Energy efficiency improvement and fuel savings in water heaters using baffles

Applied Energy 102 (2013) 520–533

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Energy efficiency improvement and fuel savings in water heaters using baffles Mahmoud Moeini Sedeh, J.M. Khodadadi ⇑ Mechanical Engineering Department, 1418 Wiggins Hall, Auburn University, AL 36849, USA

h i g h l i g h t s " Thermal efficiency improved by simple/novel design of baffles inside water reservoir. " Noticeable steady-state natural gas savings of about 5%. " Extensive 3-D numerical investigations followed by experimental verifications. " Baffle designs prototyped in identical water heaters for ANSI/US DOE test protocols. " Numerical/experimental results verified thermal efficiency improvement & fuel savings.

a r t i c l e

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Article history: Received 9 February 2012 Received in revised form 27 July 2012 Accepted 2 August 2012 Available online 9 October 2012 Keywords: Baffle Fuel savings Natural gas Optimization Thermal efficiency Water heater

a b s t r a c t Thermal efficiency improvement of a water heater was investigated numerically and experimentally in response to presence of a baffle, particularly designed for modifying the flow field within the water reservoir and enhancing heat transfer extracted into the water tank. A residential natural gas-fired water heater was selected for modifying its water tank through introducing a baffle for lowering natural gas consumption by 5% as a target. Based on the geometric features of the selected water heater, threedimensional models of the water heater subsections were developed. Upon detailed studies of flow and heat transfer in each subsection, various sub-models were integrated to a complete model of the water heater. Thermal performance of the selected water heater was investigated numerically using computational fluid dynamics analysis. Prior to baffle design process and in order to verify the developed model of the water heater, time-dependent numerically-predicted temperatures were compared to the experimentally-measured temperatures under the same conditions at six (6) different locations inside the water tank and good agreement was observed. Upon verifying the numerical model, the fluid flow and heat transfer patterns were characterized for the selected water heater. The overall design of the baffle and its location and orientation were finalized based on the numerical results and a set of parametric studies. Finally, two baffle designs were proposed, with the second design being an optimized version of the first design. The verified three-dimensional model of the water heater was modified to include the baffle designs and same thermal performance analysis was simulated confirming potential improvements in thermal efficiency. Thereafter, designed baffles were prototyped and assembled in identical water heater units and experiments were conducted according to standard water heater test procedures. Finally, numerical and experimental results verified thermal efficiency improvement in the water heater after introducing the baffles. As a result, baffle’s second design is capable of lowering the natural gas consumption of the water heater by 4.95% under steady-state thermal efficiency test condition which meets the target of this research. However, the gas savings under actual usage patterns might be less than this value. Ó 2012 Elsevier Ltd. All rights reserved.

1. Introduction Energy efficiency is crucially important in operation of heat exchangers and fuel-consuming devices and its improvement leads to fuel savings and environmental benefits of emission reduction. Baffles are flat or curved plates that are extensively used in various ⇑ Corresponding author. Tel.: +1 334 844 3333; fax: +1 334 844 3307. E-mail address: [email protected] (J.M. Khodadadi). 0306-2619/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.apenergy.2012.08.034

applications for stabilizing and directing flow, controlling sloshing or waves, overflow prevention, and mixing enhancement purposes [1,2]. Considering the coupling of velocity and temperature fields in fluids (through advection terms in the energy equation, natural convection and effects of turbulence), baffles can affect the temperature field and heat transfer as well. In other words, it is possible to utilize a baffle to manipulate the flow field so that it affects the temperature field by maximizing or minimizing heat transfer from/to the fluid. For instance, if the baffle increases heat transfer

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Nomenclature Cp C1 C2 C3 Cl E Gb h HHV J K k m p Pr ui u0i Sh Sij T t xi

specific heat, J kg1 K1 constant in the standard k–e turbulence model, equal to 1.44 constant in the standard k–e turbulence model, equal to 1.92 constant in the standard k–e turbulence model, equal to 0.33 turbulent viscosity constant, equal to 0.09 energy per unit mass, W kg1 generation of turbulent kinetic energy due to buoyancy, kg m1 s3 specific enthalpy, J kg1 higher heating value, J kg1 diffusion flux of species, kg m2 s1 thermal conductivity, W m1 K1 turbulent kinetic energy, m2 s2 mass, kg pressure, N m2 Prandtl number time-averaged velocity components, m s1 fluctuating components of velocity, m s1 volumetric heat source including heat release from chemical reactions, W m3 rate of strain tensor, s1 temperature, K time, s Cartesian coordinates

from combustion products to another fluid in a gas-fired heat exchanger, then the baffle is effective in thermal efficiency improvement. There are several cases reported in the literature showing that introduction of baffles can affect the heat transfer rate and temperature field in different applications such as heat exchangers, thermal regenerators, electronic cooling devices, autoclaves for crystal growth, internal cooling systems of gas turbine blades and cooling water jackets. Depending on the specific application, there are a wide variety of baffle shapes and configurations that affect heat transfer and flow patterns. The shape and orientation of these baffles depend on the geometry and flow characteristics of the specific application. Usually, heat transfer enhancement and control over the fluid flow velocity are the immediate results of utilizing baffles that has been studied and reported for different cases. A primary academic study on this topic was reported by Berner et al. [3] who considered the effect of baffle presence in a shell and tube heat exchanger model using an approximate two-dimensional model. They simplified the problem by neglecting the interference of tubes with flow inside the shell to find the general characteristics of the flow (e.g. separation regions, circulation, stagnation points, boundary layers, pressure drop, flow pattern and periodicity). They used the Laser Doppler Anemometry (LDA) method in PlexiglasÒ and PyrexÒ-glass channels with a total number of ten baffles connected to the top and bottom walls successively normal to the flow direction. Kim and Anand [4] studied the periodically fully-developed turbulent flow and heat transfer between a series of conducting parallel plates with surface-mounted heat sources. Using a twodimensional numerical model of the channel and plates and the k–e turbulence model, they found that presence of the plates (as baffles in electronic cooling channels) will directly affect the friction factor and the Nusselt number and will lead to an increase in heat transfer rate. Dutta and Dutta [5] carried out an experimental and numerical investigation of friction loss and heat transfer of turbulent flow in a

