NL2022901B1 - Pressure-difference sensitive stack - Google Patents
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- NL2022901B1 NL2022901B1 NL2022901A NL2022901A NL2022901B1 NL 2022901 B1 NL2022901 B1 NL 2022901B1 NL 2022901 A NL2022901 A NL 2022901A NL 2022901 A NL2022901 A NL 2022901A NL 2022901 B1 NL2022901 B1 NL 2022901B1
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Classifications
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01L—MEASURING FORCE, STRESS, TORQUE, WORK, MECHANICAL POWER, MECHANICAL EFFICIENCY, OR FLUID PRESSURE
- G01L1/00—Measuring force or stress, in general
- G01L1/24—Measuring force or stress, in general by measuring variations of optical properties of material when it is stressed, e.g. by photoelastic stress analysis using infrared, visible light, ultraviolet
- G01L1/247—Measuring force or stress, in general by measuring variations of optical properties of material when it is stressed, e.g. by photoelastic stress analysis using infrared, visible light, ultraviolet using distributed sensing elements, e.g. microcapsules
Abstract
The present invention is in the field of a pressure— dif— ference sensitive stack comprising an elastic material, a method of producing said stack, a sensor comprising said stack, a detector system comprising said sensor, and a use of 5 the sensor or measurement system for determining surface pres— sure fluctuations in a hydrodynamic system.
Description
Pressure-difference sensitive stack
FIELD OF THE INVENTION The present invention is in the field of a pressure- dif- ference sensitive stack comprising an elastic material, a method of producing said stack, a sensor comprising said stack, a detector system comprising said sensor, and a use of the sensor or detector for determining surface pressure fluc- tuations in a hydrodynamic system.
BACKGROUND OF THE INVENTION Interaction of compliant surfaces with their wall-bounded flow have been studied over decades. The main research topic comprehends the potential to delay laminar/turbulent transi- tion, to reduce skin friction drag and/or to suppress flow-in- duced noise and vibrations. Theoretical analysis on system ex- perimental investigations, instabilities, and direct numerical simulations over the years have shown the (im)possibili-ties of compliant materials for the desired purpose of applications and resulted in a series of contradictions and controversies. Velocity fluctuations contribute to the near-wall pressure fluctuations, indicated by the conservation of momentum for incompressible flows. Pressure fluctuations are found to de- form the flexible wall, dependent on the material properties of a compliant layer. The response of a compliant surface to the pressure fluctuations in a turbulent boundary layer (TBL) flow was theoretically examined. A stable response could be directly linked to the pressure pulses that represent the tur- bulent flow structures in a TBL. Pressure-sensitive paints (PSP) are widely applied in re- search that makes use of aerodynamic flow systems (e.g. wind tunnels). The interaction of the paint with the local oxygen concentration delivers the surface pressure, as the air pres- sure is found to be proportional to the oxygen partial pres- sure. The method of pressure-sensitive paints is not applica- ble in hydrodynamic flow systems (e.g. water channels, cavita- tion tunnels and towing tanks), due to the absence of air (containing oxygen). It is found difficult to measure surface pressure distri- butions on objects. As an alternative typically global force measurements are performed to indicate, for example, the ship hull resistance. However, global force measurements are not specific, for instance they do not quantify which part of the object experience the highest pressure-resistance. An alterna- tive is the use of standard pressure sensors, which are often limited due to their dimensions and installation requirements. Furthermore, a pressure sensor delivers only one local data- point and conseguently requires a necessary array of pressure sensors to measure the spatial pressure distribution, which is a time-consuming and expensive process. In addition standard pressure sensors are limited in use due to their dimensions and installation requirements, as well as the use delivers only one local data-point. An array of pressure sensors is then necessary to measure the spatial pressure distribution, which is a time-consuming and expensive process.
The present invention therefore relates to a pressure- difference sensor, which solves one or more of the above prob- lems and drawbacks of the prior art, providing reliable re- sults, without jeopardizing functionality and advantages.
