Quantitative Contribution Effect Analysis of Working Fluid Viscosity on COP of High-Temperature Heat Pump Systems

Abstract

Irreversible loss caused by viscosity-dominated viscous dissipation is an important factor affecting high-temperature heat pump (HTHP) performance. To quantify the effect of viscosity on the coefficient of performance (COP) of HTHP systems, this study developed a contribution analysis model based on data samples from multiple working conditions, working fluids, and device types. Factor analysis and Varimax orthogonal rotation were employed to achieve multi-factor dimensionality reduction and mapping, quantitatively analyze viscosity factors, and compare the weight contribution distributions of other influencing factors with and without viscosity parameters. Results show that, in the global sample, viscosity corresponding to condensation temperature ranks among the top three negatively correlated factors, with a contribution of 7.40%. The sum of the absolute contributions of viscosity corresponding to condensation temperature and evaporation temperature reaches 9.86%, second only to temperature lift (16.10%). In the three local temperature ranges, the contributions of viscosity corresponding to condensation temperature are 6.31%, 6.75%, and 7.11%, respectively. The total contribution of irreversible loss parameters increases from 46.21% to 49.39%, and the increase reaches 12.02% in the high-temperature range. These results provide a theoretical basis for HTHP system design, working fluid selection, and performance improvement under high-temperature operating conditions.

1. Introduction

High-temperature heat pump (HTHP) technology has received wide attention in fields such as building heating, industrial waste heat recovery, and high-temperature heating because of its high efficiency, energy-saving potential, and wide applicability [1,2]. With the improvement of HTHP system performance as a core objective, many studies have focused on the effects of factors such as condensation temperature, evaporation temperature, system pressure ratio, and working fluid type on HTHP coefficient of performance (COP). However, during the actual operation of a HTHP, system performance is affected not only by working condition parameters, such as condensation temperature [3] and temperature lift [4], and by the thermodynamic properties of the working fluid [5,6], but also strongly restricted by the fluid flow process. Irreversible loss in the flow process is one of the important sources of the complexity of fluid–solid coupling in heat pump systems [7]. Among these factors, viscosity, as a key physical property characterizing the momentum diffusion capability of a fluid, plays an important role in governing fluid shear stress and flow resistance and further affects the overall system performance by influencing pressure drop, heat transfer behavior, and flow irreversibility [8,9]. Therefore, it is of great significance to analyze the role of viscosity in heat pump systems in depth.

In this context, viscous dissipation, as a viscosity-dominated flow irreversible loss, has gradually attracted attention. Viscous dissipation essentially reflects the irreversible conversion of fluid mechanical energy into internal energy. Its enhancement increases flow resistance and changes the temperature field, thereby reducing heat transfer efficiency and increasing irreversible loss in heat pump systems. For example, Li et al. [10] analyzed flow characteristics from the perspective of irreversible energy dissipation and found that viscous dissipation was the main source of energy loss in a hydrogen circulation pump (HCP), accounting for more than 70% of the HCP energy loss. To study the effect of viscous dissipation in flow and heat transfer more conveniently and accurately, some researchers focused on microchannels. For example, Ting et al. [11] compared the differences in thermal characteristics and entropy generation between models with and without viscous dissipation, and the results showed that neglecting viscous dissipation led to an overestimation of total entropy generation and fluid friction irreversibility by about 10%. Koo et al. [12] analyzed the key factors affecting viscous dissipation and found that, for liquid working fluids, the viscous dissipation effect decreased as fluid temperature increased. In contrast, as the channel size decreased, viscous dissipation increased rapidly, and neglecting this effect could lead to deviations in the prediction of flow and heat transfer. Chebbi et al. [13] investigated the effect of viscous dissipation in flow and heat transfer. Herzog et al. [14] established a general dimensionless analytical equation including viscous dissipation. Manai et al. [15] developed a mathematical model considering viscous dissipation and other factors to evaluate the combined effects in flow and heat transfer.

