Vapor Volume Research Articles

A numerical investigation of the wettability effect on minitube flow boiling using the volume of fluid method

Flow boiling within minitubes holds immense promise for efficient heat dissipation owing to its substantial latent heat exchange capacity. The performance and efficacy of the pump, crucial beyond just necessitating high heat flux, are closely tied to maintaining a low-pressure drop. Surface treatment stands out as one of the techniques to augment thermal efficiency. While the significance of microscale surface properties, particularly wettability, in influencing flow boiling has been established, only a limited number of studies have explored its impact on pressure drop. This study rigorously investigates the wettability's influence on flow boiling within minitubes using the VOF approach. It reports key parameters within a 200 ms interval, including vapor volume fraction, average heat flux, and pressure drop. Employing a mass flux of 560 kg/m2s along a 10 mm length minitube, the study attains an impressive average heat flux of up to 324,966.9 W/m2 on a hydrophilic surface exhibiting a 5° contact angle. In contrast, a hydrophobic surface boasting a 150° contact angle achieves a significantly reduced total pressure drop (∆p) of 698.4 Pa, effectively preventing tube-clogging. Simultaneously accounting for heat flux and pressure considerations, it is conceivable that selecting a surface featuring a contact angle of 105° could represent an optimal choice for a 30 mm length minitube. The findings highlight that the hydrophilic surface encourages greater liquid presence, enhancing heat exchange efficiency considerably. Conversely, hydrophobic surfaces facilitate vapor layer stabilization, leading to reduced total pressure drop and minimized fluctuations. This work offers comprehensive insights into the fundamental relationship between wettability, flow boiling, and pressure drop, thereby providing valuable guidance for future miniube design strategies in cooling applications. Such insights hold immense potential to revolutionize various industrial and engineering sectors.

Flow Investigation and Optimization Design of a Radial Outflow Liquid Turbine Expander for Liquid CO2 Energy Storage System

Abstract The radial outflow liquid turbine expander (LTEROF) draws increasing attention for enhancing the efficiency of the liquid CO2 energy storage (LCES) system. However, the detrimental cavitation deteriorates the flow behavior, which demands an in-depth study of the flow physics and then effective attenuation. This study aims to effectively mitigate thermosensitive fluid cavitation and reduce energy dissipation. First, a preliminary expander design methodology taking into account the large specific volume variation of working fluid is implemented. Next, the entropy production analysis method (EPAM) is proposed to characterize energy dissipation and cavitation. Furthermore, the improved cavitation and turbulence models are validated through simulating Hord's liquid hydrogen hydrofoil. To suppress the cavitation and energy dissipation, the optimization design method based on the particle swarm optimization (PSO) algorithm together with the Kriging-based adaptive surrogate model is developed. Among them, the nonuniform relational B-splines and free form deformation (NURBS-FFD) method is applied to flexibly deform the profiles of nozzle and rotor, and a novel objective function incorporating vapor volume fraction and local entropy production rate (LEPR) is constructed to capture the cavitation and energy dissipation. During optimization, the optimizer is driven by the objective function to search globally toward the cavitation-resistance and low-dissipation geometry. With the optimization, the LEPR region shrinks and the cavitation is obviously weakened, the performance significantly improves both under design condition and under off-design conditions.

Unsteady assessment and alleviation of inter-blade vortex in Francis turbine

Inter-blade vortex refers to a specific type vortex cavitation observed in Francis turbines under partial loads and its adverse impact is widely recognized as a crucial factor that limits the safety and stability of hydraulic turbines. The present study endeavors to examine the spatiotemporal evolution attributes of inter-blade vortex and its contribution to the generation of unstable pressure fluctuations. To achieve this, a comprehensive investigation is conducted using a reduced-scale Francis model turbine with low head, combining numerical investigations and visualization experiments. The study demonstrates that the vapor volume associated with the inter-blade vortex experiences periodic pulsation, with a frequency proximate to the rotational frequency of the runner. Within the turbine runner, cavitation exhibits a dynamic cycle of incipience, growth, expansion, and localized collapse. The most remarkable cavitation disintegration occurs at the convergence point of the trailing edge of the runner blade and the band, wherein the most pronounced amplitude of pressure fluctuation is also discerned. In addition, this research establishes a direct correlation between pressure fluctuations and vapor volume, revealing that the acceleration of the vapor volume is accountable for the occurrence of pressure fluctuations with heightened magnitude. Furthermore, an optimization campaign successfully reduces the cavitation volume by 88.58% and 78.99% at two specific points of interest, resulting in the nearly complete elimination of high-amplitude pressure pulsations. Building upon these findings, data mining techniques are implemented to identify that the blade profile at a spanwise height of 0.75 significantly influences the enhancement of turbine hydraulic performance. Additionally, it has been ascertained that the design parameter governing the geometric placement of the blade trailing edge plays a pivotal role in reducing the intensity of the inter-blade vortex. This study yields invaluable insights into the underlying mechanism of unsteady phenomena induced by inter-blade vortex and formulates a hydraulic optimization approach capable of enhancing the operating stability of the Francis turbine.

