Heat Transfer Estimation in Flow Boiling of R134a within Microfin Tubes: Development of Explainable Machine Learning-Based Pipelines
Abstract
:1. Introduction
1.1. Artificial Intelligence and Machine Learning Models
1.2. The Contributions of The Present Study
- Utilizing the experimental dataset on R134a flow under diverse operating conditions undergoing the evaporation process within microfin tubes.
- Gathering widely adopted empirical correlations for heat transfer estimation of two-phase flows from the literature and applying them to the available experimental dataset to obtain their performance.
- Developing various ML pipelines utilizing a range of ML algorithms including extra trees regressor and assessing their performance.
- Providing a feature selection procedure to identify the most promising set of features by employing various combinations of features systematically in the prediction of the target and assessing their performance, leading to a notable reduction in the number of features, reducing model complexity, and facilitating physical interpretation of the results.
- Utilizing a genetic algorithm-based pipeline optimization tool, with a focus on identifying the most suitable algorithm from a broad array of machine learning solutions, refining the tuning parameters, and their sequence in the pipeline.
- Employing an in-house algorithm (forward feature combination), taking the optimal pipeline and the selected features as inputs, and demonstrating the contribution of each feature to the overall achieved accuracy, providing a trade-off between the complexity of the model and the obtained accuracy.
2. Experimental Activity and the Employed Dataset
2.1. The Laboratory Setup
2.2. The Test Section
Temperature Measurement
2.3. Experiments
3. Dimensionless Numbers of Phase-Changing Flow
Dimensionless Number | Formulation | No. |
---|---|---|
Nusselt number | (2) | |
Reynolds number | (3) | |
Weber number | (4) | |
Froude number | (5) | |
Prandtl number | (6) | |
Boiling number | (7) | |
Jakob number | (8) | |
Bond number | (9) | |
Convection number | (10) | |
Kapitza number | (11) | |
Galileo number | (12) | |
Suratman number | (13) | |
Lockhart–Martinelli parameter [39] | (14) | |
Dimensionless vapor velocity [40] | (15) | |
Reduced pressure | (16) |
4. Empirical and Semi-Empirical Correlations
5. Methodology and Implemented Pipelines
5.1. Feature Selection
5.2. Pipeline Optimization
5.3. Performance Evaluation
5.4. Machine Learning Models
5.4.1. Ridge Regression
5.4.2. Elastic Net
5.4.3. Random Forest
5.4.4. Extra Trees Regressor
5.4.5. Feature Processors
- PolynomialFeatures: A feature matrix is constructed that encompasses all polynomial terms of the input features up to a given degree. For example, with a two-dimensional input [a, b], the polynomial features up to degree 2 would include [1, a, b, a2, ab, b2] [59].
- MaxAbsScaler: This tool scales each feature so that its maximum absolute value is 1 while preserving the original data distribution by not shifting or centering the values [54].
- RobustScaler: It operates by normalizing data according to the range between the quantiles, excluding the median from the scaling process. Each feature is scaled and centered independently by calculating relevant statistics from the training data. These statistics (the median and interquartile range) are then stored and applied to transform any new data accordingly.
5.5. Contribution of Each Feature to Optimal Accuracy
6. Results and Discussion
6.1. Accuracy of Physical Models Available in the Literature
6.2. Initial Pipeline and Feature Selection Results
6.3. Machine Learning Pipeline Optimization
6.4. Forward Feature Combination
7. Conclusions
- The feature selection algorithm managed to select 6 features (, , , , , ) among the pool of 21 features. The physical interpretation of the selected features confirmed their higher order of relevance to the target of the predictions.
- The optimized pipeline improved the prediction accuracy and obtained an MARD value of 7.71% on the validation set and an MARD value of 8.84% on the test set, while the most promising empirical model (Rollmann and Spindler’s model Equation (19)) achieved MARD values of 23.1% and 19.7%, respectively on the validation and the test sets. Moreover, the proposed optimal pipeline accompanied by the employed dataset will be made publicly available.
- In future works, the employed dataset should be extended, incorporating data obtained from multiple experimental facilities, which will permit training the algorithms using the data belonging to a test rig while utilizing datasets obtained from other experimental facilities as the test set [30,60,61,62].
