Heat transfer and residence time distribution of liquid flow in direct contact evaporation heat exchanger

Journal Pre-proof Heat Transfer and Residence Time Distribution of Liquid Flow in Direct Contact Evaporation Heat Exchanger Hailing Fu (Conceptualization) (Methodology) (Software) (Data curation) (Visualization) (Investigation) (Validation)

PII:

S0255-2701(19)31289-9

DOI:

https://doi.org/10.1016/j.cep.2020.107829

Reference:

CEP 107829

To appear in:

Chemical Engineering and Processing - Process Intensification

Received Date:

14 October 2019

Revised Date:

19 December 2019

Accepted Date:

20 January 2020

Please cite this article as: Fu H, Heat Transfer and Residence Time Distribution of Liquid Flow in Direct Contact Evaporation Heat Exchanger, Chemical Engineering and Processing Process Intensification (2020), doi: https://doi.org/10.1016/j.cep.2020.107829

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Heat Transfer and Residence Time Distribution of Liquid Flow in Direct Contact Evaporation Heat Exchanger

Hailing Fu*,†

†

School of Control Engineering, Northeastern University at Qinghuangdao, Hebei Qinhuangdao 066000, China

AUTHOR INFORMATION

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Corresponding Author *E-mail: [email protected]

ORCID

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Hailing Fu: 0000-0001-7306-3203

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Highlights:

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Graphical Abstract

SK direct contact heat exchanger is used to exploit low-grade thermal energy.

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The effect of SK elements on heat transfer performance is analyzed.



Effect of number, length-diameter ratio of elements and pipe diameter are studied. 1



MRT and heat transfer coefficient are significantly increased by SK elements.

ABSTRACT: To enhance the heat transfer of liquids, a new gas-liquid-liquid three-phase exchanger based on the SK elements was proposed for utilization in energy recovery. Visual experimental investigation of the particle transport characteristics was carried out. The effects of the flow velocity, pipe diameter, arrangement, number and length-to-diameter ratio of elements on the mean residence time (MRT) were studied. An analysis of the velocity distribution of the particles of the operated cell through the SK element was performed. A

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pentane-water direct contact evaporation heat transfer experiment was carried out to investigate the effect of the SK elements on the heat transfer performance. The results indicated that the SK elements reduced the evaporation height, and the volumetric heat transfer coefficient was more than two times greater than that in

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the heat exchanger without the SK elements.

Keywords: Residence time distribution; Mean residence time; SK; Direct contact heat exchanger; Heat

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transfer coefficient.

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Abbreviations COV= coefficient of variation Pe =Peclet number

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CS= cross section

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DCEHE= direct contact evaporation heat exchanger MRT= mean residence time RTD= residence time distribution

NOMENCLATURE A= cross-sectional area of heat exchanger, m2 2

c= concentration, mol/L 𝐶𝑝 = water specific heat, KJ /(kg∙°C) D= diameter of heat exchanger, mm E(t)= residence time distribution function ℎ= pentane latent heat of vaporization, KJ/kg ℎ𝑣 = volumetric heat transfer coefficient, KW/(m3·°C) H= effective height of heat transfer, m

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L/D= length-diameter ratio of element 𝑚𝑐 = mass flow rate of water, kg/h 𝑚𝑑 = mass flow rate of pentane, kg/h

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𝑁= number of elements

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Q= heat, KJ

𝑡𝑚 = mean residence time, s

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t= dimensional time, s

∆T= log-mean temperature difference, °C

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T= axial temperature, °C

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𝑇𝑖 = inlet water temperature, °C

𝑇𝑜 = outlet water temperature, °C

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𝑇𝑑 = boiling temperature of pentane. °C u= water flow velocity, m/s 𝜎 2 = variance

1. INTRODUCTION Energy conservation has become an important subject as energy shortages have worsened and the 3

worldwide demand for energy has rapidly grown in recent decades 1. Accordingly, heat recovery processes, especially the processes that exploit industrial and interfacial low-grade thermal energy resources, have received an increasing amount of attention 2. One challenge that arises in waste heat recovery scenarios is that the thermal energy availability may not be synchronized with the demand3, 4. The use of a direct contact evaporation heat exchanger (DCEHE) in such processes could be suitable due to its high thermal efficiency and low cost. Direct contact heat transfer is the core technology in DCEHE and has been considered to be an effective approach for the reasonable utilization of existing energy. DCEHE has many advantages over the

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traditional surface type heat exchanger for the enhancement of the overall energy conversion efficiency and output power. For example, the direct contact device can work at a lower temperature difference between the continuous phase and diffusion phase fluids, and obtain a larger heat transfer coefficient5. Because of direct

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contact evaporation heat exchangers’ promising capabilities, it is the focus of current research. These

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investigations were performed within the context of many different industrial processes, such as water desalination, heat pump, power generation from geothermal energy and heat recovery from low-grade energy

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resources 6.

