A NUMERICAL STUDY OF SINGLE-PHASE FORCED CONVECTIVE HEAT TRANSFER WITH FLOW FRICTION IN ROUND TUBE HEAT EXCHANGERS

Transcription

1 A NUMERICAL STUDY OF SINGLE-PHASE FORCED CONVECTIVE HEAT TRANSFER WITH FLOW FRICTION IN ROUND TUBE HEAT EXCHANGERS Pedram Mohajeri Khameneh 1,*, Iraj Miraie 2, Nader Pourmahmoud 3, Mostaa Rahimi 4 & Samad Majidyar 5 1,2,3,4,5 Department o Mechanical Engineering, Faculty o Engineering, Urmia University, 11 th km o Serow road, Urmia, Iran ABSTRACT Three dimensional simulation o the single-phase laminar low and orced convective heat transer o water in a round tube counter low type heat exchanger is investigated numerically. In this article, rerigerant side heat transer characteristics are studied by simulating a round tube counter low heat exchanger. The geometry and operating conditions o that indicated heat exchanger are created using a inite volume-based computational luid dynamics technique. The aims o this paper are to obtain computational Nusselt number and validate it with available experimental studies. The results in this numerical method are in a good agreement with experimental results within an error in acceptable range. Ater that, at each Z-location, variation o dimensionless local temperatures, nondimensional local heat lux variation and dimensionless local Nusselt number distribution along the tube length are obtained numerically. Finally, in this paper, sensitivity analysis or round tube counter low type heat exchanger model o this numerical simulation is explored. Keywords: Heat exchanger, Laminar low, Numerical simulation, Nusselt number, Round tube 1. INTRODUCTION Heat exchangers serve a straightorward purpose: controlling a system s or substance s temperature by adding or removing thermal energy. According to Butterworth and Mascone [1], the area that might represent one o the more important aspects o a heat transer engineer's job is compact heat exchangers. The design lexibility or selecting geometric conigurations is a major advantage o compact heat exchangers. On the other hand, it may represent a major hurdle, because no comprehensive guideline can be easily developed or dierent kinds o compact heat exchangers. They have advantageous design eatures or selected applications [2], [3]; however, they are not the irst choice or the design engineer in the process industries. The major technical and non-technical barriers must be removed in order to make compact heat exchangers the irst choice. Although there are many dierent sies, levels o sophistication, and types o heat exchangers, they all use a thermally conducting element usually in the orm o a tube or plate to separate two luids, such that one can transer thermal energy to the other. Home heating systems use a heat exchanger to transer combustion gas heat to water or air, which is circulated through the house. Power plants use locally available water or ambient air in quite large heat exchangers to condense steam rom the turbines. Many industrial applications use small heat exchangers to establish or maintain a required temperature. In industry, heat exchangers perorm many tasks, ranging rom cooling lasers to establishing a controlled sample temperature prior to chromatography. Anyone who wants to use a heat exchanger aces a undamental challenge: ully deining the problem to be solved, which requires an understanding o the thermodynamic and transport properties o luids. Such knowledge can be combined with some simple calculations to deine a speciic heat transer problem and select an appropriate heat exchanger. Heat exchangers come in a wide variety o types and sies. Here are a ew o the most common ones. Coil heat exchangers have a long, small diameter tube placed concentrically within a larger tube, the combined tubes being wound or bent in a helix. One luid passes through the inner tube, and the other luid passes through the outer tube. This type o heat exchanger is robust capable o handling high pressures and wide temperature dierences. Although these exchangers tend to be inexpensive, they provide rather poor thermal perormance because o a small heat-transer area. Nevertheless, a coil heat exchanger may be the best choice or low-low situations, because the single tube passage creates higher low velocity and a higher Reynolds number. These exchangers are commonly used to establish a ixed temperature or a process-stream sample prior to taking measurements. These exchangers can also be used to condense high-temperature stream samples. Plate heat exchangers consist o a stack o parallel thin plates that lie between heavy end plates. Each luid stream passes alternately between adjoining plates in the stack, exchanging heat through the plates. The plates are corrugated or strength and to enhance heat transer by directing the low and increasing turbulence. These 407

