Commercial Computational Fluid Dynamics Code Research Articles

CFD Investigation of Methane Combustion with Excess Air in Can-Type Gas Turbine Combustor

This paper presents an investigation on the effect of excess air to combustion characteristics in a full-scale, gas turbine combustor, commonly used in power plant. The investigation was carried out using Computational Fluid Dynamics (CFD), and prior validation was made with the actual operation data of a power station, as well as the adiabatic flame temperature of methane. The mass fraction of CO<sub>2</sub>, O<sub>2</sub> and NO<sub>x</sub> emissions for blended methane with different percentages of excess air explosions was also investigated. The stoichiometric excess air varies from 0% to 30% with air-fuel mixture of 2.7 kg/s. The geometric model of the combustor is extracted from actual gas turbine combustor using 3D scanner and converted into CAD model for simulation. The Navier-Stokes equations were solved using commercial CFD code, ANSYS Fluent, with RNG k-ε chosen to close the turbulence. For reacting species, the species transport model is assumed. Results showed that the addition of excess air during combustor has little effect on the velocity and temperature distribution, both at the combustor interior, as well as at the exit. For the emission of CO<sub>2</sub> and O<sub>2</sub>, though there was no clear trend on the relations between the emission of these species and the excess air, the impact was quite significant. The production of NO<sub>x</sub> was also found to be independent on the excess air ratio, but instead, was a strong function of combustion and exhaust gas temperature.

A learning-centred computational fluid dynamics course for undergraduate engineering students

The great demands for computational fluid dynamics (CFD) practitioners in industry have motivated universities to integrate CFD courses into undergraduate curricula. This article introduces a learning-centred CFD course that aims to train critical users of commercial CFD codes. The main features of the course include a project-based approach to learning and assessment-guided learning activities, both scaffolded by technologies. The implementation of the course is informed by contemporary pedagogical theories that encourage students to have the ownership of their own learning and constructively build their knowledge in an inclusive and supportive learning environment. The students upon completing the course have developed a conceptual understanding of the CFD principles and the importance of performing CFD simulations in a critical way, making them ready for more advanced CFD learning and practices. Course evaluation based on feedback from various sources demonstrates that the learning-centred approach is the key to the success of the course.

A CFD modelling for optimizing geometry parameters for improved performance using clean energy geothermal ground-to-air tunnel heat exchangers

In this numerical study, different geometric parameters have been optimized for improved performance using a clean energy geothermal Ground to Air Tunnel Heat Exchanger (GATHE). A commercial computational fluid dynamic code ANSYS Fluent was used, and the code has been validated with the available experimental and analytical results. Three soil samples were used to analyze the thermal properties, each with a thermal conductivity of 0.65, 1.25 and 3.50 Wm−1K−1. The critical soil thickness was found to be 10 times the pipe diameter and the lowest outlet temperature of 300.1 K was achieved for a 60 m pipe with a soil thermal conductivity of 3.50 Wm−1K−1. To further enhance the performance of the system, multiple fin arrays were introduced into the ductwork at 0.5 m, 1.0 m and 2.0 m pitches. For a 10 m long pipe with fins installed every 0.5 m, an outlet temperature of 306.7 K was observed. With 4 fins for temperature variation, performance increased by 19.4 % compared to the case without fins. When the fin spacing is 1 m, the temperature drop increases by 5.6 %, and when the fin spacing is 2 m, the temperature drop increases to 7 %, with an outlet temperature of 306.1 K. Finally, a novel set of multiple blocks in diverging and converging patterns was introduced to restrict airflow and further improve heat dissipation. Compared to a single-fin block, the outlet temperature of the 4-fin block was reduced by 14.52 % due to the increased contact area, thus improving the thermal performance of the heat exchanger system.

