Thick Boundary Research Articles

Simulation of heat transfer performance of silicone-based insulation coatings

In order to investigate the heat transfer properties and insulation effect of silica-based insulation coating in pipe insulation, an ANSYS workbench is used, in this research work, to establish a thermal insulation model for heat transport pipes. The simulation study is carried out for silicon-based insulation coating, aerogel, aluminium silicate fibre, calcium silicate board, and other insulation materials with different thicknesses, different insulation structures, and different pipeline temperatures to compare their insulation effects, and the simulation results are verified with the tests that are carried out on the actual thermal pipelines, which show that silicon-based insulation coatings have a better thermal insulation effect than aluminium silicate fibre and calcium silicate board under the same boundary conditions and thickness, silicon-based insulation coatings have a better thermal insulation effect when the temperature is higher than 300°C.

Improved Differential Quadrature Finite Element Method for Free Vibration of Mindlin Plates with Arbitrary Elastic Boundaries

This paper proposes an improved differential quadrature finite element method (DQFEM) by combining the virtual boundary spring technique with the standard DQFEM, in order to deal with free vibration of Mindlin plates with arbitrary elastic constraints. The incorporation of the virtual boundary spring technique makes it easy to impose general elastic constraints including some classical boundary conditions and avoids the deficiencies of the classical elimination method, which is widely used to process boundary conditions. The improved DQFEM formulation for rectangular and curvilinear quadrilateral elements is established. Convergence characteristics of the present approach are discussed, and the minimum number of nodes to derive convergent results and the appropriate value of the boundary spring stiffness to simulate classical boundary are obtained. Numerical examples are carried out for Mindlin plates with various boundary conditions and thickness ratios, covering both rectangular and irregular geometries. By numerical comparisons, the high accuracy and the remarkable efficiency of the present method are demonstrated. Additionally, adopting the virtual spring boundary can improve the efficiency to some extent compared with the standard DQFEM.

Experimental study on the evolution characteristics of near-surface airflow in limited waters

气流作为湖泊、湿地等有限水域的主要驱动力之一，其演化特征是研究水-气间能量与物质传递的基础，决定了水域水环境与水生态格局，具有重要研究意义.采用室内风洞水槽，通过设置不同试验风速，研究近水面气流与风速和吹程的响应关系与演化特征，并将光滑壁面条件下的气流特征作为试验对照组，分析时间域内风速垂向分布形式、摩阻风速、特征粗糙度等变化规律，剖析频率域内风速的主频变化与波致气流边界层厚度等参数的分布特征.结果表明：近水面时均风速符合对数分布，摩阻风速与特征粗糙度均与风速呈正相关，且同等风速与吹程条件下两者均大于光滑壁面条件，波致气流边界层厚度与风速和吹程均呈正相关.分析了采用风速作为气流动力参数存在不妥的原因，认为采用摩阻风速或切应力作为气流动力参数更具合理性，基于前人研究数据的统计分析，给出了特征粗糙度与风速、吹程和水深的回归关系式.探讨了气流-风浪“同频率”的互馈模式，发现波致气流边界层厚度不只与波长有关，还受波高、波周期和水深等多因素影响，建立了考虑风浪非线性特征的波致气流边界层厚度关系式.;As one of the main driving forces of limited water areas such as lakes and wetlands, the evolution characteristics of airflow are the basis for the study of water-air energy and material transfer, which determines the water environment as well as water ecological pattern of water area, and has important research significance. Using wind tunnel flume, by setting different wind speeds, the response relationship and evolution law of near-surface airflow with wind speed and blowing distance were studied, particularly, flow characteristics under the condition of smooth wall were taken as the test control group, vertical distributions of wind speed, friction wind speed, roughness and so on were analyzed in time domain, and domain frequency change of wind speed and boundary layer thickness of wave-induced airflow are analyzed in the frequency. Results show that the average wind speed near the water surface conforms to the logarithmic distribution, the friction wind speed and characteristic roughness are all positively correlated with the wind speed, and both of them are greater than the smooth wall condition under the same wind speed and blowing distance, and the wave-induced airflow boundary layer thickness is positively correlated with the wind speed and blowing distance. The reasons for the improper use of wind speed as the aerodynamic dynamic parameter are analyzed, and it is considered that it is more reasonable to use friction wind speed or shear stress as the aerodynamic dynamic parameter, and the regression relationship between characteristic roughness and wind speed, blowing distance and water depth is given. The mutual feed model of airflow and wind wave with same frequency is discussed, it is found that the thickness of the wave-induced airflow boundary layer is not only related to the wavelength, but also affected by wave height, wave period and water depth, and the relation formula of the wave-induced airflow boundary thickness considering the nonlinear characteristics of wind and wave is established.

