💥💥💥 How to adjust the curve - validations methods

Curve adjustment is the process of modifying a model's parameters to improve its fit to the data. Validation is the process of evaluating a model's performance on a separate set of data that was not used for training. Validation methods are the techniques used to split the data into training and validation sets, and to measure the model's accuracy, precision, recall, etc.

One common validation method is the **validation curve**, which plots the training and validation scores for different values of a single hyperparameter. This can help you find the optimal value of the hyperparameter that minimizes the bias and variance of the model. You can use the `validation_curve` function from the `sklearn.model_selection` module to generate validation curves for different estimators¹².

Another validation method is the **learning curve**, which plots the training and validation scores for different sizes of the training set. This can help you determine if the model benefits from more training data, or if it suffers from overfitting or underfitting. You can use the `learning_curve` function from the `sklearn.model_selection` module to generate learning curves for different estimators¹.

There are other validation methods, such as cross-validation, bootstrap, hold-out, etc., that you can use depending on your data and model. You can find more information about them in the [User Guide](^1^) and the [Model Validation and Testing: A Step-by-Step Guide](^3^).

Source: 

(1) 3.4. Validation curves: plotting scores to evaluate models. https://scikit-learn.org/stable/modules/learning_curve.html.

(2) sklearn.model_selection.validation_curve - scikit-learn. https://scikit-learn.org/stable/modules/generated/sklearn.model_selection.validation_curve.html.

(3) 3.4. Validation curves: plotting scores to evaluate models. https://scikit-learn.org/stable/modules/learning_curve.html.

(4) Model Validation and Testing: A Step-by-Step Guide | Built In. https://builtin.com/data-science/model-validation-test.

(5) Validation Curve - GeeksforGeeks. https://www.geeksforgeeks.org/validation-curve/.

(6) Validation – Adjustment of NIR Calibrations | PerkinElmer Blog. https://blog.perkinelmer.com/posts/validation-adjustment-of-nir-calibrations/.

**Cross-validation** is a method that divides your data into **k** equal and non-overlapping subsets, called **folds**. Then, it trains your model on **k-1** folds, and tests it on the remaining fold. This process is repeated **k** times, so that each fold is used as the test set once. The average of the test scores across the **k** folds is the final performance measure of your model¹.

**Bootstrap** is a method that samples your data **with replacement**, meaning that the same data point can be selected more than once. It creates **B** new datasets, each with the same size as the original dataset, but with some data points repeated and some omitted. Then, it trains your model on each bootstrap dataset, and tests it on the original dataset. The average of the test scores across the **B** bootstrap datasets is the final performance measure of your model².

**Hold-out** is a method that splits your data into two parts: a **training set** and a **validation set**. The training set is used to fit your model, and the validation set is used to evaluate its performance. The size of the validation set is usually a fixed proportion of the original dataset, such as 20% or 30%. The performance measure of your model is the test score on the validation set³.

Each method has its advantages and disadvantages, depending on the size and characteristics of your data, and the complexity and variability of your model. You can find more information about them in the following links:

- [What is the difference between bootstrapping and cross-validation?](^1^)

- [4 Cross Validation Methods | Introduction to Applied Machine Learning](^2^)

- [Hold-out vs. Cross-validation in Machine Learning](^5^)

Source:

(1) What is the difference between bootstrapping and cross-validation?. https://datascience.stackexchange.com/questions/32264/what-is-the-difference-between-bootstrapping-and-cross-validation.

(2) 4 Cross Validation Methods | Introduction to Applied Machine Learning. https://dionysus.psych.wisc.edu/iaml_2020/unit-04.html.

(3) Are K-Fold Cross Validation , Bootstrap ,Out of Bag fundamentally same?. https://stats.stackexchange.com/questions/206807/are-k-fold-cross-validation-bootstrap-out-of-bag-fundamentally-same.

(4) What is the difference between bootstrapping and cross-validation?. https://datascience.stackexchange.com/questions/32264/what-is-the-difference-between-bootstrapping-and-cross-validation.

(5) 4 Cross Validation Methods | Introduction to Applied Machine Learning. https://dionysus.psych.wisc.edu/iaml_2020/unit-04.html.

(6) Hold-out vs. Cross-validation in Machine Learning - Medium. https://medium.com/@jaz1/holdout-vs-cross-validation-in-machine-learning-7637112d3f8f.

(7) Bootstrapping vs Cross-Validation - Doc Zamora's ML & AI. https://www.doczamora.com/bootstrapping-vs-cross-validation.

(8) en.wikipedia.org. https://en.wikipedia.org/wiki/Cross-validation_(statistics).

How do I choose the best validation method for my model?

Choosing the best validation method for your model depends on several factors, such as the size and characteristics of your data, the complexity and variability of your model, and the trade-off between bias and variance. 😊

There is no definitive answer to this question, as different validation methods have their own advantages and disadvantages. However, some general guidelines are:

- If your data is large and representative, you can use a simple **hold-out** method, where you split your data into a training set and a validation set, and use the validation set to evaluate your model's performance⁴.

- If your data is small or imbalanced, you can use a **cross-validation** method, where you divide your data into k folds, and use each fold as a validation set once, while using the rest as a training set. This way, you can use all your data for both training and validation, and reduce the variance of your model's performance¹.

- If your data is noisy or has high variance, you can use a **bootstrap** method, where you sample your data with replacement, and create new datasets that have the same size as the original dataset. Then, you can train and test your model on each bootstrap dataset, and average the performance across them. This way, you can reduce the bias of your model's performance².

You can also combine different validation methods, such as using cross-validation with hold-out, or bootstrap with cross-validation, to get more robust estimates of your model's performance.

To learn more about these validation methods, you can check out these links:

- [Model Validation and Testing: A Step-by-Step Guide](^1^)

- [The Ultimate Guide to Evaluation and Selection of Models in ML](^2^)

- [choosing model based on last or best iteration on validation set](^3^)

- [How To Choose The Right Test Options When Evaluating Machine Learning Algorithms](^4^)

Source: 

(1) How To Choose The Right Test Options When Evaluating Machine Learning .... https://machinelearningmastery.com/how-to-choose-the-right-test-options-when-evaluating-machine-learning-algorithms/.

(2) Model Validation and Testing: A Step-by-Step Guide | Built In. https://builtin.com/data-science/model-validation-test.

(3) The Ultimate Guide to Evaluation and Selection of Models in ML - neptune.ai. https://neptune.ai/blog/ml-model-evaluation-and-selection.

