Exploring the Capabilities of an LLM from CFD Simulations of Turbulent Flow in a Manifold

Abstract

Currently, the applications of Large Language Models (LLMs) have expanded to diverse areas, from code generation to the medical diagnosis of various pathologies. This work aims to explore what an LLM can achieve using information from CFD simulations of turbulent flow in a manifold, and to determine whether users or students can employ it as a guide for conducting this type of analysis. Through a case study, it is intended to investigate the following aspects of an LLM: (1) the type of information it handles regarding the behavior of turbulent flow within a manifold, (2) whether it identifies the boundary conditions necessary to perform a CFD simulation in a manifold, (3) its capacity to provide recommendations for improving CFD simulations based on the results obtained, (4) whether it can predict the results of CFD simulations based on previous results, and (5) whether users or students can use it as a guiding tool for performing CFD simulations. Among the findings, it was discovered that the LLM used has sufficient information on turbulent flows within a manifold and can make recommendations to improve the results of CFD simulations. It was also identified that LLM offers a user-friendly environment and that it is possible to predict CFD simulation results by varying the manifold boundary conditions. On the other hand, the LLM’s prediction model trained on CFD simulation data yielded RMSEs of 0.029 m/s for flow velocity and 0.33 °C for temperature, and R² values of 0.999 for flow velocity and 0.998 for temperature.

1. Introduction

The use of LLMs in CFD is important since they enable the automation and streamlining of complex processes, such as boundary condition selection, identification of the appropriate turbulence model, and selection of solution parameters. However, their effectiveness remains to be studied [1]. On the other hand, some LLMs can handle multiple CFD tasks. At the same time, smaller models, such as QwQ-32B, have limitations, especially in complex configurations and zero-shot approaches, highlighting stability and computational cost issues. Another advantage of using LLMs is that they reduce dependence on specialized expertise and broaden access, allowing simulation requirements to be described in natural language [2]. Further improvements in the generalizability, robustness, and deployment of these systems are still needed to consolidate their use in complex engineering workflows. Some studies develop LLM-based agents to automate tasks in CFD simulations with OpenFOAM [3]. This streamlines and automates complex configurations, reducing manual effort in tasks such as boundary condition adjustments and code implementation. These working methods achieve high performance using models like GPT-4o and o1 with chain-of-thought reasoning, along with an iterative correction cycle and a recovery-augmented generation (RAG) approach. This allows for the efficient resolution of diverse flow scenarios, in terms of both cost and the number of iterations. Future challenges include the need for human oversight, continuous performance monitoring, and system adaptation for critical applications, as well as its extension to solvers beyond OpenFOAM. Research has been conducted to develop non-intrusive reduced-order models (NIROMs) for CFD simulations of turbulent flow around buildings [4]. The use of AI reduces computational costs and enables faster, more accessible simulations. This approach predicts the flow field using a residual adversarial autoencoder with a Wasserstein generative adversarial network (WGAN) for dimensionality reduction, followed by a parallel bidirectional long short-term memory (BiLSTM) network to model time evolution. Transfer learning is also applied to improve results with limited data. Other studies analyze the use of artificial intelligence as a complement to CFD simulations to predict pressure in nanofluids under turbulent pipe flow [5]. The use of AI reduces computation times and reveals relationships between variables that CFD alone cannot identify. With the above, it has been possible to reproduce the CFD results with high precision using an adaptive network-based fuzzy inference system (ANFIS) model trained on simulated data, incorporating variables such as nanoparticle fraction, temperature, and spatial coordinates, thereby significantly reducing computation time.

AI-based models have been proposed to predict wind fields in offshore environments, using CFD simulation data for trajectory planning in Unmanned Aerial Vehicle (UAV) applications [6]. The incorporation of AI addresses the computational cost limitations of CFD and enables real-time predictions. This enables the reconstruction of highly accurate three-dimensional flow fields by combining convolutional autoencoders with a deep neural network trained on Reynolds-Averaged Navier–Stokes (RANS) data, achieving significant computational acceleration and enabling safe UAV navigation. Further improvements are needed in accuracy near walls and in the model’s robustness under more complex conditions. In the area of Unmanned Underwater Vehicles (UUVs), AI and CFD simulations are being integrated to balance emotional and energy-efficiency aspects in product design [7]. The use of AI in CFD allows for the simultaneous optimization of user experience and technical performance, enabling the generation and evaluation of design alternatives through generative AI, the performance of eye-tracking experiments, and the analysis of facial expressions, which are then optimized with CFD, resulting in a significant reduction in the drag coefficient in the selected option. Other studies analyze the use of deep learning models to predict indoor climate dynamics (temperature and velocity) from CFD simulation data [8]. The use of AI enables improved prediction and control of complex systems, such as heating, ventilation, and air conditioning (HVAC), by leveraging CFD data. Artificial Neural Networks (ANNs) match the performance of Long Short-Term Memory (LSTM) networks at lower computational cost, while also identifying semi-chaotic behaviors that enable reliable predictions, using hybrid physical-informed approaches that combine CFD and data models. In the design and simulation of bio-inspired underwater vehicles that integrate CFD and artificial intelligence to emulate whale locomotion and detect fish in marine environments, AI is used because it enables improvements in both hydrodynamic performance and perception capabilities for exploration and monitoring applications [9]. With these systems, a significant drag reduction is achieved through CFD simulations and a high-precision, advanced visual detection model (Ghost-YOLOv12), using tools such as SolidWorks (Premium 2017), 6-DOF kinematic modeling, and neural networks trained on specialized datasets. In the design and evaluation of a new turbojet engine (TTX2T), CFD and AI are being used to optimize efficiency, weight, and performance in aeronautical applications [10]. The integration of AI optimizes engine performance and improves adaptation to changing operating conditions. Improvements in thrust-to-weight ratio, reduced specific fuel consumption, and increased thermal stability were achieved through CFD simulations, experimental analyses, and machine-learning-based predictive models. In the optimization of impellers in turbomachinery, CFD simulations, AI-based surrogate models, and evolutionary algorithms are also being integrated [11]. The use of AI enables efficient optimization of multiple design objectives, reducing computational costs and improving performance. Significant improvements in hydraulic efficiency, mass reduction, and cavitation mitigation are achieved through the combination of methods, including the Resistive Sorting Method (RSM), Box–Behnken Design (BBD), and Non-Dominated Sorting Genetic Algorithm II (NSGA-II). In the future, the plan is to incorporate open-source tools, additive manufacturing, and deep neural networks to expand drivers’ capabilities for more advanced industrial applications.

An LLM like ChatGPT (5.5 version) is not a Self-Sustaining Model (SSM) nor a direct substitute for CFD, but it can behave as an “assisted metamodel,” with limitations. One advantage of an SSM-type scheme is that it can significantly reduce computational costs. Instead of running hundreds of CFD simulations, an initial dataset can be used to estimate trends and make quick predictions [12], which is useful during the early stages of design. It also provides agility: it can iterate faster, identify regions of interest in the design space, and prioritize which simulations to run. It can help integrate disparate knowledge (empirical correlations, design heuristics, prior experience) and serve as an “intelligent” layer for interpreting results or suggesting new configurations [13]. Its disadvantage is that an LLM does not solve the Navier–Stokes equations. Its predictions are based on patterns in the provided data, not on the conservation equations of mass, momentum, or energy, which implies a risk of errors (numerical hallucinations or physical inconsistencies). Its performance depends on the quality of the training data: if conditions outside the original range are explored, the predictions can degrade rapidly. An LLM-based SSM has structural limitations for extrapolating to new, complex geometries or to very different flow regimes (e.g., changes in Reynolds number or flow transitions). In turbulence problems, where the phenomena are highly nonlinear, this becomes even more critical [14]. It also does not replace experimental validation or high-fidelity simulations. It works best as a surrogate or hybrid model: for example, combining CFD and regression/ML models (neural networks, Gaussian Processes) and using LLM as an interface or assistant to build, adjust, or interpret those models. It is useful in preliminary optimization or sensitivity analysis. It can also be integrated into active schemes where the system itself decides which new simulations to run to improve the model. A system-based model (SSM) with ChatGPT does not replace computational fluid dynamics [15]. A study proposes a standardized evaluation framework for assessing LLM performance across CFD tasks [16], encompassing benchmarks ranging from theoretical CFD knowledge to code generation and the execution of complete simulations. It evaluates language quality, numerical consistency, and model generalizability. Unlike traditional approaches that rely solely on linguistic metrics, CFD-LLMBench emphasizes evaluating LLMs on the accuracy of results, convergence of solutions, and reproducibility of simulated flows. While this study has demonstrated the potential of LLMs to assist with general CFD tasks, there remains a need to explore their ability to predict systems with multiple simultaneous output variables from a limited set of numerical simulations. Therefore, the present work investigates whether an LLM can accurately learn and reproduce the multivariable physical response of a CFD manifold without re-simulation.