Greek Symbols thermal diffusivity, m2 s1 dij Kronecker delta e turbulent dissipation rate, m2 s3 g thermal efficiency l dynamic viscosity, kg m1 s1 q density, kg m3 rk constant in the standard k–e turbulence model, equal to 1.0 re constant in the standard k–e turbulence model, equal to 1.3 s stress tensor, N m2 sRij Reynolds stress components, N m2

a

Subscripts c cold eff effective quantities g related to gas domain h hot i, j, k indices for tensor notation mod related to modified water heater using baffle in water tank s related to solid domain st related to the selected water heater (standard base model) t turbulent quantities w related to water domain

rectangular channel with constant heat flux on the upper wall with inclined baffles attached to it. They considered the effects of the baffle size, orientation and perforation on the average and local Nusselt numbers. They found that the size, positioning and orientation of the baffle has a significant influence on internal cooling heat transfer and using optimum size, positioning and orientation, heat transfer will be maximized. They also found an optimum perforation density for perforated baffles which leads to strong jet impingement phenomenon and maximizes heat transfer. Another study on baffles was conducted by Chen et al. [6] who developed a mathematical model for three-dimensional numerical investigation of flow and heat transfer characteristics in cylindrical crystal growth systems. Modeling the raw material in the lower chamber as a porous layer, they found an upward-rising jet around the axis of the cylinder and a downward flow next to the wall of the upper chamber. The characteristics of the flow (and accordingly temperature field in the crystal growth zone) depended on the Grashof number, remaining laminar for low Grashof numbers, whereas changing to oscillatory or turbulent when the Grashof number was high. They found that using a baffle placed between the lower and upper chambers may reduce the flow strength but causes more uniform velocity and temperature distributions in the crystal growth zone (i.e. upper chamber). Finally, they found that putting a baffle between the two chambers clearly reduces the vertical velocity of upward-rising jet and produces a more uniform temperature distribution for crystal growth. Moreover, they emphasized that location, thickness, shape and porosity of the baffle can effectively influence the growth process and should be studied in detail. An experimental study on the effect of porous baffles on heat transfer enhancement in channel flow was performed by Ko and Anand [7]. The intent of using porous baffles was to reduce the pressure drop and friction loss associated with the baffle’s presence. They performed experiments on a rectangular channel with 14 successive porous baffles mounted on the top and bottom walls

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and found that flow was periodically fully-developed after the seventh baffle and utilization of porous baffles led to 300% increase in heat transfer. This enhancement was 390% for solid baffles. However, solid baffles have higher friction loss and pressure drop. Additionally, their experiments with different flow rates (Re  20,000–50,000) showed that the average Nusselt number increased with increasing of the Reynolds number. This was mainly because the turbulent transport is dominant at high Reynolds numbers and the effectiveness of baffles will be reduced. Also, for a fixed porosity, the heat transfer enhancement increased with the baffle thickness. For finding the optimum case, they defined the heat transfer performance ratio as the ratio of heat transfer enhancement to the friction loss or pumping power. As a result, they found that baffles with the pore density of 40 pores per inch (PPI) performed more effectively at low Reynolds numbers. Using a simplified two-dimensional axisymmetric model of a hydrothermal autoclave, Li et al. [8] studied the effect of baffle conduction and autoclave aspect ratio (for a single-hole baffle with 15% area opening and aspect ratios of 2, 5, 10 and 20) on the flow pattern and temperature distribution. Their results showed that conduction through the thin baffles can be neglected and when the aspect ratio increased, the vertical component of velocity increased, whereas the radial velocity component became more uniform in the center region of the growth chamber. Li et al. [9] studied the influence of a baffle on the temperature and flow separation in an autoclave and its effects on crystal growth. They compared the computed velocity and temperature distributions in a hydrothermal autoclave with and without baffle. They extracted the effects of baffle presence on the cylindrical autoclave using a single hole, round flat baffle with a 15% area opening at the median height of the autoclave. They found that although there was a significant decrease in flow velocity due to the presence of the baffle, the temperature distribution became uniform that is highly desirable for crystal growth. Moreover, they found that flow in the original autoclave, as a single cylindrical cell, was asymmetric whereas with the baffle, the velocity and temperature distribution became nearly axisymmetric. Li et al. [10] considered the effects of multi-hole baffles on the radial temperature distribution in industrial autoclaves. They focused on the number and configuration of holes and baffle opening area in a round flat baffle placed at the median height of a cylindrical hydrothermal autoclave. The results of this numerical investigation suggest that multi-hole baffles can properly affect the velocity and temperature profiles toward more uniform profiles. They studied various opening areas for a single-hole baffle and compared it with different multi-hole configurations. For a single-hole baffle, they found that a smaller opening area led to more uniform temperature profiles and higher rate of crystal growth. However, for multi-hole baffles they found the best performance corresponded to three different configurations of 8-hole baffles. Li and Braun [11] studied the effect of the baffle shape on the velocity and temperature distribution in a cylindrical hydrothermal autoclave numerically. They considered three different round flat baffle shapes: single-hole solid baffle, 16-hole solid baffle and perforated porous baffle, all with the same opening area of 15%. The results showed that all three baffles gave rise to uniform radial temperature profiles. However, radial temperature and velocity profiles were more uniform with a single-hole baffle and radial temperature and velocity gradients near the walls were higher for the perforated baffle compared to other two baffles. In addition, temperature distribution along the center-line, which is indicative of temperature variations in the vertical direction in the growth chamber, was much higher with the perforated baffle when compared to other baffles. Chang and Shiau [12] studied the heat transfer characteristics of pulsating mixed convection in a parallel vertical open channel un-

