Scaling of incipient separation in high speed laminar flows

1994 ◽  
Vol 98 (976) ◽  
pp. 227-231 ◽  
Author(s):  
G. R. Inger
Keyword(s):  
Boundary Layer ◽  
High Speed ◽  
High Reynolds Number ◽  
Theoretical Foundation ◽  
Laminar Flows ◽  
Adiabatic Wall ◽  
Hypersonic Shock ◽  
High Reynolds ◽  
Temperature Concept ◽  
Incipient Separation

Abstract This study provides the theoretical foundation for a well-established, but.heretofore empirical, criterion for incipient separation in moderately hypersonic shock/boundary layer interactions. It is based on an examination of the leading high Reynolds number approximation to triple deck theory, combined with its reformulation in terms of the reference temperature concept. The analysis further provides extensions giving the effects of both low supersonic Mach numbers and non-adiabatic wall temperatures on incipient separation.

scholarly journals Plasma Synthetic Jet Actuators for Active Flow Control

Actuators ◽  
2018 ◽  
Vol 7 (4) ◽  
pp. 77 ◽  
Author(s):  
Haohua Zong ◽  
Matteo Chiatto ◽  
Marios Kotsonis ◽  
Luigi de Luca
Keyword(s):  
Flow Control ◽  
High Speed ◽  
High Reynolds Number ◽  
Mechanical Efficiency ◽  
Synthetic Jet ◽  
High Speed Flow ◽  
Speed Flow ◽  
Jet Actuators ◽  
Characterization Studies ◽  
High Reynolds

The plasma synthetic jet actuator (PSJA), also named as sparkjet actuator, is a special type of zero-net mass flux actuator, driven thermodynamically by pulsed arc/spark discharge. Compared to widely investigated mechanical synthetic jet actuators driven by vibrating diaphragms or oscillating pistons, PSJAs exhibit the unique capability of producing high-velocity (>300 m/s) pulsed jets at high frequency (>5 kHz), thus tailored for high-Reynolds-number high-speed flow control in aerospace engineering. This paper reviews the development of PSJA in the last 15 years, covering the major achievements in the actuator working physics (i.e., characterization in quiescent air) as well as flow control applications (i.e., interaction with external crossflow). Based on the extensive non-dimensional laws obtained in characterization studies, it becomes feasible to design an actuator under several performance constraints, based on first-principles. The peak jet velocity produced by this type of actuator scales approximately with the cubic root of the non-dimensional energy deposition, and the scaling factor is determined by the electro-mechanical efficiency of the actuator (O(0.1%–1%)). To boost the electro-mechanical efficiency, the energy losses in the gas heating phase and thermodynamic cycle process should be minimized by careful design of the discharge circuitry as well as the actuator geometry. Moreover, the limit working frequency of the actuator is set by the Helmholtz natural resonance frequency of the actuator cavity, which can be tuned by the cavity volume, exit orifice area and exit nozzle length. In contrast to the fruitful characterization studies, the application studies of PSJAs have progressed relatively slower, not only due to the inherent difficulties of performing advanced numerical simulations/measurements in high-Reynolds-number high-speed flow, but also related to the complexity of designing a reliable discharge circuit that can feed multiple actuators at high repetition rate. Notwithstanding these limitations, results from existing investigations are already sufficient to demonstrate the authority of plasma synthetic jets in shock wave boundary layer interaction control, jet noise mitigation and airfoil trailing-edge flow separation.

scholarly journals Mixing and chemical reactions in a turbulent liquid mixing layer

1986 ◽  
Vol 170 ◽  
pp. 83-112 ◽  
Author(s):  
M. M. Koochesfahani ◽  
P. E. Dimotakis
Keyword(s):  
Reynolds Number ◽  
Gas Phase ◽  
Turbulent Mixing ◽  
High Speed ◽  
High Reynolds Number ◽  
Schmidt Number ◽  
Mixing Layer ◽  
Entrainment Ratio ◽  
High Reynolds ◽  
Mixed Fluid

An experimental investigation of entrainment and mixing in reacting and non-reacting turbulent mixing layers at large Schmidt number is presented. In non-reacting cases, a passive scalar is used to measure the probability density function (p.d.f.) of the composition field. Chemically reacting experiments employ a diffusion-limited acid–base reaction to directly measure the extent of molecular mixing. The measurements make use of laser-induced fluorescence diagnostics and high-speed, real-time digital image-acquisition techniques.Our results show that the vortical structures in the mixing layer initially roll-up with a large excess of fluid from the high-speed stream entrapped in the cores. During the mixing transition, not only does the amount of mixed fluid increase, but its composition also changes. It is found that the range of compositions of the mixed fluid, above the mixing transition and also throughout the transition region, is essentially uniform across the entire transverse extent of the layer. Our measurements indicate that the probability of finding unmixed fluid in the centre of the layer, above the mixing transition, can be as high as 0.45. In addition, the mean concentration of mixed fluid across the layer is found to be approximately constant at a value corresponding to the entrainment ratio. Comparisons with gas-phase data show that the normalized amount of chemical product formed in the liquid layer, at high Reynolds number, is 50% less than the corresponding quantity measured in the gas-phase case. We therefore conclude that Schmidt number plays a role in turbulent mixing of high-Reynolds-number flows.

