Method for determining the volume of a sample of an aqueous salt solution

Abstract

The invention relates to the field of temperature measurement and heat measurement and can be used in the operation of icing sensors used to determine the condition, for example, of road surfaces and runways. A method for determining the volume of a sample of an aqueous salt solution using a thermoelectric sensor consists in establishing and stabilizing a starting temperature of a contact surface by regulating a thermoelectric module, then cooling the contact surface at a constant rate by regulating the thermoelectric module, while simultaneously taking readings from a temperature sensor and a heat flux sensor. The heat capacity of a cuvette containing a sample is determined on the basis of the measurement of the quantity of heat passing through the heat flux sensor during cooling from the temperature of the start of the cooling phase to the minimum temperature before the start of crystallization (the supercooling temperature of the sample). The obtained heat flux integral divided by the difference of these temperatures represents the heat capacity of the cuvette. By subtracting the known heat capacity of the dry cuvette, the heat capacity of the sample itself is determined. On the basis of the known specific heat capacity and the physical density of water or of the sample of the aqueous salt solution, the mass and volume of the sample are determined. The technical result is an increase in measurement accuracy.

Description

[0001] METHOD FOR DETERMINING THE VOLUME OF A SAMPLE OF WATER-SALT SOLUTIONS

[0002] Field of technology

[0003] The proposed invention relates to the field of temperature measurement and heat metering and can be used in the operation of icing sensors used to determine conditions of, for example, road surfaces, runways, etc., especially in conditions of using anti-icing agents based on water and water-salt solutions.

[0004] State of the art

[0005] Currently, thermoelectric icing sensors are used to detect icing or a predisposition to icing. Their operation is based on recording the moment and characteristics of the water-ice and ice-water phase transition. In this case, such characteristics as icing temperature (ice crystallization temperature) and icing intensity (ice amount) can be determined and quantitatively assessed. Icing intensity and a predisposition to icing are determined by the volume of the sample in the sensor's measuring cuvette and / or by the thickness of the sample layer on the sensor's sensitive surface with its known area. If the sample is already in the form of ice, this is icing intensity, and if the sample is a liquid near the crystallization temperature, this is a predisposition to icing.

[0006] Water-salt anti-icing compounds are used in road construction. For their effective use, it is necessary to control the icing temperature and the amount of liquid component applied to the road surface.

[0007] These icing sensors use a Peltier element (thermoelectric module) which cyclically cools and heats the test sample in a temperature range close to the crystallization temperature.

[0008] The recording of the phase transition of crystallization or melting of aqueous solutions is based on the physical regularity of this phenomenon as a first-order phase transition. During such a phase transition, a significant amount of heat is released, and the temperature remains constant during the phase transition. The nature of the change in temperature and state of the test sample over time (e.g., heat release) allows one to determine both the temperature and the characteristic of the icing intensity. A measurement method is known from the prior art (DIKatz, Frensor: A New Smart Pavement Sensor, Transportation Research Record #1387, pp. 147-150, 1993, ISBN 0309054583 [1]), in which the icing sensor consists of a Peltier element and a temperature sensor located under the cooled surface of the Peltier element.When a water sample is cooled, according to a known physical law, a noticeable supercooling of the liquid (water or aqueous solutions) first takes place, and only after this does a spontaneous phase transition of crystallization occur with the release of a significant amount of heat and an increase in the temperature in the sample to a temperature that is interpreted as the desired phase transition temperature.

[0009] The method of determination using such a sensor consists of sequentially recording first a sharp change in temperature after supercooling (the first point) and the maximum temperature after that (the second point), which is identified as the crystallization temperature.

[0010] This method and the device implementing it have disadvantages. First of all, the intensity of crystallization is determined indirectly, not quantitatively, by the duration of the crystallization phase, recorded by measuring the temperature.

[0011] A thermoelectric icing sensor is known from the prior art (see RU2534493, class B64D15 / 20, published on 27.11.2014 [2]), which contains a thermoelectric module made in the form of a Peltier element that performs the function of a heat pump, and a temperature sensor installed on the external sensitive surface.