Research on the uniqueness and algorithm of multi-parameter identification in coupling thermal acoustic and solid problem

<p indent="0mm">In the coupled thermal-acoustic solid field, we consider the identification problem of initial boundary value from the boundary measurements of temperature and ultrasonic propagation time to reconstruct the boundary heat flux and thickness of a solid structure simultaneously. Through rigorous theoretical analysis, the uniqueness of the simultaneous identification is demonstrated, which provides theoretical support for engineering applications. By reformulating an inverse problem as an optimization problem and deriving the adjoint equation, we propose an efficient alternating iteration algorithm for solving the inverse problem. Rigorous convergence analysis of the proposed algorithm is performed. Finally, the reliability and feasibility of the algorithm are verified via numerical examples, and the algorithm’s accuracy is verified by comparing it with a single-parameter identification algorithm that only identifies heat flux.

Topological description of near-wall flows around a surface-mounted square cylinder at high Reynolds numbers

This study topologically describes near-wall flows around a surface-mounted cylinder at a high Reynolds number ( $Re$ ) of $5\times 10^4$ and in a very thick boundary layer, which were partially measured or technically approximated from the literature. For complete and rational flow construction, we use high-resolution simulations and critical-point theory. The large-scale near-wake vortex is composed of two connected segments rolled up from the sides of the cylinder and from the free end. Another large-scale side vortex clearly roots on two notable foci on the lower side wall. In the junction region, the side vortex moves upwards with a curved trajectory, which induces the formation of nodes on the ground surface. In the free-end region, the side vortex is compressed, which results in a smaller trailing-edge vortex and its downstream movement. Only tip vortices are observed in the far wake. The origin of the tip vortices and their distinction from the near-wake vortex are discussed. Further analyses suggest that $Re$ independence should be treated with high caution when $Re$ increases from 500 to ${O}(10^4)$ . The occurrence of upwash flow behind the cylinder strongly depends on the increase in $Re$ , the mechanism of which is also provided. The separation–reattachment process in the junction region and the trailing-edge vortices are discovered only at a high $Re$ . The former should significantly affect the strength of the side vortex in the junction region and the latter should cause a sharp drop in pressure near the trailing edge.

PROPELLER CAVITATION AND INDUCED VIBRATION

The demand to increase the efficiency of propellers has led to optimized propeller blade designs finding their way into the construction of high-powered commercial vessels, such as containers or LNG carriers and certain categories of passenger vessels, to mention but a few. It has become increasingly common to see the propeller tip rotate closer to the hull surface, sweeping the thick turbulent boundary layer attached to the hull, causing fluid structure interaction. At the same time, increasing the loading on marine propellers can lead to problems, such as noise, hull vibration, and cavitation. The degree above which, such phenomena as propeller cavitation can be the main perpetrators for intensive vibration during operation, their diagnosis and the solutions to mitigate this risk, such as the use of vortex generators, are discussed here, taking into account cost and longevity of the vessel as well as the involvement of classification rules.

Towards Localized Tactile Feedback on Touch Surfaces: Finite Element Analysis of a Vibrating Touch Screen Actuated by Piezo Patches

Surface haptics technologies offer an augmented user experience by providing a unique and distinctive interaction between the finger and touchscreen. In this study, we focus on a touch screen design to display vibrotactile tactile feedback to the user through piezo patches located on its surface. We investigated the effects of boundary conditions, piezo configurations, and materials of the touch surface and piezo patches that will achieve the highest deformation on the touch surface, considering the most sensible human tactile perception frequency using the ANSYS FEM software package. In our analysis, we used three different touch surface and piezo patch materials, three different boundary conditions, four different piezo patch locations, and three different touch surface thicknesses. The results showed that the boundary conditions and thickness of the glass have a significant effect on the first natural frequency of the touch surface, and the results leading to best human tactile perception were obtained by fixing four piezo patches at four sides of the touch surface. Based on the determined configuration in the modal analyses, we performed a response surface optimization study to estimate the geometry of the touch surface (width, height, thickness), which will result in maximum deformation on the touch surface. We achieved the best configuration (max total deformation at about 250 Hz first modal frequency) with 160 × 90 × 0.28 mm and 190 × 110 × 0.4 mm dimensions. In the future, we will develop models to render localized tactile feedback on a touchscreen-based on piezo patches operating at various combinations (i.e., sequence, amplitude, frequency), which will be predicted based on the FEM simulations.

