Flow Drag Research Articles

Design and Computational Modelling of AUV Tunnel Thruster Covers for Efficient Operation

Autonomous underwater vehicles have seen widespread adoption across industrial, scientific, and defence applications. They are typically utilized to perform oceanic mapping, surveillance, and inspection-type missions. Hovering AUVs, used for inspection applications, are over-actuated vehicles incorporating multiple thrusters to enable multiple degrees of freedom control at a low velocity. These vehicles, however, are extremely energy-limited, owing to their restrictive structural design that prohibits large batteries. This necessitates careful hydrodynamic design to best utilize this limited energy storage. Of particular importance are the hydrodynamic propulsion efficiencies of these vehicles. Whilst the external structure of AUV platforms is relatively well-defined and hydrodynamically optimized, one area has seen limited focus and optimization. This is the immediate surroundings of the propulsion geometry and housing. In this body of work, we propose an adaptation to the traditional through-body tunnel thruster geometry of an over-actuated AUV platform. The modification is the inclusion of a retractable internal thruster cover. Subsequently, a comparison is provided between a clean-hull AUV configuration, one with open through-body thrusters, and one fitted with the designed cover geometry. A comprehensive computational fluid dynamics analysis is then converged and assessed using the Reynolds-Averaged Navier–Stokes equations. The drag and local flow fields are determined, where the covers are found to reduce the drag coefficient and total drag of the AUV by 9.51%, primarily due to a reduction of 9.91% in the pressure drag. These findings highlight the increased operational efficiency of the cover geometry and support the adoption of such covers for energy-constrained AUVs.

EXTREME TRANSLATIONAL IMPACT OF TRIPLE-SHOCK CONFIGURATIONS OF BLAST WAVES IN A CONFINED VOLUME OF AN ORBITAL STATION

The translational effects of gas streams, which form after the triple-shock configurations at Mach reflection of blast waves with normal main shock (so-called stationary Mach configurations), were analyzed. Unlike in the case of an elevated explosions of fuel as rocket starts in initially stagnant air, which is considered here as a private case, it was supposed that this shock-wave structure moves in a preceding flow with arbitrary velocity (and corresponding flow Mach number). Analyzing relations of the dynamic pressures across the slipstream, which emanates from the triple point of the Mach reflection, it was shown that the flows after the triple-shock configuration usually differ much in their translational action on surrounding objects. It was found and discussed that some configurations drag the objects initially situated above and below the triple-point trajectory in opposite directions. Moreover, the “trigger” structure was found that remains previous flow drag action on the object above the triple-point trajectory, but switches it to exactly opposite one, if the object is situated below the triple point.

A multilayered homogeneous hydrodynamic cloak realized in a free fluid flow

In recent years, hydrodynamic invisibility cloaks have attracted significant attention from the scientific and engineering communities due to their potential in applications such as fluid flow manipulation, drag reduction, submarine stealth, and biomedical engineering. However, cloaks based on transformation mapping theory typically require porous medium flow, limiting practical implementation. To address this, we draw inspiration from Hele-Shaw flow and develop a homogeneous hydrodynamic cloak composed of multiple layers in free fluid flow at low Reynolds numbers (Re≪1). Through structural optimization, we construct a cloaking shell with ten concentric layers of alternating heights, achieving near-perfect cloaking as demonstrated by simulations and experiments. This non-porous cloak design offers valuable insights into the rapidly advancing field of hydrodynamic metamaterials and enables methods for controlling fluid flow at the microscale, with promising applications in microfluidics.

Drag reduction utilizing a wall-attached ferrofluid film in turbulent channel flow

This study explores the application of a wall-attached ferrofluid film to decrease skin-friction drag in turbulent channel flow. We conduct experiments using water as a working fluid in a turbulent channel flow set-up, where one wall is coated with a ferrofluid layer held in place by external permanent magnets. Depending on the flow conditions, the interface between the two fluids is observed to form unstable travelling waves. While ferrofluid coating has been previously employed in laminar and moderately turbulent flows (Reynolds number $Re<4000$ ) to reduce drag by creating a slip condition at the fluid interface, its effectiveness in fully developed turbulent conditions, particularly when the interface exhibits instability, remains uncertain. Our primary objective is to assess the effectiveness of ferrofluid coating in reducing turbulent drag with particular focus on scenarios when the ferrofluid layer forms unstable waves. To achieve this, we measure flow velocity using two-dimensional particle tracking velocimetry (2D-PTV), and the interface contour between the fluids is determined using an interface tracking algorithm. Our results reveal the significant potential of ferrofluid coating for drag reduction, even in scenarios where the interface between the surrounding fluid and ferrofluid exhibits instability, with observed drag reduction rates up to 95 %. In particular, waves with an amplitude significantly smaller than a viscous length scale positively contribute to drag reduction, while larger waves are detrimental, because of induced turbulent fluctuations. However, for the latter case, slip outcompetes the extra turbulence so that drag is still reduced.

