A dynamic response model for pressure sensors in continuum and high Knudsen number flows with large temperature gradients

Whitmore, Stephen A.; Petersen, Brian J.; Scott, David D.

doi:10.2514/6.1996-563

Cited by 14 publications

(4 citation statements)

References 2 publications

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“…The range of the pressure sensors is

0 \leq 2.5 kPa

with a precision of

\pm 0.03 %

of the full measurement range. The transfer function of the whole system (tubes plus sensor cavity) has been measured off‐line at a sampling frequency of

f_{s} = 1024 Hz

(for the methodology, see, e.g., Holmes & Lewis 20 and Whitmore et al 21 ). The cut‐off frequency is approximately

200 Hz

.…”

Section: Methodsmentioning

confidence: 99%

Wind tunnel study on natural instability of the normal force on a full‐scale wind turbine blade section at Reynolds number 4.7 · 10⁶

Neunaber

Danbon

Soulier³

et al. 2022

Wind Energy

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Wind turbines are exposed to the turbulent wind of the atmospheric boundary layer. Consequently, the aerodynamic forces acting on the rotor blades are highly complex. To improve the understanding, a common practice is the experimental or numerical investigation of 2d (wind turbine) blade sections. In these investigations, the flow around the 2d blade section is assumed to be two‐dimensional; however, 3d effects are known to occur. Therefore, we combine 2d CFD simulations and experimental investigations in a wind tunnel with a 2d wind turbine rotor blade section at full‐scale (i.e., chord length c=1.25m and chord‐based Reynolds number of Rec=4.7·106). In the wind tunnel, the inflow turbulence intensity is TI≈1.5%. To avoid wall effects biasing the results, the profile does not span the whole test section. The profile was equipped with two rows of pressure taps around the airfoil, close to the center, to monitor the time‐resolved aerodynamic response as well as the flow around the airfoil. The normal force, cp curves, and the separation point are analyzed. While 2d simulations and experiments match well, in the experiments, we find natural instabilities, that is, local and temporal variations of the flow separation point at angles of attack close to the maximum lift that are not triggered externally, for example, by inflow variations.

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“…The range of the pressure sensors is

0 \leq 2.5 kPa

with a precision of

\pm 0.03 %

of the full measurement range. The transfer function of the whole system (tubes plus sensor cavity) has been measured off‐line at a sampling frequency of

f_{s} = 1024 Hz

(for the methodology, see, e.g., Holmes & Lewis 20 and Whitmore et al 21 ). The cut‐off frequency is approximately

200 Hz

.…”

Section: Methodsmentioning

confidence: 99%

Wind tunnel study on natural instability of the normal force on a full‐scale wind turbine blade section at Reynolds number 4.7 · 10⁶

Neunaber

Danbon

Soulier³

et al. 2022

Wind Energy

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show abstract

“…Whitmore et al [12], Whitmore and Peterson [13], and Whitmore [14] extended the work of Berg and Tijdeman [10] to model the frequency responses of cascaded pneumatic systems with temperature gradients and rarefied flow conditions. Data presented in [11] were used, in part, to validate the model presented in [11][12][13]. Englund and Richards [2] and Whitmore [15] also extended the model of Berg and Tijdeman [10] to apply to pneumatic systems with branched components.…”

Section: Modeling the Chamber-pressure Distortionmentioning

confidence: 97%

Novel Technique for Reconstructing High-Frequency Transient Rocket Chamber-Pressure Measurements

