Abstract

An experimental study of the heat transfer characteristics of the bulk flow of sand in a sand–air heat exchanger is conducted. The study is conducted in the context of the development of a high-temperature solar gas turbine (HTSGT) system. This system is being developed by King Saud University and the Georgia Institute of Technology with the aim of demonstrating the feasibility of using sand as the heat transfer and energy storage medium in central receiver systems. Experiments are conducted on silica sand and olivine sand, both of which are attractive options due to their wide availability. The apparatus includes a tube bank consisting of eight electrically heated tubes arranged in three rows in a staggered formation. Heat transfer coefficient results are reported for bare and finned tubes for sand feed velocities of 1–3 mm/s. They were found in the range of 80–160 W/m2 K.

Introduction

Solar thermal power plants offer greatly increased potential when including a high-temperature gas cycle, since the temperatures that can be achieved, and the corresponding cycle efficiency, can exceed those of a conventional steam turbine based plant. A further advantage of a solar gas cycle system is that there is no need for water cooling, making the plant much more suitable for arid regions that are considered among the prime locations for solar energy utilization.

The idea of central receiver systems based on gas cycles has gained considerable interest during the past two decades, due to the ability of achieving very high temperatures with central receiver systems. Various gas cycle concepts have been proposed and tested, and most involve the direct heating of compressed air or other gas [1–3]. However, one of the major challenges of these systems is successful incorporation of thermal energy storage, since the effectiveness of using thermal energy storage with air or gas is relatively poor.

There has been a number of thermal energy storage solutions proposed over the past three decades. One of the most widely accepted thermal energy storage solutions is the use of molten salts [4,5]. Currently, the use of molten salts for thermal energy storage is limited to temperatures generally less than 600 °C due to temperature degradation. Another solution is the use of solid blocks to store energy during the day. This concept has been demonstrated with concrete blocks [6,7], but the temperatures are generally limited to less than 500 °C due to concrete properties, making this concept not suitable for high-temperature applications. Furthermore, since the thermal energy is stored in a static solid, the developing temperature profile during the discharging process causes a gradual decline in cycle efficiency. Yet another solution is to use sand as a storage medium [8]. The referenced concept was developed to work in conjunction with an air heating receiver. The sand is heated in an air–sand heat exchanger to a very high temperature. The sand then flows to a hot storage tank, and then to a fluidized bed exchanger, where its heat is used to generate steam that feeds a steam power cycle. The colder sand returns either to the air–sand heat exchanger or is stored in a cold storage tank. This technology resolves the temperature limit issues faced in the solid block concept. However, the main issue of the unfavorable temperature profile during discharging still persists.

To overcome the thermal energy storage issues described above, a promising solution is being developed by researchers at King Saud University and the Georgia Institute of Technology. It involves the use of sand or other fine granular materials as the primary thermal medium. Unlike the existing concepts that utilize sand for thermal energy storage, the new system allows sand to be directly heated by the incoming sunlight, as Fig. 1 shows. A portion of the heated sand exchanges heat with compressed air. The hot air leaving the sand–air heat exchanger is then fed to a suitable gas cycle. The remainder of the sand is stored in a well-insulated bin where it is stored for later use. When the sand leaves the heat exchanger, where it loses much of its energy to the air, the sand is recirculated to the top of the tower using a bucket conveyor. During nighttime, the hot stored sand is drawn into the heat exchanger, and the sand leaving the heat exchanger is then diverted to a cold bin where it resides until the solar field comes back in operation the next day. One of the main advantages of this concept is that the hot sand is stored upstream of the heat exchanger. By doing so, the temperature of sand at the beginning of the process of heat exchange with air will always be high, thereby maintaining the high efficiency of the gas cycle.