[0012] Depending on the ambient temperature and its proximity to the freezing point, the Peltier element heats or cools the sensitive surface according to a given algorithm. The temperature sensor monitors the temperature change. If there are conditions for ice formation on the surface, the temperature of the sensitive surface stabilizes during the water-ice phase transition, and the latent heat of ice formation is released. The sensor records the specified temperature, it is considered the desired phase transition temperature. And the intensity of ice formation is estimated by the value of the power supply of the Peltier element during this period, since this directly correlates with the released or absorbed heat of the phase transition.

[0013] The disadvantage of this known device is that the assessment of ice formation intensity is approximate. The energy consumption of the Peltier element depends significantly on the operating conditions (ambient temperature, heat exchange with the environment) and on the operability of the Peltier module itself. Therefore, there is no unambiguous correlation with the sample amount.

[0014] The closest to the declared method for determining the quantitative characteristics of icing is the well-known method for determining the phase transition temperature and the volume of a liquid sample using a thermoelectric icing sensor in accordance with RU 2779247 C1 (class B64D15 / 20, published 05.09.2022 [3]).

[0015] The known method is implemented using a thermoelectric icing sensor. A thermoelectric module built into such a sensor, made in the form of a Peltier element, provides a cyclic heating-cooling mode for the external sensitive surface of the cuvette with a sample of water or water-salt solution. The icing sensor may also contain a built-in heat flow sensor for measuring the intensity of icing - the amount of liquid in the sample.

[0016] In the cooling phase provided by the Peltier element, if there is a liquid sample (water or solution) in the cuvette, crystallization is recorded by a sharp change in temperature measured by the temperature sensor and a sharp jump in the signal of the heat flow measured by the sensor. In this case, the phase transition temperature is determined at the maximum of the temperature jump in the cooling phase. Also, the crystallization temperature is determined in the heating phase by a characteristic break in the temperature time curve.

[0017] The sample volume is determined by the integral of heat released in the cooling phase from the beginning of crystallization until the return of the recorded heat release to the value preceding the beginning of crystallization. The measured amount of released crystallization heat is recalculated into the sample volume using the known value of the specific heat of crystallization of water.

[0018] The known method is applicable, first of all, to determine the crystallization temperature and sample volume in the case of pure water. However, there are disadvantages associated with the fact that determining the moment of return of heat release to the initial level (before crystallization) does not yet mean complete crystallization of the sample. Therefore, the measurement result may have a significant error, especially strongly it will manifest itself with large quantities of the tested sample.

[0019] In the case of water-salt solutions, this method (and all the above analogs in general) has an even more significant drawback associated with the fact that water-salt solutions are two-component compositions (water and salt). The phase transformation must be considered in the context of a two-component phase diagram of a water-salt solution (temperature-concentration), unlike pure water. Most practically significant water-salt solutions of salts, such as NaCl, CaCh, etc., have the form of a eutectic phase diagram, characterized by the eutectic composition of the solution with the minimum crystallization temperature. The liquidus line leads to this point.

[0020] A supercooled two-component water-salt solution undergoes several stages of crystallization. First, the supercooled sample begins crystallization with the release of heat due to the crystallization of water with simultaneous saturation of the remaining solution with salt and an increase in temperature (Fig. 1). This is the first stage. The temperature cannot exceed the temperature value lying on the liquidus line at the point corresponding to the maximum increase in the sample temperature due to the released heat of crystallization. Then, crystallization of water from the solution continues, but with a decrease in temperature. This is the second stage of crystallization. Then, the water fraction of the solution also gradually crystallizes into ice, and the salt concentration of the remaining solution will further increase in accordance with the course of the liquidus line of the phase diagram. And only after reaching the temperature of the eutectic solution, the remaining part of the sample in the liquid state will crystallize with the maximum eutectic concentration. This is the third stage of crystallization.

[0021] This long three-stage process is well illustrated by the heat release curve over time (Fig. 2) during cooling of a sample of water-salt solution.

