A reduced-order solution method for room temperature and load based on multi-dimensional heat transfer

Abstract

The application belongs to the technical field of heat transfer numerical calculation method, and relates to a reduced-order solving method for room temperature and load based on multi-dimensional heat transfer, comprising the following steps: 1: analyzing heat transfer characteristics of a room building heat process, and establishing a multi-dimensional coupling numerical calculation model; 2: establishing and determining a boundary condition; 3: for the multi-dimensional coupling numerical calculation model, after discretization, an original system is established; 4: the original system is reduced to obtain a reduced-order system; 5: solving is performed to obtain solutions of state variables and output variables of the reduced-order system; and 6: multi-dimensional simulation of room dynamic temperature and load; the scale of the reduced-order system is far smaller than that of the original system, so that the calculation resources are saved, the running time of the calculation program is greatly shortened, the time consumption of simulation calculation is reduced, the cost and time are saved, a fast calculation method is provided for simulation of indoor dynamic temperature and load, and the greater the space and time domain calculated, the more obvious the efficiency of the calculation method.

Description

Technical Field

[0001] The present invention belongs to the technical field of heat transfer numerical calculation methods, and relates to a reduced-order solution method for room temperature and load based on multi-dimensional heat transfer. Background Art

[0002] With the advancement of science and technology and the popularization of smart homes, the proportion of building energy consumption in the total social energy consumption is increasing. Accurate simulation of dynamic indoor temperature and load of buildings is an important basis for the design, operation and maintenance of HVAC systems in low-energy or even zero-energy buildings. When calculating the cooling and heating loads, the existing technology is usually based on the outdoor meteorological parameters of a typical year, and when calculating the load of the envelope structure, a set of the most matching additional coefficients is selected according to the wall or thermal bridge category. Such calculations are relatively fast and can cover load simulations in most indoor and outdoor situations. However, for buildings with specific wall types and those that require dynamic control of the indoor thermal environment, it is necessary to provide real-time dynamic load simulations based on specific outdoor meteorological parameters and indoor conditions to provide a reference for building energy conservation and operational control.

[0003] In the simulation of indoor dynamic environments and energy consumption prediction, it is necessary to fully explore and understand the characteristics. The dynamic heat transfer characteristics of a building are closely related to changes in outdoor temperature, humidity, and solar radiation, the dynamic heat transfer characteristics of the enclosing structure, and changes in the indoor environment, and are manifested as non-steady-state processes. Because its governing equation is a partial differential equation related to time and space, the initial temperature distribution is unknown and requires a precise numerical solution. However, an exact solution requires the division of a large number of time and space nodes, consuming a large amount of computing resources. Especially in large buildings, the calculation time is longer and the consumption of computing resources is greater.

[0004] Therefore, a solution method that reduces computing resource consumption while maintaining accuracy is needed to solve the above technical problems. Summary of the Invention

[0005] The technical solution adopted by the present invention to solve the technical problem is: a reduced-order solution method for room temperature and load based on multi-dimensional heat transfer, comprising the following steps:

[0006] Step 1: Analyze the heat transfer characteristics of the room building thermal process and establish a multi-dimensional coupled numerical calculation model of room dynamic heat transfer;

[0007] Step 2: Establishment and determination of boundary conditions;

[0008] Step 3: Discretize the multi-dimensional coupled numerical calculation model established in step 1 and establish the original system for room temperature and load simulation;

[0009] Step 4: The original system established in step 3 is reduced in order using the Laguerre orthogonal polynomial model reduction method to obtain a reduced-order system;

[0010] Step 5: Solve; numerically solve the reduced-order system equation obtained in step 4 to obtain the solution of the reduced-order system state variables and output variables, which is the approximate solution of the original system output variables established in step 3;

[0011] Step 6: Multi-dimensional simulation of room dynamic temperature and load; pre-simulate the room heat transfer model to obtain the initial values ​​of the state variables; simulate the room temperature and load models moment by moment, and repeat the cycle until the final moment.

