EP3179192A1 - Procede de determination d'un etat d'un echangeur de chaleur - Google Patents

Procede de determination d'un etat d'un echangeur de chaleur Download PDF

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Publication number
EP3179192A1
EP3179192A1 EP15003521.0A EP15003521A EP3179192A1 EP 3179192 A1 EP3179192 A1 EP 3179192A1 EP 15003521 A EP15003521 A EP 15003521A EP 3179192 A1 EP3179192 A1 EP 3179192A1
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EP
European Patent Office
Prior art keywords
heat exchanger
process fluid
simulation
heat
heat transfer
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Withdrawn
Application number
EP15003521.0A
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German (de)
English (en)
Inventor
Manfred Steinbauer
Thomas Hecht
Christiane Kerber
Reinhold Hölzl
Pascal Freko
Axel Lehmacher
Alexander WOITALKA
Thomas Ingo
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Linde GmbH
Original Assignee
Linde GmbH
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Linde GmbH filed Critical Linde GmbH
Priority to EP15003521.0A priority Critical patent/EP3179192A1/fr
Priority to RU2017143354A priority patent/RU2734371C2/ru
Priority to CN201680031143.6A priority patent/CN107690563B/zh
Priority to EP16725767.4A priority patent/EP3311096B1/fr
Priority to PCT/EP2016/000869 priority patent/WO2016188635A1/fr
Priority to JP2017561697A priority patent/JP6797135B2/ja
Priority to US15/576,710 priority patent/US11047633B2/en
Publication of EP3179192A1 publication Critical patent/EP3179192A1/fr
Withdrawn legal-status Critical Current

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Classifications

    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F28—HEAT EXCHANGE IN GENERAL
    • F28F—DETAILS OF HEAT-EXCHANGE AND HEAT-TRANSFER APPARATUS, OF GENERAL APPLICATION
    • F28F27/00—Control arrangements or safety devices specially adapted for heat-exchange or heat-transfer apparatus
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F28—HEAT EXCHANGE IN GENERAL
    • F28F—DETAILS OF HEAT-EXCHANGE AND HEAT-TRANSFER APPARATUS, OF GENERAL APPLICATION
    • F28F2200/00—Prediction; Simulation; Testing

