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Experimental investigation on the flow and flow-rotor heat transfer in a rotor-stator spinning disk reactor
Applied Thermal Engineering 162 (2019) 114316
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Experimental investigation on the flow and flow-rotor heat transfer in a rotor-stator spinning disk reactor ⁎
Bo Hua, Xuesong Lia, Yanxia Fub, Fan Zhangc, Chunwei Gua, Xiaodong Rena, , Chuan Wangd,
T ⁎
a
Department of Energy and Power Engineering, Tsinghua University, Beijing 100084, China School of Energy and Power Engineering, Jiangsu University, Zhenjiang, Jiangsu Province 212013, China c National Research Center of Pumps, Jiangsu University, Zhenjiang, Jiangsu Province 212013, China d School of Hydraulic, Energy and Power Engineering, Yangzhou University Yangzhou, Jiangsu Province 225002, China b
H I GH L IG H T S
investigated the effects of axial gap and temperature on core swirl ratio. • We moment coefficient of rotor was analyzed according to the flow patterns. • The of the moment coefficient on the heat transfer were analyzed. • Effect • An empirical correlation for the average Nusselt number was determined.
A R T I C LE I N FO
A B S T R A C T
Keywords: Rotor-stator spinning disk reactor Core swirl ratio Moment coefficient Thermochromic liquid crystal Heat transfer
In this article, an experimental study has been conducted to provide better understanding of the flow and heat transfer characteristics in the front chamber of a rotor-stator spinning disk reactor. According to the measurements with a one-dimensional hot-wire anemometer probe, the effects of the axial gap width and the temperature on the core swirl ratio are investigated, which are ignored for the past decades. The values of the core swirl ratio are found to decrease by up to 12.2% when G increases from 0.0125 to 0.05 and reduce by up to 6% when the temperature rises from 300 K to 350 K. The measured moment coefficient, which primarily decides the energy dissipation rate, is analyzed according to the flow patterns for the first time. The transient thermochromic liquid crystal technique is used to estimate the heat transfer characteristic. The variations of the moment coefficient, the local Nusselt number and the average Nusselt number appear to be largely determined by the flow patterns. An empirical correlation of the average Nusselt number in the viscous section is determined for the first time, which is aimed to provide better predictions on the average heat transfer capacity. The interaction of the average Nusselt number with the moment coefficient is also introduced. It is speculated that the flow patterns in the chamber plays an important role in the energy dissipation and the heat transfer performance.
1. Introduction
1.1. Core swirl ratio and flow structure
The rotor-stator spinning disk reactors, abbreviated as RSSDRs, are important continuous flow reactors, where the change of turbulent flow type, energy dissipation, heat and mass transfer occur [1–6]. The model of a RSSDR is sketched in Fig. 1(a). The directions of the through-flow inside the reactor are both centrifugal (in the front chamber) and centripetal (in the back chamber). This paper takes into account the front chamber, where most of the mixing and the chemical reaction happen, as the research object. The corresponding model is a rotorstator cavity with centrifugal through-flow, shown in Fig. 1(b).
In a rotor-stator cavity, the radial distributions of the pressure p are extensively investigated and reported by a lot of researchers. The wellknown correlation, which associates the pressure with the core swirl ratio K , is defined in Eq. (1). The parameter K , defined in Eq. (2), is used to show the dominant tangential motion of the fluid. Obtaining the pressure distributions, the maximum axial thrust acting on the rotor can be predicted in order to design the bearing system.
⁎
∂p = ρ∙K 2 ∙Ω2∙r ∂r
Corresponding authors. E-mail addresses: [email protected] (X. Ren), [email protected] (C. Wang).
https://doi.org/10.1016/j.applthermaleng.2019.114316 Received 18 May 2019; Received in revised form 4 July 2019; Accepted 28 August 2019 Available online 29 August 2019 1359-4311/ © 2019 Elsevier Ltd. All rights reserved.
(1)
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Nomenclature
texp u∞ VF Vr
Latin Symbols
b Cw CM Cqr
G h
have K k l M ṁ Nu
Nuave
outer radius of the disk, mm ṁ , through-flow coefficient, − μ∙b 2∙ | M| , ρ ∙ Ω2 ∙ b5 Q ∙Reφ0.2
Vφ vr vφ x z
moment coefficient, − , local flow rate coefficient, − axial gap width, −
2 ∙ π ∙ Ω ∙r 3 s , non-dimensional b
local convective heat transfer coefficient, W/m2∙K ∫rcb 2hrdr b2 − rc 2
, average convective heat transfer coefficient,
α θ λt λtx
ζ μ ν ρ Ω Ωf
k
2hr 2dr k (b2 − rc 2)
, average Nusselt number, −
n p Q Qt q Re
speed of rotation, rpm pressure, bar volumetric flow rate per hour, m3/h volumetric flow rate per second, m3/s wall heat flux, W/m2 Ω ∙b2 , global circumferential reynolds number, −
Reφ r ri rc rrec Δr s sb so T T∞ t tmax tdisk
local circumferential reynolds number, − radial coordinate, m radial coordinate of the thermocouple no. i , mm inner radius where the measurements of h start, mm recovery factor radial gap from the disk to the wall, mm axial gap of the front chamber, mm axial gap of the back chamber, mm outlet width of the chamber, mm temperature, K temperature in the mainstream, K time, s 0.1 ∙ tdisk 2 , maximum experimental time, s α thickness of the disk
Ω∙b
non-dimensional tangential velocity, m/s non-dimensional radial velocity, m/s r , non-dimensional radial coordinate, – b radial coordinate
Greek Symbols
W/m2∙K Ωf , core swirl ratio, − Ω thermal conductivity, W/m∙K specific heat at constant pressure, J/kg∙K frictional torque, Nm ρ∙Qt , mass flow rate, kg/s h∙r , local nusselt number, − ∫rcb
time of exposure, μs velocity of the mainstream at ζ = 0.5 πb2s , volume of the front chamber, m3 vr , non-dimensional tangential velocity, − Ω∙b vφ , non-dimensional radial velocity, −
thermal diffusivity, m2/s non-dimensional temperature, − CW , turbulent flow parameter, − Re0.8 CW , flow pattern parameter, − Re1.2 z , non-dimensional s
axial coordinate, − dynamic viscosity of air, N∙s/m2 kinematic viscosity of air, m2/s , density of air, kg/m3 angular velocity of the disk, rad/s angular velocity of the fluid at half of the axial gap width, rad/s
Abbreviations B C CCD erfc FS fps HWA LDA PIV RSSDR rpm S TC TLC TR HWA
v Ω ∙r 2 , v
Batchelor Couette charge coupled device complementary error function full scale frames per second hot-wire anemometry laser doppler anemometry particle image velocimetry rotor-stator spinning disk reactor revolution per minute Stewartson thermocouple thermochromic liquid crystal thermal resistance hot-wire anemometry
Fig. 1. Meridional sketch of a RSSDR and the rotor-stator cavity model.
2
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< 0.0009
where K is the core swirl ratio, ρ is the density of the fluid.
K=
Ωf Ω
atζ = 0.5
(a) Section I
Qt ∙Reφ 0.2
s b
or Re is large, the values of λt are small, which represents the relatively stronger viscous force [11–13]. Ewa et al. [14,15] found out that, the C type flow may change to the B type flow with the increase of G or Re . Cooper and Reshotko [16] characterized the transition between the B type flow and the S type flow by LDA measurements. Debuchy et al. [17] and Hu et al. [18] investigated the velocity profiles of the above three flow types. Hu et al. [18] evaluated the effects of G and centrifugal through-flow on K when the flow change from the C type to the B type. Nguyen et al. [19] investigated the flow behaviors in a rotorstator system by PIV (Particle Image Velocimetry) measurements. According to the simulation results, Luo et al. [20] evaluated the influence of λt on the flow structure. They addressed that the parameter λt fails to entirely exclude the effects of Re . The flow pattern parameter λtx , defined in Eq. (8), appears to be a more appropriate form. When λtx is less than 0.0009, the cavity flow is in the viscous section (noted as Section 1). The mainstream totally flows to the rotor surface after entering the cavity, and then flows to the outlet near the surface of the rotor, shown in Fig. 3(a). The inlet flow rotates with the rotor due to the viscous force on the disk boundary layer in Section 1. When λtx ranges from 0.009 to 0.0028, the flow is considered in the co-determined section (marked as Section 2). The mainstream flows towards the outlet along the surfaces of both the rotor and the stator, depicted in Fig. 3(b) [20].
(4)
The main profiles of the non-dimensional tangential velocity Vφ v (= φ ) and the non-dimensional radial velocity Vr (= vr ) are shown Ω∙b Ω∙b in Fig. 2 [7,8]. By LDA (Laser Doppler Anemometry) measurements, Poncet et al. [7,8] determined Eqs. (5) and (6) to predict the amounts of K . The drawback of the equations is that the effects of G are not considered. The transition zone between the rotation dominant flow and the through-flow dominant flow is in the parameter range: 0.02 < Cqr < 0.03 [7,8]. 5
K = 2∙ (−5.9∙Cqr + 0.63) 7 − 1; Cqr ≤ 0.02
(5)
−Cqr
K = 0.032 + 0.32 × e 0.028 ; Cqr ≥ 0.03
(6)
Owen et al. [11–13] reported the significant impacts of the turbulent flow types on the characteristics of both the flow and the heat transfer in a rotor-stator system. They distinguished the S type flow from the B type flow based on the turbulent flow parameter λt , related by
Cw Re 0.8
(b) Section II
Fig. 3. Schematic drawing of the flow structures [20].
