Reduced-order modeling of high-speed jets controlled by arc filament plasma actuators

Arc filament plasma actuators applied to high-speed and high Reynolds number jets have demonstrated significant mixing enhancement when operated near the jet column mode (JCM) frequency. A feedback-oriented reduced-order model is developed for this flow from experimental data. The existent toolkit of stochastic estimation, proper orthogonal decomposition, and Galerkin projection is adapted to yield a 35-dimensional model for the unforced jet. Explicit inclusion of a "shift mode" stabilizes the model. The short-term predictive capability of instantaneous flow fields is found to degrade beyond a single flow time step, but this horizon may be adequate for feedback control. Statistical results from long-term simulations agree well with experimental observations. The model of the unforced jet is augmented to incorporate the effects of plasma actuation. Periodic forcing is modeled as a deterministic pressure wave specified on the inflow boundary of the modeling domain. Simulations of the forced model capture the nonlinear response that leads to optimal mixing enhancement in a small range of frequencies near the JCM.     

Development and characterization of plasma actuators for high-speed jet control

Active control of high Reynolds number and high-speed jets has been hampered due to the lack of suitable actuators. Some of the attributes that would make an actuator suitable for such flows are: high amplitude and bandwidth; small size for distribution around the jet; phase-locking ability for jet azimuthal mode forcing; and sufficient ruggedness for hot jets. We have been developing a class of actuators termed localized arc filament plasma actuators, which possess such characteristics. In this paper, we present the development and characterization of these actuators as well as preliminary results on their applications in high Reynolds number Mach 0.9 and ideally expanded Mach 1.3 jets.Patent pending     

On factors influencing arc filament plasma actuator performance in control of high speed jets

Localized arc filament plasma actuators (LAFPAs) have been developed and used at The Gas Dynamics and Turbulence Laboratory for the purpose of controlling high-speed and high Reynolds number jets. The ability of LAFPAs for use in both subsonic and supersonic jets has been explored, and experiments to date have shown that these actuators have significant potential for mixing enhancement and noise control applications. While it has been established that the actuators manipulate instabilities of the jet, the exact nature of how the actuation couples to the flow is still unclear. All of the results previously reported have been based on a nozzle extension that has an azimuthal groove of 1 mm width and 0.5 mm depth along the inner surface approximately 1 mm upstream of nozzle extension exit. The ring groove was initially added to shield the plasma arcs from the high-momentum flow. However, the effect of the ring groove on the actuation mechanism is not known. To explore this effect, a new nozzle extension is designed, which relocates the actuators to the nozzle extension face and eliminates the ring groove. Schlieren images, particle image velocimetry and acoustic results of a Mach 0.9 jet of Reynolds number ~6.1 × 10⁵ show similar trends and magnitudes with and without a ring groove. Thus, it is concluded that the ring groove does not play a primary role in the LAFPAs’ control mechanism. Furthermore, the effect of the duty cycle of the actuator input pulse on the LAFPAs’ control authority is investigated. The results show that the minimum duty cycle that provides complete plasma formation has the largest control over the jet.     

Comparison of near-wall treatment methods for high Reynolds number backward-facing step flow

A comparison of near-wall treatment methods using different turbulence models for flow over a backward-facing step is presented. A Reynolds number (Re) of about 38,000 (U _∞ = 44.2 m/s), based on the step height and the mean stream velocity, was considered. An appropriate near-wall treatment method is critical to the choice of turbulence model used to predict wall-bounded flow. Predictions were obtained by applying standard wall functions, non-equilibrium wall functions and a two-layer model with six different turbulence models. These results were compared with data by Driver and Seegmiller (“Backward-facing step with inclined opposite wall—experiments by driver and seegmiller”, 1985a, http://cfd.me.umist.ac.uk/ercoftac [2003, Jan 31]). Non-equilibrium wall functions with modified k ? ? models predicted the closest reattachment length. However, the two-layer model gave results more representative of the entire flow pattern. The predictions show that a proper combination of turbulence models and near-wall treatment methods give reliable results.     

Critical transition Reynolds number for plane channel flow

The determination of the critical transition Reynolds number is of practical importance for some engineering problems. However, it is not available with the current theoretical method, and has to rely on experiments. For supersonic/hypersonic boundary layer flows, the experimental method for determination is not feasible either. Therefore,in this paper, a numerical method for the determination of the critical transition Reynolds number for an incompressible plane channel flow is proposed. It is basically aimed to test the feasibility of the method. The proposed method is extended to determine the critical Reynolds number of the supersonic/hypersonic boundary layer flow in the subsequent papers.     