der the presence of a horizontal baffle. Using a numerical approach, they found that the average Nusselt number was higher for the channel with a baffle compared to the no baffle case. Additionally, they reported that imposing flow pulsation besides using a baffle will maximize heat transfer. Li and Braun [13] considered flow structure and transport mechanisms in rectangular and cylindrical enclosures with and without baffles. They found that the flow structure and transport mechanisms were qualitatively the same in both rectangular and cylindrical enclosures without baffle. However, inserting a baffle in the cylindrical enclosure divided it into two cells with distinct temperature zones. Therefore, there was a temperature-driven flow structure at the baffle position consisting of an upward-rising hot jet and a downward-sinking cold jet at the baffle opening area where exchange of momentum and energy takes place. The boundary layer thickness varied due to flow segmentation, shrinkage of the flow partitions and wall layer interactions. Presence of the baffle prevented direct wall layer interactions and circumferential partitioning of the flow. Therefore, the transport of mass and energy was reduced in comparison to the case with no baffle, and the upper and lower chambers were effectively separated into distinct temperature zones. Li et al. [14] performed an experimental and numerical investigation of the fluid flow and natural convection heat transfer in a bottom-heated, top-cooled cubic cavity with a single-hole baffle at the median height. For experiments, Thermo-chromic Liquid Crystal (TLC) particles were used in order to allow visualization of the temperature field inside the cavity and its quantitative assessment. They found that there were two jet-like streams inside the cavity, an upward-rising hot stream and a downward-sinking cold stream. These jets touched each other at the baffle opening where thermal energy was exchanged. The hot jet then impinged on the top wall, whereas the cold one impinged onto the bottom wall. Heat transfer between these streams at the baffle opening position reduced the temperature gradient in both streams and caused more-uniform temperature distribution in the cavity. As a result, the fluid in the rest of each chamber had a rather uniform temperature due to the presence of the baffle. Cheng and Tsay [15] investigated the characteristics and enhancement of the laminar forced convection heat transfer for a backward-facing step flow in a two-dimensional channel due to the presence of solid and slotted baffles placed on the channel top wall. They studied the effects of the baffle height, baffle positioning angle and different solid/slotted baffles on the flow pattern and heat transfer from the bottom wall as a constant heat flux source representing a model of an electronic chip. They considered the flow pattern and temperature distribution numerically to find the most efficient cooling on the bottom wall (heat source). They found that the maximum enhancement of the Nusselt number due to the solid baffle was about 230%, whereas this quantity was about 190% for the slotted baffle. However, the solid baffle might cause re-separation of the main stream which can lead to poor local heat transfer characteristics in the end region of heating section. Also, the pressure drop in the channel with a solid baffle was nearly doubled compared to the channel with a slotted baffle. These were considered to be the advantages of using slotted baffles in such applications. For the laminar air flow (50 6 Re 6 400), they found that the best angle for the baffle positioning was 45°. Tandiroglu and Ayhan [16] conducted an experimental study of transient heat transfer of turbulent flow in constant surface heat flux circular tubes with different combinations of baffle inserts. They found that the average Nusselt number was noticeably higher for all cases of baffle inserts compared to the case of a tube with no baffle, for all the Reynolds numbers in the range of 3000–20,000. Wang et al. [17] investigated heat transfer performance of shelland-tube heat exchangers with a helical baffle in the outer shell

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pass. In comparison with conventional shell-and-tube heat exchangers, results of their computational fluid dynamics model suggested that under the same overall heat transfer rate, the pressure drop was lower for the heat exchanger with a helical baffle. Likewise, under the same pressure drop in shell side, the overall heat transfer rate was about 5.6% higher for the heat exchanger with a helical baffle. Furthermore, Zhang et al. [18,19] studied the effect of continuous and non-continuous middle-overlapped helical baffle on the performance of a shell-and-tube heat exchanger. Based on a periodic three-dimensional computational model of the entire heat exchanger, they investigated the effect of the helix angle on the performance of heat exchanger and found the optimum helix angle of 40°. They also found that the heat exchanger with a non-continuous middle-overlapped helical baffle had higher heat transfer coefficient per unit pressure drop compared to the heat exchanger with a continuous helical baffle. Another numerical simulation of hydrothermal autoclave has been reported by Masuda et al. [20]. They discussed the effect of the shape of the baffle (flat- or funnel-shaped) on the natural convection heat transfer and temperature distribution characteristics in an axisymmetric autoclave. They found a higher flow rate between the two zones when a funnel-shaped baffle was used at the mid-height of the autoclave, and as a result, a higher crystal growth rate was realized. The best angle of the funnel-shaped baffle was reported to be about 20°. Duan et al. [21] investigated the effect of a baffle on pseudosteady-state natural convection within spherical containers. They studied the effects of insulated and isothermal baffles for different cases of the Rayleigh numbers, baffle lengths and locations. They found that placing a baffle on the inner wall of spherical containers in the radial direction led to fluid compartmentalization characterized by stratified stable layers above the baffle and natural convection-induced currents below the baffle. Therefore, regardless of baffle thermal status, it affected the flow and temperature fields inside the spherical container and this effect was more noticeable when the baffle was longer. Promvonge et al. [22] performed a numerical investigation of periodic laminar flow and heat transfer in a three-dimensional square channel with baffles installed on two opposite walls with a 30° angle inclination. The flow was steady, laminar and incompressible passing through a series of baffles and assuming periodic flow, a section of the channel was selected as the computational model including two baffles, each installed on opposing top and bottom walls. After verifying the numerical model, their results showed that for different combinations of baffles, heat transfer increased and this increment can be considerable. For instance, under the same pumping power, the ratio of the Nusselt number of the channel with baffles to that of smooth channel (with no baffle) can be as high as about 4.0 for the Reynolds number of 2000 and the baffle pitch ratio of 2.0 (i.e. baffle spacing/channel width) and the baffle blockage ratio of 0.15 (i.e. baffle length/channel width). Going through the above-reviewed papers, it can be concluded that presence of baffles can lead to modification of the temperature field in fluids and effectively improve heat transfer rate for different applications. Secondly, baffles have specific features that characterize them as simple designs hence quite effective in heat transfer control/enhancement. Structurally, a baffle consists of only a single flat or curved plate with limited thickness that can be utilized to manipulate flow and affect temperature field subsequently. In baffle applications, heat transfer enhancement is mainly because of changes in flow pattern (due to the presence of the baffle), thus leading to improvements in convection. In comparison with this convection enhancement, thermal conduction through the baffle might have a slight contribution to the total heat transfer enhancement. These characteristics differentiate baffles from fins, as fins are usually utilized in arrays with optimum thick-

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ness and distance, to enhance heat transfer by increasing heat transfer surface (the concept of extended surface) and conduction through fin bases. The purpose of the research project summarized here was to come up with a novel design of a baffle in order to enhance heat transfer as well as thermal efficiency in a natural gas-fired water heater. The design included novel features such as its helical shape, its positioning and alignment so that it manipulates the flow field and maximizes both conductive and convective heat transfer inside a water heater as a typical heat exchanger providing thermal efficiency improvement. In particular, the simplicity of baffle designs was utilized to lead to a baffle for installation inside the water tank of water heaters to realize a noticeable improvement in thermal efficiency and reduction in fuel consumption due to the modification of flow pattern inside the water tank. As a result, a 5% reduction in natural gas consumption was set as a challenging target. Through computer-aided engineering, implementation, testing and superior performance of baffles in water heaters, similar heat storage and exchange applications can benefit from the adopted optimization approach and higher efficiencies and fuel savings might be realized. Even though the present work is focused on thermal efficiency improvement based on introducing baffles to the water side of the water heaters, the reader might be interested in great amount of prior work on flue-gas baffles, e.g. [23,24]. Moreover, the reader might find a fundamental study of natural convection from the outer surface of a vertical cylinder to a liquid [25] of relevance to this class of heat transfer problems. 2. Approach The overall approach adopted to achieve the final baffle design was to conduct computer-aided engineering (CAE) analyses as well as related experiments for a specific water heater and its modified versions by adding a baffle, thus seeking a better design modification based on a criterion of greater thermal efficiency or fuel savings. This approach is summarized using a flowchart shown in Fig. 1. A currently-in-production water heater (residential type, 40gallon water capacity and natural gas-fired) was selected for detailed modeling, grid generation and Computational Fluid Dynamic (CFD) analysis followed by experimental verification of results of this analysis before going to further steps of parametric studies for designing baffle and analysis of modified water heater with baffle. A schematic view of the selected water heater and its components is shown in Fig. 2. 3. CFD analysis of the selected water heater Numerical analysis of the selected water heater is necessary to determine the prevailing flow pattern as well as heat transfer characteristics prior to proceeding with the baffle design or any other changes/modifications. This step is significantly important since the results of this analysis in the form of flow and temperature features will be used partially as a basis to design the baffle’s overall shape. Therefore, it is essential to verify the numerical results of this step against the experimental data. This analysis at this stage was conducted according to the following steps. 3.1. Modeling and grid generation A three-dimensional (3-D) model of the specific water heater was developed with the aid of computer-aided design tools. This model was selected to be three-dimensional in order to reflect important details of the water heater and the ensuing flow field and heat transfer. Furthermore, there is no symmetry in water

