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Title
Abstract
Figures
Introduction
Principle of the Uvp Method
Comparison with Optical Methods
Areas of Future Research
References

Velocity Profile Measurement by Ultrasonic Doppler Method

Profile image of Thanseer PmThanseer Pm

Abstract

The ultrasonic velocity profile measuring method has been developed at PSI for application in fluid mechanics and fluid flow measurement. It uses pulsed ultrasonic echography together with the detection of the instantaneous Doppler shift frequency. This method has the following advantages over the conventional techniques: (1) an efficient flow mapping process, (2) applicability to opaque liquids, and (3) a record of the spatiotemporal velocity field. After a brief introduction of its principle, the characteristics and specifications of the present system are given. Then examples in fluid engineering for oscillating pipe flow, T-branching flow of mercury, and recirculating flow in a square cavity are described that confirm the method's advantages. Several other works under way by other investigators are introduced. A potential for in-depth study of fluid dynamics is demonstrated by several examples from an investigation of modulated wavy flows in a rotating Couette system. The position-averaged power spectrum and the time-averaged energy spectral density were used to study the dynamic characteristics of the flow, and subsequently the velocity field was decomposed into its intrinsic wave structure based on two-dimensional Fourier analysis.

Figures (16)
Figure 1. Qualitative sketch to explain the principle of UVP. Arrangement between an ultrasound beam and a flow in a channel (top); echo signal (middle); reconstructed velocity profile (bottom). Thus a velocity profile can be obtained by analyzing the echo signal to derive instantaneous frequencies at each instant. In practice, the echo signal is processed at 128 times instants in parallel, and thus we obtain a data set
Figure 1. Qualitative sketch to explain the principle of UVP. Arrangement between an ultrasound beam and a flow in a channel (top); echo signal (middle); reconstructed velocity profile (bottom). Thus a velocity profile can be obtained by analyzing the echo signal to derive instantaneous frequencies at each instant. In practice, the echo signal is processed at 128 times instants in parallel, and thus we obtain a data set
*D = dimension of variable; C = component of vector. Table 1. Examples of Flow Configurations Where UVP Has Been Successfully Applied
*D = dimension of variable; C = component of vector. Table 1. Examples of Flow Configurations Where UVP Has Been Successfully Applied
Figure 2. Detection of an instantaneous frequency. 7,, is pulse repetition period, Tp, is total profile measuring time.
Figure 2. Detection of an instantaneous frequency. 7,, is pulse repetition period, Tp, is total profile measuring time.
Figure 3. A velocity profile of a rigid-body motion of liquid in a rotating cylinder. R is the radius of the cylinder, w the rotational speed, and Y, the distance between the line of measurement and the center of the cylinder.
Figure 3. A velocity profile of a rigid-body motion of liquid in a rotating cylinder. R is the radius of the cylinder, w the rotational speed, and Y, the distance between the line of measurement and the center of the cylinder.
Figure 4. (Top) A time-averaged velocity profile of a rigid- body motion in a rotating cylinder. (Bottom) The first deriva- tive of the velocity profile in (a).
Figure 4. (Top) A time-averaged velocity profile of a rigid- body motion in a rotating cylinder. (Bottom) The first deriva- tive of the velocity profile in (a).
Figure 5. Phase-averaged time-dependent velocity profiles in oscillating pipe flow. Only one of two profiles is shown.
Figure 5. Phase-averaged time-dependent velocity profiles in oscillating pipe flow. Only one of two profiles is shown.
Figure 7. Average velocity profiles of a T-branching flow of mercury. Open and solid circles correspond to cases of oppo- site flow directions. A flow in a square cavity was studied in order to verify the feasibility of flow mapping of a two-dimensional vector
Figure 7. Average velocity profiles of a T-branching flow of mercury. Open and solid circles correspond to cases of oppo- site flow directions. A flow in a square cavity was studied in order to verify the feasibility of flow mapping of a two-dimensional vector
Figure 6. The measuring configuration of a T-branching flow of mercury. A transducer is immersed in liquid.
Figure 6. The measuring configuration of a T-branching flow of mercury. A transducer is immersed in liquid.
Figure 8. The measuring configuration of recirculating flow in a square cavity. The transducer was scanned on the outer wall of the square cavity in two directions.
Figure 8. The measuring configuration of recirculating flow in a square cavity. The transducer was scanned on the outer wall of the square cavity in two directions.
