Study on CHF characteristics in narrow rectangular channel under complex motion condition

Journal Pre-proofs Study on CHF characteristics in narrow rectangular channel under complex motion condition Minyang Gui, Wenxi Tian, Di Wu, G.H. Su, Suizheng Qiu PII: DOI: Reference:

S1359-4311(19)34726-X https://doi.org/10.1016/j.applthermaleng.2019.114629 ATE 114629

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Applied Thermal Engineering

Received Date: Revised Date: Accepted Date:

9 July 2019 28 October 2019 2 November 2019

Please cite this article as: M. Gui, W. Tian, D. Wu, G.H. Su, S. Qiu, Study on CHF characteristics in narrow rectangular channel under complex motion condition, Applied Thermal Engineering (2019), doi: https://doi.org/ 10.1016/j.applthermaleng.2019.114629

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Study on CHF characteristics in narrow rectangular channel under complex motion condition

Minyang Gui, Wenxi Tian*, Di Wu, G.H. Su, Suizheng Qiu School of Nuclear Science and Technology, Shanxi Key Laboratory of Advanced Nuclear Energy and Technology, State Key Laboratory of Multiphase Flow in Power Engineering, Xi'an Jiaotong University, Xi'an 710049, China *Corresponding author. Phone and Fax: +86-029-82668325 Email: [email protected]

Abstract In present work, the critical heat flux (CHF) characteristics in narrow rectangular channel were theoretically investigated under complex motion condition. A three-field analysis program was developed combining with a unified form of additional forces caused by motions, and the program was validated by CHF experiment data with a better prediction accuracy. The CHF characteristics of rectangular channel were evaluated based on two types of situations: (1) oscillating inlet flow and (2) constant inlet flow with different motions including heaving, rolling and the coupled motion of heaving and rolling. The results show that the oscillation of the inlet flow has a great influence on the CHF, the increases in the amplitude and period of the inlet flow oscillation cause the dryout to occur in advance. When the inlet flow is fixed, various motion conditions have little effect on CHF for high mass flux, and the reduction of CHF does not exceed 5%. However, the CHF is obviously reduced for the low mass flux due to the significant oscillation or thinning effect of the outlet liquid film caused by motions.

Key words: critical heat flux; complex motion; narrow rectangular channel; program development

1

Nomenclature a Translational acceleration, (m·s-2) Channel cross-sectional area, (m2) A Droplet mass concentration, (kg·m-3) C De Channel equivalent diameter, (m) De Deposition mass flux, (kg·m-2·s-1) En q

Entrainment mass flux, (kg·m-2·s-1)

Ev

Vaporization mass flux, (kg·m-2·s-1) Additional acceleration of motion; friction coefficient Gravitational constant, (m·s-2) Mass flux, (kg·m-2·s-1)

f g

G

Greek symbols  Volumetric fraction Time, (s)   Rotational angle, (rad) Rotational angular velocity, (rad·s-1)   Dynamic viscosity, (kg·m-1·s-1) 

Density, (kg·m-3)



Fraction of liquid flux flowing as droplet



Liquid film thickness, (mm)

h fg

Latent heat of vaporization, (J·kg-1)

Subscripts

L M

p

Length, (m) Interface friction force, (N·m-3) Pressure, (Pa)

ann AVE cal

Prw  q 

Wetted (heated) perimeter, (m)

CHF Critical heat flux

Channel surface heat flux, (kW·m-2) Gap size, (mm) Time, (s) Motion period, (s) Velocity, (m·s-1) Width, (mm) Vapor quality Channel axial coordinate, (m)

Droplets exp Experimental value f Liquid film g Gas (vapor) in Inlet l Liquid phase r Rotation s Translation OSC Oscillation

q s t T u

w x

z

d

2

Annular flow Average Calculated value

1.

Introduction Narrow rectangular channel has been widely adopted in compact heat exchangers [1-3], plate-

type fuel nuclear reactors [4-6], micro-electronics [7-8], etc. Especially for the plate-type fuel nuclear reactor, a number of narrow rectangular flow paths are formed between the fuel elements. The reactor has the advantages of low temperature of the fuel pellet and high power-to-volume ratio, which can meet the compact requirements of the core. However, in the design and operation of the reactor, an important safety constraint is critical heat flux (CHF), beyond which the heat transfer of the cladding surface deteriorates and the temperature abruptly rises and the cladding material can lose its integrity. It is important to evaluate the operation parameters limited by CHF in narrow rectangular channel. In recent years, floating nuclear power is receiving increasing attention, some countries have been pioneering the development and application of Ocean Nuclear Power Plants (ONPPs) [9]. Compared with land-based nuclear reactors, the special characteristics of ONPPs are mainly [10]: (1) A core that must usually be small compared to land-based reactors. (2) Occurrence of abrupt changes in load accompanying maneuvering operations. (3) Subjection to complex motion such as rolling, heaving and pitching. Especially for the third issue, owing to the inertial forces caused by the complex motions, the relative positions of the equipment and the gravitational field change periodically, which induce periodic fluid flow fluctuations [11-12]. It is necessary to consider the reactor's safety behavior induced by the different complex conditions since the conventional CHF empirical correlations would no longer be applicable. Currently, there are a few published studies on CHF in the channel under motion conditions. Based on two atmospheric models of reactor core loops, Isshiki [13] studied the effects of two typical motion conditions, namely cyclic heaving and constant inclination, on core CHF. It was found that the CHF decreases linearly with increasing heaving acceleration, and the CHF also decreases in the inclined state. By experimental and theoretical considerations, a semi-empirical prediction of the decrease rate of CHF was obtained. Otsuji and Kurosawa [14] analyzed the influence of the heaving motion on the CHF under forced circulation by using Freon-113 as working fluid. The experimental results indicated that the heaving motion reduces the CHF, and the degree of reduction is related to the heaving amplitude. Subsequent theoretical studies have shown that the occurrence of CHF is mainly attributed to the oscillation of flow caused by the heaving motion [15-16]. Based on experimental data using single channel apparatus, Ishida et al. [17] modified the CHF correlation in the subchannel code COBRA-IV-I to calculate the temporal change of CHF in oscillating gravity 3