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Fig. 1. General computer-aided engineering (CAE) approach adopted in this research.

Fig. 2. Schematic diagram of the selected water heater and its components.

and gas flows inside the water heater due to presence of symmetry-breaking parts such as a dip-tube at the water inlet station and a flue-gas baffle. Therefore, two-dimensional models cannot represent the flow field correctly. The developed model represents all the geometric features of gas side, water tank, and the inlet and outlet water ports. In the gas side, the combustion chamber around the burner (located at the bottom of water heater), flue gas pipe (the center cylindrical passageway through which the combustion products flow upward and are discharged) and flue-gas baffle (a perforated metal sheet inside the flue-gas pipe that slows down the stream of buoyant-rising combustion products from escaping quickly) were modeled exactly in 3-D according to the industrial drawings of the respective parts. The water tank was also modeled in three-dimensional real scale without any simplification. Similarly, a 3-D model of the dip-tube, through which fresh cold water enters the water tank, was created in real size featuring a helixshaped part at its end to impart swirl to the incoming water stream. Additionally, for heat transfer analyses, the 3-D model of the steel wall between the gas side and water tank was created based on the drawing of the part and placed between the water and gas phases in the water heater model. Consequently, the three-dimensional model of the water heater included all the important features of water heater (Fig. 3), thus accommodating accurate prediction of the fluid flow and heat transfer. The threedimensional modeling of the water heater was followed by grid generation and grid independence studies. Due to complexities in 3-D geometry, an unstructured tetrahedral grid system was used for grid generation. Grid generation was initially performed for water heater subsections (e.g. gas side, water inlet dip-tube, water tank and solid wall between water and gas) with different grid resolutions and grid independence study was carried out for each sub-

section. Due to different specifications of the flow in each subsection, different grid resolutions are necessary to resolve the flow details. For instance, the velocity gradients of the water flow passing over the helix at the end of dip-tube are much greater than velocity gradients in other parts of the water tank. Accordingly, the grid generated for CFD analysis of water heater has different resolutions at different locations. Another important factor, especially in predicting heat transfer, is the resolution of grids within the boundary layers. In order to predict the boundary layers of water and gas accurately, there should be enough grids within these regions. This is crucially important because it affects further calculations and can produce noticeable errors in integrated quantities such as the surface heat flux. Therefore, grids are dense inside the boundary layers and areas of sharp gradients, whereas these are larger in other areas with slowly-changing flow. Using the described grid resolution for each subsection of the entire water heater model, grids of about 1.5 million cells were generated and utilized for numerical analysis. A sample of grid in different parts of water heater is shown in Fig. 4. 3.2. Governing equations Transport of heat, momentum and species is driven by combustion of natural gas/air mixture in the combustion chamber followed by turbulent flow of combustion products in the flue-gas pipe, heat conduction through the solid wall between gas and water sides, and turbulent natural or mixed convection flow of water in the water tank. Based on the Reynolds decomposition of the variables in the governing equations into the mean and fluctuating components, the Reynolds-averaged Navier–Stokes (RANS) equations in the Cartesian tensor form are [26,27]:

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Fig. 3. Three-dimensional models of (a) combustion chamber and flue-gas pipe including flue-gas baffle, (b) swirl-generating helix-shaped element at the end of dip-tube, (c) assembled model of whole water heater including water tank and dip-tube inlet pipe, (d) solid wall between combustion chamber and water tank and (e) section view of the water heater model.

heat, the standard k–e model was selected as a two-equation turbulence model to represent turbulence effects. Despite the possibility of laminarization of the flow within the upper portion of the water tank, and in view of the engineering approach adopted here, using a two-equation turbulence model is justified. As a result, the following transport equations were solved numerically for the turbulent kinetic energy (k) and its dissipation rate (e) that leads to evaluation of turbulent viscosity (lt):

@ @ @ ðq k ui Þ ¼ ðq kÞ þ @t @xi @xj



lþ





lt @k þ 2lt Sij Sij þ Gb rk @xj

 qe; @ @ @ ðq eÞ þ ðq e ui Þ ¼ @t @xi @xj

ð4Þ



lþ





lt @ e e þ C 1 ð2lt Sij Sij re @xj k q e2

þ C 3 Gb Þ  C 2

k

;

ð5Þ

2

Fig. 4. Unstructured tetrahedral grids in (a) dip-tube around the helix-shaped swirl-generator part, (b) combustion chamber and flue-gas pipe and (c) water tank including inlet and outlet pipes.