[0012] Preferably, in step 1, in the heat transfer characteristics of the room building thermal process, the control equations of the heat transfer process of the enclosure structure are respectively:

[0013]

[0014] In formulas (1) to (3), ρ represents density, and its unit is kg / m 3 ;c p represents specific heat capacity in J / (kg·℃); t represents temperature in ℃; τ represents time in h; x, y, z represent the spatial coordinates in m; λ represents thermal conductivity in W / (m·℃); S represents internal heat source in W / m 2 ;

[0015] The surface where indoor and outdoor air come into contact is the third type of boundary condition, which is expressed as:

[0016]

[0017] In formula (4), h represents the surface heat transfer coefficient, and its unit is W / (m 2 ·℃); t a Indicates the contact air temperature in °C;

[0018] The numerical calculation model of the indoor air node is:

[0019]

[0020] In formula (5), V a Indicates the indoor air volume in m 3 ;h in Indicates the convection heat transfer coefficient of the inner wall of the enclosure structure, the unit is W / (m 2 ·℃); f represents the inner wall surface area, unit is m 2 ; G o,a Indicates the amount of air exchange from the outside, in m 3 / s;t i，c , t o,a Indicates indoor and outdoor air temperature, in °C; G lin,jIndicates the ventilation volume from the adjacent room j, in m 3 / s;t lin,j represents the air temperature of the adjacent room j, in °C; Q conv Indicates the convective heat of each internal thermal disturbance, in W; Q hvac Indicates the amount of heat input into the room by air conditioning, in W; Q r It represents the hourly heat transfer caused by the steady-state heat transfer of the transparent enclosure, with the unit being W.

[0021] Preferably, in step 3, the original system is:

[0022]

[0023] In formula (13), Represents the state variable of the system, that is, the temperature of each spatial discrete node, where n is the number of spatial discrete nodes; represents the system input variables, which in this model are the various thermal disturbances affecting the indoor environment, where p is the number of input variables, p = 13; Represents the system output variable, which is the indoor temperature or indoor load; Represents the coefficient matrix, where A, B, and C are mainly related to the indoor and outdoor inputs and the location of the node; A represents the heat flow relationship between adjacent temperature nodes due to the temperature difference, B represents the effect of each thermal disturbance on each temperature node, C represents the heat storage capacity of each node under unit temperature change, and D is determined by the required output variable.

[0024] More preferably, the phase-reduced order system is:

[0025]

[0026] In formula (28), represents the coefficient matrix corresponding to the reduced-order system, V k represents the projection matrix obtained by the model reduction method; represents the state variables of the reduced-order system, represents the output variable of the reduced-order system.

[0027] Preferably, in step 3, the simulation method used to establish the multi-dimensional coupled numerical calculation model of room dynamic heat transfer includes: load simulation and temperature simulation;

[0028] Load simulation includes: simulating room loads during the heating or cooling season, maintaining the indoor temperature at the design temperature through the HVAC system; the indoor design temperature, outdoor meteorological parameters, and the heat transfer capacity of the multi-dimensional enclosure structure together form the input variables of the room dynamic heat transfer model, and the cooling and heating loads required to maintain the indoor design temperature are calculated;

[0029] Temperature simulation includes: for the transition season, the HVAC system is not in operation; the outdoor meteorological parameters and the heat transfer of the multi-dimensional enclosure structure together constitute the input variables of the room dynamic heat transfer model, and the dynamic temperature of the room at each moment is output.

[0030] Preferably, in step 6, the steps of simulating the room temperature and load models moment by moment include:

[0031] Step 6-1: Use the temperature distribution solved at the previous moment as the state variable T old Perform indoor temperature simulation to obtain the temperature T of each node at that moment new ;For the first moment in the simulation time range, use the initial value of the pre-simulation;

[0032] Step 6-2: Use the sampling matrix to determine whether the indoor air node temperature is within the design temperature range. If the HVAC system does not need to be turned on for temperature adjustment, proceed to step 6-3; otherwise, proceed to step 6-4.

[0033] Step 6-3: The room temperature is within the indoor design temperature range and no temperature control is required. The room load is 0 at this moment and the temperature distribution T is output. new Import step 6-5;

[0034] Step 6-4: Since the room temperature at this moment exceeds the design temperature range, the critical value of the design temperature is used as the input parameter (indoor air node temperature). The room multi-dimensional coupling simulation is performed through the load calculation model to obtain the dynamic load at this moment and output the temperature distribution T of each node. new Import step 6-5;

[0035] Step 6-5: Use the obtained temperature distribution value as the state variable T old Return to step 6-1 to continue solving at the next moment.

[0036] Preferably, in step 6, before simulating the room temperature and load models moment by moment, the simulation process is initialized. The process is as follows: the critical value of the indoor temperature is used as the input parameter, and the meteorological parameters of the first day are repeatedly used to pre-simulate the room heat transfer model to initialize the state variables and obtain the initial value T0 of the state variables; the result of the initialization will be used as the initial value of the state variables at the first moment to enter the formal simulation.