Influence of Rarefaction Degree and Aft-Body Geometry on Supersonic Flows

During atmospheric entry, super-/hypersonic vehicles cross distinct atmospheric layers characterized by large density variations and thus experience different flow regimes ranging from free molecular, transition, slip, to continuous regimes. Due to the distinct modeling strategy between these regimes and complex physical phenomena appearing near the vehicles (boundary-layer/shock interaction, base-flow recirculation, etc.), assessing their aerodynamic properties may be difficult. The present work focuses on supersonic flows around sharp-base geometries in both continuous and slip-flow regimes and aims at highlighting the influence of both rarefaction degree and base geometry on the vehicles’ aerodynamic features. For this purpose, three axisymmetric cone-cylinder geometries with right-angled, rounded, or flared rear parts are considered. Flow visualization, pressure, and drag measurements are carried out at Mach number Ma=4 and Knudsen numbers ranging from Kn=4×10−4 to 1×10−2 in the supersonic rarefied MARHy wind tunnel. The experimental data are compared with numerical results of simulations performed with a continuous-flow Navier–Stokes (NS) solver and two rarefied flows codes: a discrete-ordinate Bhatnagar–Gross–Krook (K) solver and a direct simulation Monte Carlo (SPARTA) solver. While the NS solver overestimates frictional drag as Kn rises, the rarefied K and SPARTA results show satisfactory agreement with experimental data. The latter numerical results highlight the main effects of rarefaction: as Kn increases, shocks become more diffuse, skin friction strengthens (leading to a significant increase in drag coefficients), and the extent of the base-recirculation decreases. Regarding the aft-body geometry, its influence on the base recirculation vanishes with increasing Kn.

Probing Coronal Mass Ejection Inclination Effects with EUHFORIA

Coronal mass ejections (CMEs) are complex magnetized plasma structures in which the magnetic field spirals around a central axis, forming what is known as a flux rope (FR). The central FR axis can be oriented at any angle with respect to the ecliptic. Throughout its journey, a CME will encounter interplanetary magnetic fields and solar winds that are neither homogeneous nor isotropic. Consequently, CMEs with different orientations will encounter different ambient medium conditions and, thus, the interaction of a CME with its surrounding environment will vary depending on the orientation of its FR axis, among other factors. This study aims to understand the effect of inclination on CME propagation. We performed simulations with the EUHFORIA 3D magnetohydrodynamic model. This study focuses on two CMEs modeled as spheromaks with nearly identical properties, differing only by their inclination. We show the effects of CME orientation on sheath evolution, MHD drag, and nonradial flows by analyzing the model data from a swarm of 81 virtual spacecraft scattered across the inner heliospheric. We have found that the sheath duration increases with radial distance from the Sun and that the rate of increase is greater on the flanks of the CME. Nonradial flows within the studied sheath region appear larger outside the ecliptic plane, indicating a “sliding” of the interplanetary magnetic field in the out-of-ecliptic plane. We found that the calculated drag parameter does not remain constant with radial distance and that the inclination dependence of the drag parameter cannot be resolved with our numerical setup.

Can boundary slip destabilize rotating microchannel flows?