(4) Model Validation and Testing: A Step-by-Step Guide | Built In. https://builtin.com/data-science/model-validation-test.

(5) The Ultimate Guide to Evaluation and Selection of Models in ML - neptune.ai. https://neptune.ai/blog/ml-model-evaluation-and-selection.

(6) choosing model based on last or best iteration on validation set. https://datascience.stackexchange.com/questions/72002/choosing-model-based-on-last-or-best-iteration-on-validation-set.

(7) How To Choose The Right Test Options When Evaluating Machine Learning .... https://machinelearningmastery.com/how-to-choose-the-right-test-options-when-evaluating-machine-learning-algorithms/.

How do I measure the performance of my model?

There are different ways to measure the performance of your model, depending on the type of problem you are solving and the metrics you are interested in. 😊

For example, if you are solving a **classification** problem, where you want to predict discrete labels for your data, you can use metrics such as **accuracy**, **precision**, **recall**, and **F1 score**. These metrics evaluate how well your model can correctly identify the true classes of your data, and avoid false positives and false negatives. You can also use plots such as **ROC curve** and **confusion matrix** to visualize the trade-off between sensitivity and specificity, and the distribution of errors across classes¹².

If you are solving a **regression** problem, where you want to predict continuous values for your data, you can use metrics such as **mean absolute error (MAE)**, **root mean square error (RMSE)**, **R-squared**, and **adjusted R-squared**. These metrics evaluate how close your model's predictions are to the true values of your data, and how well your model can explain the variance of your data. You can also use plots such as **residual plot** and **scatter plot** to visualize the error distribution and the correlation between your predictions and true values³⁴.

To learn more about these metrics and plots, and how to implement them in Python, you can check out these links:

- [Evaluate the Performance of Deep Learning Models in Keras](^1^)

- [6 Methods to Measure Performance of a Classification Model](^2^)

- [4 Best Metrics for Evaluating Regression Model Performance](^3^)

- [Predictive Performance Models Evaluation Metrics](^5^)

Source: 

(1) Evaluate the Performance of Deep Learning Models in Keras. https://machinelearningmastery.com/evaluate-performance-deep-learning-models-keras/.

(2) 6 Methods to Measure Performance of a Classification Model. https://insidelearningmachines.com/measure-performance-of-a-classification-model/.

(3) Evaluate Models Using Metrics | Machine Learning - Google Developers. https://developers.google.com/machine-learning/testing-debugging/metrics/metrics.

(4) 4 Best Metrics for Evaluating Regression Model Performance. https://www.aionlinecourse.com/tutorial/machine-learning/evaluating-regression-models-performance.

(5) Evaluate the Performance of Deep Learning Models in Keras. https://machinelearningmastery.com/evaluate-performance-deep-learning-models-keras/.

(6) 6 Methods to Measure Performance of a Classification Model. https://insidelearningmachines.com/measure-performance-of-a-classification-model/.

(7) Evaluate Models Using Metrics | Machine Learning - Google Developers. https://developers.google.com/machine-learning/testing-debugging/metrics/metrics.

(8) Predictive Performance Models Evaluation Metrics - InData Labs. https://indatalabs.com/blog/predictive-models-performance-evaluation-important.

(9) en.wikipedia.org. https://en.wikipedia.org/wiki/Keras.

What is the difference between accuracy and precision?

Accuracy and precision are both forms of measurement that define how close you are to hitting a target or achieving a goal. Accuracy evaluates how close you are to the true value of the measurement, while precision shows how close the measured values are to one another¹.

For example, if you are shooting arrows at a bullseye, accuracy is how close your arrows are to the center of the target, and precision is how close your arrows are to each other. You can have high accuracy and low precision, low accuracy and high precision, or both high accuracy and high precision².

In math, science, and engineering, accuracy and precision are used to describe the quality and reliability of measurements. Accuracy reflects how close a measurement is to the actual or accepted value, while precision reflects how consistent or reproducible the measurements are. A measurement system can be accurate but not precise, precise but not accurate, or both accurate and precise³.

Source:

(1) What Is the Difference Between Accuracy and Precision? - ThoughtCo. https://www.thoughtco.com/difference-between-accuracy-and-precision-609328.

(2) Accuracy and precision - Wikipedia. https://en.wikipedia.org/wiki/Accuracy_and_precision.

(3) What's the difference between accuracy and precision? - Asana. https://asana.com/resources/accuracy-vs-precision.

(4) What Is the Difference Between Accuracy and Precision? - ThoughtCo. https://www.thoughtco.com/difference-between-accuracy-and-precision-609328.

(5) Accuracy and precision - Wikipedia. https://en.wikipedia.org/wiki/Accuracy_and_precision.

(6) What's the difference between accuracy and precision? - Asana. https://asana.com/resources/accuracy-vs-precision.

How do I calculate accuracy and precision for my model?

Accuracy and precision are two metrics that can be used to evaluate the performance of a classification model. Accuracy is the ratio of the number of correct predictions to the total number of predictions, while precision is the ratio of the number of true positives to the total number of positive predictions¹.

To calculate accuracy and precision for your model, you need to have the true labels and the predicted labels of your data. You can use the `sklearn.metrics` module in Python to compute these metrics easily. For example, you can use the following code:

```python

from sklearn.metrics import accuracy_score, precision_score

# y_true is the list of true labels

# y_pred is the list of predicted labels

accuracy = accuracy_score(y_true, y_pred)

precision = precision_score(y_true, y_pred)

print("Accuracy:", accuracy)

print("Precision:", precision)

```

You can also use other metrics, such as recall, F1-score, ROC AUC, etc., depending on your problem and goals. You can find more information about these metrics and how to calculate them in the following links:

- [How to Calculate Precision, Recall, F1, and More for Deep Learning Models](^1^)

- [How to Calculate Precision, Recall, and F-Measure for Imbalanced Classification](^2^)

- [Model accuracy: how to determine it? - Data Science Stack Exchange](^4^)

Source: 

(1) How to Calculate Precision, Recall, F1, and More for Deep Learning Models. https://machinelearningmastery.com/how-to-calculate-precision-recall-f1-and-more-for-deep-learning-models/.

(2) How to Calculate Precision, Recall, F1, and More for Deep Learning Models. https://machinelearningmastery.com/how-to-calculate-precision-recall-f1-and-more-for-deep-learning-models/.

(3) How to Calculate Precision, Recall, and F-Measure for Imbalanced .... https://machinelearningmastery.com/precision-recall-and-f-measure-for-imbalanced-classification/.