Heat transfer characteristics of water jet impingement on high-temperature steel plate by angular nozzle

The average jet flow rate, vapor volume fraction inside the nozzle, and the distribution of pressure, shear force, turbulence intensity, temperature, and Nusselt number on the heat transfer surface were simulated when water jet impinged on a 900 °C steel plate by a straight cone nozzle and an angular nozzle under the condition of 0.7 MPa inlet pressure. Results indicate that the strong cavitation effect of the angular nozzle makes its jet impingement heat transfer intensity superior to the straight cone nozzle. Although the average jet flow rate of the angular nozzle is 3.33% lower than that of the straight cone nozzle, its shear force, turbulence intensity and Nusselt number at the stagnation point are 18.43%, 20.43%, and 18.81% higher than those of the straight cone nozzle. Experiments also show that the jet impingement heat transfer intensity of the angular nozzle is better than that of the straight cone nozzle. Its maximum cooling rate at the stagnation point increased by 13.16%, and the time to reach the maximum cooling rate decreased by 60%, compared with the straight cone nozzle. It is hoped that the results can help improve the performance of online cooling equipment for hot-rolled steel.

Erosion Characteristics and Flashing Flow of High-differential-pressure Control Valves: A Numerical Study using an Erosion-Coupled Dynamic Mesh

To address the issue of erosion in the control valves of blackwater flash systems in the coal chemical industry, this study investigates the dynamic erosion characteristics of one such control valve. Computational fluid dynamics is employed to compare the results obtained with a static mesh and an erosion-coupled dynamic mesh, and the valve erosion is investigated by analyzing the erosion rate, the particle impact velocity, trajectories and angle. Moreover, the relationship between the deformation caused by erosion and the dispersion of the flash vapor phase in the valve is studied, focusing on the flow resistance coefficient. The results indicate that over a period of 9 × 106 s, the impact velocity and subsequent collisions of particles reduce, and the impact angle decreases with the accumulated deformation of the valve core. Notably, the valve core is influenced primarily by the cutting that results from low impact angles, leading to a substantial decrease in the overall erosion rate of the valve, amounting to a reduction of 56.4%. The region facing the flow is at significant risk of erosion, and as the opening decreases, the erosion zone extends gradually to the annular region of the valve core and valve head, leading to increased erosion deformation. Furthermore, as the flow resistance coefficient decreases, so does the vapor volume fraction inside the valve. This study provides a theoretical basis for predicting faults and developing online monitoring solutions for high-differential-pressure control valves in blackwater flashing systems.

NUMERICAL INVESTIGATION OF SUBMERGED HYBRID CAVITATION JET NOZZLE BASED ON STRESS-BLENDED EDDY SIMULATION MODEL

Cavitation jet technology is extensively applied in fields such as mechanical processing, rock fragmentation, and energy development. To further enhance the cavitation capability of the nozzle, first a submerged organ pipe-angular hybrid cavitation nozzle model is established using the software SOILDWORKS. Second, the stress blended eddy simulation (SBES) technology is applied, and the jet law of internal and external flow field of submerged cavitation nozzle is studied numerically using FLUENT. Finally, the periodic shedding of cavitation clouds and the velocity characteristics and vapor volume fraction are studied for different expansion or contraction angles. The study revealed that the cavitation first occurs in the expansion section. With the development of cavitation, the asymmetry of the cavitation cloud increases significantly. Under an inlet pressure of 20 MPa, the fluctuation part of velocity is more concentrated. As the pressure increases, the maximum jet distance and velocity also increase.

