Analysis of Frictional Pressure Drop Correlations of Refrigerant Two-Phase Flow in Mini-Channel

doi:10.16183/j.cnki.jsjtu.2020.159

Abstract

Abstract:

This paper presents a comprehensive analysis of the frictional pressure drop correlations in two-phase flow in mini-channel, describes the relationship of inheritance and development between the correlations, and points out the innovation between different correlations. In order to evaluate the universality and precision of various correlations, it establishes a large frictional pressure drop database, which is specialized for mini-channels. This database includes 1302 and 1576 data points under evaporation and condensation/adiabatic conditions, respectively. Finally, it evaluates and analyzes 26 correlations under different conditions. The results show that the Sempértegui-Tapia and the Kim correlation have the best prediction ability under evaporation conditions and condensation/adiabatic conditions, respectively. This paper provides some advice on the improvement of correlation.

Key words: two-phase flow, frictional pressure drop, correlations, evalution

CLC Number:

TK124

LIU Xucheng, GU Bo, ZENG Weijie, DU Zhongxing, TIAN Zhen. Analysis of Frictional Pressure Drop Correlations of Refrigerant Two-Phase Flow in Mini-Channel[J]. Journal of Shanghai Jiao Tong University, 2021, 55(9): 1095-1107.

Figures/Tables 7

Tab.1

Correlations of homogeneous equilibrium model

文献编号	关联式	文献编号	关联式
[9]	$1 μ tp$ = $x μ g$ + $1 - x μ l$	[12]₄	μ_tp= $12$ [μ_l $2 μ l + μ g - 2 μ l - μ g x 2 μ l + μ g + μ l - μ g x$ + μ_g $2 μ g + μ l - 2 μ g - μ l 1 - x 2 μ g + μ l + μ g - μ l 1 - x$ ]
[10]	μ_tp= $2 μ g + μ l - 2 μ g - μ l 1 - x 2 μ g + μ l + μ g - μ l 1 - x$	[13]	μ_tp=xμ_g+ $1 - x$ μ_l
[11]	μ_tp=μ_l $1 - x + x ρ l / ρ g 0.5 - 1$	[14]	μ_tp= $x ρ l μ g + 1 - x ρ g μ l x ρ l + 1 - x ρ g$
[12]₁	μ_tp=μ_l $2 μ l + μ g - 2 μ l - μ g x 2 μ l + μ g + μ l - μ g x$	[15]	ω= $x ρ l ρ g + x ρ l - ρ g$ μ_tp=ωμ_g+ $1 - ω 1 + 2.5 ω$ μ_l
[12]₂	μ_tp=μ_g $2 μ g + μ l - 2 μ g - μ l 1 - x 2 μ g + μ l + μ g - μ l 1 - x$	[16]	μ_tp= $μ l μ g μ g + x 1.4 μ l - μ g$
[12]₃	μ_tp= $14$ { $3 x - 1$ μ_g+ $2 - 3 x$ μ_l+ $3 x - 1 μ g + 2 - 3 x μ l 2 + 8 μ g μ l$ }	[17]	μ_tp=C_μμ_l $1 - x$ +μ_gx, C_μ=6.195-9.178p_r