Effect of porosity and skew edges on transient response of functionally graded sandwich plates

This work for the first time presents the effect of porosity and skew edges on the transient response of functionally graded material (FGM) sandwich plates using a layerwise finite element formulation. Two configurations of FGM sandwich plates are considered. In the first configuration, the top and the bottom layers are made of the FGM and the core is made of pure metal, whereas in the second configuration, the bottom, core and the top layers are made of pure metal, FGM and pure ceramic, respectively. Four micromechanics models based on the rule of mixture are used to model porosity for these two configurations of FGM sandwich plates. A layerwise theory based on a first-order shear deformation theory for each layer that maintains the displacement continuity at the layer interface is used for the present investigation. An eight-noded isoparametric element with nine degrees of freedom per node is used to develop the finite element model (FEM). The governing equations for the present investigation are derived using Hamilton’s principle. A wide range of comparison studies are presented to establish the accuracy of the present FEM formulation. It has been shown here that the parameters like skew angle, porosity coefficient, volume fraction index, core to facesheet thickness ratio and boundary conditions have a significant effect on the transient response of FGM sandwich plates. Also, the present finite element formulation is simple and accurate.

Improved (BH)max and squareness in diffusion-processed hot-deformed Nd-Fe-B magnets by self-diffusion process under pressure

To recover the remanence (or maximum energy product ((BH)max)) and squareness with high coercivity in diffusion-processed hot-deformed Nd-Fe-B magnets, new efforts have been made in this work. Annealing at a selected temperature of 800 ℃ under pressure was applied to the hot-deformed magnets diffused by the Nd70Cu30 or Nd70Cu15Ga15 alloy. After this process, the thick powder boundary phase dissolved in the matrix and diffused into the intergranular regions. The c-axis misalignment of Nd2Fe14B grains near the diffusion surface was significantly improved, leading to increased remanence by 0.10–0.18 T and (BH)max by 47–85 kJ/m3 in the two diffusion-processed magnets. The distribution of the powder boundary phase, the proportions of the intergranular Nd-rich phase, the c-axis alignment of grains and the grain sizes from the diffusion surface to the center of the magnets tend to be relatively uniform. The squareness factor of the demagnetization curve increased from 0.89 to 0.95 for the Nd70Cu30-diffused magnet and from 0.85 to 0.93 for the Nd70Cu15Ga15-diffused magnet after the process, returning to the level of the as-deformed magnet. Microstructure analysis and micromagnetic simulations indicate that the improved squareness factor is due to the homogeneous magnetization reversal process caused by the homogeneous microstructure.

Impression of porous body and magnetic field on the double-diffusive mixed convection traits

A numerical investigation is performed to exemplify the impression of a porous triangular body on the double-diffusive mixed convection traits in a cavity under the influence of magnetic field by employing lattice Boltzmann method. Al2O3−H2O nanofluid is considered as a working fluid, and the dynamically varying effective properties are measured through the Koo-Kleinstreuer-Li (KKL) model. The prime objective of the present analysis is to assess the repercussions of Richardson number (Ri = 0, 1, 5 & 10), Darcy number (10−4≤Da≤10−2), nanofluid volume fraction (Φ = 0% & 4%), and Hartmann number (Ha = 0, 25 & 50) on flow, heat and concentration transfer characteristics in and around the porous body with high temperature and concentration. Also, the variation of thermal and concentration mixings, and their uniformities are examined. It is noticed that the flow field intensity is amplified while increasing Da, Ri and Φ, and is reduced while augmenting Ha. Besides, the effect of Ha on the reduction of heat transfer to the enclosure walls is predominant at higher Da. The formation of thick thermal boundary layer along the slant edge of porous body due to the Ri and Da is significantly reduced while including nanoparticle in the base fluid. On contrary, increment in Φ dampens the concentration transfer traits. However, such adverse effect is efficiently controlled by Ri variation. It is found that the Ri enhancement assists Da to significantly augment concentration transfer. Furthermore, the thermal and concentration mixings are mainly governed by Da and Ri. In addition, the nanoparticle inclusion can alter the behaviour of permeability on concentration mixing and its uniformity.

