In this article, the significant characteristics of wave transmission and boundary layer influence is studied for an incompressible fluid flowing through a long elastic tube using lumped parameter model. An ameliorated version of the lumped parameter model is derived, where the flow impedance is linked with Womersley number to understand the phenomena of fluid wall interaction, especially in human airways. To analyze the the flow phenomena through tubes, the flow governing equations are transformed through the Bessel series. We have observed that for the low value of Womersley number, there is a phase difference between pressure and flow rate, which produces a frequency-dependent flow impedance. The physiological relevance of this result is especially shown in the nasal-pharynx during breathing. The results are validated by ANSYS based numerical simulation as well as by experimental results.

Equivalent sand grain roughness is required for estimating friction factor for engineering applications from empirical relation via Haalands equation. The real surfaces are different from the sand grain profile. The correlations for friction factor were derived from use of discrete roughness elements with regular shapes such as cones, bars etc. The purpose of the paper is to derive analytical expression of friction factor for a 2 dimensional semi-cylindrical roughness (not exactly a 3 dimensional sand grain but for the circular profile of cross- section) using Navier Stoke equation and mixing length theory. This is compared with the modified series mathematical representation of Haalands equation for friction factor in terms of equivalent sand grain roughness. The comparison is valid for high Reynolds number where the velocity profile is almost flat beyond boundary layer and approximately linear all throughout the boundary layer. The high Reynolds number approximation for Haalands equation is derived and the series form of the friction factor compares approximately with the series form derived from first principles, where in the exponents of the series expansion are close.

Theoretical analysis of the entrance hydrodynamics of microchannels is an important design aspect in connection with the development of microfluidic devices. In this paper, pressure-driven fluid flow in the entrance region of two infinite hydrophobic parallel plates with dissimilar slip-velocities is analytically modelled. The linearized momentum equation is solved by applying the Navier-slip model at the boundaries to achieve the most generalized two-dimensional form. The velocity profile is obtained by combining the developed and developing velocities, which is estimated by invoking the separation of variable method. It is observed that the velocity profile is asymmetric and the shear-free region can be shifted from the geometrical central line by altering the wall hydrophobicity. Moreover, the zero shear zone is transferred more towards the surface having high hydrophobicity. The expression for wall shear stress is obtained analytically using Newton's law of viscosity. Moreover, the boundary layer growth from the upper and lower walls are found to be entirely different and they merge at the entrance length and is noticed to be off-setted from the geometric centre-line. The effect of slip-length on the entrance length is analysed and an empirical correlation is deduced.

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.

Impinging circular free-surface water jets are used in challenging cooling and cleaning tasks. In order to develop simulation models for process optimization, validation data are required, which are currently not available. Therefore, the flow field of these jets is studied for the first time with the novel laser Doppler velocity profile sensor. The mean velocity field and fluctuations are measured within the stagnation and adjacent redirection region for radial coordinates up to three times the nozzle diameter. In the examined parameter range with jet velocities up to 17 m/s and nozzle diameters up to 5.2 mm, i.e., Reynolds numbers up to 69 500, thin films of a few hundred micrometers are formed, which hinder the measurement with common optical measuring systems. Based on the measurement results, a comparatively low-cost volume of fluid simulation model is developed and validated that presumes a relaminarized film flow. The profiles measured and the simulated flow show very good agreement. In the future, the simulation model provides a basis for process optimization and the innovative measurement technology used will prospectively provide further detailed insights into other flows with high velocity gradients.

Enhanced longitudinal heat transfer in viscous, laminar, single-phase, oscillatory channel flow is investigated in this paper. Kurzweg (ASME J. Heat Transfer-Trans. ASME. 107 , 1985) analyzed this case theoretically and derived a correlation for a nondimensionalized effective thermal conductivity in terms of Prandtl and Womersley numbers. The present investigation contributes analysis of limiting cases and physical interpretation to the results of Kurzweg. A simplified model with isothermal walls is proposed, applicable if working fluid and channel wall material exhibit sufficiently large differences in thermal inertia. Examined over a wide range of Womersley numbers, this model reveals six distinct regimes characterized by the Prandtl number of the fluid. The respective thickness of hydrodynamic and thermal boundary layers relative to the channel width is relevant in this context. Maximum effective thermal conductivity is attained when the thermal boundary layer expands over the full channel width. The influence of Womersley number is discussed and explained in terms of the interplay of hydrodynamic and thermal flow characteristics. These patterns reveal either quasi-steady parabolic or oscillating bulk characteristics. The importance of the thermal boundary layer thickness motivates the introduction of a new nondimensional group, making it easier to classify the various regimes of enhanced longitudinal heat transfer.