Colourless distributed combustion effects on a pre‐mixed coke oven gas flame

AbstractFuels consisting of high hydrogen concentration can be consumed under colourless distributed combustion (CDC) to suppress flashback tendency in premixed conditions. Higher NOX challenges can also be overcome through CDC. For those purposes, coke oven gas was consumed under CDC within the scope of this study. To achieve CDC, or diluents were introduced into the oxidizer so that oxygen concentration in the oxidizer would be decreased from 21% O2 to its lean blow‐off limits. Excess air ratios were determined as λ = 1.2 and λ = 1.5 along with a thermal power of 10 kW under premixed conditions. A commercial computational fluid dynamics code was used to predict temperature distribution and , CO, and emissions. 162‐step reactions created with GRI‐Mech 3.0 chemical kinetics was integrated to the eddy dissipation concept combustion model. The temperature and profiles predicted were compared with the experimental results. Consistency was achieved at ~95% for temperature profiles, and almost 100% for profiles between the measured and the predicted ones. According to the results, it is concluded that a more homogeneous temperature distribution with the ~21% decrease in the maximum temperature was observed, and there was about 96% decrease in level. It was also demonstrated that using as a diluent is more effective in terms of temperature distribution over the combustor and reduction, while dilution with is more effective in terms about 70% in decrease on CO.

Quantitative Validation of Gas-Liquid Flow Regime Transition Using Eulerian-Eulerian CFD Models

Quantitative validation of a computational fluid dynamics (CFD) code is about making point-to-point comparisons over fields of data to make statements about predictive fidelity. By the very nature of CFD, these comparisons are high-performance computing and data intensive. This presentation provides an overview of workflow development toward quantitative development of two-phase CFD codes. The focus here is on multifield two-fluid model capability implemented in the commercial CFD code ANSYS CFX applicable to boiling gas-liquid two-phase flows. Applications to validating three-dimensional predictions that span two-phase flow regimes are discussed.

Research on pinhole accidental gas release in pipelines: Statistical modeling, real gas CFD simulation, and validation

The successful risk mitigation of Natural Gas (NG) leakage to reduce its environmental and economic impact depends chiefly on timely detection leaks and predicting the amount of gas release. In the present study, we investigated pinhole leaks and predicted the gas release rate for various leak to pipe diameter ratios and operating pressures ranging from 2 bar to 110 bar. We first set up a laboratory-scale experiment. The generalized likelihood ratio (GLR) is used as an advanced statistical hypothesis testing technique to detect any shifts in the mean and variance of the process measurements in real-time. These results improved the understanding of several leak detection systems and contributed to a reduction in false alarms in these systems. The presence of a leak was flagged almost immediately after it occurred, indicating the speed and efficiency of statistical techniques in detecting microleaks. The present computational fluid dynamics (CFD) study provides details on the entire leak flow field that are not possible to obtain with experimental methods. CFD is a critical tool in process safety management, helping to identify, analyze, and mitigate potential risks in natural gas pipeline. The CFD study proposes new correlations to predict the nominal leak volume flow rate by investigating the influence of leak size, pipe diameter, and pipe pressure for wide ranges of pressures. The correlations were derived from three-dimensional transient detachable eddy simulation model in a commercial CFD code (ANSYS Fluent R3). The correlations enhance the conventional models by incorporating the gas compressibility effect for high-pressure conditions. The percentage of error between the results of the CFD and delivered correlation fluctuated between 4% and − 5%, demonstrating the high accuracy of the new correlation.

Analysis of heat transfer enhancement due to helical static mixing elements inside cooling channels in machine tools

In this contribution, the effectiveness of helical static mixers in different arrangements and flow configurations/regimes is explored. By means of a thorough numerical analysis, the application limits of helical static mixers for the heat transfer enhancement inside cooling channels of machine tools are provided. The numerical simulations were processed with the commercial finite volume Computational Fluid Dynamics (CFD) code, ANSYS Fluent 2020 R2. This study shows that there exists an optimal range of application for static mixers as heat exchange intensifier depending on the flow speed, the transmitted heat flow and the thermal conductivity of the tool. The investigations of this contribution are restricted to single-phase flow in circular cross-sections and straight channel geometries. As a representative application example for a machine tooling, the cooling of a simple injection mold is investigated. The research carried out reveals that the application of static mixing elements for enhancement of heat transfer is very effective, particularly for fluid flow with low to medium Reynolds numbers, close-contour cooling, high values of heat fluxes, and high thermal conductivity of the tooling material.