During the actual operation of a heat pump system, the working fluid involved in the cycle is not always a pure refrigerant. As the refrigerant inevitably carries part of the lubricant when passing through the compressor, the circulating working fluid may actually exist as a refrigerant–lubricant mixture. The mutual dissolution between the refrigerant and lubricant can significantly change the fluid viscosity and its temperature-dependent characteristics, thereby affecting flow resistance, heat transfer performance, and the intensity of viscous dissipation. Therefore, in order to accurately evaluate the flow irreversible loss in heat pump systems and its effect on COP, some studies have focused on the viscosity variation of refrigerant–lubricant mixtures. For example, Akram et al. [16] studied the effect of mutual dissolution between refrigerants and lubricants on tribological properties and found that the friction coefficient of the HFO-1234yf/polyalkylene glycol combination was lower than those of the combinations with polyolester lubricant and mineral oil. Wang et al. [17] discussed in detail the effects of refrigerant solubility variation on parameters such as viscosity. Brocus et al. [18] measured the isothermal vapor–liquid equilibrium data of five refrigerants using a static synthetic method to investigate the viscosity change after the dissolution of refrigerants and lubricants. Nasution et al. [19] used molecular dynamics simulation to investigate the effect of different concentrations of pentaerythritol tetracaproate on the viscosity of refrigerant R32, and the results showed that viscosity was more sensitive to changes in lubricant concentration. Sun et al. [20] studied the thermophysical properties, including viscosity, of refrigerant R1243zf in two lubricants (RL 32 and RL 68). The results showed that R1243zf with POE RL 68 had better viscosity retention under high-temperature conditions. Lu et al. [21] studied the solubility of R1336mzz(Z) in the lubricants dipentaerythritol hepta/hepta ester (DiPEC7) and dipentaerythritol isononanoate (DiPEiC9), as well as the performance after mixing and dissolution.

The above studies explored viscosity and its related effects in different heat transfer systems and with different working fluids. However, because of the wide variety of refrigerant systems, existing studies still cannot fully cover all system types, operating conditions, and working fluid combinations, and the general applicability of their conclusions at the heat pump system level remains limited. Even so, existing studies generally show that viscosity variation affects flow irreversibility and overall performance of heat pump systems by influencing flow resistance, friction loss, and the intensity of viscous dissipation. Therefore, viscosity is not only an important physical property for describing fluid flow behavior but also a key basis for evaluating viscous dissipation effects and their influence on system performance. However, quantitative studies on the extent to which viscosity affects the overall performance of heat pump systems are still relatively lacking. In particular, there is still a lack of systematic analysis of the interaction between viscosity, thermodynamic parameters, and operating parameters under a multi-factor coupling framework, as well as quantitative evaluation of the relative importance of viscosity among multiple influencing factors. Viscosity not only changes the system pressure drop by affecting flow resistance but also participates in the system energy conversion process by enhancing flow irreversible loss and may therefore have an important effect on the COP of heat pump systems. Therefore, it is necessary to carry out an in-depth study of the importance of viscosity and related parameters at the system level.

Based on this, this study used data samples from multiple working conditions, working fluids, and device types, introduced viscosity as a key irreversible loss parameter characterizing fluid–solid coupling, and constructed a prediction model for the COP of HTHP systems. On this basis, a weight analysis of influencing factors was carried out to compare the differences in the weight distributions of various influencing factors with and without considering viscosity factors. Furthermore, factor analysis and the Varimax orthogonal rotation method were used to achieve multi-factor dimensionality reduction and quantitative characterization. From the perspectives of marginal contribution and feature contribution redistribution, the changes in the weight contributions of influencing factors were systematically analyzed at both global and local levels, with and without viscosity involved. Finally, by comparing the characteristics of weight distributions under different temperature ranges and different refrigerant types, the role of viscosity and the flow irreversible effect associated with it in HTHP systems was further revealed. The results can provide a more comprehensive theoretical basis for the optimal design of HTHP systems and the screening of new refrigerants. Compared with existing studies that mainly focus on local viscous dissipation phenomena or viscosity changes in refrigerant–lubricant mixtures, this study focuses on the relative importance of viscosity and its weight redistribution among multiple influencing factors at the heat pump system level under multiple operating conditions, multiple refrigerants, and multiple device types. An interpretable system-level quantitative analysis framework was established to reveal the changes in the relative effects of different factors on COP before and after viscosity was introduced.

2. Methods

2.1. Thermodynamic Cycle

Based on the experimental data of multiple refrigerants used in this study, the T-s diagram of the vapor-compression cycle of the high-temperature heat pump was plotted, as shown in Figure 1. Figure 1 shows the main thermodynamic processes of the cycle. In the figure, 1–2 and 3–4 represent the evaporation and condensation processes, respectively; 2″–3′ represents the polytropic compression process; 4′–1 represents the throttling process; 2′–2″ represents the refrigerant passing through the gas–liquid separator, while 3′–3 represents the discharge superheat from the compressor outlet to the condenser inlet. In addition, 2–2′ and 4–4′ represent the superheating and subcooling processes, respectively. The blue line represents the low-temperature water source, and the red line represents the high-temperature water source. The refrigerant exchanges heat with water in a counter-flow manner in the heat exchangers on both sides.