acceleration field, and the code was applied to the core analysis of Mutsu reactor. Gao et al. [18] carried out an experimental study on the CHF characteristics of natural circulation under steady and rolling conditions. The experimental results showed the additional inertia caused by rolling motion easily causes the natural circulation flow to oscillate. The low flow rate and flow oscillation of natural circulation lead to a decrease in CHF. Pang et al. [19] performed the forced circulation experiment under rolling conditions to study the effect of rolling motion on the CHF of atmospheric water. It was found that the rolling motion would lead to the early occurrence of CHF. Subsequently, Wang [20] extended the experimental parameters to medium-pressure conditions (0.5~3.5MPa), and found that the influence of the rolling motion on the CHF is greatly affected by the mass flow rate. Due to its complexity, the related theoretical study of the influence of motion conditions on CHF is rare. For low pressure and flow oscillation conditions, Guanghui et al. [21] applied artificial neural network (ANN) to predict CHF in vertical tubes, and the error between the model and the relevant experimental data is within 10%. In order to investigate the effects of the motion conditions on the CHF in the channel at low quality, Liu et al. [22] added the new arisen acceleration field caused by the motion to the vapor blankets on the basis of the original liquid sublayer dryout model [23]. The effects of various motion conditions on CHF were then analyzed. Based on the CHF data of R-113 from [14], Hwang et al. [24] evaluated the ability of the MARS system analysis code to predict CHF under heaving condition. The heaving condition in the experiment was converted to inlet flow oscillation for CHF calculation, and the CHF experimental conditions and results for R-113 were replaced with those for water through fluid-to-fluid (FTF) modeling with the gravity term included. Since the bubbles are easily squeezed by limited space to form vapor slug in narrow rectangular channel, the annular flow is one of the primary flow patterns, whose typical characteristic is that the part of the liquid flows along the wall as a liquid film and part as droplets in the vapor core flow. Boiling crisis occurring in annular flow is usually considered as the result of dryout of liquid film. So far, many theoretical models have been developed to predict the occurrence of dryout in flow boiling channels [25-30]. The simplest approach is to only consider mass conservation equation of the liquid film, and the liquid film mass flow rate is calculated from a first-order nonlinear differential equation, which has been reported in [25][28][30]. Besides, to fully reveal the interaction of fields (i.e. film, droplet and vapor core), the more elaborate three-field model was proposed, which includes a full set of conservation equations (mass, momentum and energy conservation equations) solved for three fields separately together with a set of closure relationships [26][29]. The quantitative comparison 4

between the dryout predictions of above models and experimental data indicates good agreement for a wide range of flow conditions. Overall, a lot of work has been done on the CHF under normal conditions, but related research under complex motion conditions is limited in publication, and most of the experimental research concentrates on the influence of gravity field changes. As the narrow rectangular channel is widely used in plate-type fuel cores and compact heat exchangers, the boiling crisis occurring in annular flow must be prevented with considering a variety of complex motion conditions. Thus, the current work focuses on the characteristics of dryout-type CHF in rectangular channel under various motion forms. Based on the previous studies [31-34] in our research group, a three-field dryout model as well as the additional forces caused by motion is proposed to investigate the transient changes in the liquid film in annular flow. The work proceeds along four successive stages. Firstly a three-field dryout analysis program is developed combining with a unified form of additional forces caused by motion, and validated separately under steady and motion conditions. Secondly, the characteristics of CHF under flow oscillation conditions are evaluated. Thirdly, the effects of several motion conditions on CHF characteristics under constant inlet flow are investigated. And, finally, the influence of motion conditions on CHF in rectangular channel is summarized, indicating that it is important to consider the effects of motion conditions to retain adequate safety margin in subsequent thermal-hydraulic designs.

2.

Physical model In this paper, the theoretical model of CHF in the rectangular channel under motion conditions

is established, in order to better describe the model, several important assumptions are necessary: (1) The annular film dryout (AFD) mechanism is used for CHF study, as shown in Fig. 1. (2) The wide sides of rectangular channel are uniformly heated while the narrow sides are adiabatic. (3) The flow is one dimensional. (4) The pressure is uniform in the radial direction and the fluid is in thermal equilibrium state. (5) Additional forces are introduced into the momentum equations for the consideration of motion conditions. Based on the above assumptions, the related models are proposed as follows. 5

Fig. 1. The schematic diagram of CHF in the rectangular channel.

2.1. Motion conditions If the coolant channel is placed in the moving environment, due to the influence of external forces, different motion states would be presented. These motion states can be classified into several simple movements such as inclination, rolling, heaving and acceleration, or some coupled motions. Fig. 2 depicts six typical forms of motion based on the axis of the coordinate system. In this paper, a unified form of equations for all motions proposed by Liu et al. [35] are used. That is, various motion states can be decomposed into two parts: linear motion and rotational motion. Since the direction vectors of the translational direction and the rotational axis could be spatially random, the unit translational direction vector ns(nsx, nsy, nsz) and unit rotational direction vector nr(nrx, nry, nrz) are defined, respectively. Assuming that both translation and rotation follow the sinusoidal law under the conditions of motion. The translational acceleration is given by:  2 t   Cs   Bs as  As sin   Ts 

(1)

The rotational angle is:

6

 2 t   Cr   Br  Tr 

  Ar sin 

(2)

where A is the amplitude; T is the motion period; C is the initial phase; B is the offset; The subscripts s and r represent translation and rotation, respectively.

Fig. 2. The schematic diagram of different forms of motion. In the inertial reference frame, the Euler equation for the ideal fluid is:



Du  p   g Dt

(3)

For the non-inertial reference frame (motion conditions), the Euler equation changes into a new form, it is:



Du d    p   g    as  2   u      r     r Dt dt  

(4)

where u is the velocity vector; g is the gravitational acceleration vector; as is the translational acceleration vector calculated by Eq. (1); r is the position vector of fluid volume in the non-inertial reference frame; ω is the rotational angular velocity vector, whose magnitude is given by:



 2 t  2 Ar cos   Cr  Tr  Tr 

(5)

For the gravitational acceleration vector g, considering the effects of rotational motion, the equivalent gravity that rotates around any axis is:

7

gx    nry sin   nrx nrz (1  cos  )     g   g y    g 0  nrx sin   nry nrz (1  cos  )   g z   cos   nrz2 (1  cos  ) 

(6)

where g0 is the gravitational acceleration in steady state. Finally, an additional acceleration vector under motion conditions is introduced, which can be shown as: d   f    as  2  u      r    r dt  

(7)

where the translational acceleration vector as and the rotational angular velocity vector ω can be decomposed into components on three coordinate axes:

n / n2  n2  n2  sx sy sz a  sx   sx    2 2 2   as   asy   as nsx / nsx  nsy  nsz    asz   2 2 2   nsx / nsx  nsy  nsz 

(8)

n / n2  n2  n2  rx ry rz  x   rx    2  2 2     y    nrx / nrx  nry  nrz    z   2 2 2  n / nrx  nry  nrz   rx 

(9)

In practice, once the motion parameters are determined, Eqs. (6) and (7) are introduced into the momentum equations for the consideration of the various motion conditions.