Figure 9. Velocity vector map of recirculating flow in a square cavity (raw data). field [9,10]. A square cavity of dimension 40 x 40 mm is attached to a parallel flow of 40-mm width (Fig. 8). A transducer was scanned along two walls with a constant step of 5 mm, in the X direction for V, and Y direction for V,. The measured profiles are thus V(x, Y) and VAX, y). From these two two-dimensional distributions, which have different grid systems, one can directly con- struct the vector velocity field of this flow by forming the velocity vectors at the crossings (7 x 6 points) of the two grid systems as shown in Fig. 9. In this figure, the shape of the primary flow is clearly represented and two small corner vortices at the bottom corners are also indicated. This structure was also observed by flow visualization using ink, and the agreement was good. By redistributing the grid system through interpolation within the same system, velocity distributions with a finer mesh were ob- tained from which the stream function distribution and
Figure 9. Velocity vector map of recirculating flow in a square cavity (raw data). field [9,10]. A square cavity of dimension 40 x 40 mm is attached to a parallel flow of 40-mm width (Fig. 8). A transducer was scanned along two walls with a constant step of 5 mm, in the X direction for V, and Y direction for V,. The measured profiles are thus V(x, Y) and VAX, y). From these two two-dimensional distributions, which have different grid systems, one can directly con- struct the vector velocity field of this flow by forming the velocity vectors at the crossings (7 x 6 points) of the two grid systems as shown in Fig. 9. In this figure, the shape of the primary flow is clearly represented and two small corner vortices at the bottom corners are also indicated. This structure was also observed by flow visualization using ink, and the agreement was good. By redistributing the grid system through interpolation within the same system, velocity distributions with a finer mesh were ob- tained from which the stream function distribution and
Figure 10. Two-dimensional representation of the oscillatory behavior of a cell structure during the initial transient after a sudden start. Only regions with positive velocity are plotted. The ordinate is height, and the abscissa is time.
Figure 10. Two-dimensional representation of the oscillatory behavior of a cell structure during the initial transient after a sudden start. Only regions with positive velocity are plotted. The ordinate is height, and the abscissa is time.
Figure 11. Time-averaged velocity profiles of axial compo- nent at the inner and outer wall positions.
Figure 11. Time-averaged velocity profiles of axial compo- nent at the inner and outer wall positions.
Figure 12. Space-averaged power spectra for (a) R* = 9.05(WVF), (b)R* = 14.08 (MWY), (c) R* = 21.27. ber with sufficient data points and resolution. Up to now, it has been a difficult task in experimental fluid dynamics to obtain an energy spectrum or spectral density as a function of wavenumber without using Taylor’s hypothe- sis. Although it is still one-dimensional (an extension to 3D measurement presents no technical difficulty), it is possible to obtain the time-dependent spectral density, so it can be a powerful tool for studying the spatiotemporal
Figure 12. Space-averaged power spectra for (a) R* = 9.05(WVF), (b)R* = 14.08 (MWY), (c) R* = 21.27. ber with sufficient data points and resolution. Up to now, it has been a difficult task in experimental fluid dynamics to obtain an energy spectrum or spectral density as a function of wavenumber without using Taylor’s hypothe- sis. Although it is still one-dimensional (an extension to 3D measurement presents no technical difficulty), it is possible to obtain the time-dependent spectral density, so it can be a powerful tool for studying the spatiotemporal
Figure 14. Partial two-dimensional Fourier spectrum as a function of wavenumber and frequency. Inset is a wavenumber spectrum at f = 0. As repeatedly mentioned, the data set obtained by this method is a spatiotemporal two-dimensional velocity field. Thus it is possible to decompose the velocity field directly by any orthogonal decomposition technique such as proper orthogonal decomposition [28-30] or a singular value de- composition [31]. However, we simply applied a two- dimensional Fourier transform to the data set referred to in the preceding sections [32]. Decomposition of the flow
Figure 14. Partial two-dimensional Fourier spectrum as a function of wavenumber and frequency. Inset is a wavenumber spectrum at f = 0. As repeatedly mentioned, the data set obtained by this method is a spatiotemporal two-dimensional velocity field. Thus it is possible to decompose the velocity field directly by any orthogonal decomposition technique such as proper orthogonal decomposition [28-30] or a singular value de- composition [31]. However, we simply applied a two- dimensional Fourier transform to the data set referred to in the preceding sections [32]. Decomposition of the flow
Figure 13. Time-averaged energy spectral density for R* = 16.40.
Figure 13. Time-averaged energy spectral density for R* = 16.40.
Figure 15. Decomposition of the velocity field. Top: Raw data. Middle: Reconstructed velocity field. Bottom: Residual. Reconstruction is based on one space component, two temporal components, and two spatiotemporal components.
Figure 15. Decomposition of the velocity field. Top: Raw data. Middle: Reconstructed velocity field. Bottom: Residual. Reconstruction is based on one space component, two temporal components, and two spatiotemporal components.

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