SUMMARY OF THE INVENTION It is an object of the invention to overcome one or more limitations of the devices of the prior art and at the very least to provide an alternative thereto. The invention is also subject of a to be published scientific paper entitled “Sur- face deformation of Compliant coatings” by amongst others Greidanus and Westerweel, which publication and its contents are incorporated by reference thereto. The interaction of coatings with a turbulent boundary layer has been investi- gated, such that the surface wave was characterized as a func- tion of the coating properties and the bulk velocity. Drag force measurements indicate that all coatings behave like a smooth surface especially for low bulk velocities. The above theoretical analysis also showed that the deformed wall does not influence the properties of the flow, so that the present method is non-intrusive. Surface deformation measurements ver- ify symmetric waves for all coatings and move in the same di- rection as the fluid flow. The wave propagation velocity sug- gests strong correlation with high-intensity turbulent pres- sure fluctuations in the turbulent boundary layer. The RMS- values of the surface deformations scale with the coating softness and increase with increasing bulk velocity. Height- time diagrams and time-series visualization indicate modula- tion of the wave-train by the fast-moving low-amplitude waves related to pressure fluctuations. Measurements have been ap- plied to the turbulent flow along the surface of a first coat- ing. The mean velocity profiles indicate a change in the very near-wall region for all bulk velocities. It is concluded that large scale turbulent structures initiate moderate deformation of the coating surface, while the fluid flow remains nearly undisturbed. The flow is capable to transfer sufficient energy towards the coating and initiate a wave-train with significant wave-amplitude that is defined by the material properties of the visco-elastic coating. A two-way coupled regime arises as the wave-train induces extra fluid motions and amplifies Reyn- olds stresses.
The coating synthesis and the optical measurement tech- nique (Background Oriented Schlieren (BOS}) are considered to be known in the field of Material Science and Fluid Mechanics respectively. The present invention makes use of a combination of these two areas. It may be used to determine the fluid pressure on object surfaces. The adaptation of the coating properties (i.e. stiffness and thickness) in contrast to the turbulent flow conditions is considered a unique feature, which makes this a very attractive measurement tool to quan- tify the pressure distribution on and around objects. In the present invention the surface pressure at an object gives rise to small deformation of the coating surface, which can be ob- served via optical measurements. The surface pressure is a function of the coating modulations and coating properties (stiffness, thickness). The latter can be adapted to the tur- bulent flow conditions. The invention makes it possible to quantify the surface pressure on for instance a ship hull dur- ing the ship design process.
In a first aspect the present invention relates to a pressure-difference sensitive stack, comprising an elastic layer, wherein the elastic layer has a thickness of 100 nm-50 mm, which thickness may vary on the elastic properties and the deformation in the elastic layer to be observed, a storage modulus of 10°2-10° Pa (ISO 6721-1/4 {2011 EN)), which storage modulus may vary accordingly, wherein the elastic layer is ca- pable of deforming 0.1-10% (in a direction perpendicular to a surface of the elastic layer) upon application of a pressure of 1-10% Pa, hence deformations in a relatively large pressure range can be observed by selecting thereto suitable elastic properties of the elastic layer and thickness thereof. Further a multitude of tracking markers in contact with the layer are provided, wherein tracking markers are adapted to reflect pressure differences applied on the surface of the layer, and wherein, in projection to a surface of the elastic layer, the tracking markers are distributed over said surface. Thereby the projection of the tracking markers provides information on local pressure differences experienced by the elastic layer, whereby the apparent movement of the tracking marker or mark- ers can be determined, such as by an optical technique, and subsequent calculation. Put differently the tracking markers, which typically remain in their location, appear to be at var- ving (increasing or decreasing) mutual distance compared to their initial mutual distance, which apparent variation is re- flecting elastic deformation of the elastic layer. The local elastic deformation is typically 0.1-10% of a layer thickness. As such pressure differences at locations on the elastic layer can be determined accurately; these pressure differences can be caused by a turbulent flow of a fluid passing along the elastic layer. The measured pressure difference in the present stack is therefore a direct measure of pressure differences in the passing turbulent fluid. As such e.g. the effect of vari- ous coatings or shape of an underlying material on fluid flow behaviour can be determined accurately with a direct measure- ment.
In a second aspect the present invention relates to a method of producing a pressure sensitive elastic layer mate- rial for the present stack, comprising mixing SEBS and paraf- fin oil at a temperature between 120-140°C for 3-4 hours, un- til a homogeneous transparent solution is obtained, cooling the solution, and obtaining the elastic layer material.
In a third aspect the present invention relates to a pressure-difference sensor comprising the present stack, and a detector capable of detecting pressure differences applied on the surface of the layer reflected by the tracking markers.
In a fourth aspect the present invention relates to a measurement system comprising more than two of the present 5 sensors, such as 3-64 sensors.
In a fourth aspect the present invention relates to a use of the present pressure-difference sensor or present measure- ment system for detecting local pressure differences, such as pressure fluctuations, such as fluctuations due to turbulent fluid flow.
The present invention provides a solution to one or more of the above-mentioned problems and overcomes drawbacks of the prior art.
Advantages of the present description are detailed throughout the description.
DETAILED DESCRIPTION OF THE INVENTION In an exemplary embodiment of the present pressure-dif- ference sensitive stack the tracking markers have a density of 1072/m2-1019/m2.
In an exemplary embodiment of the present pressure-dif- ference sensitive stack the tracking markers each individually have a size of 1077 m?-10"1 m?.
