uab - ectc 2014 proceedings - section 8 page

SECTION 8

HEAT TRANSFER

UAB School of Engineering - ECTC 2014 Proceedings - Vol. 13 205

Proceedings of the Fourteenth Annual Early Career Technical Conference The University of Alabama, Birmingham ECTC 2014 November 1 – 2, 2014 - Birmingham, Alabama USA

USE OF CFD FOR VENTILATION AND THERMAL COMFORT OF A MULTI-LEVEL ATRIUM BUILDING (BARBER VINTAGE MOTOR SPORT MUSEUM)

Mr. Aniket Bhave, Dr. Hessam Taherian The University of Alabama, Birmingham

Birmingham, Alabama, USA

Mr. Milad Majdi The University of Alabama, Birmingham


Mr. Steven Wyss The University of Alabama, Birmingham


ABSTRACT The paper illustrates the use of CFD modeling for

ventilation and thermal comfort on a multi-level building. The building analyzed is the Barber Vintage Motor Sports Museum located in Birmingham, AL. The need for this analysis came from concerns raised by the management of the museum. Some of the primary concerns presented were issues with air distribution throughout the museum, non-uniform temperature values in the different floors and larger than desired energy bills. As-built blueprints were used to create the 3D model, which was then used combined with collected data to conduct the analysis. The analysis was able to shed light on the problem areas identified by the museum, along with giving valuable data and insight into the interactions of the building. This information will be used to develop an accurate model for future research.

INRTODUCTION Thermal comfort and ventilation was analyzed in Barber

Motor Sports Museum located in Birmingham AL, a multi-level building with a complex interior structure. The management of the museum raised several concerns about the distribution of the ventilation air and temperature throughout the space; in addition they had concerns about the high cost created by running the systems when few patrons are in the museum. The concerns lead to the need for this analysis.

The analysis was conducted on the heating and cooling system for the museum. Two cases were analyzed a heating case and a cooling case, both of which used design flow rates. The simulation was focused on the exhibit hall and basement region. The exhibit hall was the primary focus of the model as patron comfort is of the upmost importance for a museum. The basement was a secondary area to be analyzed primarily because of the large open area stretching through the entire museum, and the fact that employees spend a lot of time in this region. Heat generating systems were included in the simulation including, light, people and ambient temperature.

The two cases used for the paper are a heating case and a cooling case. The two cases will shed light on how the temperature and air distribute through the building. The heating case was conducted using winter conditions along with minimum occupancy. The cooling case was conducted in summer conditions with maximum expected occupancy. The two conditions give a good idea of the two extremes which will help in developing a baseline that can be applied to other conditions in the future. These cases will also shed light on the effectiveness of the modeling method used and help to improve the model for future research.

Fig 1: Layout of Barber Vintage Motor Sport Museum

Fig 2: View of Atrium inside in the Museum


BACKGROUND One of the important efforts in building flow prediction

was air flow patterns within buildings [1].The objective of the paper was to evaluate the performance of both CFD and multi-zone airflow simulation and measurement in air supply device and room flow field. Conclusions include: simulations are useful to study sensitivity of flow patterns to small changes, and simulations are useful to predict airflow patterns for critical projects, i.e. when no measured data exist.

In another major effort, [2], Researchers applied a CFD program with radiative exchange to predict thermal comfort in both mechanically and naturally ventilated offices. Thermal comfort is evaluated in terms of predicted mean vote (PMV), and mean radiative temperature. Predictions for an office module demonstrated the importance of taking into account radiative heat exchange for the prediction of thermal comfort when the surface temperature difference is large.

Development of a CFD simulation code with an emphasis on the simulation of radiation heat transfer and its coupling with CFD has been described [3]. One application of the model was to examine the effects of radiation on the airflow in a room with displacement ventilation. It was found that radiation plays a considerable role in thermal stratification with displacement ventilation.

One of the applications of CFD is to study the performance of diffusers and different inlet and outlet arrangement [4]. A research was conducted to analyze airflow and contaminant diffusion in several types of clean rooms with different supply and exhaust diffuser arrangements. The cases modeled included three basic room geometers with variations in the number of supply outlets and exhaust inlets and in the height of the exhaust inlets. The performance of the ventilation systems is expressed by four measures based on the contaminant concentration distribution. The important result is that the arrangement of exhaust inlets has a small influence on flow fields but a large influence on contaminant diffusion fields.

Another room airflow application simulated is airflow within a large building [5]. In one detailed report, many of unique characteristics of large enclosures (capacity of space, height of ceiling, and potentially small occupied zone), ventilation design principles, and prediction methods including simple equations, scale model experiments, and CFD modeling was described. Important CFD modeling issues discussed include choice of turbulence models, grid discretization, and boundary conditions. Three cases were studied including an airport terminal lobby, an atrium between two offices buildings, and a separate atrium.

Atria have been the most commonly studied large enclosure [6], the results showed the temperature and flow field in a partially air-conditioned atrium using a CFD program including consideration of both solar and infrared radiation. Seven cases were analyzed including four cooling conditions and three heating conditions, using a variety of ambient temperatures. The results show that when the outdoor

temperature is below 27°C (80°F), rooftop ventilation is effective in exhausting the hot air accumulated below the ceiling and in reducing the cooling load of the upper bridges. In both heating and cooling cases, large-scale recirculation in the void space is promoted by an imbalance of heat transfer to the atrium. Also, in the winter, the large-scale recirculation results in a strong downwash at the bottom of the cooled side of the void space.

In CFD analysis of flow and temperature fields in atrium [7], researchers compared two techniques of modelling diffuser flow including modelling the diffuser directly and modelling the resulting flow pattern in a volume in front of the diffuser (PV method). They concluded that PV method had the best performance but it depends on diffuser specific data. In simulation of a complex air diffuser with CFD technique [8], the air flow from a curved surface diffuser was simulated using three different grid systems including cylindrical coordinates with small steps, body-fitted coordinates, and unstructured grids. They found that the body-fitted and unstructured grids produced flow patterns that agreed well with flow visualization techniques but required high labor cost for setting up the simulation. The cylindrical coordinate could not predict the airflow pattern correctly because excessively high turbulence is calculated in the boundary layer with small steps.

In case studies of displacement ventilation [9] thermal condition resulting in a large auditorium with displacement ventilation system through both CFD and measurement was studied. He observed complex airflow patterns with no stratification of the air. CFD modelling showed that temperature gradients in a large space depended on where measurements were taken.

CFD analysis of an atrium [10] provided guidance for modeling atria in CFD. The important methods of solar radiation distribution were discussed. CFD boundary conditions also reviewed including a new study to establish the most accurate way of defining natural convection boundary conditions. Five common methods of presenting boundary conditions were investigated with two different grids. He concluded that it is vital that CFD simulations of atria allow for surface–to-surface radiation exchange and that supply and exhaust openings are modeled accurately.

PROBLEM DEFINATION Two cases are studied with the purpose of ventilation and

thermal comfort of the museum: • Cooling Case (Hot Outside (95°F) & 500 people

inside) • Heating Case (Cold Outside (40°F) & 20 people

inside) The geometry and mesh remain the same for these cases

but there is change in the boundary conditions and case setup as stated in the following sections.


