Analysis and verification of calculation model of heat transfer coefficient of twin screw in the same direction

doi:10.11949/0438-1157.20241490

Abstract

Abstract:

In order to reduce the safety risk in the preparation and production of high polymer bonded explosives (PBX) and promote the continuous and large-scale production of PBX explosives, five different ratio of polymer bonded explosives were designed with non-aluminum-containing PBX substitutes as the research object. The calculation model of the heat transfer coefficient between barrel/screw and material based on the change of physical property parameters, structural parameters and operating parameters is derived and established. At the same time, the direction of heat conduction in the screw metering section during the actual extrusion process and the contribution ratio of heat conduction to the temperature rise of the material were discussed. The results show that: The heat conduction is dominant in the heat conversion in the metering section of screw. Especially in the material system with energetic oxidizer∶aluminum powder 6∶2, the heat transfer of the cylinder in the metering section is more than 10 times the viscous heat generation. The heat transfer coefficient calculation model established in this paper is more comprehensive, and the calculated results are between the results of earlier heat transfer research theories. Under the same experimental conditions, the absolute error between the theoretical exit temperature predicted by this model and the experimental measured value is within 0.2℃, and the predicted temperature rise error is within 20%.

Key words: PBX, twin-screw extruder, heat transfer, model, experimental validation

摘要：

为了降低高聚合物黏结炸药（polymer bonded explosives，PBX）在制备生产过程中的安全风险，推动PBX炸药的连续化、规模化生产，以非含铝PBX代料为研究对象，设计了五种不同配比的代料药浆体系，推导并建立了基于物性参数、结构参数和操作参数变化的机筒/螺杆与物料间传热系数的计算模型。同时，探讨了实际挤出过程中螺杆计量段热传导的方向，热传导在物料温升中的贡献比例。结果表明：螺杆计量段热量转化中热传导量占主导地位，特别是在含能氧化剂∶铝粉为6∶2的物料体系中，计量段机筒换热量在黏性生热量的10倍以上；本文建立的传热系数计算模型更为全面，且计算结果介于早期传热研究理论的结果之间；本模型在相同实验条件下预测的理论出口温度与实验测量值的绝对误差在0.2℃以内，预测温升误差在20%以内。

关键词: PBX, 双螺杆挤出机, 传热, 模型, 实验验证

CLC Number:

TJ 55

Haimei LUO, Hong WANG, Zhaoming SUN, Yanhua YIN. Analysis and verification of calculation model of heat transfer coefficient of twin screw in the same direction[J]. CIESC Journal, 2025, 76(9): 4809-4823.

罗海梅, 王泓, 孙照明, 尹艳华. 同向双螺杆传热系数计算模型的分析与验证[J]. 化工学报, 2025, 76(9): 4809-4823.

Figures/Tables 19

Fig. 1 Flow channel development drawing and twin-screw meshing drawing

Table 1 Experimental raw materials

药品	规格与性质	生产厂家
端羟基聚丁二烯(HTPB)	Ⅳ型，羟值0.79 mmol/g	天元军融化工有限公司
己二酸二辛酯(DOA)	纯度98%	东京化成工业株式会社
二氧化硅	球形，10 $μ m$	清河县安迪金属材料有限公司
无水硫酸钠	工业级	孝感广盐华源制盐有限公司
氯化钠	分析纯	上海麦克林生化科技有限公司
聚氯乙烯(PVC)	工业级	天津大沽化工股份有限公司

Table 1 Experimental raw materials

药品	规格与性质	生产厂家
端羟基聚丁二烯(HTPB)	Ⅳ型，羟值0.79 mmol/g	天元军融化工有限公司
己二酸二辛酯(DOA)	纯度98%	东京化成工业株式会社
二氧化硅	球形，10 $μ m$	清河县安迪金属材料有限公司
无水硫酸钠	工业级	孝感广盐华源制盐有限公司
氯化钠	分析纯	上海麦克林生化科技有限公司
聚氯乙烯(PVC)	工业级	天津大沽化工股份有限公司