In an exemplary embodiment of the present pressure-dif- ference sensitive stack a combined surface area of tracking markers projected on the surface area of the layer to which pressure is applied is 10-50% of the surface area of the layer.
In an exemplary embodiment of the present pressure-dif- ference sensitive stack the distribution of tracking markers is selected from pre-determined evenly distributed over the stack, pre-determined unevenly distributed over the stack, randomly distributed, regularly distributed, and combinations thereof.
In an exemplary embodiment of the present pressure-dif- ference sensitive stack tracking markers each individually have an optical intensity of at least a factor 10 higher or lower that the intensity of the elastic layer, such as white, and black.
In an exemplary embodiment of the present pressure-dif- ference sensitive stack the layer the elastic layer comprises 1-95 wt.% of a cross-linking and network forming macromole- cule, preferably 1.5-50 wt.%, more preferably 2-25 wt.%, such as 5-20 wt.%, comprising soft and hard segments and 5-99 wt.% of co-solvent compatible with the soft segments of the macro- molecule, preferably 7-85 wt.%, more preferably 10-80 wt.%, such as 15-80 wt.%, wherein the macromolecule is preferably selected from polymers, such as biopolymers, such as triblock- copolymer polystyrene-b-{ethylene-co-butylene) -b-styrene (SEBS), polyacrylamide, natural gums and natural polysaccha- rides, such as guar gum, xanthan gum, locust bean gum, chicle gum, dammar gum, and carrageenan, wherein the co-solvent is preferably selected from non-mineral oils, such as paraffin 0il, and water, or comprises a supramolecular gel, such as agar gel, and combinations thereof.
In an exemplary embodiment of the present pressure-dif- ference sensitive stack the elastic layer is removable (95- 100%). In an exemplary embodiment of the present pressure-dif- ference sensitive stack the elastic layer has a thickness of 500 nm-1 mm, preferably 1-500 um, more preferably 2-300 um, even more preferably 10-100 um, such as preferably 20-50 um.
In an exemplary embodiment of the present pressure-dif- ference sensitive stack the elastic layer has a storage modu- lus of 1072-10% Pa (ISO 6721-1/4), preferably 5*1072-5*105 Pa, more preferably 1*1071-2*10° Pa, even more preferably 5*107:-5*102 Pa, such as 1-100 Pa.
In an exemplary embodiment of the present pressure-dif- ference sensitive stack the elastic layer has an optical transparency @490 nm of > 95% (ISO 13468-1:1996), such as > 99%, In an exemplary embodiment of the present pressure-dif- ference sensitive stack tracking markers are provided in the elastic layer as moveable particles.
In an exemplary embodiment of the present pressure-dif- ference sensitive stack tracking markers are provided in a separate layer in the stack, such as on the elastic layer or below the elastic layer.
In an exemplary embodiment of the present pressure-dif- ference sensitive stack a loss modulus of the elastic layer is 103-102 Pa*sec, (reflecting a response time of Hsec-msec).
In an exemplary embodiment of the present pressure-dif- ference sensitive stack the elastic layer is a visco-elastic fluid.
In an exemplary embodiment of the present pressure-dif- ference sensitive stack the tracking markers have a density different from the density of the elastic material.
In an exemplary embodiment of the present pressure-dif- ference sensitive stack the tracking markers have a birefrin- gence different from the birefringence of the elastic mate- rial.
In an exemplary embodiment of the present pressure-dif- ference sensitive stack the tracking markers have a dichroism different from the dichroism of the elastic material.
In an exemplary embodiment of the present pressure-dif- ference sensitive stack the tracking markers have a refractive index different from the refractive index of the elastic mate- rial.
In an exemplary embodiment of the present pressure-dif- ference sensitive stack the elastic layer has a birefringence different from that of water (1.33 @ 589.3 nm), or oil (about
1.60), or air (1.00)or that of a fluid adjacent to the elastic layer.
In an exemplary embodiment of the present pressure-dif- ference sensor the detector is selected from an optical detec- tor for detecting movement or apparent movement of tracking markers, an electromagnetic detector, such as an MRI, an ul- trasound detector, and combinations thereof.
In an exemplary embodiment of the present pressure-dif- ference sensor the stack is applied on a substrate, and wherein the tracking markers are applied on the substrate and the elastic layer on the tracking markers or vice versa, or wherein the elastic layer comprising the tracking markers is applied on a substrate.
In an exemplary embodiment of the present pressure-dif- ference sensor the optical detector is capable of detecting fluid density fluctuations, preferably selected from
Schlieren, such as background oriented Schlieren, optical in- terference, Fabry Perot, optical polarization, optical absorp- tion, bright field microscopy (particle tracking), confocal microscopy, stereoscopic microscopy, defocusing microscopy, optical scattering, Mach-Zehnder interferometry, tomographic imaging, holographic interferometry, and combinations thereof.