2.2. Critical heat flux The critical heat flux in current paper is based on the annular film dryout mechanistic model. For annular flow, the essential characteristic in vertical duct is that the vapor core containing entrained droplets flows in the center and the liquid film flows along the wall. The CHF occurs when the thin liquid film is evaporated at outlet. In this process, the interaction between droplets and liquid film has a significant effect on CHF, which is manifested by the entrainment and deposition process of the droplets. In order to describe the interaction among three fields in annular flow region, i.e. the liquid film, entrained droplets and vapor core. The fundamental conservation equations have been established together with a set of closure relationships.

8

2.2.1. Conservation equations The continuity equations for liquid film (f), entrained droplets (d) and vapor core (g) are as follows:

 f f uf  qP P D  ( Prw Enh  Prq Enq )   f f     rq  rw e  z  A Ah fg

(10)

P D  (P E  P E )    u    d  d   d d d   rw e rw nh rq nq A  z

(11)

   g g u g  qPrq   g g     Ah fg  z

(12)

where α and u represent the volume fraction and axial velocity at axial location z; Prq and Prw are the heated and wetted perimeters of the channel, respectively; A is channel cross-sectional area; De is the droplet deposition rate per unit area; Enh and Enq are the shearing entrainment rate and boiling entrainment rate per unit area, respectively. Taking into account the additional forces under motion conditions, the momentum equations are given by:

 f f uf 

    u   D f

f

2 f

P

ep rw

z

A

ud 

qPrq Ah fg

uf 

Enh Prw  Enq Prq A

uf

p   f   f  f  f + g   k  M wf  M fg z    d  d ud  

   g  g ug  





   d  d ud2  z

   g g ug2  z





Dep Prw A

qPrq Ah fg

ud 

Enh Prw  Enq Prq

u f   g

A

u f   d

(13)

p   d  d  f + g   k  M gd z

p   g  g  f + g   k  M fg  M gd z

(14)

(15)

where k is coordinate vector of fluid flow; M is the friction force per unit volume. Combining the continuity equations of each phase, the above Eqs. (13) ~ (15) can be further transformed into the following forms:

 f f

dd

u f 

  f f uf

u f z

  f

D P p   f  f  f + g   k  M wf  M fg  ep rw  ud  u f z A



E P  Enq Prq ud u p   d  d ud d   d   d  d  f + g   k  M gd  nh rw  u f  ud   z z A

9

(16)

(17)

 g g

ug 

  g  g ug

ug z

  g

qP p   g  g  f + g   k  M fg  M gd  rq  u f  ug  z Ah fg

(18)

Assuming that the flow is in an equilibrium state, the energy equation is consistent for the three fields, that is:

dh qPrq  dz GA

(19)

2.2.2. Closure relationships To close the conservation equations described above, some other models are required, such as the friction forces at the phase interfaces, the thickness of liquid film, and the entrainment and deposition of droplets, etc. For the friction forces, the basic form of the equations are similar to those of Sugawara [36] and Stevanovic and Studovic [37], which are given by:

M wf 

1 fw ρ f u f u f Prw A 2

(20)

M fg 

1 f fg ρg u g  u f  u g  u f  Pr , fg A 2

(21)

1 M gd  Cd agd ρg u g  ud  u g  ud  8

(22)

where fw, ffg and agd represent wall friction coefficient, film-to-vapor interfacial friction coefficient and vapor-to-droplets interfacial area concentration, respectively. Meanwhile, in order to simplify the solution of the model, it is assumed that the liquid film at each axial position is sufficiently stirred in the circumferential direction for the annular flow, that is, the liquid film is evenly distributed along the circumferential direction of the channel, and the thickness of which can be obtained by: δ

ws

w  s

2

 4wsα f

(23)

4

where w and s are width and gap size of the rectangular channel, respectively. It should also be emphasized that, due to the lack of theoretical equations, the dryout mechanistic model described here cannot be used to reflect the circumferential non-uniform distribution of liquid film caused by inclination under low flow conditions, and the current work mainly focuses on the flow oscillation and axial transport of liquid film caused by motions. 10

In the three-field model, the entrainment and deposition process of droplets have an important influence on the prediction accuracy of the model. So far many correlations have been published in the literature, such as Wurtz-Sugawara correlations [36], Govan correlations [38] and Kataoka & Ishii correlations [39]. In this paper, Kataoka et al.’s correlations are adopt, these are, For droplet deposition rate De: De  0.022  f Re

0.74 f

 g   f

  

0.26

 0.74 / De

(24)

For droplet entrainment rate En, in addition to the shearing entrainment rate Enh proposed by Kataoka et al. [39], the boiling entrainment rate Enq is also introduced to model, which is derived from the experimental study of Milashenko et al. [40] with a wide applicability. The shearing entrainment rate is: 2 0.25  Enh De  1   /     0.72  10 9 Re1.75 f We 1       f  0.26  6.6  10 7 Re0.925We0.925   g  1   0.185 f     f   0.26  Enh De  0.185 7 0.925  g  0.925 =6.6  10 Re f We    1     l   f  E De  nh =0   f

  /    1 (25)

  /    1

 Re

lf

 Relfc 

where φ∞ is the equilibrium value of fraction entrained, φ; Relfc is the minimum liquid film Reynolds number required to entrainment. The equations are as follows:

  tanh  7.25  10-7We1.25 Re0.25  f 1.5

 y  Relfc     0.347 

 f   g

  

0.75

 g   f

(26)

1.5

  

(27)

In view of very limited experimental data, the value of y+ cannot be established firmly. Ishii and Grolmes [41] recommended y+ to be 10 based on the amplitude-film thickness relation and the standard boundary layer theory. And the boiling entrainment rate is: 1.3

1.75W f  g  3 Enq   q  10 ( )   DeL   f 

(28)

11

Besides, to estimate the properties of liquid and vapor, the correlations of the IAPWS Industrial Formulation 1997 (IAPWS-IF97) are adopted in the program, which provide an accurate representation of the thermodynamic properties of liquid and vapor, and have been widely used in the engineering.