(4) Model accuracy: how to determine it? - Data Science Stack Exchange. https://datascience.stackexchange.com/questions/83961/model-accuracy-how-to-determine-it.

(5) How to Calculate Accuracy and Precision: A Comprehensive Guide. https://www.thetechedvocate.org/how-to-calculate-accuracy-and-precision-a-comprehensive-guide/.

(6) How Compute Accuracy For Object Detection works - Esri. https://pro.arcgis.com/en/pro-app/latest/tool-reference/image-analyst/how-compute-accuracy-for-object-detection-works.htm.

💥💥💥 New year - new challenges - "OpenFoam project" part 2 (main differences between OpenFoam and Ansys Fluent)

 OpenFoam and Ansys Fluent are both software tools for computational fluid dynamics (CFD) simulations, but they have some key differences. Here are some of the main ones:

• 
  OpenFoam is an open-source software, which means it is free to use and modify, while Ansys Fluent is a commercial software, which requires a license fee to use¹².
• OpenFoam is based on a finite volume method, while Ansys Fluent can use both finite volume and finite element methods³⁴.
• OpenFoam has a more flexible and customizable solver structure, which allows users to create their own solvers and models, while Ansys Fluent has a more user-friendly and standardized interface, which makes it easier to set up and run simulations¹².
• OpenFoam has a steeper learning curve and requires more programming skills, while Ansys Fluent has more tutorials and documentation available and requires less coding¹².
• OpenFoam has a larger and more active community of users and developers, who contribute to the software development and provide support, while Ansys Fluent has more professional and technical support from the company¹².

How do I choose between OpenFoam and Ansys Fluent?

Choosing between OpenFoam and Ansys Fluent depends on several factors, such as your budget, your skill level, your problem type, and your preference. Here are some general guidelines that may help you decide:

• If you have a limited budget or you want to modify the source code, you may prefer OpenFoam, as it is free and open-source¹².
• If you want a more user-friendly and standardized interface, or you need professional and technical support, you may prefer Ansys Fluent, as it has more tutorials and documentation available and a company behind it¹².
• If you need to use both finite volume and finite element methods, or you want to use a specific solver or model that is not available in OpenFoam, you may prefer Ansys Fluent, as it has more options and features³⁴.
• If you want to create your own solvers and models, or you want to use a more flexible and customizable solver structure, you may prefer OpenFoam, as it allows you to program your own equations and algorithms¹².
• If you have a complex or large-scale problem that requires high accuracy and performance, you may need to compare the results of both software, as they may differ depending on the problem and the settings¹²⁵.

Ultimately, the best way to choose between OpenFoam and Ansys Fluent is to try them both and see which one suits your needs and preferences better. 

Which one is better for simulating turbulence?

Simulating turbulence is a challenging task that depends on the type and complexity of the flow, the accuracy and stability of the numerical methods, and the suitability and validity of the turbulence models. Therefore, there is no definitive answer to which software is better for simulating turbulence, as it may vary from case to case. However, some general considerations are:

• OpenFoam has a larger variety of turbulence models than Ansys Fluent, including some advanced models such as large eddy simulation (LES), detached eddy simulation (DES), and scale-adaptive simulation (SAS)¹². However, some of these models may require more computational resources and expertise to use properly³.
• Ansys Fluent has a more user-friendly and standardized interface for setting up and running turbulence simulations, as well as more tutorials and documentation available¹². However, some of the settings and options may be hidden or simplified, which may limit the user’s control and understanding of the simulation⁴.
• Both software have different numerical methods and solvers, which may affect the accuracy and performance of the turbulence simulations. For example, OpenFoam uses a finite volume method, while Ansys Fluent can use both finite volume and finite element methods³⁴. Moreover, OpenFoam uses a conjugate gradient solver, while Ansys Fluent uses an algebraic multigrid solver². These methods may have different advantages and disadvantages depending on the problem and the mesh⁵.

The best way to compare the software for simulating turbulence is to run the same problem with the same settings and mesh, and compare the results in terms of accuracy, convergence, and computational time. You can also consult the literature and the web for more information and examples of turbulence simulations with OpenFoam and Ansys Fluent¹²³⁴⁵. 

Which one is better for simualting Conjugate Heat Transfer ?

Conjugate heat transfer (CHT) is the process of heat transfer between a solid and a fluid, or between different solids, in contact with each other¹. Simulating CHT requires solving the energy equation for both the fluid and the solid domains, and applying appropriate boundary conditions at the interface².

Both OpenFoam and Ansys Fluent are capable of simulating CHT, but they have some differences in their approaches and features. Here are some of the main ones:

• OpenFoam uses a single solver, called chtMultiRegionFoam, for CHT simulations, which can handle multiple fluid and solid regions, and couple them using a regionCouple boundary condition³. Ansys Fluent uses different solvers for different types of CHT simulations, such as pressure-based or density-based solvers, and couples the fluid and solid regions using a coupled-wall boundary condition⁴.
• OpenFoam requires the user to create separate meshes for each fluid and solid region, and to define the interface between them in a regionProperties file³. Ansys Fluent allows the user to create a single mesh for the whole domain, and to specify the fluid and solid regions using cell zones and cell types⁴.
• OpenFoam has a more flexible and customizable solver structure, which allows the user to modify the source code and create their own models and algorithms, while Ansys Fluent has a more user-friendly and standardized interface, which makes it easier to set up and run simulations¹².
• OpenFoam has a larger variety of turbulence models and numerical schemes than Ansys Fluent, which may affect the accuracy and performance of the CHT simulations¹². However, some of these models and schemes may require more computational resources and expertise to use properly³.
• Ansys Fluent has more options and features for CHT simulations, such as radiation, phase change, porous media, and moving/deforming mesh⁴. However, some of these options and features may be hidden or simplified, which may limit the user’s control and understanding of the simulation².

💥💥💥 New year - new challenges - "OpenFoam project" - part 1 (installation)

 There are different ways to install OpenFoam on Windows, depending on your preferences and needs. One option is to use the Windows Subsystem for Linux (WSL), which allows you to run Linux applications on Windows 10. Another option is to use a virtual machine (VM), such as VirtualBox, which creates a separate Linux environment on your Windows system. Here are some brief steps for each option:

• 
  WSL: You need to activate WSL and install the Ubuntu distribution from the Microsoft Store. Then, you can download the OpenFoam package for Ubuntu and install it using the commands provided in the OpenFOAM website. You also need to install some additional dependencies and configure your bash shell to run OpenFOAM. To enable graphical applications, such as ParaView, you need to install an X server software, such as VcXsrv¹²³.
• VM: You need to download and install VirtualBox, and then create a new virtual machine with Ubuntu as the operating system. Then, you can follow the same steps as for WSL to install OpenFOAM on Ubuntu. Alternatively, you can download a pre-configured VM image with OpenFOAM from the OpenFOAM website and import it into VirtualBox⁴⁵.