(3)
2∙π∙Ω ∙r 3
Qt where Reφ is the local circumferential Reynolds number, Reφ = is the volumetric flow rate, ν is the kinematic viscosity. In the rest of the front chamber, where Cqr does not exceed 0.02, the flow is dominated by the rotation. The flow is either the Batchelor (marked as B) type or the Couette (noted as C) type flow [9,10], depending on the non-dimensional axial gap G , defined as
λt =
Stator
Rotor
Ω ∙r 2 , v
G=
0.0028
(2)
where Ωf is the angular velocity of the fluid, ζ is the non-dimensional z axial coordinate, ζ = s . In the front chamber with centrifugal through-flow, the turbulent flow is classified into three types with their own dynamic characteristics. At low radius, where the local through-flow coefficient Cqr , written in Eq. (3), are not less than 0.03, the flow is dominated by the through-flow and is named Stewartson (noted as S) type flow [7,8].
Cqr =
0.0009
λtx =
Cw Re1.2
(8)
(7)
where Cw is the through-flow coefficient, Cw =
ṁ , μ∙b
1.2. Moment coefficient
Re is the global
Ω ∙ b2
circumferential Reynolds number, Re = ν , ṁ is the mass flow rate, μ is the dynamic viscosity. The turbulent flow parameter λt represents the relative strength of the viscous force and the inertial force of the flow. When Cw is smaller
In a RSSDR, as commonly understood, the energy dissipation is associated with the mass transfer rate as well as the heat transfer behaviors. The energy dissipation rate Ed (calculated with Ed = M∙Ω/ VF ) can be quantified directly by a steady state enthalpy balance over the
Rotation dominant
Through-flow dominant
B type
C type
x
Rotor
S type
x
x
Stator
Fig. 2. Velocity profiles for the three turbulent flow types [7,8]. 3
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1.3. Transient TLC technique
reactor side chamber as well as indirectly by the moment coefficient CM , related by
2∙ |M| ρ∙Ω2∙b5
The temperature on the surface can be visualized with the transient thermochromic liquid crystals (TLC) technique. With this method, the local heat transfer coefficient h , defined in Eq. (10), is estimated from the solution of Fourier’s one-dimensional heat conduction equation. To improve the veracity of the test method, a lot of researches are conducted over the past decades. Akino et al. [27] introduced a method to minimize the error from the individual color sensation. Baughn [28] reported an application of the narrow bandwidth liquid crystals with an active range of 1 K. Gillespie et al. [29] and Newton et al. [30] derived some solutions of the one-dimensional heat conduction equation. They emphasized that the solutions are only valid when the semi-infinite boundary condition is satisfied [31]. To determine the time of discoloration accurately, Camci et al. [32] introduced a hue-based detection method. Poser et al. [33] devised an advanced approach by detecting the peak intensity of the signals from the TLC indication. Ireland and Jones [34] investigated the data reduction process to reduce the relative error. Kakade et al. [35] and Abdullah et al. [36] dedicated their research to investigate the optical properties of the TLC. It is concluded that the coatings of the TLC must be thick enough to avoid
(9)
where M is the frictional torque on a single surface. The second method has a simpler form, which depends on the accuracy of the prediction of CM . A large number of researches on CM are conducted over the past decades. By torque measurements, Owen [13] developed an expression for CM in a shrouded rotor-stator system for the B type flow. Wang et al. [21] studied the disk frictional losses in a multistage centrifugal pump. With various Cw , Kurokawa et al. [22] theoretically analyzed the amounts of CM in a rotor–stator cavity. Schlichting and Gersten [23] organized an implicit relation for CM for the turbulent flow. On the basis of torque measurements, Han et al. [24] conducted a correlation for CM on the cylinder surface of the disk. Meeuwse et al. [3] and Mendoza et al. [25] used the moment coefficient to estimate the values of Ed . After extending the two-dimensional Daily &Nece diagram into three-dimensional, Hu et al. [18,26] evaluated the effects of Cw , Re and G on CM for the two turbulent flow regimes (either small or large axial gap width).
Q
T Air at
Turbine flowmeter
° Heater
Compressor photoelectric switch
Heater air
CM =
Black sticker M
P
Torquemeter Motor
Test zone (a) Schematic drawing of the test rig Outlet
TLC (against the CCD camera) Disk painted black LED CCD camera
Front cover TC
HWA Inlet (b) Experimental set-up for heat transfer
(c) Positions of the measurements
Fig. 4. Sketch of the experimental apparatus. 4
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acquisition system. A compressor, which is driven by a frequency converter controlled motor, is used to supply the air to the test rig. The pressure at the compressor outlet is limited to 2 bar. The speed of rotation n is up to 3000 rpm. The flow rate is measured with a turbine flowmeter with a relative error of 1% (FS). The measuring range of the torquemeter is 0–10 Nm. The method of torque measurement is referenced to Hu et al. [26]. The uncertainties of M on a single surface are up to 1.5 × 10−3Nm . At the heater outlet, the temperature rise of 100 K needs less than 30 s. The temperature rise of 40–60 K in the test zone takes up to 100 s. The TLC is viewed through the transparent front cover with a CCD (Charge Coupled Device) camera (55fps) under the illumination of an infrared LED (Light Emitting Diode) source, shown in Fig. 4(b). A black sticker is pasted on the shaft. There is a photoelectric switch triggering the CCD camera when the black sticker passes through. The time of exposure delay is set to ensure that the camera can capture the area sprayed with the TLC. The front cover is made of polymethyl methacrylate. One disk is made of stainless steel for the measurements of torque while the other is made of polymethyl methacrylate for the measurements of K and h . The rest of the parts of the test zone are made of stainless steel. In the test zone, the amounts of surface roughness for the parts in contact with the experimental air are up to 1 μm . To satisfy the requirement of the penetration time for the one-dimensional semi-infinite condition, the maximum experimental time tmax is determined as 824 s according to Eq. (14) [13,20]. During the calculation of Re , the kinematic viscosity of air is estimated according to the temperature from the thermocouples. The amounts of T∞ between each two adjacent thermocouples are considered as the average values from the measurements. The parameter ranges in the experiments are as follows: Cw ≤ 44663, Re ≤ 3.17 × 106 , G = { 0.0125, 0.025, 0.0375, 0.05}.
the accelerated aging and decrease the reflectivity.
−q h= (Taw − Tw )
(10)
where q is the heat flux, Taw is the adiabatic wall temperature, u 2
Taw = T∞ + rrec ∙ 2∞∙ l , Tw is the surface temperature, T∞ is the temperature of the mainstream at ζ = 0.5, rrec is the recovery factor, rrec ≈ Pr 0.5 , u∞ is the velocity of the mainstream at ζ = 0.5, l is the specific heat at conμ∙l stant pressure, Pr is the Prandtl number, Pr = k , k is the thermal conductivity. 1.4. Heat transfer in the reactor In order to extend the service life and determine the geometry of the rotor, the heat transfer characteristics in the RSSDRs are widely investigated. Roy et al. [37] conducted an experimental study on the radial distributions of h . Using the remote infrared sensor, Metzger et al. [38] reported the variations of the average convective heat transfer coefficient have , defined in Eq. (11). They found that have is primarily dominated by Cw in the source region, while by the rotation of the flow, namely Re , in the core region.
have =
b ∫rc 2hrdr
b2 − rc 2
(11)
where rc is the inner radius where the measurements of h start. Using the transient TLC technique, Owen’s research group [11–13], Luo et al. [20] and Metzger’s research group [38–41] studied the radial distributions of h on the rotor. Luo et al. [20] addresses that, the heat transfer behaviors of the rotor are quite different in the viscous, the codetermined and the inertial sections, which are identified with λtx . Poncet et al. [42] performed a numerical investigation on the flow and the heat transfer within a rotor-stator cavity. The results from the established Reynolds stress model agree well with the experimental results. Tuliszka-Sznitko et al. [43] and Majchrowski et al. [44] performed the large-eddy simulation for the distributions of the local Nusselt numbers (Nu ) along both the stator and the rotor with the heated stator. The parameter Nu is defined in Eq. (12). Luo et al. [20] and Tuliszka-Sznitko et al. [45] conducted the numerical investigations on the flow and the heat transfer in a rotating cavity.
Nu =
h∙r k
tmax = 0.1
b 2hr 2dr k (b2 − rc 2)
(14)
where α is the thermal diffusivity, α = 1.09 × 10−7m2/s .
2.2. Measurements of the tangential velocity To measure the tangential velocity, the front cover of the test rig is produced with two holes at two radial positions ( x =0.67 at No. 9 and x =0.87 at No. 10, the non-dimensional radial coordinate x is computed r with x = b ) to install the HWA (hot-wire anemometry) probe, depicted in Fig. 4(c). In this study, one single wire probe is used to measure the tangential velocity at ζ = 0.5, based on which the values of K can be calculated. The probe is mounted on a positioning system, which can accomplish both the axial displacement and the rotation of the probe. The errors of displacement and rotation in the positioning system are ±0.05 mm and 0.5°. For Cw = 0 and Re = 3.225 × 106 , the flow type is B type at the two radial positions. The radial velocity in the central core is considered zero. The tangential flow direction is then detected with an extreme value search function that finds out the maximum value of the HWA signal, dependent on the rotation angle of the probe. After that, although the through-flow is introduced and the speed of rotation is changed, the probes do not rotate at fixed G and x values. The positioning system can be fixed at one of the two positions. The probe is calibrated in a special calibration section, namely a superposed flow pipeline.
(12)
In general, although there are a plenty of studies on the heat transfer, the experimental results of Nu and the average Nusselt number Nuave , defined in Eq. (13), on the rotor, are still not sufficient due to the complexity and the high cost of the experiments, especially those in the viscous section. Few researchers have focused on the effects of G and T∞ on K , which leads to the inaccurate predictions of the dynamic behaviors of the rotor. The experimental results of CM are still not enough for a wide range of Cw and G . The effects of CM on Nuave are also not clear. Hence, the objective of the present study is to provide more experimental data, which will provide the supports for the design processes of the RSSDRs.