The mixing performance of immiscible gas-liquid-liquid three phase fluids has an important influence

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on the direct contact evaporation heat transfer. The mixing between two immiscible liquids is also a major

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challenge in the engineering processes. Compared with the mechanical stirring elements, the energy consumption of the static mixing elements is lower 7. When the static mixing elements are installed in the pipe,

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the fluid flows through the elements and is redistributed. The main energy consumption is due to the fluid being transported through the pump, which increases with the pressure drop. Thus, the pressure drop and fluid velocity constitute the driving force of the fluid flowing through the mixing elements8. Static mixing elements increase the metal-to-fluid surface area in the traditional surface type heat exchanger. In the direct contact heat exchanger, the mixing elements change the distribution of the fluid by redistributing the fluid flow. It can 4

make the mixture of continuous phase and diffusion better, which could promote the liquid-liquid interface heat transfer and increase the heat transfer coefficients. The hydrodynamic information such as the residence time distribution (RTD) is very important not only for the design of the reactor/mixer/heat exchanger but also for the optimization of process performance9-11. The diagnostics and the characterization of the mixing process can be obtained by residence time distribution curves. The mixing or heat transfer device can be compared with the ideal mixing models by the RTD curves. Some non-ideal features of the heat exchanger, such as short circuits and dead zones, can be obtained by

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analyzing the shapes of RTD curves and so on 12. The flow velocity and element numbers are found to have an important influence on the residence time distribution in tubular reactor equipped with screen-type static mixers 13.

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The Kenics® KM mixer is considered as a heat exchanger in the study. The heat exchange efficiency of

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this heat exchanger under the same heat exchange area is compared with that of the empty tube heat exchanger, and the thermal efficiency of this heat exchanger with static mixing elements is much higher than that of the

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empty pipe14. However, current research on such devices with static mixing elements focuses on using them as mixers and reactors rather than heat exchangers

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. In previous work, RTD in a Kenics static mixer are

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studied experimentally 16, 17. SK elements are used to promote fluid mixing and thus reduce the temperature

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gradients in the process of fluid mixing. SK elements have been widely used for a variety of mixing applications, such as liquid-liquid mixing, single-phase homogenization and gas-liquid mixing.18, 19.Through

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the analysis of the literature, a large number of work have focused on the study of single phase flow, and only a few reports had studied the two-phase flow 20. Additionally, previous investigations have focused on the mixing without the phase change. In this paper, an SK direct contact evaporation heat exchanger is developed as a new type of heat transfer equipment in the heat pump. We seek to investigate the direct contact evaporation heat transfer process with 5

high-efficiency SK elements that can enhance heat transfer by improving the mixing. As a key factor in the mixing and heat transfer process, the residence time distribution is the focus of research. A series of experiments about the residence time distribution were carried out in this SK direct contact heat exchanger. The effects of the flow velocity, number of elements, pipe diameter, elements’ arrangement, and elements length-to-diameter ratio on the MRT and RTD are studied. The evaporation height and volumetric heat transfer coefficient for the SK heat exchanger and an empty pipe are compared during the heat transfer process. This is aimed at the elucidation of the influence of the addition of SK static mixing elements on the heat transfer in

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the direct contact heat exchanger.

