Abstract: This paper discusses the modeling activity of the NATO-STO Research Task Group AVT-349. The aim of this group is to improve the understanding and modeling of boundary layers in the complex flow around water vehicles. As such, the focus is on incompressible, high-Reynolds-number flows that can be subject to non-equilibrium conditions such as strong pressure gradients, three-dimensionality, and surface roughness and heterogeneity. The Task Group has identified a reduced number of simpler problems in which the above conditions can be studied separately and in controlled environments. These include two-dimensional rough-wall boundary layers under both zero and non-zero pressure gradients, two-dimensional smooth-wall boundary layers subject to pressure gradients, and boundary layers around smooth bodies of revolution and three-dimensional obstacles. An experimental and computational data set is being assembled for further analysis and insight into the flow mechanisms involved, as well as the shortcomings of state-of-the-art models. This paper gives an outlook of the modeling effort within the Task Group, as well its different objectives. These include predicting the effect of roughness in equilibrium conditions; assessing the applicability and/or extension of equilibrium models and predictions to non-equilibrium conditions, in particular when outer-layer similarity is lost; the development of near-wall models based on a reduced-order resolvent framework; and the use of machine-aided methods in closure models.

ID: CaltechAUTHORS:20220210-928380000

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Abstract: We consider a linearized Navier–Stokes based model for compressible laminar boundary layers and study the response of these equations to stochastic white-in-time forcing. In particular we look at the different components of the forcing and the response of this linear model with the aim of understanding how the different mechanisms captured by the model change with increasing compressibility effects. We therefore analyze the response of the linear operator to individual components of forcing, i.e. the forcing to each of the momentum equations, the continuity and the energy equations of the linear operator. We also analyze the response obtained in the three components of velocity, in density and in temperature individually. For a fixed Reynolds number of Re=400, we consider Mach numbers ranging between Ma=0.05 and Ma=10 and different wall-cooling ratios. We find that, for all the Mach numbers considered here, the most amplified structures are the streamwise streaks forced by streamwise vortices. Previous studies have shown that these modes are highly amplified in the incompressible regime as well. However, as the Mach number increases, the contribution of the streamwise velocity to these streaks decrease, and the contribution of density and temperature to the streaks increase. Finally, we briefly look at the resolvent operator of the flow, and find that all the components of the forcing are important for the amplification of the Mach waves of the flow, and these modes are not captured by the stochastically forced model.

ID: CaltechAUTHORS:20220210-928407000

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Abstract: Analysis of the resolvent operator is used to study the properties of high-speed turbulent boundary layers for cooled walls. Previous study [1] shows that the resolvent response modes in the relatively subsonic region of high-speed turbulent boundary layers with adiabatic wall boundary conditions follow the same scaling law as those of the incompressible boundary layer case, validating Morkovin’s hypothesis on a mode-by-mode basis. Here, we study the effect of the cooled-wall boundary condition on the individual resolvent response modes to understand the underlying mechanisms that cause the failure of Morkovin’s hypothesis and velocity transformations for increasingly non-adiabatic walls. In particular, we show that the density and temperature resolvent mode shapes for the cooled-wall case exhibit a secondary peak in the inner and logarithmic layer, which is a result of the non-monotonic mean temperature profile that is absent in adiabatic cases. We also show that the secondary peak becomes more prominent with decreasing surface temperature ratio. The deviation of the mean velocity profiles is attributed to the change in the response modes in the near-wall region, the effect of which is propagated further away from the wall through nonlinear interactions.

ID: CaltechAUTHORS:20200113-074130443

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Abstract: Analysis of the resolvent operator is used to study the properties of compressible planar Couette flow. In particular, we study how changing the Mach number affects the shape and amplitude of responses to optimal disturbances across a range of spatial and temporal frequencies. We consider Mach numbers up to 5, and show that the dependence of the resolvent norm(leading singular value) on streamwise and spanwise wavenumbers follows similar trends to the incompressible case, with the amplitude of the resolvent norm typically decreasing with increasing Mach number. An exception to this occurs when acoustic eigenmodes (which are not present in the incompressible regime) have eigenvalues sufficiently close to the temporal frequency ω such that modal resonance with this mode is the dominant contributor to the resolvent gain. This occurs, for example, for streamwise-constant disturbances for sufficiently low spanwise wavenumber. In addition, the resolvent formulation of the governing equations allows us to study independently the effects due to an altered mean/equilibrium profile due to compressibility, and the effects due to the changing linearized Navier-Stokes equations. This approach provides a framework for the study of compressible turbulent wall-bounded flows.

ID: CaltechAUTHORS:20190805-134837522

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Abstract: This work develops a framework for studying the behavior of a passive scalar field in incompressible wall-bounded turbulence using ·the resolvent operator. This approach expresses the stale of the system as the result of applying a linear (resolvent) operator to the nonlinear terms in the governing Navier-Stokes equations. By augmenting the system with a passive scalar equation, this formulation is used to study the relationship between velocity and scalar fluctuations. Additional insight into the mechanisms responsible for driving scalar fluctuations is attained by considering the resolvent form of the passive scalar equation in isolation from the momentum equations. We demonstrate that the passive scalar resolvent operator admits rescaling properties that relates the behavior or scalar fields with different diffusivities, and investigate the ability of this modeling framework to predict statistical properties of the fluctuating scalar field.