Nuave =
tdisk 2 α
∫rc
(13)
2. Experimental setup 2.1. Test rig design
Table 1 Main parameters of the test zone.
To close the knowledge gap, a test rig, schematically depicted in Fig. 4(a), is designed and built up. The main parameters of the test zone are listed in Table 1. The test rig mainly includes five parts, namely the air supply system, the heater, the pipelines, the test zone and the data 5
b (mm)
s (mm)
sb (mm)
Δr (mm)
so (mm)
n (rpm)
400
5–20
15
2
5
≤ 3000
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Table 2 Radial positions of the TCs.
n
Tw − Ti =
j=1
No.
1
2
3
4
5
6
7
8
x
0.42
0.5
0.58
0.67
0.74
0.82
0.87
0.955
To measure the radial distributions of T∞, eight K-type (Omega 5SCTT-KI-40) thermocouples (noted as TCs) are used, shown in Fig. 4(c). The error of each thermocouple is up to ± 0.2K . The sample rate of the thermocouples is 10 Hz. They are installed in the front chamber and their tips are extended to the positions at ζ = 0.5 into the front chamber. The radial positions of the TCs are presented in Table 2.
2.4. Measurements of the heat transfer coefficient on the rotor The disk made of polymethyl methacrylate is firstly painted black. After that, the SPN100R35C1W type TLC is sprayed on the rotor surface in a fan shaped region with an angle of 60°. The thermal conductivity of the TLC is 0.2 W/m∙K . The exposure time of the camera texp is very important for shooting the rotating disk. If the exposure time is too long, the light information on the disk at each position will be captured during the exposure time, resulting in the smear phenomenon. If the time is too short, the color of the picture will be dim, resulting in a significant amount of the noise points in the images. Therefore, the exposure time needs to be properly determined according to the speed of rotation. The experiments allow the disk to rotate two degrees at maximum for each exposure [11–13,47], then the amounts of texp are computed as
π 90∙Ω
Nuave =
Tw − Ti =1− T∞ − Ti
⎟
θ=
α∙t ) k
)] ∙ [ΔT∞ (j, j − 1)] (17)
2hr 2dr k (r82 − r12)
∫r1 8
(18)
The coating thickness of the TLC is around 100 μm , contributing to the relative error up to 7% for the measurements of h . With the transient liquid crystal technique, the uncertainty analysis of the transient heat transfer measurements is associated with the non-dimensional temperature θ with Eq. (19). In the current experiments, the values of θ range from 0.4 to 0.6, which contribute to the relative error less than 4.4% [46,47]. With the root sum squared method, the overall relative errors for the measurements of h are up to 8.3%.
The process of the transient TLC measurements is depicted in Fig. 5. The amounts of h are subsequently calculated with Eq. (16) based on the solution of Fourier’s one-dimensional conduction equation [11–13]. 2 ⎛ h ∙α∙t ⎞ h∙ e⎝ k 2 ⎠ ∙erfc (
k
r
(15)
⎜
α∙ (t − t j )
The TLC is calibrated by comparing the temperature measured by four thermal resistances (TRs) arranged on the surface I of the metal plate A and the color image of the TLC on the surface II of the metal plate B at the same time, which is referred to Lin et al. [47], shown in Fig. 6. The metal plates are heated at a very low rate of 0.001 K/s so that the process can be considered a steady state. After that, the color of the TLC and the temperature from the TRs are recorded. During the calibration of the TLC, the results from the four TRs are in good accordance with each other. The corresponding temperature for the discoloration of the liquid crystal is 307.5–309 K. The calibration curves of the TLC are depicted in Fig. 7. If the color is described by HueSaturation-Intensity, the values of hue increase with increasing Tw in the range of the discoloration temperature of the liquid crystal [20,47]. When describing the color by Red-Green-Blue, both the red and the green components increase first and then decrease [33]. The red component of liquid crystal reaches the peak value at Tw ≈ 307.5K , where the corresponding hue value is about 0.1. The peak value of the green component occurs at Tw ≈ 308K , while the corresponding value of hue increases dramatically to 0.3. Hence, the peak value of the green color is chosen as the characteristic color during the measurements of h . In this study, the values of Nuave on the rotor are computed with Eq. (18).
2.3. Measurements of the temperature in the mainstream
texp =
∑ [1 −
2 ⎛ h ∙ α ∙ (t − t j ) ⎞ h∙ ⎜ ⎟ k2 e⎝ ⎠ ∙erfc (
Tw − T0 T∞ − T0
(19)
(16) 3. Results and discussion
Since no step change in the mainstream occurs, a series of small step superposition is adopted to approximate the curves of the temperature rise in the mainstream. The amounts of h then can be computed with Eq. (17). During the experiments, each value of h is the average value in the circumferential direction every five degrees at the same radius. According to the results, the amounts of T∞ at the eight measuring positions are close to each other and those at the inlet of the test zone (differences are less than 5%).
3.1. Core swirl ratio K In Fig. 8, the results from the velocity measurements for G = 0.0125 and T∞ = 293K are compared with those reported by Poncet et al. [7]. The results are in relative good agreement with each other for Cqr < 0.1, which shows that the measurements of tangential velocity are reasonable.
Initial
Acquire images
Open LED
Data process
Images
Start shooting
Time of changing color
History of
Fig. 5. Process of the transient TLC measurements. 6
Start heater
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that the values of K decrease faster with the increase of G for the through-flow dominant flow. To analyze the effects of T∞, the amounts of K at Cqr = 0.00346 are investigated, depicted in Fig. 9(b). The values of K decrease with increasing T∞ in general. When T∞ rises from 300 K to 350 K, the values of K reduce by 4.1% to 6%. The recent available correlations of K , namely Eqs. (5) and (6) [7,8], however, primarily consider the impact of Cqr instead of the effects of G and T∞. The equations need to be extended so that the amounts of K can be better predicted.
Surface I
Plexiglass Metal plate A
TR2 TR3
TR1
Heating film Metal plate B
TR4
Plexiglass Surface II
(b) Arrangements of the TRs
(a) Set-ups for TLC calibration
Fig. 6. Sketch of the TLC calibration devices. 0.8
3.2. Moment coefficient CM The values of Ed can be calculated with the measured torque [3]. As Cw increases, the flow appears to change from Section 1 to Section 2 [20]. When Re equals to 0.78 × 106 and G equals to 0.0375, with the increase of Cw , there is a dramatic increase of CM in Section I, then a decrease is found in Section 2, shown in Fig. 10(a). When Re ranges from 1.27 × 106 to 2.16 × 106 , the changes of CM show the same trend. It is speculated that the flow changes from Section I to Section II at each measured Re . When Re further increases to 2.36 × 106 and 2.76 × 106 , Section II is not likely to occur. The flow is in Section I, where CM increases with increasing Cw , shown in Fig. 10(b). The variations of CM under other amounts of G show the same trends. It appears that CM is positively associated with Cw in Section I. As for Section II, however, the values of CM decrease with increasing Cw .
Green component, TR1 Red component, TR1
0.7
Hue
Component, Hue
0.6 0.5 0.4 0.3 0.2 0.1 0 305
306
307
308
309
310
311
(K)
3.3. Radial distribution of Nu
Fig. 7. Calibration of the TLC.
The relative errors of the measured Nu are up to 8.3%. Since the impacts of G are small compared with the error bars, only the results for G = 0.0375 are selected for comparisons. When Re equals to 0.78 × 106 , the flow changes from Section I to Section II with increasing Cw , depicted in Fig. 11. The values of Nu decrease with increasing Cw at each radial position in Section 2. When Re increase to 1.27 × 106 or 2.36 × 106 , the changes of Nu along the radius of the disk prove the same tendency in Section 2, shown in Fig. 12. In Section I, the amounts of Nu increase with increasing Cw .
The axial gap width G is one of the major parameters during the design process of the reactors. The chemical reactions generate a great deal of heat. In the most of the previous studies, however, the impacts of both G and T∞ on K have been largely ignored. In Fig. 9(a) the values of K / K G = 0.0125 are plotted for various Cqr and G at T∞ ≈ 295K . The amounts of K are smaller for wider axial gaps. For the rotation dominant flow, the values of K decrease by 3.3% to 12.2% when G increases from 0.0125 to 0.05. However, for the through-flow dominant flow, the corresponding decline ratios of K range from 14% to 27.6%. It seems
0.45
0.35 Through-flow dominant
Rotation dominant 0.25
G=0.0125, Exp 0.15
G=0.012 and G=0.036, Exp [7] Eq. (5) Eq. (6)
0.05 0.001
0.01 Fig. 8. Variations of K versusCqr at T∞ = 293K 7
0.1
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0.4
1.1 Rotation dominant
Through-flow dominant
0.39
1 0.38
0.37
0.9
0.36 0.8
G=0.025, green G=0.0375, orange G=0.05, red
G=0.0125, blue G=0.025, green G=0.0375, orange G=0.05, red
0.35
0.34
0.7 0.001
0.01
(a) Effect of
on
300
0.1
295
at
320
(K) 360
340
(b) Effect of
on
Fig. 9. Comparison of the experimental results for K . 0.004
0.004
0.004
0.0035
0.0035
0.0035
0.003
0.003
0.003
0.0025
0.0025
0.0025
0.002
0.002
0.002 Re=1.27×10^6
0.0015
Re=1.67×10^6
0.0015
Section I Section II 20000
40000
Re=2.76×10^6
Re=2.16×10^6
0.001 0
Re=2.36×10^6
0.0015
Re=1.9×10^6
60000
0.001
0.001 0
20000
40000
0
60000
(a) Section I to Section II
20000 40000 60000
(b) Section I
Fig. 10. Comparison of the experimental results of CM for different sections at G = 0.0375. 1
3.4. The average Nusselt number on the rotor
0.9 0.8
Owen et al. [13] stated that the parameter λt mainly determined the flow pattern inside the cavity, and then the general heat transfer caNuave − λt curves failed to entirely pacities. In Ref. [20], however, the 0.8 Re exclude the influence of Re . The parameter λtx was used instead of λt ave [20]. In this study, therefore, the effects of λtx on the amounts of Nu0.8 Re are analyzed in Fig. 13. Compared with the experimental results in Refs. [11–13,20,47], the test data in this paper are relatively smaller, which is primarily attributed to the differences of the geometry. Since the impacts of G are small compared with the error bars, only the results for ave G = 0.0375 are selected for comparisons. In Section 1, the values of Nu0.8
C_W=3903, Ȝ_Tx=0.00086
0.7
C_W=5556, Ȝ_Tx=0.00122
0.6
C_W=7507.5, Ȝ_Tx=0.00165
0.5
C_W=9234, Ȝ_Tx=0.00203
0.4
Re
200
250
300
350
400
450
ave increase with increasing λtx . The impact of Re on Nu0.8 is small and the Re differences are covered by the error bars. The trends in Section I are in good accordance with those in Ref. [20]. In Section 2, as λtx increases, ave ave the amounts of Nu0.8 decrease. The values of Nu0.8 decrease as Re in-
500
Circles: Section I; Rectangles: Section II Fig. 11. Radial distributions of Nu for Re = 0.38 × 106.