The Effect of Changing the Nozzle Arrangement in the Vacuum Dryer on Decreasing the Moisture Content of Crude Palm Oil (CPO)

Crude palm oil is obtained from the mesocarp of oil palm fruit through a pressing process. The main cause of the decline in the quality of palm oil is the highwater content. Reducing humidity can be done by optimizing the palm oil dryer or what is called a vacuum dryer. The current vacuum dryers are considered less than optimal because the crude palm oil water content is often high, with the nozzles positioned in a straight line so that the distance between the nozzles is tight. For this reason, research was carried out on the effect of varying the diameter of the nozzle arrangement on reducing crude palm oil water content in vacuum dryers. The research was carried out at different nozzle distances in a vacuum dryer with varying nozzle arrangement diameters of 290 mm, 380 mm, 470 mm, 560 mm, and 650 mm and an inter-nozzle angle of 25.71° from the center of the vacuum dryer tube. This research starts from the design stage, making preliminary models, numerical studies, making prototypes, and experimental studies. From the research carried out on this vacuum dryer, the value of the amount of water vapor volume fraction formation in the vacuum dryer outlet channel for various nozzle arrangement variations was obtained. The total volume fraction of water vapor at a nozzle arrangement diameter of 290 mm is 3.31, a nozzle arrangement diameter of 380 mm is 3.64, a nozzle arrangement diameter of 470 mm is 0.68, a nozzle arrangement diameter of 560 mm is 4.37, and a nozzle arrangement diameter of 650 mm is 4.65. From these results it can be seen that the moisture content is proven to change in each nozzle arrangement and the most optimal decrease in moisture content occurs at a nozzle arrangement diameter of 650 mm as indicated by the formation of the largest volume fraction of water vapor. Based on experiments, it was found that the efficiency of the vacuum drying machine could reach 65.67%.

Evaluation of the Cavitation Fluid Characteristics of the Bullet across the Medium into the Water at Different Velocities

This paper studies the evolution and fluid distribution characteristics of a high-speed projectile’s cavity in the water based on joint research, a method involving experiment and numerical simulation. Specifically, we develop an experimental platform and a numerical calculation model for a high-speed projectile to observe its initial cavity evolution characteristics in the water at different velocities and close ranges. Additionally, this work investigates the evolution mechanism of the cavitation process and its fluid distribution law inside the cavity and studies the evolution characteristics of the cavitation stage under different velocities. The results reveal that after the projectile enters the water, the cavity is gourd-shaped and symmetrical, with a necking phenomenon at the tail and the cavity falling off. The cavitation process can be divided into the surface closure, saturation, deep closure, and collapse stages according to the fluid distribution changes in the cavity. Suppose the projectile has a certain speed with the water, its velocity increases. In that case, the cavity generation rate decreases, the growth rate of the water vapor volume in the cavity decreases, the peak water vapor volume content reduces, and the volume of air in the saturation phase of the cavity becomes increases having a range of 6% to 9%. Additionally, the cavity surface closure dimensionless time grows logarithmically as the velocity changes from 0 m/s to 500 m/s, the cavity saturation dimensionless time decreases approximately linearly, and the cavity depth closure dimensionless time is unaffected by velocity changes.

Numerical simulation on the enhancement mechanism of the distinctive division baffle on the performance of a Venturi for process intensification

As one of the advanced oxidation processes, hydrodynamic cavitation (HC) has become a promising technology for treating industrial effluents by various cavitation devices due to the advantages of cost-effectiveness in operation, higher energy efficiencies, and large-scale operation. In this study, the effect of a distinctive division baffle on the performance of a circular Venturi is proposed focusing on the enhancement of cavitation intensity and reaction area by utilizing computational fluid dynamics. Three geometrical parameters of the distinctive division baffle, including divergent angle (β2), convergent angle (α2), and throat diameter (d2), were investigated, after a well validation of the numerical method with a previous experiment.It was found that the β2 and d2 provided relatively more significant impact on cavitation intensification. Through the comprehensive evaluation of the selected three parameters, the most appropriate geometrical configuration of the novel Venturi was determined as a divergent angle β2 of 6°, a convergent angle α2 of 16°, and a throat diameter d2 of 2.25 mm. Furthermore, the finally recommended design, significantly intensifying the cavitating process, has been tested at different pressure ratios and cavitating zone of recommended design is always much larger than original model. The recommended design achieved a vapor volume increasing rate of 102.3 %, 41 % and 57.5 % at PR = 2, 4 and 6. In conclusion, the novel strategy of Venturi with distinctive division baffle may provide inspiration and reference to the future research and industrial application of HC technology.

