition, then flow is Turbulent.

Figure 2: 2D Domain of Numerical Simulation

Table 1: Design Geometry Geometry Size (mm) Cabin: Length (�) 430 Width (�) 430 Height (�) 650 Evaporator: Pipe diameter (∅) 20

3.0 NUMERICAL MODEL AND METHOD Thermal boundary conditions can be defined in four different types in FLUENT: Uniform heat flux, constant temperature (isothermal), convection-radiation and convection. In this study, the backside wall of the cabin is influenced by evaporator’s temperatur (Appendix 1), that is the backside wall devided in 35 segments (Fig.3) that linear by divided with thermal boundary condition in FLUENT is isothermal wall per segment.The upper and bottom wall of cabin,are assumed adiabatic, because of isolated densely and the area were smaller than the other wall. Thus, it define uniform heat flux with the value is �" ? 0.As for the Front, Right, and Left wall of the cabin, using uniform heat flux for it thermal boundary condition in FLUENT (Fig.4).

To generated mesh for cabin model, ANSYS 12.1 was used. Mesh (Fig.5) structure with fine grid and high smoothing were use in this investigation, with value of grid is 63070 nodes and 58344 elements (Table 2).

From experimental data (Appendix 1), calculation of dimensionless equations was found:

Experimental data 21

�� ? 0,1482c��/ 0,2056c��/ ? 0,7208

��∗� ? 110,6c�40. �4X. [0,65�]d. 53,97�/��

0,025�/�.�

? 42622,4798

��� ? 42622,47980,7208 ? 59132,186

��ffff� ? 0,34. [42622,4798]�/V. [1,5116]X/V ? 3,8 ���59132,186 g 10V ← thus, the flow is Laminar

Figure 3:Domain of Backside Wall

Proceeding of Ocean, Mechanical and Aerospace -Science and Engineering-, Vol.2:1

November 23, 2015

63 Published by International Society of Ocean, Mechanical and Aerospace Scientists and Engineers

Figure 4: Domain of Cabin with Boundary Condition

Figure 5: Mesh of Cabin

In numerical study, ANSYS 12.1 Fluent solver was used.

Problem set up for energy equation was activated, so that the gravitational acceleration can be used at Y-direction with g ? 9,81�/ � . Viscous flow model after the calculation is standard laminar. Radiation for this model was unactived, because radiation was negligable. Solution method for pressure-velocity coupling, SIMPLE (Semi-Implicit Method for Pressure Linked Equations) algorithm has been used. Spatial discretization was used least square cell based for gradient. As for pressure, momentum, and energy was used second order upwind.

Table 2: Mesh Details

After itteration (not done yet), contours (Fig.6) and vectors (Fig.7) velocity can be ploted.

Figure 6: Contours of Total Temperature (�)

Figure 7: Vectors of Relative Velocity by Total Temperature (�) ACKNOWLEDGEMENTS

Postgraduate of Mechanical Engineering Departement, Institut Teknologi Sepuluh Nopember, 60111 Surabaya, Indonesia. REFERENCE 1. Bejan, Adrian. 2013. Convection Heat Transfer Fourth

Edition, New York: John Wiley & Sons Inc. 2. Gandhi, Mayukumar S., dkk. 2011. Two Phase Natural

Convection: CFD Simulations and PIV Measurement. International Journal of Chemical Engineering Science; 66:3152-3171.

3. Atayilmaz, S. Özgür. 2010. Transient and steady-state natural convection heat transfer from a heated horizontal concrete

Proceeding of Ocean, Mechanical and Aerospace -Science and Engineering-, Vol.2:1

November 23, 2015

64 Published by International Society of Ocean, Mechanical and Aerospace Scientists and Engineers

cylinder. International Journal of Thermal Science; 49:1933–1943.

4. Moraga, Nelson O., Jauriat, Leopoldo A., danMondaca, Roberto A. 2012. Heat and Mass Transfer In Conjugate Food Freezing/Air Natural Convection. International Journal of Refrigeration; 35:880-889.

5. Smolka, Jacek. 2013. Genetic Algorithm Shape Optimisation of A Natural Air Circulation Heating Oven Based On An Experimentally Validated 3-D CFD Model. International Journal of Thermal Science; 71:128–139.

6. Tari, IlkerdanMehrtash, Mehdi. 2013. Natural Convection Heat Transfer From Inclined Plat-Fin Heat Sink. International Journal of Heat and Mass Transfer; 56:574-593

7. Dehghan, M. R. Mokhtarzadeh. 2011. Numerical Simulation and Comparison With Experiment of Natural Convection Between Two Floors of a Building Model Via a Stairwell. International Journal of Heat and Mass Transfer; 54:19-33.

8. Starace, Giuseppe danPascalis, Lorenzo De. 2011. An Advance Analytical Model of the Diffusion Absorption Refrigerator Cycle. International Journal of Refrigeration ;35:605-612.

9. Çengel, Yunus A. 2002. Heat Transfer: A Practical Approach. Second Edition. New York: McGraw-Hill.

10. Incropera, Frank P., dkk. 2007. Fundamentals of Heat and Mass Transfer Seventh Edition, New York: John Wiley & Sons Inc.