Table 2 Composiyion of non-aluminum-containing PBX substitutes

序号	配比	固体组分质量分数/%			液体组分质量分数/%
序号	配比	SiO₂＋Na₂SO₄	NaCl	PVC	HTPB	DOA
1	7∶1	62.36	20.79	2.35	7.00	7.50
2	6∶2	65.68	17.47	2.35	7.00	7.50
3	5∶3	68.30	14.85	2.35	7.00	7.50
4	4∶4	71.27	11.88	2.35	7.00	7.50
5	3∶5	74.24	8.91	2.35	7.00	7.50

Table 3 Main experimental equipment and instruments

仪器名称	型号	生产厂家
行星式动力混合机	YH-4XZJB2	上海耀环机电设备有限公司
同向旋转双螺杆挤出机	PHSJ-20	江苏新达科技公司
旋转流变仪	HAAKE MARS 40	赛默飞世尔科技

Table 4 Extrusion experiment parameters design

序号	物料配比	机筒温度/℃	螺杆转速/(r/min)
1	7∶1	30	100
2	6∶2	30	100
3	5∶3	30	100
4	4∶4	30	100
5	3∶5	30	100
6	6∶2	30	60
7	6∶2	30	70
8	6∶2	30	80
9	6∶2	30	90
10	6∶2	40	100
11	6∶2	50	100
12	6∶2	60	100
13	6∶2	70	100

Table 5 Experimental test results

序号	T_b	测试结果
序号	T_b	T₁/℃	T₂/℃	T₃/℃	T₄/℃	$T b'$ /℃
1	30	32.33	31.93	31.33	31.25	30.80
2	30	31.97	31.47	30.93	30.71	30.23
3	30	31.53	31.27	30.93	30.80	30.40
4	30	32.07	31.73	31.33	31.20	30.67
5	30	32.23	31.87	31.43	31.25	30.63
6	30	31.37	30.90	30.53	30.49	30.23
7	30	31.53	31.03	30.67	30.53	30.27
8	30	31.73	31.20	30.77	30.61	30.50
9	30	31.87	31.43	30.90	30.66	30.27
10	40	41.53	41.23	40.77	40.40	40.27
11	50	51.30	51.07	50.83	50.65	50.47
12	60	61.17	60.87	60.57	60.48	60.23
13	70	71.03	70.70	70.37	70.29	70.03

Table 5 Experimental test results

序号	T_b	测试结果
序号	T_b	T₁/℃	T₂/℃	T₃/℃	T₄/℃	$T b'$ /℃
1	30	32.33	31.93	31.33	31.25	30.80
2	30	31.97	31.47	30.93	30.71	30.23
3	30	31.53	31.27	30.93	30.80	30.40
4	30	32.07	31.73	31.33	31.20	30.67
5	30	32.23	31.87	31.43	31.25	30.63
6	30	31.37	30.90	30.53	30.49	30.23
7	30	31.53	31.03	30.67	30.53	30.27
8	30	31.73	31.20	30.77	30.61	30.50
9	30	31.87	31.43	30.90	30.66	30.27
10	40	41.53	41.23	40.77	40.40	40.27
11	50	51.30	51.07	50.83	50.65	50.47
12	60	61.17	60.87	60.57	60.48	60.23
13	70	71.03	70.70	70.37	70.29	70.03

Fig. 2 Relationship between dimensionless numbers Hc and Br

Fig.3 Calculation results of Hc and Br in measuring section of 13 experimental screw

Table 6 Calculation results of 1/ Br

实验序号	1/ $B r$	实验序号	$1 / B r$	实验序号	1/ $B r$
1	9.90	6	12.70	11	10.69
2	11.37	7	12.12	12	16.08
3	8.05	8	10.12	13	22.96
4	6.91	9	11.75
5	4.76	10	11.09

Table 6 Calculation results of 1/ Br

实验序号	1/ $B r$	实验序号	$1 / B r$	实验序号	1/ $B r$
1	9.90	6	12.70	11	10.69
2	11.37	7	12.12	12	16.08
3	8.05	8	10.12	13	22.96
4	6.91	9	11.75
5	4.76	10	11.09