[0037] The beneficial effects of the present invention are:

[0038] 1. The present invention uses the model reduction method to construct an approximate system while maintaining the required accuracy, thereby obtaining a reduced-order system. The scale of the reduced-order system is much smaller than the original system (r-order, r<<n), thereby saving computing resources and significantly shortening the running time of the calculation program. It reduces the time consumption of simulation calculations and provides a fast calculation method for the simulation of indoor dynamic temperature and load, thereby saving cost and time. Moreover, the larger the calculated space and time domains, the more obvious the efficiency of the calculation method. The Laguerre orthogonal polynomial model reduction method can match the number of expansion coefficients of the original system output variables in the subspace composed of it while reducing the order. It has good adaptability and flexibility for the calculation of different models and performs well in a variety of systems.

[0039] 2. This invention establishes a coupled model of multidimensional thermal bridge structures and dynamic heat transfer of room temperature or load, enabling rapid model-order reduction calculations of thermal bridge structures and combined calculations of indoor dynamic heat transfer models. Combined with model-order reduction, this method enables real-time, dynamic predictions of indoor loads and temperatures, providing a reference for dynamic control strategies for indoor thermal environments. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 It is a flow chart of a dynamic simulation of room temperature and load using a reduced-order solution method for room temperature and load based on multi-dimensional heat transfer according to the present invention;

[0041] Figure 2 It is a physical model diagram of the building thermal process of the present invention;

[0042] Figure 3 It is a schematic diagram of multi-dimensional division of the enclosure structure of the present invention;

[0043] Figure 4 It is a three-dimensional node discrete schematic diagram of the present invention;

[0044] Figure 5 It is a schematic diagram of a case room of the present invention;

[0045] Figure 6 is a diagram of solar radiation and outdoor dry-bulb temperature in the calculation time domain of the present invention;

[0046] Figure 7 The present invention is a graph showing how the computational time of the LP-MOR solution varies with the order of the low-order system;

[0047] Figure 8 is a scatter plot of the relative error of the heat load solved by the LP-MOR of the present invention;

[0048] Figure 9 This is a comparison chart of the calculation results of the present invention and the mainstream software in the prior art. DETAILED DESCRIPTION

[0049] The following will provide a clear and complete description of the relevant technologies in the present invention in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the embodiments described are only part of the embodiments of the present invention, not all of them. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0050] refer to Figures 1 to 9 The present invention provides a method for reducing the order of room temperature and load based on multidimensional heat transfer, a multidimensional coupling reduction method for solving room temperature and load based on multidimensional heat transfer, combined with the Laguerre orthogonal polynomial model reduction method, to construct a low-order matrix and calculate the room load and temperature. The technical route is as follows Figure 1 The detailed steps are as follows:

[0051] Step 1: Analyze the heat transfer characteristics of the room building thermal process and establish a multi-dimensional coupled numerical calculation model for room dynamic heat transfer, as follows:

[0052] For any room, its thermal process is as follows Figure 2 As shown in the figure, heat gain mainly includes: heat transmitted through the enclosing structure by various external disturbances composed of outdoor meteorological parameters such as outdoor temperature and humidity, solar radiation, heat transfer from other internal heat sources such as personnel, lighting, equipment, heat brought by ventilation penetration, and heat input from the HVAC system.

[0053] The enclosure structure of a typical room is mainly composed of inner and outer walls, floors, roofs, floor slabs, doors and windows, etc. It can be divided into two categories: one is the opaque enclosure structure including inner and outer walls, floors, and roofs; the other is the transparent or translucent structure such as glass curtain walls and windows.

[0054] Dynamic heat transfer in opaque building envelopes is an important component of building cooling and heating loads. Because outdoor meteorological parameters have periodic variations, it can be approximated as a multi-dimensional unsteady-state heat transfer process.

[0055] Combined with the multi-dimensional heat transfer characteristics of different locations of the enclosure structure, it can be divided into multiple one-dimensional, two-dimensional, and three-dimensional structures. The governing equations of the unsteady heat transfer process are:

[0056]

[0057]

[0058] ρ: density, kg / m 3 ;c p : specific heat capacity, J / (kg·℃); t: temperature, ℃; τ: time, h; x, y, z: spatial coordinates in all directions, m; λ: thermal conductivity, W / (m·℃); S: internal heat source, W / m2 .

[0059] For the main surface of the opaque enclosure structure, since the length and width of the central area of ​​the enclosure structure are much greater than the thickness, it is assumed to be a one-dimensional heat transfer problem, as shown in Equation (1); for the intersection of two walls, it can be simplified to an L-shape and processed in two dimensions, as shown in Equation (2); but for the corner structure composed of three-sided enclosure structures, one-dimensional or two-dimensional simplification is not enough to meet the requirements, and three-dimensional processing is required. The control equation is Equation (3).