METHODOLOGY Geometry:

A 1:1 scale 3D model of the Barber Motor Sport Museum located in Birmingham, AL was created base on the architectural drawing. In the 3D model, the behavior of air inside duct system was not of interest, so the model left out the duct system to reduce complexity of the model. Only the diffusers were modeled with exact dimension and location, in a way it could apply the same air flow for any diffuser. Also all the air returns of the building were maintained with the exact location and dimension.

The primary focus of this simulation is on the main open exhibit area where visitors will spend the most time. Offices, closets, and maintenance areas in the basement were assumed to be closed spaces with no air flow and left out of the model. The staircase, the elevator and furniture also were left out of the model to reduce complexity as they would have little effect on the air flow and temperature distribution. The final geometry is as shown in Fig 3.

Fig 3: Layout of the Barber Motorsports Museum for CFD

simulation showing diffuser locations

Mesh: A tri-surface mesh of 0.025 m to 0.10 m has been created

along all walls. A volume mesh with the first grid size of 0.04m with a growth rate of 1.2 has been generated along all walls to allow for accurate resolution of surface temperatures, radiation flux and convective wall heat flux. The surface mesh is as shown in Fig. 4.

Fig 4: Surface Mesh of the Museum

The mesh near the diffuser openings and air returns has been created with a finer size of 0.005 as shown in Fig. 5 in order to capture the flow physics during entry and exit more accurately. The total cell count of the model is around 4.6 million.

Fig 5: Fine mesh near the diffusers

Physics Setup: Models Selected:

• 3 Dimensional • Steady State • Standard k-Epsilon (Enhanced wall treatment) • Gas (Air)

o Density = Ideal gas calculation o Dynamic viscosity = 1.85508-5 Pa·s

• Coupled Flow & Energy


Table 1: Boundary Conditions for CFD Analysis Location Boundary

Conditions Value

Basement Diffuser 1 Velocity Inlet 0.4052 m/s

Basement Diffuser 2 Velocity Inlet 0.5113 m/s

First Floor Diffuser 1 Velocity Inlet 0.7194 m/s




Second Floor Diffuser 1 Velocity Inlet 0.7194 m/s




Third Floor Diffuser 3 Velocity Inlet 0.4803 m/s

Third Floor Diffuser 4 Velocity Inlet 0.5406 m/s

All Air Returns Pressure Outlet 0 Pa. (Gauge) All Ceilings

(Light Bulb Load) Heat Flux Wall Heat Flux = 1.956 W/m2

All Windows (Cooling Case)

Environmental Wall

(Conv. + Rad.)

Heat Flux = 24.27 W/m2 amb. temp.=95°F(308K)

HTC = 7.7W/m2-K

All Windows (Heating Case)

Environmental Wall

(Convection)

amb. temp.= 40°F(277K) HTC = 7.7W/m2-K

Basement Floor, Walls (Cooling Case) No Slip Wall Heat Flux = 0.106 W/m2

Basement Floor, Walls (Heating Case) No Slip Wall Heat Flux = -0.063 W/m2

All Other Vertical Walls (Cooling Case) No Slip Wall Heat Flux = 3.14 W/m2

All Other Vertical Walls (Heating Case) No Slip Wall Heat Flux = -5.58 W/m2

The diffuser velocities have been calculated as per the flow

rate specified in the drawings provided by the Barber Museum. During the cooling case the air exiting the diffusers is at 58°F (288K) and 82F (301K) during heating case as per the restrictions at the Museum site. Radiation flux has been calculated for windows according to ASHRAE manual and applied in cooling case, but in heating case we have considered worst case scenario of no radiation flux from outside. Total heat load due to light bulbs have been calculated and is applied as a surface flux on the ceiling for each floor. Cell zone Conditions:

Heat load due to people is a major source of load in the museum. According to ASHRAE standards the heat load is given as 100 W/m2 for normal office working activities. Total heat load due to people is calculated as stated below and a volumetric heat source is applied to the model. Surface area of a typical person can be given by Eqn (1) according to heating and cooling of buildings [11]

AS = 0.202m0.425 h0.725 …. Eqn.(1)

where m= mass in kg and h= height of the person in m For an average person of m = 75 kg and h = 1.7m the Area

=1.859m2. Table 2: Volumetric heat load per person

Load per person 100 W/m2

Average Area 1.86 m2

Heat Load per person 186 W Total Volume 69912.19 m3 Volumetric Heat load per person 0.00266 W/m3

Thus for cooling case with 500 people, the heat load of

1.33 W/m3 is applied and in heating case with 20 people a heat source of 0.053 W/m3 is applied.

Assumptions for Ventilation Simulation 1. All maintenance rooms and offices have been subtracted

from the model. 2. Only the exit points of the diffusers of the ducts have been

modeled. 3. Duct design is considered to be correct and the flow

distribution is according to the areas of the openings.

RESULTS AND DISCUSSION Residuals:

Fig. 6: Residuals / Convergence Criteria

The simulation was run for 3000 iterations and the results

are presented below. It took around 10 hours of computer time for the simulation to complete. The residuals for convergence are as shown in Fig 6. The residuals of continuity, momentum, turbulent kinetic energy, dissipation rate have flattened below 10-4, energy residual is below 10-6 and both are stable which shows that the case has converged. Post Processing:

Velocity and temperature contours are taken at the diffuser height and 1.5m height (around chest height of an average person) from bottom of each floor. The post processing planes can be seen as shown in Figs. 7 and 8.


Fig 7: Cut planes at Diffuser Height

Fig 8: Cut planes at 1.5m Height from each floor

Two vertical cut planes were created in the museum which gives an idea of the overall air movement in the museum. The cut planes can be seen in Figs. 9 and 10.

Fig 9: Vertical cut plane – 1 in the Museum

Fig 10: Vertical cut plane – 2 in the Museum

Velocity Contours for Cooling and Heating Case:

(m/s)

Basement

First Floor

Second Floor

Third Floor

Fig 11: Velocity Contours at the Diffuser Height As the Velocity magnitudes are the same in cooling as well

as heating case, only one set of results is presented. As shown in Fig 11, the diffusers are able to spread the air efficiently through the domain. There can be some additional diffusers near the top and bottom right end of the second and third floor.


(m/s)

Basement

First Floor

Second Floor

Third Floor

Fig 12: Velocity Contours at 1.5m Height from floor The velocities at 1.5m as shown in in Fig. 12 are slightly

lesser than the desirable range of 0.15m/s to 0.25m/s according to ASHRAE standards. This is due to the fact that the diffusers are located at a much higher height than average height of people and are supplying air horizontally rather than vertically. If some diffusers supply air from the duct vertically downward

or at an angle, then the velocity pattern at 1.5m height would improve.

(m/s)

Fig. 13: Velocity Distribution in the Museum

(Cut Plane 1)

Fig. 14: Velocity Distribution in the Museum

(Cut Plane 2)

The flow is uniformly distributed in each of the floors. The flow in the atrium is mostly rising towards the air returns located on the third and fourth floor as seen in Fig. 13. Higher velocity patches can be seen near the air returns in Fig 14. Cooling Case Results:

(°F)

Fig. 15: Temperature Distribution in the Museum

(Cut Plane 1)


(Cut Plane 2)

The temperature in the basement is much cooler than at the top floors as seen in Fig. 15. Slightly higher temperature can be seen near the windows and ceiling due to the high solar radiation load and lights as shown in Fig. 16. The area near the lobby is slightly cooler than rest of the building. A scenario of open doors and letting ambient air enter the building should also be studied to give an idea of real world scenario observed during full occupancy.