Re
creases. The parameter
Nuave Re0.8
Re
appears to depend on both λtx and Re . On
the other hand, It is found that 8
Nuave Re0.8
is mainly controlled by λtx and the
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1
1
Section I
Section II
0.9
0.9
0.8
0.8
0.7
0.7
0.6
0.6
0.5
0.5
0.4 0
500
1000
C_W=3097, Ȝ_Tx=0.00014 C_W=9586, Ȝ_Tx=0.00045
0.4
1500
0
500
C_W=22318, Ȝ_Tx=0.00105 C_W=47528, Ȝ_Tx=0.00224
C_W=5013, Ȝ_Tx=0.00024 C_W=14901, Ȝ_Tx=0.00069
1000
1500
C_W=33963, Ȝ_Tx=0.00145
(a) 1
1
Section II
Section I 0.9
0.9
0.8
0.8
0.7
0.7
0.6
0.6
0.5
0.5
0.4
0.4 900
1400
1900
C_W=3162, Ȝ_Tx=6.9×10^-5 C_W=9519, Ȝ_Tx=0.00021 C_W=21906, Ȝ_Tx=0.00056
2400
900
C_W=4098, Ȝ_Tx=0.00011 C_W=14514, Ȝ_Tx=0.00034 C_W=33678, Ȝ_Tx=0.00088
1400
1900
2400
C_W=46978, Ȝ_Tx=0.001
(b) Fig. 12. Comparison of the measured radial distributions of Nu.
Nuave = (0.0034∙ln(λtx ) + 0.041) ∙Re 0.8
effect of Re is quite weak in Ref. [20]. The dissimilarity deserves further investigations. ave To estimate the influence of CM on Nu0.8 , the experimental data are
Where Cw ≤ 44663, Re ≤ 3.225 × 106 , G={0.0125, 0.025, 0.0375, 0.05}. There are still some limitations of this work. We only measure the tangential velocity at two radial positions. Since the effects of G and T on K appear to be not negligible, the velocity will be measured at more radial coordinates. More detailed information on the flow will be discussed in the future work. At low radius, the characteristics of heat transfer coefficient are not studied due to the construction of the geometry. The performances of heat transfer in Section 2 are still inave sufficiently investigated. In Section 2, the effect of Re on Nu0.8 should Re also be determined. The relative error during the measurements of h is up to 8.3% . Some methods should be taken to further improve the precision of the measurements so that the effect of G can be estimated in the future.
Re
plotted in Fig. 14. When Re ranges from 1.27 × 106 to 2.77 × 106 , with ave the increase of Cw , most of the flow is in Section I. The amounts of Nu0.8 Re increase with the increase of CM in general, shown in Fig. 14(a). In the ave case when Re is 0.767 × 106 , the parameter Nu0.8 shows no correlation Re with CM , depicted in Fig. 14(b). The reason appears to be that with the increase of Cw , the flow are in different sections. In Section 1, the ave parameter Nu0.8 is an increased function of CM in general. In Section 2, Re
however, it seems that
Nuave Re0.8
(20)
drops slowly with increasing CM .
3.5. The average Nusselt number in section I Based on the measurements, a correlation of Nuave is determined in Eq. (20) for Section 1. As λtx increases, the values of Nuave increase at a ave fixed Re value, depicted in Fig. 15. The increase of Nu0.8 becomes graRe dual at relatively large λtx .
4. Conclusions The flow, the moment coefficient and the flow-rotor heat transfer in 9
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0.02
0.015
0.01 Section I
Section II
(Viscous section)
(Co-determined section)
0.005 Re=0.383×10^6 Re=0.796×10^6 Re=2.211×10^6 Re=3.225×10^6
Re=0.462×10^6 Re=1.27×10^6 Re=2.327×10^6 Ȝ_Tx=0.0009
Re=0.773×10^6 Re=1.652×10^6 Re=2.788×10^6
0 0
0.0004
0.0008
0.0012 Nuave Re0.8
Fig. 13. Variation of
0.0016
0.002
0.0024
0.0028
in dependence of λtx for different sections.
0.02
0.022
0.015 0.018
Section I 0.01
Section II 0.014 Re=1.27×10^6 Re=1.67×10^6 Re=2.23×10^6 Re=2.38×10^6 Re=2.77×10^6
0.005
0 0.002
0.003
0.004
0.01 0.002
0.003
(a)
0.004
(b) Fig. 14. Variation of
Nuave Re0.8
in dependence of CM for various Re.
0.02
0.015
0.01
0.005 0.0001
0.0002
Re=0.383×10^6
Re=0.773×10^6
Re=1.652×10^6
Re=2.211×10^6
Re=2.327×10^6
Re=2.788×10^6
Re=3.225×10^6
Eq. (20)
0.0003
0.0004
Fig. 15. Main
Nuave Re0.8
0.0005
0.0006
0.0007
(λtx ) curves in Section 1. 10
0.0008
0.0009
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the front chamber of a rotor-stator spinning disk reactor are investigated experimentally. Some conclusions can be drawn as follows: The impacts of G and T∞ on K are strong and should not be ignored. With the increase of G or T∞, the amounts of K decrease. With increasing Cw , there is an initial and a dramatic increase of CM in Section 1, then a decrease is found in Section 2. In Section 1, there is a positive correlation between the amounts of Nu and Cw . The values of Nu decrease with the increase of Cw at the same radius in Section 2. The heat transfer characteristics vary according to the flow patterns. ave In Section 1, the parameter Nu0.8 is governed by λtx . An empirical corRe relation is determined according to the experimental results. In Section ave 2, the parameter Nu0.8 appears to be influenced by both λtx and Re . Re
The impacts of CM on 1,
Nuave Re0.8
Nuave Re0.8
[19] [20] [21]
[22]
[23] [24]
[25]
depend on the flow structures. In Section
increases with increasing CM in general.
[26]
Acknowledgments [27]
This study is funded by National Major Science and Technology Project No. 2017-II-0007-0021, National Defense Key Laboratory Fund No. 6142A0501020317, by Natural Science Foundation of China No. 51806118, No. 51609107 and by Natural Science Foundation of Jiangsu Province No. BK20160539.