Fig. 4 Axial temperature rise of material in the measuring section measured by experiment

Fig. 5 Comparison between theoretical axial temperature curves of 13 groups of experiments and actual tests

Table 7 Error analysis of theoretical calculation and experimental comparison of outlet temperature and temperature rise of 13 groups of experimental materials

实验序号	T₄/℃			$∆ T$ /℃			相对误差/%
实验序号	实验测试	理论计算	绝对误差	实验测试	理论计算	绝对误差	相对误差/%
1	31.25	31.10	0.15	1.08	1.23	0.15	13.84
2	30.71	30.52	0.19	1.26	1.44	0.19	14.96
3	30.80	30.71	0.10	0.73	0.83	0.10	12.69
4	31.20	31.10	0.10	0.87	0.97	0.10	12.10
5	31.25	31.12	0.13	0.98	1.11	0.13	12.72
6	30.49	30.32	0.17	0.88	1.04	0.17	18.88
7	30.53	30.40	0.13	1.00	1.14	0.14	13.28
8	30.61	30.43	0.18	1.12	1.30	0.18	15.59
9	30.66	30.50	0.16	1.21	1.37	0.16	13.33
10	40.68	40.55	0.13	0.85	0.98	0.13	15.40
11	50.65	50.62	0.03	0.65	0.68	0.03	4.10
12	60.48	60.40	0.08	0.69	0.77	0.08	11.82
13	70.29	70.20	0.09	0.74	0.83	0.09	11.63

Table 7 Error analysis of theoretical calculation and experimental comparison of outlet temperature and temperature rise of 13 groups of experimental materials

实验序号	T₄/℃			$∆ T$ /℃			相对误差/%
实验序号	实验测试	理论计算	绝对误差	实验测试	理论计算	绝对误差	相对误差/%
1	31.25	31.10	0.15	1.08	1.23	0.15	13.84
2	30.71	30.52	0.19	1.26	1.44	0.19	14.96
3	30.80	30.71	0.10	0.73	0.83	0.10	12.69
4	31.20	31.10	0.10	0.87	0.97	0.10	12.10
5	31.25	31.12	0.13	0.98	1.11	0.13	12.72
6	30.49	30.32	0.17	0.88	1.04	0.17	18.88
7	30.53	30.40	0.13	1.00	1.14	0.14	13.28
8	30.61	30.43	0.18	1.12	1.30	0.18	15.59
9	30.66	30.50	0.16	1.21	1.37	0.16	13.33
10	40.68	40.55	0.13	0.85	0.98	0.13	15.40
11	50.65	50.62	0.03	0.65	0.68	0.03	4.10
12	60.48	60.40	0.08	0.69	0.77	0.08	11.82
13	70.29	70.20	0.09	0.74	0.83	0.09	11.63

Fig. 6 Solid-liquid phase separation occurs when extruding the material

Table 8 Factor level table of different physical property parameter settings under variable ratios

水平	因素
水平	$ρ$ /(g/ml)	c/(J/(g $⋅$ K))	$k$ /(W/(m $⋅$ K))	$η$ /(Pa $⋅$ s)
水平1	1.8660	1.0243	0.8510	17.0899
水平2	1.9280	0.9813	0.8823	23.5260
水平3	1.8760	1.4087	0.8077	18.8830

Table 8 Factor level table of different physical property parameter settings under variable ratios

水平	因素
水平	$ρ$ /(g/ml)	c/(J/(g $⋅$ K))	$k$ /(W/(m $⋅$ K))	$η$ /(Pa $⋅$ s)
水平1	1.8660	1.0243	0.8510	17.0899
水平2	1.9280	0.9813	0.8823	23.5260
水平3	1.8760	1.4087	0.8077	18.8830

Table 9 Intuitive analysis table of the influence of different physical property parameters on the heat transfer coefficient between the barrel/screw and the material under variable ratios