2. EXPERIMENTS

2.1 Residence time distribution experiment. The experimental setup consisted of a heat exchanger

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with eight SK elements. Fig.1 showed the heat exchanger setup used to study the residence time and mixing

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characteristics in the heat exchanger with SK elements. The heat transfer was configured vertically, with the water entering at the bottom. In order to observe the flow state and the mixing and evaporation phenomena,

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the SK heat exchanger was made of glass. The total height of the heat exchanger was 1000 mm, and the experimental parameters were shown in Table 1. The SK heat exchanger consisted of eight mixing elements

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aligned at 90°. These SK elements were arranged in three different ways (F1, F2, and F3) in the heat exchanger

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for different experiments in order to study the influence of the arrangement of the SK elements. In F1, the elements were arranged axially according to alternating clockwise and counterclockwise twists within a tube

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so that the leading edge of an element was at a right angle to the trailing edge of the previous element. For F2, the elements were arranged with two clockwise and two counterclockwise twists so that the first two elements had the same twist direction. For F3, the elements were arranged with four clockwise and four counterclockwise twists so that the first four elements had the same twist direction. A monitor was placed after each pair of SK elements, and measurements were conducted for four pairs of mixing elements at the same 6

time. The experiment consisted of two parts, the RTD experiment and the direct contact heat transfer experiment. In the residence time experiment, RTD was determined by the pulse input-response method. The water was pumped into the SK direct contact heat exchanger through the flow meter and the pentane inlet valve was closed. A saturated salt solution (NaCl) was used as a tracer and was injected instantaneously during the experiment. The change in the conductivity with the time was measured by a conductivity meter. The conductivity voltage signal was sampled using a data logger (DI-710, Quatronix Company, USA) and the salt

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solution concentration was determined through linear relations.

2.2 Direct contact evaporation heat transfer experiment. To evaluate the effect of the SK elements on the direct contact vaporization heat transfer in the SK heat exchanger, water and pentane were

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used as the working fluids, and the properties of n-pentane were listed in Table 2. The experiment device

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schematic diagram was depicted in Fig.1. The water tank was fitted with a heating device and designed as a constant temperature water bath. Water and pentane were injected from the bottom of the pipe by the pump

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through the flow meter, separately. To enable better dispersal of pentane, a distributor was made with twelve circular holes with a diameter of 3 mm. In the pentane-water direct contact heat transfer during the experiment,

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the pentane liquid was heated to pentane vapor by hot water, and gas-liquid mixtures were separated in the

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gas-liquid separator. The separated pentane vapor was condensed into pentane liquid through the shell and tube heat exchanger, and then flowed back to the pentane tank. On the other hand, the separated water flowed

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back to the water tank and heated to the desired temperature of the experiment. Two Pt100 resistance thermometers were placed at the inlet and outlet of the heat exchanger, respectively, to measure the water temperature. The water and pentane flow rates were measured by a flowmeter (LZB-4, accuracy ±1.0%, Jiangsu Dong Xin Instrument Co., Ltd., China). A standard thermocouple was used to calibrate the thermocouples used in the experiment. Due to the heat conduction in the steady state, the wall 7

temperature of the heat exchanger body could reflect the trend in the temperature variation. To calculate the evaporation height, a thermal infrared imager (SAT-90, image resolution 640×480, accuracy ±2°C, Guangzhou SAT Infrared Technology Co., Ltd., China) was used to obtain continuous variation of the axial temperature along the heat exchanger when evaporation occurred. IR thermography was highly accurate for the temperature differences but was not as precise for the temperature magnitude. Therefore, an in situ calibration was used for accurate temperature measurement21.

3. METHODOLOGY

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3.1. RTD analysis. The residence time distribution is an important parameter for quantifying the fluid flow and mixing performance in heat exchanger 22. The in-line measurement is an important approach to obtain the residence time distribution. The residence time distribution density function, E(t), can be written as 23:

E(t) = ∑𝑛

𝑐(𝑡𝑖 )

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𝑖=1 𝑐(𝑡𝑖 )∆𝑡

(1)

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where c(t) is the molar concentration in the measured section.

The mean residence time (MRT) can be used to characterize dead zones and short circuits in the heat

∑𝑛 𝑖=1 𝐸(𝑡𝑖 )

=

∑𝑛 𝑖=1 𝑡𝑖 𝑐(𝑡𝑖 ) ∑𝑛 𝑖=1 𝑐(𝑡𝑖 )

(2)

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𝑡𝑚 =

∑𝑛 𝑖=1 𝑡𝑖 𝐸(𝑡𝑖 )

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exchanger. The mean residence time, t 𝑚 , can be defined as follows:

Another important parameter is the coefficient of variation, which reflects a combination of the first and

𝜎 𝑡𝑚

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COV =

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second moments of the distribution 24. The coefficient of variation, COV, can be written as follows: (3)

where σ is the concentration variance in the measurement cross section: 2

𝜎 =

2 ∑𝑛 𝑖=1 𝑡𝑖 𝑐(𝑡𝑖 )

∑𝑛 𝑖=1 𝑐(𝑡𝑖 )

2 − 𝑡𝑚

(4)

COV = 0 represents a complete distributive mixing, while COV = 1 represents a total segregation 24. The Peclet number is the ratio of the convection rate to the diffusion rate, which indicates the degree of 8

axial dispersion of heat exchanger. The Pe can be calculated as follows 25: 𝜎2 2 𝑡𝑚

=

2𝑃𝑒+8

(5)

𝑃𝑒 2

A larger 𝑃𝑒 value indicates smaller dispersion in the direct contact evaporation heat exchanger.