2.3. Calculation procedure and boundary condition Combining the above equations, a computational program is developed to calculate CHF in rectangular channel under motion conditions. The CHF model is solved by the finite difference method. For the spatial discretization, a staggered grid is adopted, that is, the momentum mesh (including the variables uf, ud, ug) and the scalar mesh (including the variables p, αf, αd, αg, ρf, ρd, ρg) are utilized which are staggered from one another. For the time discretization, the semi-implicit difference scheme is applied. The remarkable advantage of staggered difference method is that the pressure gradient and velocity terms in the equations can be naturally coupled together, and when the Courant number is satisfied, the discrete equations can form a diagonally dominant matrix. The discrete form of the governing equations is shown in table 1. Fig. 3 shows the flow chart of the program calculation. A more specific description of the calculation process can be found in previous work [34]. Once the inlet and outlet boundary conditions (i.e. inlet mass flow rate and enthalpy, outlet pressure) are given, the annular flow length Lann can be calculated by:

Lann  L 

 xann  xin  GAh fg

(29)

qPrq

where xin is the inlet equilibrium quality; xann is the quality at the onset of annular flow proposed by [42], which is given by: xann 

0.6  0.4  f   f   g  gDe / G

(30)

0.6   f /  g

In the annular flow region (Lann>0), the liquid film mass flow rate will decrease with the comprehensive effects of vaporization of the liquid film, deposition and entrainment of droplets. The dryout occurs once the liquid film completely disappears or the liquid film volumetric fraction reduces to a certain value at outlet. In this paper it is set as zero. An initial value of heat flux is set, which is then constantly adjusted based on binary search until the outlet meets the dryout condition. 12

Table 1. The discrete form of the governing equations. Mass continuity equations:

     n 1

f

f

i

n 1 i

n 1

     n 1

g i

i

i

   d i  d i n

n

i







n i

f

n

f

i



f

i

n 1 1 2

i

  f 

n

   u  n

i 1

f

f

i 1

n 1 i

1 2

z

  d i  d i  ud i  1    d i 1  d i 1  ud i  1 n 1

n

n

n

   g   g 

      u  n

n



n 1

g i

n



  d i  d i n 1

   f   f 

n 1

n

n

2

2

z

      u  n

n

n 1

g i

g i

g i 1 2

  g 

n

   u  n

i 1

z

n

n

  Prw Dep  ( Prw Enh  Prq Enq )      A i i  n

 P D  ( Prw Enh  Prq Enq )     rw ep  A  i

n 1

g i 1 2

g i 1

 qP    rq  Ah  fg

 qP   rq   Ah fg

n

  i

Momentum conservation equations:

     n

f

i

f

  M wf 

n

      M 

n 1

g i

g i

  M fg 

n 1 i 1/ 2

n 1

i 1/ 2

n

 u f 

E 

u 

u 

n i 1/ 2



   f   f   u f  n

n

i n

i

 Dep Prw    Dep Prw 

 ud i 1/ 2   ud i 1/ 2

n 1

n

fg

n 1 i 1/ 2



i 1/ 2

n

  M gd 

f

i

  d i  d i n

u 

n

i

n

f

i 1

n

 ud i 1/ 2   ud i 1/ 2 n

 n n P  Enq Prq    Enh Prw  Enq Prq 

nh rw

2A

n 1

g i 1/ 2

  ug 



n i 1/ 2

   g   g   ug  n

n

n

n

z

i 1

i

u 

n

g i 1/ 2

  ug 

n 1

i

   f 

n i

n pin11  pin 1   f  f   f + g   k i z

   d i

n

pin11  pin 1 n   d  d i  f + g   k z

  u  n 1   u  n 1  d i 1/ 2   f i 1/ 2  n i 1/ 2

i i i 1/ 2 z 2qPrq n 1 n 1 1   u u   M gd       f i 1/ 2 g i 1/ 2  n n  i 1/ 2 i 1/ 2  A  h fg    h fg   n 1

n i 1/ 2

  u  n 1   u  n 1  f i 1/ 2   d i 1/ 2 

   d i  d i  ud i 1/ 2 n

 u f  z

i 1/ 2 n

2A n

n i 1/ 2

i 1

Energy conservation equation: hi  hi 1  qPrq    z  GA i

13

   g 

n i

n pin11  pin 1   g  g   f + g   k i z

Start Input boundary parameters Initialization Calculate motion additional terms Guess initial heat flux Solve the velocity with respect to the pressure Solve the pressure matrix by direct elimination

Modify the time step

Calculate the velocity and volume fraction u ∆τ/∆z < 1?

No

Yes Yes, decrease the heat flux

No, increase the heat flux

αf
αf
Output End

Fig. 3. The flow chart of the program calculation. 3.

Program validation The program is validated separately under steady and motion conditions. For steady state, the

CHF prediction results are compared with experimental data in uniformly heated vertical round tubes reported by Becker [43], Thompson and Macbeth [44], as well as uniformly heated vertical rectangular channels reported by Siman-Tov et al. [45], Jacket et al. [46] and Troy et al. [47]. Fig. 4 shows that almost all of these data are predicted within the error range of ±20%.

14

Data of circular tubes Data of rectangular channels

6

+25% +20%

5

qcal/MWm-2

4

-20%

3 2

P=0.99~13.79MPa G=93.58~5434.49kgm-2s-1 in=3.9~247.6K

1 0 0

1

2

3

4

5

6

qexp/MWm-2

Fig. 4. The validation results of CHF model under steady state. Due to the scarce data of CHF for motion conditions in publication, the program validation is only carried out based on the form of motion for the inlet flow oscillation, which is similar to heaving condition. The experimental data points were obtained from Zhao et al. [33], who conducted an experimental research on CHF in vertical tube with forced sinusoidal inlet flow oscillation. The oscillation period is 1~11s, and normalized amplitude of inlet flow oscillation is 0~3.0. In this paper, the CHF value calculated by the established CHF program was compared with the experimental results under different transient conditions, as shown in Fig. 5. The solid data points represent experimental values, and the hollow ones are calculated values. The vertical coordinate is the ratio of the CHF value under the flow oscillation condition to the steady-state CHF value corresponding to the average flow rate. It can be found that the calculated results have the same trend as the experimental results, and the prediction accuracy of the model decreases slightly with the increase of the oscillation amplitude, which may be attributed to the fact that the dryout is triggered by the flash of liquid film under larger flow oscillation in the experiment. 1.1

P=2.0MPa, GAVE=170kgm-2s-1

1.0

P=3.0MPa, GAVE=170kgm-2s-1

1.0 0.9

0.9

0.8

qOSC / q0

qOSC / q0

0.8

0.7

0.7 0.6

TOSC=10.6s

TOSC=10.6s

0.5

0.6

TOSC=5.2s

TOSC=5.2s

0.4

0.5

TOSC=2.1s

TOSC=2.1s

TOSC=1.04s

TOSC=1.04s

0.0

0.1

0.2

0.3

0.4

0.3 0.5

0.6

0.7

G / GAVE

0.2 0.0

TOSC=10.6s

TOSC=10.6s

TOSC=5.2s

TOSC=5.2s

TOSC=2.1s

TOSC=2.1s

TOSC=1.04s

TOSC=1.04s

0.2

0.4

0.6

0.8

G / GAVE

Fig. 5. The validation results of CHF model under the inlet flow oscillation conditions. 15

1.0

4.