In this work, a hybrid methodology is used that combines CFD simulation, predictive modeling, and assistance via a Large Language Model (ChatGPT). First, a CFD simulation of turbulent flow within the manifold is generated under different boundary conditions, such as inlet velocity and temperature, as well as wall temperature. Some boundary conditions and meshing parameters are omitted to evaluate the LLM’s ability to provide feedback or guide the user, thereby improving simulation results. Consequently, these simulation results serve two functions of the LLM: first, to act as a query tool capable of interpreting flows, identifying boundary conditions, and suggesting simulation improvements; and second, to use these results to train a predictive model that allows for estimating new velocity and temperature responses without the need to run additional simulations. Recent studies show that this type of LLM–CFD integration is increasingly used to automate analysis, optimization, and support complex simulation processes. The main advantage of this methodology over traditional CFD is the significant reduction in computation time and technical complexity. While conventional CFD methods require meshing, solver configuration, turbulence model selection, and lengthy computation times for each new case, the trained model can predict results almost instantaneously within the studied range of conditions. Furthermore, unlike classic machine learning surrogate models—such as neural networks or regression methods—which only deliver numerical values, the use of LLMs adds a layer of conversational reasoning capable of explaining flow trends, recommending adjustments, and guiding the user on potential improvements. This makes the system not only a fast predictor but also an assistant for CFD analysis. Another important advantage is its educational and accessibility potential, as it allows students or less experienced users to interact with CFD results in natural language and receive guidance. The reported error values (RMSE of 0.029 m/s and 0.33 °C, with R² values close to 1) indicate that the predictive model successfully reproduced the original numerical results in the analyzed domain, supporting its usefulness for rapid parametric studies. Overall, this methodology surpasses existing approaches because it not only partially replaces existing simulations but also integrates prediction, technical interpretation, and user support within a single environment, approaching the concept of self-supporting CFD systems. A major problem with using artificial intelligence in CFD analysis is that, while Large Language Models (LLMs) can provide quick predictions or technical recommendations based on results, they remain entirely dependent on the quality, quantity, and interval of the data used for training [17]. In other words, the model can generate seemingly consistent but physically incorrect responses (hallucinations). Furthermore, unlike CFD solvers that solve conservation equations, LLMs do not guarantee conservation of mass, momentum, or energy. Therefore, there is a risk that inexperienced users will rely on predictions without performing numerical validation. These systems should be understood as support tools rather than absolute replacements for rigorous CFD analysis.

As seen in research on LLMs, many models are experimental and are housed at research centers or universities, where external users do not have routine access. Some of these models have been created to solve specific problems. This work aims to evaluate a free, unrestricted LLM to guide novice users in implementing CFD simulations and those who need guidance to improve their results. If the LLM is used to continue working on this type of case study (cooling tower manifold), we would suggest implementing a CFD benchmark. This would be geared towards solving and comparing solutions of this type.

2. LLMs and Prompt Engineering

Prompt Engineering enables communication between LLMs through structured templates, semantic example selection, and guided reasoning [18]. Some studies have developed educational labs to teach generative AI, including Prompt Engineering, to information systems students [19]. Prompt Engineering empowers students to interact effectively with generative models and build functional applications without requiring advanced programming knowledge. The use of Prompt Engineering in generating clinical summaries by LLMs requires comparing structured prompts versus vague prompts [20]. Structured prompts based on role, task, tone, and format have been shown to outperform vague prompts, as evaluated by human experts across multiple models and clinical scenarios. Prompt Engineering significantly influences LLM performance, and some have been used to detect software vulnerabilities [21]. Advanced models such as GPT-40 and Claude-3.5 Sonnet have been found to significantly outperform GPT-3.5 Turbo, especially when using Step-by-Step prompts and utilizing data from the Software Assurance Reference Dataset (SARD) in multiple programming languages. Prompt Engineering focuses on designing and optimizing prompts to guide LLM behavior, thereby improving performance by enabling more effective user interaction [22].

Another application of Prompt Engineering is in intelligent tutoring systems, where it generates recommendations or “tips” for solving mathematical problems [23]. The development of performance metrics for further refinement is still required. Other studies review the use of generative AI to write educational materials in plain language in the healthcare field, using Prompt Engineering as a technique [24]. Prompt Engineering is crucial because strategies such as specifying reading level, audience, or context improve the clarity and readability of the generated texts. Prompt Engineering improves the accuracy, fairness, and usefulness of LLMs by systematically adapting and evaluating prompts in sensitive contexts, such as healthcare [25], where the aim is to synthesize evidence using a structured methodology (JBI) and analyze the literature in multiple databases to identify strategies, trends, and best practices in prompt design and evaluation. To create effective prompts, studies have proposed a practical guide based on a literature review and real-world examples, including best practices such as using high-quality data, comparing models, validating results, and performing factor analysis for calibration [26]. Among the challenges of Prompt Engineering are risks such as hallucinations, biases, and ethical problems, as well as the need for human validation, transparency, and accountability. It is emphasized that AI does not replace critical thinking or methodological rigor [27].

One classification of prompts is based on the number of examples provided to the LLM [28]: one example is called One-shot, several examples are called Few-shot, and no examples are called Zero-shot. A second classification is by the type of structure [29]: when it uses a single instruction, it is known as Directive; if it includes additional context, it is called Contextual; if it uses a dialogue, it is Conversational; and if it requires the user to adopt a role, it is Role-Based. A third classification is by the technique used [30]: Chain-of-Thought (CoT) for step-by-step reasoning. Self-consistency for multiple responses and consensus, Tree-of-Thoughts for a tree-like exploration, and Retrieval-Augmented (RAG) for external information. Strategies for creating an appropriate prompt consist of precisely defining what is required [31], avoiding ambiguities (Clarity and Specificity), dividing the desired sequence into steps (Structure), providing key data (Relevant Context), specifying the perspective or role (Role or Perspective), providing examples (Few-shot), defining length, format, tone, and specific variables (Constraints), and adjusting the prompt based on previous results (Iteration). The effectiveness of a prompt depends on its objective [32]. Still, it can be evaluated by determining how accurate its response is (Accuracy), how well it addresses the request (Relevance), whether it produces similar results for the same prompt (Consistency), whether it performs well with small variations (Robustness), whether it requires fewer iterations (Efficiency), and, if possible, employing predictions such as RMSE, R², BLEU, or ROUGE (Quantitative Metrics).