Trailing-edge dynamics of a morphing NACA0012 aileron at high Reynolds number by high-speed PIV

Particle image velocimetry (piv) measurements are made at the trailing edge of a piezoelectric actuated aileron in order to investigate the physical effect on the flow via high-frequency low-amplitude actuation at high Reynolds numbers. The measurements at different actuation frequencies show the modification of the primary frequency components of the flow with the actuation frequency. A statistical analysis reveals the reduction of the Reynolds stress components which increases with the actuation frequency. Proper orthogonal decomposition (pod) analysis shows the modification of the spatial modes illustrating the vortex breakdown in the shear-layer and the reduction of the temporal mode spectral energy depending on the actuation. It has been shown that a specific low amplitude actuation frequency produces a significant reduction of the predominant shear-layer frequency.     

Passive control of wake flow by two small control cylinders at Reynolds number 80

Passive control of the wake behind a circular cylinder in uniform flow is studied by numerical simulation at Re_D=80. Two small control cylinders are placed symmetrically along the separating shear layers at various stream locations. In the present study, the detailed flow mechanisms that lead to a significant reduction in the fluctuating lift but maintain the shedding vortex street are clearly revealed. When the stream locations lie within 0.8≤X_C/D≤3.0, the alternate shedding vortex street remains behind the control cylinders. In this case, the symmetric standing eddies immediately behind the main cylinder and the downstream delay of the shedding vortex street are the two primary mechanisms that lead to a 70–80% reduction of the fluctuating lift on the main cylinder. Furthermore, the total drag of all the cylinders still has a maximum 5% reduction. This benefit is primarily attributed to the significant reduction of the pressure drag on the main cylinder. Within X_C/D>3.0, the symmetry of the standing eddy breaks down and the staggered vortex street is similar to that behind a single cylinder at the same Reynolds number. In the latter case, the mean pressure drag and the fluctuating lift coefficients on the main cylinder will recover to the values of a single cylinder.     

Stall control at high angle of attack with plasma sheet actuators

We analyzed the modifications of the airflow around an NACA 0015 airfoil when the flow was perturbed with electrohydrodynamic forces. The actuation was produced with a plasma sheet device (PSD) consisting in two bare electrodes flush mounted on the surface of the wing profile operated to obtain a discharge contouring the body in the inter-electrode space. We analyze the influence of different parameters of the actuation (frequency, input power, electrodes position) on the aerodynamic performance of the airfoil, basing our study on measurements of the surface pressure distribution and of the flow fields with particle image velocimetry technique. The experiments indicated that at moderate Reynolds numbers (150,000 < Re < 333,000) and at high angles of attack, steady or periodic actuations enabled large improvement of the lift and drag/lift aerodynamic coefficients by reattaching the flow along the extrados. However, to attain the same results steady actuations required larger power consumption. When exciting the flow with a moderate value of non-dimensional power coefficient (ratio of electric power flow with the kinetic power flow), a frequency of excitation produced a peak on the coefficients that evaluate the airfoil performance. This peak in terms of a non-dimensional frequency was close to 0.4 and can be associated to an optimal frequency of excitation. However, our work indicates that this peak is not constant for all stalled flow conditions and should be analyzed considering scale factors that take into account the ratio of the length where the forcing acts and the cord length.     

Wake flow pattern modified by small control cylinders at low Reynolds number

Passive wake control behind a circular cylinder in uniform flow is studied by numerical simulation for Re_D ranging from 80 to 300. Two small control cylinders, with diameter d/D=1/8, are placed at x/D=0.5 and y/D=±0.6. Unlike the 1990 results of Strykowski and Sreenivasan, in the present study, the vortex street behind the main cylinder still exists but the fluctuating lift and the form drag on the main cylinder reduces significantly and monotonously as the Reynolds number increases from 80 to 300. Obstruction of the control cylinders to the incoming flow deflects part of the fluid to pass through the gap between the main and control cylinders, forming two symmetric streams. These streams not only eliminate the flow separation along the rear surface of the main cylinder, they also merge toward the wake centerline to create an advancing momentum in the immediate near-wake region. These two effects significantly reduce the wake width behind the main cylinder and lead to monotonous decrease of the form drag as the Reynolds number increases. As the Reynolds number gets higher, a large amount of the downstream advancing momentum significantly delays the vortex formation farther downstream, leading to a more symmetric flow structure in the near-wake region of the main cylinder. As the Reynolds number increases from 80 to 300, both increasing symmetry of the flow structure in the near-wake and significant delay of the vortex formation are the main reasons for the fluctuating lift to decrease monotonously.     