Fig. 1
Section of the tower concept
Fig. 1
Section of the tower concept
Close modal

The new system, called the HTSGT system, builds on the experience and the outcomes of the solid particle receiver project that was introduced and tested at the National Solar Thermal Test Facility in Sandia National Laboratories [9,10], the main differences being an alternative receiver design and the incorporation of thermal energy storage. To demonstrate the merits of the new concept, a pilot-scale, 300 kW (thermal) central receiver plant will be built on the campus of King Saud University, in Riyadh, Saudi Arabia. Construction is already underway and is expected to be completed in late 2012.

The current study focuses on one of the components of the system, namely the sand–air heat exchanger. The aim of the study is to understand the heat transfer characteristics of the heat exchanger such that it can be designed properly. A number of studies on the heat transfer between granular material and a flat plate have been carried out, e.g., Refs. [11,12]. Studies on the heat transfer between granular material and tube banks were also carried out, two of them are of particular interest [13,14]. The two studies considered different tube arrangements and, therefore, led to significantly different values of the effective heat transfer coefficient of the particulates. In Ref. [13], polypropylene particles ranging in size from 350 to 710 μm were allowed to flow past a single row and two rows of tubes. The local heat transfer coefficient around the tubes of a two-row arrangement was reported to range from approximately 25 to 120 W/m2 K for velocities ranging from 0.4 to 6.7 mm/s. In Ref. [14], a more extensive tube bank containing 68 tubes was used. Four particle types were studied: ash (average particle size: 475 μm), sand (average particle size: 203 μm), sand (average particle size: 637 μm), and corundum (average particle size: 195 μm). The study reported that the effective average heat transfer coefficient for staggered tube bank ranged from approximately 90 to 220 W/m2 K at various mass fluxes, with corundum generally showing the highest effective average heat transfer coefficient.

The present study considers the bulk flow of sand in a tube bank. Two types of sand that exhibit high-purity and small grain size were studied. The experimental setup is described next.

Experimental Setup

The research team has built an experimental apparatus that enables the study of the effect of a number of parameters on the heat transfer characteristics of the bulk flow of sand in a tube bank. Figure 2 shows the instrumented apparatus.

Fig. 2
Experimental apparatus (a) test section,
                        (b) bare tubes experiment, and (c) finned
                        tubes experiment
Fig. 2
Experimental apparatus (a) test section,
                        (b) bare tubes experiment, and (c) finned
                        tubes experiment
Close modal

The apparatus shown in Figs. 2(a) and 2(b) is for the bare tubes experiment. It consists of three main parts as follows:

  • sand hopper

  • test section

  • movable grates

The sand hopper is used to admit the sand into the test section at controlled flow rates. The hopper has a 114 mm by 114 mm (4.5 in. × 4.5 in.) cross section, and it is attached directly to the test section. The test section is made of a transparent polymer box which contains horizontal tubes. These tubes can be varied in size and arrangement. The data presented in this paper pertain to an arrangement of eight horizontal tubes, made out of carbon steel, distributed on three rows in a 60 deg staggered formation (Fig. 2(a)). The eight tubes are electrically heated by heater cartridges. The input power to the cartridges is controlled by a variable autotransformer. To control the flow rate of sand through the test section, movable grates are fitted beneath the test section.

To measure the local heat transfer coefficient on the surface of tubes for the bare tube case, five thermocouples are placed on the surfaces of the upper middle tube and the lower middle tube (Fig. 3). Assuming symmetry in the temperature profile, the thermocouples are placed at 0 deg, 45 deg, 90 deg, 135 deg, and 180 deg angles on one side of the tube. For the finned tubes experiment, however, only three thermocouples at 0 deg, 90 deg, and 180 deg have been used. In addition to the thermocouples on the tube surface, a thermocouple is placed within the sand hopper, just upstream of the test section, to measure the “free stream” temperature of the incoming sand flow.