Definitions

  • the invention relates to a method for determining a condition, such as a strength of a heat exchanger device.
  • a condition such as a strength of a heat exchanger device.
  • plate heat exchangers are considered and further proposed methods for producing a heat exchanger and / or a process plant.
  • the invention relates to a method for operating heat exchangers or heat exchangers or process plants.
  • the one or more process streams may be material streams and in particular may be formed by fluid streams of a respective process fluid or by energy flows.
  • a method for determining a state of a heat exchanger device having means for heat transfer by means of fluid streams of a process fluid is proposed, in which a thermohydraulic simulation of the fluid flows of the process fluid through passages in the heat exchanger device for determining temperature and / or Heat transfer coefficient profiles of the means for heat transfer takes place.
  • the process fluid is in particular a fluid medium of a cryogenic plant, such as liquids, liquefied gases or gas mixtures. It is conceivable, for example, water, liquefied petroleum gas, liquefied air or air separation products.
  • the state to be determined of the heat exchanger device is in particular a thermohydraulic state. It is also conceivable to determine a strength state.
  • heat exchanger in the sense of this description also includes devices that transmit or conduct heat.
  • a so-called heat pipe or a heat pipe can be regarded as a heat exchanger device.
  • a heat-conducting element in a system so a means for heat transfer, can be understood as a heat exchanger device.
  • a heat exchanger device also applies a so-called regenerator, in which heat first - for example, a first fluid withdrawn and - is stored and the heat then - for example, to a second fluid - is discharged.
  • the heat exchange device is configured to transfer an amount of heat from a first fluid to a second fluid.
  • a recuperator One speaks also of a recuperator.
  • the proposed method refers to general devices that can transfer heat
  • thermohydraulic simulation preferably temporally variable temperature boundary conditions and / or heat transfer coefficient profiles, in particular at the means for heat transfer, are determined.
  • concentration and / or vapor content profiles of the process fluid are also determined.
  • the temporally varying temperature boundary conditions are in embodiments using a model for a phase transition of the process fluid, for a separation of components of the process fluid or a separation of Components of the process fluid, determined for a Auf Stahlgang with the process fluid and / or fluid dynamic instabilities of the process fluid.
  • a respective passage with a coupled means for heat transfer is imaged onto a one-dimensional model system with a process stream feed, a heat transfer path and a process stream outfeed, along the heat transfer path a particular one-dimensionally extended body with a heat capacity is applied.
  • a heat capacity value and / or a heat transfer value for the one-dimensional expanded body are increased stepwise or continuously to ensure numerical convergence of the one-dimensional model system.
  • Embodiments of the method are used to forecast a lifetime of parts of a process plant, such as a heat exchanger, under the influence of thermal changes during operation of the plant.
  • a lifetime consumption analysis the state of the heat exchanger device is determined as a life consumption in the manner of a Wöhler curve, wherein a stress in dependence on a number of operating cycles of the heat exchanger device is determined.
  • the means for heat transfer may comprise a pipe, a plate, a separating plate, a profile part, a lamella or a rib.
  • the state of the heat exchanger device is optionally determined by means of a finite element method (FEM) for a structural analysis of the state as a function of the variable temperature boundary conditions.
  • FEM finite element method
  • voltage states (locally and temporally distributed) of the heat exchanger device can be determined.
  • At least one structural parameter is in particular a solder joint, a material thickness or a material selection.
  • the design of the system or the heat exchanger can be adjusted so that an improved life expectancy occurs.
  • fins, length or width specifications, layer patterns, two-phase feeds or other design measures can be taken.
  • Manufacturing is to be understood as meaning that existing plants are modified with, for example, installed heat exchangers in order to achieve improved simulated or predicted lifetimes. In this respect, it is also possible to speak of a method for converting a system or heat exchanger device if a change in the system takes place on the basis of simulations carried out.
  • the design or operation of the system or the heat exchanger can be adjusted so that an improved life expectancy occurs.
  • the simulation thus enables optimized operation of systems comprising heat exchangers.
  • a computer program product which causes the execution of the method or methods explained above on a program-controlled device. It is conceivable, for example, the implementation using a computer or a control room computer for a process plant.
  • the determination of the (thermo-hydraulic) state of the respective heat exchanger can be implemented in the manner of a process simulator. As a result, interactions of the considered heat exchanger with other parts of the system can be taken into account, in particular modular.
  • the process simulator can be part of a simulation software.