3.2 Numerical procedure. For computational efficiency, the current simulation is performed only in a 2D domain, which is found to be sufficiently accurate to predict the RTD. The residence time distribution and velocity fields of SK heat exchanger are simulated with FLUENT software. To carry out the unsteady numerical simulations of the flow, the fluid is modeled, and the equations are solved by the Eulerian method.

𝜕𝑡

+ ∇ ∙ (𝜌𝑣⃗) = 0 ⃗⃗ 𝜕𝑣

ρ( 𝜕

𝜕𝑡

𝜕𝑡

+ 𝑣⃗ ∙ ∇𝑣⃗) = −∇p + μ∇2 𝑣⃗

𝜌𝑌𝑘 + ∇(𝜌𝑣⃗𝑌𝑖 ) = −∇ ∙ ⃗⃗⃗⃗ 𝐽𝑘

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𝜕𝜌

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The mass conservation, Navier-Stokes and species transport equation are expressed as follows23: (6) (7) (8)

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where 𝑌𝑘 is the mass fraction of the species and ⃗⃗⃗⃗ 𝐽𝑘 is the diffusion flux of the species. A method for online measurement of the RTD that was previously used by Zhang29 is utilized in this study.

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The simulation of residence time distribution is divided into two steps. The first step, the Eulerian method with RNG k–ε model is used in order to get the velocity fields inside the SK heat exchanger accurately. The

𝜕𝑥𝑖 𝜕 𝜕𝑥𝑗

(𝜌𝑔 𝑘𝑢𝑖 ) = (𝜌𝑔 𝜖𝑢𝑖 ) =

𝜕 𝜕𝑥𝑗 𝜕

)

𝜕𝑘

[(𝜇 + 𝑡)

𝜕𝜀

[(𝜇 +

𝜇𝑡

𝜎𝑘 𝜕𝑥𝑗

𝜇

] + 𝐺𝐾 − 𝜌𝑔𝜀

] + 𝐶1𝜀

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𝜕

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K Equation and ε Equation are expressed as follows30:

𝜕𝑥𝑗

𝜎𝜀 𝜕𝑥𝑗

𝜀

𝑘

𝐺𝐾 − 𝐶2𝜀 𝜌𝑔

(9) 𝜀2 𝑘

(10)

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The second step is to simulate the virtual tracer experiment of residence time, in which a non-reacting tracer transport equation is solved by using the flow field obtained in the previously step. The virtual tracer and simulation fluid are the same as those of the experiment. At the tracer entrance, to achieve the impulse input, its injection time is set to a time step. The tracer concentration at the four different cross-sections varies with time is monitored starting immediately after the “tracer injection”. The instantaneous tracer concentration 9

is computed in the measure section using an area-weighted average approach. The tube wall inner surface is set to non-slip and adiabatic boundary conditions. The rest of the operating conditions and the data processing methods are the same as the experiment. The local magnification of the SK direct contact heat exchanger is shown in Fig.2.

3.3 Heat transfer analysis. The direct contact evaporation heat transfer mainly occurs on the liquidliquid contact interface between dispersed phase pentane liquid and continuous phase hot water. During the heat transfer experiment, the dispersed droplet in the continuous phase solution will become a droplet with

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the coexistence of vapor and liquid phases due to the process of vaporization. These gas-liquid droplets are called bubbles. In the process of rising, the pentane drobbles are affected by various forces. It is difficult to obtain the area of liquid-liquid heat transfer accurately because of the coalescence and breakup of drobbles

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group. In order to study the overall heat transfer characteristics of heat exchanger, the overall volumetric

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heat transfer coefficient ℎ𝑣 is proposed to represent vaporization heat transfer performance of drobbles group. The volumetric heat transfer coefficient can be written as follows 26, 27: 𝑄

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ℎ𝑣 =

𝐴𝐻∆𝑇

(11)

where Q is the heat exchange rate from the hot water to the pentane droplets in the heat exchanger, A is the

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temperature difference.

