* Aldibekova A. N.** Voronin A. M.

*

Kazakh National Technical University named after K. Satpayev, Kazakhstan

**

Almaty Technological University, Kazakhstan

Non-contact measurement of fluid flow by nuclear magnetic resonance

Nuclear magnetic resonance (NMR) is a resonant absorption of radiofrequency and electromagnetic energy by a substance with nonzero magnetic moment of nuclei located in an external constant magnetic field. A nonzero nuclear magnetic moment has the nucleus ¹H, ²H, ¹³C, ¹⁴N, ¹⁵N, ¹⁹F, ²⁹Si, ³¹P and etc. Usually NMR is a uniform magnetic field В₀, on which there is superimposed a weak radio frequency field В₁ perpendicular to the field В₀. For substances for which the nuclear spin I = ½ (¹H, ¹³C, ¹⁵N, ¹⁹F, ²⁹Si, ³¹P and etc.) there are two possible orientations of the magnetic dipole moment of the nucleus in the field В₀: "in the field" and "against the field". Appeared two energy levels E due to the interaction of the magnetic moment of the nucleus with the field В₀ are separated by the interval. Upon condition that, or , where h – Planck's constant, – frequency of the radiofrequency field В₁, – angular frequency, the so-called gyromagnetic ratio of the nucleus , there is resonant absorption of energy of fields B₁, called NMR [1]. For nuclides ¹H, ¹³C, ³¹P NMR frequency in the field В₀=11,7 T are equal, respectively, to (MHz): 500, 160,42 and 202,4; values (in MHz/T): 42.58, 10.68 and 17.24. According to quantum model in the field В₀ there are arise energy levels 2I + 1 between which the transitions are allowed when, where m – the magnetic quantum number.

NMR is the base for the phenomenon of NMR spectroscopy. NMR spectra were recorded by the using of radio spectrometers.

The main elements of NMR-analyzers and flow meters are magnets for generating the primary resonance field. The quality of magnets and magnetic fields in the homogeneity of the magnet gap has high demands. The relative homogeneity of the field in the work area must be 10^-6 до 10^-10.

As it was already noted, the method of signal observing of free nuclear induction in the earth's magnetic field В₀ implies the polarization of the nuclear spins by the additional magnetic field В₁ (B₁ B₀ , ), which is turned off during the measurement and followed by the activation of spin by the radiofrequency field В₁ (90⁰ impulse).

The signal from the free nuclear induction (i.e. the absorption signal) is given by the formula:

where J₁ – electric current flowing through the polarizing coil, V – the volume of the sample, χ – magnetic susceptibility.

If the installation uses the frame type coils [2] and the fluid moves on both sides of the flat sensor, the total free nuclear induction signal will have the form (see Fig. 1) ,

where . Consequently, at the nuclear envelope of the free induction signal there are oscillations of the type In this case b is the distance between the centers of successively located coils in the flat sensor. At first sight it may seem that the unilateral and bilateral flow of the sensor differ from each other by the extremely change of the fill factor. However, experiments clearly show the validity of the above mentioned equations.

Fig. 1. Bilateral NMR sensor.

In the experiments, water is used as the sample liquid. The free nuclear induction signal is observed on protons in a uniform geomagnetic field. For induction of this the magnetic field (50 mT) the resonant frequency has the quantity of the order of 2 kHz. This value is used to account the influence of variations in the geomagnetic field on the results of experiments.

During the work [3] it is proposed to use nuclear magnetic resonance sensors of various types, as the converter of fluid velocity in frequency. The ratio between the period P and the geometry of the sensor is shown in Table 1. Here P is the repetition period of the distribution of the initial phases.

Analytical equation for the kinematic shear can be written as , if the frequency is measured in Hz this equation will be.

Table 1.

Dependence of the kinematic shift of the frequency of the free nuclear signal from the induction on the geometry of the sensors

Type of the sensor	Kinematic shift	repetition period Р
Toroid	v/R	2πR
NMR-ring
Flat		2b

Below there is described the circuitry of the measuring system, developed on the basis of NMR - pulse setting, namely – transmitters and receivers of signals from the coils disposed in the working area of the magnet.

The base of the reception and transmission block is a matching device (MD), which is presented as one or more inductive coils, inside of which there are placed the objects of study (Fig. 2). The hardware of the block can be adapted to the resonant frequency of virtually any substance placed in a test tube, by the changing the operating frequency of all the nodes of the block. For the formation of all possible frequencies in the system there is used one reference oscillator of 10 MHz. For the synthesis of reference frequency synthesizers there are used DDS (Direct Digital Synthesis) of the company Analog Devices in the block. To generate a signal in the range of tenths of hertz to 100 MHz and more to the DDS device there is a need to use only a clock source, the stability of which determines the stability of all the frequencies generated by the synthesizer.