Characterization of the Custom-Designed, High Reynolds Number Water Tunnel

2016 ◽  
Author(s):  
Yasaman Farsiani ◽  
Brian R. Elbing
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Test Section ◽  
High Reynolds Number ◽  
Layer Growth ◽  
Water Tunnel ◽  
Freestream Velocity ◽  
Section Design ◽  
High Reynolds

This paper reports on the characterization of the custom-designed high-Reynolds number recirculating water tunnel located at Oklahoma State University. The characterization includes the verification of the test section design, pump calibration and the velocity distribution within the test section. This includes an assessment of the boundary layer growth within the test section. The tunnel was designed to achieve a downstream distance based Reynolds number of 10 million, provide optical access for flow visualization and minimize inlet flow non-uniformity. The test section is 1 m long with 15.2 cm (6-inch) square cross section and acrylic walls to allow direct line of sight at the tunnel walls. The verification of the test section design was accomplished by comparing the flow quality at different location downstream of the flow inlet. The pump was calibrated with the freestream velocity with three pump frequencies and velocity profiles were measured at defined locations for three pump speeds. Boundary layer thicknesses were measured from velocity profile results and compared with analytical calculations. These measurements were also compared against the facility design calculations.

scholarly journals Wall-attached structures of velocity fluctuations in a turbulent boundary layer

2018 ◽  
Vol 856 ◽  
pp. 958-983 ◽  
Author(s):  
Jinyul Hwang ◽  
Hyung Jin Sung
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
High Reynolds Number ◽  
Wall Turbulence ◽  
Velocity Fluctuations ◽  
Moderate Reynolds Number ◽  
Wide Range ◽  
Logarithmic Region ◽  
High Reynolds ◽  
Attached Eddies

Wall turbulence is a ubiquitous phenomenon in nature and engineering applications, yet predicting such turbulence is difficult due to its complexity. High-Reynolds-number turbulence arises in most practical flows, and is particularly complicated because of its wide range of scales. Although the attached-eddy hypothesis postulated by Townsend can be used to predict turbulence intensities and serves as a unified theory for the asymptotic behaviours of turbulence, the presence of coherent structures that contribute to the logarithmic behaviours has not been observed in instantaneous flow fields. Here, we demonstrate the logarithmic region of the turbulence intensity by identifying wall-attached structures of the velocity fluctuations ($u_{i}$) through the direct numerical simulation of a moderate-Reynolds-number boundary layer ($Re_{\unicode[STIX]{x1D70F}}\approx 1000$). The wall-attached structures are self-similar with respect to their heights ($l_{y}$), and in particular the population density of the streamwise component ($u$) scales inversely with $l_{y}$, reminiscent of the hierarchy of attached eddies. The turbulence intensities contained within the wall-parallel components ($u$ and $w$) exhibit the logarithmic behaviour. The tall attached structures ($l_{y}^{+}>100$) of $u$ are composed of multiple uniform momentum zones (UMZs) with long streamwise extents, whereas those of the cross-stream components ($v$ and $w$) are relatively short with a comparable width, suggesting the presence of tall vortical structures associated with multiple UMZs. The magnitude of the near-wall peak observed in the streamwise turbulent intensity increases with increasing $l_{y}$, reflecting the nested hierarchies of the attached $u$ structures. These findings suggest that the identified structures are prime candidates for Townsend’s attached-eddy hypothesis and that they can serve as cornerstones for understanding the multiscale phenomena of high-Reynolds-number boundary layers.

scholarly journals Instabilities in a high-Reynolds-number boundary layer on a film-coated surface

1997 ◽  
Vol 353 ◽  
pp. 163-195 ◽  
Author(s):  
S. N. TIMOSHIN
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
High Reynolds Number ◽  
Film Flow ◽  
Lower Branch ◽  
Interfacial Instabilities ◽  
Layer Potential ◽  
Tollmien Schlichting ◽  
High Reynolds ◽  
Film Viscosity

A high-Reynolds-number asymptotic theory is developed for linear instability waves in a two-dimensional incompressible boundary layer on a flat surface coated with a thin film of a different fluid. The focus in this study is on the influence of the film flow on the lower-branch Tollmien–Schlichting waves, and also on the effect of boundary-layer/potential flow interaction on interfacial instabilities. Accordingly, the film thickness is assumed to be comparable to the thickness of a viscous sublayer in a three-tier asymptotic structure of lower-branch Tollmien–Schlichting disturbances. A fully nonlinear viscous/inviscid interaction formulation is derived, and computational and analytical solutions for small disturbances are obtained for both Tollmien–Schlichting and interfacial instabilities for a range of density and viscosity ratios of the fluids, and for various values of the surface tension coefficient and the Froude number. It is shown that the interfacial instability contains the fastest growing modes and an upper-branch neutral point within the chosen flow regime if the film viscosity is greater than the viscosity of the ambient fluid. For a less viscous film the theory predicts a lower neutral branch of shorter-scale interfacial waves. The film flow is found to have a strong effect on the Tollmien–Schlichting instability, the most dramatic outcome being a powerful destabilization of the flow due to a linear resonance between growing Tollmien–Schlichting and decaying capillary modes. Increased film viscosity also destabilizes Tollmien–Schlichting disturbances, with the maximum growth rate shifted towards shorter waves. Qualitative and quantitative comparisons are made with experimental observations by Ludwieg & Hornung (1989).

Friction Factor Comparison Between Mixing Length Theory and Empirical Correlation

2022 ◽  
Author(s):  
M Prasad
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Friction Factor ◽  
High Reynolds Number ◽  
Mathematical Representation ◽  
Mixing Length ◽  
Series Form ◽  
High Reynolds ◽  
Mixing Length Theory ◽  
Grain Roughness

Abstract 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.

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