rus
Issue #3-4/2022
A.Yu.Kochetkov, E.Yu.Kotlyarov, A.F.Shabarchin, E.V.Shemetova
CONCEPT DEVELOPMENT: DESIGN AND EXPERIMENTAL ANALYSIS OF THE HEAT EXCHANGER / HEAT METER OPERATING CHARACTERISTICS FOR PERFORMING THERMAL VACUUM TESTS AT LOW TEMPERATURE USEFUL WORKLOAD FOR SPACECRAFTS
CONCEPT DEVELOPMENT: DESIGN AND EXPERIMENTAL ANALYSIS OF THE HEAT EXCHANGER / HEAT METER OPERATING CHARACTERISTICS FOR PERFORMING THERMAL VACUUM TESTS AT LOW TEMPERATURE USEFUL WORKLOAD FOR SPACECRAFTS
DOI: 10.22184/1993-8578.2022.15.3-4.204.215
The concept of a heat meter is proposed to measure the heat load supplied to the thermal control system (TCS) from the scientific equipment operating at a temperature of minus 100 °С. A stable low temperature level maintained by the controlled phase transition of liquid flow. To maintain the preset temperature, a heater is applied.
The concept of a heat meter is proposed to measure the heat load supplied to the thermal control system (TCS) from the scientific equipment operating at a temperature of minus 100 °С. A stable low temperature level maintained by the controlled phase transition of liquid flow. To maintain the preset temperature, a heater is applied.
Теги: heater heat meter preset temperature thermal control нагреватель стабилизация температуры тепломер
Received: 17.05.2022 | Accepted: 25.05.2022 | DOI: https://doi.org/10.22184/1993-8578.2022.15.3-4.204.215
Original paper
CONCEPT DEVELOPMENT: DESIGN AND EXPERIMENTAL ANALYSIS OF THE HEAT EXCHANGER / HEAT METER OPERATING CHARACTERISTICS FOR PERFORMING THERMAL VACUUM TESTS AT LOW TEMPERATURE USEFUL WORKLOAD FOR SPACECRAFTS
A.Yu.Kochetkov1, Head of Department
E.Yu.Kotlyarov1, Cand. of Sci. (Tech), Leading Mathematician
A.F.Shabarchin1, Cand. of Sci. (Tech), Project Engineer
E.V.Shemetova1, Cand. of Sci. (Tech), Test Engineer / kochetkov@laspace.ru
Abstract. The concept of a heat meter is proposed to measure the heat load supplied to the thermal control system (TCS) from the scientific equipment operating at a temperature of minus 100 °С. A stable low temperature level maintained by the controlled phase transition of liquid flow. To maintain the preset temperature, a heater is applied.
Keywords: heat meter, preset temperature, thermal control, heater
For citation: A.Yu. Kochetkov, E.Yu. Kotlyarov, A.F. Shabarchin, E.V. Shemetova. Concept development, calculating and experimental analysis of the heat exchanger and heat load meter operating characteristics for implementation of thermal vacuum tests with low temperature equipment for space application. NANOINDUSTRY. 2022. V. 15, no. 3–4. PP. 204–215. https://doi.org/10.22184/1993-8578.2022.15.3–4.204.215
INTRODUCTION AND PROBLEM DEFINITION
When designing and producing temperature control systems (TCS), which make a part of a spacecraft (SC), it is necessary to define parameters of the so-called thermal interfaces. The term "thermal interface" is relatively modern and borrowed from international projects, but by its meaning and in terms of requirements, it describes thermal boundary conditions in a junction zone (interaction) of subsystems, which has been applied when developing SCs since long ago. The interacting subsystems can be an instrument panel and an instrument assembly, a heat sink, etc. In our case the interface is a flat contact surface, having dimensions of 140 × 80 mm, to which a heat flow of no more than 15 W is delivered from workload (WL) using heat pipes, if the temperature on this surface is about –110 °С.
The second subsystem is a WL heat dissipation path, i.e. a separate TCS which dissipates the specified heat flow into the environment. In order to ensure specified operating conditions of the WL within a spacecraft, the temperature at the junction of two subsystems (WL and TCS) must not exceed –110 °С. Additional conditions of mechanical connection of the subsystems, influencing thermal conditions in particular, require that the contacting surfaces pressing force, use of a filler in a contact gap, etc., are stipulated. Before the connection of the TCS with the WL, it must be checked separately that the TCS dissipates at least 15 W and the WL supplies no more than 15 W at a given limit temperature.