Deviation from the traditional no-slip boundary condition due to factors like surface roughness and wettability is of paramount importance in microfluidics and nanofluidics, as it is attributable to its significance in drag reduction, flow control and enhancement and improved mixing. Augmentation in mixing, in turn, is known to strongly correlate with potential instabilities in the flow structure. Reported research studies indicate that slip is an inherent flow stabilizer in microfluidics, to the extent that with sufficient slip, the flow becomes linearly stable against all wavelike disturbances for all wavelengths and Reynolds numbers [“The linear stability of slip channel flows,” Phys. Fluids 34,074103(2022)]. Contrary to such intuitive proposition, here we show that slip effects can destabilize microchannel flows under spanwise rotation, delving on the interplay of rotational forces and slippery hydrodynamics. Our results reveal that increasing the slip length decreases the critical rotation speed, indicating lower rotational effort required to destabilize the flow, whereas the critical Reynolds number for the flow remains effectively unaltered for different slip lengths in a spanwise rotating system. As the slip length increases progressively, the critical rotation number (dimensionless rotational speed) for the onset of instability decreases further, then remains constant up to a certain limit, and subsequently declines with additional enhancement in the slip length. This indicates the potential for deploying customized hydrophobic (slippery) substrates to facilitate transitions from stable to unstable modes by simple tuning of the rotational speed—a paradigm that offers great promise in various applications ranging from materials synthesis to biomedical technology.

Two-dimensional boundary layer receptivity to finite periodic disturbances

Receptivity is the focus and frontier of the research on boundary layer transition and flow drag reduction, but the temporal and spatial evolution of Tollmien–Schlichting waves (T-S waves) is not yet fully investigated, limiting the development of highly efficient laminar flow control techniques. In the present study, the local receptivity problem of the laminar boundary layer on a zero-pressure-gradient flat plate is investigated by using the direct numerical simulation, considering both the temporal and spatial evolution characteristics of the T-S waves. External disturbances at fixed frequencies are introduced in the form of velocity pulsations with different periods to excite T-S waves. The temporal and spatial evolution characteristics of the T-S waves excited by different forms and periods of disturbances are studied. It is found that the amplitude, frequency, and wave velocity of the T-S wave induced by the external multi-period disturbances are different from those induced by the constant disturbances. These conclusions are the same as those of T-S wave induced by wall inhalation. After a further investigation on this particular phenomenon, the influence mechanism of external disturbances on the receptivity process is revealed. This new research finding enriches the instability theory and provides a reference for more efficient applications on active laminar flow control technologies.

A multivariate piecewise interpolation model for viscosity representation and its application to the numerical simulation of non-isothermal polymer melt flow

In this study, a multivariate piecewise interpolation model is introduced to represent melt viscosity based on temperature and shear rate. The model does not require a predefined functional form for the entire data range, instead finding a suitable line between adjacent measured viscosity data points to obtain viscosity as a function of shear rate and temperature. To assess the effect of viscosity representation on polymer melt flow, a two-dimensional (2D) flow past a cylinder problem and a three-dimensional (3D) single screw extruder problem are numerically solved using different viscosity models. The pressure drop (ΔP) from the shift-factor model deviates by more than 10% at an average velocity (Uav) of 1 m/s due to overestimation of viscosity in the high shear rate region. The dimensionless thicknesses of the thermal boundary layer near the channel wall (δT/H) at wall temperature (Tw) of 210 °C are also misevaluated by more than 4% using both the shift-factor model and the Klein model, reflecting their poor viscosity evaluation. It is noteworthy that in all viscosity models, a high Tw leads to the formation of a thin thermal boundary layer, which adversely affects the heat transfer. In single screw extruder applications, viscosity misevaluation in high shear rate regions causes issues in pure drag flow cases, while misevaluation in low shear rate regions causes issues in pure back-pressure flow cases. These analyses highlight the accuracy and versatility of our multivariate piecewise interpolation model compared to existing viscosity models.

Experimental Study on the Effect of Skin Friction Drag and Convective Heat Transfer for Viscoelastic and Pseudoplastic Fluid Flow

Drag Reducing Agents (DRAs) have a huge impact and major concern in engineering and industrial applications. It makes the fluid flow turbulent to laminar, dampens eddy reduces head loss by up to a certain limit, and saves pumping energy costs. Viscosity is the property that dampens eddy due to the viscous effect, which increases the fluidity up to a certain limit. Pseudoplasticity is the shear thinning effect that decreases viscosity when the flow rate increases. So, for the viscoelastic effect, we can increase the concentration up to a certain limit to reduce head loss. Still, during flow due to the pseudoplastic effect, the viscosity will start decreasing which is a negative effect. So, these combined effects are studied to reduce skin friction drag in the pipeline and save energy costs which will be convenient for the food industry, chemical, and medicine industries. In this investigation, investigation is carried out for 0.3 g/L, 0.2 g/L, and 0.15 g/L of xanthan gum in turbulent flow to observe the pressure drop and heat transfer rate. The study reveals that after increasing viscosity the pressure drop reduced significantly. Conversely, the heat transfer rate was also reduced due to the poor mixing effect. A higher performance and less vibration of the pump was also observed. It was concluded that the frictional pressure drop was reduced up to 85 % and the heat transfer rate was reduced by up to 90% by increasing the concentration of the DRA up to 0.3 g/L at 10 LPM than the pure water or base fluid as a working substance on the double pipe heat exchanger. As the heat transfer rate reduced up to 90% with reducing pressure drop another aim of the study was to establish a concentration and flowrate for which the heat transfer rate is maximum and it was found at a concentration of 0.15 g/L of DRAs (drag reducing agents) at 22 LPM (maximum flowrate at this setup).