(F)

Basement

First Floor

Second Floor

Third Floor

Fig. 17: Temperature distribution at 1.5m from floor for Cooling Case

The temperature near the windows is much higher due to high solar radiation as shown in Fig. 17. The temperature in the corridors of basement is inaccurate and can be ignored, since the rooms and offices supplying air to the corridor are ignored. A few more diffusers can be placed in second and third floors. Heating Case Results:

(F)

Basement

First Floor

Second Floor

Third Floor

Fig. 18: Temperature distribution at 1.5m from floor for Heating Case

At 1.5m the temperature is more or else uniform in each floor as shown in Fig. 18. This gives an indication that the system is performing efficiently during winter conditions and off-season occupancy. The average temp in each floor is slightly higher than the desired range.


(F)


(Cut Plane 1)


(Cut Plane 2)

Even in cut section of the building, the temperature is more uniformly distributed in each of the floors as shown in Figs. 19 and 20. If the number of visitors increases, reducing the flow rates from the air handling unit (AHU) will improve the temperature distribution even further.

CONCLUSIONS This model helped us to find many of the areas that need to

be revised while also giving insight into how the air flow and temperature interact. This step was essential in moving forward with the project to create a baseline that accurately models the current data collected in the museum. This baseline information will be used in future versions of this project to begin finding out how to improve the efficiency of the building and reduce power bills for the client while not sacrificing the comfort of employees and visitors.

The model was successful in showing the interaction around the building and how the temperature is affected. The temperature around people chest height of about 1.5m was in a range which in both cases is relatively comfortable. Modifications to the model will help to take these values closer to an ideal temperature range of 72°F – 80°F.

One of the modifications that can be suggested is rather than having all the diffuser supplying air horizontally, some of the diffuser can be made vertical or pointed at angle in order to improve the velocity and temperature at 1.5m height.

ACKNOWLEDGMENT The authors wish to thank Mr. Jeff Thomas of Barber

Vintage Motorsports Museum for presenting the problem and providing valuable input data for modeling.

FUTURE WORK Transient simulation can be performed to solve the

problem, which will represent the problem more accurately.

Offices, rooms and service areas need to be considered so the flow distribution inside the entire museum will be studied.

A case with opening and closing of the loading doors and letting ambient air inside the building can also be studied during full occupancy condition.

REFERENCES [1] Moser A. (1991) The message of Annex 20: Air flow

patterns within buildings. 12th AIVC Conference, Ottawa, Canada.

[2] Awbi H.B. and Gan G. (1991) Computational fluid dynamics in ventilation. Proceedings of CFD Seminar for Environmental and Building Services Engineer, 67-79. Institute of Mechanical Engineers, London.

[3] Li Y. (1992) Simulation of flow and heat transfer in ventilated rooms. Royal Institute of Technology, Stockholm, Sweden.

[4] Murakami S. and Kato S. (1989) Numerical and experimental study on room airflow-3D predictions using the k-ε turbulence model. Building and Environment, 24 (1), 85-97.

[5] Murakami S. (1992) Prediction, analysis and design for indoor climate in large enclosures. Roomvent’92.

[6] Kato S., Murakami S., Shoya S., Hanyu F. and Zeng J. (1995) CFD analysis of flow and temperature fields in atrium with ceiling height of 130 m. ASHRAE Transactions, 101 (2).

[7] Skovgaard M. and Nielsen P.V. (1991) Modelling complex inlet geometries in CFD – applied to airflow in ventilated rooms. Air movement and ventilation control (AIVC) within buildings conference, Ottawa (Canada).

[8] Chen Q. and Jiang Z. (1996) Simulation of a complex air diffuser with CFD technique. Roomvent’96, 1.

[9] Mathisen HM. (1989) Case studies of displacement ventilation in public halls. ASHRAE Transactions Vol. 95.

[10] Schild P.G. (1996) CFD analysis of an atrium, using a conjugate heat transfer model incorporating long-wave and solar radiation. Roomvent’96, 2.

[11] Kreider J, Rabl A, (2010), Heating and Cooling of Buildings, McGraw Hill 2nd Ed., Chap 16



WATER HEATING OPTIONS AT McWANE SCIENCE CENTER - BIRMINGHAM, AL

Justin Hill, Mary Clark Noble

University of Alabama at Birmingham Birmingham, AL, United States

Hessam Taherian, PhD University of Alabama at Birmingham

Birmingham, AL, United States

ABSTRACT The University of Alabama at Birmingham was

approached by a local children’s science center – McWane Science Center – to perform an engineering analysis of their current domestic water heating system which was at the end of its useful life. The engineering analysis performed provided recommendations for increasing the efficiency and effectiveness of the system with a simplified total cost vs. benefit analysis for each system type analyzed.

Analysis for the building’s domestic hot water (DHW) system included development of a baseline of the current usage. This was developed through multiple site visits, an inventory fixtures and usage as well as utilizing ASHRAE standards. Once the baseline was calculated, several high efficiency water heating options were analyzed. These systems included condensing natural gas water heating, tankless gas water heating, heat pump water heating, solar water heating and a system with a combination of select systems of these heating sources.

The analysis showed the heat pump water heater provided the most annual cost savings but begins with a high initial cost, solar water heating was able to save over $2,000 a year in annual operating costs but due to roof space could only provide about 10% of the building’s demand thus, the solar water heating could only be recommended to preheat the incoming water for a supplemental heating source. Finally, natural gas tankless water heating was analyzed and shown to reduce the annual operating costs by just under $8,000. This information was utilized by the McWane Center’s internal engineering staff to decide what energy efficient technology would replace their current, inefficient product.

KEYWORDS Solar water heater, condensing natural gas water heater,

heat pump, heating capacity, thermal efficiency, refrigeration cycle

WATER HEATING BASELINE CALCULATION The current domestic hot water heater system is

approaching the end of its life cycle. Since there are several options for replacing the unit, alternative systems were evaluated that provide the building with improved energy efficiency and reduced operating costs. It is desired that the new system not only meet the desired demands but also be

economical and environmentally appropriate. The requirements for the system are summarized in Table 1.

Table 1. Input values for calculations Max.

Monthly Attendance

Days of Operation

Set point

Temp. Types of Fixtures

49,000 31 125ºF Sinks 66 2.2 gpm Shower 1 10 gpm

To perform the calculations, the team was required to

perform an analysis and estimate the current DHW consumption throughout the year as well as the amount of energy and cost of the fuel the system was using. To do so, multiple walkthroughs and meetings were had to gain more knowledge of the system characteristics. This led to the realization that the energy and water usage was not directly measured and would need to be estimated using ASHRAE guidelines [1]. This analysis required some assumptions to be made about the facility type, the first step in utilizing the ASHRAE guidelines. Since there are no published guidelines for museum type or children’s science center type buildings, the center was modeled as an elementary school as their usage pattern and majority of their visitors mimicked that of an elementary school closely. This assumption leads to assuming the daily average usage is 0.6 gallons per student per day. The center operates 360 days a year for an average of 8 hours a day but their busiest month is July – about 49,000 visitors in that month. Therefore July was chosen as the occupancy pattern for the design of each of the systems.