[0060] For surfaces in contact with indoor and outdoor air, the third type of boundary conditions are used:

[0061]

[0062] h: surface heat transfer coefficient, W / (m 2 ·℃); t a : Contact air temperature, ℃.

[0063] For indoor air, due to the convection heat transfer generated by the contact between the inner walls of each enclosure structure, the convection heat brought by each internal heat source, the steady-state heat transfer of the transparent enclosure structure, the heat brought by the fresh air, and the heat input from the HVAC system, the numerical calculation model of the indoor air node is:

[0064]

[0065] V a : Indoor air volume, m 3 ;h in : Convection heat transfer coefficient of the inner wall of the enclosure structure, W / (m 2 ·℃); f: inner wall surface area, m 2 ; G o,a : Air exchange volume from the outside, m 3 / s;t i，a , t o,a Indoor and outdoor air temperature, ℃; G lin,j : Air exchange volume from adjacent room j, m 3 / s;t lin,j : air temperature of adjacent room j, °C; Q conv : Convective heat of each internal thermal disturbance, W; Q hvac : Air conditioning heat input into the room, W; Q r : Hourly heat transfer due to steady-state heat transfer of transparent enclosure, W.

[0066] For transparent and translucent enclosures, the heat entering the room through them can be decomposed into two parts. The first part is the one-dimensional transient heat transfer problem formed by temperature difference heat transfer; the second part is the solar radiation heat Q that directly enters the room through the transparent enclosure. τ(W), this part of heat is transferred to the inner wall surface of each enclosure structure and the surface of indoor furniture through long-wave radiation. It is first absorbed and heated by the surface of each component, and then released from each component to the indoor air in the form of heat convection. The solar radiation entering the room through the transparent enclosure structure is:

[0067] Q τ =αC Z f win I (6)

[0068] α: transmittance coefficient;

[0069] C Z : comprehensive occlusion coefficient;

[0070] f win : Surface area of ​​transparent structure, m 2 ;

[0071] I: Solar radiation, W / m 2 .

[0072] The factors affecting the indoor air heat balance include: convective heat transfer generated by the contact between each component and the indoor air, convective heat brought by each internal heat source, steady-state heat transfer of the transparent envelope structure, heat brought by fresh air and infiltration, and heat input from the HVAC system. The heat balance equation of the indoor air node is formula (5).

[0073] The internal heat disturbance caused by lighting, equipment and personnel is affected by the room's usage and shows different characteristics and hourly changing trends. l (W), equipment sensible heat Q s (W) and personnel sensible heat Q p The calculation formulas of (W) are shown in formulas (7) to (9):

[0074] Q l =n1N (7)

[0075] n1: lamps simultaneous use coefficient;

[0076] N: lamp installation power or lighting power density multiplied by area, W.

[0077] Q s =p s S (8)

[0078] p s : Equipment power density, W / m 2 ;

[0079] S: room area, m 2 .

[0080]

[0081] Clustering coefficient;

[0082] n2: total number of people in the air-conditioned area, people;

[0083] q: Sensible heat dissipation of an adult male per hour, W / person.

[0084] Fresh air sensible heat load Q v (W):

[0085] Q v =C p ρVN(t o -t a ) (10)

[0086] N: ventilation rate, times / h;

[0087] t o : Outdoor air temperature, ℃.

[0088] By solving the heat balance equation and the thermal disturbance equation, the indoor load and temperature of any room can be simulated.

[0089] Step 2: Establish and determine boundary conditions.

[0090] The following assumptions are made for the above physical model:

[0091] (a) The enclosure structure is discretized into one-dimensional, two-dimensional and three-dimensional heat transfer processes according to its position, such as Figure 3 As shown;

[0092] (b) The enclosure structure is divided using the finite volume method. Taking three-dimensional discretization as an example, the node situation is as follows Figure 4 As shown, the physical properties of the wall do not change with time;

[0093] (c) Indoor air is lumped into a single node.

[0094] In order to numerically solve the governing equations, their boundary conditions need to be determined according to the problem.

[0095] The indoor and outdoor temperatures are determined by the HVAC system on / off status and outdoor meteorological parameters. The boundary conditions of the inner walls of each enclosure structure are:

[0096]

[0097] q r : The amount of solar radiation entering the room absorbed by the wall, W·m -2 ;

[0098] hr: long-wave radiation heat transfer coefficient between inner walls, W / (m 2 ℃);

[0099] q r : The amount of heat radiated to the surface from other indoor heat sources, W·m -2 .

[0100] Boundary conditions of the outer wall of the enclosure structure:

[0101]

[0102] t o : outer wall temperature, °C;

[0103] h o : Comprehensive heat transfer coefficient of outer wall, W / (m 2 ℃);

[0104] t o,a : Comprehensive outdoor temperature, ℃.