However, prompts are not entirely reliable on their own (hallucinations, biases, lack of rigor); they function better as assistants than as replacements, and their performance depends largely on their application [33]. Prompt Engineering determines the quality of the output and, depending on its components, improves accuracy, interpretability, contextual relevance, and alignment with specific objectives. Prompt creation is becoming a cross-cutting skill (education, medicine, research, programming, etc.). The true “control” of LLMs lies not in the model, but in the prompt [34]. LLMs do not fail so much because of the model itself, but because of how they are asked questions. The more critical the domain (medicine, statistics, education, research, or CFD), the more important the structure of the prompts becomes, and expert knowledge must be integrated [35].

For this work, the Prompt Engineering strategy used was based on context-ambiguities-solution: that is, the context of the topic to be addressed was initially provided; subsequently, any ambiguities were resolved to clarify the statements; and finally, the problem was solved, describing its characteristics, scope, and solution variables.

The prompt structure was data-based: initially, the task to be performed, “TASK” was described, specifying the boundary conditions, as well as the configuration and dimensions of the manifold; subsequently, the relevant information was detailed using the “DATA” section, and any ambiguities were resolved; and finally, the “OUTPUT” section requested the solution to the problem.

The Prompt Iteration Process followed was to refine an initial prompt, evaluate it based on the response obtained, and finally, improve it for retesting. This process generated different responses for each prompt.

3. Research Context and Computational Resources

The use of LLMs has expanded across various disciplines, and with the help of Prompt Engineering, users can interact with them in a simple, user-friendly way [36]. Every day, LLMs perform increasingly complex tasks, from generating code to recognizing and creating images. The research questions for this work are: To what extent can LLMs help users perform CFD simulations? What information do they handle about the behavior of turbulent flows in different systems? Can they guide the user in defining boundary conditions? With the results of CFD simulations, can LLMs predict any behavior for which further CFD simulations are no longer necessary? To understand the capabilities of LLMs, the following objectives were established: (1) to identify the type of information they possess regarding turbulent flow behavior within a manifold, (2) to determine if they can define the boundary conditions necessary for performing a CFD simulation, (3) to evaluate if they can provide recommendations for improving CFD simulations based on the results obtained, (4) to investigate if they can predict CFD simulation results based on previous results, and (5) to determine if novice users or students unfamiliar with this type of CFD simulation can use LLMs as a guide to perform this type of analysis. To answer the above questions, a case study was chosen based on the information available to the LLM. This work does not aim to design the case study through the LLM; the primary objective is to investigate the information the LLM can provide when sharing CFD simulation data.

The software application used to perform the CFD simulations was Fluent in ANSYS Workbench 2025 R2, as this is the tool available at the university and is recognized in this field of simulation.

The LLM used was ChatGPT running on GPT-5.2, which allows for improvements to future versions through feedback in the interface using the like and dislike buttons, as well as reporting incorrect or harmful answers [37]. The free version was used, as it is accessible to any user with access to a computer and an internet connection.

The difference between this work and other existing research lies in the LLM used, ChatGPT, which offers free access and can be used without belonging to a research group or a particular university.

The computers used for this work had an Intel(R) Xeon(R) W-2125 CPU at 4.00 GHz and 32.0 GB of RAM, running a 64-bit operating system.

4. Methodology

The methodology consisted of a four-step research process (see Figure 1).

4.1. Asking the LLM for Information on Turbulent Flow Manifolds

Initially, ChatGPT was asked what information it knew about manifolds. This would allow us to determine the case study [38] and the LLM’s expertise on this topic. For this first question, the prompt used was: “Are you familiar with turbulent flow manifolds?”.

Subsequently, the focus shifted to manifolds for cooling towers, since they use water and fluid mixtures are not necessary, and the CAD model would be based on simple geometries, such as cylinders. For this second question, the prompt used was: “What are the applications of manifolds used in water-cooling towers? What types are there?”.

To determine if ChatGPT was familiar with the geometries of the different cooling tower manifolds, it was asked to generate an image of each of the manifolds described above. The prompt for this third question was: “Could you generate an image of each of the following manifolds so I can identify them? Header-lateral manifold, Ring (loop) manifold, Grid manifold, By hydraulic mode”.

To verify LLM’s understanding of the variables involved in manifold design, it was asked to describe the equations for a header-lateral manifold. The prompt for this fourth question was: “Can we go into design equations for header-lateral manifolds?”.

Finally, it was decided to investigate whether ChatGPT could specify the boundary conditions necessary to perform a CFD simulation of a header-lateral manifold. The prompt for this last question was: “If I wanted to perform a CFD simulation of a header-lateral manifold, what boundary conditions would I need to use?”.

4.2. Defining the Case Study

When ChatGPT was asked if it was familiar with turbulent flow manifolds, it mentioned that one of its areas of work was CFD simulation to analyze the effects of the curved walls of its geometries. Since this work was the first evaluation of LLMs in this type of geometry and application, it was decided to use a manifold with varying geometries but handling a single-phase fluid, as in the header-lateral manifolds of cooling towers for air conditioning systems. Furthermore, LLM was familiar with the components of this type of system, having generated an image and listed the boundary conditions necessary for its CFD simulation. Therefore, the case study involved a header-lateral manifold feeding a cooling tower for an air conditioning system; this manifold is shown in Figure 2.

The case study consists of a single main header with a diameter of 0.4 m, six laterals with a diameter of 0.1 m, and two nozzles per lateral with a diameter of 0.1 m. Nozzle diameters are normally specified smaller than those of the laterals; in this case, they were left unchanged to investigate whether ChatGPT would provide any recommendations [39]. On the other hand, the fluid circulating in the manifold will be water.

4.3. Running CFD Simulations

A CFD simulation of the case study was performed with the boundary conditions shown in Figure 3. Water enters the manifold at 80 °C at a velocity of 0.955 m/s; the manifold walls are at 20 °C, and the nozzle outlets are at atmospheric pressure. The boundary conditions are listed in

Table 1. Boundary conditions.

Variable	Magnitude
Vinlet	0.955 m/s
Re	924,534.55 (turbulent flow)
Tempwater	80 °C
Tempwalls	20 °C
Poutlets	Patm
Constant roughness	0.00003 m
Manifold Material	Steel
Turbulence model	k-ω SST

. The mesh parameters for the case study were left on automatic so that, depending on the results, ChatGPT could be asked for suggestions for improvement. The automatic method uses quad elements with a sweep strategy. Gravity was not activated to investigate whether ChatGPT would recommend any adjustments.

4.4. Predicting Results Using the LLM

The water streamlines within the manifold were obtained using CFD simulations; these are shown in Figure 4. The flow distribution is not uniform; the central area shows high velocities, and the distribution changes at the ends, with a more intense flow on the right side than on the left. The central upper inlet appears to promote the formation of vortices and local turbulence, thereby increasing minor losses and reducing the collector’s distribution efficiency.

A cross-section of the manifold was created in a horizontal plane to visualize the distributions of velocity (Figure 5), temperature (Figure 6), and pressure (Figure 7) in greater detail. The input variables were parameterized: inlet water velocity (Inlet_velocity), manifold wall temperature (Temp_walls), and inlet water temperature (Temp_Inlet). Figure 5 shows that the velocity profile indicates the main inlet behaves as a low-velocity distribution chamber, while acceleration occurs at the inlet of each side branch. The branches exhibit a progressive decrease in velocity along their length and receive a relatively similar momentum. Slight irregularities persist due to the redistribution of internal pressure and the centralized inlet. Figure 6 shows that the temperature profile reveals a non-uniform thermal field within the main inlet. The cooler regions in the central header indicate prolonged dwell time and greater heat transfer to the walls, while the warmer areas near the ends suggest high-momentum bypass paths. The side branches exhibit progressive longitudinal cooling, confirming convective heat exchange with the cold collector walls. However, the isothermal condition imposed on the walls likely exaggerates the absolute temperature drop. Figure 7 shows that the manifold transports the fluid through the six side branches; however, the central impact inlet generates significant internal recirculation, non-uniform static pressure, and preferential flow paths. Consequently, the hydraulic and thermal distribution among the branches is not perfectly balanced, indicating that the current geometry works, but a uniform outlet is not achieved.