Fragmented thermo-vacuum tests are used quite often when developing the SC thermal management systems [1]. This is necessary to develop the TCS, as well as to perform subsequently a diagnostic of the thermal characteristics of subsystems. Below, Fig.1 shows a schematic diagram of the "staging" of autonomous tests of the WL as a subsystem. There are three heat emission sources as part of the WL, as well as three heat conductive connections that "deliver" all of the emitted heat to the common (considered here) interface. Together with its own heat emission, the WL assembly receives parasitic heat "leaks" into the transport areas and the structural elements of the WL. All heat flows from the WL to the interface, in the normal case, must be dissipated by the SCs TCS, however, in the case of autonomous WL tests, heat dissipation is planned to be provided with a heat exchanger/temperature meter.
The WL-side contact interface has dimensions of 140 × 85 mm and is made of an aluminium alloy. The return contact interface is also a parallelepiped made of an aluminium alloy with a flat contact surface of suitable dimensions. The mechanical connection between the contact plate and the heat exchanger is "bolted" and is essentially a heat meter. It is further shown that the operating temperature difference at the heat meter must be kept almost constant during the test, so the device (heat exchanger/heat meter) is provided with a compensating heater 6 mounted on the inside of the heat meter contact plate.
The specific features of the technical problem solved here can be characterised by the fact that when conducting autonomous WL tests, the heat exchanger-thermometer must ensure that the target temperature is maintained at the interface with the WL and, at the same time, measure the heat flux dissipated from the WL (via the interface).
THE PROPOSED PRINCIPLE OF WL HEAT FLOW MEASUREMENT
A preliminary analysis of applicability of low-temperature laboratory thermostats (commercially available), as well as the experience of using our own "set" of bench-top equipment for such tests, has shown the following:
Experience in small heat flows measurements for low WL temperature and units has shown that the most preferable and reliable methods of heat flow measurement are the steady-state method (based on the steady-state temperature difference at the "calibrated" thermal resistance) and the regular mode method (non-steady-state). Accuracy of calorimetric method, by measuring flow rate and temperature difference of coolant, (for small flows) is unsatisfactory.
In our case the measured heat flow is strictly bound to the temperature state of the PWL, so the regular mode method application (i.e. non-stationary method) can also be considered unjustified.
The heat flux measurement concept proposed here is based on the following principles:
Obviously, a heat meter must be pre-calibrated and no modifications must be made in its design (prior to WL testing), including assembly procedures that may change the internal thermal resistances (in the heat exchanger-thermometer assembly).
Formally, the proposed idea of measuring the heat flux QПН coming from a WL low temperature can be represented as follows:
, (1)
where ТИФ – temperature of the interface plate, °С (on the side of the heat meter, it must be maintained at –110 °С); ТТО – heat exchanger array temperature in the heat supply surface area, °С; RТМ – thermal resistance of the heat meter determined experimentally, K/W; WН – power of the compensating heater, W, which is selected to achieve the specified ТИФ temperature.
COMPUTATIONAL EXPERIMENT WITH HEAT EXCHANGER/HEAT METER
In order to conduct a computational experiment with a heat exchanger/heat meter implementing the proposed concept of QПН measurement, a mathematical model shown in Fig.2 was developed.
Here, 8 bolt connections hold the TCS contact interface simulator plate and provide its connection to the nitrogen heat exchanger. The number of bolts and the material which they are made of can be changed as required to obtain a given heat flow from the interface to the heat exchanger (HE). The preliminary analysis has shown that the contact resistances, at the bolt-to-metal interface, provide a significant and sometimes dominant contribution to the "calibrated" thermal resistance, i.e. the exact thermal resistance value of the heat exchanger will have to be determined "as-is". From this point of view, the ability to change the number of bolts is essential to perform a successful WL experiment, going forward.
Determine the radiant component of the heat flux that can come through the heat meter (2).
Here, an emissivity of no more than 0.1 on each side can be achieved by placing one single screen of the screen vacuum spacecraft thermal insulation (SVSTI) on the heat exchanger itself and another on the inside of the contact plate of the heat exchanger/heat meter. The flow through the SVSTI into the heat meter area, i.e. from the sides of the bolts holding the plate, can be estimated as (3).
Thus, heat fluxes and the radiant heat flux (in the area of the dominant temperature difference) can be neglected.