2 Khameneh & al. Single-Phase Forced Convective Heat Transer exchangers have high heat transer coeicients and area, the pressure drop is also typically low, and they oten provide very high eectiveness. However, they have relatively low pressure capability. Shell-and-tube heat exchangers consist o a bundle o parallel tubes that provide the heat-transer surace separating the two luid streams. The tube side luid passes axially through the inside o the tubes; the shell-side luid passes over the outside o the tubes. Bales external and perpendicular to the tubes direct the low across the tubes and provide tube support. Tube sheets seal the ends o the tubes, ensuring separation o the two streams. The process luid is usually placed inside the tubes or ease o cleaning or to take advantage o the higher pressure capability inside the tubes. The thermal perormance o such an exchanger usually surpasses a coil type but is less than a plate type. Pressure capability o shell-and-tube exchangers is generally higher than a plate type but lower than a coil type. Laminar parallel-plate heat exchangers are a avorable design, since they provide high heat transer or a given pressure drop [4]. They are avorable or miniature cryocooler designs [5] because o the large heat transer coeicients and compactness, The problem with laminar plate heat exchangers is that i low maldistribution occurs, it severely degrades the perormance o high thermal eective heat exchangers [4,6,7]. In recent years, practical heat transer enhancement techniques have been developed and many articles have been devoted to this area [8, 9]. The biggest beneit rom heat transer enhancement is reduction in the sie o heat exchangers. For the same heat load requirement, much smaller heat transer area is needed due to a higher overall heat transer coeicient. Second, the heat transer or the same load can be carried out or smaller driving orces, which implies higher thermodynamic eiciency. Third, a higher heat load can be exchanged or the same area and the same driving orce. On the other hand, enhancement techniques have been developed or the shell side as well. Especially in cases o a viscous luid with high ouling tendencies, it is better to place this process stream into the shell side o a heat exchanger. In this case, exchangers with helical bales can be considered as a very eective way or enhancement [10, 11]. The present work was undertaken to obtain computational Nusselt number and compare it with available experimental results. Ater that, variation o dimensionless local temperatures, local heat lux and local Nusselt number along the tube length were investigated numerically. Finally, sensitivity analysis o this numerical simulation o this round tube heat exchanger model was explored. 2. DESCRIPTION OF NUMERICAL SIMULATION PROCEDURE In this article, a numerical method is developed to measure heat transer parameters o commercially available round tube heat exchangers. For this reason the rerigerant side heat transer coeicient is investigated numerically and rerigerant side heat transer characteristics are studied by simulating a round tube counter low type heat exchanger. By using this numerical simulation, a computational 3D virtual domain is created to simulate this heat exchanger tube in terms o its internal cooling capacity. As a simulation model, tube in tube counter low heat exchanger coniguration is conducted by this numerical simulation. Since the counter low design provides higher temperature dierence between hot and cold luids, the maximum heat transer capacity o these heat exchanger tubes could be analyed with this numerical method. Based on Padhmanabhan et al. s study [12] conventional sie round tube geometry is created in computational domain. In addition, single phase, laminar, counter low, water jacket is simulated around heat exchanger tube as a test environment. By doing so, heat exchanger tube s cooling eect is measured according to the changes within the surrounding water jacket low and iterative results are compared to identiy heat exchangers internal thermal perormance. 