Additional information on the system was received from personnel about the number of fixtures in the building that use DHW and their estimated usage and flow rate. These include approximately sixty (60) restroom sinks, five (5) café sinks, one (1) eye wash station and one (1) shower. Also the system’s storage tank was found to be 600 gallons and existing heaters were found to have a nameplate capacity of 399,999 Btu/hr. Finally the system water temperature setpoint was provided to be 125°F and a minimum incoming city water temperature of 40°F was used. This water temperature was assumed in order to account for any possible extreme cases. This will result in a slightly oversized design. Availability of hot water under extreme weather conditions was the main goal. Also, based on the age and type of water heating system installed, an overall


efficiency of 65% was used to represent realistic baseline energy consumption.

The previously described parameters were utilized to calculate the water heating capacity required to meet the demand of the building’s DHW system must be at least 342,583 Btu/hr. This analysis also shows that the annual energy cost for the existing system is $22,715, assuming a natural gas cost of $13/MMBtu and $0.12/kWh.

CONDENSING NATURAL GAS WATER HEATING After the baseline analysis was performed, the first high

efficiency option that was investigated was the condensing natural gas water heater. This system operates similar to a standard natural gas water heater but is able to recover additional heat energy from the exhaust gas which is simply rejected to the atmosphere in a typical natural gas water heating setup. This additional heat recovery allows for the system to reach thermal efficiencies of over 90% compared to around 80% or less for traditional systems.

The analysis for the condensing natural gas water heating option was very similar to the baseline calculation, with all the same operating parameters. The only difference in the analysis was the overall efficiency of the heating source which was claimed by manufacturers to be 96% [2], [3]. With this information inputted into the model, an annual savings of $9,700 was seen. When compared to an installed cost of about $10,000 ($11,453 for one manufacturer and $9,000 for another) equipment cost (labor costs were assumed to be minimal since existing staff is utilized for installation), the system can pay for itself in around one year.

HEAT PUMP WATER HEATING The next system analyzed for the client was a heat pump

water heater (HPWH) which utilizes the reverse of the vapor-compression refrigeration cycle to pull heat from the ambient air and insert it into the incoming water while rejecting cold air back to the space – this can be an additional benefit to the customer because it can offset HVAC consumption or provide space cooling to previously unconditioned spaces. The HPWH is the most energy efficient method available for heating water due to this thermodynamic cycle, with “efficiencies” reaching well over 200% (for every one Watt of electric energy input to the compressor, two Watts of energy are delivered to the water; the system has a coefficient of performance (COP) of 2) [4]. This “efficiency” of over 100% occurs because the vapor-compression cycle which allows for “moving” heat energy from the atmosphere around the HPWH and placing it into the water. This is compared to other technologies which cannot physically reach efficiencies of over 100%. Other electric and natural gas options create heat by converting their fuel source directly into it through either combustion or electric resistance which limits them to an efficiency of less than 100% [5].

While these systems provide the highest efficiency option available, it generally takes a longer amount of time to increase

the incoming water temperature to the desired set point. To compensate for this extended amount of time, a secondary heating system is generally needed as backup to meet the DHW demand during times of high usage when the HPWH is not able to maintain the system temperature. This can also be compensated for by installing a larger storage tank to allow the HPWH longer run times and for the storage tank to act as a buffer between the HPWH and the end user. However for this application the storage tank was already in place and space and cost requirements prohibited this from being an option. Therefore for the analysis, the existing natural gas water heater was assumed to be used as supplemental heating. The system setup is shown in Figure 1.

Figure 1. Heat Pump System Layout

For the analysis, three scenarios were investigated. The

first demonstrates installing enough HPWH capacity to meet the entire demand for the building (this is broken into two calculations, one with added HPWH capacity and one with additional storage volume, this is for demonstration purposes to understand the magnitude of additional storage needed. The second analysis shows installing a HPWH with natural gas backup heater, while the third sizes the HPWH to meet half of the building demand and the remainder is compensated for by a gas water heater.

The first analysis, in which it is assumed full load met with only the HPWH, requires a total of 19 tons (228,000 Btu/hr) of water heating capacity which has a purchase price of about $46,000. This system is a costly design and is only required to meet the high hot water demand during the day and runs relatively little at night. This is contrary to the optimized design where the HPWH has a very high load factor where it is operating continuously throughout the day and night to create hot water for the storage tank. Even with this oversized system, the annual savings for the system compared to a 65% efficient gas water heater is $12,000 which translates to a simple payback of less than 4 years. The secondary analysis where one 11 ton HPWH was considered and the storage volume was increased, shows that a 2,500 gallon tank would be needed to meet the system demand. This is an increase of over 300% compared to the installed tank capacity. However this increases the annual savings to over $14,000 a year due to the optimized run time.

The second HPWH analysis includes one 11 ton unit with the existing 600 gallon storage tank. This analysis also assumes a 65% efficient natural gas water heater, just like the baseline calculation to reduce the implementation cost. This

Heat Pump Water Heater

To Bldg. orAux heating

600 GallonStorage Tank

Tank Bypass Loop


setup provides an annual cost savings of $4,400 and has a simple payback of just over six years.

Finally the HPWH system was modeled to meet approximately half of the system demand for DHW. This analysis was used because the consensus became that the initial estimates of DHW demand had been over estimated. This is because ASHRAE guidelines for elementary school were used. Therefore this analysis shows the results if the building demand was reduced from 475 gallons per hour to 238 gallons per hour. The HPWH unit would need to be 4 tons in capacity and have the 65% efficiency natural gas as backup. This analysis shows that the annual savings would be $2,500 and a payback of less than four years. This low annual savings can be deceiving however, since the demand for DHW is reduced in half, the advantages of operating a higher efficiency unit are reduced due to the reduction in run time.

The results from the HPWH analyses are summarized in Table 2.

Table 2. HPWH Summary of Results

HPWH Capacity

(tons)

Hot Water Demand

(gallons/hr) Annual Energy Savings ($/yr)

Upfront Costs ($)

19 475 $ 12,000 $ 46,000 11 475 $ 4,500 $ 27,391 4 238 $ 2,500 $ 9,467

SOLAR WATER HEATING Solar water heating is an effective method of utilizing the

sun’s thermal energy in a productive manner to offset the use of fossil fuels and/or electricity and can offer substantial long-term operational cost reductions. The system operates utilizing solar water heating collector panels placed on the roof to collect the sun’s radiation and transfer it to the water (or water and glycol solution to prevent freezing at night in the winter). This liquid is then pumped through a heat exchanger that transfers the energy to the DHW loop without contaminating the DHW system.

The major hurdles for this type of system are the upfront cost and the requirement of large amounts of open (unshaded) roof space facing south. The latter was the issue for this location where there was only about 450 ft2 of space which greatly limited the capability of the solar water heating system to meet the full amount of the DHW demand for the year. Therefore the calculations discussed in this section show how much energy could be offset using the solar water heating system.