Tab.1

Tab.2

Tab.3

Separate flow correlations and empirical correlations

文献编号	关联式	实验信息等
[18]	$f tp = 0.0196 W e c - 0.372 R e lf 0.318$	适用于小通道和常规通道,流型为环状流,D_h=0.517~31.7 mm,工质为水、R134a、R245fa及多种二元混合物,G=39.4~3498 kg/(s·m²),x=0.01~0.97;平均相对偏差为13.1%,几乎所有数据涵盖在±30%的误差带中;工况为绝热
[26]	C=21 $1 - exp - 0.319 D h$	基于文献[25]修正;圆形和矩形光滑管,小通道和常规通道,二元工质,水平流动和竖直流动;大部分数据误差在±12%之内;工况为绝热;D_h单位为mm
文献编号	关联式	实验信息等
[27]	X=18.65 $ρ g ρ l 0.5 1 - x x R e g 0.1 R e l 0.5$ $φ l 2$ =X^-1.9	基于文献[25]修正;圆形小通道,D_h=2.98 mm,工质为水,流态为液相层流-气相湍流,G=50~200 kg/(s·m²),压力范围为200 kPa;平均相对偏差为7%;工况为蒸发
[28]	C=0.227 $R e lo 0.452$ X^-0.320 $N con - 0.820$ N_con= $1 D h σ g (ρ l - ρ g) 0.5$	基于文献[25]修正;圆形微通道/小通道,D_h=0.244~0.792 mm,工质为R134a,G=140~950 kg/(s·m²);平均相对偏差为8.1%;工况为蒸发
[29]	C= $0.39 R e lo 0.03 S u go 0.10 ρ l ρ g 0.35 R e l ≥ 2000, R e g ≥ 2000 8.7 × 10 - 4 R e lo 0.17 S u go 0.50 ρ l ρ g 0.14 R e l ≥ 2000, R e g < 2000 1.5 × 10 - 3 R e lo 0.59 S u go 0.19 ρ l ρ g 0.36 R e l < 2000, R e g ≥ 2000 3.5 × 10 - 5 R e lo 0.44 S u go 0.50 ρ l ρ g 0.48 R e l < 2000, R e g < 2000$	基于文献[25]修正;包括了多种工质、管道截面类型和广阔的工况范围,D_h=0.0695~6.22 mm,应用于冷凝或绝热工况;总体平均相对偏差为23.3%;基于 7115 个绝热/冷凝的小/微通道压降数据的数据库而开发
[30]	C= $C non - bo 1 + 60 W e lo 0.32 Bo P H P F 0.78 R e l ≥ 2000 C non - bo 1 + 530 W e lo 0.52 Bo P H P F 1.09 R e l < 2000$	基于文献[29]修正;包括了多种工质、管道截面类型和广阔的工况范围,D_h=0.349~5.35 mm,应用在蒸发工况;平均相对偏差为17.2%;基于 2378 个蒸发的小/微通道压降数据的数据库而开发;C_non-bo使用Kim关联式计算
[31]	C=4.6468×10^-6 $p r 5.5866$ R $e l 0.4387 ρ l ρ g 5.7189$ X^-0.4243	基于文献[25]修正;多管矩形小通道,D_h=1.16 mm,工质为R1234yf、R134a和R32,Re_l=528~8200, p_r为0.182~0.603;平均相对偏差为8.32%;工况为冷凝
[32]	$ϕ g 2$ =1+C $X n tt$ + $X tt 2$ n=2-1.5exp $- 0.025 Fr$ C=21 $1 - exp - 0.28 B d 0.5 2 - 1.9 exp - 0.016 F r 1.4$	基于文献[25]修正;4.35 mm内径光滑单管,工质为R1234ze(E)、R32、R410A、二甲醚和R1234ze(E)/R32混合物,G=147~403 kg/(s·m²),x=0.0065~0.9724;平均相对偏差为9.51%;工况为冷凝
[33]	C=20R $e l - 0.15 S r 1.15$ Bd^-0.2 S_r= $ρ l ρ g x 1 - x 1 - α α$	基于文献[25]修正;管道为光滑单管,内径为7.75和14.45 mm,工质为R290,G=150~450 kg/(s·m²),p_r=0.25~0.95;平均相对偏差为19%;工况为冷凝