实验		因素				$h b$ / (W/(m² $⋅$ K))	$h s$ / (W/(m² $⋅$ K))
实验		$ρ$	$c$	$k$	$η$	$h b$ / (W/(m² $⋅$ K))	$h s$ / (W/(m² $⋅$ K))
实验1		1	1	1	1	550.829	388.336
实验2		1	2	2	2	556.228	392.142
实验3		1	3	3	3	591.584	417.067
实验4		2	1	2	3	570.418	402.146
实验5		2	1	2	3	530.163	373.707
实验6		2	3	1	2	619.269	436.586
实验7		3	1	3	2	532.917	375.707
实验8		3	2	1	3	543.979	383.506
实验9		3	3	2	1	628.587	443.155
$h b$ 直观分析	$k 1$	566.213	551.390	571.360	569.860
	$k 2$	573.283	543.457	585.080	569.473
	$k 3$	568.497	613.147	551.553	568.660
	$R$	7.070	69.690	33.527	1.200
	主次顺序	$c$ > $k$ > $ρ$ > $η$
$h s$ 直观分析	$k 1$	399.182	388.730	402.809	401.752
	$k 2$	404.166	383.138	412.481	401.478
	$k 3$	400.789	432.269	388.847	400.906
	$R$	4.984	49.131	23.634	0.846
	主次顺序	$c$ > $k$ > $ρ$ > $η$

Table 9 Intuitive analysis table of the influence of different physical property parameters on the heat transfer coefficient between the barrel/screw and the material under variable ratios

实验		因素				$h b$ / (W/(m² $⋅$ K))	$h s$ / (W/(m² $⋅$ K))
实验		$ρ$	$c$	$k$	$η$	$h b$ / (W/(m² $⋅$ K))	$h s$ / (W/(m² $⋅$ K))
实验1		1	1	1	1	550.829	388.336
实验2		1	2	2	2	556.228	392.142
实验3		1	3	3	3	591.584	417.067
实验4		2	1	2	3	570.418	402.146
实验5		2	1	2	3	530.163	373.707
实验6		2	3	1	2	619.269	436.586
实验7		3	1	3	2	532.917	375.707
实验8		3	2	1	3	543.979	383.506
实验9		3	3	2	1	628.587	443.155
$h b$ 直观分析	$k 1$	566.213	551.390	571.360	569.860
	$k 2$	573.283	543.457	585.080	569.473
	$k 3$	568.497	613.147	551.553	568.660
	$R$	7.070	69.690	33.527	1.200
	主次顺序	$c$ > $k$ > $ρ$ > $η$
$h s$ 直观分析	$k 1$	399.182	388.730	402.809	401.752
	$k 2$	404.166	383.138	412.481	401.478
	$k 3$	400.789	432.269	388.847	400.906
	$R$	4.984	49.131	23.634	0.846
	主次顺序	$c$ > $k$ > $ρ$ > $η$

Table 10 Analysis of variance table for the influence of different physical property parameters on the heat transfer coefficient between the barrel/screw and the material under variable ratios

因素		偏差平方和	自由度	$F$ 比	$F 0.05$	$F 0.01$	显著性
$h b$ 方差分析	$ρ$	78.111	2	35.172	19.000	99.000	*
	$c$	8733.520	2	3945.501	19.000	99.000	**
	$k$	1704.580	2	770.238	19.000	99.000	**
	$η$	2.247	2	1.000	19.000	99.000
	误差	2.247	2
$h s$ 方差分析	$ρ$	38.508	2	35.955	19.000	99.000	*
	$c$	4342.701	2	4054.810	19.000	99.000	**
	$k$	848.447	2	792.210	19.000	99.000	**
	$η$	1.071	2	1.000	19.000	99.000
	误差	1.071	2

Table 10 Analysis of variance table for the influence of different physical property parameters on the heat transfer coefficient between the barrel/screw and the material under variable ratios

因素		偏差平方和	自由度	$F$ 比	$F 0.05$	$F 0.01$	显著性
$h b$ 方差分析	$ρ$	78.111	2	35.172	19.000	99.000	*
	$c$	8733.520	2	3945.501	19.000	99.000	**
	$k$	1704.580	2	770.238	19.000	99.000	**
	$η$	2.247	2	1.000	19.000	99.000
	误差	2.247	2
$h s$ 方差分析	$ρ$	38.508	2	35.955	19.000	99.000	*
	$c$	4342.701	2	4054.810	19.000	99.000	**
	$k$	848.447	2	792.210	19.000	99.000	**
	$η$	1.071	2	1.000	19.000	99.000
	误差	1.071	2