On the Effectiveness of Scale-Averaged RANS and Scale-Resolved IDDES Turbulence Simulation Approaches in Predicting the Pressure Field over a NASCAR Racecar

Racecar aerodynamic development requires well-correlated simulation data for rapid and incremental development cycles. Computational Fluid Dynamics (CFD) simulations and wind tunnel testing are industry-wide tools to perform such development, and the best use of these tools can define a race team’s ability to compete. With CFD usage being limited by the sanctioning bodies, large-scale mesh and large-time-step CFD simulations based on Reynolds-Averaged Navier–Stokes (RANS) approaches are popular. In order to provide the necessary aerodynamic performance advantages sought by CFD development, increasing confidence in the validity of CFD simulations is required. A previous study on a Scale-Averaged Simulation (SAS) approach using RANS simulations of a Gen-6 NASCAR, validated against moving-ground, open-jet wind tunnel data at multiple configurations, produced a framework with good wind tunnel correlation (within 2%) in aerodynamic coefficients of lift and drag predictions, but significant error in front-to-rear downforce balance (negative lift) predictions. A subsequent author’s publication on a Scale-Resolved Simulation (SRS) approach using Improved Delayed Detached Eddy Simulation (IDDES) for the same geometry showed a good correlation in front-to-rear downforce balance, but lift and drag were overpredicted relative to wind tunnel data. The current study compares the surface pressure distribution collected from a full-scale wind tunnel test on a Gen-6 NASCAR to the SAS and SRS predictions (both utilizing SST k−ω turbulence models). CFD simulations were performed with a finite-volume commercial CFD code, Star-CCM+ by Siemens, utilizing a high-resolution CAD model of the same vehicle. A direct comparison of the surface pressure distributions from the wind tunnel and CFD data clearly showed regions of high and low correlations. The associated flow features were studied to further explore the strengths and areas of improvement needed in the CFD predictions. While RANS was seen to be more accurate in terms of lift and drag, it was a result of the cancellation of positive and negative errors. Whereas IDDES overpredicted lift and drag and requires an order of magnitude more computational resources, it was able to capture the trend of surface pressure seen in the wind tunnel measurements.

Numerical investigation on the performance of a Solar Chimney Power Plant System (SCPP)

AbstractIn this work, a parametric two‐dimensional computational fluid dynamics (CFD) analysis of solar chimney power plant was performed to describe the physical mechanism in order to establish realistic predictions for the operation of such plants in different location in Algeria. The developed numerical model includes a solar radiation model within the collector; an energy storage model; an air flow and heat transfer model, and a turbine model. It is based on the solution of the Navier‐Stokes equation for turbulent flow using the standard k − ϵ model. The Boussinesq model was adopted in this simulation for the density of the fluid. The boundary conditions were adapted according to the selected sites and the effect of this on the SCPP performance was studied. The numerical simulation was performed using the commercial computational fluid dynamics (CFD) code “Ansys Fluent 19.2”.

Aerodynamics of Landing Maneuvering of an Unmanned Aerial Vehicle in Close Proximity to a Ground Vehicle

<div class="section abstract"><div class="htmlview paragraph">Autonomous takeoff and landing maneuvers of an unmanned aerial vehicle (UAV) from/on a moving ground vehicle (GV) have been an area of active research for the past several years. For military missions requiring repeated flight operations of the UAV, precise landing ability is important for autonomous docking into a recharging station, since such stations are often mounted on a ground vehicle. The development of precise and efficient control algorithms for this autonomous maneuvering has two key challenges; one is related to flight aerodynamics and the other is related to a precise detection of the landing zone. The aerodynamic challenges include understanding the complex interaction of the flows over the UAV and GV, potential ground effects at the proximity of the landing surface, and the impact of the variations in the surrounding wind flow and ambient conditions. While a large body of work in this area can be found on the control aspect of the UAV landing and takeoff maneuvers, research on the aerodynamic aspects of such maneuvers is non-existent. This paper presents an in-depth computational fluid dynamics (CFD) based aerodynamic characterization of the transient flow fields associated with the landing of a hobby-model quadcopter (the UAV) on an idealized road vehicle (the GV), the 35-degree slant angle Ahmed body. Transient improved delayed detached eddy simulations (IDDES) are carried out using the commercial CFD code STAR-CCM+. Our study indicates that the pressure field is the first flow property that gets impacted by the proximity of the UAV to the GV.</div></div>

Numerical Evaluation of the Hydrothermal Process in a Water-Surrounded Heater of Natural Gas Pressure Reduction Plants