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Han Hongbiao, Gao Shanqun, Li Jishun, Zhang Yongzhen, Exploring fluid resistance of disk rotor based on boundary layer theory, Mech. Sci. Technol. Aerospace Eng. 34 (2015) 1621–1625. P. Granados Mendoza, S.J.C. Weusten, M.T. de Groot, J.T.F. Keuretjes, J.C. Shouten, J. Van der Schaaf, Liquid-solid mass transfer to a rotating mesh electrode in a rotorstator spinning disk configuration, Int. J. Heat Mass Transf. 104 (2017) 650–657. B. Hu, D. Brillert, H.J. Dohmen, F.-K. Benra, Investigation on the flow in a rotorstator cavity with centripetal through-flow, Int. J. Turbomach. Propuls. Power 2 (2017) 18, https://doi.org/10.3390/ijtpp2040018. N. Akino, T. Kunugi, K. Ichimiya, K. Mitsushiro, M. Ueda, Improved liquid–crystal thermometry excluding human color sensation, J. Heat Transf. 111 (1989) 558–565. J.W. Baughn, Liquid crystal methods for studying turbulent heat transfer, Int. J. Heat Fluid Flow 16 (1995) 365–375. D.R.H. Gillespie, Z. Wang, P.T. Ireland, Full surface local heat transfer coefficient measurements in a model of an integrally cast impingement cooling geometry, J. Turbomach. 120 (1998) 92–99. P.J. Newton, Y. Yan, N.E. Stevens, S.T. Evatt, G.D. Lock, M.J. Owen, Transient heat transfer measurements using thermochromic liquid crystal. Part 1: an improved technique, Int. J. Heat Fluid Flow 24 (2003) 14–22. G. Vogel, B. Weigand, A new evaluation method for transient liquid crystal experiments, in: National Heat Transfer Conference, NHTC2001-20250, California, USA, 2001. C. Camci, K. Kim, S.A. Hippensteele, A new hue capturing technique for quantitative interpretation of liquid crystal images used in convective heat transfer studies, J. Turbomach. 114 (1992) 765–775. R. Poser, J.R. Ferguson, J.v. Wolfersdorf. Temporal signal preprocessing and evaluation of thermochromic liquid crystal indications in transient heat transfer experiments, in: 8th European Conference on Turbomachinery Fluid Dynamics and Thermodynamics, 2009, pp. 785–795. P.T. Ireland, T.V. Jones, Liquid crystal measurements of heat transfer and surface shear stress, Meas. Sci. Technol. 11 (2000) 969–986. V.U. Kakade, G.D. Lock, M. Wilson, J.M. Owen, J.E. Mayhew, Accurate Heat transfer measurements using thermochromic liquid crystal. Part 1: calibration and characteristics of crystals, Int. J. Heat Fluid Flow 30 (2009) 939–949. N. Abdullah, A.R.A. Talib, H.R.M. Saiah, A.A. Jaafar, M.A.M. Salleh, Film thickness effects on calibrations of a narrowband thermochromic liquid crystal, Exp. Therm. Fluid Sci. 33 (2009) 561–578. R.P. Roy, G. Xu, J. Feng, A study of convective heat transfer in a model rotor-stator disk cavity, J. Turbomach. 123 (2001) 621–632. D.E. Metzger, Heat transfer and pumping on a rotating disk with freely induced and forced cooling, J. Eng. Power 92 (1970) 342–348. D.E. Metzger, R.S. Bunker, G. Bosch, Transient liquid crystal measurement of local heat transfer on a rotating disk with jet impingement, J. Turbomach 113 (1991) 52–59. R.S. Bunker, D.E. Metzger, S. Wittig, Local heat transfer in turbine disk cavities. Part I: rotor and stator cooling with hub injection of coolant, J. Turbomach. 114 (1992) 211–220. R.S. Bunker, D.E. Metzger, S. Wittig, Local heat transfer in turbine disk cavities. Part II: rotor cooling with radial injection of coolant, J. Turbomach. 114 (1992) 221–228. S. Poncet, R. Schiestel, Numerical modeling of heat transfer and fluid flow in rotorstator cavities with throughflow, J. Heat Mass Transf. 50 (2007) 1528–1544. E. Tuliszka-Sznitko, A. Zielinski, W. Majchrowski, LES and DNS of the non-isothermal transitional flow in rotating cavity, Int. J. Heat Fluid Flow 30 (2009) 534–548. W. Majchrowski, K. 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Contents lists available at ScienceDirect
Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Experimental investigation on the flow and flow-rotor heat transfer in a rotor-stator spinning disk reactor ⁎
Bo Hua, Xuesong Lia, Yanxia Fub, Fan Zhangc, Chunwei Gua, Xiaodong Rena, , Chuan Wangd,
T ⁎
a
Department of Energy and Power Engineering, Tsinghua University, Beijing 100084, China School of Energy and Power Engineering, Jiangsu University, Zhenjiang, Jiangsu Province 212013, China c National Research Center of Pumps, Jiangsu University, Zhenjiang, Jiangsu Province 212013, China d School of Hydraulic, Energy and Power Engineering, Yangzhou University Yangzhou, Jiangsu Province 225002, China b
H I GH L IG H T S
investigated the effects of axial gap and temperature on core swirl ratio. • We moment coefficient of rotor was analyzed according to the flow patterns. • The of the moment coefficient on the heat transfer were analyzed. • Effect • An empirical correlation for the average Nusselt number was determined.
A R T I C LE I N FO
A B S T R A C T
Keywords: Rotor-stator spinning disk reactor Core swirl ratio Moment coefficient Thermochromic liquid crystal Heat transfer
In this article, an experimental study has been conducted to provide better understanding of the flow and heat transfer characteristics in the front chamber of a rotor-stator spinning disk reactor. According to the measurements with a one-dimensional hot-wire anemometer probe, the effects of the axial gap width and the temperature on the core swirl ratio are investigated, which are ignored for the past decades. The values of the core swirl ratio are found to decrease by up to 12.2% when G increases from 0.0125 to 0.05 and reduce by up to 6% when the temperature rises from 300 K to 350 K. The measured moment coefficient, which primarily decides the energy dissipation rate, is analyzed according to the flow patterns for the first time. The transient thermochromic liquid crystal technique is used to estimate the heat transfer characteristic. The variations of the moment coefficient, the local Nusselt number and the average Nusselt number appear to be largely determined by the flow patterns. An empirical correlation of the average Nusselt number in the viscous section is determined for the first time, which is aimed to provide better predictions on the average heat transfer capacity. The interaction of the average Nusselt number with the moment coefficient is also introduced. It is speculated that the flow patterns in the chamber plays an important role in the energy dissipation and the heat transfer performance.
1. Introduction
1.1. Core swirl ratio and flow structure
The rotor-stator spinning disk reactors, abbreviated as RSSDRs, are important continuous flow reactors, where the change of turbulent flow type, energy dissipation, heat and mass transfer occur [1–6]. The model of a RSSDR is sketched in Fig. 1(a). The directions of the through-flow inside the reactor are both centrifugal (in the front chamber) and centripetal (in the back chamber). This paper takes into account the front chamber, where most of the mixing and the chemical reaction happen, as the research object. The corresponding model is a rotorstator cavity with centrifugal through-flow, shown in Fig. 1(b).
In a rotor-stator cavity, the radial distributions of the pressure p are extensively investigated and reported by a lot of researchers. The wellknown correlation, which associates the pressure with the core swirl ratio K , is defined in Eq. (1). The parameter K , defined in Eq. (2), is used to show the dominant tangential motion of the fluid. Obtaining the pressure distributions, the maximum axial thrust acting on the rotor can be predicted in order to design the bearing system.
⁎
∂p = ρ∙K 2 ∙Ω2∙r ∂r
Corresponding authors. E-mail addresses: [email protected] (X. Ren), [email protected] (C. Wang).
https://doi.org/10.1016/j.applthermaleng.2019.114316 Received 18 May 2019; Received in revised form 4 July 2019; Accepted 28 August 2019 Available online 29 August 2019 1359-4311/ © 2019 Elsevier Ltd. All rights reserved.
(1)
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Nomenclature
texp u∞ VF Vr
Latin Symbols
b Cw CM Cqr
G h
have K k l M ṁ Nu
Nuave
outer radius of the disk, mm ṁ , through-flow coefficient, − μ∙b 2∙ | M| , ρ ∙ Ω2 ∙ b5 Q ∙Reφ0.2
Vφ vr vφ x z
moment coefficient, − , local flow rate coefficient, − axial gap width, −
2 ∙ π ∙ Ω ∙r 3 s , non-dimensional b
local convective heat transfer coefficient, W/m2∙K ∫rcb 2hrdr b2 − rc 2
, average convective heat transfer coefficient,
α θ λt λtx
ζ μ ν ρ Ω Ωf
k
2hr 2dr k (b2 − rc 2)
, average Nusselt number, −
n p Q Qt q Re
speed of rotation, rpm pressure, bar volumetric flow rate per hour, m3/h volumetric flow rate per second, m3/s wall heat flux, W/m2 Ω ∙b2 , global circumferential reynolds number, −
Reφ r ri rc rrec Δr s sb so T T∞ t tmax tdisk
local circumferential reynolds number, − radial coordinate, m radial coordinate of the thermocouple no. i , mm inner radius where the measurements of h start, mm recovery factor radial gap from the disk to the wall, mm axial gap of the front chamber, mm axial gap of the back chamber, mm outlet width of the chamber, mm temperature, K temperature in the mainstream, K time, s 0.1 ∙ tdisk 2 , maximum experimental time, s α thickness of the disk
Ω∙b
non-dimensional tangential velocity, m/s non-dimensional radial velocity, m/s r , non-dimensional radial coordinate, – b radial coordinate
Greek Symbols
W/m2∙K Ωf , core swirl ratio, − Ω thermal conductivity, W/m∙K specific heat at constant pressure, J/kg∙K frictional torque, Nm ρ∙Qt , mass flow rate, kg/s h∙r , local nusselt number, − ∫rcb
time of exposure, μs velocity of the mainstream at ζ = 0.5 πb2s , volume of the front chamber, m3 vr , non-dimensional tangential velocity, − Ω∙b vφ , non-dimensional radial velocity, −
thermal diffusivity, m2/s non-dimensional temperature, − CW , turbulent flow parameter, − Re0.8 CW , flow pattern parameter, − Re1.2 z , non-dimensional s
axial coordinate, − dynamic viscosity of air, N∙s/m2 kinematic viscosity of air, m2/s , density of air, kg/m3 angular velocity of the disk, rad/s angular velocity of the fluid at half of the axial gap width, rad/s
Abbreviations B C CCD erfc FS fps HWA LDA PIV RSSDR rpm S TC TLC TR HWA
v Ω ∙r 2 , v
Batchelor Couette charge coupled device complementary error function full scale frames per second hot-wire anemometry laser doppler anemometry particle image velocimetry rotor-stator spinning disk reactor revolution per minute Stewartson thermocouple thermochromic liquid crystal thermal resistance hot-wire anemometry
Fig. 1. Meridional sketch of a RSSDR and the rotor-stator cavity model.
2
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B. Hu, et al.
< 0.0009
where K is the core swirl ratio, ρ is the density of the fluid.