3. COMPUTATIONAL PRE-PROCESSING AND ASSUMPTIONS OF PHYSICAL MODEL As it mentioned earlier, Padmanabhan et al. s work [12] is selected as a reerence study to deine the heat exchanger tube geometry and to set boundary conditions. For the outer water jacket, a suitable design is required in order to have a reasonable comparison. According to commercially available products, a counter low heat exchanger model is deined, which could be applicable in this numerical simulation. The material and the diameter o the water jacket are deined by commercially available product o aluminum tube with 30 mm diameter. Since the total tube length o (L tube ) is longer than the hydrodynamic entrance region (L h ), based on Langhaar et al. s correlation given in the textbook (Introduction to Heat Transer, Incropera et al. [13]), water low is assumed to be ully developed and laminar. The L h value is obtained according to Re Dh and D h as shown in equation (1): Lh 0.05ReDh Dh (1) As it illustrated in igure 1, counter low heat exchanger coniguration is simulated in this numerical method by inserting round tube in a counter water low. Within laminar region, water jacket is cooled by and local changes in 408

3 Khameneh & al. Single-Phase Forced Convective Heat Transer its thermal properties along tube length (L tube ) are reported. Fig. 1 Sketch o the counter low tube heat exchanger with round tube inside A cross section o the heat exchanger structure used in this investigation is shown in igure 2. In order to increase the computational eiciency and by using symmetry boundary conditions, quarter geometry is created according to heat exchanger tube s geometric speciications which are listed in table 1. Fig. 2 Cross-section o round tube heat exchanger This round tube heat exchanger dimensions are expressed with round tube s inner radius (R round-tube in ), round tube thickness (t round-tube ), round tube outer length (L round-tube ), jacket radius (R jacket) and overall tube length (L tube ). Table 1. Geometric parameters or round tube heat exchanger Parameter Length (mm) R round-tube in 4.84 t round-tube 0.30 R jacket 15 L round tube 8.08 L tube 1200 Additionally, equally spaced grid points are applied based on round tube s inner radius (R round-tube in ) and jacket radius (R jacket ) to round tube thickness (t round-tube ) ratio, respectively. For the arc length, round tube outer length (L round-tube ) to channel thickness ratio is applied to create equal tangential grid spacing. Resultant mesh quality or this grid study is presented in igure

4 Khameneh & al. Single-Phase Forced Convective Heat Transer Fig.3 Partial geometry and grid generated o round tube heat exchanger This simulation is perormed based on these ollowing assumptions: (1) The governing equations based on Navier-Stokes equations can be used to describe the physical model. (2) The process is steady and the luid is incompressible. (3) The water low is assumed to be ully developed and laminar. (4) The body orces are neglected. (5) The thermal properties o water are varying with the temperature and the thermal properties o solid are constants. (6) Radiation heat transer and natural convective heat transer are neglected. 4. GOVERNING EQUATIONS AND BOUNDARY CONDITIONS According to the above assumptions, the three dimensional Navier-Stokes and energy equations are used to describe the luid low and heat transer in round tube heat exchanger. The governing equations are given in equations (2), (3), (4), as: Continuity: Momentum: Energy:.( V ) 0.( VV ) P.( V ).( V( c, T)).( k T ) (2) (3) p Where k is the thermal conductivity o water, V is the overall velocity vector o the water low and μ, ρ, c p,, represent molecular viscosity, density and speciic heat at constant pressure o water low, respectively. First, SYMMETRY boundary conditions are used or each sectional ace cuts to provide complete solutions in this partial geometry. Furthermore, MASS FLOW INLET is applied to deine inlet boundaries in channel low due to available experimental data. On the other side, in order to obtain a better convergence and avoid backlows during convergence o this numerical method, PRESSURE OUTLET is used to deine outlet boundaries in tube outlets. In this