[0022] Therefore, the fundamental disadvantage of the known method [3] is that the amount of heat measured in it is interpreted as the heat of crystallization of the entire sample. According to it, the mass ω is calculated, interpreted as the mass (and through the density - the volume v) of the entire sample. However, for a water-salt solution, during crystallization up to reaching the temperature of the eutectic solution, the sample will consist of two phases of crystallized ice and enriched salt solution, i.e. not the entire sample has crystallized if the temperature has not dropped to and below the temperature Te of the eutectic composition of the solution. And in addition, the composition of the solution (what salt is present) is unknown in advance, and this lower temperature is unknown. The values ​​ω and v measured in the known method cannot be interpreted as the total mass M and volume V of the sample, respectively. The discrepancy is significant - several times for water-salt solutions, and depending on the initial concentration. Disclosure of the invention

[0023] The objective of the invention is to create a method for operating a thermoelectric icing sensor in order to obtain accurate, reliable quantitative characteristics of ice formation in water and water-salt solutions.

[0024] The technical result of the proposed invention, which is objectively manifested during its implementation, is an increase in the accuracy of measurements.

[0025] The stated problem is solved, and the technical result is achieved due to the following.

[0026] The Peltier element of the thermoelectric icing sensor ensures a cycle of heating and cooling of the solution sample. First, there is a heating phase to a temperature significantly higher than the crystallization temperature, for example +15°C. This allows the sample to melt if it was originally ice. Then, at a constant rate, the sample is cooled until it reaches the lower limit, which is obviously significantly lower than the crystallization temperature.

[0027] The fact of the onset of crystallization in the presence of a water sample or a water-salt solution is recorded by the icing sensor by a sharp change in temperature (built-in temperature sensor) from the local minimum temperature Tc (this is the supercooling temperature) and a sharp jump in the signal from the built-in heat flow sensor.

[0028] The intensity of ice formation (amount of ice, water) is determined by the measurement result of the heat flow sensor. The integral of the heat passed from the moment of the beginning of cooling to the moment of the beginning of crystallization from the supercooled state, measured by the heat flow sensor, is used. The value obtained by dividing this heat by the difference between the initial and final cooling temperatures is the effective heat capacity of the cuvette (with or without a sample), and the sensor cuvette constant is determined by the value of the previously measured heat capacity of a dry cuvette without a sample.

[0029] The difference between the measured heat capacity of the cuvette with and without the sample is the heat capacity of the sample itself. From here, the mass and volume of the sample can be determined with good accuracy by dividing the heat capacity measured in this way by the specific heat capacity and, accordingly, then by the specific density. The corresponding known parameters of water can be used.

[0030] If the thermoelectric icing sensor simultaneously measures the crystallization temperature of the sample (water or water-salt solution), then the measured crystallization temperature is used to determine the salt concentration and hence its actual specific heat capacity and density, which differ from the corresponding characteristics of pure water. Then the mass and volume of the sample are determined with greater accuracy.

[0031] Brief description of the drawings

[0032] Fig. 1a shows the phase diagram of a water-salt solution using NaCl as an example and typical changes in temperature T and concentration X over time during crystallization with supercooling. The following are marked: the point of temperature TfO of crystallization of the solution of initial concentration XfO, the point of temperature Tc of supercooling and the point (Td, Xd) on the liquidus line to which the temperature recorded by the sensor will rise, as well as the final point (Tfin, Xfin) on the liquidus line corresponding to the temperature of the end of the measurement cycle, the point (Te, Xe) of the eutectic solution.

[0033] Fig. 16 shows a typical time course of heat release of a sample during cooling from the beginning of crystallization from the moment of the ultimate supercooling (Tc), first with a rise in temperature to the value Td, then cooling to complete crystallization of the sample upon reaching the temperature Te of the eutectic solution. Measurements are usually stopped earlier, at the temperature Tfin.

[0034] Fig. 2 shows an example of the method implementation at the initial temperature Ta of the environment Ta = 0 °C. The concentration of the NaCl salt XO in the sample and the sample crystallization temperature TfO are 3.34 wt.% and -2 °C, respectively. The sample volume is 50 μl. The change in temperature Ti and the heat flux q) measured with a time step i are shown. The characteristic moments are marked: i = 0 - the beginning of the experiment from the ambient temperature T = Ta; i = nl - stabilization of the initial temperature Tn0 = T0, the beginning of the cooling phase; i = n2 - the ultimate supercooling of the water sample to Tnl = Tc; i = n3 - the point of the local maximum temperature Tn2 = Td; i = n3 - the end of the crystallization measurement; i = n4, the end point Tn4 = Tfin.