K=
Ωf Ω
atζ = 0.5
(a) Section I
Qt ∙Reφ 0.2
s b
or Re is large, the values of λt are small, which represents the relatively stronger viscous force [11–13]. Ewa et al. [14,15] found out that, the C type flow may change to the B type flow with the increase of G or Re . Cooper and Reshotko [16] characterized the transition between the B type flow and the S type flow by LDA measurements. Debuchy et al. [17] and Hu et al. [18] investigated the velocity profiles of the above three flow types. Hu et al. [18] evaluated the effects of G and centrifugal through-flow on K when the flow change from the C type to the B type. Nguyen et al. [19] investigated the flow behaviors in a rotorstator system by PIV (Particle Image Velocimetry) measurements. According to the simulation results, Luo et al. [20] evaluated the influence of λt on the flow structure. They addressed that the parameter λt fails to entirely exclude the effects of Re . The flow pattern parameter λtx , defined in Eq. (8), appears to be a more appropriate form. When λtx is less than 0.0009, the cavity flow is in the viscous section (noted as Section 1). The mainstream totally flows to the rotor surface after entering the cavity, and then flows to the outlet near the surface of the rotor, shown in Fig. 3(a). The inlet flow rotates with the rotor due to the viscous force on the disk boundary layer in Section 1. When λtx ranges from 0.009 to 0.0028, the flow is considered in the co-determined section (marked as Section 2). The mainstream flows towards the outlet along the surfaces of both the rotor and the stator, depicted in Fig. 3(b) [20].
(4)
The main profiles of the non-dimensional tangential velocity Vφ v (= φ ) and the non-dimensional radial velocity Vr (= vr ) are shown Ω∙b Ω∙b in Fig. 2 [7,8]. By LDA (Laser Doppler Anemometry) measurements, Poncet et al. [7,8] determined Eqs. (5) and (6) to predict the amounts of K . The drawback of the equations is that the effects of G are not considered. The transition zone between the rotation dominant flow and the through-flow dominant flow is in the parameter range: 0.02 < Cqr < 0.03 [7,8]. 5
K = 2∙ (−5.9∙Cqr + 0.63) 7 − 1; Cqr ≤ 0.02
(5)
−Cqr
K = 0.032 + 0.32 × e 0.028 ; Cqr ≥ 0.03
(6)
Owen et al. [11–13] reported the significant impacts of the turbulent flow types on the characteristics of both the flow and the heat transfer in a rotor-stator system. They distinguished the S type flow from the B type flow based on the turbulent flow parameter λt , related by
Cw Re 0.8
(b) Section II
Fig. 3. Schematic drawing of the flow structures [20].
(3)
2∙π∙Ω ∙r 3
Qt where Reφ is the local circumferential Reynolds number, Reφ = is the volumetric flow rate, ν is the kinematic viscosity. In the rest of the front chamber, where Cqr does not exceed 0.02, the flow is dominated by the rotation. The flow is either the Batchelor (marked as B) type or the Couette (noted as C) type flow [9,10], depending on the non-dimensional axial gap G , defined as
λt =
Stator
Rotor
Ω ∙r 2 , v
G=
0.0028
(2)
where Ωf is the angular velocity of the fluid, ζ is the non-dimensional z axial coordinate, ζ = s . In the front chamber with centrifugal through-flow, the turbulent flow is classified into three types with their own dynamic characteristics. At low radius, where the local through-flow coefficient Cqr , written in Eq. (3), are not less than 0.03, the flow is dominated by the through-flow and is named Stewartson (noted as S) type flow [7,8].
Cqr =
0.0009
λtx =
Cw Re1.2
(8)
(7)
where Cw is the through-flow coefficient, Cw =
ṁ , μ∙b
1.2. Moment coefficient
Re is the global
Ω ∙ b2
circumferential Reynolds number, Re = ν , ṁ is the mass flow rate, μ is the dynamic viscosity. The turbulent flow parameter λt represents the relative strength of the viscous force and the inertial force of the flow. When Cw is smaller
In a RSSDR, as commonly understood, the energy dissipation is associated with the mass transfer rate as well as the heat transfer behaviors. The energy dissipation rate Ed (calculated with Ed = M∙Ω/ VF ) can be quantified directly by a steady state enthalpy balance over the
Rotation dominant
Through-flow dominant
B type
C type
x
Rotor
S type
x
x
Stator
Fig. 2. Velocity profiles for the three turbulent flow types [7,8]. 3
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1.3. Transient TLC technique
reactor side chamber as well as indirectly by the moment coefficient CM , related by
2∙ |M| ρ∙Ω2∙b5
The temperature on the surface can be visualized with the transient thermochromic liquid crystals (TLC) technique. With this method, the local heat transfer coefficient h , defined in Eq. (10), is estimated from the solution of Fourier’s one-dimensional heat conduction equation. To improve the veracity of the test method, a lot of researches are conducted over the past decades. Akino et al. [27] introduced a method to minimize the error from the individual color sensation. Baughn [28] reported an application of the narrow bandwidth liquid crystals with an active range of 1 K. Gillespie et al. [29] and Newton et al. [30] derived some solutions of the one-dimensional heat conduction equation. They emphasized that the solutions are only valid when the semi-infinite boundary condition is satisfied [31]. To determine the time of discoloration accurately, Camci et al. [32] introduced a hue-based detection method. Poser et al. [33] devised an advanced approach by detecting the peak intensity of the signals from the TLC indication. Ireland and Jones [34] investigated the data reduction process to reduce the relative error. Kakade et al. [35] and Abdullah et al. [36] dedicated their research to investigate the optical properties of the TLC. It is concluded that the coatings of the TLC must be thick enough to avoid
(9)
where M is the frictional torque on a single surface. The second method has a simpler form, which depends on the accuracy of the prediction of CM . A large number of researches on CM are conducted over the past decades. By torque measurements, Owen [13] developed an expression for CM in a shrouded rotor-stator system for the B type flow. Wang et al. [21] studied the disk frictional losses in a multistage centrifugal pump. With various Cw , Kurokawa et al. [22] theoretically analyzed the amounts of CM in a rotor–stator cavity. Schlichting and Gersten [23] organized an implicit relation for CM for the turbulent flow. On the basis of torque measurements, Han et al. [24] conducted a correlation for CM on the cylinder surface of the disk. Meeuwse et al. [3] and Mendoza et al. [25] used the moment coefficient to estimate the values of Ed . After extending the two-dimensional Daily &Nece diagram into three-dimensional, Hu et al. [18,26] evaluated the effects of Cw , Re and G on CM for the two turbulent flow regimes (either small or large axial gap width).
Q
T Air at
Turbine flowmeter
° Heater
Compressor photoelectric switch
Heater air
CM =
Black sticker M
P
Torquemeter Motor
Test zone (a) Schematic drawing of the test rig Outlet
TLC (against the CCD camera) Disk painted black LED CCD camera
Front cover TC
HWA Inlet (b) Experimental set-up for heat transfer
(c) Positions of the measurements
Fig. 4. Sketch of the experimental apparatus. 4
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acquisition system. A compressor, which is driven by a frequency converter controlled motor, is used to supply the air to the test rig. The pressure at the compressor outlet is limited to 2 bar. The speed of rotation n is up to 3000 rpm. The flow rate is measured with a turbine flowmeter with a relative error of 1% (FS). The measuring range of the torquemeter is 0–10 Nm. The method of torque measurement is referenced to Hu et al. [26]. The uncertainties of M on a single surface are up to 1.5 × 10−3Nm . At the heater outlet, the temperature rise of 100 K needs less than 30 s. The temperature rise of 40–60 K in the test zone takes up to 100 s. The TLC is viewed through the transparent front cover with a CCD (Charge Coupled Device) camera (55fps) under the illumination of an infrared LED (Light Emitting Diode) source, shown in Fig. 4(b). A black sticker is pasted on the shaft. There is a photoelectric switch triggering the CCD camera when the black sticker passes through. The time of exposure delay is set to ensure that the camera can capture the area sprayed with the TLC. The front cover is made of polymethyl methacrylate. One disk is made of stainless steel for the measurements of torque while the other is made of polymethyl methacrylate for the measurements of K and h . The rest of the parts of the test zone are made of stainless steel. In the test zone, the amounts of surface roughness for the parts in contact with the experimental air are up to 1 μm . To satisfy the requirement of the penetration time for the one-dimensional semi-infinite condition, the maximum experimental time tmax is determined as 824 s according to Eq. (14) [13,20]. During the calculation of Re , the kinematic viscosity of air is estimated according to the temperature from the thermocouples. The amounts of T∞ between each two adjacent thermocouples are considered as the average values from the measurements. The parameter ranges in the experiments are as follows: Cw ≤ 44663, Re ≤ 3.17 × 106 , G = { 0.0125, 0.025, 0.0375, 0.05}.
the accelerated aging and decrease the reflectivity.
−q h= (Taw − Tw )
(10)
where q is the heat flux, Taw is the adiabatic wall temperature, u 2
Taw = T∞ + rrec ∙ 2∞∙ l , Tw is the surface temperature, T∞ is the temperature of the mainstream at ζ = 0.5, rrec is the recovery factor, rrec ≈ Pr 0.5 , u∞ is the velocity of the mainstream at ζ = 0.5, l is the specific heat at conμ∙l stant pressure, Pr is the Prandtl number, Pr = k , k is the thermal conductivity. 1.4. Heat transfer in the reactor In order to extend the service life and determine the geometry of the rotor, the heat transfer characteristics in the RSSDRs are widely investigated. Roy et al. [37] conducted an experimental study on the radial distributions of h . Using the remote infrared sensor, Metzger et al. [38] reported the variations of the average convective heat transfer coefficient have , defined in Eq. (11). They found that have is primarily dominated by Cw in the source region, while by the rotation of the flow, namely Re , in the core region.
have =
b ∫rc 2hrdr
b2 − rc 2
(11)
where rc is the inner radius where the measurements of h start. Using the transient TLC technique, Owen’s research group [11–13], Luo et al. [20] and Metzger’s research group [38–41] studied the radial distributions of h on the rotor. Luo et al. [20] addresses that, the heat transfer behaviors of the rotor are quite different in the viscous, the codetermined and the inertial sections, which are identified with λtx . Poncet et al. [42] performed a numerical investigation on the flow and the heat transfer within a rotor-stator cavity. The results from the established Reynolds stress model agree well with the experimental results. Tuliszka-Sznitko et al. [43] and Majchrowski et al. [44] performed the large-eddy simulation for the distributions of the local Nusselt numbers (Nu ) along both the stator and the rotor with the heated stator. The parameter Nu is defined in Eq. (12). Luo et al. [20] and Tuliszka-Sznitko et al. [45] conducted the numerical investigations on the flow and the heat transfer in a rotating cavity.