The gas pressure in the main network of transmission lines is about 700 to 1000 psi (4826.33 to 6894.76 kPa), which is reduced to 250 psi (1723.69 kPa) at the entrance station of a city. This reduction process, which occurs in the regulator, causes a severe drop in gas temperature. The drop in the gas temperature produces hydrates and even causes the water vapor in the gas to freeze. As a result, there is a possibility that the passage of gas in the regulator is blocked and the gas flow is cut off. By employing heaters (indirect water heaters), the temperature of the gas entering the regulator can be preheated to eliminate the possibility of freezing in the regulator. This heater is fueled with natural gas and it operates for 24 hr a day, especially in the cold seasons. Therefore, one of the main challenges in using this type of heater is its high fuel consumption. Consequently, researchers are looking for a solution to reduce the fuel consumption (natural gas) of gas heaters. In this paper, the heat transfer and fluid flow in a heater of a natural gas pressure reduction plant, the Aliabad Power Plant (Iran), are numerically investigated using a commercial Computational Fluid Dynamics (CFD) code, ANSYS FLUENT 18.2. The considered heater consists of three parts, including (i) gas coils, (ii) a water bath (shell), and (iii) a fire tube. The indirect heat transfer process takes place between the hot liquid flow in the fire tube (combustion exhaust) and the cold liquid flow (natural gas) using the natural convection flows generated in the water bath. Numeric modeling is performed for four different gas mass flows, including 6 × 104, 8 × 104, 1 × 105, and 12 × 105 standard cubic meters per hour (or 16.67, 22.22, 27.78, and 33.33 m3/s). The results indicate that the natural gas outlet temperature achieved to a temperature higher than required. By installing a regulator on the burner, the gas consumption can be reduced, resulting in station cost savings, and also reducing the environmental impacts. The outcomes depict that the maximum possible reductions in monthly gas consumption and economic savings in the proposed system are 67,500 m3 and IRR 25 million at a gas mass flow rate of 60,000 SCMH.

Numerical Analysis on Dynamic Behavior Characteristics of an Amphibious Assault Vehicle during Water Entry

In the present study, the dynamic behavior characteristics of an amphibious assault vehicle during water entry were analyzed using STAR-CCM+, a commercial computational fluid dynamics(CFD) code. All computations were performed using an overset mesh system and a RANS based flow-solver coupled with dynamic fluid-body interaction(DFBI) solver for simulating three degrees of freedom motion. For numerical validation of the solver, a water entry simulation of inclined circular cylinder was conducted and it was compared between an existing experiment data and CFD results. The pitch angle variation and the trajectory of the circular cylinder during water entry shows good agreement with previous experimental and numerical studies. For the water entry simulations of the amphibious assault vehicle, the analysis of dynamic behaviors of the amphibious assault vehicle with different slope angles, submerged depths and initial velocities were conducted. It is confirmed that the steep slope angle increases the submerged volume of the amphibious assault vehicle, so the buoyancy acting on the vehicle is increased and the moved distance for the re-flotation is decreased. It is also revealed that the submerged volume is increased, bow-up phenomenon occur earlier.

Numerical and experimental analysis of the effects of tar components on single planar SOFC under high fuel utilization

One of the main challenges and obstacles for the application of SOFCs with wood gas is the degradation of Nickel anode caused by heavier hydrocarbons from the gasification process. The unclear conversion process on the anode and the fluctuant content of tars in wood gas will cause problems like the excess of critical fuel cell utilization and thus the oxidation of Nickel anode. This work focuses on the experimental and numerical analysis of tar conversion on the single SOFC under different conditions. A three-dimensional Computational Fluid Dynamics (CFD) model for an electrolyte-supported single cell was developed using the commercial CFD code FLUENT. The conversion kinetics of tar is validated by experimental results and implemented into the model. With this model, local distributions of Nernst voltage across the anode area are demonstrated. Areas, where an oxidation of Nickel is to be feared, are identified. Both experimental and simulative results have proved the positive effect of toluene reforming on preventing Ni from re-oxidation.

Analyis of aerodynamic performance of passenger ship with different frontal accommodations using CFD

Research on aerodynamic performance and reduced wind drag acting on hull and large windward areas of high superstructures, such as passenger ships, container ships, roll on - roll off car ferries, and other ships, remains essential marine transportation. In this study, the wind drag acting on a passenger ship's above water hull was computed using ANSYS-Fluent, a commercial Computational Fluid Dynamics (CFD) code. Using CFD, the wind drag components, friction viscous wind drag, and pressure viscous wind drag acting on the hull of the original passenger ship were investigated. Based on the pressure and velocity distributions around the hull, several new hull forms with different frontal accommodation shapes have been proposed to reduce wind drag and improve the aerodynamic performances of the ship. By comparing the CFD results, a new above water surface hull with reduced wind drag was indentified in this study.