In an exemplary embodiment of the present pressure-dif- ference sensor the electro-magnetic detector is selected from a capacitive detector, an inductive detector, a resistance de- tector, and combinations thereof.
In an exemplary embodiment of the present pressure-dif- ference sensor the stack extends over 1-100% of the/a sub- strate, and wherein the optical detector is adapted to detect local fluctuations in the layer over 1-100% of the elastic layer in one detection.
In an exemplary embodiment of the present pressure-dif- ference sensor optionally includes a stack, further comprising a data input, a data output, wherein the data input is adapted to receive characteristics of the stack, characteristics of the substrate, boundary conditions, such as of a fluid apply- ing pressure, shape of the substrate, ambient temperature, am- bient pressure, calibration information, refractive index of the fluid, refractive index of the elastic layer, wherein in- put data is provided to the sensor, wherein the sensor is adapted to process the data input, for instance by providing a calibration, wherein the measured data is averaged, data reso- lution is applied, statistical convergence is obtained, etc.
In an exemplary embodiment of the present pressure-dif- ference sensor the detector is adapted to detect a pressure difference within a time of 10 nsec- 10 msec.
In an exemplary embodiment of the present pressure-dif- ference sensor operates at a detection frequency of 1 Hz-100 kHz, preferably 2-200 Hz for low frequency images, such as PIV images, e.g. 3-100 Hz, and 1200-50000 Hz for high frequency images, such as 5000-20000 Hz.
In an exemplary embodiment of the present use is for de- termining pressure fluctuations in a hydrodynamic system, such as on a ship hull, a vortex, such as a vortex behind a cylin- der, a ship propeller, and at the bow or rear of a ship.
In an exemplary embodiment of the present use pressure differences in the stack substantially do not affect the fluid dynamics of a substrate on which the stack is applied.
The invention will hereafter be further elucidated through the following examples which are exemplary and explan- atory of nature and are not intended to be considered limiting of the invention. To the person skilled in the art it may be clear that many variants, being obvious or not, may be con- ceivable falling within the scope of protection, defined by the present claims.
SUMMARY OF THE FIGURES Figs. 1-5 show some experimental results.
DETAILED DESCRIPTION OF FIGURES Fig. la shows a random image of a deformed dot-pattern and fig. lb a computed gradient vector field and reconstructed height-field.
Fig. 2a shows root-mean-square values as a function of bulk velocity Uy and fig. 2b shows scaled rms-values to coat- ing thickness he in relation to scaled pressure fluctuations Dems TO coating shear modulus G*. The scaling factor of 0.0031 of the one-way coupled regime is a fit parameter.
Fig.3a shows a surface deformation field with cross-sec- tion lines AA’ and BB’. Fig. 3b shows surface cross-section line AA’ and fig. 3c BB’ with surface zero-crossings and local minimum and maximum.
Figs. 4a-f show height-time diagrams (left) and spatio- temporal correlation maps (right) of velocities Wh=3.5, 4.5, and 5.4 m/s, respectively.
Figs. bSa-c show deformation of a flat plate (fig. ba) and coatings (figs. bb and 5c) under a flow.
Examples In an example inventors studied the interaction of com- pliant surfaces with a turbulent boundary layer flow is inves- tigated. The main objectives are to study the compliant wall respond to a fully turbulent boundary layer and to explore the ability to reduce turbulent skin friction. Three in-house pro- duced compliant coatings with different material properties are applied to explore the interface wave characteristics as a function of the coating properties and the bulk velocity (Ub).
The coatings are tested on flat plates in the TU Delft water tunnel.
The fluid-surface interaction has been quantified by Plate force measurements to determine the skin friction, Back- ground Oriented Schlieren (BOS) measurements to reconstruct the instantaneous surface deformation field of the coating surface, and Particle Image Velocimetry (PIV) measurements to measure the streamwise and wall-normal velocity components u and v of the fluid flow.
Experimental setup The experiments have been performed in the cavitation tunnel at Delft University of Technology (TU Delft). The test section of the tunnel is open at the top, which makes it pos- sible to mount test plates in order to determine the fric- tional properties of various surfaces via a force balance sys- tem.
The inlet cross-section area is 300x300 mm?, and the out- let cross-section area is 300x315 mm® due to an inclined bot- tom wall.
The sloped wall partially compensates the boundary layer growth in stream-wise direction, such that a nearly con- stant bulk velocity Ups is maintained.
The maximum bulk veloc- ity is 6 m/s («500 L/s). Walls are tripped just before the test section to ensure turbulent boundary layers at all rele- vant tunnel velocities.
The test plates have a total surface area of 1998x297 mm: and have free movement during the force measurements.
Sealing of the gaps around the test plate mini- mized flow disturbances.
The test section is fully optical ac- cessible, which makes it possible to apply BOS and PIV meas- urements.