A volume‐averaging and stochastic turbulence modeling framework for homogeneous roughness‐induced drag in turbulent flows

AbstractThe goal of this work is the formulation of a model for the parameterization of homogeneous roughness‐induced drag in turbulent flow simulations. We characterize rough surfaces using their surface‐area moments of roughness‐peaks. Additionally, we consider a probabilistic self‐similar power law distribution for the roughness heights, in such a way that an assumed set of discrete roughness elements can behave as a probabilistic fractal set. Upon these assumptions, the surface characterization is complete and yields wall‐normal profiles of porosity, average roughness element diameter, and equivalent pore diameter of the roughness affected porous flow. The profiles are supplied to a (pore‐based) Reynolds number and porosity‐based drag parameterization for staggered cylinder arrays available in the literature, as well as a one‐dimensional map‐based turbulence model, the one‐dimensional turbulence (ODT) model. The purpose of the latter is a way to provide the missing effects of the equivalent dispersion tensor in the porous flow close to the rough surface, as well as that of the nonlinear turbulent transport away from the wall. Simulations are then carried out in order to evaluate the effects of two different rough surfaces on a turbulent channel flow, comparing results with existing direct numerical simulation (DNS) data. Overall, reasonable agreement is obtained, which suggests that, by using the proposed model, it is possible to model the effects of rough surfaces on wall‐bounded turbulent flows, without the explicit need of the full topological representation of the surface on the numerical domain. To that extent, one clear flow control application for the suggested approach would be that of drag‐based surface optimization.

Design of integrated evolutionary finite differences for nonlinear electrohydrodynamics ion drag flow in cylindrical conduit model

This research implements an evolutionary optimized finite differences scheme (FDS) for nonlinear electrohydrodynamics ion drag flow dynamics in a cylindrical conduit (EHD-IDFCC). In the scheme, finite differences are exploited to discretize governing expressions of EHD-IDFCC, represented with a nonlinear singular seconder order differential equation, into a nonlinear equations-based system. The fitness function based on residual error is constructed for the FDS-based discretized EHD-IDFCC model. Its optimization is conducted with the global search capability of genetic algorithms (GAs) aided by the local search efficacy of the interior-point method (IPM), i.e., FDS-GA-IPM. The performance of the designed stochastic numerical solver FDS-GA-IPM is evaluated for a variant of the EHD-IDFCC model for different scenarios to measure the effect of axial flow velocity by varying the electric Hartmann numbers, as well as the nonlinearity factor. Statistical interpretations based on histogram illustrations, probability plots, and boxplots in terms of the cost function, mean absolute error (MAE), Thai inequality coefficients (TIC), and coefficient of determination metrics (R2) are used to endorse the accuracy, convergence, stability, and strength of the FDS-GA-IPM.

Flow field characteristics and drag reduction performance of high–low velocity stripes on the biomimetic imbricated fish scale surfaces

AbstractImproving energy efficiency and cost reduction is a perennial challenge in engineering. Natural biological systems have evolved unique functional surfaces or special physiological functions over centuries to adapt to their complex environments. Among these biological wonders, fish, one of the oldest vertebrate groups, has garnered significant attention due to its exceptional fluid dynamics capabilities. Researchers are actively exploring the potential of fish skin's distinctive structural and material characteristics in reducing resistance. In this study, models of biomimetic imbricated fish scale are established, and the evolution characteristics of the flow field and drag reduction performance on these bionic surfaces are investigated. The results showed a close relationship between the high–low velocity stripes generated and the fluid motion by the imbricated fish scale surface. The stripes' prominence increases with the spacing of the adjacent scales and tilt angle of the fish scale, and the velocity amplitude of the stripes decreases as the exposed length of the imbricated fish scale surface increases. Moreover, the biomimetic imbricated fish scale surface can decrease the velocity gradient and thereby reduce the wall shear stress. The insights gained from the fish skin‐inspired imbricated fish surface provide valuable perspectives for an in‐depth analysis of fish hydrodynamics and offer fresh inspiration for drag reduction and antifouling strategies in engineering applications.