The output variables were also parameterized: water velocity at outlet 1 (Outlet_velocity1), temperature at outlet 1 (Outlet_temperature1), and the same two variables for the remaining outlets. Twenty-three simulations were performed, varying the values of the three parameterized inputs, and 24 output values were obtained for each.

Table 2. The results of the 23 simulations were presented as a function of three input variables.

Simulation	Inlet Vel (m/s)	Temp Walls (°C)	Temp Inlet (°C)	Outlet Vel 1 (m/s)	Outlet Vel 2 (m/s)	Outlet Vel 3 (m/s)	Outlet Vel 4 (m/s)	Outlet Vel 5 (m/s)	Outlet Vel 6 (m/s)
1	0.955	20	80	1.25466	1.80999	1.22838	1.8053	1.34525	1.73497
2	1	19	80	1.35044	1.92338	1.32116	1.86866	1.42323	1.81078
.	.	.	.	.	.	.	.	.	.
22	1.75	17	83	2.30962	3.35957	2.29337	3.25306	2.52137	3.08176
23	1.8	23	87	2.37434	3.45639	2.36166	3.34216	2.59446	3.166
Simulation	Outlet Vel 7 (m/s)	Outlet Vel 8 (m/s)	Outlet Vel 9 (m/s)	Outlet Vel 10 (m/s)	Outlet Vel 11 (m/s)	Outlet Vel 12 (m/s)	Outlet Temp 1 (°C)	Outlet Temp 2 (°C)	Outlet Temp 3 (°C)
1	1.23728	1.79261	1.19051	1.88414	1.34173	1.79716	43.477	54.131	47.002
2	1.31546	1.86497	1.30703	1.86598	1.34956	1.91842	45.855	51.309	47.351
.	.	.	.	.	.	.	.	.	.
22	2.22773	3.29674	2.12367	3.52548	2.25611	3.44066	46.806	52.147	48.428
23	2.28121	3.39978	2.18247	3.61619	2.32226	3.54225	48.653	54.177	50.176
Simulation	Outlet Temp 4 (°C)	Outlet Temp 5 (°C)	Outlet Temp 6 (°C)	Outlet Temp 7 (°C)	Outlet Temp 8 (°C)	Outlet Temp 9 (°C)	Outlet Temp 10 (°C)	Outlet Temp 11 (°C)	Outlet Temp 12 (°C)
1	55.391	49.801	56.714	48.174	56.131	45.445	57.712	45.102	47.56
2	54.608	49.795	57.566	48.222	55.971	45.657	56.266	45.018	50.745
.	.	.	.	.	.	.	.	.	.
22	55.92	51.498	58.54	48.834	57.737	46.135	59.692	45.05	52.248
23	58.228	53.501	61.163	50.583	60.364	47.651	62.322	46.473	54.041

shows the three input variables and their 24 output variables for simulations 1, 2, 22, and 23. The reduced number of simulations was selected to investigate whether the LLM would have any observations to inform its prediction model during creation.

The 23 simulation samples were used to assess whether the LLM recommended increasing the sample size or provided any other comments on the stability of the results. In Section 5.3, “Predict results using the LLM,” the LLM’s observations are presented.

Once the outlet velocities and temperatures were obtained, it was investigated whether the LLM could predict these 24 outcomes from the three input variables. ChatGPT was then asked to generate a predictive model from the results of the first 21 simulations. Subsequently, to evaluate this model, three input data points were provided, and the 24 outputs were predicted.

To evaluate the prediction results, the values from simulations 22 and 23 were used; these tests were referred to as the first and second predictions, respectively.

To ensure the reproducibility of the study, the methodological steps are summarized below: The methodological procedure was structured in four integrated stages to evaluate the use of a language model in manifold analysis. First, a guided exploration of the Language Learning Module (LLM) was conducted using a series of sequential prompts to identify its knowledge of turbulent flow manifolds, their applications in cooling towers, their geometries, design equations, and boundary conditions for CFD simulations. Based on these responses, a case study was defined consisting of a header-lateral manifold transporting water, with specific dimensions (one main header, six branches, and two nozzles per branch). Subsequently, a CFD simulation of the system was performed using established boundary conditions (water inlet at 80 °C and 0.955 m/s, walls at 20 °C, and outlets at atmospheric pressure), with automatic meshing and without gravity, to evaluate possible recommendations from the LLM. Finally, three input variables (inlet velocity and temperature, and wall temperature) and 24 output variables (velocity and temperature at each outlet) were parameterized, and 23 simulations were run. Using results from the first 21 simulations, the LLM trained a predictive model. This model was validated by comparing its predictions with the simulation results from simulations 22 and 23, thereby enabling evaluation of its generalizability and contribution to the system analysis.

5. Results Analysis

5.1. Asking the LLM for Information on Turbulent Flow in Manifolds

When ChatGPT was asked about its knowledge of manifolds, it categorized them into applications for Physics, Robotics, CFD/Mechanics, Machine Learning, and Differential Equations.

Table 3. Classification of manifolds according to the LLM used.

Manifold Application	Uses
Physics	spacetime, general relativity
Robotics	configuration spaces
CFD/mechanics	curved surfaces, shells
Machine learning	data lies on a low-dimensional manifold
Differential equations	solution spaces

summarizes the LLM’s classification. This indicates that it has sufficient information about manifold applications and is familiar with CFD.

When asked about the applications of manifolds used in water-cooling towers, ChatGPT categorized them by purpose, function, and geometry (see

Table 4. Applications of manifolds used in water-cooling towers according to the LLM used.

Classification	Function	Uses
By purpose	Hot water distribution (spray manifold)	Takes hot water from the condenser loop
		Spreads it evenly over the fill media
		Maximizes surface area for evaporation
	Cold water collection manifolds	Collect cooled water from multiple outlets Feed it uniformly into the basin or the pump suction
	Make-up water manifolds	Add fresh water to replace evaporation + blowdown Distribute it gently to avoid disturbing the airflow or fill
By function	Spray distribution manifolds	Main header + lateral pipes Nozzles or orifices along laterals
	Collection manifolds	Combine the flow from multiple outlets Used in closed circuits or hybrid towers
By geometry	Header–lateral manifold	Crossflow towers Counterflow towers
	Ring (loop) manifold	Circular or rectangular loop Helps equalize pressure Very uniform flow
	Grid manifold	Network of pipes in X–Y pattern Very uniform distribution

), suggesting a case study on manifold geometry for CFD simulations.

To demonstrate that ChatGPT understood the difference between the manifold geometries—Header-lateral manifold, Ring (loop) manifold, Grid manifold, and hydraulic mode—it was asked to generate an image of each, shown in Figure 8. It can be observed that each configuration includes the main details, confirming that ChatGPT distinguishes between them.

Subsequently, ChatGPT was asked to describe the equations for the header-lateral manifold. The equations provided by ChatGPT are listed below, along with the sequence of use and recommended considerations:

Design goal for a header with laterals and nozzles (each nozzle gets the same flow):

$$Q_1=Q_2=Q_3=\cdots =Q_N$$

(1)

$$P_{\mathrm{nozzle},1}\approx P_{\mathrm{nozzle},2}\approx \cdots$$

(2)

5.1.1. Flow from Each Nozzle (Orifice Equation)

$$Q_n=C_d{A}_n\sqrt{{\displaystyle \frac{2(P_h-P_{atm})}{\rho }}}$$

(3)

• where:

$Q_n$ = flow per nozzle

$C_d$ = discharge coefficient (≈0.6–0.9)

$A_n$ = nozzle area

$P_h$ = pressure in the lateral at the nozzle

$\rho$ = water density

Uniform flow ⇒ uniform $P_h$.