ID: CaltechAUTHORS:20190816-111358078

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Abstract: Vertical axis wind turbine blades undergo dynamic stall due to the large angle of attack variation they experience during a turbine rotation. Particle image velocimetry on a pitching and surging airfoil was used to perform time resolved measurements at blade Reynolds numbers near turbine operating conditions of 10^5. These experiments were compared to simulations performed in the rotating turbine frame as well as the linear, experimental, frame at a Reynolds number of 10^3 to investigate rotational and Reynolds number effects. The flow was shown to develop similarly prior to separation, but the kinematics of vortices shed post separation were reference frame dependent.

No.: 185 ISSN: 0930-8989

ID: CaltechAUTHORS:20161202-082406384

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Abstract: As part of an effort to examine the impact of vortical gusts on airfoils, a simple gust generator has been built and investigated. This consists of a heaving at plate capable of following a specifed transverse trajectory across a water tunnel. The relationship between the trajectory and the properties of the gusts that are shed downstream is characterized for non-periodic heaving motion described by Eldredge's smooth motion equation. PIV experiments show that the circulation of the vortical gust is proportional to the heaving speed of the plate. Tests with a downstream NACA 0018 airfoil demonstrate repeatable forces in response to the produced gusts.

Publication: AIAA JournalISSN: 0001-1452

ID: CaltechAUTHORS:20161128-141948592

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Abstract: A large scale spatio-temporally periodic disturbance was excited in a turbulent boundary layer via a wall-actuated dynamic roughness. Streamwise velocity, wall pressure, and direct wall shear stress measurements were made with a hot wire, pressure microphone, and a micro-scale differential capacitive sensor, respectively. Phase-averaged fields for the three quantities were calculated and analyzed. A phase calibration between the various sensors was performed with an acoustic plane wave tube over a range of operating conditions to validate a direct phase comparison between the respective quantities. Results suggest encouraging agreement between the phase of the wall shear stress and velocity near the wall; however, more refined velocity measurements are needed to make quantitative comparisons to the wall pressure. Overall, this work highlights the potential for wall-based control with applications towards reducing turbulent drag.

ID: CaltechAUTHORS:20161128-143308353

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Abstract: The present contribution explores the relationship between response and forcing via amplification mechanisms in the Navier–Stokes equations applied to a turbulent pipe flow. A novel numerical method coupling direct numerical simulation with the resolvent model [J. Fluid Mech. 658, 336-382 (2010)] is developed in order to reveal the exact distribution of the nonlinear forcing terms, originally unknown in the model. The obtained results highlight the major role of the nonlinear terms in the energy spectra.

No.: 165 ISSN: 0930-8989

ID: CaltechAUTHORS:20161111-092925356

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Abstract: Vertical axis wind turbine blades undergo a large angle of attack and velocity variation during every turbine rotation. The flow over a NACA 0018 airfoil undergoing sinusoidal pitch, surge and combined motions at similar frequency, amplitude and Reynolds number as a commercial turbine was measured to investigate the effect of the different motions on the flow field. Two-dimensional, time resolved velocity fields were acquired using particle image velocimetry. Vorticity contours of the phase-averaged flow were used to visualize the separation process and shear layer development. The pitch-only ease is seen to separate earlier and at a lower angle of attack than the combined case. Results for surging airfoils at two angles of attack are presented, one fully separated, and one partially separated. Surge forward is shown to move the separation point toward the leading edge, while surge back moved it aft. The dynamics of the leading edge vortex in the combined pitch/surge and pitch motions are discussed.

ID: CaltechAUTHORS:20190828-110109774

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Abstract: Recent experimental investigations of the canonical turbulent boundary layer at high Reynolds numbers has provided evidence on the active role of very large‐scale structures, extending in the streamwise direction for several boundary layer heights, and modulating near‐wall turbulence from the energy containing eddy scales down to the dissipative scales. However, the physical mechanisms governing such interactions are not completely clear yet, and the reason may be related to the fact that the structure of wall turbulence at high Reynolds numbers still deserves further investigation. In this contribution we present recent results on the structural population in wall turbulence. We compare statistical trends obtained in two very different Reynolds number experiments, one in the atmospheric surface layer at SLTEST and one in a flat plate turbulent boundary layer. While the very large‐scale structures of turbulence and the near‐wall turbulent streaks are observed to have a well‐defined location in physical space and in the energetic domain, based on the frequency or wave number spectra, the intermediate scale motions that manifest as ramplike structures still seem to suffer from Reynolds number effects. Results suggest that outer scaling may not be appropriate, implying that ramplike structures are more likely confined to the near‐wall region in very high Reynolds‐number flows such as the atmospheric surface layer. Spatially resolved measurements at high Reynolds numbers are needed to univocally define the correct scaling of ramplike structures and to assess Reynolds number effects in the structural description of zero pressure gradient turbulent boundary layers.