Is threre possibilty to install OpenFoam directly on Windows ?

No, there is no possibility to install OpenFoam directly on Windows, as OpenFoam is a Linux-based software that requires a Linux environment to run. However, as I mentioned before, you can use WSL or VM to create a Linux environment on your Windows system and install OpenFoam there. These methods are well-documented and supported by the OpenFoam community¹²³. 

How to install OpenFoam on Windows by the WSL method?

To install OpenFoam on Windows by the WSL method, you need to follow these steps:

• Activate Windows Subsystem for Linux (WSL) and install the Ubuntu distribution from the Microsoft Store¹.
• Launch the Ubuntu distribution through WSL and download the OpenFoam package for Ubuntu using the commands provided in the OpenFOAM website.
• Install some additional dependencies and configure your bash shell to run OpenFOAM¹.
• Install an X server software, such as VcXsrv, to enable graphical applications, such as ParaView¹²³.

What is the difference between WSL and VM?

WSL and VM are two different ways to run Linux applications on Windows. WSL stands for Windows Subsystem for Linux, and VM stands for Virtual Machine. Here are some of the main differences between them:

• WSL uses the Windows kernel to implement Linux system calls, while VM uses a separate Linux kernel running on a hypervisor¹².
• WSL has better performance and integration with Windows, while VM has better compatibility and isolation with Linux¹².
• WSL is more lightweight and easy to set up, while VM is more flexible and customizable¹²³.
• WSL supports only command-line applications, while VM supports both command-line and graphical applications¹²⁴.

What are the advantages of using WSL over VM?

Some of the advantages of using WSL over VM are:

• WSL is more lightweight and easy to set up than VM, as it does not require allocating resources from the host machine or installing heavy ISO files¹².
• WSL has better performance and integration with Windows than VM, as it uses the Windows kernel to implement Linux system calls instead of a separate Linux kernel running on a hypervisor³⁴.
• WSL is faster to launch and more convenient to use than VM, as it does not need to boot a full Linux system or switch between different machines⁴².
• WSL supports most of the Linux command-line tools, languages, and compilers that developers need, while VM supports both command-line and graphical applications³⁴.

What are the advantages of using VM over WSL?

Some of the advantages of using VM over WSL are:

• VM is more compatible and isolated with Linux than WSL, as it uses a separate Linux kernel running on a hypervisor instead of the Windows kernel to implement Linux system calls¹².
• VM is more flexible and customizable than WSL, as it allows you to configure virtual devices, allocate resources, and install different operating systems on the same machine²³⁴.
• VM supports both command-line and graphical applications, while WSL supports only command-line applications (although Microsoft promises support for GUI apps in WSL in the future)¹²⁵.
• VM gives you a more authentic Linux experience than WSL, as it runs a full Linux system with all the processes and features that Linux has to offer²⁵.

💥💥💥 What is k-epsilon model in Ansys Fluent and what is used for ?

 The k-epsilon model is a type of turbulence model that is used in computational fluid dynamics (CFD) simulations. It is based on two transport equations for the turbulence kinetic energy (k) and its dissipation rate (epsilon). The k-epsilon model can capture the effects of mean velocity gradients, buoyancy, compressibility, and heat and mass transfer on the turbulent flow. It is one of the most widely used turbulence models in engineering applications because of its robustness, economy, and reasonable accuracy for a wide range of flows¹².

Ansys Fluent is a software package that allows users to perform CFD simulations using various turbulence models, including the k-epsilon model. Ansys Fluent provides three variants of the k-epsilon model: the standard, the RNG, and the realizable k-epsilon models. Each variant has different methods of calculating the turbulent viscosity, the turbulent Prandtl numbers, and the generation and destruction terms in the epsilon equation³. The k-epsilon model in Ansys Fluent can be used for modeling internal and external flows, separated flows, jets, flows with high-pressure gradients, and flows through curved geometries⁴⁵.

Source:

(1) ANSYS FLUENT 12.0 User's Guide - 33.3.3 Viscous Model Dialog Box - ENEA. https://www.afs.enea.it/project/neptunius/docs/fluent/html/ug/node1022.htm.

(2) 12.4.1 Standard k Model Overview - University of Washington. https://courses.washington.edu/mengr544/handouts-10/Fluent-k-epsilon.pdf.

(3) ANSYS FLUENT 12.0 User's Guide - 12.4 Steps in Using a Turbulence Model. https://www.afs.enea.it/project/neptunius/docs/fluent/html/ug/node411.htm.

(4) Difference between K-epsilon and K-omega Turbulence Model - Ansys .... https://forum.ansys.com/forums/topic/difference-between-k-epsilon-and-k-omega-turbulence-model/.

(5) k-epsilon and Laminar differrence - Ansys Learning Forum. https://forum.ansys.com/forums/topic/k-epsilon-and-laminar-differrence/.

What are the limitations of k-epsilon model?

The k-epsilon model is a popular and widely used turbulence model, but it also has some limitations that affect its accuracy and applicability. Some of the limitations are:

- It assumes that the turbulence is isotropic, which means that the ratio between Reynolds stress and mean rate of deformation is the same in all directions. This is not true for flows with strong anisotropy, such as swirling, rotating, or curved flows²³.

- It requires a high Reynolds number, which means that the inertial forces are much larger than the viscous forces. This is not true for flows near the wall, where the viscous effects are important. Therefore, the k-epsilon model needs a near-wall treatment, such as wall functions or low-Reynolds number corrections, to account for the wall effects¹².

- It does not capture the effects of history and rapid distortion on the turbulence. This means that the model cannot handle flows with large adverse pressure gradients, boundary layer separation, or shock waves. Therefore, the k-epsilon model may under-predict the extent of recirculation zones or over-predict the turbulent kinetic energy at stagnation points¹⁴⁵.

These limitations can be overcome by using more advanced turbulence models, such as Reynolds stress models, large eddy simulation, or detached eddy simulation, which can account for the effects of anisotropy, compressibility, history, and distortion on the turbulence. However, these models are also more complex, computationally expensive, and sensitive to initial and boundary conditions. Therefore, the choice of the turbulence model depends on the trade-off between accuracy and efficiency for a given flow problem.