simulation, each wall at interaced sections separates into two aces with generating wall Shadow. This operation makes it possible to analye each aces o interaced walls individually. In this investigation, a suitable boundary condition is required to deine luid/solid interace to get a conjugated solution or convection and conduction in round tube heat exchanger model. Hence, in wall thermal boundary condition, Couple option is selected to solve energy equation or the wall and its shadow simultaneously. Finally, ater creating the geometry based on indicated geometric dimensions and choosing the mesh quality and assigning appropriate boundary conditions, pre-processing in this numerical method is completed. 5. ROUND TUBE HEAT EXCHANGER NUMERICAL SOLUTION In order to have a accurate simulation model it is important to represent in and tube working condition precisely in this numerical method. Based on equation (5), the round tube mass low rate ( m (4) round tube ) is calculated by dividing 410

5 Khameneh & al. Single-Phase Forced Convective Heat Transer the given in and tube rerigerant mass low rate ( m m in tube ) into its total circuit s number (N circuit ), as: intube roundtube (5) Ncircuit m For the outer water jacket, the mass low rate is selected according to critical Reynolds number or laminar region constrains or cylindrical tubes (Re laminar < 2300). Additionally, round tube and outer water jacket initial temperatures are deined based on indoor and outdoor test conditions o Padhmanabhan et al. s experimental study [12]. The Darcy Weisbach correlation, equation 6, as given in Incropera [13] is applicable or laminar low in smooth tubes. Resultant initial conditions are listed below in table 2. For pressure outlet boundary condition, equation (6) is used to estimate the pressure loss and the riction actor ( ) is estimated according to the equation (7) in laminar low. 2 L V p.. (6) D 2 h 64 (7) Re Where Re is the Reynolds number calculated based on the low inside the tube and jacket o this heat exchanger and D h, equation (8), is the hydraulic diameter: 4 ( cross section area) D h (8) Wetted perimeter Table 2. Initial conditions o round tube heat exchanger Parameter Tube Jacket T in (K) V (m/s) m (kg/s) Re P gauge In order to investigate the sudden temperature change eect on luid thermal properties in tube and jacket o this heat exchanger, luid properties are deined as a polynomial unction o temperature. Once all the boundary conditions are set, iterative study is started. In order to increase the accuracy o the results second order upwind discretiation is applied in this numerical simulation. In the ollowing section, numerical results or this indicated model will be analyed and compared with Driker and Meyer s experimental study [14]. 6. RESULTS AND DISCUSSION 6.1. Non-dimensioning Procedure The aim o this study is to report the cooling eect o round tube heat exchanger inside a counter low water jacket. Thus, heat transer properties are measured in this numerical method. First, local values by averaging the numerical results based on number o grid points are calculated. Additionally, in order to simpliy the results and eliminate the units in this solution, each local value is non-dimensionalied which are shown in equations (9),(10),(11). Non-dimensional length: L tube (9) Non-dimensional temperature: T( ) T ( ) T T max min min (10) Non-dimensional heat lux: * q''( ) q'' ( ) q'' 6.2. Dimensionless Local Heat Transer Properties Results Dimensionless local temperature change is calculated by using equation (10). As it presented in igure 4, temperature dierence between water jacket ( ) ) and channel surace ( ) ) change is obtained according to counter low coniguration. ( jacket max ( wall (11) 411