For the heat transfer with liquid nitrogen flow, let us consider the conditionally pessimistic case, i.e., the situation when the vapor content at the inlet to the heat exchanger (HE) is zero (which, in fact, is the goal to be achieved when selecting the flow rate of nitrogen in the tests). The heat transfer coefficient according to [2] can, in this case, be determined by the Mikheev’s formula:
. (4)
Ignoring the temperature difference between the liquid and the wall and the effect of the length of the HE hydraulic circuit, it can be obtained approximately (5).
The flow rate value and the nominal diameter of the channel are approximately preset based on the data obtained from the autonomous vacuum isolated pipe (VIP) of the real heat exchanger (described in the next section). Thermal properties of N2 are taken from [3, 4]. The simplest estimation of the average two-phase heat transfer coefficient by Kutateladze formula is performed according to recommendations [5]:
, (6)
where αб.о. represents an estimate of the heat transfer coefficient for boiling in "large" volume, and αw. for single-phase liquid convection. Experimental estimates for αб.о. in nitrogen boiling can be found in many sources. For example, from the diagram presented in [6] the heat transfer coefficient during boiling can be found in the range of 500–1,000 W/m2K. Thus, in addition to Mikheev’s formula, we can estimate the effect of the phase transition as
(7)
The temperature potential at which the phase transition inside the heat exchanger stabilizes is related to the operating pressure inside. According to observations in various experiments, where liquid nitrogen was used to provide heat removal, pressure and temperature are not "kept" stably in the working volumes of small thermoplates, as there is objectively a jump in hydraulic resistance and change in external thermal influence on the coolant/refrigerant flow (in relation to losses in the nitrogen supply line). Assuming that the pressure in the HE is by 0.4 bar lower than in the Dewar vessel, then, using the Clausius-Clapeyron equation, we can approximate a change in the saturation temperature:
. (8)
Here r means the heat of vaporization, J/kg, r – means density, kg/m3; P means pressure, Pa, T means temperature, K. In other words, if the saturation temperature at the inlet to the supply main is –187 °С, then in the flow that has reached the heat exchanger, it may shift to –189 °С, i.e. insignificantly. For the computational experiment performed with the aid of the model in Fig.2, to provide a margin and, as the first approximation, assume a low temperature potential of –180 °С. In the future, (to ensure validity), it is at VIP that the level of temperature stabilisation of the heat exchanger under conditions where it is actually affected by: oscillating pressure (in the coolant), heat inflows through fixings and thermal insulation, and the thermal load from a WL, or its simulator, will be evaluated. All influences will result in temperature gradients in the metal heat exchanger, which will have to be taken into account in the practical application of the heat exchanger-heat gauge.
The results of computational experiment using the finite element method (FEM) model according to Fig.2 allowed to determine the calculated value of the heat flow coming from the plate to the heat exchanger. Thus, in the case of aluminium (= 115 W/mK) steel (= 15 W/mK) and titanium (= 22 W/mK) bolts, the fluxes of 55 W, 27 W and 30 W respectively were obtained. Strange as it may be, all three cases are applicable to the task, as the compensated load is 15 W.
The following boundary conditions (steady-state problem) were applied to the calculations in the computational experiment:
An error in determining the contact thermal resistances values (at the points of contact between the bolts and the structural elements), will most significantly affect the actual performance of the heat exchanger. However, by selecting the number of bolts and meeting the given requirements for their installation, it is planned to achieve the required temperature difference on the heat exchanger/heat meter structure at the value of the transmitted power in the range of 30–60 W and the given temperature level. As shown by the results of the 3D model calculations, this is a solvable task.
TESTING OF THE HEAT EXCHANGER PROTOTYPE
The prototype nitrogen heat exchanger used for the thermal vacuum tests (TVT) is shown in Fig.3. Using this prototype, the authors planned to confirm that supplying nitrogen with low vapour content would keep the heat exchanger temperature close to the phase transition temperature, as well as stabilise this temperature acceptably.
In the process of the TVT of this heat exchanger, nitrogen was supplied at a rate of 150 kg/hour (the rate was determined, approximately once an hour, by the total mass of nitrogen consumed from the Dewar flask). In order to ensure guaranteed phase transition conditions (boiling) in the internal channels of the heat exchanger, the test operator ensured visual inspection of the "pouring out of liquid nitrogen" from the drain hose at the outlet of the vacuum chamber (VC) wherein the heat exchanger under test was installed.