Fig. 3
Thermocouple positions for the bare tube experiment. (a)
                        Locations on the tube surface. (b) The upper and lower
                        middle tubes were selected.
Fig. 3
Thermocouple positions for the bare tube experiment. (a)
                        Locations on the tube surface. (b) The upper and lower
                        middle tubes were selected.
Close modal

The bare tube experiment used a hopper full of sand without recirculation. At the start of the experiment, the sand hopper is filled with sand. The heated cartridges are turned on, and the grates are opened to allow the desired flow rate of sand. The sand then passes through the staggered tube bank, and temperature readings are collected using a modular data acquisition system (Agilent 34970A) comprising a multiplexer and a 6½ digit multimeter. The flow rate across the heat exchanger is measured using a collecting beaker and a stopwatch.

The heat transfer coefficient can be found by applying Newton's law of cooling
hbase=q"T¯tube-Tinc
(1)

where q" is the heat flux through the tube, T¯tube is the arithmetic average surface temperature as inferred from the thermocouple readings, and Tinc is the temperature of the incoming sand.

Two parameters were varied in this study: power input and flow rate. The power input ranged from 100 W to 350 W, whereas the flow rate was controlled such that two inlet velocities were obtained: 1 and 3 mm/s. In Fig. 4, it can be seen that the heat transfer coefficient reaches a steady-state value after about 3 min. For the finned tubes experiment, the apparatus was modified as shown in Fig. 2(c) to include recirculation. This allowed the system to reach a more reliable steady state.

Fig. 4
Steady-state hbase of Olivine sand at 3.0 mm/s
                        with (a) bare tubes and (b) finned
                        tubes
Fig. 4
Steady-state hbase of Olivine sand at 3.0 mm/s
                        with (a) bare tubes and (b) finned
                        tubes
Close modal

Typical bare tube data are shown in Fig. 4(a). The initial high values of the heat transfer coefficient in Fig. 4(a) are a transient effect because the tubes are initially cool. The convection coefficient drops to a lower steady-state value as the tubes warm up.

For the finned tube experiment, Fig. 4(b), the experimental procedure was modified to ensure steady-state operation. First, the recirculation system is started, the heaters are turned on at 100 W, and data are collected for 30 min. Then, the power is increased by 50 W, and the data are collected again for 30 min. This sequence is repeated until power reaches 350 W. The reason for this procedure is to ensure a constant flow rate by having the grates at the same opening for each power. Note that after an initial decline due to transient operation, the heat transfer coefficient typically reaches a reasonably steady average value with some fluctuation after approximately 15 min. The initial decline after increasing the power is an expected transient effect as the heater adjusts to new conditions. The fluctuations are most likely due to slight uncontrolled variations in the flow rate and ambient conditions that are not systematic and are within the range of expected error.

An interesting, but expected, observation is that the input power does not have a systematic effect on the steady-state value of the heat transfer coefficient. This observation can be explained as follows. In analogy to the flow of fluids, the heat transfer coefficient of the bulk flow of sand is expected to depend on flow velocity and sand properties. The flow velocity is deliberately kept constant at different values of input power. As for sand properties, the increase in input power can cause them to change due to the change in sand temperature close to the tube surface. The only influential property is likely to be the thermal conductivity, and the thermal conductivity of quartz may increase around 4% over the typical experimental surface temperature range of 30 °C–60 °C [15]. If the convection coefficient varies directly with conductivity as in a simple fluid, such a change might be marginally noticeable. However, for the range of input power that we examined, the increase in sand temperature was not enough to cause a systematic increase in observed convection coefficient with increasing power and temperature.

The possibility of enhancing the convection coefficient is of interest and was investigated superficially. In this investigation, the heat exchanger section was vibrated in order investigate the possible effect of the vibration on the heat transfer coefficient. As detailed below, no increase and actually a significant decrease in the convection coefficient was observed.

Results

Experiments were conducted on two types of sand, silica and olivine. The mean diameter of silica sand was 104 μm, while the average grain size of olivine sand was approximately 92 μm. It was found that the type of sand has little effect on the heat transfer coefficient of these samples, with olivine slightly higher than silica (olivine has somewhat higher density and specific heat), as shown in Table 1.