  • a computer program product such as a computer program means may, for example, be used as a storage medium, e.g. Memory card, USB stick, CD-ROM, DVD, or even in the form of a downloadable file provided by a server in a network or delivered. This can be done, for example, in a wireless communication network by the transmission of a corresponding file with the computer program product or the computer program means.
  • the method (s) are in particular software-implemented, and in the following also synonymously is spoken by a simulation software and / or a process simulator.
  • the user interface includes a display device configured to visually represent a network of passages, first selection means for selecting a displayed passage, second selection means for assigning a one-dimensional model to a selected passage, and third selection means for assigning simulation parameters to the one-dimensional model assigned to the selected passage, the user interface being communicatively coupled to the process simulator.
  • the user interface display device is further configured to display multiple variants of one-dimensional models for selection, the variants including consideration of a temporal mass enrichment of the process fluid, a bulk mass transport of the process fluid, a reaction rate, a temporal impulse accumulation of the process fluid, a spatial impulse transport of the process fluid, a spatial pressure gradient, a spatial friction, effects of gravity on the process fluid, a temporal energy enrichment of the process fluid, a spatial enthalpy transport of the process fluid, an expansion work of the process fluid, friction dissipation and / or a heat input or an acoustic entry from the outside for the respective passage allow.
  • the variants including consideration of a temporal mass enrichment of the process fluid, a bulk mass transport of the process fluid, a reaction rate, a temporal impulse accumulation of the process fluid, a spatial impulse transport of the process fluid, a spatial pressure gradient, a spatial friction, effects of gravity on the process fluid, a temporal energy enrichment of the process fluid, a spatial enthalpy
  • a simulation facility then includes at least one process simulator and user interface as described above and below, and the user interface passes the selected and assigned indications for the selected passages, the respective assigned one-dimensional model variants, and the assigned simulation parameters to the process simulator.
  • Fig. 1 shows as an example of a heat transfer device, a plate heat exchanger 10 from the outside.
  • the plate heat exchanger 10 has a central cuboid 8 with a length L of about 6 m and a width or height B, H of 1.2 m each.
  • nozzle 7 Through nozzle 7, the plate heat exchanger 10, a process fluid, for example, water, supplied or this be removed again. Thus, when flowing through, a process stream is obtained.
  • the attachments 6 and 6a serve to distribute the water introduced through the nozzles 7 or to collect and to concentrate the water to be taken from the plate heat exchanger 10.
  • the various water streams then exchange heat.
  • the in Fig. 1 shown plate heat exchanger 10 is designed to pass more than two process streams in separate passages for heat exchange with each other. A part of the streams can be passed in opposite directions, another part crosswise. To further illustrate, the simplified situation is considered where two process streams flow past each other in separate alternating passages. In principle, larger numbers of process streams can also be handled and taken into account in a simulation.
  • the cuboid 8 thus has alternately parallel to the flow directions lying passages 14 and dividers 1. Both the dividers 1 and the passages 14 are made of aluminum. On their sides are the passages 14 through bars 4 made of aluminum, so that a side wall is formed by the stacking construction with the dividing plates 1. The outer passages 14 of the cuboid 8 are covered by a parallel to the passages and the partitions 1 lying cover 5 made of aluminum.
  • Fig. 3 shows one of the passages 14 of the in the Fig. 1 and 2 shown plate heat exchanger.
  • the direction of flow of the water is indicated by arrows.
  • the water flows in to be distributed in the associated distributor profile 3 over the entire width of the passage 14. Subsequently, the water flows through the heat exchange profile 2 and is concentrated after the heat exchange from the other distributor profile 3 on the output side distributor profile access 9.
  • the passage 14 is bounded by the bars 4.
  • the dividing plates 1 and the profiles 2 and 3 undergo thermal expansion changes. This can lead to thermal stresses that can fatigue the plate heat exchanger 10 and eventually damage.
  • thermohydraulic simulation of the temperature distribution based on these heat flows in the plate heat exchanger 10 the stress distribution is determined in particular by means of a structural mechanical calculation. Based on these simulated stress distributions, it is possible to estimate failure risks, design improved plate heat exchangers 10 and, in particular, optimize operating modes.
  • thermohydraulic simulation In order to determine the stress distribution in a plate heat exchanger, first of all the spatial and temporal temperature distribution is determined by means of a thermohydraulic simulation and from this the stress distribution is calculated.
  • the momentum dynamics can be taken into account as needed.
  • c p are the specific heat capacity, ⁇ the process fluid density, T the temperature, v the speed of the process fluid , z the one-dimensional position, and q ⁇ a heat input as heat flow line density.
  • the equation (1) corresponds to a heated pipe or a passage, for example, the length L.
  • Fig. 4 shows an example of three passages S1, S2, S3 and a partition wall 11 with a heat capacity CW.