@q @ ðq ui Þ ¼ 0; þ @t @xi    @ @ @p @ @u @u 2 @u ðq ui Þ þ ðq ui uj Þ ¼  þ l i þ j  dij i @t @xj @xi @xj @xj @xi 3 @xi @ ðq u0i u0j Þ; þ @xj

ð1Þ

s ¼ q

u0i u0j

  @ui @uj 2 2  ðq kÞ dij ¼ 2lt Sij  ðq kÞdij : ¼ lt þ 3 3 @xj @xi

k

e

ð6Þ

:

Having turbulent viscosity (lt) estimated via the k–e turbulence model, the general form of the energy equation is thus given by:

  @ @ @ @T X ½ui ðq E þ pÞ ¼ K eff  hj J j þ ui ðseff Þ þ Sh ; ðq EÞ þ j @t @xi @xj @xj ð7Þ

ð2Þ

in which the term ðqu0i u0j Þ represents the Reynolds stresses and can be related to the mean velocity gradients using the Boussinesq hypothesis as [26,27]: R ij

lt ¼ q C l

ð3Þ

As flow fields within both gas and water sides are turbulent and turbulence has a significant share in transport of momentum and

where E is the total energy and the first three terms on the right side of Eq. (7) represent the energy transfer due to conduction, diffusion of species and viscous dissipation, respectively. Additionally, Sh represents the volumetric heat source term and includes the heat of chemical reactions. Also, the effective thermal conductivity (Keff) and deviatoric stress tensor (seff) are calculated from the following relations:

C p lt ; Prt

ð8Þ

  @ui @uj 2 @uk  leff þ dij : 3 @xj @xi @xk

ð9Þ

K eff ¼ K þ K t ¼ K þ

seff ¼ leff

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The relation leff = l + lt represents the effective viscosity due to the molecular and turbulent effects [27]. It should be mentioned that due to modeling of partially-premixed combustion of natural gas and air in gas burner, all terms are present in the energy equation while it is solved for gas domain. Thus, Jj stands for the diffusion flux of species j according to the partially-premixed combustion model and Sh represents the amount of heat release from chemical reactions. Simultaneously, there is no chemical reaction and heat source in the water tank and therefore the energy equation simplifies to Eq. (10) representing the roles of convection and turbulence in transport of energy.

  @ @ @ @T ðq EÞ þ ½ui ðq E þ pÞ ¼ K eff þ ui ðseff Þ : @t @xi @xj @xj

ð10Þ

Furthermore, the equation of energy in the solid wall between the water and gas sides simplifies to the heat conduction equation (Eq. (11)) in which as represents thermal diffusivity of solid wall, i.e. as = ks/(qCp):

  @T @ @T : ¼ as @t @xj @xj

ð11Þ

The corresponding governing equations were solved numerically for the gas and water domains as well as the solid wall between these domains using the finite volume approach. These equations were subjected to the appropriate boundary conditions that are discussed in Section 3.3. 3.3. Boundary conditions Since the purpose of the numerical analysis was to provide a realistic understanding of the transport processes within various components of the water heater during its operation, boundary conditions were set according to the experimental conditions of water heater. These experiments were performed according to the American National Standards Institute (ANSI) and United States Department of Energy (US DOE) standard water heater test procedures to evaluate the performance of water heater under both steady and transient operations [28,29]. The numerical results that were obtained based on the developed models in each stage were compared to the experimental results to verify the model as well as the ensuing efficiency improvement and fuel savings. The type of boundary conditions used for the inlet and outlet boundaries of the gas and water regions were selected according to:

solved numerically using the finite volume approach. The CFD Fluent 6.3 package [27] was used with a pressure-based formulation for numerical simulation of fluid flow and heat transfer. A variety of CFD analyses were performed to investigate the flow fields in water heater subsections as well as grid independence study for each subsection using different grid resolutions. Subsequently, applying the described boundary conditions, CFD analysis of the whole water heater was carried out. In order to refine the simulation and include the buoyancy effects in the water tank, water density was defined as a polynomial function of temperature over the operating temperature range of the water heater. Considering the large number of three-dimensional grids in the water heater model along with the disparate spatial and temporal scales (especially scales of turbulent fluctuations), numerical solution of the discretized equations requires an extensive computational effort. Therefore, the numerical analyses were performed using a high-performance computing cluster. The threedimensional model contains more than 1.4 million tetrahedral grids and parallel processing was utilized for this simulation. Using six parallel CPU cores, it took about 60 h to run the water heater model in a steady-state operational mode. This numerical simulation was performed not only to provide a set of benchmark data for the selected water heater, elucidating flow patterns in gas and water as well as heat exchange, temperature and heat flux distribution details, but also to have a baseline for different quantities for comparison with experimental measurements and verification of the model. Since the outcome of this numerical simulation was used as a basis for the baffle design and thermal efficiency improvement efforts, it was essential to verify the results before taking further steps. Based on the results of the steady-state analysis, Fig. 5 depicts 3-D flow pathlines (colored by temperature) in the water tank (Fig. 5a) and in the vicinity of the swirling jet of fresh water (Fig. 5b) entering the water tank. One can observe the complicated 3-D flow patterns of water in the water tank with a steady flow of cold water entering the tank and hot water leaving it in Fig. 5a. The positions of the inlet water pipe and the outlet port are clearly observed at an instant corresponding to withdrawal of hot water from the top of the water heater and vertically-downward charging of cold water into the tank at about mid-height of the water tank. The expanding swirling jet of the cold water is directed downward until it interacts with the lower hot curved surface of the water tank (which absorbs heat from the top surface of solid wall located between gas and water)

– gas inlet: mass flow rate and temperature of air and natural gas were fixed to 0.5 kg/min of a stoichiometric mixture of air and natural gas and 21 °C, respectively, – gas outlet: outflow boundary condition was used (same mass flow rate), – water inlet: mass flow rate and temperature of inlet water were set to 3.75 kg/min and 21 °C, respectively, – water outlet: outflow boundary condition was used (same mass flow rate). The no-slip velocity boundary condition was applied on the walls and for heat transfer purposes, conjugate heat transfer walls were defined properly. Accounting for presence of insulation, a zero heat flux thermal boundary condition was applied to the outer wall of the water heater. Additionally, for time-dependent simulations, the initial conditions of water heater were set according to the corresponding experiments. 3.4. Results and discussion The governing equations for each domain (i.e. gas, solid wall, and water) were discretized using second order schemes and

Fig. 5. Three-dimensional flow pathlines colored by temperature (°C) (a) in the water tank of the water heater and (b) within the inlet swirling jet of water passing the helix-shaped part at the end of dip-tube.