A computational analysis of the impact of boundary conditions on a particle-laden flow: A case study in a pressurized oxy-coal combustor

Designing an effective burner is vital for the development of coal combustion technologies. Because of high pressure, the volumetric fraction of the coal particles at the fuel inlet of the POC burner approaches or even exceeds the limitations allowed by the commercial computational fluid dynamics (CFD) codes (e.g., Ansys FLUENT). Consequently, for such high particle volumetric fractions, the interplay between the particles, the fluid flow, and the wall need to be re-evaluated. The present computational work is a first step in a systematic analysis of the roles of various characteristics, specifically, the method of particle release, its location, and the particle size. In the POC process, pulverized coal is burned under elevated pressure in an O2/CO2 environment. Specifically, a 15-bar, 100 kWth, POC combustor is modeled with Ansys FLUENT using the Reynolds-averaged Navier-Stokes (RANS) approach. It is revealed that for this pilot-scale, pressurized burner, the gas phase flow velocity in the near-wall region exhibits some anomalies. In order to scrutinize the role of particle loading in the near-wall region, the particle release location is investigated. The numerical simulations incorporate coupling between the turbulent flow and the particles. It is found that the tuning of the particle release location makes the gas phase flow velocity consistent with the pure gas flow velocity profile. Moreover, the particle releasing location also influences the flame stability. The particle size is also found to have a significant impact on the particle trajectory, flame stability, and temperature.

Swirl Brake Design for Improved Rotordynamic Vibration Stability Based on Computational Fluid Dynamics System Level Modeling

Abstract The accurate characterization of compressor rotordynamic coefficients during the design phase reduces the risk of subsynchronous vibration problems occurring in the field. Although rotordynamists extensively investigate discrete compressor components (such as seals and front shrouds) to tackle instability issues, integrated or system-level analysis of compressor rotordynamics is very sparse. In reality, the impeller, eye-labyrinth seal, and the front shroud heavily influence one another; and the collective dynamic behavior of the system differs from the sum of the dynamic behavior of isolated components. A computational fluid dynamics (CFD)-based approach is taken to evaluate the dynamic behavior of the system as a whole. The geometry and operating conditions in this work are based on the recent experimental study of Song et al. (2019, “Non-Axisymmetric Flows and Rotordynamic Forces in an Eccentric Shrouded Centrifugal Compressor—Part 1: Measurement,” ASME J. Eng. Gas Turbines Power, 141(11), p. 111014. 10.1115/1.4044874) on centrifugal compressor. The commercial CFD code cfx 19.0 is used to resolve Reynolds-averaged Navier–Stokes equations to quantify the eye-labyrinth seal and front cavity stiffness, damping, and added mass. The entire compressor stage is modeled to uncover the coupled behavior of the components and assess the stability of the whole system instead of just discrete components. In the current work, three CFD approaches, namely quasi-steady, transient static eccentricity, and transient mesh deformation techniques are studied and benchmarked against analytical and experimental results from the literature. Having established the efficacy of the proposed approach, four types of swirl brakes are proposed and analyzed for stability. The novel swirl brakes create negative swirls at the brake cavities and stabilize both the front shroud and the eye-labyrinth seal simultaneously.

Thermofluid-dynamic assessment of the EU-DEMO divertor single-circuit cooling option

