Boundary Layer Behavior Research Articles

Comprehensive CFD Analysis of Hypersonic Missile Nose Cone

Abstract: This study employs high-fidelity CFD to analyze a hypersonic missile nose cone's aerodynamics and boundary layer behavior (Mach > 5, zero angles of attack) under idealized conditions. The simulation leverages ideal gas assumptions for simplicity while incorporating advanced turbulence models to capture hypersonic flow phenomena. The analysis focuses on pressure distribution across the nose cone to assess shockwave and streamline curvature effects. Lift and drag forces are computed to evaluate overall aerodynamic performance. Critically, the investigation delves into the boundary layer, evaluating parameters like thickness, velocity profile, and potential separation points to understand pressure and temperature variations crucial for heat transfer and flow stability

Numerical solutions for unsteady laminar boundary layer flow and heat transfer over a horizontal sheet with radiation and nonuniform heat Source/Sink

This paper investigates the unsteady laminar boundary layer flow and heat transfer over a horizontal sheet subjected to radiation and a nonuniform heat source/sink. The governing partial differential equations are transformed into ordinary differential equations using similarity transformations and solved via the bvp4c numerical method. The key findings indicate that increasing the unsteadiness parameter leads to a reduction in both velocity profiles and heat flux, while higher values of the Prandtl number reduce thermal boundary layer thickness. In contrast, the radiation and magnetic parameters enhance the temperature profile within the boundary layer. The study offers new insights into the effects of flow parameters on boundary layer behaviour, validated through table and graphical comparisons with existing literature. These findings provide practical approaches for optimizing heat transfer systems in engineering applications.

Numerical Solution of Burgers Equation Using Finite Difference Methods: Analysis of Shock Waves in Aircraft Dynamics

In this research, the Lax, the Upwind, and the MacCormack finite difference methods are applied to the experimental solving of the one-dimensional (1D) unsteady Burger's Equation, a Hyperbolic Partial Differential Equation. These three numerical analysis-solving methods are implemented for accurate modeling of shock wave behavior high-speed flows that are necessary for aerospace engineering design. This research analysis proves that the MacCormack technique is the one that treats the differential equations with second-order accuracy. This method is quite preferred when it comes to numerical simulations because of its advanced level of accuracy. Although the Upwind and Lax methods are slightly less accurate, they show the development of shock waves that give visualizations to better understand the flow dynamics. Also, in this study, the impact of varying viscosity coefficients on fluid flow characteristics by using the lax (a numerical method for solving the viscous Burgers equation) is investigated. This identification of the phenomenon sheds light on the behavior of boundary layers, which, in turn, can be used to improve the design of high-speed vehicles and lead to a greater understanding of the area of ​​fluid dynamics.

Hypersonic Flow past LD-Haack Series, Parabolic Series, Power Series Nose Cone: A Comparative Study

This research paper presents a detailed aerodynamic analysis of three rocket nose cone designs—LD-Haack, Parabolic, and Power Series—under hypersonic conditions ranging from Mach 5 to Mach 12. Using advanced Computational Fluid Dynamics (CFD) simulations in ANSYS Fluent, the study focuses on key aerodynamic parameters, including drag force, drag coefficient, velocity, pressure, and temperature distributions. The results indicate that the Parabolic Nose Cone offers the most favorable aerodynamic performance, with the lowest drag force and drag coefficient across all Mach numbers. This superior performance can be attributed to its ability to streamline airflow and minimize boundary layer separation, effectively reducing pressure drag and limiting the onset of turbulent wake regions. In contrast, the LD-Haack Series Nose Cone, though designed to minimize wave drag at supersonic speeds, shows moderate drag at hypersonic velocities due to its less optimal control of boundary layer behavior. The Power Series Nose Cone, despite its highly tapered shape, experiences the highest drag. This is largely caused by increased flow separation and turbulent wake generation, which exacerbate pressure drag, particularly at higher Mach numbers. These findings highlight the critical influence of nose cone geometry on aerodynamic efficiency and emphasize the importance of optimizing designs for hypersonic applications. This study provides valuable insights for aerospace engineers seeking to reduce drag and improve performance in high-speed flight scenarios.