[0035] Implementation of the invention

[0036] The proposed method for measuring the thermoelectric icing sensor is implemented as follows (Fig. 2).

[0037] At the beginning of the measurement cycle, the temperature of the sample is raised from the initial ambient temperature Ta by a fixed value TO, for example by 15°C, using the Peltier module regulation, and stabilized for a short time. This temperature is significantly higher than the crystallization temperature of the water-salt solution, which is usually below 0°C. The holding time allows the sample to melt in the form of ice, if it was originally ice (for example, at low ambient temperatures).

[0038] Then, at a constant speed, the sample is cooled by the Peltier module towards the lower limit - temperature Tc, which is obviously significantly lower than the crystallization temperature. At the same time, the heat flow sensor measures the accumulated heat release during the cooling process from TO to Tc.

[0039] If there is no sample in the cuvette, the limiting temperature Tc will be reached without phase transition events, and the measurement ends.

[0040] This measurement of a dry cuvette is intentionally done for calibration and determination of the sensor constant - the heat capacity characteristic of a dry CsO cuvette, which will then be used in subsequent measurements, namely: where At is the time step for measuring the heat flux; qo is the heat flux at the beginning of the cooling phase of the measurement cycle; qi is the heat flux at the i-th measurement step from the beginning of crystallization (i=l is the beginning of crystallization), n is the last measurement step - upon reaching Tc; Cs is the heat capacity of the cuvette (for a dry cuvette - CsO); TO is the initial temperature of summation of the measured heat.

[0041] Since the cuvette is obviously empty (dry) during calibration, the measured heat capacity is a sensor constant and is used for subsequent measurements: c s0 = C s (3)

[0042] If there is a liquid sample (water or water-salt solution) in the cuvette, then the fact of the beginning of crystallization is recorded in both measuring channels - by a sharp change in temperature from the supercooled state Tc, measured by the temperature sensor, and a sharp jump in the signal of the heat flow measured by the sensor from the released heat of crystallization.

[0043] In this case, the measured heat capacity of the cuvette with the sample according to formulas (1) and (2) will already be the heat capacity of the cuvette with the Cs sample.

[0044] The temperature Td after the onset of crystallization, which is determined at the point of the maximum jump, is then used to calculate the crystallization temperature Tf of the initial solution. The intensity of ice formation (sample amount) is determined by the difference in heat capacities measured with the sample and the sensor constant - the heat capacity of the dry cuvette.

[0045] Approximately the sample quantity (mass and volume) is determined with known heat capacity q0 and density p0 of water as

[0046] And if the icing sensor measured the crystallization temperature Tf of the sample, then from this temperature it is possible to calculate the concentration X of the salt in the solution, and then its density p х at a given concentration and specific heat capacity q . Then, using formulas (4) and (5), a more accurate value of the sample quantity (mass and volume) is determined using the density and specific heat capacity of the solution thus determined. In formulas (4) and (5), instead of q0 and p0, p are used, respectively. х and q .

[0047] Examples of implementation

[0048] An experimental icing sensor was manufactured according to description RU209777 (class G08B / 19 / 02, published on 23.03.2022 [4]), consisting of a thermoelectric module (Peltier element), wherein the thermoelectric sensor is equipped with a thermoelectric heat flux sensor connected with its lower part to the Peltier element, the opposite upper part of which forms an external surface sensitive to ice formation and is equipped with a temperature sensor.

[0049] Measurements were carried out at two ambient temperatures Ta: +0°C and -15°C using aqueous-salt solutions of NaCl with three specified crystallization temperatures TfO: -2°C, -5°C and -8°C, as well as pure water samples (TfO=O°C).

[0050] The specified samples of water-salt solutions with a given crystallization temperature were prepared according to the known relationship between the crystallization temperature and the concentration of the given salt NaCl (respectively 3.34 wt.%, 7.88 wt.% and 11.75 wt.%).

[0051] At each temperature Ta and for a solution with a given crystallization temperature TfO, measurements were carried out with different amounts of sample volume V0, set precisely in the range of 10-50 µl (three volumes V0 were set: 10, 30 and 50 µl).