A flow rate of 150 kg/hr allows a load of about m·r = 150/3600·188,000 = 7,800 W to be removed by evaporation of liquid nitrogen alone. Some part of this cooling capacity is "wasted" on compensation of heat inputs in the multi-meter long liquid nitrogen supply line to the vacuum chamber (VC); however, since liquid nitrogen always flows from the outlet of the line (drain from the heat exchanger), we can speak of a significant reserve of the cooling capacity in the heat exchanger itself, which is designed to remove only tens of watts.
Figure 4 shows how steadily the heat exchanger temperature is maintained during the test period of about 6 hours when the power of the heater simulating flow from the WL side is varied.
The level of heat input to the heat exchanger (estimated from other works) can be estimated as 8 W through the SVSTI and a value of 12 W through the mountings. The maximum power input to the electric heater simulating the useful load was 80 W.
As can be seen from Fig.4, in the tests the power to the heat exchanger was applied in "steps". In this case, the values set were 20, 40, 60 and 80 W. The curves show that the temperature level of the casing and the heat transfer surface is determined more by the cooling flow than by the heating effect. The average temperature at the heat exchanger operating surface is about minus 175 °С, the recorded temperature variation across the heat exchanger is about 10 K, but it is less at the heat supply surface. The oscillation amplitude is, on average, of the order of 2 K, taking into account the planned operating differential at the heat meter of 50–60 K and taking into account the high oscillation frequency, this factor can be considered acceptable, not preventing reliable measurement of the heat flow from the WL. An additional diagram, plotted on top of the main one (see Fig.4), shows the temperature oscillations obtained for the 60 W mode on an enlarged scale.
Analysing the carried out measurements as well as the presented calculated estimates, it can be concluded that the reason for the relatively high temperature (stabilisation) recorded at the heat exchanger is not due to a temperature gradient across the shell, heat inflows to the shell or a reduction in the heat transfer coefficient (from coolant to shell), but mainly due to presence of superheated liquid coolant entering the heat exchanger, relative to the equilibrium phase temperature (superheating occurs during the nitrogen transport along the major pipeline.
Based on the results of the TVT heat exchanger, it can be concluded that the proposed concept of maintaining the interface setpoint temperature with simultaneous measurement of the heat flux from the WL is efficient and feasible.
METHODOLOGICAL ASPECTS OF TVT WORKLOAD PERFORMANCE
As stated above, the methodology for determining the heat flow from WL is based on the stable maintenance of two temperature potentials, namely the nitrogen boiling in the heat exchanger on the one hand and the required temperature at the interface of –110 °С on the other. In order to maintain a constant temperature of –110 °С in the interface area of the subsystems, the heat meter heater must develop a suitable differential at the heat meter (by itself), as well as have its own power above the power supplied by WL. However, if the actual power from the WL is up to 40 W, the heat dissipation path, which is a sub-system consisting of heat pipes and maintenance scheduler (MS), need to be redesigned.
When preparing the test stand and performing the MS, the main tasks in preparing the heat exchanger/heat meter for its application are:
CONCLUSIONS
In the process of defining the concept of heat exchanger/heat meter the authors developed a methodology for experimental testing of low-temperature useful load of a spacecraft. Based on heat-vacuum tests of the heat exchanger prototype and computational experiment, a comprehensive work proving the applicability of this approach, in terms of using a heat exchanger operating with liquid nitrogen and a heat exchanger with a compensating heater was carried out. The design of the heat exchanger/heat meter has been developed, and a generalized scenario of heat-vacuum testing (HVT) has been defined. Implementation of the technical solutions presented herein will make it possible to improve the quality of HVT of various low-temperature payloads, in the form of autonomous WL SC, as well as to reduce the cost of such tests.
PEER REVIEW INFO
Editorial board thanks the anonymous reviewer(s) for their contribution to the peer review of this work. It is also grateful for their consent to publish papers on the journal’s website and SEL eLibrary eLIBRARY.RU.
Declaration of Competing Interest. The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Original paper
CONCEPT DEVELOPMENT: DESIGN AND EXPERIMENTAL ANALYSIS OF THE HEAT EXCHANGER / HEAT METER OPERATING CHARACTERISTICS FOR PERFORMING THERMAL VACUUM TESTS AT LOW TEMPERATURE USEFUL WORKLOAD FOR SPACECRAFTS
A.Yu.Kochetkov1, Head of Department
E.Yu.Kotlyarov1, Cand. of Sci. (Tech), Leading Mathematician
A.F.Shabarchin1, Cand. of Sci. (Tech), Project Engineer
E.V.Shemetova1, Cand. of Sci. (Tech), Test Engineer / kochetkov@laspace.ru
Abstract. The concept of a heat meter is proposed to measure the heat load supplied to the thermal control system (TCS) from the scientific equipment operating at a temperature of minus 100 °С. A stable low temperature level maintained by the controlled phase transition of liquid flow. To maintain the preset temperature, a heater is applied.