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and a complicated stagnation-like flow is expected on that surface. Upon heating of water and due to confinement of the tank, the lighter hot water rises in the tank and continues extracting more heat from the flue-gas pipe. Two distinct 3-D vortex-like flow structures that occupy the two halves of the tank are clearly observed. The swirl-generating helix-shaped element at the end of dip-tube imparts circumferential momentum to the cold water before it is introduced into the water tank. This element is deemed to be beneficial to greater mixing of water in the tank. A close-up view of the pathlines of water (colored by temperature) passing over this element and its entrainment effect through deviation of pathlines around the jet can be observed in Fig. 5b. Contours of temperature (in °C) within the gas side (including combustion chamber and flue-gas pipe) on a vertical plane that contains the axis of the water heater and is normal to the plane of the flue-gas baffle are given in Fig. 6a. An outline of the fluegas baffle cross section can also be observed in Fig. 6a. The fluegas blades embedded on the flue-gas baffle slow down the hot rising buoyant flow of combustion products, thus assisting in greater heat exchange with the water tank. This effect can be seen in Fig. 6a in which the temperature of the combustion products decreases considerably during travel over the flue-gas baffle blades, especially the first five (5) blades. The distribution of the surface heat flux on the outer surface of solid wall placed between the gas and water sides is shown in Fig. 6b. The surface heat flux data that are derived from the predicted temperature distributions was critical to the process of the design and placement of the baffle on the water side of the water heater. For easier discrimination, the heat flux was defined positive for the surface of the flue-gas pipe when heat transfers outward in the radial direction and was defined negative for the bottom wall when heat transfers vertically upward from the solid wall to the water. Therefore, the distribution and magnitude of heat flux on each part of the solid wall are clearly distinguished. The highest heat flux is observed near the bottom of the flue-gas pipe where the vertical tube connects to the curved bottom dome of the water tank, on which the surface heat flux distribution exhibits a pseudo-circumferential symmetry with a phase angle of 90 degrees. Lower values of surface heat flux are observed directly below the inlet pipe (dark blue spots in Fig. 6b) due to impingement of inlet water jet. In addition to the steady-state analysis, transient analysis of the selected water heater was also performed and the time-dependent numerical data were used to verify the developed model and numerical approach as explained in Section 4.

Fig. 6. Contours of (a) temperature on a vertical plane in the gas side (°C) and (b) three-dimensional contours of heat flux on the outer surface of solid wall between gas and water (W/m2).

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4. Verification of the numerical results Upon including the temporal terms of the governing equations, the results of the transient simulation of the water heater were compared to the experimental measurements to verify the computational model and numerical approach. A time-dependent simulation was conducted based on part of a standard water heater test procedure [29] to simulate the transient operation of the water heater upon start of drawing of hot water from the water heater. For this transient simulation, water heater is initially warmed up, natural gas is burning, water in water tank is hot (about 52 °C) and there is no water flow to/from the water heater. Then, a hot water draw is initiated under a constant flow rate condition. During the hot water draw process, fresh cold water is brought into the tank with the same mass flow rate through the dip-tube near the bottom of the water heater. Although the burner is continuously on during the hot water drawing, the bulk water tank temperature declines with time because of the relatively high water flow rate. Considering the initial stratification of water inside the water tank and the positions of the inlet and outlet ports, temperature of water varies from point to point. As a result, temperature measurements are taken at six (6) different positions inside the water tank during the test. These water temperature measurement points inside the water tank [29] are identified in Fig. 7. Thus, the same locations were monitored in the numerical model for temperature comparison purposes. Defining the boundary conditions according to the experimental test conditions described in the test procedure, the transient numerical analysis of the water heater was carried out for a time period of 6 min and the numerically-predicted temperatures were compared to the experimental measurements for each of the six (6) different thermocouples. The comparison of the numerical and experimental temperature curves for the six (6) thermocouples are given in Fig. 8. The maximum observed deviation between the numerical predictions and measured temperatures was 6.67% and was associated with the second thermocouple (Fig. 8). As one can observe, thermocouples that are closer to the bottom of the tank and incoming jet of cold water (#5 and 6 in Fig. 7) register a steeper decline of the water temperature. Since there is an observable temperature difference of about 22 °C between the top and bottom of the water tank (e.g. thermocouples 1 and 6), it was crucially important to use realistic values

Fig. 7. Locations of the six (6) thermocouples measured from the bottom of water tank [29].

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Fig. 8. Comparison of the transient experimental temperature measurements against numerical predictions for six (6) thermocouples placed in the water tank.

of the water density for an exact representation of the buoyancy effects and reducing the deviation between the numerical and experimental values. As a conclusion, there is a good agreement between the numerical predictions and experimental measurements meaning that the developed model and its features are verified and the results can be reliably used as a basis for the baffle design as well as further numerical analyses.

5. Design of the baffle Upon verifying the developed model of the water heater based on the transient simulation, the results of this model were used to determine the general design of a baffle. Further parametric studies were conducted to finalize the design and positioning of baffle inside the water tank. The shape and orientation of baffle were linked to the flow pattern of the cold water emerging into the water tank. As a fundamental step in designing the shape of the baffle, one should consider the existing flow patterns within the water tank and possible ways to modify these based on the notion of manipulating the incoming cold water jet towards the hot surfaces for heat transfer promotion. Considering the flow pattern in

the water tank and in the vicinity of the cold water inlet jet, it is clear that the downward-discharging jet impinges on the bottom surface of the water tank and then deflects upward. As a result, heat transfers effectively from the hot bottom surface to the impinging jet (which is an advantage), however the extent of the transferred thermal energy is limited nearly to only half of the water tank’s bottom surface (which is a disadvantage). Therefore, one could be led to the overall shape of the baffle as a helical surface that is capable of accommodating a partial impingement with incoming jet of water (preserving the existing advantage) as well as deflecting the downward water jet towards the bottom surface of water heater and the lower portion of flue-gas pipe (which are hot surfaces with high values of surface heat flux). Using the proper pitch in a helical geometry, this concept design can also cause water to rotate around the water heater axis and travel tangent to the existing hot surfaces. Consequently, using a modified flow pattern, a greater portion of the cold incoming jet of water will be exposed to a larger amount of hot surfaces, thus leading to the desired heat transfer enhancement. Based on these arguments, the first baffle design (shown in Fig. 9) featured a helical baffle connected to the flue-gas pipe below the end of dip-tube so that it can interact well with incoming cold jet of water.

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Fig. 9. General design of the baffle shape based on the analysis of water flow pattern in the water heater. 200

Heat Flux (kW/m2)

150

Position of inlet swirling water jet 100

50

0 0

10

20

30

40

50

60

70

80

90

100

110

Height (cm)

120

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Several parametric studies were conducted to finalize the position, orientation and dimensions of the baffle. In order to find the best position of the baffle, there are two important criteria, namely the interaction of the baffle with the inlet water jet to maximize heat convection and access to high heat flux surfaces to maximize heat conduction. Therefore, the surface heat flux distribution along the flue-gas pipe was acquired from the CFD results of the base water heater and is given in Fig. 10. Additionally, the inlet water jet and its spreading as well as decay of the water jet were studied to determine the best position for the baffle so that the water jet spreads adequately and also has enough momentum to be deflected around the flue-gas pipe as it is necessary for maximizing the convective heat transfer. The results of inlet water jet study are displayed in Fig. 11 where the contours of the velocity magnitude are shown on different horizontal planes normal to jet axis. Spreading of the jet and decay of its core are clearly observed considering that the concentrated contours near the exit of the jet (Fig. 11a) are modified at lower planes away from the dip tube. Consequently, the best location was selected for the baffle where both of the above-mentioned criteria were satisfied which means that both mechanisms of heat transfer (i.e. conduction through baffle as well as convection to the cold water flow moving tangent to hot surfaces) are maximized. A set of theoretical flow estimations and numerical analyses were performed to finalize the amount of the pitch for the baffle as well as the orientation of the baffle. Eventually, the orientation, alignment and pitch angle values were set and the first design of the baffle was completed (as it is shown in Fig. 12). The outer diameter of the first baffle design

Fig. 10. Surface heat flux distribution along the flue-gas pipe.