  • a respective passage eg S3, has a fluid inlet 13 and a fluid outlet 12.
  • the heat capacity CW or heat capacities
  • heat transfer is described as a one-dimensional extended heat flux density profile.
  • the two passages S1 and S2 pass the two passages S1 and S2 at the point 15 or a.
  • the start temperature distribution can be set arbitrarily.
  • the length L along the one-dimensional axis z is indicated.
  • the heat input for the passage S2 would be denoted by q ⁇ CW, S2 .
  • Adiabatic boundary conditions can be used for the heat conduction of the one-dimensionally assumed partition wall (for example made of metal), that is to say: ⁇ T ⁇ z
  • Fig. 5 shows two examples of an initial temperature distribution as a function of the position z. On the left a start temperature distribution is shown, which comes from a stationary assumed energy balance and on the right an arbitrarily assumed distribution. The initial distribution can z. B. be used for one of the passages.
  • the temporal discretization takes place, for example, with the aid of a BDF method (Backward Differentiation Formula), which is not discussed in detail here.
  • BDF methods for solving differential equations are known.
  • the 8 and 9 show results from investigations by the applicant for a so-called Shell and Tube Heat Exchanger (STHE) 16.
  • STHE Shell and Tube Heat Exchanger
  • tube bundle 18 are surrounded by an outer jacket wall 17.
  • the z-axis is horizontal and a scenario has been simulated where one of the two process streams fails ( Fig. 8, Fig. 9 ).
  • Fig. 9 The right-hand diagram shows the temperature difference between the tube bundle and the heat exchanger jacket after the failure of the process fluid flow according to the one-dimensional modeling or simulation.
  • the Fig. 10 shows results from the applicant's investigations for a so-called Coil Wound Heat Exchanger (CWHE) 19.
  • CWHE Coil Wound Heat Exchanger
  • the upper left part of Fig. 10 shows an image of a corresponding heat exchanger.
  • the temporal temperature curves and heat transfer coefficient profiles can now serve as input data for a structural-mechanical stress analysis, so that a strength state of the respective heat exchanger can be determined taking into account thermohydraulic properties.
  • FIG. 11 some process steps for a corresponding method are summarized. The method is carried out, for example, with the aid of a process simulator, which can be implemented as a computer program on a computer system, such as a PC.
  • the Fig. 12 illustrates a possible embodiment for a process simulator. to Operation of the process simulator may serve a user interface. An example of an appropriate interface is one of Fig. 13 shown. In the following, a variant of the simulation method based on Fig. 11 - 13 explained.
  • the Indian Fig. 12 indicated process simulator 20 has a calculation module 21, a plurality of model modules 22 1 - 22 N , a memory module 23 and simulation modules 24 1 - 24 3 .
  • the modules 21-24 are implemented, for example, as software-implemented routines, program parts or functions.
  • the process simulator 20 may be part of a software library.
  • a hardware implementation is also conceivable in which the functions of the modules or units explained below are hardwired, implemented as ASICs or even FPGAs.
  • a user interface 25 communicatively coupled to the process simulator 25.
  • the user interface 25 and the process simulator 20 form a simulation device to determine conditions of heat exchangers by means of a thermo-hydraulic simulation.
  • the user interface 25 includes a display device 26 configured to visually represent a network of passages S i of a heat exchanger, first selection means for selecting a displayed passage, second selection means for assigning a one-dimensional model to a selected passage, and third selection means for assigning simulation parameters to the one-dimensional model assigned to the selected passage.
  • the user interface 25, for example, displays various variants of one-dimensional models 27 1 -27 N for selection and further enables a set of simulation parameters to be assigned to a respective selected model for a passage, the process simulator 20 then performing corresponding simulations through the simulation module 24 1 .
  • simulation parameters that apply to the selected passage.
  • selection means 29 for example, clickable buttons are provided.
  • the length of the passage and the pressure of the process fluid present at the outfeed are determined (arrows P4 and P5).
  • simulation parameters are, for example, a process fluid velocity, a heat flow line density, a number of interpolation points along the length for the spatial discretization, a fluid temperature at the inlet or a heat capacity. Further simulation parameters are conceivable, the quantities to be assigned depending on the selected one-dimensional model.
  • step St2 ( Fig. 11 ) is now a simulation of the process fluid flow and the temperature distribution based on Navier-Stokes equations.
  • the simulation module 24 1 accesses the model modules 22 1 - 22 N and the simulation parameters present in the memory module 23 and carries out the respective numerical calculations.
  • step St3 dynamic temperature distributions are obtained on the surfaces of the heat exchanger elements such as plates, pipes, attachments, dividing plates, etc.
  • the density, speed etc. are related to the process fluid as a whole.
  • the density ⁇ is, for example, the mixing density of the entire flowing fluid with its constituents.
  • each fluid component j can in principle also be stated for each fluid component j and be used as a basis for the simulation. For example, a segregation of the components or constituents of the respective process fluid can thus also be detected.