In this study, the heat absorbed on the high-temperature water side was taken as the heating capacity of the unit, while the heat released on the low-temperature water side was taken as the heat absorption capacity. In addition, the input power of the compressor was measured by a three-phase multi-functional meter. The heat absorption capacity of the high-temperature heat pump unit was calculated by Equation (1) as follows:

$$Q_e=m_{ls}{c}_p\left(T_{ls}^{in}-T_{ls}^{out}\right)$$

(1)

where $m_{ls}$ is the mass flow rate of the low-temperature water, $c_p$ is the specific heat capacity of water at constant pressure, and $T_{ls}^{in}$, $T_{ls}^{out}$ are the inlet and outlet water temperatures on the low-temperature side, respectively.

The heating capacity of the high-temperature heat pump unit was calculated by Equation (2) as follows:

$$Q_{con}=m_{hs}{c}_p\left(T_{hs}^{out}-T_{hs}^{in}\right)$$

(2)

where $m_{hs}$ is the mass flow rate of the high-temperature water, and $T_{hs}^{out}$, $T_{hs}^{in}$ are the outlet and inlet water temperatures on the high-temperature side, respectively.

Accordingly, the COP of the heat pump cycle was calculated by Equation (3) as follows:

$$\mathrm{C}\mathrm{O}\mathrm{P}={\displaystyle \frac{m_{hs}{c}_p\left(T_{hs}^{out}-T_{hs}^{in}\right)}{W_{in}}}$$

(3)

where $W_{in}$ is the input power of the compressor.

2.2. Mathematical Method

To reveal the influencing mechanism of actual cycle performance in HTHP systems, this study employed a multi-factor contribution analysis model centered on factor weight contributions, with a focus on the effects with and without considering viscosity factor, as well as the relative roles and influence degrees of multiple factors in system performance formation.

Based on experimental data and thermophysical property calculations, a multi-dimensional set of influencing factors was constructed, including working condition parameters, thermodynamic properties of the working fluid, and irreversible loss parameters related to viscosity. To eliminate the interference of differences in dimensions and magnitudes on the analysis results, all variables were standardized. This process achieved a mapping from the original variable space to a low-dimensional latent factor space, thereby revealing the internal structure of multi-factor coupling relationships. Factor extraction was performed using the principal component method. The number of retained factors was mainly determined according to the eigenvalue-greater-than-one criterion. In this study, six factors were retained, and their cumulative variance contribution rate reached 90.053%, indicating that most of the information contained in the original variables was preserved. The total variance explained is shown in

Table 1. Total variance explained.

	Extraction Sums of Squared Loadings			Rotation Sums of Squared Loadings
Component	Total	Variance Contribution Rate	Cumulative Contribution Rate	Total	Percentage of Variance	Cumulative
		%	%		%	%
1	6.655	33.273	33.273	6.293	31.467	31.467
2	3.897	19.486	52.76	2.983	14.916	46.382
3	2.504	12.522	65.282	2.889	14.446	60.828
4	1.806	9.032	78.314	1.966	9.83	74.659
5	1.422	7.11	86.423	1.928	9.639	85.297
6	1.126	5.63	90.053	1.351	6.756	90.053

. Varimax orthogonal rotation was applied to the initial factor loading matrix. As a result, each variable had relatively high loadings on a few factors and relatively low loadings on the others. This improved the clarity and interpretability of the factor structure and facilitated the subsequent mapping of the regression results in the factor space back to the original variable space. To quantitatively characterize the contribution of each original variable to system performance, a weight mapping relationship was established based on the factor loading matrix and factor scores. The information in the latent factor space was then projected back to the original variable space to obtain the normalized weights of each influencing factor. The related calculation formulas are given below.

$$\widetilde{{\mathrm{X}}_{\mathrm{i}}}=\mathsf{\Lambda }{\mathrm{f}}_{\mathrm{i}}+{\mathsf{\epsilon }}_{\mathrm{i}},\hspace{1em}{\mathrm{f}}_{\mathrm{i}}~\mathsf{Ͷ}\left(0,\mathrm{I}\right),\hspace{1em}{\mathsf{\epsilon }}_{\mathrm{i}}~\left(0,\mathsf{\Psi }\right)$$

(4)

where $\mathsf{\Lambda }$ in ${\mathrm{R}}^{18\times \mathrm{k}}$ is the factor loading matrix, ${\mathsf{\epsilon }}_{\mathrm{i}}$ in ${\mathrm{R}}^{\mathrm{p}}$ is the error term of the i-th sample, and ${\mathrm{f}}_{\mathrm{i}}$ in ${\mathrm{R}}^{\mathrm{k}}$ denotes the latent factor score vector of the i-th sample. I represent the $\mathrm{k} \times \mathrm{k}$ identity matrix, $\mathsf{\Psi }$ is the diagonal matrix of uniqueness, and $\mathrm{k}$ is the number of retained factors. The factor scores are estimated using the regression method:

$${\widehat{\mathrm{f}}}_{\mathrm{i}}=\mathrm{W}\widetilde{{\mathrm{X}}_{\mathrm{i}}},\hspace{1em}\mathrm{W}=\left({\mathsf{\Lambda }}^{\mathrm{T}}{\mathsf{\Psi }}^{-1}\mathsf{\Lambda }+\mathrm{I}\right) {\mathsf{\Lambda }}^{\mathrm{T}}{\mathsf{\Psi }}^{-1}$$

(5)

where f_i is the estimated factor score of the i-th sample and W is the scoring matrix.