To perform the calculations, a free software program developed by Natural Resources Canada and several other entities, RETScreen [6] was used. RETScreen is an acronym for Renewable Energy and Energy efficient technologies Screen and is used as a quick and easy software tool to analyze a

potential project to determine if it makes financial sense before going into a more detailed analysis. The program is especially useful for solar water heating applications where it has built-in templates and takes actual solar radiation data from the project’s city weather data base and uses it to calculate the fraction of energy which can be supplied by the solar panels or solar factor. Additionally, manufacturer’s performance data for different types of panels is loaded into the program to allow for a comparison and optimization of the design.

For this site, two types of solar water heating collector panels were analyzed. The first was an evacuated tube design which was capable of providing approximately 11% of the hot water demand for the year. The second type of panel analyzed was a simple, flat plate collector design. Due to the form factor of the plate itself, it is capable of providing about 12% of the total demand. The breakdown of the analysis for both systems is shown in Table 3. Solar Fraction is defined as the fraction of the annual DHW demand of the building/project supplied by solar energy alone.

Table 3. Solar Analysis Breakdown

Plate Type Evac. Tube Flat Plate Solar Fraction 11% 12% Installation Costs $18,500 $ 20,000 Annual Energy Savings $ 2,350 $ 2,600 Simple Payback 7.9 yrs 7.7 yrs

Similar to the analysis done for the HPWH in the previous

section, the solar water heating analysis was performed again for a condition with half flow demand – a reduction from 475 to 238 gallons per hour. This analysis ended with a very similar overall payback as the full flow analysis however the solar fractions were roughly doubled for both. It should be noted that the analysis shows a solar fraction of nearly double as the DHW demand is halved. This is not perfect because of the nature of solar water heating in that it can only absorb so much heat at any given time and it is only available during hours of the year where the solar radiation is present on the collectors.

TANKLESS WATER HEATING The final water heating technology evaluated for the

project was a purely tankless system that proposes to install multiple large capacity water heaters in line with the DHW piping that will only operate when needed to provide hot water directly to the end user. To present the end user with a uniform temperature of water and prevent scalding, it is common practice to install a mixing valve after the water heaters [7]. These types of water heaters offer advantages over more traditional, tanked designs including a dramatic decrease in standby heat loss from a storage tank as well as taking up much less physical space [8] . These units do typically operate at a slightly less efficient level due to the varying demands on the DHW system and required variation in output from the heater


which does not allow it to operate at its most efficient level continuously. This inefficiency is generally compensated for by the reduced standby losses, making it more attractive.

However since the water must be heated on-demand, a new sizing analysis must be performed to ensure the system is capable of providing the desired water temperature. To do this, ASHRAE guidelines presented in Table 15 of the AHRAE Handbook [9] were used. This analysis, along with discussions with tankless water heater vendors led to the following potential designs.

Table 4. Tankless Water Heater Configuration Options Company A B Unit Count 4 2 Combined max input rate (Btu/h) 796,000 799,600 Thermal Efficiency 94% 94%

The heating units in Table 4 would be configured in series

where the first heating unit operates as a preheater for the remainder of the system, typically operating at full capacity to heat the water from the incoming city water temperature closer to the set point temperature. This process continues as the water travels through the system with each water-heating unit adding as much heat as needed to reach the desired temperature.

With this configuration in place, the building is expected to save nearly $8,000 a year in operating costs compared to the baseline analysis. The cost breakdown and payback information is shown in Table 5.

Table 5. Tankless Water Heating Summary

Company A B Installed Cost $6,250 $4,640 Annual Energy Savings $7,816 $7,816 Simple Payback (yrs) >1 yr >1 yr

COMBINED SOLAR AND TANKLESS WATER HEATING

In addition to the analysis performed for tankless and solar water heating options, a hybrid system of the two was also evaluated. This system would utilize the solar water heating collector system with a storage tank as a preheater to the water going into the tankless system. This reduces the amount of work that must be performed by the fossil fuel system and offsets that with energy for the sun. This system is no longer a true tankless setup, as there will be a tank required to store the energy from the solar water heating system, however, once the water exits the storage tank it will be handled just as if it were a true tankless system.

Since the tankless system is now able to utilize the energy from the solar water heating setup, it can be reduced in capacity to 266,167 Btu/hr. This is because the incoming city water temperature is now preheated by the solar water heating system

and there is also additional hot water storage capabilities in the DHW system which allows the unit capacity to be reduced in size. This results in only needing to install half of the tankless water heating capacity compared to the previous setup. Although this reduces the cost to install the tankless water heating portion, the installed cost of the solar water heating is substantially more – as mentioned in the section on Solar Water Heating. This setup is also only expected to reduce the annual operating costs by about $3,000 when compared to the straight tankless water heating system.

SUMMARY OF RESULTS Table 6 shows a summarization of the previous analysis on

efficient water heating options for the McWane Science Center.

Table 6. Summary of Results

System

Man

ufac

ture

r

Impl

emen

tatio

n C

ost

Ann

ual

Ope

ratin

g C

ost

Ann

ual E

nerg

y Sa

ving

s

Baseline $22,715 n/a

Condensing Water Heating

Lochinvar $11,453 $13,014 $9,700

Laars $9,000 $13,0141 $9,700

Heat Pump Water Heating

Colmac (19 tons) $46,000 $10,715 $12,000

Colmac (11 tons) $27,391 $18,215 $4,500

Colmac (4 tons) $9,467 $20,215 $2,500

Solar Water Heating

Thermomax (100%) $18,500 $20,365 $2,350

Rheem (100%) $20,000 $20,115 $2,600

Tankless Water Heating

Rinnai $6,250 $14,899 $7,816

Rheem $4,640 $14,899 $7,816

Combined Solar and Tankless Water Heating

Rheem $2,500 $11,592 $11,123

Rinnai $2,706 $11,592 $11,123

1 The base-case cost was calculated with the assumption of 65% thermal

efficiency of old water heaters.


RECOMMENDATIONS Several different water heating designs were reviewed for

the McWane’s Science Center, located in Downtown Birmingham, AL. The traditional water heaters cost nearly $2,000 more to install than the tankless units quoted for the project. The heat pump was found to be the most expensive to install due to its high equipment cost, with the solar heating system being the second most expensive unit. The savings calculated and reported by the solar water heating system was nearly $2,500. This amount was about half that reported by the heat pump. The hybrid system that involved solar preheating of water for tankless heaters was found to not be an effective option for reducing required energy. The tankless system was found to be the least expensive to install however had a higher annual operating cost than other, more efficient options. The heat pump which met half the demand calculated had the minimum annual operating cost and was one of the less expensive unit cost. For the specific location and set of operating conditions, the tankless water heating system was recommended to the customer. Also since the facility was interested in reducing their overall impact to the environment, a flat-plate solar water heating system was also recommended to be installed to preheat the incoming water as much as possible using the existing infrastructure as much as possible.

The authors of this report would also like to add that greenhouse gas (GHG) emission reduction should be considered an important and decisive factor in making a decision of this kind. Although a detailed GHG analysis was not performed at this stage, it is quite obvious that in that respect, the solar water heating offers the most reduction followed by the heat pump option. Another added benefit of a heat pump water heating system is the cold air supply as a byproduct of water heating. In a facility such as the McWane’s Science Center, the provided cold air can contribute to reducing the cooling load of the building or to provide comfort cooling to a space where it was not previously available [10].