Table 11 Factor level table for different operational parameter settings

水平	因素
水平	$N$ /(r/min)	$M$ /(kg/h)	$T b$ /℃
水平1	60	10	30
水平2	100	16	70

Table 11 Factor level table for different operational parameter settings

水平	因素
水平	$N$ /(r/min)	$M$ /(kg/h)	$T b$ /℃
水平1	60	10	30
水平2	100	16	70

Table 12 Intuitive analysis table of heat transfer coefficients between barrel/screw and materials under different operational parameters

实验		因素			$h b$ / (W/(m² $⋅$ K))	$h s$ / (W/(m² $⋅$ K))
实验		$N$	$M$	$T b$	$h b$ / (W/(m² $⋅$ K))	$h s$ / (W/(m² $⋅$ K))
实验1		1	1	1	480.307	338.277
实验2		1	2	2	466.453	323.294
实验3		2	1	2	578.029	411.069
实验4		2	2	1	571.444	402.869
$h b$ 直观分析	$k 1$	473.380	529.168	525.875
	$k 2$	574.736	518.948	522.241
	$R$	101.356	10.220	3.634
	主次顺序	$N$ > $M$ > $T b$
$h s$ 直观分析	$k 1$	330.785	374.673	370.573
	$k 2$	406.969	363.082	367.182
	$R$	76.184	11.591	3.391
	主次顺序	$N$ > $M$ > $T b$

Table 12 Intuitive analysis table of heat transfer coefficients between barrel/screw and materials under different operational parameters

实验		因素			$h b$ / (W/(m² $⋅$ K))	$h s$ / (W/(m² $⋅$ K))
实验		$N$	$M$	$T b$	$h b$ / (W/(m² $⋅$ K))	$h s$ / (W/(m² $⋅$ K))
实验1		1	1	1	480.307	338.277
实验2		1	2	2	466.453	323.294
实验3		2	1	2	578.029	411.069
实验4		2	2	1	571.444	402.869
$h b$ 直观分析	$k 1$	473.380	529.168	525.875
	$k 2$	574.736	518.948	522.241
	$R$	101.356	10.220	3.634
	主次顺序	$N$ > $M$ > $T b$
$h s$ 直观分析	$k 1$	330.785	374.673	370.573
	$k 2$	406.969	363.082	367.182
	$R$	76.184	11.591	3.391
	主次顺序	$N$ > $M$ > $T b$

Table 13 Analysis of variance table for heat transfer coefficients between barrel/screw and materials under different operational parameters

因素		偏差平方和	自由度	$F$ 比	$F 0.05$	$F 0.01$	显著性
$h b$ 方差分析	$N$	10273.140	1	777.679	161.000	405.000	**
$h b$ 方差分析	$M$	104.438	1	7.906	161.000	405.000
	$T b$	13.210	1	1.000	161.000	405.000
	误差	13.210	1
$h s$ 方差分析	$N$	5803.926	1	504.601	161.000	405.000	**
	$M$	134.363	1	11.682	161.000	405.000
	$T b$	11.502	1	1.000	161.000	405.000
	误差	11.502	1

Table 13 Analysis of variance table for heat transfer coefficients between barrel/screw and materials under different operational parameters

因素		偏差平方和	自由度	$F$ 比	$F 0.05$	$F 0.01$	显著性
$h b$ 方差分析	$N$	10273.140	1	777.679	161.000	405.000	**
$h b$ 方差分析	$M$	104.438	1	7.906	161.000	405.000
	$T b$	13.210	1	1.000	161.000	405.000
	误差	13.210	1
$h s$ 方差分析	$N$	5803.926	1	504.601	161.000	405.000	**
	$M$	134.363	1	11.682	161.000	405.000
	$T b$	11.502	1	1.000	161.000	405.000
	误差	11.502	1

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