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cross section area of heat exchanger, H is the effective height of heat exchanger, and ∆𝑇 is the log-mean

It is assumed that pentane droplets are vaporized completely in the SK direct contact heat exchanger, the

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heat transfer rate Q could be calculated as follows: Q = 𝑚𝑐 𝐶𝑝 (𝑇𝑖 − 𝑇𝑜 ) = 𝑚𝑑 ℎ

(12)

where 𝑚𝑐 is the mass flow rates of water, 𝑚𝑑 is the mass flow rate of pentane liquid, 𝑇𝑖 is the inlet water temperature, 𝑇𝑜 is the outlet water temperature, ℎ is the latent heat of pentane vaporization and 𝐶𝑝 is the specific heat capacity of water. 10

The log-mean temperature difference is considered to be the actual temperature driving force in a heat exchanger. The log-mean temperature difference, ∆T, can be written as follows:

∆T =

(𝑇𝑖 −𝑇𝑑 )−(𝑇𝑜 −𝑇𝑑 )

(13)

𝑇 −𝑇 log( 𝑖 𝑑 ) 𝑇𝑜 −𝑇𝑑

where 𝑇𝑑 is the boiling temperature of pentane.

4. RESULTS AND DISCUSSION 4.1. Influence on MRT in the SK direct contact evaporation heat exchanger. The performance of MRT has a great influence on heat transfer efficiency in the direct contact evaporation heat exchanger, and

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the MRT is mainly affected by various operating conditions and equipment parameters 18. The effects of the pipe diameter on MRT with elements length-to-diameter ratio of 1.5 and elements arrangement of F1 are

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shown in Fig.3. The MRT is shortened with the decreasing pipe diameter. The origin of this phenomenon may be explained as follows. Under the same length-to-diameter ratio of the element, the increased diameter result

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in the length increase of heat exchanger. Thus, the residence time is longer at the larger diameter heat

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exchanger.

As seen from Fig.3, the MRT inside the SK direct contact heat exchanger increases along with increasing

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the number of elements within the scope of the study. Axial transport of the particles mainly occurs on the surfaces of the SK elements, which affects the MRT. With the number of elements increases, more time will

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be required in every cycle of the “cutting- moving- rejunction” process. Thus, the time spent by the particles

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on the detection surface increases, decreasing the particle axial velocity and finally leading to the increase in the MRT.

In general, dynamic characteristics of the particles are directly determined by the flow velocity. Fig. 4 shows the MRT for the fluid flow in the heat exchangers with different arrangements of elements and compares the result to that obtained in an empty pipe with the equivalent cross section. In the direct contact evaporation heat exchanger with a length-to-diameter ratio of the elements of 1.5, the flow velocity increases from 0.06 11

m/s to 0.12 m/s, and the MRT decreases from 54.13 s to 13.23 s. The decreasing ratio is approximately 75.6% for the MRT when the change in the flow velocity is 100%. Similarly, in the empty pipe, when the flow velocity increases from 0.06 m/s to 0.12 m/s, the MRT decreases from 10.16 s to 3.43 s, and the MRT decreases nearly 66.2%. In the direct contact evaporation heat exchanger, the particles are transported by the SK elements. During the “cutting- moving- rejunction” process, the axial dispersion is enhanced. On the other hand, the SK elements hindered the flow of the fluid. In the interaction of the flow and SK elements, the MRT increased Compared to the increase in the flow velocity, the change in the SK elements arrangement has little

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influence on the MRT. The dimensionless variance is presented in order to compare the influence of different length-to-diameter ratios of the SK elements in Table 3. The analysis for 𝜎𝜃2 indicates that the value for L/D=1 is less 60% of

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that of L/D=1.5. The RTD for L/D=1 shows more convergence and an absence of obvious back flow, and the

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flow tends to be the ideal flow. The reasons can be explained as follows. On the one hand, a helical motion under the pressure of the axial gradient is present when the fluid moves through the SK mixing elements.

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The update frequency of the tracer in the radial direction increased. The fluid turbulent intensity is intensified by the SK mixing elements because of the strengthening of periodic dissection and secondary flow in the

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radial direction at the smaller length-to-diameter ratio elements. On the other hand, decreasing the length-

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diameter ratio can reduce the stagnation zone and channeling within the heat exchanger.