Numerical Study of Effect of Sawtooth Riblets on Low-Reynolds-Number Airfoil Flow Characteristic and Aerodynamic Performance

Riblets with an appropriate size can effectively restrain turbulent boundary layer thickness and reduce viscous drag, but the effects of riblets strongly depend on the appearance of the fabric that is to be applied and its operating conditions. In this study, in order to improve the aerodynamic performance of a low-pressure fan by using riblet technology, sawtooth riblets on NACA4412 airfoil are examined at the low Reynolds number of 1 × 105, and the airfoil is operated at angles of attack (AOAs) ranging from approximately 0° to 12°. The numerical simulation is carried out by employing the SST k–ω turbulence model through the Ansys Fluent, and the effects of the riblets’ length and height on aerodynamic performance and flow characteristics of the airfoil are investigated. The results indicate that the amount of drag reduction varies greatly with riblet length and height and the AOA of airfoil flow. By contrast, the riblets are detrimental to the airfoil in some cases. The most effective riblet length is found to be a length of 0.8 chord, which increases the lift and reduces the drag under whole AOA conditions, and the maximum improvements in both are 17.46% and 15.04%, respectively. The most effective height for the riblet with the length of 0.5 chord is 0.6 mm. This also improves the aerodynamic performance and achieves a change rate of 12.67% and 14.8% in the lift and drag coefficients, respectively. In addition, the riblets facilitate a greater improvement in airfoil at larger AOAs. The flow fields demonstrate that the riblets with a drag reduction effect form “the antifriction-bearing” structure near the airfoil surface and effectively restrain the trailing separation vortex. The ultimate cause of the riblet drag reduction effect is the velocity gradient at the bottom of the boundary layers being increased by the riblets, which results in a decrease in boundary thickness and energy loss.

Thickness dependence of phase stability in epitaxial (HfxZr1−x)O2 films

The thickness dependence of the crystal structure in epitaxial $({\mathrm{Hf}}_{x}{\mathrm{Zr}}_{1\ensuremath{-}x}){\mathrm{O}}_{2}$ $(x=0,0.5,1)$ films is demonstrated. X-ray diffraction measurements suggest that the crystal phase changes from the monoclinic to the orthorhombic and tetragonal phases sequentially as film thickness decreases in $\mathrm{Hf}{\mathrm{O}}_{2}$ and $({\mathrm{Hf}}_{0.5}{\mathrm{Zr}}_{0.5}){\mathrm{O}}_{2}$ films. Both films are very thin at the ferroelectric orthorhombic phase $(&lt;5\phantom{\rule{0.16em}{0ex}}\mathrm{nm})$, but the $({\mathrm{Hf}}_{0.5}{\mathrm{Zr}}_{0.5}){\mathrm{O}}_{2}$ films are thicker than the $\mathrm{Hf}{\mathrm{O}}_{2}$ films. In $\mathrm{Zr}{\mathrm{O}}_{2}$ films, the monoclinic phase changes into the tetragonal phase as film thickness decreases. This means that the ferroelectric orthorhombic phase was not observed in the present study. However, ferroelectricity was observed for the present $\mathrm{Zr}{\mathrm{O}}_{2}$ films in the film thickness around the thickness boundary where the tetragonal and monoclinic phases stabilize. We confirmed the field-induced phase transition from the tetragonal to the orthorhombic phase in these $\mathrm{Zr}{\mathrm{O}}_{2}$ films by micro-x-ray diffraction measurement, which suggested that the phase transition takes place due to the small free energy difference between the ferroelectric orthorhombic phase and paraelectric tetragonal phase. Our experimental results agree with theoretical reports of the thickness dependence of the crystal structure in epitaxial films with a surface energy effect.