Compliant material Pure polydimethylsiloxane (PDMS) could be applied as com- pliant visco-elastic material in fluid-surface interaction studies.
However, due to a continuous progress of covalent crosslink reactions between polymer chains, PDMS samples expe- rience an ageing process that modifies the mechanical proper- ties of the material.
Due to prospective research on the coat- ing-equipped test plates, it was essential to use a visco- elastic material that remains its mechanical properties over a period of time.
Therefore, three in-house produced compliant coatings have been produced from a mixture of triblock-copolymer polystyrene-b-(ethylene-co-butylene)-b-styrene (SEBS) and mid- block selective paraffin oil. The styrene end-blocks are in- soluble in paraffin oil and assemble themselves into micelles to minimise interfacial area, which are considered to be the cross-link points in the material. The ethylene/butylene mid- blocks connect these points via physical crosslinking and give formation to a three-dimensional network. A higher concentra- tion of SEBS increases the micelles and crosslink density, which among others determines the mechanical properties of the visco-elastic material. Other parameters that influence the mechanical properties of the visco-elastic material are the molar mass and styrene content of the triblock copolymer and the type of applied hydrocarbon oil.
Material preparation & characterization The polystyrene-b- (ethylene-co-butylene) -b-styrene (SERS, Kraton G-1650E) with a molar mass of + 100.000 g/mol and sty- rene content of around 29% was provided by Kraton Polymers. The paraffin oil (Sigma-Aldrich, 18512) was obtained from Sigma-Aldrich and has a dynamic viscosity of 110-230 mPa.s and a density of 0.827-0.89 g/cm? at 20°C. The flash point tempera- ture of the paraffin oil is 215°C, which is point of awareness during the material synthesis process.
The coating-equipped test plate has a total surface area of 1998x297 mm? with an intended coating thickness of 5 mm, which makes the total volume of the coating around 3 L (~2.6 kg). For each coating composition, sufficient amounts of SEBS and paraffin oil were carefully weighted and were combined in a bL glass beaker at room temperature. The glass beaker was placed in an isolated oil bath, which itself was placed on a heating plate (max. 1000 W, IKA C-MAG HS7) equipped with a temperature feedback sensor. The temperature was raised up to 120°C and maintained for 30 min. The mixture was then mechani- cally stirred for 3-4 hours at 120-140°C, until a homogeneous transparent solution was obtained. The stirrer was removed and the solution was cooled down to room temperature by natural convection.
The SEBS-concentration determines the material properties of the three coatings (e.g. coating stiffness G*). The mi- celles density is larger when the SEBS-concentration is increased, which results in a higher material stiffness. At room temperature, the three coatings are rubber-like transpar- ent material. Rheological behaviour measurements were per- formed by a commercial rheometer (ARES-G2, TA Instruments) with a parallel plate geometry with a diameter of 25 mm. The storage modulus G' and loss modulus G” at 20°C are measured as a function of strain between 10-3 % and 10% at an angular fre- quency of 2% rad/s and as a function of frequency between 0.1-100 rad/s at 0.5% strain. The results confirm the material stiffness in- crease with increasing SEBS-concentration.
Temperature-sweeping was used to estimate the melting transition temperature Tm with a temperature increase of
2.5°C/min. The temperature range was 20-150 °C, with an angular frequency of 2m rad/s and 0.5% strain. The melting transition temperature is around 90 °C (coating 1), 100 °C (coating 2), and 115 °C (coating 3). The melting transition temperature Tn is considered of great interest for the material post-process- ing to obtain a homogeneous smooth coating surface on the test plate.
The surface deformation of the coatings under turbulent boundary layer flow is determined by Background Oriented Schlieren (BOS) based on the refraction method. The refractive index of the coating is required to calculate the surface height at the interface. The refractive indices ni; were meas- ured with an Abbe refractometer, which is able to determine the critical angle oi. The refractive index is given by ni=1/sin (oi). The working principle of the refractometer is validated using distilled water (n.==1.33) and glass test sam- ple (Niest=1.5165) at room temperature (20°C).
Coating processing Standard test plates are often manufactured from plexi- glas (PMMA) and has a glass transition temperature of Tg=110°C, which is in the range of the melting transition temperature of the coatings. Therefore, the coatings have been applied on 10 mm thick flat polycarbonate plates, which has a glass tran- sition temperature of Tg=147°C. The polycarbonate plate was levelled inside a large oven with high precision. At room tem- perature, pieces of the visco-elastic material (~2.6 kg} were deposit on the plate, which was constructed with an extra raised edge of 5 mm. The temperature was increased 10°C above the melting transition temperature of the specific material under slow heating to avoid thermal stresses (2°C/min). The oven temperature was maintained for 2 hours, such that the ma- terial could spread out over the entire plate as a very vis- cous liquid. After slowly cooling to room temperature (1°C/min), the result is a transparent coating layer with a homogeneous coating thickness of 5 mm.