4.2. RTD in SK direct contact evaporation heat exchanger. The channeling is not found in the

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SK direct contact evaporation heat exchanger because all RTD curves are single-peak distributions, As seen from Fig.5, the earliest sharp peak is observed in N=2 (testing section CS1)because the tracer signal is observed earliest for N=2 and N=8 (testing section CS4) is the last. The curve peaks decrease, and the curve widths increase axially at the same flow velocity. The particle amounts in the forward region are large as seen from the steep slope of the RTD curve. This shows that the flow was influenced by the by-passing, and a 12

deviation from the perfect flow is observed in the system. It is the same as that in the back-mixing analysis in that the effect of by-passing on the flow can be reduced by increasing the number of elements. With the decreasing pipe diameter, the peak value increases gradually. Fig.6 shows the effect of the pipe diameter at 40 mm and 80 mm on the E(t) curves at different flow velocities (0.06, 0.08,0.10 and 0.12 m/s) at the same testing section with elements length-to-diameter ratio of 1.5 and elements arrangement of F1. As with the same water flow velocity, increasing the pipe diameter significantly increases the residence time and shifts the E(t) curves to the right. As the pipe diameter decreases, the curve of RTD becomes narrow, and shifts

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to an ideal plug flow. In the case of higher velocity, the residence time of the particles in the SK direct contact heat exchanger is reduced and the peak of the E(t) curve moves towards a short residence time. On the other hand, the E(t) curve is narrower and there is no obvious trailing. This means that the back mixing could be

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reduced by an increase in the flow velocity or a decrease in the pipe diameter. The dead zone exists in the SK

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direct contact evaporation heat exchanger because the RTD curves showed some delay. However, the dead zone could be shortened by increasing the flow velocity or by decreasing the pipe diameter because the decay

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phenomenon is not obvious with an increase in flow velocity. This is clearly observed in Fig.6 where the E(t) of two heat exchanger diameters at different flow velocities are plotted.

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Fig.7 shows the variation in the Peclet number (Pe) with the flow velocity for a constant number of

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elements with elements length-to-diameter ratio of 1.5 and elements arrangement of F1. The results indicate that the Peclet number decreases with an increase in the flow velocity both with and without the SK elements.

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The values of the Peclet number with the SK elements are higher than those without the SK elements. With the introduction of the SK elements into the direct contact evaporation heat exchanger, one important aspects is that the SK elements causes more axial diffusion as the velocity increased. The higher Peclet number indicates an increase in the convection rate, and the higher convection rate is beneficial for the direct contact evaporation heat transfer. Fig.7 also shows the comparison of the Pe between the two different diameters heat 13

exchangers. The results indicate that the values of the Pe in the 40-mm diameter heat exchanger are larger than those in the 80-mm diameter heat exchanger at the same flow velocity. Similar behavior can be found when comparing the coefficient of variation in the SK heat exchanger with elements length-to-diameter ratio of 1.5 and elements arrangement of F1. As seen from Fig.8, the COV increases while the flow velocity increases. Compared with an empty pipe, the values of COV computed for the heat exchanger equipped with SK elements consistently is smaller. The results show that the SK direct contact heat exchanger leads to the better flow homogenization when compared to the empty tube.

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4.3 CFD simulation. The simulation operating parameters are shown in Table 4. Fig.9 shows that the computational curve agrees well with the experimental curve. The E(t) first increases and then decreases. The simulated data show

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the same trend, but the maximum is slightly different. The peak residence times are approximately 39 s, 24 s,

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13 s and 7 s for the four different flow velocities. The results of the calculation show minor differences compared to the experiment data available (less than 10%). This indicates that the simulation method can

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predict the RTD in the SK heat exchanger within certain error limits, and the simulation results are accurate and reliable. The mean residence times are approximately 42.08 s, 20.64 s, 15.44 s and 9.23 s, which are not

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in the flow process.