[34]	$ϕ l 2$ =1+ $C X tt$ + $1 X tt 2$ C=λx^0.35 $1 - x 0.25 p r 0.31$ R $e tp 0.09$ W $e tp 0.09$	基于文献[25]修正;管道为多管小通道,D_h=0.64 mm和0.81 mm,G=50~200 kg/(s·m²),x=0.1~0.9;平均相对偏差为17.4%;工况为绝热
[35-36]	$C = aR e tp b x c V μ tp d$	基于文献[25]修正;管道为多口管/单管小通道及微通道;单管关联式平均相对偏差为17.4%;多口管关联式平均相对偏差为18.9%
[37]	$ϕ lo 2 = 1 - x 2 + 2.87 x 2 p r - 1 + 1.68 x 0.8 1 - x 0.25 p r - 1.64$	基于文献[49]修正;小通道和常规通道,工质为R134a、R22、R404A,G=20~1000 kg/(s·m²),饱和温度 T_s=20~65 ℃,x=0.2~0.89;85%的数据在±20%的误差带中,平均相对偏差为11.5%;工况为绝热
[39]	$ϕ lo 2 = 1 - x 2 + 2.87 x 2 p r - 1 + 1.54 B d 0.19 ρ l - ρ g ρ tp 0.81$	基于文献[38]修正;小通道,工质为12种常见制冷剂,质流密度范围为140~2000 kg/(s·m²),适用范围为 Bd≥0.1且BdR $e l 0.5$ ≤ 200;81.7%的数据在±30%的误差带中;工况为绝热
文献编号	关联式	实验信息等
[40]	$ϕ lo 2 = ϕ lo, M - S 2 1 + 1.54 1 - x 0.5 L a 1.47 La = σ / g ρ l - ρ g$	基于文献[45]修正;小通道和常规通道,工质为15种常见制冷剂,G=25.4~1150 kg/(s·m²),热流密度 q=0.6~150 kW/m²;平均相对偏差为25.5%;工况为蒸发
[41]	$ϕ lo 2 = 1 + Γ 2 - 1 B x 0.5 1 - x 0.5 + x Γ = μ g / μ l / ρ l / ρ g B = 169.6258 G - 0.5747$	基于文献[42]修正;三角形光滑多口微通道,工质为丙酮,G=65.52~289.61 kg/(s·m²),q=141.92~481.08 kW/m²,工况为蒸发;平均相对偏差为12.56%
[43]	$ϕ go 2 = {x 1.8 + 1 - x 1.8 ρ g f lo ρ l f go + 0.65 x 0.68 1 - x 0.43 μ l μ g 1.25 ρ g ρ l 0.75}$	基于文献[47]修正;适用于矩形截面小通道,工质为R134a、R32、R1234ze(E)和R410A,G=100~400 kg/(s·m²),T_s=40~60 ℃,工况为冷凝;平均相对偏差为9.6%
[44]	$φ lo 2 = 1 + ω Y 2 - 1 x 1 - x 1 / 2.31 + Y 2 x 2.31 ω = 3.01 exp - 0.00464 R e go / 1000$	基于文献[44]修正;所用的管道为圆形、方形和三角形单管小通道,工质为R134a、R1234ze(E)、R1234yf和R600a,G=100~1600 kg/(s·m²),x=0.05~0.95,工况为冷凝;平均相对偏差为10.2%
[45]	$ϕ lo 2 = E + 0.5 H x 0.22 1 - x 0.784 W e tp 0.35 f l / f g - 0.56 E = 1 - x 2 + x 2 Y 2 H = ρ l ρ g 0.91 μ g μ l 0.19 1 - μ g μ l 0.7$	基于文献[49]修正;所用管道为矩形多口微通道,工质为去离子水,G=47~1267.80 kg/(s·m²),q=5.38~116.89 kW/m²,工况为蒸发;平均相对偏差为12.23%
[47]	$d p d z tp, F = f int 1 D h G 2 x 2 2 ρ g α 2.5 f int f l = A X a R e l b φ c φ = j l μ l σ$	基于文献[48]修正;小通道和常规通道,D_h=0.5~4.91 mm,工质为R134a,G=150~750 kg/(s·m²),x=0~1,82%的数据在±20%的误差带中;工况为冷凝