Until 2019, the thermo-hydraulic development of the EU-DEMO divertor was based on the “double-circuit” concept, in which two independent cooling circuits served by two different Primary Heat Transfer Systems were used to cool the Plasma-Facing Components (PFC) and the Cassette Body (CB). During the Divertor Final Design Review Meeting, held in May 2020, the possibility to adopt a single cooling circuit to serve both components was suggested. This new cooling circuit was originally conceived with the aim of simplifying remote maintenance, with potential benefits for some aspects of safety and balance of plant design and integration. During the years from 2020 to 2022, in the framework of the Work Package DIV 1 - “Divertor Cassette Design and Integration” of the EUROfusion action, University of Palermo and ENEA carried out a research campaign focussed on the preliminary thermofluid-dynamic assessment of this new concept, highlighting its strengths and weaknesses. The research campaign was carried out following a theoretical–computational approach based on the finite volume method and adopting the commercial computational fluid-dynamic code ANSYS-CFX. The steady-state thermal-hydraulic performances of the single-circuit DEMO divertor concept were assessed in terms of coolant pressure drop and flow velocity distribution, mainly in order to check coolant aptitude to provide a uniform and effective cooling to CB, shielding liner, reflector plates, PFCs and the newly introduced neutron shields to improve the shielding of the vacuum vessel. Moreover, the margin against critical heat flux distributions among the plasma-facing channels were assessed by adopting appropriate correlations, to check the compliance with the applicable constraints. Models, loads and boundary conditions assumed for the analyses are herewith reported and critically discussed, together with the main results obtained.

Numerical investigation of flammable vapour cloud formation from pools of heated organic liquids

The aim of this work is to study the effects of wind velocity, pool length and thickness on the flammable vapour cloud formation from pools of heated organic liquids, covering a wide range of substance properties such as molecular weights and boiling temperatures. To achieve that goal, the computational fluid dynamics (CFD) model has been built and implemented in the commercial CFD code ANSYS Fluent. The mathematical model is validated against published experimental data with respect to both pool evaporation and vapour dispersion simulation. The vapour cloud formation is studied in terms of evaporated mass per unit area of the pool, flammable mass of vapours and its fraction of the total released mass, and maximum downwind extent of the flammable cloud. The results of numerical simulation presented in this work provide a better understanding of evaporation and dispersion processes accompanying the formation of a flammable vapour cloud from pools of heated hydrocarbon liquids.

Nuclear spent fuel cask full scope simulation using coupled Computational Fluid Dynamics models

The interest in medium to long-term nuclear spent fuel storage is growing worldwide. After being cooled during several years in the spent fuel pool, the fuel can be stored in dry casks in a second phase, being moved to a temporary repository for the mid-term and/or into a deep storage facility for the long-term. To ensure the fuel integrity, the peak cladding temperature (PCT) is a common safety parameter. The PCT can be estimated by performing simulations, and Computational Fluid Dynamics (CFD) codes have been widely used for this purpose. In this paper, the commercial CFD code ANSYS CFX 2019 R3 has been used to estimate the PCT in a generic spent fuel dry cask of 32 fuel elements.Although CFD codes are useful tools for that purpose, they also have drawbacks, mainly their computational cost to perform complex simulations. To overcome this issue, a methodology which splits the simulation in two separated but coupled models has been used, significantly reducing the required hardware. The results shown an adequate behavior of the fluid flow together with a best estimate estimation of the PCT for the most conservative thermal load of the cask.

Investigation on entropy generation and flow characteristics of 7-pin sodium cooled wrapped-wire fuel bundle

The fuel assembly of sodium-cooled fast reactor (SFR) is considered a compact heat interchanger with the intricate flow. The wire-wrapped make a great difference on the secondary flow and transverse momentum mixing. The investigations on fully developed convective heat transfer in a 7-pin fuel bundle with wrapped-wire are conducted for particular Reynolds number from 2 × 104 to 2 × 105, and heat flux at 500 to 1500 kW/m2 employing commercial computational fluid dynamic (CFD) code based on the finite volume method (FVM). The SST k-ω turbulent model and periodic boundary conditions are adopted at the inlet and outlet to obtain the fully developed fluid field and capture the detailed information in the near-wall region. The model validation and mesh independence verification are conducted, and the maximum error is 10.3%. The results are analyzed in view of sensitivities of secondary flow and thermodynamic irreversibility to mass flow rate and heat flux from the local and systemic scales by means of the entropy generation analysis approach. The axial profiles of secondary flow and entropy generation rate under different working conditions are studied. The results indicate that due to the helical structure of the wrapped-wire, the secondary flow, and entropy generation present similar periodical fluctuation and symmetric distributions in axial direction. Also, the secondary flow enhance has an impact on the heat transfer. The thermal irreversibility is also analyzed, and the result shows that heat conduction is the leading cause of the irreversible losses. Ep decreases with the Reynolds number, and increases with heat flux, which means the better thermal economic performance occurs at lower velocity and higher heat flux.