Keywords: heat meter, preset temperature, thermal control, heater
For citation: A.Yu. Kochetkov, E.Yu. Kotlyarov, A.F. Shabarchin, E.V. Shemetova. Concept development, calculating and experimental analysis of the heat exchanger and heat load meter operating characteristics for implementation of thermal vacuum tests with low temperature equipment for space application. NANOINDUSTRY. 2022. V. 15, no. 3–4. PP. 204–215. https://doi.org/10.22184/1993-8578.2022.15.3–4.204.215
INTRODUCTION AND PROBLEM DEFINITION
When designing and producing temperature control systems (TCS), which make a part of a spacecraft (SC), it is necessary to define parameters of the so-called thermal interfaces. The term "thermal interface" is relatively modern and borrowed from international projects, but by its meaning and in terms of requirements, it describes thermal boundary conditions in a junction zone (interaction) of subsystems, which has been applied when developing SCs since long ago. The interacting subsystems can be an instrument panel and an instrument assembly, a heat sink, etc. In our case the interface is a flat contact surface, having dimensions of 140 × 80 mm, to which a heat flow of no more than 15 W is delivered from workload (WL) using heat pipes, if the temperature on this surface is about –110 °С.
The second subsystem is a WL heat dissipation path, i.e. a separate TCS which dissipates the specified heat flow into the environment. In order to ensure specified operating conditions of the WL within a spacecraft, the temperature at the junction of two subsystems (WL and TCS) must not exceed –110 °С. Additional conditions of mechanical connection of the subsystems, influencing thermal conditions in particular, require that the contacting surfaces pressing force, use of a filler in a contact gap, etc., are stipulated. Before the connection of the TCS with the WL, it must be checked separately that the TCS dissipates at least 15 W and the WL supplies no more than 15 W at a given limit temperature.
Fragmented thermo-vacuum tests are used quite often when developing the SC thermal management systems [1]. This is necessary to develop the TCS, as well as to perform subsequently a diagnostic of the thermal characteristics of subsystems. Below, Fig.1 shows a schematic diagram of the "staging" of autonomous tests of the WL as a subsystem. There are three heat emission sources as part of the WL, as well as three heat conductive connections that "deliver" all of the emitted heat to the common (considered here) interface. Together with its own heat emission, the WL assembly receives parasitic heat "leaks" into the transport areas and the structural elements of the WL. All heat flows from the WL to the interface, in the normal case, must be dissipated by the SCs TCS, however, in the case of autonomous WL tests, heat dissipation is planned to be provided with a heat exchanger/temperature meter.
The WL-side contact interface has dimensions of 140 × 85 mm and is made of an aluminium alloy. The return contact interface is also a parallelepiped made of an aluminium alloy with a flat contact surface of suitable dimensions. The mechanical connection between the contact plate and the heat exchanger is "bolted" and is essentially a heat meter. It is further shown that the operating temperature difference at the heat meter must be kept almost constant during the test, so the device (heat exchanger/heat meter) is provided with a compensating heater 6 mounted on the inside of the heat meter contact plate.
The specific features of the technical problem solved here can be characterised by the fact that when conducting autonomous WL tests, the heat exchanger-thermometer must ensure that the target temperature is maintained at the interface with the WL and, at the same time, measure the heat flux dissipated from the WL (via the interface).
THE PROPOSED PRINCIPLE OF WL HEAT FLOW MEASUREMENT
A preliminary analysis of applicability of low-temperature laboratory thermostats (commercially available), as well as the experience of using our own "set" of bench-top equipment for such tests, has shown the following:
- The use of regulated thermostats based on intermediate circulating single-phase low-temperature coolants will significantly complicate and increase the cost of both the test bench equipment and the WL tests themselves. In addition, test bench preparation time will increase significantly;
- The attempts to stabilize different temperatures in the range (–150...–80 °С) by direct supply of two-phase nitrogen to the contact heat exchanger (from remotely located Dewar flasks) are characterised by the difficulties connected with uncontrolled changes in the two-phase nitrogen flow.