Tab.3

Tab.4

Tab.5

Fig.1

Fig.2

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文献编号	工况	D_h/mm	工质	G/(kg·s^-1·m^-2)	x	管道类型	数据量
[3]	蒸发工况	1.5	R744	300~600	0.02~0.98	水平圆管	265
[52]	蒸发工况	1.7	R290	100~500	0.09~1.00	垂直圆管	64
[53]	蒸发工况	1.224、1.7	R717	100~500	0.05~0.98	垂直圆管	238
[54]	蒸发工况	1.42	R744	300~600	0.04~1.00	水平圆管	276
[55]	蒸发工况	2.6	R600a、R134a	240~440	0.10~0.77	水平圆管	21
[56-57]	蒸发工况	2.32	R134a、R245fa	200~500	0.21~0.99	水平圆管	100
[58]	蒸发工况	1.0、2.2	R32	200~400	0.04~0.92	水平矩管	79
[59]	蒸发工况	0.68	R134a	600~1400	0.11~0.21	水平矩形管	83
[60]	蒸发工况	2	R32	100~400	0.02~0.90	水平圆管	69
[61]	蒸发工况	1.6	R134a、R1234yf	400~500	0.07~0.52	垂直圆管	78
[62]	蒸发工况	0.83、1.22、1.70	R134a	100~400	0.04~0.36	垂直圆管	29
[17]	冷凝/绝热工况	0.529	R744	200~1400	0.00~1.00	圆管	304
[44]	冷凝/绝热工况	1.1	R134a、1234yf、 R1234ze(E)、R600a	100~1200	0.03~0.97	圆管	330
[63]	冷凝/绝热工况	0.762	R134a、1234ze(E)	200~800	0.10~0.96	圆管	100
[64]	冷凝/绝热工况	0.952、1.152	R152a	200~800	0.11~0.90	圆形和矩形管	76
[65]	冷凝/绝热工况	0.509、0.79	R134a、245fa	350~2000	0.00~0.92	圆管	305
[66]	冷凝/绝热工况	0.96、2.00、1.23	R134a、1234yf	200~800	0.10~1.00	圆管	265
[67]	冷凝/绝热工况	0.96	R290	200~800	0.10~0.96	圆管	48
[68]	冷凝/绝热工况	1.152、0.952、1.304	R32、R22、R152a	200~600	0.08~0.92	圆形和方形管	148

模型	关联式	蒸发工况		冷凝/绝热工况
模型	关联式	MAE/%	θ₃₀/%	MAE/%	θ₃₀/%
均相	文献[9]	47.41	13.44	37.00	37.73
	文献[12]₁	39.04	26.96	29.53	61.45
	文献[12]₂	43.36	20.12	34.05	48.83
	文献[12]₃	40.32	25.50	31.30	56.18
	文献[12]₄	40.69	24.42	31.45	56.31
	文献[13]	38.01	29.03	28.54	67.15
	文献[15]	44.55	17.59	34.26	48.45
	文献[17]	47.02	36.25	56.22	58.97
单相增强型	文献[26]	30.36	48.23	31.10	54.98
	文献[27]	79.73	0	74.15	0.70
	文献[28]	56.40	35.79	52.69	38.24
	文献[29]	29.34	53.00	24.68	72.86
	文献[31]	41.01	32.10	35.65	44.77
	文献[32]	42.95	29.95	69.57	43.56
	文献[33]	61.42	47.31	132.95	7.86
	文献[34]	94.30	26.50	228.11	12.62
	文献[35,36]	53.88	33.33	125.56	15.61
全相增强型	文献[38]	37.83	39.65	29.47	69.61
	文献[39]	29.82	61.62	37.39	52.44
	文献[40]	98.00	10.29	161.31	5.64
	文献[41]	61.47	12.44	69.91	5.90
	文献[43]	31.19	47.24	31.14	65.76
	文献[44]	25.65	67.90	32.55	61.64
	文献[45]	29.14	52.23	27.42	69.44
	文献[46]	99.20	26.42	129.83	21.05
	文献[49]	37.85	36.02	38.35	41.92