  • the first term in the mass-conservation equation (3) stands for mass enrichment
  • the second for mass transport and the right-hand side corresponds to the reaction rate.
  • the momentum conservation equation (4) the first term on the left side is for momentum accumulation, the second term for impulse transport.
  • the first term considers acceleration due to a pressure gradient, the second term friction, and the third term gravity.
  • the variables given in the model equations can be used in particular as simulation parameters.
  • heat capacity values and / or heat transfer value for the one-dimensional extended body are initially disregarded and increased only slowly, stepwise or continuously, to numerically converge the one-dimensional model system realized with the aid of the model modules 22 1 -22 N will ensure. That is, it is started by a non-heat coupled model system, and heat transport is ramped up to the desired value according to the particular simulation parameter.
  • step St3 The boundary conditions provided by the simulation module 24 1 in step St3 are now used for further calculations and simulation of structural mechanical properties of the heat transfer means installed in the heat exchanger. Thus, temperature and / or heat transfer coefficient profiles of the means for heat transfer are obtained, which can be used in subsequent FEM calculations (step St4).
  • the second simulation module 24 2 of the process simulator 20 is set up to perform a corresponding FEM method.
  • the second leads Simulation module 24 2 a method according to the EP 1 830 149 B1 by which reference is hereby made to the full extent (incorporated by reference).
  • the FEM calculations yield stress curves, comparative stress data, or similar state determining quantities that can be used to estimate the lifetime of particular elements in the heat exchanger.
  • a lifetime for example, determined by a sheet in the heat exchanger.
  • the third simulation module 24 3 is set up to calculate a lifetime consumption of the system or of the heat exchanger as a function of the structural mechanical determination of temperature-induced voltages.
  • a corresponding simulation system such as the process simulator 20, is thus based on the combination of the thermo-fluid dynamic simulation with a finite element analysis and lifetime estimation.
  • FIG. 3 is a flowchart for another embodiment of an advanced simulation method for determining states of a heat exchanger.
  • step St21 critical operating scenarios are identified and defined with regard to thermal stresses and thus to the expected service life of the heat exchanger. For example, startup or shutdown scenarios can be determined.
  • step St22 to St24 based on the scenario definition, the thermohydraulic modeling, validation and simulation of the corresponding heat exchanger (s). The effects considered in the simulation are the same as those explained for steps St2, St3 above.
  • step St25 dynamic temperature and heat transfer coefficient profiles are created as a result of the simulations. These represent the input data for the subsequent structural mechanical calculations, which are performed in step St26.
  • the structural mechanics calculations provide, for example, fatigue curves for the calculated operating scenarios, from which the expected lifetime consumption for the individual scenarios (step St27) is determined. In Consequently, for the entirety of the defined operating scenarios, the resulting total lifetime consumption for the heat exchanger under consideration can be determined (step St28).
  • the Fig. 15 schematically shows an application of a process simulator 20 to support a plant controller 30 in a method for operating a process plant 40.
  • the plant controller 30 controls by means of control signals CT the system, such as a cryogenic plant for air separation, gas liquefaction or the like.
  • the system controller 30 receives measurement or sensor signals MS from measuring sensors in the system. For example, temperatures, pressures and flows are detected and evaluated by the plant controller 30 so that intended operations can be set.
  • a process simulator 20 which performs a simulation of the completed operations or modifications of the planned operations. How to Fig. 11 1, a life cycle consumption estimate is made (see step St5) so that an operating procedure or parameter may be changed by the plant controller 30 to allow for improved or extended operating time, for example with a prolonged maintenance interval.
  • the process simulator 20 provides lifetime estimates LD to the plant controller 30 or operating personnel. As part of a maintenance cycle, the further operation can take place with the improved operating parameters or the improved operating sequence.
  • the system controller 30 then outputs possibly modified control signals CT '. Consequently, the operation of the plant 40 is optimized depending on the simulation by the process simulator 20.
  • the process simulator 20 may, for example, in the maintenance intervals hints for operating recommendations to be changed for the operator, but it also It is conceivable that on the basis of the simulation results LD, the system controller 30 automatically makes adjustments to the respective operating sequence or to the operating parameters.
  • thermo-hydraulic simulation production, planning, design, conversion or operation of a process plant can be carried out as a function of the thermo-hydraulic simulation, as described above. It is also possible to determine structural parameters, such as a choice of material, plate thicknesses, tube lengths or the like, before the production of the system or of the heat exchanger.