A multivariate and wavelet-based analysis on the wall pressure fluctuations for propellers in ground effect

This study, conducted at the University of Bristol’s aeroacoustic facility, explores the aeroacoustic characteristics of a 10-inch APC propeller in pusher configuration within ground effect conditions. Tested at a rotational speed of 7000 r/min, the propeller’s performance was evaluated at varying distances from the ground. Wall pressure fluctuations near the propeller were measured at eight radial points, complemented by far-field acoustic measurements. Consistent with previous research, distinctive thrust and torque behaviours were observed when operating both in and out of ground effect. Notably, a significant noise increase of approximately 5 dB was observed on the ground’s reflected side, while a reduction of about 14 dB was detected on the shielded side. Higher-order statistical analysis such as skewness and kurtosis revealed substantial effects of tip vortex impingement in ground effect conditions. This study applies two-point statistics and the Corcos model to analyze propeller-induced wall pressure fluctuations. The coherence function effectively captures the intricate dynamics of pressure variations across different spatial locations and frequencies. This approach offers novel insights into the behaviour of boundary layers and flow-induced pressures in the context of propellers operating in the ground effect. Wavelet decomposition was utilized to differentiate the influences of the boundary layer and the acoustic field. This comprehensive analysis highlights the intricate dynamics of propeller operation in ground effect, contributing valuable insights to the field of aeroacoustic research.

Local nonsimilar solution and heat analysis of mixed convective flow across whole spherical shape with nonisothermal surface temperature

This study investigates the behavior of a mixed convective boundary layer flowing around a rigid spherical shape with non-isothermal wall temperature. The fluid assumed in this examination exhibits both incompressibility and viscosity. The major purpose is to examine the impact of the non-uniform surface temperature on the flow patterns, including velocity outlines and temperature outlines. An examination is conducted on the modified conservation equations of the boundary layer flow utilizing the local non-similarity method. The MATLAB built-in code bvp4c is used to find computational solutions. The outcomes are then shown for both air and water, specifically at a temperature of 21°C. The influence of several factors, such as the mixed convective variable [Formula: see text] and the exponent [Formula: see text] in the wall temperature function [Formula: see text]), is shown in velocity and temperature profiles. In addition, the study computes the local frictional force factor and local wall heat transport factor and compares these values with results from earlier research. Significantly, the study expands upon data made around the lower stagnating point to include other sites within the sphere, thereby offering a thorough comprehension of the whole flowing field.

Wavelet-based approximation for two-dimensional singularly perturbed elliptic problems

In this research article, we explore the application of non-uniform Haar wavelets (NUHWs) to tackle a two-dimensional singularly perturbed elliptic problem (TDSPEP) on an exponentially graded mesh (EGM). The solution to the type of problem considered in this article exhibits boundary layers near the edges x=0 and y=0. Using an EGM, one can resolve the solution’s boundary layer behavior. The proposed method involves the approximation of the highest-order mixed derivative using NUHWs, followed by successive integration to obtain an approximate Haar solution. We conducted an error analysis for the proposed method, which demonstrates that it achieves second-order accuracy. The performance of the method is corroborated in practice through numerical experiments on three examples. The method can be easily used in any programming language.

Effects of roughness on non-equilibrium turbulent boundary layers

The effects of roughness were considered as part of a NATO Advanced Vehicle Technology effort titled ‘Non-Equilibrium Turbulent Boundary Layers at High Reynolds Numbers’ (NATO AVT-349). This paper comments on the current state of understanding of the flow physics and modelling efforts to predict rough-wall boundary layer behaviour. Outer layer similarity to smooth wall flows and Reynolds number effects are discussed for zero, favourable, and adverse pressure gradients based on the results of experiments and numerical simulations. Various types of modelling are considered including Reynolds averaged Navier-Stokes (RANS) models with different roughness and turbulence models, wall-modelled large eddy simulations (WMLES), and resolvent models. Current needs and gaps in present understanding are discussed along with recommendations for future experiments and computations.