Analysis of Cavitation-Induced Unsteady Flow Conditions in Francis Turbines under High-Load Conditions

Hydraulic vibrations in Francis turbines caused by cavitation profoundly impact the overall hydraulic performance and operational stability. Therefore, to investigate the influence of cavitation phenomena under high-load conditions, a three-dimensional unsteady numerical simulation is carried out for a Francis turbine with different head operating conditions, which is combined with the SST k-w turbulence model and two-phase flow cavitation model to capture the evolution of cavitation under high-load conditions. Additionally, utilizing entropy production theory, the hydraulic losses of the Francis turbine during cavitation development are assessed. Contrary to the pressure-drop method, the entropy production theory can quantitatively reflect the characteristics of the local hydraulic loss distribution, with a calculated error coefficient τ not exceeding 2%. The specific findings include: the primary sources of energy loss inside the turbine are the airfoil cavitation and cavitation vortex rope, constituting 26% and 71% of the total hydraulic losses, respectively. According to the comparison with model tests, the vapor volume fraction (VVF) inside the draft tube fluctuates periodically under high-load conditions, causing low-frequency pressure pulsation in the turbine’s power, flow rate, and other external characteristic parameters at 0.37 Hz, and the runner radial force fluctuates at a frequency of 1.85 Hz.

Numerical investigation on the effect of Al2O3-water nanofluid on direct steam generation in parabolic trough collectors

The utilization of solar energy through direct steam generation (DSG) in parabolic trough collectors is a novel approach. In addition, due to higher thermophysical properties, the effect of using nanofluid as the coolant has been the subject of some of the recent studies but the applicability of the nanofluids in DSG process has not been studied before. In this study, the flow boiling of Al2O3 nanofluid at volume fractions 1%, 1.5% and 2%, under uniform and non-uniform heat fluxes has been studied numerically. The Eulerian model was used and non-equilibrium RPI was applied as the boiling model. The validation was done for flow boiling of pure water and Al2O3 nanofluid separately, with the available data in the literature. The results showed that the vapor volume fraction at the outlet is higher under non-uniform heat flux and adding nanoparticles would increase the vapor generation in the tube. Adding nanoparticles to the pure water increased the vapor volume fraction at the outlet up to about 8.64% in respect to pure water under uniform and non-uniform heat fluxes. The average Nu was up to 544% higher under non-uniform heat flux compared to uniform heat flux. Due to the presence of stratified flow, increasing nanofluid concentration reduced the average Nu up to 21.24% and 10.24% under uniform and non-uniform heat flux, respectively.

Feasibility study on finishing the inner surface of SLA small holes by volume alternating cavitation shock wave

Aiming at the technical problem of finishing the inner surface of additive manufacturing small holes, a novel volume alternating cavitation shock wave finishing (VACSWF) method was innovatively proposed. Using simulation and experiment methods, the distribution law of the vapor volume fraction in the alternating cavitation flow field of the small hole is studied, and the influence of volume alternating frequency and volume variation on the flow field is analyzed. Using the self-designed volume alternating cavitation experimental device, the inner surface of complex small holes processed by the Stereo Lithography Appearance (SLA) method was completed, and the feasibility of finishing the inner surface of complex small holes by the VACSWF method was verified. The collapse process of the volume alternating cavitation bubbles is analyzed, and the material removal mechanism of VACSWF is revealed.

Conjugate heat transfer characteristics numerical simulation on steam generator tube of lead-cooled fast reactor

The safety assessment of the Steam Generator Tube Rupture (SGTR) accident is a crucial step in the design process of the Lead-cooled Fast Reactor (LFR). To begin with, it is necessary to simulate the steady-state heat transfer of the LFR Heat Exchanger (HX) in order to determine the initial conditions of the SGTR accident. In this study, the heat transfer characteristics of the fluids on both sides of the LFR HX are analyzed. The appropriate models are modified based on the heat transfer characteristics of liquid metal and boiling water. The accuracy of the boiling models is verified by comparing the simulation results with the outcomes of boiling heat transfer experiments. Additionally, the simulation results are compared with the results obtained from ATHLET calculation and empirical formulas. On the secondary side, the supercooled water undergoes heating until it reaches the superheated steam phase. The preheating section spans from 0 to 600 mm, the saturated boiling section ranges from 600 to 3000 mm, and the superheating section extends from 3000 to 6600 mm. Ultimately, the distributions of steady-state temperature, pressure, and vapor volume fractions of the LFR HX are determined, providing the necessary initial conditions for the occurrence of the SGTR accident.