Optical measurement techniques for high Reynolds number train investigations

This article reports on experimental aerodynamic investigations on a generic high-speed train configuration performed within two different wind tunnels. Both wind tunnels are specialized facilities for high Reynolds number investigations and offer low turbulence levels. The wind tunnels are the cryogenic wind tunnel located in Cologne (KKK) and in the high-pressure wind tunnel located in Göttingen (HDG). Both facilities are part of the German–Dutch wind tunnel association (DNW). The adaptation and application of three optical measurement techniques for such high Reynolds number investigations is described in the article. The optical methods are: Particle Image Velocimetry for the measurement of velocity fields, Background Oriented Schlieren technique for density gradient measurements, and a white light Digital Speckle Photography technique for model deformation monitoring.     

A finite element method for high Reynolds number viscous fluid flow using two step explicit scheme

This paper presents the finite element method for the analysis of unsteady viscous flow of fluid at high Reynolds numbers. The method is based on the explicit numerical integration scheme in time and uses three node triangular finite elements. For the convenience of the formulation, slight compressibility is considered. For the explicit scheme, the selective lumping two step scheme has been successfully employed. Vortex shedding behind a cylinder has been computed and compared with the conventional experimental results. The results agree favourably when both schemes are compared.     

Stability of low Reynolds number flow with viscous heating

Summary The stability of fully developed plane Couette flow and pipe flow with viscous heating is studied at low Reynolds number for a Newtonian liquid with a temperature-dependent viscosity. The solution is obtained by a direct integration method of the eigenfunction equations, with eigenvalues located in the complex plane by means of the argument principle of complex variable theory. An instability will occur in plane Couette flow, but outside the parameter range which will be encountered in practice. There is no comparable instability in pipe flow. It can be concluded that a thermal mechanism does not cause the low Reynolds number instabilities observed in polymer processing operations.

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Zusammenfassung Für eine newtonsche Flüssigkeit mit temperaturabhängiger Viskosität wird die Stabilität der voll entwickelten ebenen Couette-Strömung und Rohrströmung bei niedrigen Reynolds-Zahlen untersucht. Die Lösung wird durch direkte Integration der Eigenwert-Gleichungen gewonnen, wobei das Argument-Prinzip der Funktionentheorie auf die in der komplexen Ebene gelegenen Eigenwerte angewandt wird. In der ebenen Couette-Strömung wird eine Instabilität gefunden, jedoch außerhalb des in der Praxis realisierten Parameter-Bereichs. In der Rohrströmung gibt es dagegen keine vergleichbare Instabilität. Man kommt zu dem Schluß, daß thermische Mechanismen nicht für die in Polymer-Verarbeitungsprozessen beobachteten bei niedrigen Reynolds-Zahlen auftretenden Instabilitäten verantwortlich gemacht werden können.

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With 6 figures and 1 table     

Simultaneous entrainment of oil and water droplets in high Reynolds number gas turbulence in horizontal pipe flow

We develop a 1D cross sectional concentration profile model for oil and water droplets that coexist in the turbulent gas phase (of Re ∼ 10⁶) in near horizontal stratified pipe flows. Entrainment of the oil and water mixture from a liquid film near the bottom of the pipe into the gas is modeled based on earlier single-fluid entrainment correlations. A Gamma distribution for the droplet sizes based on the breakup of liquid filaments, is adopted. An explicit algebraic–exponential formula for the total concentration profile for either phase can then be derived.     

Optimisation of two-dimensional undulatory swimming at high Reynolds number

The propulsion performance of a flexible plate undergoing an arbitrary harmonic motion in a two-dimensional and inviscid fluid is addressed. This plate being free of external forces, heaving and pitching cannot be imposed and are the results of recoil conditions on the body. Linear unsteady airfoil theory is first used to calculate the average thrust and power required for swimming. The propulsive performance is then discussed in terms of hydrodynamic efficiency, energy consumption and average swimming speed and two different asymptotic regimes are identified: the low-velocity regime and the high-velocity regime. The optimal swimming gaits are calculated in the different regimes as a function of the plate mass ratio and leading-edge suction. Finally an empirical non-linear model is proposed to complement the linear model and the optimal swimming modes are calculated and discussed within this framework. For a fixed number of degrees of freedom, it is found that the Strouhal number of the optimal mode is almost constant, independently of the swimming regime.     

