小通道内制冷剂两相流动摩擦压降关联式分析

doi:10.16183/j.cnki.jsjtu.2020.159

摘要/Abstract

摘要：

针对小通道内两相流动摩擦压降的关联式进行了全面分析,描述关联式之间的继承发展关系,并指出不同关联式之间的创新之处.为了评估各种关联式在小通道中的通用性和精度,建立了一个大型摩擦压降数据库,此数据库在蒸发和冷凝/绝热工况下分别有 1302 和 1576 个数据点.对26种关联式分工况进行评估分析,并发现Sempértegui-Tapia和Kim关联式分别在蒸发工况、冷凝/绝热工况下具有最佳的预测能力,最后提出了关于关联式改进的建议.

关键词: 两相流, 摩擦压降, 关联式, 评估

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

中图分类号:

TK124

刘勖诚, 谷波, 曾炜杰, 杜仲星, 田镇. 小通道内制冷剂两相流动摩擦压降关联式分析[J]. 上海交通大学学报, 2021, 55(9): 1095-1107.

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.

图/表 7

表1

均相模型关联式

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

表1

表2

表3

分相模型关联式和经验关联式

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

表3

表4

表5

图1

图2

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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