Results and discussion Based on the previous experiments and theoretical analysis, it has been found that the influence

of motion conditions on CHF is usually unfavorable. This adverse effect is pronounced especially for low pressure and low flow rates as well as natural circulation conditions. In general, in addition to introducing into the additional forces, the motion conditions may periodically change the height of the equipment, which would eventually force the fluid in the heated channel to oscillate. The oscillation period is roughly equivalent to the motion period. In order to study the influence of motion conditions on CHF characteristics in rectangular channel, the two split parts are studied in this paper: (1) the characteristics of CHF under flow oscillation conditions; (2) the effect of motion conditions on CHF characteristics under constant inlet flow.

4.1. The characteristics of CHF under flow oscillation conditions A typical rectangular channel with 40 mm × 2 mm × 2 m (Width × Gap size × Length) size is selected as the research object to study CHF characteristics under flow oscillation conditions. Assuming that the inlet mass flux follows the sinusoidal law, which is given by: Gin  GAVE  G sin(

2 t ) To

(31)

where GAVE is average inlet mass flux; ∆G is the maximum oscillation amplitude of mass flux; To is the oscillation period. Fig. 6 shows the mass fluxes of vapor core, entrained droplets and liquid film at outlet under a flow oscillation condition. It can be seen that the liquid film, entrained droplets and vapor core will oscillate with the same period but different phases over time. Because of the periodic oscillation of the liquid film, it is important to determine the minimum heat flux corresponding to the dryout of the outlet wall. In this paper, a small wall heat flux is firstly given, and its value is gradually increased until the trough of liquid film flow at the outlet is exactly equal to 0 within an oscillation period. The heat flux corresponding to the first dryout of the wall surface is taken as CHF under flow oscillation condition.

16

600

P=8.0MPa, GAVE=600kgm-2s-1, G=300kgm-2s-1 500

Liquid film

Gout/kgm-2s-1

400 300

Vapor core

200 100

Liquid droplets

0 1

2

3

4

5

6

t/s

Fig. 6. The trend of mass fluxes of outlet liquid film, droplets and vapor core with time.

Fig.7 depicts the variation trend of CHF in the rectangular channel with the oscillation amplitude and period under inlet flow oscillation. It can be clearly seen from the figure that, under the same inlet average flow, the CHF corresponding to flow oscillation is significantly smaller than that under steady state. With the increase of amplitude and oscillation period, the CHF gradually decreases but the variation trend gradually slows down. In particular, for the small oscillation period, the CHF decreases rapidly with the increase of oscillation period and then decreases by a small margin. In addition, under the condition of flow oscillation, CHF is not equal to the steady-state CHF corresponding to the minimum inlet flow or that corresponding to the average inlet flow, but between these two values. The reason for the above phenomenon can be attributed to the stirring effect of the axial flow in the channel, as shown in Fig. 8. In Fig. 8(a)~(c), the variation of the liquid films along the length of the channel are compared under different oscillation periods and amplitudes. The different lines in the graph represent the mass flux at different times during an oscillation period, that is, the axial distributions of the liquid film at 10 time steps are depicted separately at intervals of 0.1TOSC. Due to the axial turbulence of the liquid film flow, the oscillation amplitude of the film mass flux is attenuated along the flow direction, and the amplitude at outlet (ΔGo) is significantly lower than that at inlet (ΔGi). On the one hand, with the increase of the oscillation period, the axial stirring frequency of the liquid film at the same mass flow rate will slow down, resulting in an increase in the oscillation amplitude of the liquid film at the outlet, which in turn leads to the occurrence of intermittent dryout. At the same time, when the oscillation period is fixed, the greater the oscillation amplitude of the inlet flow is, the greater the fluctuation of the outlet liquid film will be, which will also lead to the occurrence of dryout in advance. On the other hand, as the amplitude increases, the 17

axial transport effect of the liquid film is enhanced, which can be seen from the figure is that the average mass flux of the outlet liquid film is shifted upward, thus the trend of CHF begins to deviate from that under the minimum inlet mass flux condition. 500 400

p=8.0MPa, GAVE=600kgm-2s-1

380

400

CHF for GAVE CHF for flow oscillation CHF for G=GAVE-G

300

qCHF/kWm-2

qCHF / kWm-2

360

200

CHF for flow oscillation CHF for G=GAVE-G

0 0.0

0.2

320

P=8.0MPa GAVE=600kgm-2s-1, G=300kgm-2s-1

300

CHF for GAVE

100

340

280

0.4

0.6

0.8

260

1.0

0

2

4

G / GAVE

6

8

10

12

TOSC / s

(a)

(b)

Fig. 7. The variation trend of CHF in the rectangular channel with (a) oscillation amplitude, (b) oscillation period. 1000 900

P=8.0MPa, GAVE=600kgm-2s-1,

800

G=300kgm-2s-1, TOSC=1s

Gf/kgm-2s-1

700 600

2Gi

500 400

2Go

300

Go/Gi=0.36

200

0.0

GAVEo=326.6kgm-2s-1

0.5

1.0

1.5

2.0

L/m

(a) 1000 900

P=8.0MPa, GAVE=600kgm-2s-1,

800

G=300kgm-2s-1, TOSC=2s

Gf/kgm-2s-1

700 600

2Gi

500 400

2Go

300 200 100

Go/Gi=0.72 0.0

GAVEo=342kgm-2s-1

0.5

1.0

L/m

18

1.5

2.0

(b) P=8.0MPa, GAVE=600kgm-2s-1,

1000

G=400kgm-2s-1, TOSC=2s

Gf/kgm-2s-1

800

600

2Gi

400

2Go 200

0

GAVEo=347kgm-2s-1

Go/Gi=0.73 0.0

1.0

0.5

1.5

2.0

z/m

(c) Fig. 8. The variation of the liquid films along the channel length (The different curves represent the mass flux at different times during an oscillation period). (a) ΔG=300kg·m-2·s-1, Tosc=1s; (b) ΔG=300kg·m-2·s-1, Tosc=2s; (c) ΔG=400kg·m-2·s-1, Tosc=2s.