Source: 

(1) The k-ε Turbulence Model - COMSOL Multiphysics. https://doc.comsol.com/5.5/doc/com.comsol.help.cfd/cfd_ug_fluidflow_single.06.088.html.

(2) OpenFOAM: User Guide: k-epsilon. https://www.openfoam.com/documentation/guides/latest/doc/guide-turbulence-ras-k-epsilon.html.

(3) K-epsilon turbulence model - Wikipedia. https://en.wikipedia.org/wiki/K-epsilon_turbulence_model.

(4) Validation and analysis of turbulence modeling in pipe elbow under .... https://link.springer.com/article/10.1007/s40430-022-03899-9.

(5) Limitations and empirical extensions of the k-epsilon model as applied .... https://ntrs.nasa.gov/search.jsp?R=19840035309.

Is k-epsilon model good for low quality meshes ?

The k-epsilon model is not very suitable for low quality meshes, especially near the wall regions. This is because the k-epsilon model requires a high Reynolds number, which means that the inertial forces are much larger than the viscous forces. This is not true for flows near the wall, where the viscous effects are important. Therefore, the k-epsilon model needs a near-wall treatment, such as wall functions or low-Reynolds number corrections, to account for the wall effects¹². However, these treatments are sensitive to the mesh quality and resolution, and may not work well for coarse or skewed meshes³⁴.

A better alternative for low quality meshes is the k-omega model, which is more robust and accurate for near-wall flows. The k-omega model does not require a high Reynolds number, and can handle flows with large adverse pressure gradients, boundary layer separation, or shock waves. The k-omega model is also good in resolving internal flows, separated flows and jets and flows with high-pressure gradient and also internal flows through curved geometries³. However, the k-omega model may be more computationally expensive and sensitive to initial and boundary conditions than the k-epsilon model². Therefore, the choice of the turbulence model depends on the trade-off between accuracy and efficiency for a given flow problem.

Source: 

(1) K-epsilon Turbulence Model | Global Settings | SimScale. https://www.simscale.com/docs/simulation-setup/global-settings/k-epsilon/.

(2) K-epsilon turbulence model - Wikipedia. https://en.wikipedia.org/wiki/K-epsilon_turbulence_model.

(3) Difference between K-epsilon and K-omega Turbulence Model. https://forum.ansys.com/forums/topic/difference-between-k-epsilon-and-k-omega-turbulence-model/.

(4) k-epsilon model: which criteria do I have to meet for the near wall mesh?. https://forum.ansys.com/forums/topic/k-epsilon-model-which-criteria-do-i-have-to-meet-for-the-near-wall-mesh/.

What is the difference between k-epsilon and k-omega models?

The k-epsilon and k-omega models are both types of turbulence models that are used in computational fluid dynamics (CFD) simulations. They are based on two transport equations for the turbulence kinetic energy (k) and either its dissipation rate (epsilon) or its specific dissipation rate (omega). The main difference between them is that the k-epsilon model is more suitable for flow away from the wall, while the k-omega model is more accurate for near-wall flow regions¹².

The k-epsilon model assumes that the turbulence is isotropic, which means that the ratio between Reynolds stress and mean rate of deformation is the same in all directions. This is not true for flows with strong anisotropy, such as swirling, rotating, or curved flows. The k-epsilon model also requires a high Reynolds number, which means that the inertial forces are much larger than the viscous forces. This is not true for flows near the wall, where the viscous effects are important. Therefore, the k-epsilon model needs a near-wall treatment, such as wall functions or low-Reynolds number corrections, to account for the wall effects. However, these treatments are sensitive to the mesh quality and resolution, and may not work well for coarse or skewed meshes¹².

The k-omega model does not assume isotropy, and can handle flows with large adverse pressure gradients, boundary layer separation, or shock waves. The k-omega model does not require a high Reynolds number, and can resolve the viscous layer without wall functions. The k-omega model is also good in resolving internal flows, separated flows, jets, flows with high-pressure gradients, and flows through curved geometries¹³. However, the k-omega model may be more computationally expensive and sensitive to initial and boundary conditions than the k-epsilon model².

A common variant of the k-omega model is the SST (shear stress transport) model, which blends the k-epsilon and k-omega models to achieve the best of both worlds. The SST model uses the k-omega formulation in the near-wall region and switches to the k-epsilon formulation in the free-stream region. The SST model can capture the effects of mean velocity gradients, buoyancy, compressibility, and heat and mass transfer on the turbulent flow. The SST model is one of the most widely used turbulence models in engineering applications because of its robustness, economy, and reasonable accuracy for a wide range of flows¹⁴.

Source: 

(1) Which Turbulence Model Should I Choose for My CFD Application?. https://www.comsol.com/blogs/which-turbulence-model-should-choose-cfd-application/.

(2) Use of k-epsilon and k-omega Models - CFD Online. https://www.cfd-online.com/Forums/main/75554-use-k-epsilon-k-omega-models.html.

(3) Difference between K-epsilon and K-omega Turbulence Model. https://forum.ansys.com/forums/topic/difference-between-k-epsilon-and-k-omega-turbulence-model/.

(4) What is the difference between k-epsilon and k-omega model .... https://rampfest-hudson.com/what-is-the-difference-between-k-epsilon-and-k-omega-model/.

(5) What is the difference between k-epsilon and K-Omega?. https://vidque.com/what-is-the-difference-between-k-epsilon-and-k-omega/.

🎅 🎅 🎅 The story of Santa Claus who, with a hangover on New Year's Eve, had to test Ansys Mechanical a bit

 Santa Claus had a wild night on New Year's Eve. He drank too much eggnog, danced with the elves, and sang karaoke with Rudolph. He woke up the next morning with a hangover and a terrible headache. He groaned and reached for his phone, hoping to check his messages and go back to sleep.

But he was in for a rude awakening. He had received an urgent email from Ansys, the company that provided him with the software for designing his sleigh and toys. They wanted him to test their new product, Ansys Mechanical, a finite element analysis (FEA) software for structural engineering. They said it was a great opportunity for him to improve his designs and optimize his performance.

Santa Claus was not in the mood for this. He hated learning new software, especially when he had a headache. He wished he could just stick to his old methods, but he knew he had to keep up with the times. He decided to give it a try, hoping it would be easy and intuitive.

He downloaded Ansys Mechanical and opened it on his laptop. He was greeted by a user interface that looked complicated and confusing. He saw a lot of buttons, menus, and icons, but he had no idea what they did. He looked for a tutorial or a help guide, but he couldn't find any. He felt frustrated and overwhelmed.