Large eddy simulation of cavitating flow around a pitching hydrofoil

This numerical investigation employs advanced computational fluid dynamics techniques to examine the intricate physics of cavitating flows around a pitching NACA 66 hydrofoil. Unsteady simulations are conducted using both large eddy simulation (LES) and K-Omega SST turbulence models. The pitching motions range from 0 to 15°, encompassing four cavitation numbers (3.25, 3.5, 3.75, 4) and a Reynolds number of 750,000. The study comprehensively analyzes various flow field characteristics, including pressure distribution, velocity, vorticity, shear stress, vapor volume fraction, and turbulence kinetic energy. The kinematics of pitching significantly influence hydrodynamic loads and the surrounding flow structures in cavitating conditions. Flow visualizations illustrate the evolution of sheet/cloud cavitation, reentrant jet, and vortex dynamics throughout a pitching cycle. Notable findings demonstrate the impact of cavitation number on cavity shape and the relationship between angle of attack, reentrant jet location, and vortex size. Additionally, negative vorticity dilatation is observed to be correlated with cavity size.

Direct comparison of isobaric and isochoric vitrification of two aqueous solutions with photon counting X-ray computed tomography

Vitrification is a promising approach for ice-free cryopreservation of biological material, but progress is hindered by the limited set of experimental tools for studying processes in the interior of the vitrified matter. Isochoric cryopreservation chambers are often metallic, and their opacity prevents direct visual observation. In this study, we introduce photon counting X-ray computed tomography (CT) to compare the effects of rigid isochoric and unconfined isobaric conditions on vitrification and ice formation during cooling of two aqueous solutions: 50 wt% DMSO and a coral vitrification solution, CVS1. Previous studies have only compared vitrification in isochoric systems with isobaric systems that have an exposed air-liquid interface. We use a movable piston to replicate the surface and thermal boundary conditions of the isochoric system yet maintain isobaric conditions. When controlling for the boundary conditions we find that similar ice and vapor volume fractions form during cooling in isochoric and isobaric conditions. Interestingly, we observe distinct ice and vapor cavity morphology in the isochoric systems, possibly due to vapor outgassing or cavitation as rapid cooling causes the pressure to drop in the confined systems. These observations highlight the array of thermal-fluid processes that occur during vitrification in confined aqueous systems and motivate the further application of imaging techniques such as photon counting X-ray CT in fundamental studies of vitrification.

Large eddy simulations of cavitation around a pitching–plunging hydrofoil

In this study, we numerically examine the behavior of the NACA (National Advisory Committee for Aeronautics) 66 hydrofoil under combined oscillatory motion, considering different cavitation numbers. The large eddy simulation method is used for the turbulence modeling. The vertical oscillation (combined oscillation) creates an effective angle of attack, leading to reduced drag force. Our findings indicate that increasing the speed of hydrofoil oscillation leads to a delayed onset and increased production of cavity clouds. Moreover, an increase in the angle of attack during combined oscillatory motion decreases the detachment length of cavitation bubbles. Further investigations show that cavitation on the hydrofoil's surface can accelerate the shift from a laminar to turbulent boundary layer, reinforcing the turbulent boundary layer's strength and thereby delaying the onset of flow separation. Additionally, we accurately examine the terms of the vorticity transport equation in this research. It is evident that the vorticity dilatation term forms near the boundary layers close to the hydrofoil surface and correlates well with the vapor volume fraction. This term plays a vital role in the cavitation inception process.

Dynamics of large cavity induced by valve closure in an undulating pipeline

The dynamics of large cavity and the accompanied water column separation and rejoining induced by fast closing of a butterfly valve in an undulating pipeline system are investigated in this study. The three-dimensional computational fluid dynamics numerical simulations are performed using a newly developed interfacial surface tension-based model (ISTM) that accounts for the surface tension effect on large cavities. The applicability of the ISTM model is validated with the experimental data, showing better accuracy in predicting pressure fluctuations and cavity evolutions than three typical cavitation models. Differences in cavitation characteristics are observed between upstream and downstream of the valve. Upstream the valve, cavitation primarily appears at the pipe top, with the vapor volume fraction varying sharply due to the rarefaction pressure waves (maximum value of 0.0073). Downstream the valve, the complete water-column separation occurs, and vapor volume fraction changes slowly correspond with the growth and collapse of the large cavity (maximum value of 0.647). The maximum length of the large cavity can reach about six times the pipe diameter, with a minimum water vapor interface angle of 16°. The cavitation evolution displays a transition from a clustered inception to a sheet-like growth and collapse pattern. These findings contribute to the design and operation guidance for complex hydraulic systems during transient processes.