Experience in small heat flows measurements for low WL temperature and units has shown that the most preferable and reliable methods of heat flow measurement are the steady-state method (based on the steady-state temperature difference at the "calibrated" thermal resistance) and the regular mode method (non-steady-state). Accuracy of calorimetric method, by measuring flow rate and temperature difference of coolant, (for small flows) is unsatisfactory.
In our case the measured heat flow is strictly bound to the temperature state of the PWL, so the regular mode method application (i.e. non-stationary method) can also be considered unjustified.
The heat flux measurement concept proposed here is based on the following principles:
- the contact heat exchanger should be kept at a minimum temperature, which can be achieved by pouring liquid nitrogen through. The nitrogen flow should be so high that the heat exchanger (thermoplate) is insensitive to variations in heat load and to the effects of bench heat fluxes occurring in these tests. Let us assume this temperature is minus –180 °С;
- the heat meter connecting the heat exchanger to the thermal interface must produce a temperature differential well above the temperature oscillations associated with evaporation/boiling and nitrogen flow regimes in the heat exchanger. In our case this difference is limited to values of –110 °С (top) and –180 °С (bottom), i.e. it can reach no more than 70 K;
- since the exact value of the WL heat flow is not known, i.e. the desired value, the heater must be installed at the interface, knowingly of a higher rating (than all the heat coming from the WL), which will maintain a stable temperature of –110 °С at the interface at all times;
- knowing the heater power, which is necessary to maintain the interface temperature at –110 °С, in the absence of a WL and, reducing the power of this heater after the connection of the WL (until the specified temperature is reached), we obtain from the difference of the two power values the component coming from the WL. In other words, the WL power will replace/compensate a part of the bench heater power to keep the specified temperature of –110 °С.
Obviously, a heat meter must be pre-calibrated and no modifications must be made in its design (prior to WL testing), including assembly procedures that may change the internal thermal resistances (in the heat exchanger-thermometer assembly).
Formally, the proposed idea of measuring the heat flux QПН coming from a WL low temperature can be represented as follows:
, (1)
where ТИФ – temperature of the interface plate, °С (on the side of the heat meter, it must be maintained at –110 °С); ТТО – heat exchanger array temperature in the heat supply surface area, °С; RТМ – thermal resistance of the heat meter determined experimentally, K/W; WН – power of the compensating heater, W, which is selected to achieve the specified ТИФ temperature.
COMPUTATIONAL EXPERIMENT WITH HEAT EXCHANGER/HEAT METER
In order to conduct a computational experiment with a heat exchanger/heat meter implementing the proposed concept of QПН measurement, a mathematical model shown in Fig.2 was developed.
Here, 8 bolt connections hold the TCS contact interface simulator plate and provide its connection to the nitrogen heat exchanger. The number of bolts and the material which they are made of can be changed as required to obtain a given heat flow from the interface to the heat exchanger (HE). The preliminary analysis has shown that the contact resistances, at the bolt-to-metal interface, provide a significant and sometimes dominant contribution to the "calibrated" thermal resistance, i.e. the exact thermal resistance value of the heat exchanger will have to be determined "as-is". From this point of view, the ability to change the number of bolts is essential to perform a successful WL experiment, going forward.
Determine the radiant component of the heat flux that can come through the heat meter (2).
Here, an emissivity of no more than 0.1 on each side can be achieved by placing one single screen of the screen vacuum spacecraft thermal insulation (SVSTI) on the heat exchanger itself and another on the inside of the contact plate of the heat exchanger/heat meter. The flow through the SVSTI into the heat meter area, i.e. from the sides of the bolts holding the plate, can be estimated as (3).
Thus, heat fluxes and the radiant heat flux (in the area of the dominant temperature difference) can be neglected.
For the heat transfer with liquid nitrogen flow, let us consider the conditionally pessimistic case, i.e., the situation when the vapor content at the inlet to the heat exchanger (HE) is zero (which, in fact, is the goal to be achieved when selecting the flow rate of nitrogen in the tests). The heat transfer coefficient according to [2] can, in this case, be determined by the Mikheev’s formula:
. (4)
Ignoring the temperature difference between the liquid and the wall and the effect of the length of the HE hydraulic circuit, it can be obtained approximately (5).