Nu =
h∙r k
tmax = 0.1
b 2hr 2dr k (b2 − rc 2)
(14)
where α is the thermal diffusivity, α = 1.09 × 10−7m2/s .
2.2. Measurements of the tangential velocity To measure the tangential velocity, the front cover of the test rig is produced with two holes at two radial positions ( x =0.67 at No. 9 and x =0.87 at No. 10, the non-dimensional radial coordinate x is computed r with x = b ) to install the HWA (hot-wire anemometry) probe, depicted in Fig. 4(c). In this study, one single wire probe is used to measure the tangential velocity at ζ = 0.5, based on which the values of K can be calculated. The probe is mounted on a positioning system, which can accomplish both the axial displacement and the rotation of the probe. The errors of displacement and rotation in the positioning system are ±0.05 mm and 0.5°. For Cw = 0 and Re = 3.225 × 106 , the flow type is B type at the two radial positions. The radial velocity in the central core is considered zero. The tangential flow direction is then detected with an extreme value search function that finds out the maximum value of the HWA signal, dependent on the rotation angle of the probe. After that, although the through-flow is introduced and the speed of rotation is changed, the probes do not rotate at fixed G and x values. The positioning system can be fixed at one of the two positions. The probe is calibrated in a special calibration section, namely a superposed flow pipeline.
(12)
In general, although there are a plenty of studies on the heat transfer, the experimental results of Nu and the average Nusselt number Nuave , defined in Eq. (13), on the rotor, are still not sufficient due to the complexity and the high cost of the experiments, especially those in the viscous section. Few researchers have focused on the effects of G and T∞ on K , which leads to the inaccurate predictions of the dynamic behaviors of the rotor. The experimental results of CM are still not enough for a wide range of Cw and G . The effects of CM on Nuave are also not clear. Hence, the objective of the present study is to provide more experimental data, which will provide the supports for the design processes of the RSSDRs.
Nuave =
tdisk 2 α
∫rc
(13)
2. Experimental setup 2.1. Test rig design
Table 1 Main parameters of the test zone.
To close the knowledge gap, a test rig, schematically depicted in Fig. 4(a), is designed and built up. The main parameters of the test zone are listed in Table 1. The test rig mainly includes five parts, namely the air supply system, the heater, the pipelines, the test zone and the data 5
b (mm)
s (mm)
sb (mm)
Δr (mm)
so (mm)
n (rpm)
400
5–20
15
2
5
≤ 3000
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Table 2 Radial positions of the TCs.
n
Tw − Ti =
j=1
No.
1
2
3
4
5
6
7
8
x
0.42
0.5
0.58
0.67
0.74
0.82
0.87
0.955
To measure the radial distributions of T∞, eight K-type (Omega 5SCTT-KI-40) thermocouples (noted as TCs) are used, shown in Fig. 4(c). The error of each thermocouple is up to ± 0.2K . The sample rate of the thermocouples is 10 Hz. They are installed in the front chamber and their tips are extended to the positions at ζ = 0.5 into the front chamber. The radial positions of the TCs are presented in Table 2.
2.4. Measurements of the heat transfer coefficient on the rotor The disk made of polymethyl methacrylate is firstly painted black. After that, the SPN100R35C1W type TLC is sprayed on the rotor surface in a fan shaped region with an angle of 60°. The thermal conductivity of the TLC is 0.2 W/m∙K . The exposure time of the camera texp is very important for shooting the rotating disk. If the exposure time is too long, the light information on the disk at each position will be captured during the exposure time, resulting in the smear phenomenon. If the time is too short, the color of the picture will be dim, resulting in a significant amount of the noise points in the images. Therefore, the exposure time needs to be properly determined according to the speed of rotation. The experiments allow the disk to rotate two degrees at maximum for each exposure [11–13,47], then the amounts of texp are computed as
π 90∙Ω
Nuave =
Tw − Ti =1− T∞ − Ti
⎟
θ=
α∙t ) k
)] ∙ [ΔT∞ (j, j − 1)] (17)
2hr 2dr k (r82 − r12)
∫r1 8
(18)
The coating thickness of the TLC is around 100 μm , contributing to the relative error up to 7% for the measurements of h . With the transient liquid crystal technique, the uncertainty analysis of the transient heat transfer measurements is associated with the non-dimensional temperature θ with Eq. (19). In the current experiments, the values of θ range from 0.4 to 0.6, which contribute to the relative error less than 4.4% [46,47]. With the root sum squared method, the overall relative errors for the measurements of h are up to 8.3%.
The process of the transient TLC measurements is depicted in Fig. 5. The amounts of h are subsequently calculated with Eq. (16) based on the solution of Fourier’s one-dimensional conduction equation [11–13]. 2 ⎛ h ∙α∙t ⎞ h∙ e⎝ k 2 ⎠ ∙erfc (
k
r
(15)
⎜
α∙ (t − t j )
The TLC is calibrated by comparing the temperature measured by four thermal resistances (TRs) arranged on the surface I of the metal plate A and the color image of the TLC on the surface II of the metal plate B at the same time, which is referred to Lin et al. [47], shown in Fig. 6. The metal plates are heated at a very low rate of 0.001 K/s so that the process can be considered a steady state. After that, the color of the TLC and the temperature from the TRs are recorded. During the calibration of the TLC, the results from the four TRs are in good accordance with each other. The corresponding temperature for the discoloration of the liquid crystal is 307.5–309 K. The calibration curves of the TLC are depicted in Fig. 7. If the color is described by HueSaturation-Intensity, the values of hue increase with increasing Tw in the range of the discoloration temperature of the liquid crystal [20,47]. When describing the color by Red-Green-Blue, both the red and the green components increase first and then decrease [33]. The red component of liquid crystal reaches the peak value at Tw ≈ 307.5K , where the corresponding hue value is about 0.1. The peak value of the green component occurs at Tw ≈ 308K , while the corresponding value of hue increases dramatically to 0.3. Hence, the peak value of the green color is chosen as the characteristic color during the measurements of h . In this study, the values of Nuave on the rotor are computed with Eq. (18).
2.3. Measurements of the temperature in the mainstream
texp =
∑ [1 −
2 ⎛ h ∙ α ∙ (t − t j ) ⎞ h∙ ⎜ ⎟ k2 e⎝ ⎠ ∙erfc (
Tw − T0 T∞ − T0
(19)
(16) 3. Results and discussion
Since no step change in the mainstream occurs, a series of small step superposition is adopted to approximate the curves of the temperature rise in the mainstream. The amounts of h then can be computed with Eq. (17). During the experiments, each value of h is the average value in the circumferential direction every five degrees at the same radius. According to the results, the amounts of T∞ at the eight measuring positions are close to each other and those at the inlet of the test zone (differences are less than 5%).
3.1. Core swirl ratio K In Fig. 8, the results from the velocity measurements for G = 0.0125 and T∞ = 293K are compared with those reported by Poncet et al. [7]. The results are in relative good agreement with each other for Cqr < 0.1, which shows that the measurements of tangential velocity are reasonable.
Initial
Acquire images
Open LED
Data process
Images
Start shooting
Time of changing color
History of
Fig. 5. Process of the transient TLC measurements. 6
Start heater
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that the values of K decrease faster with the increase of G for the through-flow dominant flow. To analyze the effects of T∞, the amounts of K at Cqr = 0.00346 are investigated, depicted in Fig. 9(b). The values of K decrease with increasing T∞ in general. When T∞ rises from 300 K to 350 K, the values of K reduce by 4.1% to 6%. The recent available correlations of K , namely Eqs. (5) and (6) [7,8], however, primarily consider the impact of Cqr instead of the effects of G and T∞. The equations need to be extended so that the amounts of K can be better predicted.
Surface I
Plexiglass Metal plate A
TR2 TR3
TR1
Heating film Metal plate B
TR4
Plexiglass Surface II
(b) Arrangements of the TRs
(a) Set-ups for TLC calibration
Fig. 6. Sketch of the TLC calibration devices. 0.8
3.2. Moment coefficient CM The values of Ed can be calculated with the measured torque [3]. As Cw increases, the flow appears to change from Section 1 to Section 2 [20]. When Re equals to 0.78 × 106 and G equals to 0.0375, with the increase of Cw , there is a dramatic increase of CM in Section I, then a decrease is found in Section 2, shown in Fig. 10(a). When Re ranges from 1.27 × 106 to 2.16 × 106 , the changes of CM show the same trend. It is speculated that the flow changes from Section I to Section II at each measured Re . When Re further increases to 2.36 × 106 and 2.76 × 106 , Section II is not likely to occur. The flow is in Section I, where CM increases with increasing Cw , shown in Fig. 10(b). The variations of CM under other amounts of G show the same trends. It appears that CM is positively associated with Cw in Section I. As for Section II, however, the values of CM decrease with increasing Cw .
Green component, TR1 Red component, TR1
0.7
Hue
Component, Hue
0.6 0.5 0.4 0.3 0.2 0.1 0 305
306
307
308
309
310
311
(K)
3.3. Radial distribution of Nu
Fig. 7. Calibration of the TLC.
The relative errors of the measured Nu are up to 8.3%. Since the impacts of G are small compared with the error bars, only the results for G = 0.0375 are selected for comparisons. When Re equals to 0.78 × 106 , the flow changes from Section I to Section II with increasing Cw , depicted in Fig. 11. The values of Nu decrease with increasing Cw at each radial position in Section 2. When Re increase to 1.27 × 106 or 2.36 × 106 , the changes of Nu along the radius of the disk prove the same tendency in Section 2, shown in Fig. 12. In Section I, the amounts of Nu increase with increasing Cw .