Fig. 9(a)~(d) presents the simulations of the influence of average mass flux, heated length, pressure and gap size on the CHF under inlet flow oscillation, respectively. As expected, when other boundary conditions are fixed, the CHF increases with the increase of mass flux and gap size, and with the decrease of heated length. If the steady-state CHF corresponding to the average inlet flow is defined as CHFmax, and the one corresponding to the minimum inlet flow is defined as CHFmin, Fig. 9(a) and (b) clearly show that the transient CHF moves asymptotically from CHFmax to CHFmin with the increase of average mass flux and the decrease of heated length, which is similar to the law reflected in Fig. 7(b). The reason for the above rules is still mainly attributed to the change of the oscillation intensity of the liquid film at the outlet. On the whole, an increase in average mass flux and a decrease in heated length will lead to an increase in CHF. However, given the ratio of the oscillation amplitude to the average mass flux (i.e. ∆G/GAVE), the oscillation amplitude of the liquid film increases with inlet mass flux as well, while the stirring effect of the axial liquid film will weaken. Consequently, the outlet wall is more prone to dryout periodically in which the heat flux corresponds to CHFmin. At the same time, Fig. 8 has indicated that the oscillation intensity of the liquid film will gradually decrease along the heated length. It can be expected that when the heated length is very short, the oscillation amplitude of the outlet flow tends to that of the inlet, thus the trough of outlet liquid film flow tends to the steady liquid film flow corresponding to the minimum inlet flow. 19

Furthermore, it can be confirmed from the figure that when the average flow inlet mass flux is small enough or the heated length is very long, the oscillation of the inlet flow has little effect on CHF. Fig. 9(d) shows that the CHF increases with an increase in gap size at fixed inlet average mass flux and oscillation amplitude. This is related to the fact that although the heated perimeter of the channel remains unchanged, its equivalent diameter increases with the gap size, resulting in an increase in mass flow rate as well as CHF. On the other hand, under the fixed oscillation amplitude, it seems that the change of gap size has little effect on the axial stirring of liquid film. Although the change of equivalent diameter of channel will affect the entrainment and deposition behavior of liquid droplets, the transient CHF corresponding to different gap sizes does not show a similar pattern with other boundary variables, which has a consistent trend with the CHFmin. In comparison, the effect of pressure on CHF in the narrow rectangular channel is more complicated, which presents different trends in the two pressure ranges. As shown in Fig. 9(c), the CHF increases rapidly as the pressure increases and then has a maximum value at a pressure of about 2–4 MPa, and above this pressure, the CHF decreases slowly with further increasing pressure. This phenomenon may be explained by the following reasons. In annular flow, dryout is the result of competition of droplet deposition, entrainment and film evaporation. Liquid is lost from the film due to droplet entrainment and water evaporation, and it is gained as a result of droplet deposition. On the one hand, as the pressure increases, the slip ratio and density difference between the vapor and the liquid film will decrease, and the shearing entrainment is weakened, at the same time, the increase in the vapor-liquid viscosity ratio will also increase the droplet deposition rate, which leads to an increase in CHF. On the other hand, because of the decrease of the latent heat with an increase in pressure, the evaporation rate increases and CHF will decrease. Combining these two converse factors, the entrainment and deposition of droplets may be more dominant at lower pressure, while the evaporation of liquid film at higher pressure has a greater impact on CHF, which can be used to explain the trend of CHF in the Fig. 9(c). Furthermore, it can be found that the pressure corresponding to the maximum value of the CHF varies with inlet mass fluxes, which is owing to the fact that with the decrease of inlet mass flux, the relative velocity between vapor core and liquid film increases, and the shear effect of vapor core on liquid film is enhanced, resulting in an increase in entrainment rate. Consequently, a decrease in inlet mass flux will lead to a decrease in pressure corresponding to the maximum value of the CHF. Fig.9(c) also indicates that the variation of CHF under flow 20

oscillation conditions is consistent with the CHF at minimum inlet mass flux, except that the CHF starts to shift upward under larger pressure, which is attributed to the axial agitation of the liquid film. 1000 800

CHF for GAVE CHF for flow oscillation CHF for G=GAVE-G

700

CHF for GAVE

600

CHF for flow oscillation CHF for G=GAVE-G

500

600

qCHF / kWm-2

qCHF / kWm-2

800

400

p=8.0MPa, G=0.5GAVE

200

400

P=8.0MPa GAVE=600kgm-2s-1, G=300kgm-2s-1

300 200 100 0

0

500

1000

1500

2000 0

GAVE

2

4

L/m

(a)

6

8

10

(b)

500 700

CHF for GAVE CHF for flow oscillation CHF for G=GAVE-G

450 400

CHF for GAVE CHF for flow oscillation CHF for G=GAVE-G

600

qCHF / kWm-2

qCHF / kWm-2

500

350

GAVE=600kgm-2s-1, G=0.5GAVE

300 250

400 300

200

200

150

100

0

2

4

6

8

10

12

14

P=8.0MPa GAVE=600kgm-2s-1, G=0.5GAVE 1.0

1.5

2.0

P / MPa

2.5

3.0

3.5

4.0

s / mm

(c)

(d)

Fig. 9. Effect of different parameters on CHF in rectangular channel under flow oscillation conditions. (a) Inlet average mass flux; (b) Heated length; (3) Pressure; (4) Gap size.