The flow rate value and the nominal diameter of the channel are approximately preset based on the data obtained from the autonomous vacuum isolated pipe (VIP) of the real heat exchanger (described in the next section). Thermal properties of N2 are taken from [3, 4]. The simplest estimation of the average two-phase heat transfer coefficient by Kutateladze formula is performed according to recommendations [5]:
, (6)
where αб.о. represents an estimate of the heat transfer coefficient for boiling in "large" volume, and αw. for single-phase liquid convection. Experimental estimates for αб.о. in nitrogen boiling can be found in many sources. For example, from the diagram presented in [6] the heat transfer coefficient during boiling can be found in the range of 500–1,000 W/m2K. Thus, in addition to Mikheev’s formula, we can estimate the effect of the phase transition as
(7)
The temperature potential at which the phase transition inside the heat exchanger stabilizes is related to the operating pressure inside. According to observations in various experiments, where liquid nitrogen was used to provide heat removal, pressure and temperature are not "kept" stably in the working volumes of small thermoplates, as there is objectively a jump in hydraulic resistance and change in external thermal influence on the coolant/refrigerant flow (in relation to losses in the nitrogen supply line). Assuming that the pressure in the HE is by 0.4 bar lower than in the Dewar vessel, then, using the Clausius-Clapeyron equation, we can approximate a change in the saturation temperature:
. (8)
Here r means the heat of vaporization, J/kg, r – means density, kg/m3; P means pressure, Pa, T means temperature, K. In other words, if the saturation temperature at the inlet to the supply main is –187 °С, then in the flow that has reached the heat exchanger, it may shift to –189 °С, i.e. insignificantly. For the computational experiment performed with the aid of the model in Fig.2, to provide a margin and, as the first approximation, assume a low temperature potential of –180 °С. In the future, (to ensure validity), it is at VIP that the level of temperature stabilisation of the heat exchanger under conditions where it is actually affected by: oscillating pressure (in the coolant), heat inflows through fixings and thermal insulation, and the thermal load from a WL, or its simulator, will be evaluated. All influences will result in temperature gradients in the metal heat exchanger, which will have to be taken into account in the practical application of the heat exchanger-heat gauge.
The results of computational experiment using the finite element method (FEM) model according to Fig.2 allowed to determine the calculated value of the heat flow coming from the plate to the heat exchanger. Thus, in the case of aluminium (= 115 W/mK) steel (= 15 W/mK) and titanium (= 22 W/mK) bolts, the fluxes of 55 W, 27 W and 30 W respectively were obtained. Strange as it may be, all three cases are applicable to the task, as the compensated load is 15 W.
The following boundary conditions (steady-state problem) were applied to the calculations in the computational experiment:
- the value of the total heat inputs distributed over the non-heated surfaces of the heat exchanger casing is 20 W;
- in the area of the nitrogen-cooled channels, the boundary conditions of the third kind apply: temperature –180 °C and = 500 W/m2K;
- at the interface between the heat meter and WL, the boundary conditions of the first kind (T = –110 °С) apply;
- the plate and heat exchanger material is aluminium alloy (= 115 W/mK);
- the heat transfer coefficient at the bolt contacts with the heat exchanger and with the interface contact plate equals 15,000 W/m2K.
An error in determining the contact thermal resistances values (at the points of contact between the bolts and the structural elements), will most significantly affect the actual performance of the heat exchanger. However, by selecting the number of bolts and meeting the given requirements for their installation, it is planned to achieve the required temperature difference on the heat exchanger/heat meter structure at the value of the transmitted power in the range of 30–60 W and the given temperature level. As shown by the results of the 3D model calculations, this is a solvable task.
TESTING OF THE HEAT EXCHANGER PROTOTYPE
The prototype nitrogen heat exchanger used for the thermal vacuum tests (TVT) is shown in Fig.3. Using this prototype, the authors planned to confirm that supplying nitrogen with low vapour content would keep the heat exchanger temperature close to the phase transition temperature, as well as stabilise this temperature acceptably.
In the process of the TVT of this heat exchanger, nitrogen was supplied at a rate of 150 kg/hour (the rate was determined, approximately once an hour, by the total mass of nitrogen consumed from the Dewar flask). In order to ensure guaranteed phase transition conditions (boiling) in the internal channels of the heat exchanger, the test operator ensured visual inspection of the "pouring out of liquid nitrogen" from the drain hose at the outlet of the vacuum chamber (VC) wherein the heat exchanger under test was installed.