Numerical simulation of the thermomechanical buckling analysis of bidirectional porous functionally graded plate using collocation meshfree method

This paper presents some new and valuable numerical results for the thermo-mechanical buckling analysis of bidirectional porous functionally graded plates with uniform and non-uniform temperature rise. The strong form formulation is implemented for thermo-mechanical buckling in the framework of higher-order shear deformation theory. The material property with four schemes of porosity distribution of bidirectional porous functionally graded plate is taken by a modified power law. The governing differential equations are accomplished utilizing the principle of virtual works. The multi-quadric radial basis function is implemented for discretizing the governing differential equations. The multi-quadric radial basis function Euclidean norm is modified to analyze the square as well as rectangular plates without changing the shape parameters. Convergence and validation studies are performed to show the accuracy, effectiveness, and consistency of the present meshfree collocation method. The influence of different porosity distributions, span to thickness ratios, aspect ratios, grading index, temperature raise, boundary conditions, and porosity index on thermomechanical buckling load is evaluated. Some novel results for the bidirectional porous functionally graded plate are also enumerated that can be utilized as benchmark results for future reference.

A computational analysis of universal behavior of thermal groove in a moving grain boundary

We report the existence of universal behavior of a mobile thermal groove in polycrystalline thin films using a novel three-dimensional phase-field model. The universal behavior is independent of film thickness, surface diffusivity and grain boundary mobility when grain boundary motion is in steady-state. Moreover, the simulated universal curve shows excellent agreement with Mullins’ theory of mobile grooves for any groove shape. Onset of universality of surface profiles is concomitant with the attainment of steady-state motion of the grain boundary and a constant value of groove depth. On the other hand, in the case of thinner films, the interaction between the groove and the grain boundary leads to partial stagnation of the boundary. Even for grooves attached to decelerating boundaries we observe self-similarity of surface profiles, although this self-similar behavior is different from the ones associated with steady-state boundaries.

Abstract 13024: Excessive Slow Flow and Thick Boundary Layers Cause Non ST Segment Elevation in Patients With Patent Coronary Arteries

Introduction: Many patients arrived to emergency room with atypical chest pain, borderline ST segment elevation, troponin level significantly elevated however the coronary angiogram was normal. Why? Hypothesis: Based on damages by flow disturbances in pipes, our research is built on the hypothesis that flow abnormalities disrupt delivery of oxygenated blood to the myocardium. Our strategy is to use today’s practice of fluid mechanics to unlock the mechanism of non-ST Segment elevation myocardial infarction (non-NSTEMI) and patent coronary arteries. What coronary flow abnormalities were the culprit? Methods: Patients with non-STEMI were enrolled if the coronary arteries were patent. In our new dynamic angiographic protocol, contrast was injected until the index coronary artery was completely opacified. Once the manual injection stopped, the blood moved in, displacing the contrast. The movements and directions of the blood flow in “white” color on top of a “black contrast” background could be clearly analyzed. The main focuses were the types of flows and their duration, direction and length. Results: 12 patients with non-STEMI and patent coronary arteries were enrolled. 100% patients had severe slow flow with prolonged arterial phase (&gt;1.8secs) compared with historical control (0.72 secs) (p&lt;0.05). 83% patients had retention flow with thick stagnant boundary layers at the proximal and mid segment of right coronary artery. The retrograde flow was short (0.18secs). Two patients showed excessive contraction of left ventricle. 4 patients revealed history of intense emotional stress however no sign of adrenergic excess (elevated blood pressure, heart rate or extreme peripheral vasoconstriction). All patients recovered and remained asymptomatic after one year follow-up. Conclusions: In non-STEMI and patent coronary arteries, severe slow flow and prolonged retention of thick boundary layers were the culprits. Besides the ischemia caused by delayed delivery of new blood to myocardium, the prolonged retention of thick boundary layers could prevent the intima from absorbing new oxygenated blood and provoked local ischemia. These new discoveries open new management and preventive options for patients with non-STEMI and patent coronary arteries.

Transient Heat Transfer Characteristics of Twisted Structure Heated by Exponential Heat Flux

This study was conducted to investigate the transient heat transfer characteristics of a twisted structure. The twisted structure was heated according to exponential function (Q=Q0×exp(t/τ), where Q0 is the initial heat generation rate, W/m3; t is time, s; and τ is the period of heat generation rate). A wide range of τ from 37 ms to 14 s was applied for the experimental study. A platinum plate with five pitches (each was 180° twisted with 20 mm in length) was used in the experiment. Helium gas with inlet temperature of 298 K under 500 kPa was used as the coolant. The heat transfer coefficient is found to increase with the decrease of τ, and the transition point was estimated to be at τ≈1s, which means that, when the increasing ratio of heat generation rate satisfies dQdt≥Q0⋅et, the heat transfer enhancement phenomenon will be observed. The response analysis for transient heat transfer at fluid-solid interface was conducted by applying the concept of penetration depth. It is considered that, when the penetration depth is smaller than the thermal boundary thickness, the heat transfer from the interface (wall surface) to the fluid domain is not fully developed during the disturbance.