Table 1 summarizes the determined material properties within this study. The shear wave velocity Ct are within the range of the flow velocity of the water tunnel and flow-in- duced surface instabilities (FISI) might be expected. The bulk modulus of the material was not measured, but the material is considered to be incompressible within the range of operation, which presumes the Poisson’s ratio o~0.5.
~~ JseBs |e |G lp. [CG [Tw [n | wt kPa |kPa lkg/m® ms [°C | wf En ER
7.8
13.9 Table 1. Coating properties. Surface deformation measurements The instantaneous deformation field ((x,vy,t) of the com- pliant surface has been measured via the Free Surface-Syn- thetic Schlieren (FS-5S) method, which is a non-intrusive op- tical detection technique that is based on the Background Ori- ented Schlieren (BOS) principle. A random dot pattern is placed behind the coating-fluid interface and is back-illumi- nated by a homogeneous LED light-screen to obtain a high con- trast. The dot pattern is front-observed by a high-speed 4Mpx- camera via a mirror, which is placed below the water tunnel.
The distorted image of the reference dot pattern is the result of light rays passing through the deformed compliant surface. The apparent displacement of the reference image in- duced by this refraction is found directly proportional to the surface gradient. The displacement field is computed via an in-house Digital Image Correlation (DIC) algorithm, where groups of dots inside a small interrogation window are corre- lated to obtain the local displacement. DIC algorithms are accurate and robust for PIV measurements. A multi-pass corre- lation was used with a final interrogation window of 16x16 pixels with a 50% overlap. The median filter method is applied to remove bad vectors and are replaced by linear interpola- tion. Integration of the displacement field provides the in- stantaneous height of the coating surface.
The refraction method preferably fulfils at least two re- quirements for optimal reconstruction of the surface defor- mation. First, the camera-pattern distance is large enough to meet the paraxial approximation. In the present case, the field of view has an area of 100x100 mm? in the centre of the plate and the camera-pattern distance is around H=1400 mm and satisfies the paraxial approximation (B<2.8°). Second, the wave amplitude and surface slope are weak to confine the lin- ear approximation. However, when strong surface deformations occur a Dot Tracking Algorithm (DTA) would be more appropriate when strong deformations occur. The pattern-surface distance is preferably minimally 15 mm (=hethy) and can be increased by inserting glass spacer plates of various thicknesses. An in- crease in pattern-surface distance amplifies the deformations and with that the resolution.
2000 successive images were taken with a fixed sampling frequency Fs of 1200 Hz for coating 1 with glass spacers hy=2 mm. For the other measurements, the sampling frequency Fs is linearly increased in contrast to the bulk velocity Us, namely from Fs=200 Hz at U=0.87 m/s to Fs=1240 Hz at Up=5.39 m/s.
PIV measurements Particle Image Velocimetry (PIV) was used to study the instantaneous velocity fields and turbulent statistics of the turbulent flow. A standard 2D-2C PIV configuration is applied to the test facility. The field of view (FOV) is around 8.7 x7.0 mm? in streamwise and wall-normal direction respectively and is situated 1.7 m downstream from the entrance of the test section. The FOV is illuminated by a light sheet using a dou- ble-pulsed 50 mW Nd:YAG laser (Litron L-class 50-50) and is located in the centre of the tunnel. The images are recorded by a 1280 x 1024 pixel CCD-camera (FlowMaster, LaVision) and show a part of the wall and the near-wall flow region. Hollow sphericell particles (dp = 10/um) are used as tracers, with a particle density of approximately pa = 1.1x10° kg/m’. The re- sponse time scale of particle relaxation 5.6 us. The particles are expected to follow the flow even in the near-wall regime as the expected inner turbulence time-scale is >20 us. Cali- bration is done using a calibration grid with dot-spacing of
0.5 mm. The pixel size is determined to be 6.7 um, resulting in a 1 to 1 magnification.
500 successive PIV image pairs were taken at low fre- quency (3-4 Hz) to ensure reliable statistical convergence of the mean velocity field and turbulent parameters. The time de- lay At between the first and second image is chosen such that the particle displacement between the two images is around 8- 10 pixels far-away from the wall. Data analysis is performed using software (DaVis, LaVison). A multi-pass correlation was used, with a final interrogation window size of 64 X 64 pixels with 75% overlap, resulting in a vector spacing of 0.11 mm. The final 64 X 64 pixels window was the minimum size to sat- isfy the criterion of 5 particles per interrogation window.
Particle Tracking Velocimetry (PTV) is used to determine the displacement of individual particles close to the wall (y<1 mm) and to enhance the spatial resolution of the mean ve- locity profile up to 1 pixel. The particle velocities are av- eraged with respect to the mean wall to obtain the mean veloc- ity.