Singular layer physics informed neural network method for plane parallel flows

We construct in this article the semi-analytic Physics Informed Neural Networks (PINNs), called singular layer PINNs (or sl-PINNs), that are suitable to predict the stiff solutions of plane-parallel flows at a small viscosity. Recalling the boundary layer analysis, we first find the corrector for the problem which describes the singular behavior of the viscous flow inside boundary layers. Then, using the components of the corrector and its curl, we build our new sl-PINN predictions for the velocity and the vorticity by either embedding the explicit expression of the corrector (or its curl) in the structure of PINNs or by training the implicit parts of the corrector (or its curl) together with the PINN predictions. Numerical experiments confirm that our new sl-PINNs produce stable and accurate predicted solutions for the plane-parallel flows at a small viscosity.

Influence of real gas properties on aerodynamic stability of a SCO2 centrifugal compressor

The safe operation of closed-Bryton-cycle system is hindered by the nonlinear real gas properties in a supercritical carbon dioxide (SCO2) centrifugal compressor for waste heat recovery in a powertrain system. This paper aims to understand the influence of real gas properties on the aerodynamic stability of a shrouded SCO2 centrifugal compressor designed for waste heat recovery. Firstly, the numerical method was calibrated and validated using experimental results from the Sandia SCO2 centrifugal compressor. Next, based on the numerical method, the stability performance of an inhouse-design shrouded SCO2 compressor was discussed through a direct comparison with the identical compressor using air. The results showed that the performance of the SCO2 compressor was significantly different from that of the air compressor. Particularly, the impeller was the most unstable component featuring a notable recirculating region near the shroud at the leading edge. Further analysis is carried out to understand the discrepancies in the stability performance between the two compressors with different fluids. It is revealed that the boundary layer on the SCO2 impeller suction surface thickens at a faster rate, leading to stronger flow separation. Meanwhile, the stronger accumulation of low-momentum secondary flow near the SCO2 impeller outlet enhances the ‘wake’ structure near the shroud of suction surface at the impeller tailing edge, resulting in considerable backflow. The different behaviors of boundary layer were attributed to pressure gradient normal to the suction surface. Specifically, the pressure gradient on the suction surface for SCO2 impeller is orders of magnitude higher than that of the air impeller. The stronger gradient weakens momentum exchange in the boundary layer, thus increasing the thickness of boundary layer more rapidly along the streamwise direction. Moreover, the boundary layer is pushed towards the shroud of suction surface by the strong pressure gradient, resulting in the evident accumulation of secondary flow nearby. At the meantime, the low-momentum flow near the impeller outlet reduced the inlet flow velocity of the diffuser, causing more recirculation at the top of the vaneless diffuser in all circumferential directions, thus worsening its instability.

Effects of interface friction states on plastic deformation in metal surface and bulk

Interface friction at the tool/die-material interface plays a pivotal role in metal plastic processes, significantly impacting material deformation behavior near the contact surface. This study focuses on understanding friction-induced deformation, particularly the plastic boundary layer and surface expansion behavior, at the tool/die-material interface by employing direct in-situ observations, coupled with high-speed imaging and particle image velocimetry techniques. It proves that interface friction determines the wall-slip behaviors and subsequently results in the non-uniform surface expansion distribution. Moreover, our results indicate that the application of lubricant alters the wall-slip velocity and localized surface expansion by 60% and 76%, respectively, at the contact interface. Based on these observations, a quantitative method for assessing the effectiveness of lubrication is proposed.