[0052] For example, at an ambient temperature of Ta=+0°C, a precisely measured drop of a water-salt solution with a given crystallization temperature of Tf=-2°C (NaCl salt concentration of 3.34 wt.%) and a volume of V0=50 µl was placed in the measuring cuvette of the icing sensor.

[0053] In this case, the mass of the sample is also known from the known dependence of the density of the water-salt solution (in this case, NaCl) on the salt concentration.

[0054] An explanation of a specific example of a measurement cycle is given in Fig. 2.

[0055] By controlling the thermoelectric cooler (Peltier element), the temperature of the water sample in the cuvette, measured by the temperature sensor, is brought from the initial ambient Ta=+0°C to the temperature T0=+15°C. This is the preliminary phase of stabilization of the initial temperature TO. In this case, the Peltier element works as a heater (from Ta=+0°C to T0=+15°C).

[0056] In this case, the readings of the temperature sensor Ti and the heat flow sensor qi are recorded at equal time intervals At=0.14 s, where Ti, qi are the readings of the temperature and heat flow, respectively, in the i-th time interval (i=0...N, where 0 is the start of the measurements, N is the end of the measurements).

[0057] Thus, an array of data Ti and qi for i=0...N is accumulated.

[0058] After the temperature stabilizes at T0=+15°C, a gradual, uniform decrease in temperature is set by controlling the thermoelectric cooler.

[0059] The readings of the heat flow sensor before the start of the temperature decrease are stored separately as qnO, as is the corresponding time interval number i=nO.

[0060] When the maximum temperature Tc of supercooling of the liquid is reached, which is unknown in advance (noticeably below +0°C), spontaneous crystallization begins.

[0061] This moment is fixed by a sharp change in temperature towards increase. The temperature value Tp1 is remembered, as well as the number i=nl. This is the supercooling temperature Tp1=Tc.

[0062] The heat flow sensor readings also show a change (a sharp increase) in the signal associated with the release of crystallization heat (Fig. 2). In this case, the heat flow value before this change is stored separately as qnl in the time interval i=nl.

[0063] The temperature increases and reaches a local maximum, which is also remembered as Tp2 (for i=n2). Temperature Tp2 is the temperature Td on the liquidus line of the phase diagram. It correlates with the crystallization temperature Tf of the initial solution. Crystallization of the water sample in the cuvette continues for some time with a duration that depends on the amount of the sample. In this case, a gradual decrease in the measured temperature Ti and the heat flow qi is observed.

[0064] The moment i=n3 is monitored using the heat flow sensor, when the value of the heat flow qn3 becomes equal to or less than the value of the heat flow at point i=n 1 , i.e. when qn3 < qnl.

[0065] The number of this time interval i=n3 and the corresponding temperature TпЗ are remembered. This is the end of the measurement cycle, where TпЗ is the temperature of the end of the measurement cycle Tfin.

[0066] In the entire time interval i=nl...n3, all values ​​of the heat flow sensor readings qi=qnl...qn3 are stored.

[0067] After the end of the measurement cycle (i=n3), mathematical processing of the measured and stored data arrays is carried out, namely, the following calculations are performed.

[0068] 1. Calculation of the heat of crystallization of the sample, its mass and volume.

[0069] From the array of heat flow values ​​in the interval qi=qn1 to qi=qn2 (from i=n1 to i=n2), the total amount of heat associated with the change in the temperature of the sample cell from the start of cooling to the start of crystallization is found, as

[0070] Next, the heat capacity of the sample cell is found using the measured values ​​of the initial and final cooling temperatures (respectively T п1 and T п2 )

[0071] The heat capacity of an empty cuvette is known C s0according to a previously conducted similar measurement (calibration of a dry cuvette) in the absence of a sample. Then the heat capacity of the measured sample will be: c = c s - C s0 (8)

[0072] The mass M of the sample is found using the known value of the specific heat capacity of water q = 4.2 J / g. Namely: And according to the known specific density of water p = 1 g / ml, we find the volume of the sample:

[0073] 2. Clarification of the mass and volume of the sample.