A numerical investigation of subcooled flow boiling heat transfer in twisted elliptical tubes

Twisted elliptical tubes possess superior heat transfer performance due to their unique geometry. It is necessary to further explore their potential applications in high-efficiency heat transfer devices. This study conducted a numerical simulation investigation to analyze the flow boiling heat transfer characteristics of subcooled water inside twisted elliptical tubes. The results show that the spiral flow inside twisted elliptical tube causes the fluid with relatively small vapor volume fraction to tend to distribute near the wall, while also increases turbulence intensity and promotes interactions among bubbles. Moreover, increasing the aspect ratio of the twisted elliptical tube can effectively improve the heat transfer coefficient and has a relatively small impact on the pressure drop of the fluid in the tube. Simulation data show that when the aspect ratio increases from 1.41 to 1.80, the heat transfer coefficient of the pipe increases by 15.21 %, while the pressure drop increases by 3.34 %.

CFD analyses of large-scale tests highlighting the effects of thermal radiation in steam-containing atmospheres

In simulations of heat transfer in large gaseous volumes under moderate temperatures, thermal radiation is traditionally neglected to simplify the computations. In recent years however, some small as well as large-scale experiments have demonstrated that thermal radiation may have a strong effect on the temperature field if the atmosphere contains an infrared absorbing gas such as vapor, even in small concentrations. This has in particular been shown in the H2P2 series of tests performed in the large-scale PANDA facility at the Paul Scherrer Institute. For these tests an air-helium-steam mixture was compressed with a helium injection, which caused the formation of a hot bubble. The initial vapor volume fraction varied between 0.1 % and 60%. In this paper, we report the results of CFD simulations conducted for the five H2P2 tests. The turbulence model k-ω SST was used, while thermal radiation was considered using the simple P1 model as a default, in conjunction with the Weighted Sum of Gray Gases Model (WSGGM) to specify steam absorptivity. For comparison purposes we also made use of the more advanced Monte-Carlo model for selected experiments. CFD Best Practice Guidelines were employed, in particular through preliminary grid and time-step sensitivity studies.The temperature and helium concentration fields matched the experimental data quite accurately, except for the test with very low vapor content (H2P2_1_2, 0.1% vol. steam), where the temperature was somewhat over-estimated. This may be due to the inadequacy of the radiation models at these extreme conditions. Two major conclusions can be drawn from this study: 1) ignoring thermal radiation can lead to large over-predictions of temperature, even when the steam content is low (order of 1%) and 2) the simple P1 model provides sufficient accuracy. Use of the more sophisticated Monte-Carlo model yielded similar and slightly more accurate results, albeit at a considerably larger CPU expenditure (5–7 times).

Investigation of nozzle geometry and wall roughness effects on diesel injector flow

The flow and design of fuel injector nozzles have a considerable influence on the spray and combustion characteristics of a diesel engine. In-cylinder combustion, atomization, and primary breakdown are all highly influenced by the cavitation and turbulence in the fuel injector nozzle. In this paper, the effect of the nozzle geometry parameters, wall roughness parameters, and pressure difference on the swirl number, mass flow rate, turbulent kinetic energy, and vapor volume fraction is explored. U-type nozzle hole geometry, a well-known benchmark for the injector nozzle flow, is used to evaluate mesh independence and model validation. Large-eddy simulations are performed to provide a precise presentation of the flow structures and turbulent eddies inside the nozzle. Multiphase flow is studied using the mixture model, whereas cavitation is studied using the Schnerr–Sauer model based on the Rayleigh–Plesset equation. We find that the wall roughness parameters have an exciting impact on the discharge coefficient, swirl number, and vapor volume fraction. Due to the non-monotonic dependence of nozzle flow characteristics on the pressure difference and the wall roughness parameters, we can always find such values of these input parameters that render optimal nozzle flow characteristics. In this way, these parameters provide good control of spray formation and consequently on the quality and rate of combustion in the diesel engine.