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  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • Thermal Sciences (AREA)
  • Mechanical Engineering (AREA)
  • General Engineering & Computer Science (AREA)
  • Management, Administration, Business Operations System, And Electronic Commerce (AREA)
EP15003521.0A 2015-05-28 2015-12-10 Procede de determination d'un etat d'un echangeur de chaleur Withdrawn EP3179192A1 (fr)

Priority Applications (7)

Application Number Priority Date Filing Date Title
EP15003521.0A EP3179192A1 (fr) 2015-12-10 2015-12-10 Procede de determination d'un etat d'un echangeur de chaleur
RU2017143354A RU2734371C2 (ru) 2015-05-28 2016-05-25 Способ определения состояния теплообменного устройства
CN201680031143.6A CN107690563B (zh) 2015-05-28 2016-05-25 用于确定热交换器装置的状态的方法
EP16725767.4A EP3311096B1 (fr) 2015-05-28 2016-05-25 Procédé de détermination d'un état d'un échangeur de chaleur
PCT/EP2016/000869 WO2016188635A1 (fr) 2015-05-28 2016-05-25 Procédé pour déterminer l'état d'un dispositif d'échange de chaleur
JP2017561697A JP6797135B2 (ja) 2015-05-28 2016-05-25 熱交換装置の状態を特定する方法
US15/576,710 US11047633B2 (en) 2015-05-28 2016-05-25 Method for determining a state of a heat exchanger device

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Application Number Priority Date Filing Date Title
EP15003521.0A EP3179192A1 (fr) 2015-12-10 2015-12-10 Procede de determination d'un etat d'un echangeur de chaleur

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EP3179192A1 true EP3179192A1 (fr) 2017-06-14

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EP15003521.0A Withdrawn EP3179192A1 (fr) 2015-05-28 2015-12-10 Procede de determination d'un etat d'un echangeur de chaleur

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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN110598268A (zh) * 2019-08-20 2019-12-20 珠海格力电器股份有限公司 换热器的设计方法、装置、存储介质及电子设备
CN112997043A (zh) * 2018-09-13 2021-06-18 林德有限责任公司 用于计算流体流过的工艺设备的强度和使用寿命的方法

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US20030062149A1 (en) * 2001-09-28 2003-04-03 Goodson Kenneth E. Electroosmotic microchannel cooling system
DE10360240A1 (de) * 2003-08-21 2005-03-17 Visteon Global Technologies, Inc., Dearborn Rippe für Wärmeübertrager
DE102004048660A1 (de) * 2004-10-04 2006-06-14 Said Toumi Methodik zur Temperaturabsenkung von berippten Oberflächen (Berechnung des mittleren Wärmeübergangskoeffizienten α unter Einsatz numerischer Verfahren)
EP1830149B1 (fr) 2005-12-13 2009-03-18 Linde Aktiengesellschaft Procédé de détermination de la rigidité d'un échangeur de chaleur à plaques et procédé pour leur fabrication.
DE102010040029A1 (de) * 2010-08-31 2012-03-01 Behr Gmbh & Co. Kg Verfahren zum Betrieb eines thermisch zyklierten Bauteils und nach diesem Verfahren betriebenes Bauteil, insbesondere Schichtwärmeübertrager

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Publication number Priority date Publication date Assignee Title
US20030062149A1 (en) * 2001-09-28 2003-04-03 Goodson Kenneth E. Electroosmotic microchannel cooling system
DE10360240A1 (de) * 2003-08-21 2005-03-17 Visteon Global Technologies, Inc., Dearborn Rippe für Wärmeübertrager
DE102004048660A1 (de) * 2004-10-04 2006-06-14 Said Toumi Methodik zur Temperaturabsenkung von berippten Oberflächen (Berechnung des mittleren Wärmeübergangskoeffizienten α unter Einsatz numerischer Verfahren)
EP1830149B1 (fr) 2005-12-13 2009-03-18 Linde Aktiengesellschaft Procédé de détermination de la rigidité d'un échangeur de chaleur à plaques et procédé pour leur fabrication.
DE102010040029A1 (de) * 2010-08-31 2012-03-01 Behr Gmbh & Co. Kg Verfahren zum Betrieb eines thermisch zyklierten Bauteils und nach diesem Verfahren betriebenes Bauteil, insbesondere Schichtwärmeübertrager

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Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112997043A (zh) * 2018-09-13 2021-06-18 林德有限责任公司 用于计算流体流过的工艺设备的强度和使用寿命的方法
CN110598268A (zh) * 2019-08-20 2019-12-20 珠海格力电器股份有限公司 换热器的设计方法、装置、存储介质及电子设备
CN110598268B (zh) * 2019-08-20 2021-05-28 珠海格力电器股份有限公司 换热器的设计方法、装置、存储介质及电子设备

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