ID: CaltechAUTHORS:20140826-104525799

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Abstract: In shear coaxial injectors, commonly used for cryogenic liquid rocket engines, propellants traveling at different velocities are separated by the inner jet post before they come into contact with each other, mix, and combust. Knowing how the fluids mix and how susceptible they are to hydrodynamic instabilities is paramount for a successful liquid rocket engine. In this study, the wake behind a blunt trailing edge of a long plate, similar to an unwrapped coaxial injector, was studied in a water tunnel. Two fluid streams of different velocities were introduced on opposite sides of the plate. PIV was used to visualize and determine the influence of the velocity ratio of the split stream on the wake behavior. Measurements of the vortex shedding frequency were taken at various velocity ratios and compared with well characterized cases with a uniform free stream. Operating conditions ranged from Reynolds number 6,000 to 22,000 and velocity ratios 0.30 to 1.00.

ID: CaltechAUTHORS:20190826-092412052

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Abstract: The laminar separation over a symmetric, idealized airfoil was altered by employing a leading edge roughness element ahead of the separation point. Experimental tests were performed with a dynamic roughness, with a time-dependent amplitude, in order to determine the range of control authority associated with this type of leading edge manipulation. The dynamic roughness tests demonstrated the sensitivity of the separation to frequency perturbations at the leading edge induced by the roughness element. Two low dimensional analysis techniques, Proper Orthogonal Decomposition and Dynamic Mode Decomposition, were employed to examine the coupling between the wall motion and the flow, with a view to investigating the practicality of using leading edge roughness perturbations to in future closed loop control configurations.

ID: CaltechAUTHORS:20190826-092412147

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Abstract: Turbulent flow over a “dynamically rough” wall is modeled by considering time-dependent velocity perturbations in the streamwise and wall-normal directions imposed at the wall, a crude linearization. Analysis of the linearized Navier-Stokes operator is performed to select roughness parameters that are predicted to lead to a large disturbance amplification in the body of the flow. Direct numerical simulations of turbulent channel flow at Re_τ ~ 500 with three different roughness amplitudes, a^+, indicate that for a^+ = 10 the response of the flow approximates this predicted form, including the development of a significant span-wise velocity component. The turbulence characteristics, as a function of amplitude, are hypothesized to offer insight of relevance to the static roughness problem.

No.: 22
ID: CaltechAUTHORS:20110713-114512764

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Abstract: Measurements of the steady pressure in a fluid flow may be required to determine other thermodynamic properties, to determine forces on a body due to the pressure distribution over it, or in order to determine the dynamic head and flow velocity (for further details on the latter see Sect. 5.1. Pressure is a scalar representation of molecular activity, a measure of the nondirectional molecular motions. Thus it must, by definition, be measured by a device at rest relative to the flow. Whilst the common practice in the fluid mechanics community is to denote the pressure as static (as opposed to the coordinate-dependent total pressure, Sect. 3.1), this terminology introduces a fundamental redundancy. In practice, pressure is commonly measured both at walls and in the freestream using the types of measurement device shown in Fig. 4.1 connected to a transducer of suitable sensitivity and range. The orifice of a small wall tapping represents a simple way to obtain the pressure impressed on the wall by the external flow. So-called static pressure tubes approximate the local fluid pressure in the freestream if the disturbance presented to the flow can either be accounted for or is not large to begin with. However this can only ever be strictly true for steady laminar flow due to the normal velocity component introduced when a flow becomes turbulent. Measurement of freestream pressure is one of the hardest challenges in fluid mechanics. Fig. 4.1 This chapter addresses measurement of pressure using wall tappings (Sect. 4.1) and static pressure tubes (Sect. 4.2), and especially errors due to the intrusive flow presence of real, finite-sized devices and calibrations to correct for these. Bryer and Pankhurst [4.1] and Chue [4.2] provided seminal monographs on the general topic of pressure probes in 1971 and 1975, respectively, which give detailed descriptions of measurement devices, coverage of the background to the various corrections and a survey of older data. The topic is covered here more concisely, with a view to practical use by the engineer, and with reference to modern literature. The reader is referred to Bryer and Pankhurst [4.1] and Chue [4.2] for further details on most sections. In more recent years a further method for obtaining pressure on the surface of a wind tunnel model has been developed, based on pressure sensitive paints (PSP). The introduction of PSP provides a method to measure the pressure on the surface of a model directly without the transducers and tubing associated with conventional means. A paint, the luminescence of which is dependent on air pressure, is applied to the surface of a wind tunnel model and the pressure distribution is obtained from the images produced by proper illumination. In Sect. 4.4 the basics of PSP are discussed and further subsections address in detail different paints, paint application procedures, imaging systems and image processing. In discussing the achievable accuracy of PSP techniques, both the spatial and temporal resolution is examined. The thermal sensitivity of the paint dye is introduced and this is closely linked to temperature-sensitive paints (TSP), as discussed in Chap. 7, Sect. 7.4.

ID: CaltechAUTHORS:20141024-122054736

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