The COP regression model is then established using the factor scores as explanatory variables:

$${\mathrm{COP}}_{\mathrm{i}}={\widehat{\mathsf{\beta }}}_0+{{\widehat{\mathsf{\beta }}}_{\mathrm{f}}}^{\mathrm{T}}{\widehat{\mathrm{f}}}_{\ast }+{\widehat{\mathsf{\gamma }}}^{\mathrm{T}}{\mathrm{Z}}_{\ast }+{\mathsf{\epsilon }}_{\mathrm{i}},\hspace{1em}{\mathsf{\epsilon }}_{\mathrm{i}}~\mathsf{Ͷ}\left(0,{\mathsf{\sigma }}^2\right)$$

(6)

where $\widehat{{\mathsf{\beta }}_0}$ is the intercept, $\widehat{{\mathsf{\beta }}_{\mathrm{f}}}$ in ${\mathrm{R}}^{\mathrm{k}}$ denotes the factor regression coefficients, $\widehat{\mathsf{\gamma }}$ represents the coefficients of control terms, and ${\mathsf{\sigma }}^2$ is the variance of the regression residual ${\mathsf{\epsilon }}_{\mathrm{i}}$.

After obtaining the regression coefficients in the factor space, they are projected back to the original variable space through the rotated loading matrix. In this way, the comprehensive effect coefficient of each original variable on COP under multi-factor coupling can be obtained. Let the rotated loading matrix be $\mathsf{\Lambda }$ and the factor coefficient vector be ${\mathsf{\beta }}_{\mathrm{f}}$. Then, the overall impact coefficient of the $\mathrm{j}$-th original indicator can be defined as:

$${\mathrm{w}}_{\mathrm{j}}=\sum _{\mathrm{m}=1}^{\mathrm{k}}{\mathsf{\Lambda }}_{\mathrm{jm}}{\mathsf{\beta }}_{\mathrm{f},\mathrm{m}}$$

(7)

where ${\mathsf{\Lambda }}_{\mathrm{jm}}$ is the factor loading of the $\mathrm{j}$-th variable on the m-th factor, m denotes the factor index, and ${\mathsf{\beta }}_{\mathrm{f},\mathrm{m}}$ is the coefficient corresponding to the m-th factor in the factor-based regression. The contribution weight of each original variable was further defined as the absolute value of its comprehensive effect coefficient divided by the sum of the absolute values of the comprehensive effect coefficients of all variables. This weight does not represent a thermodynamic contribution share in the strict sense. Instead, it is a relative importance indicator obtained by normalizing the comprehensive influence strength of each original variable within the factor analysis–regression mapping framework. The resulting ranking may be affected, to some extent, by the choice of factor rotation method and regression specification. Therefore, in this study, it is regarded as an interpretable statistical indicator of relative contribution. Accordingly, the sign of the comprehensive effect coefficient indicates the direction of its influence on COP, while the normalized absolute value reflects the relative contribution of that variable among all influencing factors. It is therefore more suitable for ranking and comparison under multi-factor coupling conditions.

Through this process, the relative importance of different parameters in system performance formation can be quantitatively evaluated, and the procedure is shown in Figure 2.

KMO and Bartlett’s test were performed, and the results are shown in

Table 2. Results of the KMO and Bartlett’s test.

KMO measure of sampling adequacy		0.808
Bartlett’s test of sphericity	approximate chi-square	6468.972
	degrees of freedom	190
	significance	0

. The results show that the KMO value was 0.808, indicating that the sample data were suitable for factor analysis. The Bartlett’s sphericity test gave an approximate chi-square value of 6468.972, with 190 degrees of freedom and a significance level of p < 0.001, which satisfies the requirement for factor analysis.

3. Model Data

3.1. Data on Working Conditions, Working Fluids, and Devices

A total of 144 sets of experimental data were used to establish the model in this study. Among them, 114 sets were obtained from the high-temperature heat pump experimental platform built by our research group, 9 sets were taken from the steam-compression high-temperature heat pump system reported in Ref. [22], and another 21 sets were derived from the cascade high-temperature heat pump (CHTHP) system in Ref. [23] after being separated into two independent single-stage heat pump cycles. The data used in this study covered the following ranges:

Range of working condition parameters: the condensation temperature was 43.3–139.6 °C, and the temperature lift was 27.8–73.3 °C;

Working fluid types involved: eight working fluids were included, namely HCFC (R22 and R142b), HFC (R410a, R134a, and R245fa), the natural working fluid (water), and independently developed working fluids (Beiyang series: BY-5 and NBY-1);

Types of experimental devices: the evaporators included tube-in-tube, falling-film, and plate types; the compressors included scroll, twin-screw, and piston types; the condensers included tube-in-tube and plate types; and all throttling devices were electronic expansion valves.