Table 1

Sand samples used in the tests

Olivine
Mean diameter: 92 μm
Standard deviation: 19 μm
Fine silica
Mean diameter: 104 μm
Standard deviation: 27 μm
Fracking sand
Mean diameter: 253 μm
Standard deviation: 60 μm
Olivine
Mean diameter: 92 μm
Standard deviation: 19 μm
Fine silica
Mean diameter: 104 μm
Standard deviation: 27 μm
Fracking sand
Mean diameter: 253 μm
Standard deviation: 60 μm

These results are in qualitative agreement with those reported in Ref [14]. A third sample is silica sand used as a proppant for hydrofracturing or “fracking.” This particular silica sand has a larger grain size, so it was tested in the finned tubes experiment to investigate the effect of grain size. It was found that grain size does not have an obvious effect on the heat transfer coefficient possibly because the difference in bulk thermal conductivity is insignificant for the grain sizes examined.

Bare Tubes Experiment.

The measured values for the heat transfer coefficient are reported in Table 2. The bare tubes are 0.621 in. in diameter and 4.5 in. long.

Table 2

Mean heat transfer coefficient for bare tubesa

Sand velocity mm/sSand typeh W/m2 KUncertainty W/m2 K
1.0Olivine117.29±1.14
Fine silica107.05±1.00
3.0Olivine161.02±1.97
Fine silica141.03±1.85
Sand velocity mm/sSand typeh W/m2 KUncertainty W/m2 K
1.0Olivine117.29±1.14
Fine silica107.05±1.00
3.0Olivine161.02±1.97
Fine silica141.03±1.85
a

These values are a slight modification of our previously published report in SolarPACES 2011 [16].

Finned Tubes Experiment.

The measured values for the heat transfer coefficient are reported in Table 3. In this table, the heat transfer coefficients have been adjusted for surface efficiency as described below. The dimensions of the finned tubes are as shown in Fig. 5.

Fig. 5
Dimensions (in inches) for the finned tubes used in the experiments, fin
                            pitch is 1/8 in
Fig. 5
Dimensions (in inches) for the finned tubes used in the experiments, fin
                            pitch is 1/8 in
Close modal
Table 3

Mean heat transfer coefficient for finned tubes

Sand velocity mm/sSand typeηfin %ηarea %h W/m2 KUncertainty W/m2 K
1.0Olivine88.1589.2547.81±1.23
Fine silica86.5487.7857.70±3.94
Fracking sand89.0590.0642.54±1.71
3.0Olivine81.5083.2191.70±4.97
Fine silica79.8081.66104.30±1.01
Fracking sand79.6281.50105.62±5.08
Sand velocity mm/sSand typeηfin %ηarea %h W/m2 KUncertainty W/m2 K
1.0Olivine88.1589.2547.81±1.23
Fine silica86.5487.7857.70±3.94
Fracking sand89.0590.0642.54±1.71
3.0Olivine81.5083.2191.70±4.97
Fine silica79.8081.66104.30±1.01
Fracking sand79.6281.50105.62±5.08

Sand Vibration Experiment.

Even though it might seem intuitive that the heat transfer coefficient of sand should increase by vibrating the surfaces, experiments with finned tubes shows that this is not true. To asses this possibility, a vibrator was attached to a wooden adapter covering a wall of the test section of the finned tube experiment (Fig. 2(c)), and the frequency of the vibration was increased by increasing the vibrator's voltage. As shown in Fig. 6, as the frequency of the vibration is increased, the average surface temperature of the upper (Tavg,ut) and the lower (Tavg,lt) finned tubes increases, while the incoming sand temperature (Tinc) is not affected strongly by the vibrations. As a result, the heat transfer coefficient drops. The simplest explanation may be the well-known tendency of particles to move apart under a shearing stress. If this happens at the surface, then the solid particles will move away from the heat transfer surface and thereby increase the void fraction around the tube. This results in an effectively thicker air layer and lower convection coefficient.