A Josephson–Anderson relation for drag in classical channel flows with streamwise periodicity: Effects of wall roughness

The detailed Josephson–Anderson relation equates the instantaneous work by pressure drop over any streamwise segment of a general channel and the wall-normal flux of spanwise vorticity spatially integrated over that section. This relation was first derived by Huggins for quantum superfluids, but it holds also for internal flows of classical fluids and for external flows around solid bodies, corresponding there to relations of Burgers, Lighthill, Kambe, Howe, and others. All of these prior results employ a background potential Euler flow with the same inflow/outflow as the physical flow, just as in Kelvin's minimum energy theorem, so that the reference potential incorporates information about flow geometry. We here generalize the detailed Josephson–Anderson relation to streamwise periodic channels appropriate for numerical simulation of classical fluid turbulence. We show that the original Neumann b.c. used by Huggins for the background potential creates an unphysical vortex sheet in a periodic channel, so that we substitute instead Dirichlet b.c. We show that the minimum energy theorem still holds and our new Josephson–Anderson relation again equates work by pressure drop instantaneously to integrated flux of spanwise vorticity. The result holds for both Newtonian and non-Newtonian fluids and for general curvilinear walls. We illustrate our new formula with numerical results in a periodic channel flow with a single smooth bump, which reveals how vortex separation from the roughness element creates drag at each time instant. Drag and dissipation are thus related to vorticity structure and dynamics locally in space and time, with important applications to drag-reduction and to explanation of anomalous dissipation at high Reynolds numbers.

Effect of particle Froude number on sub-grid effective drag, filtered and residual stresses in fluidized gas-particle flows

Sub-grid effective drag, filtered and residual stresses in the meso-scale of gas-particle fluidized flows are intrinsically affected by underlying micro-scale conditions as well as non-local effects related to macro-scale conditions. In this work we applied microscopic two-fluid modeling to experiment with particle Froude number in order to evaluate the impact of this micro-scale condition over the concerning meso-scale derived sub-grid parameters. We performed highly resolved simulations in periodic domains for particle Froude numbers from 12.21 to 799.22, for a wide range of macro-scale conditions. Results were filtered and classified by ranges of meso-scale markers for the various particle Froude numbers. The particle Froude number was found to considerably affect the structural refinement of the heterogeneous flow fields thereby directly impacting effective drag, filtered and residual stresses. All of those parameters showed systematic behaviors in relation to particle Froude number, thereby providing sound data for new sub-grid modeling propositions.

Drag reduction in hypersonic flows with viscous compressible fluid–solid coupling: The role of elastic spikes and lateral jets

This article introduces a novel fluid–solid interaction (FSI) method designed for high-speed flow scenarios, which addresses the intricate interactions between viscous compressible fluids and elastic solids. The proposed method, grounded in the finite volume method, balances computational efficiency and stability while accurately capturing fluid dynamics and structural elasticity. Validation against experimental and numerical data from previous studies confirmed the algorithm's effectiveness. The validated FSI model is applied to study drag reduction in elastic spikes with lateral jets under hypersonic conditions, highlighting significant changes in flow characteristics due to structural deformation and lateral jets. The study extensively examined the effects of jet total pressure, jet orifice position, and spike material density on drag reduction, deformation, and flow field characteristics. Key findings include the influence of compressible FSI on temperature, pressure, and drag distribution, the benefits of increased jet pressure ratio for thermal protection, the impact of jet position on flow characteristics, and the relationship between spike deformation and material density. This study offers valuable perspectives and effective strategies for structure design and minimizing aerodynamic resistance in superspeed fluid situations. Nevertheless, there are still obstacles to overcome, such as non-linear deformation, thermal coupling, and computational precision, highlighting the necessity for further enhancement of FSI techniques.