Experimental free coating flows at high capillary and Reynolds number

 Experimental studies are carried out to enhance the fundamental understanding of coating processes over a broad parametric range. Experiments herein identify the phenomena leading to the formation of an asymptotic meniscus profile, which eventually develops a cusp at the interface. The non-dimensional parameters that describe these phenomena are identified. In addition, flow visualization is carried out to reveal the entire flow structure using a visible laser. Two phenomena of free coating are identified depending on a parameter called the property number(Po). When Po is larger than about 0.5, the non-dimensional final film thickness (T ₀) becomes constant beyond the capillary number(Ca) of about unity. When Po is less than about 0.1, T ₀ depends on Ca and the Reynolds number(Re) but it becomes constant beyond the Weber number(=Ca Re) of about 0.2. In both cases T ₀ becomes constant as the effect of surface tension on the meniscus becomes relatively unimportant. The cusp formation is due to the effect of inertia(Re). The effect of applicator dimensions on T ₀ is also investigated for large Re flows. Received: 12 May 1998/Accepted: 19 January 1999     

Smooth and rough turbulent boundary layers at high Reynolds number

A 2-D turbulent boundary layer experiment with zero pressure gradient (ZPG) has been carried out over a rough and a smooth surface using two cross hot-wire probes. Wind tunnel speeds of 10 m/s and 20 m/s were set up in order to investigate the effects of the upstream conditions and the Reynolds number on the downstream flow. For a given set of upstream conditions, such as the wind tunnel speed, trip wire size and location, the three components of the velocity field were measured from about 14 m from the inlet of the wind tunnel to 30 m downstream. This experiment is unique because it achieves Reynolds numbers as high as R120,000, for which measurements of the mean velocity are reported. It is shown that by fixing the upstream conditions, the mean deficit profiles collapse with the freestream velocity, , but to different curves depending on the upstream conditions and surface roughness. Moreover, the effects of the upstream conditions, the Reynolds number, and roughness are completely removed from the outer flow when the mean deficit profiles are normalized by the Zagarola/Smits scaling, . Consequently, the true asymptotic profile in the turbulent boundary layer is found in ZPG flow regardless of the range of Reynolds number, surface conditions and initial conditions.     

Large-scale dynamics in high Reynolds number jets and jet flames

The far-field large-scale dynamics of a momentum-driven Re = 2 × 10⁸ non-reacting jet and a Re = 3 × 10⁷ jet diffusion flame are presented and compared. The results are derived from computer graphic volume rendering of a set of sequential images of each flow. When compared to conventional display techniques, volume rendering, by allowing many frames of a movie sequence to be presented simultaneously, more clearly shows the detailed flow evolution. For the non-reacting jet we see the passage and growth of large-scale organized structures up through the jet column, the axial velocity decay of the structures, the fluid entrainment patterns, and occasional pairing events. A rendering of a non-sequential set of images shows no discernible organized component. Volume rendering of the reacting jet shows a similar pattern of burning large-scale organized structures which convert over considerable axial distances but without the corresponding velocity decay, similar to observations of laboratory flames. The images presented here are believed to be some of the most direct visual evidence to date for large-scale organized motions in the far-field of high Reynolds number, fully developed jets and jet flames. Since conditional sampling techniques are not used, we believe that the volume renderings seen here are likely to be representative of the natural development of jet flows.     

Very high Reynolds number boundary layers over 3D sparse roughness and obstacles: the mean flow

Hot-wire and oil-film interferometry measurements are taken for 3D rough wall boundary layers at very high Reynolds numbers (61,000 < Re θ < 120,000) with low blockage ratios, 10 < δ/H < 135, and high roughness, 100 < H ⁺ < 4,900. The results cover flows over both rough walls and over obstacles and are compared with and provide extension to recent lower Reynolds number results. The validity of the Townsend ‘wall similarity hypothesis’ in relation to consistently increasing 3D roughness is interrogated. In agreement with recent work, Schultz and Flack (J Fluid Mech 580:381–405, 2007) and Castro (J Fluid Mech 585:469–485, 2007) found that, for relatively low roughness, Townsend’s hypothesis holds for the mean velocity field. With increasing roughness, the equilibrium layer diminishes and gradually vanishes. The viscous component of the wall shear stress decreases, while the turbulent component increases as the roughness effects extend across the boundary layer.     

The use of plasma actuators for bluff body broadband noise control

Experiments were conducted using plasma actuators to control broadband noise generated by a bluff body flow. The motivation behind the study was to explore the potential of plasma actuators to reduce landing gear noise during approach phase of an aircraft. The control effectiveness of both dielectric barrier discharge and sliding discharge plasma actuators were tested in laboratory environment, using a representative bluff body consisting of a circular cylinder and an oblique strut. Noise measurements were taken in an anechoic chamber using a phased microphone array and far-field microphones. Results showed that the upstream directed plasma forcing, located at ±90 deg on the upstream cylinder with respect to the approaching flow, could effectively attenuate the broadband noise radiated from the wake flow interaction with the downstream strut. With the same AC electrical power consumption, the sliding discharge with additional DC voltage was found to be more effective due to its elongated plasma distribution and higher induced flow momentum. Measurements using particle image velocimetry suggested that the flow speed impinging on the downstream strut was reduced by the upstream plasma forcing, contributing to the reduced noise.