Fig. 6
Effect of vibration on the surface temperature and heat transfer
                            coefficient
Fig. 6
Effect of vibration on the surface temperature and heat transfer
                            coefficient
Close modal

Discussion

In evaluation of our results, it can be seen from Tables 2 and 3 that the heat transfer coefficient of bare tubes is larger than that of finned tubes. However, heat transfer is still enhanced by the larger area in the finned tubes case, which in our experiment is about 12 times the area of bare tubes
hbaretubes=qtApθb   hfinnedtubes=qtηareaAtθb
(2)

Note that in the finned tube case a surface efficiency must be introduced because the fins are at lower temperature than the tube wall, which is the base of the fins. The surface efficiency depends on the fin efficiency, which in turn depends on the convection coefficient.

The fin efficiency accounts for the temperature drop across the fins. The purpose of fin efficiency calculations is to provide a measure of the actual heat transfer coefficient. As quoted in Incropera [17], the fin efficiency of annular fins can be calculated as a function of radius ratio and a dimensionless transport group resembling the square root of a Biot number, or
ηfin=f(r2r1,Lc32(hkAp)12)
(3)
And the total area efficiency is
ηarea=qtqmax=qthAtθb=hbaseh
(4)

The heat transfer rate was measured for each run using an Instek GPM-8212 electronic power meter. The finned tube area At can be calculated from the tube dimensions shown in Fig. 5. Hence, hbase defined by Eq. (1) (this value assumes a 100% fin efficiency), can be calculated. This value for the convection coefficient can be used to determine the fin efficiency according to Eq. (3). The actual heat transfer coefficient for the finned tube, h, and the fin efficiency can then be found by iteration as outlined in Appendix A. The relationship between the fin efficiency and the heat transfer coefficient is shown in Fig. 7.

Fig. 7
Fin efficiency for annular tubes correlation used in Refs. [17] and [18]
Fig. 7
Fin efficiency for annular tubes correlation used in Refs. [17] and [18]
Close modal

The absolute uncertainty for thermocouple readings was measured using a water bath (Fig. 8) to be 0.28 °C. It can be seen from Eq. (1) that the uncertainty for the heat transfer coefficient is highly dependent on the uncertainty of the temperature difference, ΔT, between the tube's surface and the sand flow. For a small ΔT (around 2.5 °C for the 100 W case), the uncertainty in the ΔT becomes comparable to the temperature difference itself, leading to a high level of uncertainty. Since the heat transfer coefficient is not influenced by the power input to the heat exchanger (as can be seen in Fig. 4(b)), the uncertainty was calculated for the high power case only (350 W). Using a software tool called Engineering Equations Solver (EES) [18], uncertainty propagation analysis was performed to evaluate the bias error, Ub, due to the uncertainty in the fin dimensions and the bias in temperature readings. The random error, Ua, was found by taking the 95% confidence limit for the heat transfer coefficient. The procedure for this calculation is given in Appendix B. Combined uncertainty results are reported in Tables 2 and 3. It can be seen that the uncertainty increases with the flow rate. The reason is that the temperature difference becomes lower at higher flow rates, which increases the uncertainty.

Fig. 8
Thermocouple calibration using water bath
Fig. 8
Thermocouple calibration using water bath
Close modal

Conclusions

This study was conducted within the framework of a project where sand is used as the heat transfer and energy storage medium in central receiver systems. This system employs a sand–air heat exchanger that is intended to transfer the heat gained by the sand from the heliostat field to air, which can then be fed to an appropriate gas cycle. Due to the importance of proper sizing of the sand–air heat exchanger in such a system, it was necessary to understand the heat transfer characteristics of bulk flow of sand across tube banks. In this paper, preliminary experimental results were presented for the bulk flow of silica and olivine sand across a tube bank consisting of eight tubes arranged in three rows in a staggered formation. The tubes were heated, and two of them were instrumented with five thermocouples on their surfaces to assist in measuring the effective heat transfer coefficient. In another arrangement, finned tubes were instrumented with three thermocouples. The effect of input power and sand velocities were studied. We have found that the heat transfer coefficient was virtually independent of the power input for the range we examined. It was also found that the grain size and the type of sand (olivine or silica) do not influence the heat transfer coefficient noticeably. Vibrating the apparatus, instead of enhancing heat transfer, was found to have adverse effects on the heat transfer coefficient. Increasing sand velocity, however, was found to improve the heat transfer coefficient significantly, and this effect is currently under more research.