The numbering and corresponding names of the 20 influencing factors involved in this study, including viscosity factors, are listed in

Table 3. Numbers and names of the influencing factors.

Numbers	Symbol	Parameter Name	Numbers	Symbol	Parameter Name
#1	$T_{\mathit{cond}}$	condensation temperature	#11	${\mu }_{\mathit{cond}}$	viscosity corresponding to condensation temperature
#2	${\mathsf{∆}T}_{\mathit{up}}$	temperature lift	#12	${\mu }_e$	viscosity corresponding to evaporation temperature
#3	$T_c$	critical temperature	#13	$\mathsf{∆}{T}_{\mathit{lmtd},\mathit{ht}}$	the difference between condensation temperature and heating temperature
#4	$P_c$	critical pressure	#14	$\mathsf{∆}{T}_{\mathit{lmtd},\mathit{lt}}$	the difference between evaporation temperature and heat source temperature
#5	$T_b$	normal boiling point	#15	$T_{\mathit{sup}}$	superheat
#6	$s_e$	evaporation entropy	#16	$T_{\mathit{sub}}$	subcooling
#7	$k_{\mathit{sv},\mathit{cond}}$	saturated gas line slope at condensation temperature	#17	${\eta }_s$	isentropic efficiency
#8	$k_{\mathit{sv},e}$	saturated gas line slope at evaporation temperature	#18	$k_{\mathit{thr}}$	throttling perfection degree
#9	$k_{\mathit{sl},\mathit{cond}}$	saturated liquid line slope at condensation temperature	#19	$\mathsf{∆}{T}_{\mathit{lt}}$	temperature difference between inlet and outlet of low-temperature water side
#10	$P_{\mathit{cond}}$	condensation pressure	#20	$\mathsf{∆}{T}_{\mathit{ht}}$	temperature difference between inlet and outlet of high-temperature water side

.

The different temperature ranges were classified based on the outlet temperature on the heating side of the heat pump, T_out, with reference to the relevant classification method in Current Status and Substitution Direction of Refrigerants in China [24]. The samples were divided into low-, medium-, and high-temperature ranges. Specifically, the low-temperature range was defined as T_out < 60 °C, including 14 data points in total, namely R22 (12 sets) and R410a (2 sets). The medium-temperature range was defined as 60 ≤ T_out < 100 °C, including 17 data points in total, namely R134a (3 sets), R142b (6 sets), R245fa (3 sets), and NBY-1 (5 sets). The high-temperature range was defined as 100 ≤ T_out < 160 °C, including 113 data points in total, namely R245fa (9 sets), BY-5 (55 sets), NBY-1 (40 sets), and water (9 sets).

3.2. Viscosity Data

3.2.1. Viscosity Calculation

Many studies on working fluid viscosity have investigated methods for obtaining refrigerant viscosity. In experiments, commonly used methods include the tandem capillary tube method [25,26,27] and the vibrating-wire viscometer [28]. In theory, the main methods include the extended corresponding states (ECS) model [29,30], the residual entropy scaling method [31,32,33], semi-empirical correlations [34,35], and artificial neural network models [36,37,38]. These methods have shown high prediction accuracy and provide a reliable basis for quantitative viscosity analysis. Such studies have laid an important data foundation for later evaluating viscous dissipation and its effects at the system level. In this study, the extended corresponding states (ECS) model developed by NIST was used to calculate viscosity [29].

3.2.2. Viscosity Values

All literature published from 1998 to 2025 on high-temperature heat pumps and industrial heat pumps was retrieved from the Web of Science Core Collection. To ensure that the retrieved literature focused on high-temperature industrial heat pumps and did not include studies from other fields, the search query was set as Topic = (“high temperature heat pump*” OR “industrial heat pump*” OR “hthp*”). After the retrieval, manual screening was carried out to exclude patents and irrelevant articles, and more than 700 research papers were finally obtained. Among them, all papers involving working fluid research were further screened. Figure 3 shows the yearly distribution of published papers by refrigerant type. Only pure refrigerants were considered in this literature analysis, while mixed refrigerants were excluded.

The results show that, in recent years, working fluid research has mainly focused on low global warming potential (GWP) working fluids such as R245fa, R1233zd(E), R1234ze(E), and R1234ze(Z), as well as some traditional refrigerants such as the R600 series. Among them, the numbers of published papers on R245fa and R1233zd(E) have increased most significantly, making them important working fluid directions in current HTHP research. Meanwhile, the natural working fluids R717 and R718 have also received increasing attention.