Reynolds boundary condition realization in journal bearings: Location of oil film rupture boundary with layering-sliding mesh method

A layering-sliding mesh method was developed to realize Reynolds boundary condition in three-dimensional Computational Fluid Dynamics (CFD) analysis of journal bearings. Hybrid dynamic mesh method and pseudo transient analysis were employed to locate the oil film rupture boundary. A numerical model of a full circular journal bearing was established to obtain the steady-state full-Sommerfeld solution. Using the solution as the initial condition, a pseudo transient analysis was performed. The axial boundary of maximum film thickness in the negative pressure region was specified as moving boundary. A dynamic layering method was employed to degenerate the mesh of the divergent clearance region along circumference, and a sliding mesh method was employed to locate the curvature of the moving boundary. The oil film rupture boundary was precisely captured through the criterion of local Reynolds boundary condition. The resulting oil film pressure was validated by comparison with the results of Reynolds equation and published works. The proposed method realized the Reynolds boundary condition in the Navier–Stokes approach. It is an alternative to other cavitation models.

Heat transport mechanism via ion-slip and Hall current in viscoplastic flow along a porous elastic sheet

Heat transfer phenomena occur in most of the natural as well as engineering or manufacturing production plants. Such significant industrial processes utilize various modes for the transportation of heat and energy. In this veneration, the existing research is an attempt to explore heat transmission in a viscoplastic fluid under thermal radiation in the presence of ion and Hall current. The properties of Hall and ion current have enormous uses, particularly when measured in the presence of heat transferal phenomena with suction and injection. The most relevant examples of such mechanisms are fridge spirals, magnetohydrodynamics accelerators, and control generators. Also, the field of biomechanics under the influence of these characteristics is widely used especially in the flowing of blood and magnetic resonance imaging, which helps in producing magnetic resonance images of the thorax, abdomen, brain, kidney, etc. Furthermore, directed medication transport inside the human body needs a tough and heavy magnetic field. Hence, these vital applications of Hall and ion current cannot be overlooked. Transport phenomena are examined past a porous elastic sheet. The prevailing physical model is adapted as a non-linear system of ordinary differential equations by means of proper similarity alterations. The graphical representation shows the physical implication of all related constraints on the velocity and temperature distribution of viscoplastic fluids. Momentum, as well as thermal boundary thickness, is significantly affected by Hall currents and ion slip parameters in the presence of suction/injection phenomena. The temperature of the fluid rises for Eckert number and radiation parameter and also the skin friction coefficient at the surface rises with the suction parameter. An excellent match of numerical results correctly up to three decimal places are obtained for the limiting case when compared to the already published literature.

Free Vibration Analysis of Laminated Composite Spherical Shell with Variable Thickness and Different Boundary Conditions

Free Vibration Analysis of Laminated Composite Spherical Shell with Variable Thickness and Different Boundary Conditions

A Parametric Study on the Fluid Dynamics and Performance Characteristic of Micronozzle Flows

Abstract This study investigates the fluid dynamics and performance characteristics in micronozzle flows with changes in various geometric parameters using Navier–Stokes simulation based on slip wall boundary conditions. The various geometric parameters considered for the study are (1) area ratio with fixed throat dimension and (2) the semidivergence angle variation with no change in area ratio. The simulation results show that the flow choking for micronozzle happens not at the geometric throat; rather pushed downstream to the divergent channel of the nozzle. This is due to the thick boundary layer growth, which reduces the effective flow area and shifts the minimum allowable flow area downstream to the throat. The distance to which the choking point shifts downstream to the throat reduces with Maxwell's slip wall conditions compared to the conventional no-slip wall condition. The downstream movement of the choking point from the throat reduces with an increase in area ratio and with increase in divergence angle with fixed area ratio. This is due to the fact that the increase in area ratio and divergence angle increases the nozzle height at any particular section in the divergent portion of the nozzle. As a result of this, the boundary layer profile also moves upward and the restriction of potential core by the thick boundary layer reduces, which in turn leads to an increase in the effective minimum flow area downstream to the throat.