5.1.2. Pressure Drops Along a Lateral (Darcy–Weisbach), for Each Lateral

$$\mathsf{\Delta }{P}_f=f{\displaystyle \frac{L}{D}}{\displaystyle \frac{\rho V^2}{2}}$$

(4)

Velocity decreases as water exits through nozzles, so more properly:

$$\mathsf{\Delta }{P}_{lateral}=\sum _{i}f{\displaystyle \frac{\mathsf{\Delta }x}{D}}{\displaystyle \frac{\rho V_i^2}{2}}$$

(5)

Engineering approximation (common in cooling tower design):

$$\mathsf{\Delta }{P}_{lateral}\le 0.2 \mathsf{\Delta }{P}_{nozzle}$$

(6)

5.1.3. Header Pressure Drops, Same Idea for the Main Header

$$\mathsf{\Delta }{P}_{header}=f{\displaystyle \frac{L_h}{D_h}}{\displaystyle \frac{\rho V_h^2}{2}}$$

(7)

$$\mathsf{\Delta }{P}_{header}\le 0.1 \mathsf{\Delta }{P}_{nozzle}$$

(8)

$$\mathsf{\Delta }{P}_{pipes}\le 0.3 \mathsf{\Delta }{P}_{nozzle}$$

(9)

The equations above ensure pressure at all laterals is nearly the same.

5.1.4. Nozzle Spacing and Count

Total flow = $Q_T$

Number of nozzles = N

$$Q_n={\displaystyle \frac{Q_T}{N}}$$

(10)

Select nozzle size from:

$$A_n={\displaystyle \frac{Q_n}{C_d\sqrt{2\mathsf{\Delta }{P}_n/\rho }}}$$

(11)

Spacing $s$ usually:

$$s\approx 0.3 \mathrm{to} 0.6 \mathrm{m}$$

(12)

5.1.5. Lateral Diameter Sizing

At the inlet of the lateral:

$$Q_{lat}=n{Q}_n$$

(13)

Choose velocity:

$$V_{lat,in}=1–2 \mathrm{m}/\mathrm{s}$$

(14)

$$D_{lat}=\sqrt{{\displaystyle \frac{4Q_{lat}}{\pi V_{lat}}}}$$

(15)

Check friction loss:

$$\mathsf{\Delta }{P}_{lateral}\le 0.2\mathsf{\Delta }{P}_{nozzle}$$

(16)

5.1.6. Header Diameter Sizing

Total flow:

$$Q_h=Q_T$$

(17)

Choose velocity:

$$V_h=1.5–3 \mathrm{m}/\mathrm{s}$$

(18)

$$D_h=\sqrt{{\displaystyle \frac{4Q_h}{\pi V_h}}}$$

(19)

Check:

$$\mathsf{\Delta }{P}_{header}\le 0.1\mathsf{\Delta }{P}_{nozzle}$$

(20)

5.1.7. Uniformity Criterion

Uniformity error:

$$ϵ={\displaystyle \frac{Q_{max}-Q_{min}}{Q_{avg}}}$$

(21)

Good design:

$$ϵ\le 5\%$$

(22)

Achieved if:

$${\displaystyle \frac{\mathsf{\Delta }{P}_{pipes}}{\mathsf{\Delta }{P}_{nozzle}}}\le 0.3$$

(23)

Typical numbers (cooling tower spray system).

Nozzle ΔP: 20–50 kPa

Lateral friction: ≤5–10 kPa

Header friction: ≤3–5 kPa

Nozzle spacing: 300–600 mm

Cd: 0.7–0.85

From the above, it can be observed that ChatGPT identifies the main variables involved in the design of a header-lateral manifold. While some equations lacked definitions for certain variables, it can generally be stated that they distinguish the essential variables for the design.

When ChatGPT was asked about the boundary conditions required to perform a CFD simulation of a header-lateral manifold, it specified the sequence of steps illustrated in Figure 9.

Initially, the boundary conditions of the main inlet (header) must be defined; specifically, whether to register the mass flow inlet or the velocity inlet. Subsequently, the boundary conditions for the outlets are specified by defining either a mass-flow or a pressure outlet. Following this, it is specified that the walls have no movement or displacement, that gravity is activated, that turbulent flow is specified, and, finally, that the fluid type is indicated, specifying whether it is single-phase or multi-phase. It appears that ChatGPT has a general understanding of what needs to be defined to perform a CFD simulation. Furthermore, ChatGPT mentioned that the expected results would be the flow rate per nozzle, the pressure distribution along the manifold, the velocity field, and the streamlines.

5.2. Running CFD Simulations

Using the case study in Figure 2 and the boundary conditions in Table 1, a CFD simulation was performed. The mesh was generated using the automatic method; the resulting mesh is shown in Figure 10. The general mesh parameters are shown in Figure 11, and the mesh inflation and sizing parameters are shown in Figure 12. The mesh parameter figures show that the CFD simulation was generated with an overall element size of 0.40438 m, resulting in 63,207 nodes and 296,886 elements. This discretization yielded a qualitatively consistent solution; however, the element size is relatively large compared to the manifold’s characteristic dimensions, particularly in the laterals and nozzles, limiting the resolution of local velocity, pressure, and recirculation gradients. Although smooth-transition inflation with a growth rate of 1.2 was implemented, only five inflation layers were considered, a small number for a turbulent k-ω SST model, thus reducing the accuracy in capturing the boundary layer and wall shear stresses. Similarly, the generated mesh exhibits a virtually uniform distribution, with no visible local refinements in critical areas, such as the central inlet and the header-lateral junctions, where the greatest hydrodynamic changes occur. The mesh used appears adequate for identifying the overall flow behavior and distribution trend within the manifold; however, with localized refinement, the quantitative reliability of the results could be significantly improved. As mentioned in the boundary conditions, these parameters were used to explore whether the LLM offered suggestions for improving the mesh and, consequently, the results. The results section shows that LLM recommends improvements to the mesh parameters.

A few iterations (100) were performed to investigate whether ChatGPT suggested any recommended values. On the other hand, the mass balance between the inlet and the 12 outlets was verified, as shown in Figure 13. The difference between the mass of the inlet and the mass of the 12 outlets was 0.0958004 kg/s. To improve this result, ChatGPT was provided with the case study and mesh parameters. LLM was then asked what should be corrected or done to reduce the difference between the inlet mass and the mass of the 12 outlets.

From the images provided to ChatGPT, it identified the dimensions of the main header, laterals, and nozzles. The first observation was that the nozzles should have a smaller diameter than the laterals, since they should generate the greatest pressure loss to ensure flow uniformity. Otherwise, the flow could become unbalanced: the first nozzles might discharge more water, or the last ones might receive less. It also identified the boundary conditions and calculated the Reynolds number, which matched the value presented in Table 1. Regarding the temperatures on the walls and in the water, it was concluded that when simulating the cooling of the water inside the manifold, intense cooling occurs in the cooling tower, and that, in the manifold, little heat is normally lost. It mentioned that, in the results, a maximum pressure should be observed near the inlet and a progressive decrease along the 7.6 m. The flow should enter strongly in the first few laterals and decrease gradually. The hot water should be near the inlet, and we would expect gradual cooling near the walls, with thermal mixing in the header. However, the effect would be small because the residence time is short. It also commented that it recommended activating gravity at 9.81 m/s², since the fluid was water. Regarding the mesh parameters, the first observation was the element size of 0.404 m, since the main header diameter was 0.4 m. This would not be represented or could cause errors, as it exceeded the diameter of the sides and nozzles. It indicated that, in CFD, it typically aims for 10–20 cells across the tube diameter.