Velocity analysis Only coating 1 has been selected for further considera- tion to analyse the interaction between fluid flow and compli- ant surface. The raw images are used to determine the fluid- surface interface roughly, followed by characterization of the surface deformation. The velocity data is obtained by PIV, as well as PTV for the region close to the wall. The instantane- ous velocity data is used to construct the mean velocity pro- files and to investigate the turbulent flow statistics. The velocimetry measurements are performed at five bulk veloci- ties; three pre-transition bulk velocities Uyp=1.7, 3.5 and
4.4 m/s and two post-transition velocities Us=4.8 and 5.2 m/s.
Wave characteristics The deformation of the surface interface is clearly visi- ble on the raw images, and indicates a typical shape of a wave. The flow direction for all PIV recordings is from right to left. The image shows a homogeneous grey-scale colour re- garding the region of the coating, while the fluid flow mainly consists of a black background with random white spots repre- senting the tracer particles. Bright white spots at the coat- ing/fluid boundary are substantial reflections from the inter- face. The coating/fluid boundary is determined by allocation of 5 points (manually) on the interface with equal spacing, followed by a polynomial fit. The surface height distribution is very identical to the distribution obtained by the BOS measurements. The root-mean-square values of the surface height have been computed for the five bulk velocities and have been compared to the rms-values obtained by BOS. The two measurement techniques show exceptional agreement.
Mean flow analysis Three examples of instantaneous velocity fields at bulk velocity Ub=5.2 m/s are investigated, (a) flat smooth plate, (b) coating with minimal surface deformation and (c} coating with excessive surface deformation. When the coating surface deforms extremely, two main distinction in the velocity field are observed; 1) close to the wall; a region with very low (and possibly negative) velocities at the leeward side of the wave and 2) further away from the wall; higher velocities, which indicates higher turbulent activities. A more detailed investigation of the velocity data is performed to quantify the influence of the coating on the near-wall velocity field (<5 mm) .
The PIV reconstruction determine the velocity in the log layer, while the super-resolution method (i.e. PTV) recon- struct the velocity in the region close to the wall up to the first part of the log layer. The obtained mean velocity pro- files are compared to the theoretical profile of a smooth sur- face. First, the results of the smooth plate. As expected, the velocity close to the wall match very well with the theoreti- cal profile for smooth surfaces. The velocity profile for high bulk velocities deviate only slightly from the expected pro- file. For the sake of searching the following section is added.
1. Pressure-difference sensitive stack, comprising an elastic layer, wherein the elastic layer has a thickness of 100 nm-50 mm, a storage modulus of 1072-10°% Pa (ISO 6721-1 (2011 EN) ), wherein the elastic layer is capable of de- forming 0.1-10% in a direction perpendicular to a surface of the elastic layer upon application of a pressure of 1- 10¢ Pa, and a multitude of tracking markers in contact with the layer, wherein tracking markers are adapted to reflect pressure differences applied on the surface of the layer, and wherein, in projection to a surface of the elastic layer, the tracking markers are distributed over said surface.
2. Pressure sensitive stack according to embodiment 1, wherein the tracking markers have a density of 107 /m2- 1019/m?2, and/or wherein the tracking markers each individually have a size of 1077 m2-107 m?, and/or wherein a combined surface area of tracking markers pro- jected on the surface area of the layer to which pressure is applied is 10-50% of the surface area of the layer.
3. Pressure sensitive stack according to embodiment 1 or 2, wherein the distribution of tracking markers is selected from pre-determined evenly distributed over the stack, pre-determined unevenly distributed over the stack, ran- domly distributed, regularly distributed, and combinations thereof.
4. Pressure sensitive stack according to any of embodiments 1-3, wherein tracking markers each individually have an optical intensity of at least a factor 10 higher or lower that the intensity of the elastic layer, such as white, and black.
5. Pressure sensitive stack according to any of embodiments 1-4, wherein the elastic layer comprises 1-95 wt. of a cross-linking and network forming macromolecule comprising soft and hard segments and 5-99 wt.% of co-solvent compat- ible with the soft segments of the macromolecule, wherein the macromolecule is preferably selected from polymers, such as biopolymers, such as triblock-copolymer polysty- rene-b-{(ethylene-co-butylene)}-b-styrene (SEBS), polyacryl- amide, natural gums and natural polysaccharides, such as guar gum, xanthan gum, locust bean gum, chicle gum, dammar gum, and carrageenan, wherein the co-solvent is prefera- bly selected from non-mineral oils, such as paraffin oil, and water, or comprises a supramolecular gel, such as agar gel, and combinations thereof.