Fig. 2. Block diagram of the reception and transmission block

In synthesizers there is provided a possibility of synchronized operation of multiple DDS chips from one clock source, which is a basic requirement for working with NMR signals.

The value of the synthesized frequencies is set by the CPU system. The transmitting part of the device, in addition to direct digital synthesis synthesizer, contains a key that generates a short impulse filled by the frequency of synthesizer, and a broadband power amplifier of short impulse (BPA). The aim of BPA - to amplify the synthesizer signal of the transmitter DDS1 without distorting the impulse in a wide frequency range from a few to 100 MHz. The transmitting pulse duration, its leading and trailing edges are controlled from a central processor.

The work of three frequency synthesizers are synchronized between each other exactly up to a phase, that give the possibility to get rid of the combination of interference.

The receiver is made under the scheme of super heterodyne with the single frequency conversion.

The capacity of the first mixer is presented by the intermediate frequency filter (IFF). It is a fourth-order filter, the main task of which is the selection of the desired signal of intermediate frequency (IF) from the interference and products of conversion mixer.

After the IFF there is the key, the same to the key in the transmission path, but which performs the opposite effect: when the key of the transmitter is opened, the key of the receiver is closed and do not allow transmitting a powerful impulse to the amplifier input. When the pulse the transmitter key is opened and the entire signal of the "echo" of the test substance is applied to further processing.

Then the highlighted useful signal is amplified in the intermediate frequency amplifier (IFA). Due to the quartz filter IFF it is possible to get rid from contour coils in IFA and to apply for amplifier ща BA chip with digital amplifying control that allowed obtaining on the output of the intermediate frequency amplifier the undistorted impulse of the "echo" of the NMR signal.

For the formation of the spectrum using the Fourier-transforming there is needed the real and imaginary parts of the signal. For their allocation there is used a phase detector (PhD) with the reference frequency, four times more than the inverter. Both parts of the phase detector signal passes through a low frequency filter ( LFF ) with an adjustable bandwidth and are read using a 16-bit ADC of the successive approximation to the central processor, which sends the digitized two-channel signal to a personal computer with installed software.

The structure of stabilization block of the field is identical to the structure of the reception - transmission block, except the moment, when the signal from the phase detector goes to the control device of the spectrometer magnetic field.

The architecture of the universal transceiver block allows controlling from the CPU of a big amount of devices which support two-wire interface. In each block of reception and transmission there are used multiple microcontrollers. Another controller is used to control the ADC and to receive digital data from it.

The connection with PC via USB is made using special chip – adapter USB-UART of the company FTDI. This chip is a highly integrated USB-COM adapter which allows organizing a serial data exchange between the external device on the microcontroller and the PC via the USB using a minimum of external components (connector and passive components).

Typically, the density of probability of the fluid flow is called distribution, which is used to visualize the Fourier-transform of NMR signal as a function of q_v. Normally, only one component of q_v is changed, distribution spreads depending on the displacement at a predetermined time interval and do not depend on the speed. This is used to diffuse movement.

The velocity distribution is most easily measured with a pulsating gradient field with a pair of impulses of antiphase gradient field, while the associated echo amplitude is recorded as a function of the amplitude of the gradient.

Such experiment can be carried out with the time-constant gradient fields by changing the echo time t_Э to the echo experiment.

The velocity profile for laminar flow through a pipe of circular cross section is parabolic (Figure 3).

Fig. 3. Laminar flow in a pipe of circular cross section

The speed distribution can be obtained by equating the probability density of finding the velocity components between v and v + dv to the circle area with the radius r with the increment dr, where these components have been found.

This distribution is constant for all speeds, it is close to zero near the pipe wall, close to in the center and is zero elsewhere, and such distribution has the type of a parabola function.

From the theory it is seen, that .

The velocity distribution is very sensitive to even small flaws in the experimental system, it is better seen the process outputs than the images of speed velocities.

Fig. 4. Experimental data of laminar flow. The data were obtained at constant in time and space gradient fields.

The above approach can be used to create automated systems for monitoring production processes in various work cycles [4, 5].

References

1. Блюмих Б. Основы ЯМР. М: Техносфера , 2007. – 160 с.

2. Бородин П. М., Вечерухин Н. М. Релаксометр ЯМР в земном поле. //Научное приборостроение, 1998. Т. 8, № 1-2. С. 51-55.

3. Вечерухин Н. М., Мельников А. В. Датчики ядерного магнитного резонанса как преобразователи скорости движения жидкости в частоту. //Научное приборостроение, 2007, том 17, № 2. С. 39-47.

4. Неронов Ю. И., Иванов В. К. Разработка мини-ЯМР-томографа для учебных и научно-исследовательских целей. //Научное приборостроение, 2006, том 16, № 2.

5. Voronin A. M., Aldibekova A. N. Application of NMR in technological processes of dairy production. //Вестник Национальной инженерной академии Республики Казахстан, 2013, № 4(50). С. 106-112.