4.2. Effect of motion conditions on CHF characteristics under constant inlet flow In this paper, the effects of three typical motion conditions on CHF in rectangular channel (40 mm × 2 mm × 2 m) are analyzed, including heaving, rolling and the coupled motion of heaving and rolling. Assuming that the law of heaving and rolling is a standard sinusoidal form. The calculation condition parameters are shown in Table 2. Table 2. Calculation condition parameters Parameters

Range

Pressure (MPa)

6~10 21

Inlet mass flux (kg·m-2·s-1)

300~1000

Inlet subcooling (K)

0~80

Heaving acceleration amplitude (g)

0~0.8

Heaving period (s)

1~5

Rolling angle (°)

0~45

Rolling period (s)

2~10

4.2.1 The effect of heaving motion The channel is assumed to heave along the z axis, and the acceleration is positive in the upward direction, the additional acceleration vector f is:

f =  a t  k

(32)

The term (g+f)·k in the momentum equations is:

 f  g   k =   g0  a  t  

(33)

Under the heaving condition, the liquid film will be periodically oscillated due to the axial periodic additional force. As shown in Fig. 10, the axial distributions of the liquid film at 10 time steps are presented separately at intervals of 0.1T. It can be found that the oscillation amplitude of the liquid film gradually increases from the inlet along the channel direction, and then remains almost unchanged until the exit is reached. Fig. 11 plots the oscillation amplitude of the liquid film with different heaving acceleration amplitudes and periods. The amplitude of the oscillation increases with the increase of the acceleration amplitude, and with the decrease of the period. That is because the additional force caused by the heaving motion causes the pressure in flow passage to change periodically, which in turn affects the entrainment and deposition rate of the droplets and the evaporation of the liquid film, as well as the axial agitation of the liquid film. At larger heaving acceleration amplitudes and smaller heaving periods, the above effects are more pronounced and the oscillation of the liquid film is more obvious.

22

600

P=8.0MPa, Gin=600kgm-2s-1, a=0.6g, T=2s

550

450

370

360

400

Gf/kgm-2s-1

Gf/kgm-2s-1

500

350

340

350

330 0.0

0.5

1.0

1.5

2.0

t/s

300 0.0

0.5

1.0

1.5

2.0

z/m

Fig. 10. The variation of the liquid film along the channel length under the heaving motion (The different curves represent the mass flux at different times during an oscillation period). 400

T=2s, a=0.6g T=2s, a=0.3g T=3s, a=0.3g

Gf/kgm-2s-1

380

360

340

320

1

2

3

4

5

6

7

8

t/s

Fig. 11. The oscillation amplitude of the liquid film with different heaving acceleration amplitudes and periods. Figs. 12~14 present the CHF as a function of heaving acceleration amplitude and period with different pressures, inlet mass fluxes and inlet subcoolings. As expected, for the larger heaving acceleration amplitudes and smaller heaving periods, the oscillation of the liquid film is more pronounced, which causes the outlet wall to appear intermittently dryout earlier. The CHF decreases as the heaving acceleration amplitude increases and the heaving period decreases. But when the period increases to a certain value, the impact of the heaving motion on CHF will become small. In general, within the parameters of this paper, the heaving motion has little effect on the CHF in the rectangular channel except for the low mass flux, in which the CHF will decrease to the original 10%.

23

480

480

470

470

P=6MPa P=8MPa P=10MPa

460

P=6MPa P=8MPa P=10MPa

450

qCHF / kWm-2

qCHF / kWm-2

450

460

440 430 420

440 430 420 410

410

400

400 0.0

0.2

0.4

0.6

390

0.8

1

2

3

a/g

4

5

T/s

Fig. 12. The Effect of different heaving acceleration amplitudes and periods on CHF in rectangular channel with different pressures. 700

700

600

-2

Gin=600kgm s 500

Gin=300kgm-2s-1

-1

Gin=1000kgm-2s-1

qCHF / kWm-2

qCHF / kWm-2

600

Gin=300kgm-2s-1

400

300

Gin=600kgm-2s-1

500

Gin=1000kgm-2s-1

400

300

200

200 0.0

0.2

0.4

0.6

0.8

1

2

3

a/g

4

5

T/s

Fig. 13. The Effect of different heaving acceleration amplitudes and periods on CHF in rectangular channel with different inlet mass fluxes. 560

560

540

Tin=0K Tin=40K

520

Tin=0K Tin=40K

520

Tin=80K qCHF / kWm-2

qCHF / kWm-2

540

500 480

Tin=80K

500 480 460

460

440

440 0.0

0.2

0.4

0.6

0.8

1

2

a/g

3

4

5

T/s

Fig. 14. The Effect of different heaving acceleration amplitudes and periods on CHF in rectangular channel with different inlet subcoolings.

4.2.2 The effect of rolling motion 24

For the rolling motion, the channel is assumed to roll around the x axis, the angular velocity is

    t  i , the radius vector is r = xi + yj + zk . The additional acceleration vector f and the equivalent gravity vector are given by: d  (t ) d  (t )   yk  zj  f    2 (t )u(t ) j   2 (t ) yj   2 (t ) zk + dt dt  

(34)

g =  g 0 cos  (t )k  g 0 sin  (t ) j

(35)

The term (g+f)·k in the momentum equations is:

 f  g   k =   g0 cos  t    2 (t ) z  

d  (t )  y dt 

(36)

The effect of the maximum rolling angle and the rolling period on the mass flux of the liquid film at the outlet is shown in Fig. 15. Similar to the heaving condition, the mass flux of the liquid film oscillates periodically with time, and the amplitude increases with the maximum rolling angle, and decreases as the rolling period increases. The difference is that when the period is 3s, there are two crests for the liquid film during one rolling period. The following reason may be responsible for this phenomenon. In addition to the gravity term (g), the additional acceleration (f) generated by the rolling motion mainly consists of two parts: tangential acceleration and centripetal acceleration. The component of the centripetal acceleration in the z-axis direction always coincides with the flow direction, while the component direction of the tangential acceleration periodically changes with time (Fig. 16). The secondary oscillation of the liquid film is the result of the superposition of the two types of additional accelerations. In particular, with the increase of rolling period, the axial transport of liquid film becomes weaker, and the above effects would appear. 380

T=2s, m=30 T=2s, m=45

360

qCHF / kWm-2

T=3s, m=30 340

320

300

280 2

3

4

5

6

7

8

t/s

Fig. 15. The effect of the maximum rolling angle and the rolling period on the mass flux of the liquid film at the outlet. 25

6

Total additional acceleration Tangential acceleration Centripetal acceleration

5 4

a/ms-2

3 2 1 0 -1 -2 -3 2

3

4

5

6

7

8

t/s

Fig. 16. The trend of the additional accelerations at the outlet with time. The effects of maximum rolling angle and rolling period on CHF under different pressures, mass fluxes and inlet subcoolings are shown in Figs. 17~19. It can be seen that CHF gradually decreases with the increase of the maximum rolling angle. In the case of small mass flux, the effect of rolling on CHF is relatively large, whose value is decreased by 9.3%. But for the high mass flux, the effect is almost negligible. At the same maximum rolling angle, CHF increases with the rolling period. Similar to the heaving condition, the longer the rolling period, the less the effect of the rolling motion on CHF. 480 480

470

450

P=6MPa P=8MPa P=10MPa

460 450

440

qCHF / kWm-2

qCHF / kWm-2

470

P=6MPa P=8MPa P=10MPa

460

430 420

440 430 420

410 410

400 400

390 0

10

20

30

40

50

390 2

m/

4

6

8

10

T/s

Fig. 17. The Effect of different maximum rolling angles and rolling periods on CHF in rectangular channel with different pressures.