The data samples used in this study cover typical working fluids such as R22, R142b, R410a, R134a, R245fa, R1233zd(E), and R718, as well as the self-developed working fluids BY-5 and NBY-1 from our research group. These working fluids include not only traditional HCFC and HFC refrigerants but also HCFO and natural working fluids, which are current research focuses for low-GWP applications. The sample types are diverse and can, to some extent, reflect the overall characteristics of current working fluid research for HTHP. Therefore, the analysis results have good representativeness and reference value. The viscosities of the experimental samples for different working fluids are shown in Figure 4.

To visually present the performance distribution of different refrigerants over a wide range of operating conditions, the COP distributions of all refrigerants are shown in Figure 5.

3.3. Model Accuracy and Comparison

To assess the reliability of the proposed model, R² and RMSE were selected to describe its fitting ability and prediction error. The model performance is presented in

Table 4. Model accuracy.

Indicator	This Model	Standard Linear Regression
R2	0.913	0.839
RMSE	0.273	0.432

, indicating that the proposed model has good accuracy. Furthermore, a standard linear regression model was adopted as a baseline for comparison, and its predictive performance is also shown in Table 4. In comparison, the proposed model performs better in both evaluation metrics evaluation metrics. These results (R² = 0.913, RMSE = 0.273) indicate that the proposed model can capture the observed trends with good accuracy and has better error control under multi-factor coupling conditions.

4. Results and Discussion

4.1. Weight Contribution Change of Influencing Factors at Global and Local Levels with and Without Viscosity Involved

To compare the differences in the weight distributions of influencing factors under different operating temperature ranges and reveal their variation patterns, this study carried out global weight analysis and local weight analysis, and the results are shown in Figure 6. The global analysis was performed based on all sample data, while the local analysis was conducted based on subsamples from the low-temperature range, medium-temperature range, and high-temperature range. In the global sample, without viscosity included in the irreversible loss parameters, the top three negatively correlated factors affecting COP were temperature lift (16.10%), condensation pressure (8.93%), and saturated gas line slope at condensation temperature (7.55%). With viscosity included in the irreversible loss parameters, the top three negatively correlated factors became temperature lift (15.46%), condensation pressure (8.12%), and viscosity corresponding to condensation temperature (7.40%). The sum of the absolute weights of viscosity corresponding to condensation temperature and viscosity at evaporation temperature was 9.86%, ranking second among all factors after temperature lift. In the three local temperature ranges, viscosity corresponding to condensation temperature ranked among the top three negatively correlated factors in all cases, ranking third in the low-temperature range (6.31%), second in the medium-temperature range (6.75%), and third in the high-temperature range (7.11%). This further indicates that viscosity is one of the important factors affecting HTHP system COP.

With increasing temperature range, the weight contribution of viscosity corresponding to condensation temperature increased, while that corresponding to evaporation temperature decreased. At the same time, in both the global sample and all local samples, the weight contribution of viscosity corresponding to evaporation temperature is lower than that corresponding to condensation temperature. In the low-temperature range, the weight contribution of viscosity corresponding to condensation temperature is 6.31%, while it increases by 6.97% and 12.70% in the medium-temperature range and high-temperature range, respectively, compared with that in the low-temperature range. Based on the above sample data, system performance is more sensitive to viscosity changes at condensation temperature, which is a key influencing factor under high-temperature operating conditions. This result is mainly related to the more pronounced high-temperature effect and viscosity dissipation effect on the condenser side. The condenser side corresponds to the high-temperature heat rejection end. As the condensation temperature increases, the system usually requires a larger temperature lift and a higher compression ratio, which makes this region more sensitive to flow resistance, pressure drop, and heat transfer matching. Therefore, the viscosity at the condensation temperature generally shows greater importance than the viscosity at the evaporation temperature. In addition, as the operating temperature range increases, the compression, heat transfer, and flow processes are more likely to deviate from the ideal reversible state. As a result, system irreversibility becomes stronger, and the pressure drop, flow resistance, and viscosity-related dissipation effects are further amplified. This helps explain why viscosity-related factors become more important under high-temperature operating conditions. Therefore, under high-temperature working conditions, more attention should be paid to the viscosity characteristics of the working fluid near condensation temperature, and working fluids with lower viscosity at high temperatures should be preferred to reduce flow loss and improve system performance.