This preliminary investigation has shown that the values of the heat transfer coefficient are high enough to make the size of sand–air heat exchangers manageable and affordable. This finding is particularly relevant to the future design of large-scale systems, where it is crucial that the economics of using sand as the heat transfer and energy storage medium be favorable compared to existing systems.

    Nomenclature
     
  • Af =

    total finned area (m2)

  •  
  • Ap =

    prime area, surface of the tube (m2)

  •  
  • At =

    total heat transfer area for finned tubes, surface of the tube plus the surface of the fins (m2)

  •  
  • h =

    heat transfer coefficient (W/m2 K)

  •  
  • hbaretubes =

    heat transfer coefficient of bare tubes (W/m2 K)

  •  
  • hbase =

    heat transfer coefficient at the base (W/m2 K)

  •  
  • hfinnedtubes =

    heat transfer coefficient of bare tubes (W/m2 K)

  •  
  • h¯ =

    average value for the heat transfer coefficient at steady-state (W/m2 K)

  •  
  • k =

    thermal conductivity (W/m K)

  •  
  • Lc =

    characteristic length (m)

  •  
  • qt =

    total heat transferred across the tube (W)

  •  
  • qmax =

    maximum heat that could be transferred across the tube

  •  
  • q" =

    heat flux (W/m2)

  •  
  • r1 =

    outer radius of the tube (m)

  •  
  • r2 =

    distance from the center of the tube to the tip of the fin (m)

  •  
  • Tinc =

    incoming sand temperature ( °C)

  •  
  • T¯tube =

    average sand temperature ( °C)

  •  
  • Ua =

    random uncertainty (W/m2 K)

  •  
  • Ub =

    bias uncertainty (W/m2 K)

  •  
  • Uc =

    combined uncertainty (W/m2 K)

  •  
  • ηarea =

    overall surface efficiency (%)

  •  
  • ηfin =

    fin efficiency (%)

  •  
  • θb =

    temperature difference between the tube and the incoming sand ( °C)

  •  
  • σh =

    standard deviation of the heat transfer coefficient (W/m2 K)

Appendix A: Calculating Fin Efficiency

Procedure for calculating the heat transfer coefficient from experimental data is given in Eqs. (A1)(A4). First, start by an estimate of h by assuming 100% fin efficiency
hi=hbase=qtAtθb
(A1)
Then, find the estimated fin efficiency
ηfin,i=f(r2r1,Lc32(hikAp)12)
(A2)
and the corresponding area efficiency
ηarea,i=1-AfAt(1-ηfin,i)
(A3)
which gives improved estimate of h
hi+1=qtηarea,iAtθb
(A4)

then iterate until the estimated and calculated values of h agree (repeat Eqs. (A2)(A4) until hi+1=hi).

Appendix B: Calculating Error

EES [18] calculates the propagation of bias error from each of the experimental variables xi

Using the familiar formula
Ub2=i=1n(hxiUb,xi)2
(B1)

The bias error was taken to be 0.001 in. due to resolution limits for all fin dimensions and 0.281 °C for temperature readings from the calibration results. The power input is 350 W with error of 2.7 W based on manufacturers specs.

The average value at steady-state and the standard deviation is calculated from
h¯=1ni=1nhi
(B2)
σh=1n-1i=1n(hi-h¯)2
(B3)
This calculation was performed for each run, the random error (95% confidence) is found from
Ua2=(1.96σhn)2
(B4)

This random error includes the random error in temperature readings and power fluctuations.

The combined error is
Uc=Ua2+Ub2
(B5)

For the finned tubes, the nominal heat transfer coefficient (and its uncertainties) defined in Eq. (3), was evaluated and then corrected by the area efficiency.

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