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much different from the peak residence times. This proves that there is no secondary flow in the heat exchanger

In order to investigate the effects of the geometric construction on the local velocity fields, the particle

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velocity distribution diagrams are shown in Fig.10. At the same flow velocity, the velocity profiles of these four different cross-sections were compared to evaluate the influence of SK elements and the position changes on the flow field. Fig.10 shows cross-sectional of the heat exchanger relative to its axial coordinates of Z = 1

/2L, L, and3/2L, 2L where L is the element length. At the end of the first element (Z=L), the appearance of the

four velocity fields is caused by the splitting and merging of the two flow fields from the previous element to 14

the latter element. It also causes a more violent collision and mixing of the fluid. When the fluid passes through the junction of two components, the four velocity fields become two velocity fields with a higher velocity in the center and a lower velocity in the sidewall. The time required to transport the particles near the wall out of the heat exchanger becomes very long, while the particles in the center are quickly transported out. Thus, an annular distribution of particles, as shown in Fig.10, is established. The non-uniform distribution of liquid velocity in the riser column can result in the back-mixing of particles. Then, longitudinal vortexes are formed, and many studies have showed that the longitudinal vortexes can reduce the temperature gradient and produce

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a more uniform temperature distribution. The fluid flows from the center of the element to the wall and back to the center continuously. This kind of flow improves the radial mixing and eliminates the temperature gradients. The heat exchanger with SK elements has double benefits because it can improve the heat transfer

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and increase the fluid mixing simultaneously. Fig.10 depicts the velocity distribution of the fluid across the

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sections of the SK mixed elements, which may correspond to the different features of the particle RTD curve. The back-mixing is further enhanced by the wall effect, prolonging the particle residence and hence giving

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rise to the trailing.

4.4 Evaporation height of the SK direct contact evaporation heat exchanger. The evaporation

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height is the heat exchanger height necessary for the volatile liquid to evaporate completely without

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superheating. Fig.11 shows an example of the measured method to get evaporation height. Fig.11a is IR color image. It is obtained by the thermal infrared imager, and used to determine the axial temperature distribution

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of the SK direct contact evaporation heat exchanger. Axis L1 is drawn up and Fig.11b is the temperature distribution corresponding to L1. Then the evaporation height is determined by this axial temperature distribution. The evaporation height results are presented in Fig.12. It is indicated that a higher inlet water temperature leads to a smaller optimal height for spontaneous evaporation. The evaporation height was varied from 0.7 m to 0.2 m during the inlet water temperature from 37°C to 44°C. On the other hand, the evaporation 15

height is significantly reduced because of the SK elements. The biggest drop was about 35% when the inlet water temperature was smaller than 41°C. Thus, filling with SK elements could reduce the height of the heat exchangers and optimize the heat exchanger structure.

4.5 Overall volumetric heat transfer coefficient of the SK direct contact heat exchanger. The overall volumetric heat transfer coefficient was an important index for the characterization of heat transfer capacity. Fig.13 shows the relationship between the volumetric heat transfer coefficient and the inlet water temperature of SK heat exchanger and empty pipe. The experiment results indicate that the overall volumetric

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heat transfer coefficient decreases with the increase of inlet water temperature from 37°C -42°C. Meanwhile, hv has a little change under the inlet water temperature of 42°C -44°C. The overall volumetric heat transfer coefficient varies between 66 and 243 kW/(m3∙°C) in the presence of SK elements, while values of 23 and

-p

123 kW/(m3∙°C)) are observed without SK elements under the inlet water temperature 𝑇𝑖 < 44°C. It is quite

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notable that the hv in the heat exchanger with the SK elements is almost two times greater than that without the SK elements. The heat transfer capacity is enhanced by the SK elements because of the excellent

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performance of mixing in SK direct contact heat exchanger especially in lower temperature difference. In the process of rising, the pentane droplets absorb heat from hot water and vaporize to drobbles. Pentane drobbles

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grow rapidly and produce polymerization and rupture, which could bring a violent disturbance to the fluid.

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The SK elements further promote the turbulence flow of the fluid, which could destroy the thermal boundary layer around the drobbles. It could result in the enhancement of the convective heat transfer between the

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pentane liquid and the hot water. On the other hand, the presence of the SK elements results in the transformation of the larger pentane drobbles to more numerous smaller drobbles. An increase in the number of drobbles will increase the pentane-water direct contact interface area. Overall, the new types of SK direct contact heat exchanger could improve the heat transfer performance, providing guidance for engineering applications. 16

5. CONCLUSIONS In this paper, a visual experimental investigation on the particle transport characteristics and heat transfer performance inside the SK pentane-water direct contact heat exchanger was carried out. The influences of the flow velocity, pipe diameter, arrangement, number and length-to-diameter ratio of elements on the residence time were studied. The velocity distribution diagrams were used to interpret the flow performance of particles through the SK element. The influences of the SK mixing elements on the evaporation height and volumetric heat transfer coefficient were studied.