He decided to start with something simple. He wanted to model a toy car and see how it would behave under different loads and conditions. He imported a CAD model of the car and tried to mesh it. He clicked on the mesh button and waited for the results. He expected to see a nice and smooth mesh, but he was shocked by what he saw. The mesh was coarse and distorted, with a lot of poor elements and gaps. He didn't know what went wrong or how to fix it.

He tried to adjust the mesh settings, but he only made it worse. He tried to apply boundary conditions and loads, but he got a lot of errors and warnings. He tried to run the analysis, but he got a message saying that the solution was not converged. He tried to view the results, but he got a blank screen. He tried to use the post-processing tools, but he didn't understand what they meant.

He spent hours trying to figure out how to use Ansys Mechanical, but he only got more frustrated and angry. He felt like he was wasting his time and energy. He cursed and slammed his laptop shut. He decided to give up on Ansys Mechanical and go back to his old software. He thought it was too complicated and difficult for him. He wondered why Ansys wanted him to use it in the first place.

He didn't realize that Ansys Mechanical was actually a powerful and versatile tool that could help him solve complex structural engineering problems and make better, faster design decisions. He didn't know that it had a dynamic and integrated platform that could connect with other physics for even greater fidelity. He didn't know that it had a persistent, dependable, and accurate solver technology that could handle linear and nonlinear, static and dynamic, and thermal and acoustic analyses. He didn't know that it had a lot of features and capabilities that could help him with advanced materials modeling, vibration, coupled field, explicit, acoustics, crack and fracture, structural optimization, fatigue life, and more.

He also didn't know that Ansys Mechanical had a lot of resources and events that could help him learn and use it effectively. He didn't know that he could access online courses, webinars, blogs, forums, and support communities that could provide him with guidance and tips. He didn't know that he could find a lot of tutorials, examples, and documentation that could show him how to use the software step by step. He didn't know that he could contact Ansys experts and engineers who could answer his questions and solve his problems.

Santa Claus missed a great opportunity to improve his skills and designs with Ansys Mechanical. He could have learned a lot and had a lot of fun with it. He could have made his sleigh and toys more efficient, reliable, and safe. He could have delivered more joy and happiness to the children of the world.

But he didn't. He chose to stay in his comfort zone and ignore the new possibilities. He was too stubborn and lazy to try something new. He was too proud and arrogant to ask for help. He was too drunk and hungover to think clearly.

He regretted his decision later, when he realized what he had missed. He wished he had given Ansys Mechanical a chance. He wished he had been more open-minded and curious. He wished he had been more smart and brave.

But it was too late. He had lost his chance. He had lost his edge. He had lost his magic.

The end.

💥💥💥HAPPY AND HEALTHY NEW YEAR !!!💥💥💥

🎅 🎅 🎅 What are the main differences between Ansys Fluent and CFX ?

Ansys Fluent and CFX are both powerful computational fluid dynamics (CFD) solvers, but they have some differences in their features, capabilities, and applications. Here are some of the main differences between them:

- Fluent uses a cell-centered approach while CFX uses a vertex-centered approach. This means that Fluent can handle more complex mesh topologies, such as polyhedral and cutcell meshes, while CFX is limited to tetrahedral and hexahedral meshes¹².

- Fluent has post-processing capabilities of its own while CFX needs a dedicated post-processor, such as CFD-Post¹². Fluent also has more options for mesh adaption and simulation acceleration with a GPU².

- CFX has a built-in expression language (CEL) that allows users to define algebraic equations and monitor them during the run¹². Fluent requires user-defined functions (UDFs) for customization, which can be more challenging for beginners¹.

- CFX is more suitable for turbomachinery applications, as it has specialized features for rotating machinery, such as frozen rotor and transient blade row models²³. Fluent is more preferred for high Mach number flows, such as supersonic and hypersonic flows².

Source: 

(1) What are the differences between CFX and Fluent? - Ansys Learning Forum. https://forum.ansys.com/forums/topic/what-are-the-differences-between-cfx-and-fluent/.

(2) Compare Ansys CFX vs. Ansys Fluent | G2. https://www.g2.com/compare/ansys-cfx-vs-ansys-fluent.

(3) Reply To: What are the differences between CFX and Fluent?. https://forum.ansys.com/forums/reply/58903/.

(4) What are the differences between CFX and Fluent? - Ansys Learning Forum. https://forum.ansys.com/forums/topic/what-are-the-differences-between-cfx-and-fluent/.

(5) Compare Ansys CFX vs. Ansys Fluent | G2. https://www.g2.com/compare/ansys-cfx-vs-ansys-fluent.

(6) Reply To: What are the differences between CFX and Fluent?. https://forum.ansys.com/forums/reply/58903/.

(7) Getty Images. https://www.gettyimages.com/detail/news-photo/in-this-photo-illustration-the-ansys-logo-seen-displayed-on-news-photo/1212478964. 

Which one is more popular in industry?

That's a good question, but it's not easy to answer. The popularity of Ansys Fluent and CFX may depend on the industry, the region, the application, and the preference of the users. According to some sources, Fluent is more widely used than CFX in general, especially in the aerospace, automotive, and chemical industries¹². However, CFX has a strong presence in the power generation and turbomachinery sectors¹³. Ultimately, both solvers have their strengths and weaknesses, and the best choice may depend on the specific problem and the user's experience.

Source: 

(1) What are the differences between CFX and Fluent? - Ansys Learning Forum. https://forum.ansys.com/forums/topic/what-are-the-differences-between-cfx-and-fluent/.

(2) Ansys CFX or Ansys Fluent : r/CFD - Reddit. https://www.reddit.com/r/CFD/comments/yp3vf0/ansys_cfx_or_ansys_fluent/.

(3) Compare Ansys CFX vs. Ansys Fluent | G2. https://www.g2.com/compare/ansys-cfx-vs-ansys-fluent.

Which one  is more accurate on Conjugate Heat Transfer analysis? Ansys Fluent or CFX?

Conjugate heat transfer (CHT) analysis is a type of simulation that models the heat transfer within and between fluids and solids¹. The accuracy of CHT analysis depends on many factors, such as the mesh quality, the boundary conditions, the solver settings, and the physical models²³. Therefore, it is not possible to say which solver, Ansys Fluent or CFX, is more accurate in general, as the results may vary depending on the specific problem and the user's expertise.