A further detailed analysis of DHW use including GHG analysis of each of the water heating options is recommended. Such a study should include actual DHW use monitoring and measurement for an extended period of time (1 year).

ACKNOWLEDGEMENT The authors would like to thank Mr. Lamar Smith of

McWane’s Science Center for introducing the issue and also providing access to their facilities to collect required input data.

REFERENCES [1] ASHRAE, 2010, ASHRAE Handbook - HVAC

Applications. [2] "Armor Condensing Water Heater," Lochinvar, [Online].

Available: http://www.lochinvar.com/products/Default.aspx?type=ProductLine&lineid=22. [Accessed 17 August 2013].

[3] "Commercial Products," Laars Heating Systems Company,

[Online]. Available: www.laars.com. [Accessed 29 September 2013].

[4] "Heat Pump Water Heaters," U.S. Department of Energy, 4 May 2012. [Online]. Available: http://energy.gov/energysaver/articles/heat-pump-water-heaters. [Accessed 5 September 2013].

[5] ACEEE, "Water Heating," 2012. [Online]. Available: http://www.aceee.org/consumer/water-heating.

[6] National Resources Canada, "RETScreen International," 23 May 2014. [Online]. Available: http://www.retscreen.net/ang/home.php. [Accessed 21 September 2014].

[7] "Calloway Engineered Systems," [Online]. Available: http://callowayengineeredsystems.com. [Accessed 2 August 2013].

[8] [9]

"Tankless or Demand Type Water Heaters," Energy.gov, 2 May 2012. [Online]. Available: energy.gov. [Accessed 8 August 2013]. ASHRAE, 2009, ASHRAE Handbook - Fundamentals

[10] C. R. Nave, "Heat Pump," HyperPhysics by Georgia State University, 2013. [Online]. Available: http://hyperphysics.phy-astr.gsu.edu. [Accessed 5 September 2013].



DEVELOPMENT OF A FLUENT MODEL FOR PARTICLE FLOW THROUGH A POROUS PARTICLE-HEATING RECEIVER

Jonathan Roop, Clayton Nguyen, Said Abdel-Khalik, Sheldon Jeter Georgia Institute of Technology

Atlanta, GA USA

ABSTRACT Particle heating receivers promise an efficient new method

of collecting solar energy in concentrated solar power systems. Current research being conducted at Georgia Tech and Sandia National Laboratories considers a receiver with porous obstructions to slow the flow of particles through the receiver, allowing them to be irradiated for a longer time.

This paper describes the development of a Fluent CFD model for such a receiver. The model began as a simple 2D representation which eventually evolved into a 3D unit cell model that captures the complex geometry of a wire mesh obstruction. The simulation utilizes the unique method of representing the wires as strings of particles frozen in place, so that the surrounding finite element cells may be much larger than the particles. A heat transfer analysis is also detailed, and ultimately predicts the efficiency of a receiver with a 1m2 aperture under 1 MW/m2 irradiation.

1. INTRODUCTION Particle heating receivers (PHR) in central receiver power

tower systems offer a promising new way to efficiently capture the energy of the Sun in concentrated solar power systems. Such receivers have the potential to operate under a much wider range of temperatures, avoiding the issues of chemical degradation at high temperatures that limit most solar salts to around 700oC (1292oF) and liquid-solid phase change at lower temperatures.

Research at Georgia Tech (GT) and Sandia National Laboratories (SNL), with funding under the SunShot program, is focused on developing a highly efficient and economical concentrated solar power plant. Two particle heating receiver designs are being considered in this research: A free-falling curtain of particles, possibly with recirculation of the particles for a second pass through the receiver, and a receiver in which the particle flow is disrupted by some porous media, such as

wire meshes or ceramic foam. The obstruction slows the average particle velocity, allowing a larger temperature rise in a single pass. Experimentation and modeling are necessary to predict receiver efficiencies at large scale and to determine ways of improving the designs.

2. THE DISCRETE ELEMENT AND DENSE DISCRETE PHASE MODELS

ANSYS Fluent (see Figure 1) provides several methods for modeling particle flow. The Discrete Element Model (DEM) represents the particles as circles or spheres and tracks their motion through the computational domain. The flow of fluid around the particles affects the particle motion through momentum exchange terms. Likewise, the model can include the effect of particle motion on the surrounding fluid, as well as heat exchange to and from the particles. A second approach models the particle flow in an Eulerian framework, treating the particle flow essentially as a second continuous phase superposed on the primary phase. Special parameters, such as granular viscosity and packing limit, are defined and used to modify the governing flow equations for the discrete phase. Interphase momentum and heat transfer may also be included.

Lastly, the Dense Discrete Phase Model (DDPM) is a hybrid of the two approaches, primarily modeling the flow as a second continuous phase, but using results from particle tracking to identify where the volume fraction of the particles phase becomes high. In these regions, the governing equations are modified, because the usual Eulerian treatment otherwise assumes that the particle volume fraction everywhere is low (<~10%).

At first, the fluent models constructed in the study used the Dense Discrete Phase Model. However, since particle-particle and particle-wall collisions critically affect the motion of particles through the system, the DEM was eventually pursued instead. The Eulerian model does not track collisions, and while


particle-particle collisions can be enabled for the DDPM model, the additional Eulerian treatment for DDPM becomes superfluous once the collision model is already enabled in its particle tracking.

3. "PARTICLES" VS "PARCELS" The Discrete Element Model (DEM) represents the

particles as circles, and calculates collision forces based on the overlap between two circles. To reduce the number of particles that need to be tracked, Fluent will represent a cluster of particles as a single circle with equivalent bulk properties of the cluster. These cluster representations are referred to as "parcels." However, since particle-particle interference is the mechanism by which the flow is restricted in the receiver, and since the spacing between wires in a wire mesh obstruction is only several particle diameters thick, this simplification would likely reduce the accuracy of the model. Therefore, parameters were chosen such that each parcel would represent one and only one particle, and possess the same diameter and material properties as a grain of ID50-k foundry product, the current material of choice for these receivers [1].

4. PARTICLE COLLISION PARAMETERS AND TIME STEP

The DEM model is notoriously stiff, and requires a very small time step to avoid divergence. This results in very long simulation times, especially when every individual particle is being tracked. One method that researchers in the past have used to allow larger time steps without divergence is to make the particles "softer" by reducing the spring constant used in calculating the particle-particle collision force. The tradeoff is that particles will penetrate deeper into each other during a collision.

A short study was conducted to investigate how much inter-penetration would result from different values of k, the collision spring constant. The maximum particle velocity observed in an early 2D model without particle-particle collision was 1.3 m/s (4.3 ft/s), so two particle were collided head-on at a relative velocity of 2.6 m/s (8.5 ft/s) as a representation for the most violet collisions that can occur in this system. All less-violent collisions will observe less inter-particle penetration.

A k-value of 1.0 N/m (0.069 lbf/ft) resulted in a maximum particle-particle penetration of about 10%, and allows a time step as large as 1e-4 seconds. Considering the amount of computational time saved by allowing a larger time step without resulting in particle penetration that would affect the overall flow characteristics too much, this k-value was chosen for the receiver simulation.

Initial runs of the simulation exhibited divergence originating in particle-particle collisions, which was remedied by reducing the time step to 1e-5 seconds. After this, particles throughout the system maintained reasonable velocities, and no further divergence due to particle collisions occurred.