4.2. Weight Contribution of Irreversible Loss Based on the T-s Diagram

The irreversibility within the system mainly arises from the evaporation heat transfer, condensation heat transfer, compression, and throttling processes. Viscosity is an important thermophysical property that affects flow resistance, pressure drop, heat transfer resistance, and viscous dissipation and therefore further influences the irreversibility of these processes and the overall system performance. Therefore, irreversible loss was jointly characterized by viscosity and the parameters of the four processes of the cycle, and the distribution of their weights in the temperature−entropy diagram is shown in Figure 7. The weight of each process is defined as the sum of the absolute values of the weights of all factors constituting that process, and the bar corresponding to each weight indicates its magnitude. Among the four processes of the cycle, the evaporation heat transfer process has the highest weight, reaching 18.36%, and is composed of the difference between evaporation temperature and heat source temperature (7.97%), the temperature difference between inlet and outlet of the low-temperature water side (5.52%), and superheat (−4.87%). The weight of the condensation heat transfer process is 10.38%, and it is composed of the difference between condensation temperature and heating temperature (0.53%), the temperature difference between inlet and outlet of the high-temperature water side (7.23%), and subcooling (2.63%). The weight of the compression process is 8.38%, and that of the throttling process is 2.42%.

The viscosity factor consists of viscosity corresponding to condensation temperature (−7.40%) and viscosity corresponding to evaporation temperature (−2.46%), with a total weight of 9.86%. As shown in the figure above, the weight of the viscosity factors is higher than that of the compression process (8.38%) and close to that of the condensation heat transfer process (10.38%), indicating that viscosity has a non-negligible effect on system performance. From the perspective of fluid dynamics, viscosity reflects viscous dissipation in the flow process. Its microscopic viscous resistance is manifested macroscopically as irreversible loss in each process of the cycle. Therefore, the losses in the cycle processes are closely related to fluid viscous dissipation to a certain extent. The influence of viscosity on system performance is mainly reflected in two aspects: increased pressure drop and increased heat transfer resistance. A higher viscosity enhances flow friction and increases both frictional and local pressure drops, thereby increasing compressor power consumption. At the same time, a higher viscosity weakens convective heat transfer and increases thermal resistance, so that a larger temperature difference is required to maintain heat transfer, which ultimately leads to a decrease in COP.

4.3. Weight Contribution Change of Irreversible Parameters at Global and Local Levels with and Without Viscosity Involved

The total weights of irreversible loss factors in the global sample and local temperature range samples, defined as the sum of the absolute weights of all related factors, are shown in Figure 8. With considering viscosity factor, the overall weight of irreversible loss parameters increases significantly. In the global sample, the weight of irreversible loss parameters increases from 46.21% to 49.39%, with an increase of 3.18%. In the low-temperature range, medium-temperature range, and high-temperature range, the weight increases by 3.65% (from 42.13% to 45.78%), 6.68% (from 43.33% to 50.01%), and 12.02% (from 40.06% to 52.08%), respectively. It can be seen that, after introducing viscosity, the importance of irreversible loss parameters is significantly enhanced, and this enhancement becomes more obvious as the operating temperature increases. This indicates that, under high-temperature working conditions, the irreversible loss caused by flow viscosity has a more significant effect on system performance. Therefore, more attention should be paid to the viscosity characteristics of the working fluid under high-temperature conditions. This means that high-temperature operation increases irreversibility in the compression, heat transfer, and flow processes. Under such conditions, the pressure drop, flow resistance, and viscosity dissipation effects caused by viscosity are more easily amplified, and therefore their negative influence on system performance becomes more significant in the high-temperature range.

4.4. Weight Contributions of Influencing Factors for Different Working Fluid Types

The distribution of the absolute weight contributions of influencing factors for different working fluid types is shown in Figure 9. Owing to differences in data distribution, parameters such as critical temperature, critical pressure, and normal boiling point were not included in the analyses of HCFO and natural working fluids. The results show that, in HCFC, the top three negatively correlated influencing factors are temperature lift (12.83%), viscosity corresponding to condensation temperature (7.12%), and condensation pressure (6.83%). In HFC, the top three negatively correlated influencing factors are temperature lift (13.21%), condensation pressure (7.15%), and viscosity corresponding to condensation temperature (7.11%). In HCFO, the top three negatively correlated influencing factors are temperature lift (13.74%), condensation pressure (8.30%), and condensation temperature (7.94%), while viscosity corresponding to condensation temperature ranks fourth (6.84%). In natural working fluids, the top three negatively correlated influencing factors are temperature lift (10.16%), viscosity at evaporation temperature (7.95%), and viscosity corresponding to condensation temperature (7.38%). Overall, viscosity corresponding to condensation temperature ranks among the top three negatively correlated influencing factors in HCFC, HFC, and natural working fluids and ranks fourth in HCFO.

In HCFC, HFC, and natural working fluids, the weight contribution of viscosity corresponding to condensation temperature is nearly equal to or slightly higher than that of condensation pressure. In HCFO, however, the weight contribution of viscosity corresponding to condensation temperature is 13.85% lower than that of condensation pressure. This is because HCFO have relatively low viscosity in the high-temperature range, which weakens their effect on COP and makes their weight contribution significantly lower than that of condensation pressure.