However, some studies have compared the performance of Fluent and CFX for different CHT applications, such as liquid-cooled IGBT assemblies⁴, heat exchangers⁵, and turbomachinery. These studies have shown that both solvers can produce similar results, but they may have different advantages and disadvantages in terms of computational efficiency, convergence behavior, and ease of use. For example, Fluent may have more options for mesh adaption and acceleration with a GPU², while CFX may have more features for rotating machinery and expression language³.

Therefore, the best way to determine which solver is more accurate for your CHT analysis is to try both of them and compare the results with experimental data or analytical solutions, if available. You can also consult the Ansys documentation and forums for more guidance and tips on how to use Fluent and CFX for CHT analysis. 😊

Source:

(1) How does the "Loosely Coupled Conjugate Heat Transfer" function work .... https://forum.ansys.com/forums/topic/how-does-the-loosely-coupled-conjugate-heat-transfer-function-work/.

(2) THERMAL ANALYSIS/CONJUGATE HEAT TRANSFER ANALYSIS IN ANSYS CFX THERMAL .... https://www.youtube.com/watch?v=Jx39uFHtHbs.

(3) CHT analysis using Fluent Solver | Ansys Courses. https://courses.ansys.com/index.php/courses/conjugate-heat-transfer/lessons/cht-analysis-of-liquid-cooled-igbt-assembly/topic/part-3-using-fluent-solver/.

(4) CHT Analysis in Ansys Discovery | Ansys Courses. https://courses.ansys.com/index.php/courses/conjugate-heat-transfer/.

(5) Ansys Fluent Heat Transfer Modeling | Ansys Training. https://www.ansys.com/training-center/course-catalog/fluids/ansys-fluent-heat-transfer-modeling.

(6) CHT Analysis in Ansys Discovery | Ansys Courses. https://courses.ansys.com/index.php/courses/conjugate-heat-transfer/.

(7) Ansys Fluent Heat Transfer Modeling | Ansys Training. https://www.ansys.com/training-center/course-catalog/fluids/ansys-fluent-heat-transfer-modeling.

(8) CHT analysis using Fluent Solver | Ansys Courses. https://courses.ansys.com/index.php/courses/conjugate-heat-transfer/lessons/cht-analysis-of-liquid-cooled-igbt-assembly/topic/part-3-using-fluent-solver/.

(9) CHT analysis using Fluent Solver | Ansys Courses. https://courses.ansys.com/index.php/courses/conjugate-heat-transfer/lessons/cht-analysis-of-liquid-cooled-igbt-assembly/topic/part-3-using-fluent-solver/.

What is the difference between Fluent and Star-CCM+?

Fluent and Star-CCM+ are both commercial computational fluid dynamics (CFD) software packages developed by Ansys and Siemens, respectively. They have some similarities and differences in their features, capabilities, and applications. Here are some of the main differences between them:

- Fluent uses a cell-centered finite volume method while Star-CCM+ uses a vertex-centered finite volume method. This means that Fluent can handle more complex mesh topologies, such as polyhedral and cutcell meshes, while Star-CCM+ is limited to tetrahedral and hexahedral meshes¹².

- Fluent has its own post-processing capabilities while Star-CCM+ requires a separate post-processor, such as CFD-Post or FieldView¹². Fluent also has more options for mesh adaption and simulation acceleration with a GPU².

- Star-CCM+ has a built-in expression language (CEL) that allows users to define algebraic equations and monitor them during the run¹². Fluent requires user-defined functions (UDFs) for customization, which can be more challenging for beginners¹.

- Star-CCM+ is more suitable for turbomachinery applications, as it has specialized features for rotating machinery, such as frozen rotor and transient blade row models²³. Fluent is more preferred for high Mach number flows, such as supersonic and hypersonic flows².

Source: 

(1) Siemens STAR CCM+ Vs. ANSYS Fluent | Resolved Analytics. https://www.resolvedanalytics.com/theflux/comparing-cfd-software-part-4-comprehensive-cfd-software-packages.

(2) Fluent vs Star CCM vs Openfoam -- CFD Online Discussion Forums. https://www.cfd-online.com/Forums/ansys/213810-fluent-vs-star-ccm-vs-openfoam.html.

(3) Compare Ansys Fluent vs. Simcenter STAR-CCM+ | G2. https://www.g2.com/compare/ansys-fluent-vs-simcenter-star-ccm.

(4) Siemens STAR CCM+ Vs. ANSYS Fluent | Resolved Analytics. https://www.resolvedanalytics.com/theflux/comparing-cfd-software-part-4-comprehensive-cfd-software-packages.

(5) Fluent vs Star CCM vs Openfoam -- CFD Online Discussion Forums. https://www.cfd-online.com/Forums/ansys/213810-fluent-vs-star-ccm-vs-openfoam.html.

(6) Comparison of STAR-CCM+ and ANSYS Fluent for Simulating Indoor Airflows. https://engineering.purdue.edu/~yanchen/paper/2018-1.pdf.

🎅 🎅 🎅 Using Ansys Fluent on Dronamics Case Study - The Black Swan

 Dronamics is a company that is developing and operating a cargo drone airline, using its flagship unmanned drone, the Black Swan¹. The Black Swan is a new type of cargo drone, remotely-piloted and fuel-efficient, suitable for a longer range and higher load factor than electric solutions². It can carry 350 kg of cargo up to 2,500 km, at an 80% lower cost than any aircraft³. It is also designed to run on biofuels and hydrogen-based fuels, making it more sustainable and eco-friendly². 

AI image od default drone (not connected to Black Swan project) 

Dronamics aims to enable same-day delivery for everyone, everywhere, by creating an air cargo ecosystem that can serve the needs of people and industries in all corners of the planet¹. Dronamics has already licensed its technology to fly in the EU, and has partnered with various airports and logistics providers to launch its service⁴⁵. Dronamics is a pioneer in the field of cargo drone aviation, and has been recognized as the "2022 and 2023 Sustainable Drone Technology Company of the Year" by Freightweek².

Source: 

(1) World's First Cargo Drone Airline | Dronamics. https://www.dronamics.com/.

(2) The Black Swan | Dronamics. https://www.dronamics.com/theblackswan.

(3) Dronamics launches drone-based cargo airline - Air Cargo News. https://www.aircargonews.net/airlines/dronamics-launches-drone-based-cargo-airline/.

(4) Dronamics to unveil first production Black Swan aircraft. https://www.aircargonews.net/airlines/drones/dronamics-to-unveil-first-production-black-swan-aircraft/.