Evaluation of Streamline on Aerofoil with Suction Hole in Wind Tunnel

This study looks into the impact of pressure suction holes in the NACA 0012 airfoil on aerodynamic performance. The goal is to use wind tunnel tests to compute the lift and drag forces for the NACA 0012 airfoil with suction holes at various air speeds and angles of attack. The relationship between air speed, angle of attack, drag coefficient, and lift coefficient will be determined by analysing the obtained data. The goal of the research is to better understand the flow patterns and variations in streamlines of the NACA 0012 airfoil at different velocity and attack angles. The test model will use the NACA 0012 airfoil, which is recognised for its symmetrical shape. Suction holes, varying from one to four, will be installed to provide insight into the influence of pressure suction on the boundary layer and streamline behaviour of the airfoil. The study will be carried out in a low-speed wind tunnel within the Fluid Mechanics laboratory, with the streamlines visualised using a smoke generator. This study is significant because it contributes to our understanding of flow characteristics, pressure distributions, and boundary layer control in aerodynamic design. It also provides excellent exposure to wind tunnel testing procedures, aviation industry practises, and continuing airfoil design research. This study adds to the body of knowledge on optimising airfoil performance by evaluating the effect of pressure suction holes on the NACA 0012 airfoil. The findings will be useful to researchers, aerodynamic enthusiasts, and aviation experts, allowing them to further investigate the potential benefits of pressure suction techniques in improving airfoil efficiency and performance.

Molten salt flow visualization to characterize boundary layer behavior and heat transfer in a natural circulation loop

Experimental data for the natural circulation of high-Prandtl number fluids in molten salt systems has not yet been sufficiently studied to ensure safe operation in the event of a loss of forced coolant. A natural circulation loop facility was designed to mitigate major challenges in flow visualization experiments of molten salt. Experiments were conducted with molten salt and water, and four experimental data sets were obtained for each working fluid at increased heater power. Particle image velocimetry (PIV) measurements were performed, and the boundary layer was analyzed as a function of the Prandtl number. Velocity peaks near the walls were found in results for molten salt due to the underdevelopment of the thermal boundary layers, in contrast to the parabolic velocity profile found in results for water. The overall system behavior was characterized using velocity and temperature measurements. Temperature distributions in the loop demonstrated the developing thermal boundary layers at high Prandtl numbers. The wall shear stress was obtained from near-wall PIV measurements to determine the friction factor and a non-dimensional analysis of the boundary layer showed the expected relationship for laminar flow in all test cases. The local and mean Nusselt numbers were calculated and compared between fluids. The local Nusselt number for water stabilized as expected for the laminar flow, while results for salt showed evidence of continually developing flow. Results for the Nusselt number and friction factor were compared with correlations, and the most accurate predictions were identified for the current application.

Into the boundary layer behavior of segmented grinding wheels and its illustration on Ti6Al4V

Segmented grinding wheels, with active abrasive regions and passive slots, have been reported as a promising choice for controlling the grinding force via an intermittent cutting scheme. With an appropriate selection of feed and other operating variables, segmented grinding could mark its merits of improved thermal performance and grinding efficiency, typically in difficult-to-machine aerospace materials. However, the formation of a boundary layer around a rotating grinding wheel is always a barrier to effective cutting fluid delivery in the grinding zone. This article attempts to investigate the boundary layer characteristics of segmented grinding wheels, typically with a comparison of 8-segmented and 32-segmented grinding wheels with a non-porous electroplated structure and its comparison with traditional porous grinding wheel configuration. The regression model proposed in this article can predict boundary layer thickness and tangential air velocity in the grinding zone during the rotation of the wheel. A closer look at flow aspects has been covered using computational fluid flow modeling/simulation, followed by experimental assessments through particle image velocimetry and shadowgraphs. The influence of segmentation and its configuration (typically the number of segments) have been illustrated through a case study of wet grinding on Ti6Al4V.