26

700

700

600

Gin=300kgm-2s-1 Gin=600kgm-2s-1

500

Gin=300kgm-2s-1 Gin=600kgm-2s-1

500

Gin=1000kgm-2s-1

qCHF / kWm-2

qCHF / kWm-2

600

400

Gin=1000kgm-2s-1

400

300

300

200

200 0

10

20

30

40

50

2

m/

4

6

8

10

T/s

Fig. 18. The Effect of different maximum rolling angles and rolling periods on CHF in rectangular channel with different inlet mass fluxes. 560

560

540

Tin=0K

540

Tin=40K

520

520

Tin=80K 500

qCHF / kWm-2

qCHF / kWm-2

Tin=0K Tin=40K

480 460

Tin=80K

500 480 460

440

440 420 0

10

20

30

40

50

2

m/

4

6

8

10

T/s

Fig. 19. The Effect of different maximum rolling angles and rolling periods on CHF in rectangular channel with different inlet subcooling.

4.2.3 The effect of coupling motion of heaving and rolling Assuming that the channel makes a heaving motion along the z-axis with acceleration a(t) while performing a rolling motion about the x-axis with rolling angle θ(t). The angular velocity is

    t  i , and the radius vector is r = xi + yj + zk . By Eqs. (6) and (7), the additional acceleration vector f and the equivalent gravity vector g are as follows: d  (t ) d  (t )   f    a(t )sin  (t ) j  a(t )cos  (t )k  2 (t )u(t ) j   2 (t ) yj   2 (t ) zk + yk  zj  dt dt  

g =  g0

(38)

The term (g+f)·k in the momentum equations is:

27

(37)

 f  g   k =   g0 +a(t ) cos (t )   2 (t ) z  

d  (t )  y dt 

(39)

Fig. 20 shows the coupled effect of the different amplitudes of the heaving acceleration and the rolling angles on CHF. Both the heaving motion and the rolling motion are harmful to CHF, but the effect of the coupled motion on CHF is not a simple superposition effect of them. It can be seen from the figure that as the amplitude of the rolling angle increases, the impact of the heaving motion on CHF is gradually decreased. In addition, similar to the single motion form, the coupled motion has a non-negligible effect on the CHF at low mass flux. As shown in Fig. 21, under the current working conditions with a mass flux of 300 kg·m-2·s-1, the CHF can be reduced by 11.9%. 442 440

Static CHF

438

qCHF / kWm-2

436 434 432 430

a=0 a=0.3g a=0.6g

428 426 424 0

10

20

30

40

50

m/

Fig. 20. The coupled effect of the different amplitudes of the heaving acceleration and the rolling angle on CHF. 460

Static CHF

440

qCHF / kWm-2

420

Gin=300kgm-2s-1

400

Gin=600kgm-2s-1

240

Static CHF 220 200 180 0

10

20

30

40

50

m/

Fig. 21. The influence of the inlet mass flow on CHF under the coupled motion conditions (a=0.6g, T=2s). 28

5.

Conclusions In this paper, the dryout-type CHF characteristics in narrow rectangular channel under complex

motion condition were studied by a validated three-field analysis program. Considering that the motion conditions would introduce an additional force field and cause flow to oscillate in the channel, the two split parts were analyzed separately: (1) The characteristics of CHF under inlet flow oscillation conditions; (2) The effect of motions including heaving, rolling and the coupled motion of heaving and rolling on CHF characteristics under constant inlet flow. Several conclusions could be drawn as follows: (1) Under inlet flow oscillation conditions, the mass flux of the liquid film at the outlet will also periodically oscillate with time. As the heated heat flux increases, the intermittent dryout may occur. The heat flux corresponding to the first evaporation of the wall surface is taken as CHF under flow oscillation condition. (2) Under inlet flow oscillation conditions, the flow oscillating amplitude will steadily decrease along the flow direction due to the mixing of the axial flow. The CHF is between the steady-state CHF corresponding to the inlet average mass flux and the one corresponding to the inlet minimum mass flux, and it decreases with the increase of the inlet flow oscillation amplitude and period. The variation of CHF characteristics with average mass flux, heated length, pressure and gap size is similar to that under steady-state condition. (3) Under the motion conditions with fixed inlet flow, due to the additional forces caused by the heaving and rolling motion, the mass flux of the liquid film at the outlet will periodically oscillate. The CHF decreases with the increase of the maximum amplitude of the heaving and rolling motion, and increases with the increase of the heaving and the rolling period. The effect of the motion conditions on CHF is relatively small (within 5%) except for the small mass flux, in which the CHF can be reduced by 10%. (4) Under the coupled motion of heaving and rolling conditions with fixed inlet flow, the effect of the coupled conditions on CHF is greater than any single motion. As the amplitude of the rolling angle increases, the impact of the heaving motion on CHF is gradually decreased. (5) Small average mass flux and large flow oscillation have a greater impact on CHF in rectangular narrow channels under motion conditions. In the safety assessment of floating nuclear powers, 29

especially for barge-type ONPPs, the negative effects of motion conditions on CHF need to be fully considered to ensure adequate safety margin. Of course, the modeling in this paper still has some shortcomings that need to be emphasized. In particular, the morphology of liquid film in the annular flow region is simplified, for example, the influence of interfacial waves is weakened, and the circumferential distribution uniformity of the liquid film is assumed. It is expected that the subsequent models can be further improved and optimized.

Conflict of interest We declare that we have no conflict of interest.

Acknowledgement The authors appreciate the support from Natural Science Foundation of China (Grant No. 11622541) and National Key R&D Program of China (Grant No. 2017YFE0302100).

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34

Highlights 

The CHF characteristics in rectangular channel were theoretically investigated.



A three-fluid based analysis program was developed and validated.



The additional forces caused by motion were considered in the program.



The effects of various forms of motion on CHF were comprehensively analyzed.



The additional forces at low flow rate have a significant effect on CHF.

35