An experimental investigation on the flow separation of a hypersonic laminar boundary layer flow over a compression ramp with angles of 32 deg, 36 deg, and 40 deg is carried out in a Mach 5 hypersonic wind tunnel. The detailed structures are measured by particle image velocimetry (PIV), and some typical flow structures, such as a shear layer, separation shock, recirculation zone and reattachment shock, are clearly captured. In the 32 deg compression ramp flow, the hypersonic laminar flow does not experience flow separation, and the boundary layer always attaches to the ramp surface. When the ramp angle increases to 36 deg, a typical flow separation appears in the hypersonic laminar flow, and a shear layer and reattachment shock arise within the flow field. As the ramp angle increases to 40 deg, the separation shock moves upstream, the reattachment shock moves downstream, and the recirculation zone expands. Proper orthogonal decomposition (POD) analysis is performed on the velocity contours for three cases, revealing the spatial structure of the flow field. As the ramp angle increases, the coherent flow structures are captured more effectively by less POD modes, and there are more coherent structures in the flow field of a large-angle compression ramp. Finally, numerical investigations of the flow separation on three different compression ramps are carried out, and the simulation results are consistent with the measurement results.

In a boundary layer ingesting (BLI) propulsion system, the fan is continuously exposed to inflow distortions. The distorted inflows lead to nonuniform loss distributions along the radial and circumferential directions. Since the rotor tip suffers from higher intensive distortion, the local loss increment is a major contributor to the BLI fan performance penalty. To explore the effects of distorted inflows on tip leakage flow evolutions and associated mechanisms for increased loss in a BLI fan, three-dimensional full-annulus unsteady simulations are conducted. Results show that about 54% of total additional losses due to distortion are formed in the tip region and more than 80% of tip region entropy generation is related to the tip leakage flow. The intensities of leakage vortex–shock interactions vary at different annulus locations. When the rotor moves into the distorted region, the vortex–shock interaction is weaker than the undistorted locations due to attenuated leakage flow. At the locations where the rotor is moving out from the distorted region, the vortex–shock interaction is notably enhanced because the front part of the blade tip airfoil suffers a higher load, resulting in a rapid vortex core expansion and eventually vortex breakdown. The increase of flow blockage in the front section of blade tip passages at local circumferential positions leads to a corresponding rise of flow loss. The findings in this study highlight the impacts of tip leakage flow on aerodynamic loss of fan working under BLI inflow distortion and provide improved understandings of loss mechanisms in a BLI fan.

Computational fluid dynamics (CFD) simulation of flow over a three-dimensional (3D) axisymmetric hill presents a unique set of challenges for turbulence modeling. The flow past the crest of the hill is characterized by boundary layer separation, complex vortical structures, and unsteady wake flow. As a result, traditional eddy-viscosity Reynolds-averaged Navier–Stokes (RANS) models have been found to perform poorly for this benchmark test case. Recent studies have focused on the use of large eddy simulation (LES) and hybrid RANS–LES (HRL) methods to improve accuracy. In this study, several different HRL models are investigated, and results from the different models are evaluated relative to each other, to an eddy-viscosity RANS model, and to previously documented high-fidelity LESs and experimental data. Results obtained from the simulations in terms of mean flow statistics, surface pressure distribution, and turbulence characteristics are presented and discussed in detail. Results indicate that eddy-viscosity based HRL models can improve predictions over comparable eddy-viscosity based RANS models such as the shear stress transport (SST) k– ω model used in this study, but only when the development of turbulent velocity fluctuations in the separated shear layer and recirculation region are well resolved.

Temporally developing direct numerical simulations (T-DNS) are performed for freestream turbulence induced bypass transition flow with zero-pressure gradient over a flat-plate boundary layer for a range of freestream turbulence intensities ( Tu ) of 1.4 % to 6 % . The objective is to understand the role of pressure–strain terms on bypass transition onset and to propose and validate a phenomenological hypothesis for the identification of a robust transition onset marker for use in transition-sensitive Reynolds-averaged Navier–Stokes (RANS) simulations. Results show that transition initiates at a location where the slow pressure–strain term becomes more dominant than the rapid term in the pretransitional boundary layer region. A simple transition onset marker based on one-point statistical quantities is derived from the scaling of the ratio of the slow and rapid pressure fluctuation source terms. The critical value of the marker is found to vary within a narrow range ( ± 2.8 % ) and satisfies previously identified criteria for a robust transition onset marker.