6 Khameneh & al. Single-Phase Forced Convective Heat Transer Fig. 4 Dimensionless local water jacket and wall temperatures In igure 4, () proile varies between round tube and jacket inlet temperatures and despite its linear proile at wall the tube mid-section, sudden changes are reported at low inlet sections due to constant initial temperature boundaries. By applying equation (11), non-dimensional local heat transer rates rom water jacket to channel surace ( q '' * ( )) are evaluated or each surace node point. Results are presented in igure 5. Fig. 5 Dimensionless local heat lux distribution According to igure 5, highest heat transer intensity is observed at the water jacket inlet section due to sudden decrease in the luid temperature. Ater stabiliing its heat transer rate in the midsection, additional increase is investigated in jacket cooling rate at the low exit, similarly, due to sudden decrease in wall temperature. By applying heat transer properties which are calculated in previous sections, non-dimensional local Nusselt number along the tube length or round tube counter low type heat exchanger is calculated by using equation (12), as: * Nu( ) Nu ( ) (12) Numax In order to evaluate Nu * ( ), local Nusselt number at each Z-location should be calculated based on equation (13) or round tube heat exchanger model, as: q Dh Nu ''( ) ( ) Ts T (13) ( ) ( ) k Cosequently, by applying equations (12), (13), distribution o dimensionless local Nusselt number along the tube length or round tube counter low heat exchanger model is shown in igure

7 Khameneh & al. Single-Phase Forced Convective Heat Transer Fig. 6 Dimensionless local Nusselt number distribution Based on equation (12), maximum Nusselt number value is evaluated at the inlet as a result o beginning o thermal boundary layer ormation. Finally, averaged Nusselt number o the jacket is evaluated by numerically integrating the discrete values over the tube length, L. The trapeoidal rule is applied by using previously calculated averaged local Nusselt number values which is shown in equation (14), as: Nu avgnumerical 1 L Z L n Z 0 Nu( Nu( ) d L 0 ) Nu( 2 n ) n1 k1 Nu( Where, Δ is the equally spaced grid point distance and n is the total number o grid points and resultant average Nusselt number is evaluated as: Nu avgnumerical Validation Results For Round Tube Heat Exchanger Model Based on equation (15), validation o this Numerical method is perormed or round tube heat exchanger model and computational results are compared with corresponding Driker and Meyer s analytical Nusselt number correlation or concentric annuli [14],as: Where, And, Nu avganalytical 1 C 3 0 Re 1 C Pr Dh wall 0.14 k ) (14) (15) a C 0 (16) a 0.674a 2.225a a C 1. e (17) D h VDh Re D (18) h ( D D ) out (19) jacket roundtube D jacket a (20) D roundtube out By calculating luid properties (ρ, µ, Pr and µ wall ) in this numerical method, corresponding luid properties are computed and then by substituting these variables in equation (15), annular jacket side Nusselt number or round tube heat exchanger model is calculated as: 413

8 Khameneh & al. Single-Phase Forced Convective Heat Transer Nu avganalytical 8.89 Finally, in this heat exchanger model, the dierence between computationally obtained Nusselt number Nu ) is reported as 10%. It is concluded Nu ) and its corresponding analytical correlation ( avg analytical ( avg Numerical that a comparison between analytical and numerical studies is provided a good agreement in rerigerant side thermal analysis o round tube counter low heat exchanger model. Based on Driker and Meyer s experimental study [14], sensitivity analysis o this numerical method is studied and results are presented in next section Numerical Sensitivity Analysis For Round Tube Heat Exchanger Model Beore analying the calculated results, it is required to investigate the sensitivity o this method and understand which variable eects more on heat transer perormance o the water to water, single phase, laminar, counter low heat exchanger simulation. Thus, according to variation o both jacket and round tube Reynolds number within laminar region, a sensitivity analysis is studied to measure its eect on averaged water jacket Nusselt number. First, the jacket Reynolds number eect is measured by repeating the same procedure with two dierent jacket mass low rates, which resulted higher and lower Reynolds number than initial value; Re jacket = Based on iterative results, previously presented procedure is applied to calculate the Nusselt number variations. Additionally, Driker and Meyer s experimental Nusselt correlation [14], which can predict the averaged Nusselt number value in 3% uncertainty, is used to measure the dierence between their analytical solution and this numerical method. According to table 3, an average 50% increase in water jacket Reynolds number is enhanced the Nusselt number around 15%. Compared to experimental correlation, in igure 7 a similar trend is obtained in Nusselt number variation with 20% averaged