$$\mathsf{\Delta }x\approx {\displaystyle \frac{D}{15}} ; \mathsf{\Delta }x\approx {\displaystyle \frac{0.4}{15}}\approx 0.027 \mathrm{m}$$

(24)

Regarding the k-ω SST turbulence model, it was noted that it is an excellent choice, as it is well-suited for internal flows, flow separations, adverse pressure gradients, and T-shaped junctions (such as those found on laterals). It added that many industrial studies use this model for manifolds. It recommended a skewness < 0.85; if possible, a skewness < 0.5 would be excellent. It suggested refining the mesh at the header-lateral connection, where flow separation and pressure redistribution occur. Refining the mesh at the header inlet is also recommended, as this is where flow development and the velocity gradient are recorded. Furthermore, it emphasized the need to refine the nozzle mesh due to the large accelerations and pressure drops. If the element size is reduced to 0.03 m, the mesh would likely increase to 2–4 million elements, which would be typical in a CFD case like this. For inflation parameters, he recommends 10–15 layers and a growth rate of approximately 1.2. Regarding the mass balance, it identified a mass of 117.832 kg/s at the inlet and approximately 117.736 kg/s at the outlets, resulting in a difference of 0.0958 kg/s. It mentioned that the simulation is already at approximately 0.08%, which is a very good balance, but it can be improved.

$$\mathrm{Error}={\displaystyle \frac{0.0958}{117.832}}=8.13\times {10}^{-4} ; \mathrm{Error}=0.081\%$$

(25)

To improve results, ChatGPT suggested increasing the number of iterations; for turbulent flow simulations with energy, a range of 1000–3000 iterations is recommended. The residuals for the continuity equation should be in the range of 1 × 10⁻⁴, for the momentum equation in the range of 1 × 10⁻⁵, for turbulence in the range of 1 × 10⁻⁵, and for the energy equation in the range of 1 × 10⁻⁶. For discretization, a second-order scheme is recommended for pressure, momentum, turbulence, and energy.

ChatGPT identified areas for improvement in the CFD simulation results. For a novice user or student, ChatGPT would indeed help them achieve better results in their simulations, but to address ambiguities, it will need a user familiar with CFD simulations. It is also observed that ChatGPT can read images that contain values; for example, the mesh parameter tables were images, and it extracted numerical values.

ChatGPT recommended: “For inflation parameters, 10–15 layers and a growth rate of approximately 1.2 are recommended”; however, LLM added that simply applying these parameters is insufficient; comparative numerical verification is necessary. This involves taking the current simulation as the baseline and comparing it with new, refined simulations, evaluating indicators such as the reduction in residuals, the decrease in mass balance error, the stability of the monitored variables (flow rate, pressure, and temperature at the outlets), and the variation in results between meshes of different densities through a mesh independence study. Additionally, when using the k-ω SST turbulent model, the y⁺ parameter should be checked to ensure the boundary layer is correctly resolved. If, after refinement, the residuals converge more closely, the mass imbalance decreases, and the variables of interest show minimal changes between a medium and a fine mesh, then it can be concluded that the implemented modifications improve the reliability and accuracy of the simulation results. As shown, LLM suggests the correct path for validating the CFD simulation results. Again, we find that the LLM can guide novice users or students starting out in CFD in conducting their simulations.

Table 5. Recommendations for improving the accuracy of CFD manifold simulation.

Order	Recommendation	Suggested Action	Main Objective
1	Refine the overall mesh size.	Reduce the size of the base element compared to the current size (0.404 m) to increase the number of cells in the header, sides, and nozzles.	Capture velocity, pressure, and temperature gradients more accurately.
2	Apply local refinement to critical areas.	Incorporate body sizing or face sizing at the inlet, header-side junctions, and nozzle roots.	Improve the resolution of recirculation, minor losses, and sudden accelerations.
3	Increase the inflation layers.	Increase from 5 to 10–15 layers with a growth rate of approximately 1.2	Adequately address the boundary layer and wall shear stresses.
4	Verify the y+ parameter.	Check that the values near the wall are suitable for the k-ω SST model (ideally y+ ≈ 1).	Ensure a more accurate prediction of friction and heat transfer.
5	Increase the number of iterations.	Running between 800 and 1500 iterations or until stable convergence is observed.	Reduce residuals and improve mass balance.
6	Monitor residuals and output variables.	Monitor continuity, momentum, energy, flow rates, and temperatures during the run.	Confirm actual numerical convergence of the solution.
7	Evaluate the mass balance error.	Compare the inlet flow with the sum of the 12 outlet flows	Verify overall consistency and mass conservation.
8	Perform a mesh independence study	Compare results between the current, medium, and fine meshes.	(e.g., final mesh size, number of elements, final mass balance error, and residual values after refinement).

shows ChatGPT’s recommendations for improving CFD simulation results, along with the order and descriptions for applying them.

5.3. Predict Results Using the LLM

To predict the 24 outputs (velocity and temperature), given three inputs (inlet velocity, manifold wall temperature, and water inlet temperature), ChatGPT was provided with an Excel spreadsheet containing the results of 23 CFD simulations. To develop the prediction model, it was necessary to define a data structure, establishing the inlet velocity, wall temperature, and fluid inlet temperature as input variables, and the 12 velocities and 12 temperatures corresponding to each manifold outlet as output variables. Additionally, a data preprocessing stage was required, which included organizing the Excel file, separating the input and output matrices, and performing implicit normalization during training to improve learning stability. Finally, to evaluate the model’s robustness, error metrics (RMSE, MAPE, and R²), parity plots, analysis of the slope and intercept of the regression lines, and 6-fold cross-validation were implemented. The following prompt asked them to describe the variables in the file: “Could you describe the Excel file? What data is in it? How many variables are there, and what are their units?”

Table 6. Results of the file analysis performed by ChatGPT.

Structure	Description
File Size	Total Rows: 24
	Total Columns: 28
	Total Rows: 24
Row Structure	Row 1: Units of the variables. Rows 2–24: Experimental data or simulations (23 records named Data 1, Data 2, …).
Summary of input/control variables	Inlet velocity (m/s) Temp_walls (°C) Temp_Inlet (°C)
Summary of output variables	12 outlet velocities 12 outlet temperatures
Total variables:	3 input variables 24 output variables
Inlet velocity ranges	0.955–2.0 m/s
Outlet temperature ranges	47.6–54.6 °C
High-flow outlets	Outlets 2, 4, 8, 10, and 12 Velocity ≈ 2.7–2.9 m/s
Low-flow outlets	Outlets 1, 3, 7, 9, and 11 Velocity ≈ 1.8–1.9 m/s

summarizes the structure of the file identified by ChatGPT. Table 5 shows that ChatGPT identified the dataset generated from the CFD simulations as containing 24 records and 28 columns, including both input and output variables of the manifold. It visualized three control variables: inlet velocity, wall temperature, and inlet fluid temperature, while the response variables correspond to 12 outlet velocities and 12 outlet temperatures, one for each nozzle in the system. The inlet velocity range considered in the simulations was 0.955 to 2.0 m/s, enabling evaluation of the manifold’s hydraulic behavior under different operating conditions. Based on these cases, the outlet temperatures ranged from 47.6 to 54.6 °C, confirming appreciable fluid cooling along the flow path due to the wall-imposed thermal conditions. In terms of hydraulic distribution, the table shows a clear lack of uniformity in the flow rate discharged by the nozzles, with high-flow outlets (Outlets 2, 4, 8, 10, and 12) exhibiting velocities of approximately 2.7–2.9 m/s, and low-flow outlets (Outlets 1, 3, 7, 9, and 11) with velocities close to 1.8–1.9 m/s. This difference confirms that the manifold does not distribute the fluid homogeneously but rather exhibits preferential flow paths and local pressure variation. It was mentioned that it built a simple s, consistent with the velocity and pressure contours and the streamlines previously analyzed.