Fig. 11. Contours of the velocity magnitude (m s1) near the inlet water jet displayed on horizontal planes located at (a) 1.25 cm, (b) 6.35 cm, (c) 16.5 cm, and (d) 26.7 cm from the end of the dip-tube.

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Dip-tube (water inlet jet)

25

Fig. 12. Baffle’s first design and its position/orientation in the water heater.

was selected primarily based on the required modifications of the water flow pattern. However, there are other criteria for optimizing the outer diameter such as conductive heat transfer in the baffle. Thus, in order to optimize the outer diameter of the baffle, further parametric study was carried out to investigate heat conduction in baffle. The temperature contours under the same thermal boundary conditions are shown for the baffle with different outer diameters in Fig. 13. One can observe that the selected outer diameter is greater than the required diameter. However, sharp reduction in outer diameter can alter the main role of baffle in flow pattern modification and heat convection enhancement. Therefore, a new combination of the outer diameter and baffle thickness was selected so that the flow pattern modification (e.g. convective heat transfer) remains unchanged and heat conduction through the baffle increases. Using these modifications, not only the heat transfer was maximized compared to the first design, but also less amount of material will be used for fabrication of the baffle. The second design of the baffle is shown in Fig. 14. The 3-D models of the baffle’s first and second designs were added to the developed 3-D model of the water heater for further CFD analysis of the modified water heater and extraction of expected thermal efficiency improvements.

(a)) Ouuter diametter = 35.5 ccm

(b) Outter ddiam meteer = 33 ccm

(c)) Ouuter diametter = 300.5 ccm

(d) Outter ddiam meteer = 25.44 cm m

(e)) Ouuter diametter = 200.3 ccm

(f) O Outer ddiam meterr = 115.224 cm m

Fig. 13. Contours of temperature (°C) for the baffle conduction analysis and optimization of baffle’s outer diameter.

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6.2. Results and discussion

Fig. 14. Isometric and top-views of the baffle’s second design (optimized outer diameter and thickness).

6. Analysis of the modified water heater with baffle Pursuant to designing the baffles based on the flow characteristics and structural features of the water heater, numerical analysis of the modified water heaters with helical baffle designs was carried out in the next step of this research.

6.1. Computational details Designed baffles were added to the 3-D model of the water heater according to their orientation specifications in order to investigate the effects of the baffles on flow field in the water tank and the expected improvements of the thermal efficiencies of the modified water heaters. Unstructured tetrahedral grid systems were generated for the 3-D model of the modified water heaters. In order to predict the flow pattern and heat transfer characteristics more accurately, the grid is dense around the baffle compared to other parts of the water tank. Similar grid features were used for other parts of the water heater according to previous grid independence studies and numerical analyses. The total number of grids for the modified water heater was about 1.5 million tetrahedral grids. There were no changes in the governing equations and the boundary conditions. As before, the boundary conditions were selected similar to the experimental conditions in order to accommodate comparison of the results and verification of numerical predictions.

Similar to Section 3, numerical analyses were performed for the modified water heaters with the first and second baffles using the same approach and under the same boundary conditions (extracted from the standard water heater test procedure conditions) so that one can compare the results with previous CFD analysis of the selected water heater (with no baffle) and experimental results. The flow and temperature fields as well as derived heat transfer characteristics were calculated. Flow pathlines in the water tank in presence of the baffle’s first design are shown in Fig. 15. As one can observe, due to the presence of the baffle the flow pattern is different in the water tank when compared to the pathlines of Fig. 5a. The main portion of the inlet water jet is redirected towards the bottom surface of water heater through the baffle pitch window. This part of the cold incoming water flow then experiences rotation around the flue-gas pipe and tangent to the bottom surface of water heater (top dome-shaped surface of the combustion chamber) which are hot surfaces. As a result, heat transfer to the fresh cold water will be enhanced since it is being exposed to these hot surfaces. Moreover, a small portion of the inlet water jet after impinging on the surface of the baffle, deflects upward with a damped speed. Since the baffle is located at a high surface heat flux area of the flue-gas pipe, it can easily conduct heat during the impingement of water jet and promote heat transfer. Finally, this slowly-upward-rising portion of the water mixes

Fig. 16. Contours of temperature (°C) in the water tank of the modified water heater with baffle’s first design.

Fig. 15. Flow pathlines colored by the velocity magnitude in the water tank of the modified water heater with baffle’s first design. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 17. Prototypes of the baffle’s first design (left) and second design (right).

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Table 1 Experimental results of the thermal efficiency tests. Description

Selected base water heater unit

Water heater with baffle’s first design

Water heater with baffle’s second design

Capacity (Gallons) Heating rate (Btu/h) Thermal efficiency (experimental) Thermal efficiency improvement (experimental) Thermal efficiency improvement (numerical) Deviation (%) Savings in natural gas consumption based on experimental results (%)

38.37 39,975 73.40% N/A N/A N/A N/A

38.43 39,843 74.65% 1.25% 4.2% 2.95 1.674

38.42 39,763 76.71% and 77.74% 3.31% and 4.34% (average = 3.83%) 6.4% 2.57 4.31 and 5.6 (average = 4.95)