6. Pressure sensitive stack according to any of embodiments 1-5, wherein the elastic layer is removable.
7. Pressure sensitive stack according to any of embodiments 1-6, wherein the elastic layer has a thickness of 500 nm-1 mm, preferably 1-500 um, more preferably 2-300 um, even more preferably 10-100 um, such as prefera- bly 20-50 um, and/or a storage modulus of 1072-10% Pa (ISO 6721-4), preferably 5*1072-5*10° Pa, more preferably 1*107+-2*102 Pa, even more preferably 5*10°1-5*10¢ Pa, such as 1-100 Pa, and/or an optical transparency ©@490 nm of > 95% (ISO 13468- 1:1996), such as > 99%, and/or wherein tracking markers are provided in the elastic layer as moveable particles, and/or wherein tracking markers are provided in a separate layer in the stack, such as on the elastic layer or below the elastic layer, and/or wherein a loss modulus of the elastic layer is 10-3-10% Pa*sec, and/or wherein the elastic layer is a visco-elastic fluid, and/or wherein the tracking markers have a density different from the density of the elastic material, and/or wherein the tracking markers have a birefringence differ- ent from the birefringence of the elastic material, and/or wherein the tracking markers have a dichroism different from the dichroism of the elastic material, and/or wherein the tracking markers have a refractive index dif- ferent from the refractive index of the elastic material, and/or wherein the elastic layer has a birefringence different from that of water (1.33 @ 589.3 nm), or oil (about 1.60), or air (1.00), or that of a fluid adjacent to the elastic layer.
8. Method of producing a pressure sensitive elastic layer ma- terial for a stack according to any of embodiments 1-7, comprising mixing SEBS and paraffin oil at a temperature between 120- 140°C for 3-4 hours, until a homogeneous transparent solu- tion is obtained, cooling the solution, and obtaining the elastic layer material.
9. Pressure-difference sensor comprising a stack according to any of embodiments 1-7, and a detector capable of detecting pressure differences ap- plied on the surface of the layer reflected by the track- ing markers.
10. Pressure sensor according to embodiment 9, wherein the de- tector is selected from an optical detector for detecting movement or apparent movement of tracking markers, an electromagnetic detector, such as an MRI, an ultrasound detector, and combinations thereof.
11. Pressure sensor according to embodiment 9 or 10, wherein the stack is applied on a substrate, and wherein the tracking markers are applied on the substrate and the elastic layer on the tracking markers or vice versa.
12. Pressure sensor according to embodiment 9 or 10, wherein the elastic layer comprising the tracking markers is ap- plied on a substrate.
13. Pressure sensor according to any of embodiments 10-12, wherein the optical detector is capable of detecting fluid density fluctuations, preferably selected from Schlieren, such as background oriented Schlieren, optical interfer- ence, Fabry Perot, optical polarization, optical absorp- tion, bright field microscopy, confocal microscopy, stere- oscopic microscopy, defocusing microscopy, optical scat- tering, Mach-Zehnder interferometry, tomographic imaging, holographic interferometry, and combinations thereof.
14. Pressure sensor according to any of embodiments 10-13, wherein the electro-magnetic detector is selected from a capacitive detector, an inductive detector, a resistance detector, and combinations thereof.
15. Pressure sensor according to any of embodiments 9-14, wherein the stack extends over 1-100% of the/a substrate, and wherein the optical detector is adapted to detect lo- cal fluctuations in the layer over 1-100% of the elastic layer in one detection.
16. Pressure sensor according to any of embodiments 9-15, op- tionally including a stack, further comprising a data in- put, a data output, wherein the data input is adapted to receive characteristics of the stack, characteristics of the substrate, boundary conditions, such as of a fluid ap- plying pressure, shape of the substrate, ambient tempera- ture, ambient pressure, calibration information, refrac- tive index of the fluid, refractive index of the elastic layer, wherein input data is provided to the sensor, wherein the sensor is adapted to process the data input.
17. Pressure sensor according to any of embodiments 9-16, wherein the detector is adapted to detect a pressure dif- ference within a time of 10 usec- 10 msec, and/or operates at a detection frequency of 1-100 kHz.
18. Measurement system comprising more than two sensors ac- cording to embodiments 9-17.
19. Use of a pressure difference sensor according to any of embodiments 9-17 or measurement system according to embod- iment 18, for detecting local pressure differences, such as pressure fluctuations, such as fluctuations due to tur- bulent fluid flow.
20. Use according to embodiment 19, for determining pressure fluctuations in a hydrodynamic system, such as on a ship hull, a vortex, such as a vortex behind a cylinder, a ship propeller, and at the bow or rear of a ship.
21. Use according to embodiment 19 or 20, wherein pressure differences in the stack substantially do not affect the fluid dynamics of a substrate on which the stack is ap- plied.
Claims (21)
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