The predictions were tested only for interpolation, not extrapolation.

ChatGPT was subsequently asked to create a predictive model using data from the Excel file and to predict 24 output variables given three input values (Inlet Velocity, Wall Temperature, and Inlet Temperature). Data 22 was used as data input for the first prediction. The prompt used to make the first prediction is shown in Figure 14.

ChatGPT mentioned that it built a simple multivariable linear regression model using CFD data, excluding Data 22 and Data 23, as requested. Linear regression was considered given the small range of input speed variation. The summary of the prediction model variables is shown in Figure 15. The model is a multi-output multiple linear regression model, where all outputs are predicted simultaneously and is mathematically represented as:

$$Y=B_0+B_1{V}_{in}+B_2{T}_{wall}+B_3{T}_{in}$$

(26)

where:

$Y$ = vector of 24 output variables

$V_{in}$ = inlet velocity

$T_{wall}$ = wall temperature

$T_{in}$ = inlet temperature

Figure 15. Summary of the prediction model variables.

Figure 15. Summary of the prediction model variables.

In Machine Learning, linear regression works well with small datasets:

$$N_{data}\ge 10\times N_{parameters}$$

(27)

In many CFD problems near an operating point, velocity, pressure, and temperature respond approximately linearly to small changes in boundary conditions, especially if the flow regime or fluid properties remain unchanged. The model uses supervised learning with known inputs and outputs. The prediction type is multi-output regression, predicting 12 speeds and 12 temperatures simultaneously. The model assumes a linear relationship and independent variables.

Only two datasets were used to corroborate two predictions and verify that the RMSE and R² were preserved, which they were, thereby providing greater certainty about the behavior of the LLM prediction model. The system contains a 24-by-4 coefficient matrix B, and the model is represented by:

$$\left[\begin{array}{c}{V}_1\\ V_2\\ \cdots \\ V_{12}\\ T_1\\ T_2\\ \cdots \\ T_{12}\end{array}\right]=\mathbf{B}\left[\begin{array}{c}1\\ V_{in}\\ T_{wall}\\ T_{in}\end{array}\right]$$

(28)

ChatGPT recommended other models if more data were available. For example, with 40–100 simulations, the best models would be Random Forest Regression for small datasets, Gaussian Process Regression for CFD optimizations, Neural Networks for complex simulations (which require more data), and Polynomial Regression to capture nonlinearities.

From the data obtained for the first velocity and temperature prediction (Figure 16), the predictive model equation is:

Velocity   y = 0.9661x + 0.0802

(29)

The ideal slope is 1, but in this case, 0.9661 < 1, indicating the model slightly underestimates high values and slightly overestimates some low ones. The difference is small: 1 − 0.9661 = 0.0339 ≈ 3.4% deviation from the ideal slope. The ideal intercept is 0; in this case, b = 0.0802, indicating a small positive bias. The model tends to predict approximately 0.08 m/s higher on average when extrapolating towards the origin, which is very low.

Temperature   y = 0.9665x + 1.9563

(30)

The ideal slope is 1, but in this case, it is 0.9665 ≈ 1, indicating that the model exhibits good thermal proportionality. The ideal intercept would be 0; in this case, b = 1.9563, indicating a small bias of +2 °C. Since the temperatures range between 45 °C and 60 °C, the bias is small.

For the second prediction, the velocity and temperature are:

Velocity   y = 0.9673x + 0.0743

(31)

Temperature   y = 0.9145x + 4.0156

(32)

The velocity is similar to that in the first prediction, indicating repeatability. For temperature, the slope (0.9145) deviates slightly from 1, indicating the model predicts slightly lower values at high temperatures and slightly higher values at low temperatures. The intercept (4.0156) indicates a more pronounced thermal bias; the second temperature prediction is less ideal than the speed prediction, though it does not represent a significant error, as the RMSE remains low, indicating the metrics support each other. Therefore, it is observed that there is a strong correlation, a low bias in speed, and a moderate, though acceptable, bias in temperature.

The prediction results are presented in

Table 7. Results of the first prediction.

	Predicted Values		CFD Simulation Values
Outlet	Vel (m/s)	Temp (°C)	Vel (m/s)	Temp (°C)
1	2.332	47.12	2.30962	46.806
2	3.326	52.31	3.35957	52.147
3	2.305	48.77	2.29337	48.428
4	3.238	56.08	3.25306	55.92
5	2.5	51.36	2.52137	51.498
6	3.07	58.46	3.08176	58.54
7	2.213	49.05	2.22773	48.834
8	3.281	57.71	3.29674	57.737
9	2.108	46.42	2.12367	46.135
10	3.46	59.88	3.52548	59.692
11	2.281	45.92	2.25611	45.05
12	3.397	52.55	3.44066	52.248

, which also shows the values compared with those obtained from the CFD simulation.

Subsequently, a second prediction was performed using the Data 23 data; the prompt used is shown in Figure 17, and the prediction results are presented in

Table 8. Results of the second prediction.

	Predicted Values		CFD Simulation Values
Outlet	Vel (m/s)	Temp (°C)	Vel (m/s)	Temp (°C)
1	2.395	48.21	2.37434	48.653
2	3.42	53.64	3.45639	54.177
3	2.366	49.88	2.36166	50.176
4	3.329	57.32	3.34216	58.228
5	2.571	52.63	2.59446	53.501
6	3.161	59.84	3.166	61.163
7	2.267	50.11	2.28121	50.583
8	3.365	59.02	3.39978	60.364
9	2.154	47.51	2.18247	47.651
10	3.548	61.24	3.61619	62.322
11	2.338	46.92	2.32226	46.473
12	3.486	53.88	3.54225	54.041

. Table 7 and Table 8 show a high degree of agreement between the two datasets for both the velocities and temperatures of the 12 manifold outlets. For outlet velocities, the differences between the predicted and CFD-derived values are minimal, remaining close across all outlets and accurately reproducing the previously identified hydraulic distribution pattern, in which some nozzles exhibit higher discharge velocities than others. Similarly, the predicted temperatures closely approximate the simulated temperatures, with only minor deviations, and maintain the system’s overall thermal trend. These results indicate that the predictive model accurately captures the relationship between the input variables and the manifold’s hydraulic-thermal response, reproducing with good precision both the flow non-uniformity and the cooling behavior at the outlets.

In this study, the LLM did not perform the CFD simulation or the flow calculations within the manifold. The LLM was provided with the results of a CFD simulation and asked to predict within that range. Therefore, the statistical metrics RMSE and R² were initially used to evaluate the LLM’s prediction model. Since good results were obtained, MAPE (Mean Absolute Percentage Error) or MAE (Mean Absolute Error) was not used.

For the first and second predictions, the root mean square error (RMSE) and the coefficient of determination (R²) were calculated; the results are shown in

Table 9. RMSE and R² results.

Prediction	Values Obtained
First prediction	RMSE_velocity = 0.0290 m/s
	RMSE_temperature = 0.330 °C R2 velocity = 0.999
	R2 temperature = 0.998
Second prediction	RMSE_velocity = 0.033 m/s RMSE_temperature = 0.783 °C R2 velocity = 0.999 R2 temperature = 0.997

. Both the RMSEs for velocity and temperature are acceptable, as is the R². A parity plot (Predicted vs. CFD) was also generated for both velocity and temperature predictions. Figure 16 shows the parity plot for velocity and temperature from the first prediction, and Figure 18 shows the parity plot for the second prediction.