5. 2-DIMENSIONAL MODEL The starting point for this investigation was a simple 2-

Dimensional model of a flow of particles through an obstructed environment, constructed in ANSYS Workbench and Fluent. "Holes" were punched into the fluid domain to represent the obstructions. By changing the size and spacing of the holes, a desired porosity could be imparted on the obstructing region.

The geometry of the 2D model is shown in Figure 1. Particles were injected at the top of the domain, falling past 2 or 3 obstructing regions before exiting the bottom. A symmetry boundary condition was imparted on the sides of the computational domain, so that the simulation essentially models an infinitely wide receiver.

Figure 1. 2D Fluent Geometry

6. 3-DIMENSIONAL MODEL Although porous ceramics of a homogenous porosity were

also once being considered, the most likely choice of material for the obstructions is wire mesh constructed of a high-temperature metal alloy. Hence, the 2D geometry shown in Figure 1 has regularly-spaced holes arranged in rows. A true wire mesh, which is more like a set of crisscrossing rods, cannot be modeled in this 2D environment. The 2D model was also limited in its representation of particle flow. Particles were represented as circles, and while they could collide and go fully around each other in the 2D plane, the model was unable to represent one particle passing "behind" another in 3 dimensions. To attain a more accurate model of the particle flow, a 3-dimensional model was constructed in ANSYS Workbench. The wire mesh was represented using crisscrossing square rods, and the particles became spheres (see Figure 2).


Figure 2. 3D Model

7. EXPERIMENTAL VERIFICATION To validate the model, an experimental apparatus was

constructed. The apparatus consisted of a clear acrylic tube in which two wire mesh obstructions were installed. A profile of the particle velocities was measured using the Particle Image Velocimetry (PIV) technique, and compared to the particle velocities predicted by the simulation.

Figure 3. Velocity Results of Euler-Euler Model, Apparatus, and Discrete Element Model.

The average particle velocity from simulation was 0.364 m/s (1.19 ft/s), and the PIV measurements show 0.35 +/- 0.02 m/s (1.15 +/- 0.07 ft/s). Both experiment and the DEM model also exhibit a layer of particles about 1 to 2mm (3.9e-5 to 7.9e-5 in.) forming above the wire meshes, and a maximum mass flux through the wire meshes around 70 kg/m2s (14 lb/ft2s). The experiment is described in more detail by Nguyen [2].

8. THE DISCRETE ORDINATES RADIATION MODEL After a working model of particle flow through porous

obstructions had been developed, radiation modeling was added. Several radiation models are built into Fluent, with various

levels of complexity. Of these, two models are applicable to simulations involving particles with radiation interaction: The P-1 model and the Discrete Ordinates model. The P-1 model assumes gray irradiation, and is the simplest approximation of the generalized P-N model. It is best suited for modeling radiation heat transfer in diffuse, optically thick media. The Discrete Ordinates model is more appropriate for this simulation, which discretizes 3D space into 8 or more directions, solving the radiation transport equation for each direction. The Discrete Ordinates radiation model can also simulate multiple radiation bands, which improves the modeling of non-gray surfaces, and is suitable for both optically thin and optically thick media.

To allow a comparison between this model and the Fluent model constructed by Josh Christian at SNL for a falling particle curtain receiver, the same values for radiation input were selected. The concentrated irradiation from the heliostat field is set to 1000 suns (1 MW/m2 or 88.1 BTU/s-ft2) at the receiver aperture (the expected conditions for the on-sun test planned to take place at Sandia) and is split into 2 bands: Visible+UV and infrared.

The solar absorptance of ID50-K, obtained using the 410-Solar Reflectometer, was applied as the "emittance" value (which is also used as the absorptance value in Fluent). The measured particles had been heated to 950oC (1742oF)for 7 days. Details of this optical properties investigation are described in more detail in [3].

9. ROTATION OF THE COORDINATE SYSTEM A special consideration to take into account when using the

Discrete Ordinates model is that the model will have difficulty representing beam irradiation accurately if the beam is exactly aligned with an axis of the Cartesian coordinate system. For this reason, the coordinate system was rotated as shown in Figure 4 such that the beam direction would be equidistant from the three coordinate axes, the best configuration for beam irradiation.

Figure 4. Rotation of Coordinate System

10. DIVERGENCE DIFFICULTIES AND IMPROVED MODELING SCHEME

The 3D simulation using DEM and the Discrete Ordinates model diverged after a short time. Fluent reported the


divergence as occurring in the temperature equations. Further reduction of the time step did not eliminate this divergence.

While investigating possible sources of the divergence, it was found that the DEM model, when coupled with the surrounding continuous medium, assumes that the particles are significantly smaller than the cells of the Finite Element mesh. This was not the case with the model at the time, in which the particles and Finite Element cells were comparable in size. The cell sizes could not easily be reduced, however, since they need to be small enough to represent the wires and the spacing between the wires of the wire mesh obstruction. Therefore, a new approach was applied to model the wire mesh obstruction while allowing larger Finite Element cells.

Rather than building the wire mesh structure using the DesignModeler software package of ANSYS, the wires were instead represented as strings of particles, frozen in place (see Figure 5). Hence, the wire mesh structure could be constructed independently of the Finite Element mesh, and the Finite Element cells could be made as large as desired.

Figure 5. Frozen particles can be used to model obstacles.

The improved model has a uniform, Cartesian grid Finite Element mesh possessing fewer Finite Element cells, and runs significantly faster than the prior model. As shown in the figure, the model was also updated at this time to model a unit cell of the porous receiver, rather than simple horizontal meshes.

To initially place the "frozen" particles, an injection file was generated using Matlab, specifying the position of each particle. These particles were "injected" just once, at the start of the simulation. The injection file also specifies the diameter and mass of every frozen particle.

Once the particles are injected, they are frozen in place through the use of two User-Defined Functions (UDFs). UDFs

are written by the user in C language, with special functions provided in Fluent's libraries for integration into Fluent's computations. The first UDF applies an upward acceleration to the particles to cancel the effect of gravity, and the second sets the particle velocity to zero at the end of every iteration.

11. CONVECTION HEAT LOSS THROUGH THE APERTURE

A number of studies have been done in the past investing heat loss via advection through receiver apertures [4, 5, 6, and 7]. Several of these correlations were evaluated to estimate the heat loss coefficient over the 1m2 aperture area of a test receiver being developed by GT and SNL. The calculation results are given in Table 1:

Table 1. Convection Coefficients Predicted by Various Correlations.

Model Convection Coefficient, W/m2-K (BTU/hr-ft2-oF)

Le Quere et al. [4] 5.95 (1.05)

Clausing [5] 2.32 (0.409)

Modified Clausing [6] 6.25 (1.10)

Siebers and Kraabel [7] 10.68 (1.88)

A rather conservative value of 15 W/m2K (2.64 BTU/hr-ft2-

oF) was chosen, and applied as an external convection heat transfer boundary condition on the aperture.

12. HEAT BALANCE Thermal energy enters the computational domain in the

form of concentrated solar irradiation. The incoming radiation can be absorbed by the particles, absorbed by the back wall, escape through the aperture (as a result of reflection by the back wall and back-scattering by the particles), or pass to an adjacent unit cell. The energy that was absorbed will eventually exit the domain with the particles in the form of internal energy or be convected into the air surrounding the particles and then escape the domain via advection.