The axial gap width G is one of the major parameters during the design process of the reactors. The chemical reactions generate a great deal of heat. In the most of the previous studies, however, the impacts of both G and T∞ on K have been largely ignored. In Fig. 9(a) the values of K / K G = 0.0125 are plotted for various Cqr and G at T∞ ≈ 295K . The amounts of K are smaller for wider axial gaps. For the rotation dominant flow, the values of K decrease by 3.3% to 12.2% when G increases from 0.0125 to 0.05. However, for the through-flow dominant flow, the corresponding decline ratios of K range from 14% to 27.6%. It seems
0.45
0.35 Through-flow dominant
Rotation dominant 0.25
G=0.0125, Exp 0.15
G=0.012 and G=0.036, Exp [7] Eq. (5) Eq. (6)
0.05 0.001
0.01 Fig. 8. Variations of K versusCqr at T∞ = 293K 7
0.1
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0.4
1.1 Rotation dominant
Through-flow dominant
0.39
1 0.38
0.37
0.9
0.36 0.8
G=0.025, green G=0.0375, orange G=0.05, red
G=0.0125, blue G=0.025, green G=0.0375, orange G=0.05, red
0.35
0.34
0.7 0.001
0.01
(a) Effect of
on
300
0.1
295
at
320
(K) 360
340
(b) Effect of
on
Fig. 9. Comparison of the experimental results for K . 0.004
0.004
0.004
0.0035
0.0035
0.0035
0.003
0.003
0.003
0.0025
0.0025
0.0025
0.002
0.002
0.002 Re=1.27×10^6
0.0015
Re=1.67×10^6
0.0015
Section I Section II 20000
40000
Re=2.76×10^6
Re=2.16×10^6
0.001 0
Re=2.36×10^6
0.0015
Re=1.9×10^6
60000
0.001
0.001 0
20000
40000
0
60000
(a) Section I to Section II
20000 40000 60000
(b) Section I
Fig. 10. Comparison of the experimental results of CM for different sections at G = 0.0375. 1
3.4. The average Nusselt number on the rotor
0.9 0.8
Owen et al. [13] stated that the parameter λt mainly determined the flow pattern inside the cavity, and then the general heat transfer caNuave − λt curves failed to entirely pacities. In Ref. [20], however, the 0.8 Re exclude the influence of Re . The parameter λtx was used instead of λt ave [20]. In this study, therefore, the effects of λtx on the amounts of Nu0.8 Re are analyzed in Fig. 13. Compared with the experimental results in Refs. [11–13,20,47], the test data in this paper are relatively smaller, which is primarily attributed to the differences of the geometry. Since the impacts of G are small compared with the error bars, only the results for ave G = 0.0375 are selected for comparisons. In Section 1, the values of Nu0.8
C_W=3903, Ȝ_Tx=0.00086
0.7
C_W=5556, Ȝ_Tx=0.00122
0.6
C_W=7507.5, Ȝ_Tx=0.00165
0.5
C_W=9234, Ȝ_Tx=0.00203
0.4
Re
200
250
300
350
400
450
ave increase with increasing λtx . The impact of Re on Nu0.8 is small and the Re differences are covered by the error bars. The trends in Section I are in good accordance with those in Ref. [20]. In Section 2, as λtx increases, ave ave the amounts of Nu0.8 decrease. The values of Nu0.8 decrease as Re in-
500
Circles: Section I; Rectangles: Section II Fig. 11. Radial distributions of Nu for Re = 0.38 × 106.
Re
creases. The parameter
Nuave Re0.8
Re
appears to depend on both λtx and Re . On
the other hand, It is found that 8
Nuave Re0.8
is mainly controlled by λtx and the
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1
1
Section I
Section II
0.9
0.9
0.8
0.8
0.7
0.7
0.6
0.6
0.5
0.5
0.4 0
500
1000
C_W=3097, Ȝ_Tx=0.00014 C_W=9586, Ȝ_Tx=0.00045
0.4
1500
0
500
C_W=22318, Ȝ_Tx=0.00105 C_W=47528, Ȝ_Tx=0.00224
C_W=5013, Ȝ_Tx=0.00024 C_W=14901, Ȝ_Tx=0.00069
1000
1500
C_W=33963, Ȝ_Tx=0.00145
(a) 1
1
Section II
Section I 0.9
0.9
0.8
0.8
0.7
0.7
0.6
0.6
0.5
0.5
0.4
0.4 900
1400
1900
C_W=3162, Ȝ_Tx=6.9×10^-5 C_W=9519, Ȝ_Tx=0.00021 C_W=21906, Ȝ_Tx=0.00056
2400
900
C_W=4098, Ȝ_Tx=0.00011 C_W=14514, Ȝ_Tx=0.00034 C_W=33678, Ȝ_Tx=0.00088
1400
1900
2400
C_W=46978, Ȝ_Tx=0.001
(b) Fig. 12. Comparison of the measured radial distributions of Nu.
Nuave = (0.0034∙ln(λtx ) + 0.041) ∙Re 0.8
effect of Re is quite weak in Ref. [20]. The dissimilarity deserves further investigations. ave To estimate the influence of CM on Nu0.8 , the experimental data are
Where Cw ≤ 44663, Re ≤ 3.225 × 106 , G={0.0125, 0.025, 0.0375, 0.05}. There are still some limitations of this work. We only measure the tangential velocity at two radial positions. Since the effects of G and T on K appear to be not negligible, the velocity will be measured at more radial coordinates. More detailed information on the flow will be discussed in the future work. At low radius, the characteristics of heat transfer coefficient are not studied due to the construction of the geometry. The performances of heat transfer in Section 2 are still inave sufficiently investigated. In Section 2, the effect of Re on Nu0.8 should Re also be determined. The relative error during the measurements of h is up to 8.3% . Some methods should be taken to further improve the precision of the measurements so that the effect of G can be estimated in the future.
Re
plotted in Fig. 14. When Re ranges from 1.27 × 106 to 2.77 × 106 , with ave the increase of Cw , most of the flow is in Section I. The amounts of Nu0.8 Re increase with the increase of CM in general, shown in Fig. 14(a). In the ave case when Re is 0.767 × 106 , the parameter Nu0.8 shows no correlation Re with CM , depicted in Fig. 14(b). The reason appears to be that with the increase of Cw , the flow are in different sections. In Section 1, the ave parameter Nu0.8 is an increased function of CM in general. In Section 2, Re
however, it seems that
Nuave Re0.8
(20)
drops slowly with increasing CM .
3.5. The average Nusselt number in section I Based on the measurements, a correlation of Nuave is determined in Eq. (20) for Section 1. As λtx increases, the values of Nuave increase at a ave fixed Re value, depicted in Fig. 15. The increase of Nu0.8 becomes graRe dual at relatively large λtx .
4. Conclusions The flow, the moment coefficient and the flow-rotor heat transfer in 9
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0.02
0.015
0.01 Section I
Section II
(Viscous section)
(Co-determined section)
0.005 Re=0.383×10^6 Re=0.796×10^6 Re=2.211×10^6 Re=3.225×10^6
Re=0.462×10^6 Re=1.27×10^6 Re=2.327×10^6 Ȝ_Tx=0.0009
Re=0.773×10^6 Re=1.652×10^6 Re=2.788×10^6
0 0
0.0004
0.0008
0.0012 Nuave Re0.8
Fig. 13. Variation of
0.0016
0.002
0.0024
0.0028
in dependence of λtx for different sections.
0.02
0.022
0.015 0.018
Section I 0.01
Section II 0.014 Re=1.27×10^6 Re=1.67×10^6 Re=2.23×10^6 Re=2.38×10^6 Re=2.77×10^6
0.005
0 0.002
0.003
0.004
0.01 0.002
0.003
(a)
0.004
(b) Fig. 14. Variation of
Nuave Re0.8
in dependence of CM for various Re.
0.02
0.015
0.01
0.005 0.0001
0.0002
Re=0.383×10^6
Re=0.773×10^6
Re=1.652×10^6
Re=2.211×10^6
Re=2.327×10^6
Re=2.788×10^6
Re=3.225×10^6
Eq. (20)
0.0003
0.0004
Fig. 15. Main
Nuave Re0.8
0.0005
0.0006
0.0007
(λtx ) curves in Section 1. 10
0.0008
0.0009
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the front chamber of a rotor-stator spinning disk reactor are investigated experimentally. Some conclusions can be drawn as follows: The impacts of G and T∞ on K are strong and should not be ignored. With the increase of G or T∞, the amounts of K decrease. With increasing Cw , there is an initial and a dramatic increase of CM in Section 1, then a decrease is found in Section 2. In Section 1, there is a positive correlation between the amounts of Nu and Cw . The values of Nu decrease with the increase of Cw at the same radius in Section 2. The heat transfer characteristics vary according to the flow patterns. ave In Section 1, the parameter Nu0.8 is governed by λtx . An empirical corRe relation is determined according to the experimental results. In Section ave 2, the parameter Nu0.8 appears to be influenced by both λtx and Re . Re
The impacts of CM on 1,
Nuave Re0.8
Nuave Re0.8
[19] [20] [21]
[22]
[23] [24]
[25]
depend on the flow structures. In Section
increases with increasing CM in general.
[26]
Acknowledgments [27]
This study is funded by National Major Science and Technology Project No. 2017-II-0007-0021, National Defense Key Laboratory Fund No. 6142A0501020317, by Natural Science Foundation of China No. 51806118, No. 51609107 and by Natural Science Foundation of Jiangsu Province No. BK20160539.
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