with hot water in tank and starts rotating around the flue-gas pipe above the baffle until attaining a uniform temperature. Furthermore, contours of the water temperature (°C) are given for the modified water heater with the first baffle design in Fig. 16. Finally, the heat flux distributions on heat transfer surfaces and the total heat transfer from the gas to the water side were evaluated. Since the amount of natural gas and air is constant for the performed analyses, thermal efficiency can be calculated and compared to the case of the original water heater in order to determine the improvement. As a result, based on the numerical predictions, thermal efficiency improvements of 4.2% and 6.4% were obtained using the baffle’s first and second designs, respectively. It should be noticed that the second baffle design which has smaller outer diameter and uses less amount of material brings about more improvement to thermal efficiency. Upon computing the above-mentioned thermal efficiency improvements, the water pressure drop in the modified water heaters were checked as it might have possibly increased dramatically in heat exchangers due to skin friction increase. In fact, the possible effect of baffle on skin friction factor and water pressure drop was checked. It was found that the pressure drops were just 2.3% and 2.0% higher in the water heaters equipped with the first and second baffle designs, respectively. Thus, the heat transfer enhancement brought about by introducing the baffle is not realized at an expense of excessive pressure drop increase. This critical achievement is quite a desirable outcome in design of more efficient heat exchangers. Finally, in order to verify these findings, designed baffles were prototyped and assembled in water heaters identical to the selected water heater for experimental purposes. Photographs of the fabricated baffle’s first and second designs are shown in Fig. 17. Experiments were performed on these water heaters and experimental results were compared to numerical predictions. 7. Experimental results and verification of the baffle designs Three water heater units were constructed using identical parts and assemblies for experimental evaluations and measurements. Fabricated prototypes of baffle’s first and second designs were positioned inside the water tanks of two water heater units according to specified design orientations. Therefore, the only difference between these three water heater units is the presence of baffle designs in two of them, whereas the third unit is considered as the base water heater. Performance and thermal efficiency tests were conducted on these three units according to standard test procedures [28,29]. Before testing these units, the water tank capacity, heating rate, combustion efficiency and emission levels of each unit was checked to ensure that units have the same capacity and performance. For measuring the thermal efficiency, a steadystate measurement was performed during which there was a constant water flow rate and constant rate of natural gas combustion in the water heater. During these standard industry tests, water inlet temperature should be maintained in the range of 21 ± 1 °C

(70 ± 2°F) and gas flow rate should be adjusted at the normal inlet gas pressure for the water heater. Water flow rate, inlet and outlet water temperatures were measured over a period of at least 30 min as well as the total amount of consumed natural gas and its higher heating value (HHV). Upon evaluating the average water inlet and outlet temperatures, the water heater’s steady-state thermal efficiency can be calculated from the following equation:

Energy stored in water Total energy consumed mw C p ðT h  T c Þ ¼ : mg HHV

Thermal efficiency ¼ g ¼

ð12Þ

As outlined earlier, identical steady-state thermal efficiency tests were performed for the three water heater units. The results of these tests and the corresponding thermal efficiency improvements are presented in Table 1. The percentage of savings in natural gas consumption was calculated from Eq. (13). More details about the experiments and obtained results can be found in [30,31].

Sav ings in natural gas consumption ¼



1



gst  100: gmod

ð13Þ

It should be noticed that for this set of tests, the water heater unit equipped with the baffle’s second design was tested twice and the average of the two tests was used in the evaluations. As a result, the experimental values are reliable, and there is a good agreement between the experimental and numerical findings. Furthermore, both experimental and numerical trends are in agreement suggesting that the patented [31] baffle’s second design, for which less amount of material was used, contributes to a greater rise to the thermal efficiency. This fact clearly elucidates the difference between the extended surfaces and baffles explicating the notion of heat transfer enhancement/control using baffles. Finally, the amount of fuel savings was evaluated to be 4.95% for the baffle’s second design. This amount is quite close to the target of this research, i.e. 5% fuel savings. As a conclusion, the baffle’s second design was substantiated as the final design capable of fulfilling the target. The DOE Energy Factor (EF), Heat Recovery and Standby Heat Loss tests were performed for the 3 identical water heaters differing only in the baffle design. In view of the scope of the project and the length requirements of journals, such data were not presented here. These data are available to the interested parties upon request. 8. Conclusions Adopting a numerical approach followed by experimental verifications, two baffles were designed for thermal efficiency improvement and greater fuel savings in a selected model of a natural gas-fired water heater. Based on the geometric features of the selected water heater, 3-D models of the water heater subsections were developed including combustion of natural gas, up-rising

M. Moeini Sedeh, J.M. Khodadadi / Applied Energy 102 (2013) 520–533

flow of combustion products through the flue-gas pipe, water tank and the solid wall between the gas side and water tank. Subsequently, details of the fluid flow and heat transfer fields were studied numerically in each subsection. Integrating 3-D models of the subsections, the complete model of the water heater was developed. Thermal performance of the selected water heater was investigated numerically using computational fluid dynamics analysis. Prior to the baffle design process and in order to verify the developed model of the water heater, time-dependent numerically-predicted temperatures were compared to the experimentally-measured temperatures obtained under the same conditions at six different locations inside the water tank. Accounting for the variation of density of water as a function of temperature to consider natural convection effects in the water tank, the maximum deviation at six locations in the water tank was 6.67% that is indicative of a very good agreement between numerical predictions and experimental results. Upon verifying the numerical model, the fluid flow and heat transfer patterns were characterized for the selected water heater. The overall design of the baffles and its location were finalized based on the results of the numerical model and a set of parametric studies. Finally, two designs were proposed for the baffle with the second design being an optimized version of the first design. The verified three-dimensional model of the water heater was modified to include the adopted baffle designs and thermal performance analyses were simulated. Based on the numerical model, thermal efficiency enhancements were 4.2% and 6.4% for the first and second designs, respectively. The designed baffles were prototyped and assembled in identical water heater units and thermal efficiency and performance experiments were conducted according to the industry’s standard water heater test procedures. Finally, experimental results of thermal efficiency tests revealed 1.25 and 3.83 percent improvements using the first and second baffles, respectively. Consequently, the baffle’s second design accommodates lowering of the natural gas consumption of the water heater by 4.95% under steady-state operation that meets the target of this research, suggesting that the designed baffles have strong merits in terms of improving thermal efficiency and saving fuel in gas-fired water heaters. One should note that the real usage of water heaters includes different operational modes such as firing with no water flow (known as heat recovery and standby heat loss modes) and firing with constant water flow (steady-state mode) or even variable water flow rates. Therefore, the amount of gas savings in real usage of water heaters might be less than 4.95% achieved under steadystate operation of the water heaters of this study. Acknowledgments The authors acknowledge the California Energy Commission for funding this research through the Energy Innovation Small Grant – Natural Gas Program (Grant # 55688A/07-02G) and an industrial collaborator of this research for providing support in prototyping and testing water heaters. The first author also acknowledges the Samuel Ginn College of Engineering and the Department of Mechanical Engineering at Auburn University for partial financial support of his Dean and College Fellowships since Fall 2009. Moreover, the Samuel Ginn College of Engineering provided supercomputing facilities for numerical simulations and the Department of Mechanical Engineering contributed travel funds associated with conducting the experimental work outlined in this project. References [1] Hashimoto S, Natami K, Inoue Y. Mechanism of mixing enhancement with baffles in impeller-agitated vessel. Part I: a case study based on cross-sections of streak sheet. J Chem Eng Sci 2011;66:4690–701.

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