To HCFC, HFC, and HCFO working fluids, the weight contribution of viscosity corresponding to condensation temperature is higher than that of viscosity corresponding to evaporation temperature. In natural working fluids, however, the weight contribution of viscosity corresponding to evaporation temperature is slightly higher, reaching 7.95%. Overall, viscosity shows relatively high importance in different working fluid systems, further indicating that flow viscosity has a general effect on heat pump system performance.

The above results are generally consistent with previous studies on viscous dissipation and flow heat transfer, showing that higher viscosity usually increases flow resistance, pressure drop, and viscous dissipation and thus increases system irreversibility and reduces COP [10]. The results of this study show that viscosity-related factors also have high importance at the heat pump system level, especially that the viscosity corresponding to the condensation temperature is more sensitive in the high-temperature range.

5. Conclusions

Based on data samples from multiple working conditions, working fluids, and device types, this study constructed a weight contribution analysis model for the factors affecting heat pump system COP. The study focused on the change in the distribution of multi-factor weights with and without considering viscosity factors and quantitatively evaluated the effect of viscosity on heat pump system performance from three aspects: the global sample, local samples in different temperature ranges, and samples with different working fluid types. The main conclusions are as follows:

(1)

In the 144 global samples, with viscosity not involved, the top three negatively correlated factors affecting COP were temperature lift (16.10%), condensation pressure (8.93%), and saturated gas line slope at condensation temperature (7.55%). With viscosity involved, viscosity corresponding to condensation temperature entered the top three negatively correlated factors affecting COP, with a contribution of 7.40%. The sum of the absolute weight contributions of viscosity corresponding to condensation temperature and viscosity corresponding to evaporation temperature reached 9.86%, second only to temperature lift, indicating that viscosity is one of the important factors affecting heat pump system COP.

(2)

According to the local analysis results for different temperature ranges, viscosity corresponding to condensation temperature ranked among the top three negatively correlated factors in the low-temperature range, medium-temperature range, and high-temperature range, and its weight increased with the operating temperature range. In contrast, the weight of viscosity corresponding to evaporation temperature decreased as the temperature range increased. This indicates that system performance is more sensitive to viscosity changes near condensation temperature, and under high-temperature operating conditions, more attention should be paid to the viscosity characteristics of the working fluid at condensation temperature.

(3)

The weight contribution results based on the temperature-entropy diagram show that the total weight of viscosity factors was 9.86%, which was higher than that of the compression process (8.38%) and close to that of the condensation heat transfer process (10.38%). This shows that the flow viscous dissipation effect represented by viscosity plays an important role in the formation of system irreversible loss, and its influence cannot be ignored.

(4)

With viscosity, the total weight of irreversible loss parameters in the global sample increased from 46.21% to 49.39%, and it increased by 3.65%, 6.68%, and 12.02% in the low-temperature range, medium-temperature range, and high-temperature range, respectively. This result shows that introducing viscosity significantly enhanced the relative importance of irreversible loss parameters in system performance, and this enhancement was more obvious under high-temperature working conditions.

(5)

The analysis of different working fluid types shows that viscosity corresponding to condensation temperature ranked among the top three negatively correlated factors in HCFC, HFC, and natural working fluids and ranked fourth in HCFO. Overall, viscosity showed relatively high importance in different working fluid systems, indicating that its effect on heat pump system performance is generally applicable.

In summary, viscosity is not only a key physical property for describing the flow characteristics of the working fluid but also an important factor affecting heat pump system COP and the weight contribution of irreversible loss. Its importance becomes even greater under high-temperature working conditions. Therefore, in the optimal design of heat pump systems and the screening of new refrigerants, viscosity and its related flow irreversible loss should be fully considered and included in the system performance evaluation framework, so as to achieve more accurate prediction and more effective improvement of heat pump performance.

Limitations and Outlook

Although multi-source samples were integrated as much as possible in this study so that the data cover multiple operating conditions, multiple refrigerant categories, and multiple device types, the coverage of currently available refrigerants and common device types is still insufficient. In addition, the training set consists of 144 samples, and the overall dataset size is still relatively limited. However, it should be noted that each data point corresponds to one complete cycle sample obtained after stable operation of the heat pump system, and the acquisition of high-quality and complete data requires substantial time for experimental accumulation and data organization. Overall, the current dataset is sufficient to support the model development and result analysis in this study, but its applicability under wider operating conditions, a broader range of refrigerants, and more device types still needs to be further validated in future work. In future research, we will continue to expand the sample size and extend the model to wider operating conditions, more refrigerant types, and more experimental device configurations, so as to further improve its general applicability and engineering value.