Whitmore

Wilson

Eilers

2010

Journal of Spacecraft and Rockets

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An algorithm for reconstructing transient rocket chamber pressures from attenuated time histories is presented. This method is presented as an alternative to traditional methods, in which motor pressures are sensed by transducers mounted close-coupled to the motor casing. This close-coupled installation presents several significant measurement issues, including potential structural weakening of chamber walls, overheating of the pressure sensing element, motor-case strain biasing of the sensing element, and resonance within the measurement port. A less complex, and consequently less risky, installation is to tap the case at desired locations using very small pressure ports and then transmit pressure from the port to a pressure transducer using a significant length of pneumatic transmission tubing. This installation allows the transducer to be mounted in a controlled environment and virtually eliminates any sensing errors due to motor-case strain. Very small pressure taps are far easier to integrate with motor-case walls and allow multiple longitudinal measurements to be obtained without significantly reducing the structural integrity of the motor case. The method, based on optimal deconvolution theory, amplifies attenuated pressure signals while rejecting additive noise. The method is validated using laboratory-derived data and then applied to reconstructing transient chamber pressure for a small-scale solid rocket motor. Nomenclature= characteristic velocity, m=s c = sonic velocity, m=s D = tube diameter, mm E = expectation operator G = optimal deconvolution function i = frequency index J = cost functional j = complex constant, 1 1=2 k = time index L = tube length, cm M = number of data points in record N = frequency-domain noise, kPa=s kNk 2 = measurement variance, kPa 2 n = discrete-time advance index P c = chamber pressure, kPa P L = frequency-domain response (sensed) pressure, kPa kP LL k 2 = measured pressure variance, kPa 2 . P 0 = frequency-domain input pressure to pneumatic tubing, kPa kP 0L k = covariance, kPa 2 . kP 00 k 2 = measured pressure variance, kPa 2 . p L = time-domain response pressure, kPa p 0 = time-domain input pressure to pneumatic tubing, kPatransducer volume, cm 3 x = longitudinal coordinate, cm z = discrete-frequency response variable, 1=s t = sample interval, s p = wave propagation factor = ratio of specific heats = damping ratio = time-domain noise function, kPa = dynamic viscosity, N s=m 2 = time-domain convolution function = polytropic exponent = fluid density, kg=m 3 0 = mean fluid density in tube, kg=m 3 = time lag or dummy variable, s, = frequency-domain convolution function ! = angular frequency, rad=s ! n = radian natural frequency, rad=ŝ = optimal estimate Subscripts I = imaginary component of complex number R = real component of complex number Superscript = complex conjugate

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“…Two ranges of the pressure sensors were used depending on their location, 0 kPa to 7 kPa near the leading edge suction peak and 0 to 2.5 kPa elsewhere, with a precision of ±0.03% of the full measurement range. The transfer function of the whole system (tubes plus sensor cavity) has been measured off-line at a sampling frequency of 1024 Hz following the methodology of Holmes and Lewis [4] and Whitmore et al [9]. The signal acquisition was performed using two National Instrument acquisition boards linked by real-time system integration for synchronization purposes.…”

Section: The Airfoilmentioning

confidence: 99%

Reynolds effects on wall pressure fluctuations at stall inception of a wind turbine blade section

Hanna,

Braud,

Podvin

et al. 2024

J. Phys.: Conf. Ser.

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Understanding the flow physics over airfoils near stall is of major importance for improvement of dynamic stall models. However, static stall is a first important step that remains challenging. The present study focuses on the influence of Reynolds number on the stall inception of an airfoil, one of the important parameter impacting the stall behavior. The blade, extracted from scans of an operated 2MW turbine, is investigated experimentally at full scale using two chordwise lines of unsteady wall pressure sensors with Reynolds numbers ranging from 5 × 105 to 4.2 × 106. Results reveal an important dependence of the pressure fluctuations with the Reynolds number: their relative level compared with the intrados value is progressively increased with the Reynolds number in the intermittent separation region which corresponds to the peak of pressure standard deviation.

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A dynamic response model for pressure sensors in continuum and high Knudsen number flows with large temperature gradients

Cited by 14 publications

References 2 publications

Wind tunnel study on natural instability of the normal force on a full‐scale wind turbine blade section at Reynolds number 4.7 · 10⁶

Wind tunnel study on natural instability of the normal force on a full‐scale wind turbine blade section at Reynolds number 4.7 · 10⁶

Novel Technique for Reconstructing High-Frequency Transient Rocket Chamber-Pressure Measurements

Reynolds effects on wall pressure fluctuations at stall inception of a wind turbine blade section

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A dynamic response model for pressure sensors in continuum and high Knudsen number flows with large temperature gradients

Cited by 14 publications

References 2 publications

Wind tunnel study on natural instability of the normal force on a full‐scale wind turbine blade section at Reynolds number 4.7 · 106

Wind tunnel study on natural instability of the normal force on a full‐scale wind turbine blade section at Reynolds number 4.7 · 106

Novel Technique for Reconstructing High-Frequency Transient Rocket Chamber-Pressure Measurements

Reynolds effects on wall pressure fluctuations at stall inception of a wind turbine blade section

Contact Info

Product

Resources

About

Wind tunnel study on natural instability of the normal force on a full‐scale wind turbine blade section at Reynolds number 4.7 · 10⁶

Wind tunnel study on natural instability of the normal force on a full‐scale wind turbine blade section at Reynolds number 4.7 · 10⁶