Modeling Water Transport in Polymer Electrolyte Membrane Electrolyzers Using a One-Dimensional Transport Model

In this work, we present a water transport model to quantify the movement of water across Nafion® membranes in a proton exchange membrane electrolyzer as a function of varying operating conditions and membrane parameters. This physics-based model is based on the three main water transport mechanisms: diffusion, electro-osmotic drag, and pressure-driven flow. Three sets of equations are obtained to model the movement of water on the cathode side – I. Material balances for hydrogen and water in the flow channel (z-direction), II. Water movement across the membrane in the x-direction, and III. Expressions for variable membrane properties to serve as model inputs. The condensation of water at the cathode is also modeled to understand the respective transport contributions from the vapor and liquid phases. The coupled equation sets are solved numerically with appropriate boundary conditions. An analytical solution is also obtained for the governing differential equation for the mole fraction of water in the vapor phase. This study is perhaps the first effort for a detailed physics-based transport model to predict the water transport in the electrolyzer in one dimension using the actual measured values for the physical parameters of the system. The model results are compared with the experimental data available for water transport, and a good agreement is observed over the wide range of current, temperature and pressure differentials. Further, with the help of this simple transport model, the numerical analysis is performed to delineate the effect of electrolyzer operating conditions on the net water transport across the membrane, water condensation at the cathode, individual contribution of the transport fluxes, and electrolyzer design. Finally, the model is exercised to simulate the dependence of water transport as a function of membrane thickness. This confirms the validity of the current approach of using thin reinforced membranes by electrolyzer fabricators. Figure 1

Influencing heat transfer and drag in magneto-hydrodynamic non-Newtonian fluids with polymer additives: A novel theoretical approach

This article examines the impact of polymers on boundary layer flow and heat transfer in non-Newtonian fluids over a magnetized stretching surface. Using the Oldroyd-B model, Reiner-Philippoff fluid stress deformation, and Maxwell’s equations, the study explores polymer behavior in a magnetic field. Similarity transformations are applied to derive the governing equations, which are solved numerically. The effects of polymers and magnetic fields on drag and heat transfer are illustrated graphically. The analysis highlights that introducing polymers increases skin drag and the Nusselt number while reducing the magnetic flux coefficient. Higher polymer concentrations enhance drag and heat transfer. The magnetic field significantly improves heat transfer and reduces skin drag. The research offers valuable insights into the optimal use of polymer additives to modify heat transfer and drag in non-Newtonian fluid flow, contributing to advancements in fluid dynamics and thermal management technologies.

Drag reduction and degradation by sodium alginate in turbulent flow

The utilization of drag-reducing polymers has long been hindered by their irritancy, corrosiveness, and toxicity across various domains. In this investigation, we explored sodium alginate, a natural drag reducer, for its efficacy in reducing drag and its resilience to shear in millimeter-scale pipelines. Initially, an experimental setup was devised to assess the drag reduction capabilities of sodium alginate at varying concentrations and flow rates using Response Surface Methodology (RSM). The relationship between drag reduction (DR), concentration (C), and flow rate (Q) was established by analyzing the experimental data. Subsequently, variance analysis was employed to validate the data accuracy, with a comparison between predicted and experimental DR values revealing an error margin within ± 20%. Analysis of cyclic shear testing of sodium alginate solution in tubes demonstrated its effectiveness as a shear flow drag reducer. Furthermore, results from laser particle size analysis indicated minimal molecular breakage of sodium alginate during cyclic shear.

Modeling of deposition morphology and characteristic dimensions in material extrusion additive manufacturing

Developing prediction models for deposition strand morphology is critical in Material Extrusion Additive Manufacturing (MEAM) to optimize processes and guide innovative deposition strategies, while advancing our understanding of the flow mechanics during the deposition process.This study aimed to develop an accurate, rapid, and calibration-free model for predicting deposition strand morphology, height, and width. The relationship between the flow field constraints downstream of the nozzle and the deposition morphology was analyzed. By solving the flow front boundary in the region covered by the nozzle, a model for predicting the deposition height and width under constrained conditions was developed. Moreover, a quantitative method for predicting morphological features was offered. The established model is validated through fused deposition modeling (FDM) single-layer single-path experiments, demonstrating superior accuracy. An in-depth analysis of the model errors resulting from the assumptions in the model has been carried out.This work provided deeper insights by modeling the flow front boundary, which helps to understand the distribution of pressure flow and drag flow during the deposition process. The established model has better application potential due to its advantage of not requiring prior calibration of the machine.