[0105] The indoor temperature and the required indoor heat input are determined according to the simulated working conditions.

[0106] Step 3: The original system for room temperature and load simulation: After discretization of the established numerical calculation model of the multi-dimensional coupled room, the original system is established;

[0107] Based on the control equations and various input items mentioned above, time and space are discretized and converted into a set of ordinary differential equations about time.

[0108] Combining the indoor air heat balance and boundary conditions, the original system of the room temperature and load simulation mathematical model based on multi-dimensional heat transfer expressed in state space form is obtained:

[0109]

[0110] Where, is the state variable of the system, that is, the temperature of each spatial discrete node, where n is the number of spatial discrete nodes; is the system input variable, which in this model is the various thermal disturbances that affect the indoor environment, where p is the number of input variables, p = 13; is the system output variable, which is the indoor temperature or indoor load, m is the number of output variables; q is the number of output variables, which varies according to the simulation situation.

[0111] is a coefficient matrix, where A, B, and C are primarily related to the indoor and outdoor inputs and the location of the nodes. A represents the heat flow relationship between adjacent temperature nodes due to the temperature difference, B reflects the interaction of each thermal disturbance with each temperature node, C reflects the heat storage capacity of each node per unit temperature change, and D is determined by the desired output variable.

[0112] According to the simulation method, the original system includes load simulation and temperature simulation:

[0113] First, load simulation. This involves simulating room loads during the heating or cooling season, when the HVAC system is required to maintain the indoor temperature at the design temperature. The input variables of the dynamic room heat transfer model are the design temperature, outdoor meteorological parameters, the heat transfer of the multi-dimensional enclosure, and other thermal disturbances. The cooling and heating loads required to maintain the design temperature are calculated.

[0114] Second, simulate temperature. During the transitional season, the HVAC system is not operating, and the indoor temperature is unknown. The room dynamic heat transfer model uses outdoor meteorological parameters, multi-dimensional building envelope heat transfer, and other thermal disturbances as input variables, outputting the dynamic room temperature at each moment.

[0115] When simulating room temperature, the u matrix composed of outdoor meteorological parameters and indoor thermal disturbance conditions is the input variable, and the state variable matrix T composed of the temperature of each point is the substitution variable.

[0116] Coefficient matrix

[0117]

[0118] Coefficient matrix

[0119]

[0120] In formula (15), A j is the A matrix of each enclosure structure, A air is the A matrix of indoor air, A R Indicates the radiation heat transfer of the inner wall between the enclosure structures, A conv_air,j and A conv_j,air Represents the convective heat transfer relationship between the enclosure structure j and the indoor air. Taking one-dimensional discretization as an example, the specific forms are:

[0121]

[0122] A conv_ari，j =(0 … 0 h infj ) (19)

[0123] A air =-∑ j h in f j (20)

[0124] Coefficient matrix

[0125] B=(B1 … B j… B6 B air ) T (twenty one)

[0126] In formula (21), B j is the B matrix of enclosure structure j, B air is the B matrix of indoor air. In order to realize the coupling between the one-dimensional simulation of the envelope structure and the thermal bridge, the inner wall node structure of the coefficient matrix B is designed as follows. The specific forms are:

[0127]

[0128] B air =(1 0 0 0 0 0 0 k a S sa 0 1 1 k c f win ) (twenty three)

[0129] b j : Thermal bridge heat transfer sampling coefficient (select 1 or 0 according to actual situation);

[0130] k i : the share of indoor convection heat obtained by the inner surface of the enclosure;

[0131] f1: horizontal surface area receiving sunlight, m 2 ;

[0132] f2: vertical surface area receiving sunlight, m 2 ;

[0133] S si : The fraction of direct scattered heat from incident solar radiation received by the inner wall;

[0134] k a : the share of indoor heat production obtained by indoor air;

[0135] S sa : The share of solar radiation heat received by indoor air;

[0136] k c : Heat transfer coefficient of exterior window, W·m -2 ·K -1 .

[0137] State variables

[0138] T=(T1 … T i … T n t air ) T (twenty four)

[0139] Input variables

[0140] u=(q hac Q e Q w Q n Q s Q t Q b q1 I h I s q4 q5 t dry ) T (25)

[0141] Q e ,Q w ,Q n ,Q s ,Q t ,Q b : The amount of heat transferred by thermal bridges of each enclosure structure, W;

[0142] q1: Radiant heat from indoor heat sources (lamps, equipment, and personnel), W;

[0143] I h : Radiation received by the horizontal surface of the enclosure structure, W·m -2 ;

[0144] I s : Solar radiation, W·m -2 ;

[0145] q4: Convection heat from indoor heat sources (lamps, equipment and personnel), W;

[0146] q5: fresh air load, W;

[0147] t dry : Outdoor dry-bulb temperature, ℃.