disparity. Table 3. Sensitivity analysis o jacket Reynolds number in heat transer Re jacket Nu avg-numerical Nu avg-experimental Fig.7 Sensitivity o water jacket Nu to jacket Re Similarly, increase in round tube mass low rate eect in its cooling perormance is investigated by reiterating this numerical simulation at dierent round tube Reynolds number; Re round-tube. Based on table 4 an average 35% change in the round tube Reynolds number could only aect the jacket heat transer 1.6%, which is noticed as 1% in the experimental correlation. Compared to experimental correlation, in igure 8 a similar trend is obtained in Nusselt number variation with 10% averaged disparity. Table 4. Sensitivity analysis o tube Reynolds number in heat transer Re round-tube Nu avg-numerical Nu avg-experimental

9 Khameneh & al. Single-Phase Forced Convective Heat Transer Fig. 8 Sensitivity o water jacket Nu to tube Re According to igure 7, 8 results, the ratio between averaged change in Nusselt number to corresponding Reynolds number increase ( Nu ) is evaluated or each case. In conclusion, compared to internal round tube low, 9.3 Re times higher sensitivity is calculated in round tube in tube simulation by only increasing the water jacket mass low rate. 8. OVERALL CONCLUSIONS In this article, three dimensional simulation o the single-phase laminar low and orced convective heat transer o water in a round tube counter low type heat exchanger is investigated numerically and rerigerant side heat transer characteristics were studied. Then, the eects o dimensionless local water temperatures, dimensionless local heat lux and dimensionless Nusselt number on laminar heat transer were explored individually. Ater that, this numerical simulation is validated with available experimental studies and it is ound that the results in this numerical simulation were in a good agreement with experimental results within an error in acceptable range. Finally, in this paper, numerical sensitivity analysis o this model was perormed and the results show that increase in water jacket mass low rate developed the heat transer 9.3 times more than round tube mass low rate. 10. REFERENCES [1]. D. Butterworth and C. F. Mascone, Heat Transer Heads Into the 21st Century, Chem. Eng. Prog., Sept., pp (1991). [2]. R. K. Shah, et al., Compact Heat Exchangers, Hemishphere Publishing Co., NewYork (1990). [3]. J. M. Robertson, The Development o Compact Heat Exchangers to Save Weight, Space, and Power Oshore, TEC88 Conerence: Recent Advances in Heat Exchangers, Oct , Grenoble, UK (1988). [4]. Rawlins, Timmerhaus and Radebaugh, Measurement o Perormance o a Spiral Wound Polyimide Regenerator in Pulse Tube Rerigerator, Adv. Cryogenic Eng., Vol.37, part B, p.947, (1991). [5]. J. A. Crunkleton, J. L. Smith, Jr. and Y. Iwasa, High Pressure Ratio Cryocooler with Integral Expander and Heat Exchanger, Adv. Cryogenic Eng., vol.33, p.809, (1988). [6]. E. B. Ratts, J. L. Smith, Jr. and Y. Iwasa, Heat Transer and Friction Factor Data or Gap Helical Screen Fin Counter Flow Heat Exchanger, Adv. Cryogenic Eng., vol.39, part A, pp , (1993). [7]. R. B. Fleming, The Eect o Flow Distribution In Parallel Channels o Counter Flow Heat Exchangers, Adv. Cryogenic Eng., vol.12, pp , (1967). [8]. A. E. Bergles, Heat Transer Enhancement The Encouragement and Accommodation o High Fluxes, Trans, ASME J. Heat Transer, vol. 119, pp. 8 19, (1997). [9]. R. L. Webb, Principles o Enhancement Heat Transer, Wiley, (1994). [10]. P. Stehlik, J. Nemcansky, D. Kral, and L. W. Swanson, Comparison o Correction Factors or Shell-and-Tube Heat Exchangers with Segmental or Helical Bales, Heat Transer Eng., vol. 15, pp , (1994). [11]. D. Kral, P. Stehlik, H. J. van der Ploeg and B. I. Master, "Helical Bales in Shell-and-Tube Heat Exchangers, Part I: Experimental Veriication", Heat Transer Eng., vol. 17, pp , (1996). [12]. S. Padhmanabhan, L. Cremaschi, D. Fisher and J. Knight, Comparison o rost and derost perormance between microchannel coil and in and tube coil or heat pump systems, International Rerigerant and Air Conditioning Conerence, Purdue, July , 1-8 (2008). [13]. F. P. Incropera, D. P. DeWitt, T. L. Bergman, A. S. Lavine, "Introduction to Heat Transer", Fith edition, Wiley, Newyork, (2007). [14]. J. Dirker and J. P. Meyer, Convective heat transer coeicients in concentric annuli, Heat Transer Engineering, 26(2), 38-44, (2005) 415