[0074] Since the thermoelectric icing sensor can simultaneously measure the crystallization temperature Tf of the solution sample, then the concentration X of the salt in the sample is determined from the set temperature Tf and known reference values, and the real heat capacity q is established from the reference data. x solution and its density Px-

[0075] From here, using formulas (9) and (10), starting from the obtained heat capacity of the sample, its mass and volume are calculated. In formulas (9) and (10), instead of q and p, the established values ​​of q are used, respectively. x and r х .

[0076] All measured and calculated results of the experiment with a 50 µl solution sample at T0=+0°C are entered into Table 1.

[0077] The measurements are repeated for both values ​​of the initial temperature for samples of other concentrations (crystallization temperatures) and volumes, and the results are also entered into the specified Table 1.

[0078] The result is a completely filled table 1.

[0079] Table 1. Measurement results a) Ambient temperature Ta=+0°C b) Ambient temperature Ta=-15°C

[0080] Designations in table 1:

[0081] VO, TfO - the specified volume and crystallization temperature of the water-salt solution sample, respectively; Ta, Tc, Td, Tfin - the temperatures of the environment, supercooling, maximum during crystallization, and end of measurement measured by the temperature sensor; Tf - the measured crystallization temperature; Xf

[0082] - calculated value of solution concentration at temperature Tf; px - density of salt solution with concentration Xf; Q - crystallization heat measured by the sensor; m, v

[0083] - respectively, the mass and volume, measured by a known method [3]; M, V - respectively, the mass and volume of the sample without corrections for the properties of the solution; M', V' - respectively, the mass and volume of the sample with corrections for the properties of the solution; dV - the accuracy of measuring the volume of the sample relative to the specified values ​​of TfO and V0.

[0084] Comparison of the initial values ​​of the specified sample volume V0 with the measurement results V shows good convergence in a wide range of measurement conditions. Measurement of the sample volume with an accuracy of no worse than + / - 15% fully complies with the requirements for such icing sensors - road situation sensors, according to industry standards (e.g. Standard DIN EN 15518 Winter maintenance equipment. Road weather information systems, 2011 [4]). At the same time, the values ​​of the sample volume v, which are measured by the known prototype method [3], differ significantly from the initial characteristics of the sample due to the previously given explanations. Only on pure water samples does the prototype method give similar measurement results. In the case of water-salt solutions, there are significant discrepancies: the measured volume, being, in fact, only a part of the crystallized sample, naturally differs noticeably from the specified volume, sometimes several times depending on the initial concentration of the solution.

[0085] Thus, the proposed method for measuring the thermoelectric icing sensor solves the problem of such sensors in relation to measurements of water-salt solutions in a wide range, namely, it provides a highly accurate quantitative determination of the sample size based on the readings of the heat flow sensor and processing of the results using the proposed method.

[0086] The method for measuring the intensity of icing (the amount of ice or water sample and, accordingly, the thickness of the film, with a known surface area of ​​the measuring cuvette) using a thermoelectric icing sensor, according to the proposed invention, can find wide application in industry, namely in the field of thermometry and heat metry of thermoelectric icing sensors, especially for monitoring the condition of road surfaces under conditions of using anti-icing agents based on water and water-salt solutions.

Claims

CLAUSE OF THE INVENTION 1. A method for determining the volume of a sample of a water-salt solution using a thermoelectric icing sensor comprising a thermoelectric module, a temperature sensor and a thermoelectric heat flux sensor equipped with a surface in contact with the sample, wherein the intensity of ice formation is determined using a heat flux measurement in a measuring cycle in the sample cooling phase, characterized in that the volume of the sample is determined by dividing the heat capacity of the sample by the specific heat capacity of the sample and the density of the sample solution, wherein the heat capacity of the sample is determined by the difference between the measured heat capacity of the measuring cuvette with the sample and the previously measured heat capacity of the empty cuvette, and said difference is determined as the integral of the heat flux measured by the thermoelectric heat flux sensor during the cooling time from the cooling start temperature to the crystallization start temperature, divided by the difference between the said cooling start temperature and the crystallization start temperature.

2. The method according to paragraph 1, characterized in that the corresponding data for water are used as the specific heat capacity and density.

3. The method according to paragraph 1, characterized in that when measuring the crystallization temperature and / or concentration of the salt solution of the sample, the specific heat capacity and density of the solution with the salt concentration thus established are used to determine the volume of the sample.

Images