[0148] When simulating room loads, the u matrix composed of outdoor meteorological parameters, indoor thermal disturbance conditions and indoor design temperature is the input variable, and the state variable matrix T composed of the node temperatures except the indoor temperature and the heating and cooling capacity of the HVAC is the substitution variable.

[0149] The coefficient matrix, state variables, and input parameters are rewritten based on the room temperature simulation as follows:

[0150]

[0151] Written in the form of the original system (13):

[0152]

[0153] At this time, the heat transfer of the thermal bridge of the enclosure structure is Q e,Q w ,Q n ,Q s ,Q t ,Q b Obtained by coupling calculation of multi-dimensional enclosure structure heat transfer model.

[0154] Step 4: Reduce the original system using the Laguerre orthogonal polynomial model reduction method to obtain a reduced-order system. This is shown in Equation (28), where the order r of the reduced-order system is much smaller than the order n of the original system. As r decreases, the computational effort decreases but the error increases. Therefore, for each specific problem, a preliminary simulation is required to find a reasonable reduced-order value.

[0155]

[0156] Where: is the coefficient matrix corresponding to the reduced-order system, V k is the projection matrix obtained by the model reduction method; are the state variables of the reduced-order system, is the output variable of the reduced-order system.

[0157] The obtained n-order original system (13) is reduced using the Laguerre orthogonal polynomial model reduction method (LP-MOR). The projection matrix is ​​constructed based on the time domain and frequency domain, and the number of expansion coefficients of the original system output variables in the subspace formed by it is matched while reducing the order. And integrating over the time domain [0, t], we can obtain:

[0158]

[0159] Using Laguerre polynomials as the basis, the integral value of the objective function T(t) and the input vector u(τ) is approximately calculated as follows:

[0160]

[0161] Substituting into formula (29), we get:

[0162]

[0163] For Laguerre polynomials, the following equation holds: According to the Laguerre orthogonal polynomial principle, we know that L0(t),L1(t),...,L N (t) is linearly independent, so when u0≠0:

[0164]

[0165] In formula (32):

[0166] right Each basis vector in is processed by Arnoldi process to obtain the reduction algorithm based on Laguerre orthogonal polynomials, and the reduced-order matrix V is obtained. L =[v0,v1,…,v q ],at this time Achieve order reduction of the original system.

[0167] Step 5: Solve. Numerically solve the reduced-order system equation (28) to obtain the solution of the reduced-order system state variables: and output variables This is the approximate solution of the output variable y(τ) of the original system equation (13) in step 3. The state variable T(τ) of the original system equation can be obtained based on the projection matrix V and the reduced-order system state variable obtained in step 4. and the relation The calculated result is the numerical solution of the control equation under the boundary conditions.

[0168] Step 6: Multi-dimensional simulation of room dynamic temperature and load.

[0169] (1) Pre-simulate the room heat transfer model and obtain the initial value T0 of the state variable.

[0170] Due to the thermal inertia of the building envelope, indoor temperature changes are delayed compared to outdoor temperature conditions, resulting in an error in the total output load compared to actual conditions, which in turn increases energy consumption and impacts subsequent calculations. To eliminate these factors, a coupled simulation method for multi-dimensional building envelope heat transfer and load calculations, along with temperature monitoring, was designed. This method uses the critical indoor temperature value as an input parameter and repeatedly uses the first day's meteorological parameters to perform indoor load simulations to initialize state variables. The initialization results serve as the initial values ​​of the state variables for the first moment in the formal simulation. At each moment in the simulation, the results of the previous moment are used to dynamically simulate the indoor temperature and determine whether the room temperature has met the conditions for enabling temperature control. This calculation is repeated in a loop until the final moment.

[0171] According to the actual situation, the initialization phase is carried out, and the parameters of the first day of the cycle time domain are input for calculation to obtain reliable initial values ​​to ensure the accuracy and stability of the load forecast results.

[0172] (2) The room temperature and load models are simulated moment by moment according to the following steps. The overall process is as follows: Figure 1 As shown, the cycle progresses until the final moment.

[0173] Step 6-1: Use the temperature distribution solved at the previous moment (for the first moment in the simulation time range, use the initial value of the pre-simulation) as the state variable T oldPerform indoor temperature simulation to obtain the temperature T of each node at that moment new .