(5) Dronamics' Black Swan Autonomous Freighter Achieves First Flight .... https://www.futureflight.aero/news-article/2023-05-29/dronamics-black-swan-cargo-drone-completes-first-flight-test.

Can you tell me more about the technology behind Black Swan?

The Black Swan is a cargo drone that is remotely-piloted and fuel-efficient. It uses a **Rotax engine** that can run on various fuels, including biofuels and hydrogen-based fuels⁶. It has a **wingspan of 16 m** and a **fuselage of 8 m**. It can carry up to **350 kg** of cargo in a **3.5 cbm** capacity. It can fly up to **2,500 km** at a **speed of 200 kmh**. It can operate from runways as short as **400 m**, unpaved¹. It has a **proprietary design** and a **world leading in-house avionics team** that built it specifically for cargo⁵. It is also **CarbonNeutral certified** and has **60% less emissions** than current transport options¹. It was named the **"2022 and 2023 Sustainable Drone Technology Company of the Year"** by Freightweek¹. The Black Swan is a revolutionary cargo drone that aims to enable same-day delivery for everyone, everywhere².

Source: 

(1) Black Swan: The first “cargo drone airline” in the world plans to take .... https://engineeringexploration.com/black-swan/.

(2) The Black Swan | Dronamics. https://www.dronamics.com/theblackswan.

(3) DRONAMICS Black Swan Cargo UAV Unveiling - Unmanned Systems Technology. https://www.unmannedsystemstechnology.com/2021/12/dronamics-black-swan-uav-unveiling/.

(4) World's First Cargo Drone Airline | Dronamics. https://www.dronamics.com/.

(5) The Black Swan | Dronamics. https://bing.com/search?q=Black+Swan+drone+technology.

(6) Meet Black Swan: The cargo drones to be used by DHL for urgent .... https://siliconcanals.com/news/dronamics-partners-with-dhl/.

How does the Black Swan drone fly?

The Black Swan drone flies like a conventional airplane, using a fixed wing and a gasoline-powered engine. It takes off and lands from runways as short as 400 m, and can fly up to 2,500 km at a speed of 200 kmh. It is remotely piloted by a human operator, who controls the drone from a mobile ground station. The drone uses a proprietary avionics system that ensures safe and reliable flight¹.

Source: 

(1) Dronamics' Black Swan Cargo Drone Completes First Flight Test. https://www.futureflight.aero/news-article/2023-05-29/dronamics-black-swan-cargo-drone-completes-first-flight-test.

(2) World's First Cargo Drone Airline | Dronamics. https://www.dronamics.com/.

(3) Black Swan: The first “cargo drone airline” in the world plans to take .... https://engineeringexploration.com/black-swan/.

(4) Black Swan: World's first 'cargo drone airline' aims to fly in early 2023. https://interestingengineering.com/innovation/worlds-first-cargo-drone-airline-2023.

What exactly was counted using Ansys Fluent in the Black Swan project?

Ansys Fluent is a software that can simulate the fluid dynamics and heat transfer of various systems. In the Black Swan project, Dronamics used Ansys Fluent to optimize the design and performance of their cargo drone. According to their case study¹, they used Ansys Fluent to:

- Simulate the airflow around the drone and optimize its shape for improved aerodynamics

- Simulate the combustion in the engine and optimize the fuel efficiency and emissions

- Simulate the structural stress and deformation of the drone and optimize the material and weight

By using Ansys Fluent, Dronamics was able to reduce the development and optimization time by approximately 60% and cut the design time by almost half¹. Ansys Fluent helped them to create a more efficient and eco-friendly cargo drone.

Source: 

(1) CASE STUDY - Ansys. https://www.ansys.com/content/dam/product/fluids/fluent/dronamics-case-study.pdf.

(2) CASE STUDY - Ansys. https://www.ansys.com/content/dam/product/fluids/fluent/dronamics-case-study.pdf.

(3) On the effect of Black Swans on projects - Medium. https://medium.com/nplan/on-the-effect-of-black-swans-on-projects-532c887bfe04.

(4) Black Swan Project - Wikipedia. https://en.wikipedia.org/wiki/Black_Swan_Project

Can you tell me more about cargo drone industry trends?

Cargo drones are unmanned aerial vehicles (UAVs) that can transport goods or products from one place to another. They can be used for various purposes, such as industrial delivery, emergency supplies, and last-mile delivery. Some of the key trends in the cargo drone industry are:

- **Rising demand for on-time and on-site delivery**: Cargo drones can offer faster, cheaper, and more convenient delivery services than conventional methods, especially in remote or hard-to-reach areas. They can also reduce traffic congestion, CO2 emissions, and carbon footprint. According to a market report, the cargo drone market is projected to grow from USD 534 million in 2022 to USD 17.9 billion by 2030, with a CAGR of 55.1% in that period¹.

- **Increasing use of cargo drones in military operations**: Cargo drones can also be used for military purposes, such as delivering supplies, weapons, or medical aid to soldiers in combat zones. They can also perform reconnaissance, surveillance, and intelligence missions. Cargo drones can enhance the operational efficiency, safety, and security of the military forces. According to a market report, the defense segment is expected to account for the largest share of the cargo drone market by 2030².

- **Innovation and development of new technologies**: Cargo drones are constantly evolving and improving, thanks to the innovation and development of new technologies, such as advanced sensors, software, propulsion systems, and communication systems. These technologies can enable cargo drones to perform more complex and diverse tasks, such as loading and offloading, autonomous navigation, obstacle avoidance, and collision detection. Some examples of innovative cargo drone technologies are the Black Swan drone by Dronamics³, the gas turbine by Turbotech⁴, and the freeze-drying system by CRB⁵.

Source: 

(1) Cargo drones: A potential gamechanger in the logistics industry. https://www.rolandberger.com/en/Insights/Publications/Cargo-drones-A-potential-gamechanger-in-the-logistics-industry.html.

(2) Cargo Drone Market Size, Industry Insights, Companies: A Comprehensive .... https://www.marketsandmarkets.com/Market-Reports/cargo-drones-market-252936360.html.

(3) Cargo Drones Market Growth Factors, Key Trends, Analysis, Outlook .... https://www.thebusinessresearchcompany.com/report/cargo-drones-global-market-report.

(4) Global cargo drone market size forecast 2030 | Statista. https://www.statista.com/statistics/1415129/worldwide-cargo-drone-market-revenue-forecast/.

(5) The use of drones in the logistics industry - Globalia Blog. https://www.globalialogisticsnetwork.com/blog/2023/05/03/global-drone-logistics-market-in-2023/.