Fluent can readily report the net radiation heat transfer at a surface and the total heat transfer at a surface. The DPM enthalpy source (thermal energy transfer between the particles and the continuous domain) is also reported. The heat transfer reports do not, however, report how much energy is transferred through a surface in the form of sensible heat of particles. To determine this heat flow, a special sampling surface was created in Fluent coincident with the outlet. Particle data, including


particle temperature, were recorded as particles passed through the sampling plane.

An energy balance analysis reveals whether the system has reached a steady-state configuration. At steady-state, the input solar energy should match the sum of the outputs. Currently, the simulation has not yet attained such an energy balance. The rate at which the system internal energy is increasing can be found by summing the internal energies of all the particles at different times and finding the rate of increase. It was found that the rate of increase computed this way accounts for the system energy imbalance.

13. UNIT CELL EFFICIENCY The unit cell efficiency is the ratio of power collected by

the particles to the total solar irradiation, and is estimated as follows for the non-steady configuration:

(1)

where Ḣin is the rate of enthalpy entering the system in the form of internal energy of the particles at the inlet, and Ḣout is the rate of enthalpy leaving via the particles at the outlet, Ėpass is the solar radiation passing to adjacent unit cells, ηpass is the fraction of Ėpass that is assumed to be absorbed by particles in the adjacent cells, Ėsys is the rate of accumulation of system

internal energy, is the concentrated solar flux (1 MW/m2 or 88.1 BTU/s-ft2), and A is the area of the front face of the unit cell where the input radiation enters. The rate of enthalpy entering the unit cell was found by the following formula:

(2) Where ṁ, the mass flow of particles, is known a priori via

the injection properties, Cp is the specific heat of the particles, and Tin is the inlet particle temperature. The rate of enthalpy leaving the unit cell was found by computing the slope of cumulative enthalpy leaving the outlet vs time, shown in Figure 6.

Figure 6. Cumulative Enthalpy Passing through the Outlet from t=0.1575 Seconds to t=0.1595 Seconds.

For the current case, in which particles enter the unit cell at room temperature, the unit cell efficiency comes out to 97.8%. This calculation is shown in Figure 7, along with an energy balance diagram of the unit cell. The receiver efficiency calculation can be refined once a steady-state configuration has been attained, at which time Ėsys will be zero.

High-temperature simulations, in which particles enter the domain at 600oC (1112oF) and 1000oC (1832oF) are also in progress. Current results indicate that the falling particles exhibit nearly blackbody behavior, re-radiating energy back out the front face of the unit cell according to the Stefan-Boltzmann law:

(3)

Figure 7. Unit Cell Efficiency Calculation for Room-Temperature case.

where σ = 5.67e-8 W/m2K4 (0.1714e-8 BTU/hr-ft2-oR4)is the Stefan-Boltzmann constant, ε is the emissivity (ε=1 for a

blackbody) is the average particle temperature within the unit cell (on an absolute temperature scale), and Tamb is the ambient temperature (300 K, or 540oR, was assumed). Convective heat losses are also higher at the front face of the unit cell. The unit cell efficiencies can be made by subtracting these additional losses from the energy collected by the particles:

(4)

For an average particle temperature of 300oC (572oF) (the desired temperature at the inlet of the receiver), the calculation returns 96.96%. Assuming an average particle temperature of 700oC (1292oF) (a target outlet temperature of the receiver), the unit cell efficiency is 91.89%. Hence, the overall receiver efficiency can be estimated as (0.9696+0.9189)/2 = 94.43%. A slightly higher efficiency can be expected for a receiver with a greater concentration of solar irradiation, since denominator in the efficiency calculation will be larger while the re-emission


and convection heat losses should remain about the same (assuming the same average particle temperatures).

14. CONCLUSIONS AND FUTURE MODELING Particle flow has been successfully modeled in ANSYS

Fluent, showing agreement with experiment in particle velocities, overall mass flow rates, and the formation of layers above wire meshes. The simulation takes into account particle-particle collisions and obstructions to their flow. Heat transfer has also been implemented into the simulation, modeling concentrated irradiation, reflection losses, convection losses, and absorption by particles and by the back wall of the receiver. The resulting receiver efficiency is predicted to exceed 90% for a particle temperature range of 300oC to 700oC (572oF to 1292oF). Efficiency is expected to be even greater for higher-concentration scenarios.

Additional Simulations are also underway to confirm a convection heat loss coefficient of less than 15 W/m2K (2.64 BTU/hr-ft2-oF). The simulation models the receiver cavity, the front wall of the tower, and an external domain, and will be discussed further in a future publication.

Using frozen particles to model obstructions to particle flow in the receiver is a versatile method, and is not limited to modeling simple wire meshes. Any obstruction could be modeled this way, and higher-resolution representations can be obtained by using smaller frozen particles.

Nomenclature SNL

Sandia National Laboratories

GT Georgia Institute of Technology DDPM Dense Discrete Phase Model DEM Discrete Element Model ID50-k ID50-k foundry product Ḣin Rate at which enthalpy enters the unit cell Ḣout Rate at which enthalpy exits the unit cell Ėpass Amount of Radiation passing out of the unit

cell into an adjacent unit cell ηpass Fraction of Radiation passing to an adjacent

unit cell that is presumed to be absorbed Ėsys Rate of Increase of System Internal Energy

Incoming concentrated solar flux

A Area of the front face of the unit cell ṁ Mass flow of the particles Cp Specific heat of the particles Tin Temperature at which particles enter

σ The Stefan-Boltzmann constant ε emissivity

Average particle temperature in the unit cell

ACKNOWLEDGMENT Financial support of the US Department of Energy through the SunShot research program is recognized and appreciated.

REFERENCES [1] “CarboAccucast ID-50K”, Carbo Ceramics, 2014, Houston, TX, www.carboceramics.com [2] Nguyen, C., Roop, J., Jeter, S., Abdel-Khalik, S., 2014. Preliminary Investigation of Particle Flow Characteristic Within Particle Heating Receivers. Proceedings of the Fourteenth Annual Early Career Technical Conference. Birmingham, AL USA. [3] Roop, J., Jeter, S., Abdel-Khalik, S., Ho, C., 2014. Optical Properties of Select Particulates after High-Temperature Exposure. ASME Energy Sustainability and Fuel Cell Science, Engineering, and Technology Conference. Boston, MA USA. [4] Le Quere, P., Penot, F., Mirenayat, M., 1981b. Experimental Study of Heat Loss through Natural Convection from an Isothermal Cubic Open Cavity, Sandia National Laboratories Report, SAND81-8014. [5] Clausing, A.M., 1981. An Analysis of Convective Losses from Cavity Solar Central Receivers. Solar Energy 27, 295–300. [6] Leibfried, U., Ortjohann, J., 1995. Convective Heat Loss from Upward and Downward-facing Cavity Solar Receivers: Measurements and Calculations. ASME Journal of Solar Energy Engineering 117, 75–84. [7] Siebers, D.L., Kraabel, J.S., 1984. Estimating Convective Energy Losses from Solar Central Receivers. Sandia National Laboratories Report, SAND 84-8717.


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