- Finally, it should be noted the main contribution of this study, beyond proposing an algorithm resulting in an elevated performance (even if only over the considered dataset), is identifying the most promising set of dimensionless features, which facilitates the corresponding physical interpretation.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Parameters | Tubes | Units | ||||
---|---|---|---|---|---|---|
Microfin 1 | Microfin 2 | Microfin 3 | ||||
Name of the tube | J-60 | VA 1 | HVA 1 | [-] | ||
External diameter | 9.52 | 9.52 | 9.52 | mm | ||
Internal diameter | 8.96 | 8.92 | 8.62 | mm | ||
Thickness | 0.28 | 0.3 | 0.45 | mm | ||
Cross-section area | 62.13 | 61.72 | 57.33 | mm2 | ||
Wet perimeter | 42.38 | 39.9 | 47.72 | mm | ||
Rx | 1.68 | 1.6 | 1.88 | [-] | ||
Fin type | AJ-60 | AVA | BVA | AHVA | BHVA | |
Fin height | 0.2 | 0.23 | 0.16 | 0.2 | 0.17 | mm |
Apex angle | 40 | 40 | 40 | 40 | 40 | [○] |
No. of fins | 60 | 27 | 27 | 41 | 41 | [-] |
Helix angle | 18 | 18 | 18 | 18 | 18 | [○] |
Measurement Parameters | Device | Range | Unit | Uncertainty |
---|---|---|---|---|
Demineralized water mass flow rate | Coriolis flow meter | 0;400 | 0.15% of the reading | |
Coriolis flow meter | 0;6500 | 0.3% of the reading | ||
Refrigerant mass flow rate | Coriolis flow meter | 0;400 | 0.15% of the reading | |
Water temperature | Thermocouples type K | −180;1350 | [°C] | 0.1 K |
Refrigerant temperature | Thermocouples type K | −180;1350 | [°C] | 0.1 K |
Refrigerant inlet pressure | Relative pressure transducer | 0;16 | 0.2% of full scale | |
Pressure drop | Differential pressure transducer | −15;15 | [psi] | 0.1% of full scale |
Test section tube length | - | 2000 | mm | 6 mm |
Voltage of electric heater | - | - | - | 1% of the reading |
Current of electric heater | - | - | - | 1% of the reading |
Parameters | Condition | Tubes | Units | ||
---|---|---|---|---|---|
J60 | VA | HVA | |||
Number of data points | Evaporation | 86 | 40 | 33 | [-] |
Mass fluxes range | 66.3–380.3 | 90–315.6 | 96.7–339.6 | ||
Mass quality range | 0.15–0.95 | 0.25–0.75 | 0.45–0.8 | [-] | |
Heat transfer coefficient range | 2023–9204 | 3701–8695 | 2271–7957 |
Empirical Model | MRD [%] | MARD [%] |
---|---|---|
Mehendale (2017) [7] | 54.94 | 69.7 |
Han et al. (2017) [6] | −56.38 | 56.63 |
Rollmann and Spindler (2016) [5] | 18.51 | 22.42 |
Chamra and Magro (2006) [4] | −20.98 | 28.24 |
Yun et al. (2002) [3] | −83.06 | 83.06 |
Cavallini et al. (1999) [2] | 22.52 | 34.39 |
Thome et al. (1997) [1] | 80.29 | 80.29 |
Pipeline | Input Features | Validation Set (CV) | Test Set | ||
---|---|---|---|---|---|
MRD [%] | MARD [%] | MRD [%] | MARD [%] | ||
All features—RF | , , , | 2.05 | 10.42 | 4.64 | 12.54 |
, , , , , | |||||
, , , , , | |||||
, , n, , | |||||
Selected features—RF | , , , , , | 1.76 | 9.97 | 3.94 | 12.4 |
Selected features—optimized pipeline | , , , , , | 1.54 | 7.71 | 3.32 | 8.84 |
Optimal Pipeline | Arguments | Definitions | Values |
---|---|---|---|
Step one: ExtraTreesRegressor | bootstrap | Whether the bootstraps are used when building the trees | False |
max_features | The number of considered features when building the trees | 0.35 | |
min_samples_leaf | The minimum number of samples at each leaf node | 3 | |
min_samples_split | The minimum number of samples to split an internal node | 15 | |
n_estimator | The number of the trees in the forest | 100 | |
Step two: MaxAbsScaler | - | - | 2 |
Step three: ElasticNetCV | l1_ratio | The value shows the inclination toward L1 or L2 penalty | 0.1 |
tol | The tolerance of the optimization | 0.0001 | |
Step four: RobustScaler | - | - | - |
Step five: PolynomialFeatures | degree | The degree of the polynomial | 2 |
include_bias | If True, adding an intercept term to the polynomial | False | |
interaction_only | If True, only interaction features are produced | False | |
Step six: RidgeCV | - | - | - |
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Milani, S.; Ardam, K.; Dadras Javan, F.; Najafi, B.; Lucchini, A.; Carraretto, I.M.; Colombo, L.P.M. Heat Transfer Estimation in Flow Boiling of R134a within Microfin Tubes: Development of Explainable Machine Learning-Based Pipelines. Energies 2024, 17, 4074. https://doi.org/10.3390/en17164074
Milani S, Ardam K, Dadras Javan F, Najafi B, Lucchini A, Carraretto IM, Colombo LPM. Heat Transfer Estimation in Flow Boiling of R134a within Microfin Tubes: Development of Explainable Machine Learning-Based Pipelines. Energies. 2024; 17(16):4074. https://doi.org/10.3390/en17164074
Chicago/Turabian StyleMilani, Shayan, Keivan Ardam, Farzad Dadras Javan, Behzad Najafi, Andrea Lucchini, Igor Matteo Carraretto, and Luigi Pietro Maria Colombo. 2024. "Heat Transfer Estimation in Flow Boiling of R134a within Microfin Tubes: Development of Explainable Machine Learning-Based Pipelines" Energies 17, no. 16: 4074. https://doi.org/10.3390/en17164074