A flow rate of 150 kg/hr allows a load of about m·r = 150/3600·188,000 = 7,800 W to be removed by evaporation of liquid nitrogen alone. Some part of this cooling capacity is "wasted" on compensation of heat inputs in the multi-meter long liquid nitrogen supply line to the vacuum chamber (VC); however, since liquid nitrogen always flows from the outlet of the line (drain from the heat exchanger), we can speak of a significant reserve of the cooling capacity in the heat exchanger itself, which is designed to remove only tens of watts.
Figure 4 shows how steadily the heat exchanger temperature is maintained during the test period of about 6 hours when the power of the heater simulating flow from the WL side is varied.
The level of heat input to the heat exchanger (estimated from other works) can be estimated as 8 W through the SVSTI and a value of 12 W through the mountings. The maximum power input to the electric heater simulating the useful load was 80 W.
As can be seen from Fig.4, in the tests the power to the heat exchanger was applied in "steps". In this case, the values set were 20, 40, 60 and 80 W. The curves show that the temperature level of the casing and the heat transfer surface is determined more by the cooling flow than by the heating effect. The average temperature at the heat exchanger operating surface is about minus 175 °С, the recorded temperature variation across the heat exchanger is about 10 K, but it is less at the heat supply surface. The oscillation amplitude is, on average, of the order of 2 K, taking into account the planned operating differential at the heat meter of 50–60 K and taking into account the high oscillation frequency, this factor can be considered acceptable, not preventing reliable measurement of the heat flow from the WL. An additional diagram, plotted on top of the main one (see Fig.4), shows the temperature oscillations obtained for the 60 W mode on an enlarged scale.
Analysing the carried out measurements as well as the presented calculated estimates, it can be concluded that the reason for the relatively high temperature (stabilisation) recorded at the heat exchanger is not due to a temperature gradient across the shell, heat inflows to the shell or a reduction in the heat transfer coefficient (from coolant to shell), but mainly due to presence of superheated liquid coolant entering the heat exchanger, relative to the equilibrium phase temperature (superheating occurs during the nitrogen transport along the major pipeline.
Based on the results of the TVT heat exchanger, it can be concluded that the proposed concept of maintaining the interface setpoint temperature with simultaneous measurement of the heat flux from the WL is efficient and feasible.
METHODOLOGICAL ASPECTS OF TVT WORKLOAD PERFORMANCE
As stated above, the methodology for determining the heat flow from WL is based on the stable maintenance of two temperature potentials, namely the nitrogen boiling in the heat exchanger on the one hand and the required temperature at the interface of –110 °С on the other. In order to maintain a constant temperature of –110 °С in the interface area of the subsystems, the heat meter heater must develop a suitable differential at the heat meter (by itself), as well as have its own power above the power supplied by WL. However, if the actual power from the WL is up to 40 W, the heat dissipation path, which is a sub-system consisting of heat pipes and maintenance scheduler (MS), need to be redesigned.
When preparing the test stand and performing the MS, the main tasks in preparing the heat exchanger/heat meter for its application are:
- calibration of a heat meter, which should be carried out not only for the required temperature, but also for upward and downward deviations. Additional test routines can then be performed on WL tests to show how the interface temperature affects the coming heat flow (and also interpolate to establish an exact match between the QПН and the interface temperature T = –110 °C);
- preliminary (experimental) determination of the number of conductors (bolts) of the heat meter to ensure power transfer in the range of 40–60 W for fixed interface and heat exchanger temperatures;
- maintenance of a stable nitrogen flow in the pipeline providing a low vapour content of liquid nitrogen through the heat exchanger. It is important to determine stability and repeatability of the nitrogen delivery to the heat exchanger/heat meter.
CONCLUSIONS
In the process of defining the concept of heat exchanger/heat meter the authors developed a methodology for experimental testing of low-temperature useful load of a spacecraft. Based on heat-vacuum tests of the heat exchanger prototype and computational experiment, a comprehensive work proving the applicability of this approach, in terms of using a heat exchanger operating with liquid nitrogen and a heat exchanger with a compensating heater was carried out. The design of the heat exchanger/heat meter has been developed, and a generalized scenario of heat-vacuum testing (HVT) has been defined. Implementation of the technical solutions presented herein will make it possible to improve the quality of HVT of various low-temperature payloads, in the form of autonomous WL SC, as well as to reduce the cost of such tests.
PEER REVIEW INFO
Editorial board thanks the anonymous reviewer(s) for their contribution to the peer review of this work. It is also grateful for their consent to publish papers on the journal’s website and SEL eLibrary eLIBRARY.RU.
Declaration of Competing Interest. The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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