On the evolution of turbulent boundary layers during flame–wall interaction investigated by highly resolved laser diagnostics

The turbulent boundary layer behavior in the presence of flame–wall interactions (FWI) has an important role on the mass and energy transfer at the gas/solid interface. Detailed experiments resolving the turbulent boundary layer evolution in the presence of FWI are lacking, which impedes knowledge. This work presents a combination of particle image velocimetry (flow field), dual-pump coherent anti-Stokes Raman spectroscopy (gas temperature), and OH laser induced fluorescence (flame topology) measurements to study the evolution of the boundary layer structure in the presence of FWI. Experiments are conducted in a side-wall quenching (SWQ) burner. Findings reveal that the reacting boundary layer flow adheres to the linear scaling law u+=y+ in the viscous sublayer until y+ = 5. Beyond y+ = 5, the flame modifies the velocity and temperature field such that the uz+ streamwise velocity deviates from the viscous sublayer and the law-of-the-wall scaling in the log-layer with uz+ being smaller than that of the non-reacting flow (the subscript z refers to the streamwise coordinate and is used throughout this manuscript). As the fluid approaches the flame impingement location at the wall, the gas temperature increases significantly, causing a threefold increase in kinematic viscosity, ν. Although the near-wall streamwise velocity gradient d〈Uz〉/dy|y=0mm decreases, the larger increase in ν reduces uz+ and leads to the deviation from the law-of-the-wall. Downstream the flame impingement location, ν is relatively constant and uz+ values begin to approach those of the law-of-the-wall. Trends are presented for SWQ and head-on quenching flame topologies, and are intended to help development of more accurate wall models.

Experimental and numerical study on flow field characteristics of a combustion chamber with double-stage counter-rotating swirlers

To discover a good predictive turbulent model and reveal the mechanism of turbulent mixing enhancement, a new combustion chamber equipped with a double-stage counter-rotating swirler with vane angles of both stages as 45° is proposed and the flow field characteristics are explored by combining 2D-PIV experiment and Reynolds averaged numerical simulation (RANS). Firstly, the performance of various turbulence models in predicting the flow field characteristics is evaluated by comparing them with experimental results. The study concludes that the RNG k-ε turbulence model exhibits superior performance in predicting velocity distribution, recirculation zone length, and vorticity distribution. Hence, it is selected to analyze the influence of the Reynolds number (Re) of swirlers on the flow field characteristics. In this study, seven Re numbers ranged from 5425 to 54,245 were selected for analysis. Through comparison, it appears that changes in Re number have a strengthening effect on the flow field at various locations, including the recirculation zone, wall surface, and shear layer. This suggests that Re number has an influence on turbulence or boundary layer behavior. Interestingly, there seems to be a critical value for Re number of 21,698, which may be related to a competition between Re number and wall effects.

Scaling laws for natural convection boundary layer of a Pr > 1 fluid on a vertical solid surface subject to a sinusoidal temperature in a linearly-stratified ambient fluid

The understanding of the transient behavior of natural convection boundary layer (NCBL) on a heated vertical solid surface under various heating conditions is of fundamental significance and application importance. In this study, scalings for the parameters representing the behavior of unsteady NCBL flow of a linearly-stratified Pr > 1 fluid on a semi-infinite vertical solid surface heated with a time-varying sinusoidal temperature at different development stages are developed with a scaling analysis, in terms of Ra, Pr, s, and fn, which are the Rayleigh number, Prandtl number, stratification number, and frequency of the sinusoidal temperature, respectively. These scalings are validated and quantified with a series of numerical simulations over wide ranges of Ra, Pr, s, and fn. The frequency of the fluctuations experienced by the NCBL behavior at the transitional stage, due to the stratification of the ambient fluid, is also analyzed, and it is shown that the previously obtained scaling for the unsteady NCBL case with the constant heat flux heating condition is basically applicable for the current case, Ra and fn have additional effects as well due to the time-varying nature of the applied temperature.