In this paper, the geometry of a supersonic inlet isolator is modified by the introduction of a two-dimensional (2D) bump to control the complex lip shock wave/boundary layer interaction (SWBLI). The bump is of general shape whose profile is designed primarily based on the inviscid theory of oblique shock waves, which accommodates the effect of freestream conditions; particularly, the flow Mach number. Further, the geometric constraints of the inlet are taken into consideration to generate a contoured bump. This well-designed generic bump is tested in the range of flight Mach number of 2.5 to 3.8 through numerical computations. The adopted computational methods are validated with the available experimental data. Results showed that the modified inlet using the present generic bump changes the internal shock structure, weakens the intensity of SWBLI, and subsequently reduces shock reflection phenomena which are prevalent in baseline inlet. The wall characteristics such as separation bubble (SB), skin friction, and total pressure loss are found to be reduced in inlet with bump. The SB in baseline inlet typically corresponds with the geometric profile of the bump. As a result, ramp of baseline inlet is apparently replaced by this generic bump, which eliminates the low momentum fluid adjacent to the wall and the passage of modified inlet is found to be mostly occupied by high momentum supersonic flow. The flow control and associated performance improvement are linked with this modification of supersonic inlet isolator.

In this paper, a comprehensive study has been performed to address the excitation of a separated boundary layer near the leading edge due to surface roughness. Experiments are performed on a model airfoil with the semicircular leading edge at a Reynolds number ( Re c ) of 1.6 × 10 5 , where the freestream turbulence (fst) is 1.2%. The flow features are investigated over the three rough surfaces with the roughness characteristic in the wall unit of 17, 10.5, and 8.4, which are estimated from the velocity profile at a location far downstream of reattachment. The wall roughness results in an early transition and reattachment, leading to a reduction of the laminar shear layer length apart from the bubble length. It is worthwhile to note that although the large-amplitude pretransitional perturbations are apparent from the beginning for the rough surface, the shear layer reflects the amplification of selected frequencies, where the fundamental frequency when normalized is almost the same as that of the smooth wall. The universal intermittency curve can be used to describe the transition of the shear layer, which exhibits some resemblance to the excitation of the boundary layer under fst, signifying the viscous effect.

Computational study of flow physics inside the mixed compression air intake has been carried out with and without air jets (AJs) at design Mach number of 2.2. Reynolds-averaged Navier–Stokes (RANS) equations were solved with k– ω turbulence model by using commercially available software ansys . The scope of this research is to improve the flow field inside the air intake and efficiency of supersonic air intake by implementing AJs on the ramp surface. An array of AJs containing two, four, and five AJ holes, respectively, of 1 mm each has been made on the ramp surface perpendicular to the flow with equal spacing between them. The injection pressure through AJ has been kept constant for all the cases. Flow distortion (FD) and total pressure recovery (TPR) were selected to measure the performance of air intake. All the simulations have been performed at a back-pressure ratio of 6. The results obtained suggest that implementation of proper spacing between AJs can improve the performance of air intake due to the mixing of vortices generated by AJs with freestream flow. It is revealed that an array of AJs containing four holes on ramp surface works best and helps in controlling the shock-induced separation.

Fluid flow in saturated porous media imbedded with a solid inclusion may be described by the Darcy–Brinkman equation. When the Darcy number is small, a boundary-layer theory, similar to Prandtl's theory for viscous flow, is established. The pressure and shear forces are predicted for Darcy–Brinkman flows over a variety of solid inclusions.

The discrepancy in the aerodynamic property and flowfield of a symmetric airfoil produced by the stationary and moving ground effect was quantified through surface pressure and particle-image-velocimetry measurements. The results show that the stationary ground effect produced a higher lift than the moving ground due to the flow passage restriction caused by the longitudinal boundary layer developed on its ground surface. In close ground proximity, the formation of a ground vortex beneath the airfoil's leading-edge region speeded up the flow, leading to a lower lift than its moving-ground counterpart. For the moving ground, the ground vortex was absent. In close ground proximity, the moving ground effect generated a larger wake and drag than the stationary ground effect.