The model accurately captures physical trends. The prediction model successfully reproduces the outlet velocity hierarchy, the temperature distribution pattern, and the response to inlet velocity and temperature changes. This means the dataset has a strong predictive structure, which is ideal for surrogate modeling. The table and scatter plots show that the predictive model achieves highly accurate estimates of manifold outlet velocities and temperatures. For the first prediction, an RMSE of 0.0290 m/s for velocity and 0.330 °C for temperature was obtained, while for the second prediction, the values were 0.033 m/s and 0.783 °C, respectively. These errors are low relative to the operating ranges of the analyzed variables, indicating minimal deviation between the model predictions and the CFD results. The coefficients of determination obtained were high: R² = 0.999 for velocity in both cases and R² = 0.998 and 0.997 for temperature. This confirms a near-perfect correlation between the predicted and simulated values, demonstrating that the model accurately reproduces the system’s hydraulic and thermal behavior. Scatter plots reinforce this observation, as virtually all points align with the ideal trend line, indicating a very close match between the CFD and the prediction for both speed and temperature.

To assess the possibility of overfitting due to the limited CFD dataset, a 6-fold cross-validation procedure was performed. The results are shown in

Table 10. K-fold cross-validation.

Output Variable	CV RMSE	CV MAPE (%)	CV R2
Outlet Velocity	0.022801 m/s	0.7636%	0.998958
Outlet Temperature	0.485121 °C	0.5602%	0.990976

. The model maintained average coefficients of determination of 0.9989 for velocity and 0.9910 for temperature, with MAPE values below 1%, confirming strong internal generalization and a low tendency toward overfitting.

Finally, the LLM was asked what it could infer from the nozzle temperature distributions. The prompt used was: “In the Excel file, regarding the temperature distributions in the nozzles, what do you infer?” In the answer, it was mentioned that the outlet temperatures range from ≈45 °C (coolest) to ≈59 °C (warmest), indicating a temperature spread of about 14 °C and a significant thermal imbalance among the nozzles. The highest temperatures occur at outlets 10 (~59 °C), 6 (~58 °C), 8 (~57 °C), and 4 (~56 °C); these outlets likely correspond to the main high-momentum flow paths within the manifold. One interpretation is that fluid reaching these outlets probably travels more directly from the inlet and therefore spends less time near the cooled walls, thereby losing less heat. The lowest temperatures occur at outlets 11 (~45 °C), 9 (~45.9 °C), and 1 (~46.4 °C); these branches likely experience longer residence times. The fluid interacts more with the cooler walls, leading to greater heat transfer and a lower outlet temperature. There is a strong correlation with flow distribution: high-flow outlets → higher temperatures and low-flow outlets → lower temperatures. This happens because higher velocity → shorter residence time → less cooling and lower velocity → longer residence time → more heat loss, so the hydraulic imbalance of the manifold mainly drives the thermal imbalance.

CFD results indicate that the manifold exhibits flow maldistribution, resulting in temperature maldistribution. This is common in manifolds when outlet spacing is uniform, but pressure losses along the header are not compensated. What this means for the design is that the temperature pattern suggests the manifold might benefit from progressively smaller diameters, flow-restrictor or orifice balancing, optimized outlet spacing, or a tapered manifold. These strategies help equalize the mass flow rate and residence time, thereby reducing temperature variation between nozzles.

For the CFD simulation, boundary conditions were established to represent a real-world cooling tower manifold problem; however, some variables, such as the acceleration due to gravity, were omitted, as well as some mesh parameters that would normally be used to obtain better results, such as mesh refinement. This was done to evaluate whether the LLM could provide recommendations for improving results. At the end of the study, it was observed that the LLM did indeed indicate the need to refine the mesh, increase the number of interactions, and consider convergence control.

In any case, we can analyze the results to confirm that they are correct: the mass balance was very good, with an error of 0.08%. The boundary conditions were consistent: an inlet velocity of 0.955 m/s, an outlet pressure (Patm), and water at 80 °C, representing pump-driven flow, ambient discharge, and typical cooling tower conditions. There are no physical contradictions in the model. The turbulent regime was verified at Re ≈ 10⁶, and the k-ω SST model was used, indicating it is appropriate for pipes and performs well at tee separations. The magnitude of the flow rate was realistic, with a value of Q ≈ 0.12 m³/s, which falls in a typical range of industrial systems and cooling tower cells; it is not simulating something physically absurd.

5.4. Verifying the Suggestions for Mesh and Solver Improvement

The LLM’s recommendations were implemented to improve the meshing and the CFD simulation results.

Table 11. Implementation of the parameters recommended by the LLM.

Parameter	Magnitude
Gravity	On
Skewness	0.6
Element size	0.03 m
Maximum layers	10
Growth rate	1.2
First layer thickness	0.00005 m
Number of iterations	1500

shows the parameters used: gravity was set to 9.81 m/s², the target skewness to 0.6, the element size to 0.03 m, the maximum number of layers to 10 with a growth rate of 1.2, the first layer thickness to 0.00005 m, and the simulation was run for 1500 iterations.

Once the mesh was created, the number of elements was 634,783, and despite setting 1500 iterations, the simulation converged at iteration 698.

Table 12. Residual values obtained by applying the LLM recommendations.

Iteration	Continuity	x-Velocity	y-Velocity	z-Velocity	Energy	k	ω
100	1.8644 × 10−2	1.2700 × 10−4	1.0564 × 10−4	1.5115 × 10−4	1.0113 × 10−5	1.3708 × 10−4	4.9381 × 10−4
250	1.1326 × 10−3	3.4901 × 10−6	4.2624 × 10−6	5.5010 × 10−6	2.0184 × 10−6	8.6126 × 10−6	3.6627 × 10−5
500	4.6523 × 10−4	1.0243 × 10−6	1.4387 × 10−6	1.4879 × 10−6	1.0048 × 10−6	7.7172 × 10−6	1.7077 × 10−4
698	5.1756 × 10−4	1.1313 × 10−6	1.6195 × 10−6	1.8689 × 10−6	9.9845 × 10−7	3.6295 × 10−6	1.7640 × 10−5

shows the improvement in the residual values obtained as the number of iterations increased. The residual ranges are within the acceptable range for a suitable CFD simulation.

The final mass balance identified a mass of 119.347 kg/s at the inlet and approximately 119.348 kg/s at the outlets, resulting in a difference of −0.001 kg/s. It mentioned that the simulation is already at approximately 0.00084%, which is a very good balance.

$$\mathrm{Error}={\displaystyle \frac{0.001}{119.347}}=8.4\times {10}^{-6} ; \mathrm{Error}=0.00084\%$$

(33)

The prompts used in this work are shared in Appendix A; they serve as a reference for reproducibility and for exploring the scope of other LLMs.

6. Conclusions and Future Work

The LLM used contains extensive information on turbulent flow in manifolds and can offer recommendations to improve the results of CFD simulations in this type of system.

The LLM can interpret CAD images of the manifold model and images of CFD simulation results. It was also able to interpret the variables in an Excel file, as well as the behavior of velocities and pressures.

LLM was also found to be capable of predicting turbulent flow behavior in manifolds based on its CFD simulations.

One advantage of using LLMs for predictions is that it is not necessary to program Machine Learning code; only Prompt Engineering is used to communicate with them.

An LLM can guide novice users or students starting in CFD in conducting their simulations; however, to clarify ambiguities and obtain precise results, users still need considerable knowledge of the CFD discipline and the variables involved in turbulent flows.

It is suggested to use case studies with CAD models that allow their dimensions to be modified to evaluate the scope of LLMs further.

On the other hand, it is recommended to use a fluid mixture to study the behavior and interpretation of variables in turbulent flows within manifolds using LLMs, as well as for nonlinear phenomena.

It is proposed that future studies compare the capabilities of other LLMs, such as Gemini, Claude, Qwen, and DeepSeek, within this line of research to better understand their strengths and weaknesses.