Fitted Tension Spline Scheme for a Singularly Perturbed Parabolic Problem With Time Delay

A fitted tension spline numerical scheme for a singularly perturbed parabolic problem (SPPP) with time delay is proposed. The presence of a small parameter ε as a multiple of the diffusion term leads to the suddenly changing behaviors of the solution in the boundary layer region. This results in a challenging duty to solve the problem analytically. Classical numerical methods cause spurious nonphysical oscillations unless an unacceptable number of mesh points is considered, which requires a large computational cost. To overcome this drawback, a numerical method comprising the backward Euler scheme in the time direction and the fitted spline scheme in the space direction on uniform meshes is proposed. To establish the stability and uniform convergence of the proposed method, an extensive amount of analysis is carried out. Three numerical examples are considered to validate the efficiency and applicability of the proposed scheme. It is proved that the proposed scheme is uniformly convergent of order one in both space and time. Further, the boundary layer behaviors of the solutions are given graphically.

A Parametric Kinetic Solver for Simulating Boundary-Dominated Turbulent Flow Phenomena

Boundary layer flow plays a very important role in shaping the entire flow feature near and behind obstacles inside fluids. Thus, boundary treatment methods are crucial for a physically consistent fluid simulation, especially when turbulence occurs at a high Reynolds number, in which accurately handling thin boundary layer becomes quite challenging. Traditional Navier-Stokes solvers usually construct multi-resolution body-fitted meshes to achieve high accuracy, often together with near-wall and sub-grid turbulence modeling. However, this could be time-consuming and computationally intensive even with GPU accelerations. An alternative and much faster approach is to switch to a kinetic solver, such as the lattice Boltzmann model, but boundary treatment has to be done in a cut-cell manner, sacrificing accuracy unless grid resolution is much increased. In this paper, we focus on simulating the boundary-dominated turbulent flow phenomena with an efficient kinetic solver. In order to significantly improve the cut-cell-based boundary treatment for higher accuracy without excessively increasing the simulation resolution, we propose a novel parametric boundary treatment model, including a semi-Lagrangian scheme at the wall for non-equilibrium distribution functions, together with a purely link-based near-wall analytical mesoscopic model by analogy with the macroscopic wall modeling approach, which is yet simple to compute. Such a new method is further extended to handle moving boundaries, showing increased accuracy. Comprehensive analyses are conducted, with a variety of simulation results that are both qualitatively and quantitatively validated with experiments and real life scenarios, and compared to existing methods, to indicate superiority of our method. We highlight that our method not only provides a more accurate way for boundary treatment, but also a valuable tool to control boundary layer behaviors. This has not been achieved and demonstrated before in computer graphics, which we believe will be very useful in practical engineering.

The mean wall-normal velocity in turbulent boundary layer flows under pressure gradient

Using a combination of proper variable transformation and integral methods, we rigorously derive an analytical formulation for the mean wall-normal velocity in turbulent boundary layers (TBLs) subjected to arbitrary pressure gradients. The accuracy and robustness of this novel formulation are validated extensively through comparisons with two independent sets of numerical simulation data, demonstrating excellent agreement in both near-equilibrium and non-equilibrium TBLs. In addition, the robustness of the analytical formulations to various choices of boundary-layer edge definition is further confirmed in non-equilibrium TBLs. Our formulation includes a streamwise derivative term, which has minimal significance in near-equilibrium TBLs but plays a crucial role in determining the mean wall-normal velocity in non-equilibrium TBLs. Moreover, we investigate the physical significance of the pre-factors associated with the mean wall-normal velocity components, and unveil a close connection between a previously defined pressure gradient parameter and the ratio of these pre-factors in the analytical equation governing the mean wall-normal velocity. The insights gained from the examination of the pre-factors and their connection to the pressure gradient parameter offer valuable knowledge for interpreting and predicting the behaviour of turbulent boundary layers in various practical applications.