This study investigates a new algorithm for modeling viscous transonic flow at high Reynolds number cases suitable for unstructured grids. The challenge of modeling viscous transonic flow around airfoils becomes intense at high Reynolds number cases due to a variety of flow regimes encountered, such as boundary layer growth and the shockwave/turbulent boundary-layer interaction, accompanied by large separation bubble. Therefore, it is highly demanded to develop robust and efficient models that can capture the shock-induced problems of turbulent flows for aircraft design purposes. The new model is essentially a hybrid algorithm to address the conflict between turbulence modeling and shock-capturing requirements. A skew-symmetric form of a collocated finite volume scheme with minimum aliasing errors was implemented to model the turbulent region in the combination of a semidiscrete, central difference scheme to capture discontinuities with adequately low numerical dissipation for the minimal effect on turbulent flows. To evaluate the effectiveness of the model, it was tested in three conventional cases. The computational results are close to measured data for predicting the shock locations. This implies that the model is able to predict the scale of the separation bubble and the main characteristics of turbulent transonic flow adequately.

Laminar Bingham fluid flow in the entrance region of a circular pipe is investigated using a momentum integral model. The fully developed flow is uniform in the core region, while the velocity changes in the annular part of the cross section of the pipe. The inlet-filled region concept is adopted. In the inlet region, the boundary layer thickness increases until the size of the plug flow area reaches the fully developed flow size. The model converges to the fully developed solution in the filled region. The model provides the velocity, pressure drop, and skin friction coefficient profiles. The pressure drop results are in good agreement with published experimental data. The flow results asymptotically converge to the fully developed values. In addition, the results are consistent with published Newtonian fluid flow experimental data and theoretical results for the boundary layer thickness, pressure drop, and centerline velocity for small values of the Bingham number.

This study evaluates the influence of transition and turbulence modeling on the prediction of wetted and cavitating tip vortices for an elliptical wing, while investigating the numerical errors. Transition modeling increases the quality of numerical predictions since the assumption of a fully turbulent boundary layer, commonly found in literature, contributes to underprediction of the tip vortex cavity size. By applying the local correlation-based transition model (LCTM) and controlling the boundary layer thickness using different turbulent inflow conditions, the pressure in the vortex was found to reduce by 20% for an Angle of Attack (AoA) of 5 deg. The consequent increase in cavity size was found to be of a similar order of magnitude. At 9 deg AoA, transition always occurs just downstream of the leading edge, making this AoA more suitable to investigate the effect of different turbulence modeling approaches. Azimuthal and axial velocity fields are validated against stereographic-particle image velocimetry (S-PIV) measurements. The time-averaged velocity profiles predicted by delayed detached-eddy simulation (DDES) and improved delayed detached-eddy simulation (IDDES) are close to the experiments; however, no velocity fluctuations and vortex dynamics are observed around the vortex. A comparison of wetted and cavitating simulations shows that the cavity leads to a change in the balance between production and destruction of turbulence kinetic energy, which reduces the turbulent diffusion in and around the cavity compared to wetted flow conditions. Consequently, the vapor flow exhibits the characteristics of a potential flow. Whether this is physically plausible remains to be investigated.

This technical brief presents a flow separation mitigation device, called cavity-recirculator that can be used to control flow separation during shock wave–boundary layer interaction (SBLI) in high-speed intake flows. The cavity-recirculator isolates the flow separation bubble generated at the SBLI spot, thereby thinning the boundary layer and reducing the blockage of the inviscid stream in the duct. The device has a potential application in scramjet engine intakes/isolators. The cavity-recirculator was tested on a single-ramp-compression intake model in a hypersonic shock tunnel, in a freestream of Mach 8 (±0.1). The device operation and effectiveness were assessed by flow visualization and pressure measurements in the test model. The measurements and visualization displayed a mitigation of flow separation through an improved flow field with a single shock train and the absence of flow separation shock, in the inlet.

An experimental campaign dedicated to the characterization of the wall-normal velocity correlations in a zero pressure gradient turbulent boundary layer was performed. A double set of laser Doppler velocimetry (LDV) benches were used to access two-point two-time correlations of the wall-normal velocity. The measurements analysis confirms several important hypotheses classically made to model wall pressure spectra from the velocity correlations. In particular, the ratio of the wall-normal Reynolds stress to the turbulent shear stress is confirmed to exhibit a large plateau in the logarithmic region. In addition, Taylor's hypothesis of frozen turbulence is well recovered for the wall-normal velocity fluctuations. The convection velocity for the wall-normal velocity fluctuations is also shown to evolve across the boundary layer, according to the mean velocity profile. Furthermore, the decorrelation time scale of velocity correlations appears to be increasing throughout the boundary layer thickness in accordance with the increase of the convection velocity. The results obtained with this original campaign will help improving models for wall pressure spectra, especially those based on the resolution of the Poisson equation for the pressure for which the wall pressure correlations are related to the wall-normal velocity correlations.