[0174] Step 6-2: Use the sampling matrix to determine whether the indoor air node temperature is within the design temperature range:

[0175] If the HVAC system does not need to be turned on for temperature adjustment, proceed to step (6-3); otherwise proceed to step (6-4).

[0176] Step 6-3: The room temperature is within the indoor design temperature range and no temperature control is required. The room load is 0 at this moment and the temperature distribution T is output. new Import step (6-5).

[0177] Step 6-4: Since the room temperature at this moment exceeds the design temperature range, the critical value of the design temperature is used as the input parameter (indoor air node temperature). The room multi-dimensional coupling simulation is performed through the load calculation model to obtain the dynamic load at this moment and output the temperature distribution T of each node. new Import step (6-5).

[0178] Step 6-5: Use the obtained temperature distribution value as the state variable T old Return to step (6-1) and continue solving at the next moment.

[0179] Example

[0180] This embodiment combines specific cases with the detailed steps of the above technical route and analyzes the reliability of the multi-dimensional coupled heat transfer simulation of the room of the present invention and the beneficial effects of the reduced-order method through calculation results.

[0181] For the sake of generality, we will take the ASHRAE 140 basic case base-case-900 as an example. The room is 2.7m high, 8m wide from east to west, and 6m wide from north to south. It is located in an outdoor environment. It has two windows facing south and a total area of ​​12m. 2 , double-layer windows, no external sunshade, the room's shape and structure are as follows Figure 5 As shown in the figure, the deep ground temperature is 10°C; the indoor heat source is a constant 200W, 60% of which is radiant heat and 40% is convection heat. For heat load calculation, the indoor design temperature is 20°C.

[0182] The dynamic temperature and load calculation of the room is performed based on multi-dimensional heat transfer. The input parameters are the typical annual solar radiation and outdoor dry-bulb temperature given by ASHRAE140, such as Figure 6 shown.

[0183] Program the coupled model for multi-dimensional enclosure structure and room dynamic load simulation. Based on the above settings, perform hourly simulation of room load based on multi-dimensional heat transfer. Based on the above settings, by judging the output parameters and changing the input parameters at each moment, perform year-round room thermal environment simulation based on multi-dimensional heat transfer.

[0184] Discretize the control equation. The calculation program is written in Matlab R2021a. The main configuration of the workstation used to run the program is: CPU E5-2630v4 @ 2.2GHz, 64GB of memory, and an NVIDIA Quadro P2000 graphics card. The original system order of the 3D model is 11368. When using the Laguerre orthogonal polynomial model reduction method (LP-MOR) for order reduction, the order of the reduced system is 3.5% to 4.5% of the original system coefficient matrix. The required computation time is as follows: Figure 7 .

[0185] Compared with the error mean of Krylov subspace, the Laguerre polynomial is slightly higher, at 10 -3 Left and right, such as Figure 8 The direct solution takes about 400 minutes, while the model reduction method only takes about 30 minutes, which is only 7.5% of the time of the direct solution. The total heat load result range between the software is [1.170, 2.041] MWh, with an average value of 1.745 MWh. The total heat load calculated by this method is 1.634 MWh. Within the result range between the software, Figure 9 shown.

[0186] This shows that model reduction methods not only have high computational accuracy, but also effectively shorten program execution time and significantly improve computational efficiency. Therefore, when the computational time domain or space increases, the computational time of LP-MOR is much less than that of direct solution, and its efficiency becomes more obvious.

[0187] In summary, the present invention utilizes model order reduction to construct an approximate system while maintaining the required accuracy, thereby obtaining a reduced-order system. The reduced-order system is much smaller than the original system, thus conserving computing resources, shortening the runtime of the computational program, and reducing the time required for simulation calculations, thereby saving both cost and time. Furthermore, the method's efficiency increases with the larger the spatial and temporal domains being calculated, and it exhibits excellent adaptability and flexibility for calculations involving different models.

[0188] It should be emphasized that the above are only preferred embodiments of the present invention and do not limit the present invention in any form. Any simple modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention are still within the scope of the technical solution of the present invention.