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The results indicated that for a larger heat exchanger diameter, an increase in the number of elements and the length-to-diameter ratio increased the particles’ MRT. The RTD of the particles was similar to the normal distribution, and the dead zone could be shortened by increasing the flow velocity or decreasing the pipe

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diameter. The concentration variance in the cross-section showed that a more uniform mixing could be

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achieved with the SK elements. The velocity distribution breaks the original flow pattern, and the radial velocity promotes the degree of turbulence of the fluid. SK elements could reduce the evaporation height of

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the heat exchangers, and the overall volumetric heat transfer coefficient in the direct contact evaporation heat exchanger with the SK elements was more than two times greater than that without the SK elements. Due to

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longitudinal vortexes, the heat exchanger with the SK elements had a positive impact on the heat transfer,

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especially at lower temperatures. The SK direct contact heat exchanger could be widely used in heating

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recovery from low-grade energy resources.

Declaration of interests

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper

Author Statement

Hailing Fu: Conceptualization, Methodology, Software，Data curation, Writing, 17

Visualization, Investigation, Validation.

ACKNOWLEDGEMENTS The authors are grateful for the financial support by “Fundamental Research Funds for the Central Universities No.162303002” , “Natural Science Foundation of Hebei Province No.E2017501079” and “Doctoral Scientific

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Research Foundation of Northeastern University at Qinhuangdao No.XNB201713”.

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Figure Captions: Fig.1 Schematic of experimental system. Fig.2 Computational meshes of a part of SK direct contact heat exchchanger. Fig.3 Effect of pipe diameter on MRT for: (a) u=0.06m/s, (b) u=0.08m/s, (c) u=0.10m/s, (d) u=0.12m/s. Fig.4 MRT variable with the increasing flow velocity. Fig.5 Effect of elements numbers on E(t). Fig.6 E(t) under different pipe diameter for: (a) u=0.06m/s, (b) u=0.08m/s, (c) u=0.10m/s, (d)u=0.12m/s.

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Fig.7 Effect of flow velocity on Pe Fig.8 Effect of flow velocity on COV

Fig.9 Comparison of simulated and experimental results for RTD for: (a) u=0.06m/s, (b) u=0.08m/s, (c)

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u=0.10m/s, (d) u=0.12m/s.

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Fig.10 The velocity distribution diagrams for: (a) Z=1/2L, (b) Z=L, (c) Z=3/2L, (d)Z= 2L Fig.11 IR images for evaporative height: (a) IR color image; (b) continuous axial temperature distribution

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corresponding to L1 in IR color image (H from left to right stands for axial height of L1 from top to bottom) Fig.12 Evaporation heights between SK and empty pipe.

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Figures:

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Fig.13 Overall volumetric heat transfer coefficient between SK and empty pipe.

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Fig.2

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Fig.4

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Fig.6

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Fig.8

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Fig. 10

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H=0.3471m

（b）

（a）

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Fig. 11

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Fig.12

Fig.13

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Table Captions: Table 1 Experiment conditions parameters Table 2 Properties of n-pentane at 36.1oC Table 3 The dimensionless variance between different length-diameter ratios Table 4 Simulation operating parameters

Table 1

Value

Pipe diameter (D)

40mm, 80mm

Element length to diameter ratio

1.5,1

Elements arrangement

F1, F2, F3

Flow velocity of water (u)

0.06m/s, 0.08m/s ,0.10m/s, 0.12m/s

Testing location

CS1,CS2,CS3,CS4

Gas density (kg/m3)

Boiling point (oC)

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Liquid density (kg/m3)

3.0

Latent heat of vaporization ( kJ/kg)

36.1

358.2

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610.2

𝜎𝜃2

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Table 2

Table 3

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Parameter

CS1

CS2

CS3

CS4

L/D=1

0.195

0.091

0.048

0.027

L/D=1.5

0.305

0.194

0.177

0.175

Table 4 28

Parameter

Value

Pipe diameter (D)

40 mm

Element length-to-diameter ratio (L/D)

1.5

Elements arrangement

F1

Flow velocity of water (u)

0.06 m/s, 0.08 m/s,

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0.10 m/s, 0.12 m/s

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