Claims

1. A reduced-order solution method for room temperature and load based on multidimensional heat transfer, characterized in that: The following steps are involved: Step 1: Analyze the heat transfer characteristics of the room building thermal process and establish a multi-dimensional coupled numerical calculation model of room dynamic heat transfer; Step 2: Establishment and determination of boundary conditions; Step 3: Discretize the multi-dimensional coupled numerical calculation model established in step 1 to establish an original system for room temperature and load simulation; Step 4: The original system established in step 3 is reduced in order using the Laguerre orthogonal polynomial model reduction method to obtain a reduced-order system; Step 5: Solving; numerically solving the reduced-order system equation obtained in step 4 to obtain a solution of the reduced-order system state variables and output variables, which is an approximate solution of the original system output variables established in step 3; Step 6: Multi-dimensional simulation of room dynamic temperature and load; pre-simulate the room heat transfer model to obtain the initial values ​​of the state variables; simulate the room temperature and load models moment by moment, and repeat the cycle until the final moment; In step 1, in the heat transfer characteristics of the room building thermal process, the control equations of the heat transfer process of the enclosure structure are respectively: In formulas (1) to (3), ρ represents density; c p represents specific heat capacity; t represents temperature; τ represents time; x, y, z represent the spatial coordinates; λ represents thermal conductivity; The surface where indoor and outdoor air come into contact is the third type of boundary condition, which is expressed as: In formula (4), h represents the surface heat transfer coefficient; t a Indicates contact air temperature; The numerical calculation model of the indoor air node is: In formula (5), V a Indicates the volume of indoor air; h in It represents the heat transfer coefficient on the inner wall of the enclosure structure; f represents the surface area of ​​the inner wall; G o,a Indicates the amount of ventilation from the outside; t i，c , t o,a Indicates indoor and outdoor air temperature; G lin,j represents the ventilation volume from the adjacent room j; t lin,j represents the air temperature of the adjacent room j; Q conv represents the convective heat of each internal thermal disturbance; Q hvac Indicates the amount of heat input into the room by air conditioning; Q r It represents the hourly heat transfer caused by the steady-state heat transfer of the transparent enclosure; In step 3, the original system is: In formula (13), Represents the state variables of the system; Represents system input variables; Represents the system output variable; Represents the coefficient matrix; A represents the heat flow relationship between adjacent temperature nodes due to temperature difference, B represents the effect of each thermal disturbance on each temperature node, C represents the heat storage capacity of each node under unit temperature change, and D is determined by the required output variable; The reduced-order system is: In formula (28), represents the coefficient matrix corresponding to the reduced-order system, V k represents the projection matrix obtained by the model reduction method; represents the state variables of the reduced-order system; represents the output variable of the reduced-order system.

2. The reduced-order solution method for room temperature and load based on multi-dimensional heat transfer according to claim 1 is characterized in that: In step 3, the original system established by the multi-dimensional coupled numerical calculation model of the room dynamic heat transfer includes: a load simulation original system and a temperature simulation original system; The load simulation includes: simulating room loads during the heating or cooling season, maintaining the indoor temperature at the indoor design temperature through the HVAC system; calculating the cooling and heating loads required to maintain the indoor design temperature using the indoor design temperature, outdoor meteorological parameters, and the heat transfer capacity of the multi-dimensional enclosure structure as input variables for a room dynamic heat transfer model; The temperature simulation includes: for the transition season, the HVAC system is not running; outdoor meteorological parameters and multi-dimensional enclosure structure heat transfer heat transfer constitute the input variables of the room dynamic heat transfer model, and output the dynamic temperature of the room at each moment.

3. The reduced-order solution method for room temperature and load based on multi-dimensional heat transfer according to claim 1 is characterized in that: In step 6, the steps of simulating the room temperature and load models moment by moment include: Step 6-1: Use the temperature distribution solved at the previous moment as the state variable T old Perform indoor temperature simulation to obtain the temperature T of each node at that moment new ; Step 6-2: Use the sampling matrix to determine whether the indoor air node temperature is within the design temperature range. If the HVAC system does not need to be turned on for temperature adjustment, proceed to step 6-3; otherwise, proceed to step 6-4. Step 6-3: The room temperature is within the indoor design temperature range and no temperature control is required. The room load is 0 at this moment and the temperature distribution T is output. new Import step 6-5; Step 6-4: Take the critical value of the design temperature as the input parameter, perform multi-dimensional coupling simulation of the room through the load calculation model, obtain the dynamic load at that moment, and output the temperature distribution T of each node. new Import step 6-5; Step 6-5: Use the obtained temperature distribution value as the state variable T old Return to step 6-1 to continue solving at the next moment.

4. The reduced-order solution method for room temperature and load based on multi-dimensional heat transfer according to claim 3 is characterized in that: In step 6, before simulating the room temperature and load models moment by moment, the simulation process is initialized. The process is as follows: the indoor temperature critical value is used as the input parameter, and the first day's meteorological parameters are repeatedly used to pre-simulate the room heat transfer model to initialize the state variables and obtain the initial value T0 of the state variables; the initialization result will be used as the initial value of the state variable at the first moment to enter the formal simulation.

Images