At present, China has put forward higher requirements for the thermal insulation performance of buildings, while many urban houses are still simple flat-roofed houses. Exterior wall thermal insulation is a widely promoted building thermal insulation and energy-saving technology. Compared with internal insulation, external insulation technology is reasonable and has obvious advantages. Using thermal insulation materials with the same specifications, dimensions and properties, external thermal insulation is superior to internal thermal insulation. External wall thermal insulation technology is not only suitable for new structural engineering, but also suitable for the transformation of old buildings, with wide application range and high technical content; The external insulation is wrapped around the main structure, which can protect the main structure and prolong the service life of the building; Effectively reduce the thermal bridge of the building structure and increase the effective space of the building; At the same time, dew condensation is eliminated and the living comfort is improved. Under the guidance of a series of energy-saving policies, regulations, standards and mandatory provisions, the energy-saving work of residential buildings in China has been deepened and the energy-saving standards have been continuously improved. Many new energy-saving technologies and materials have been introduced and developed, and have been vigorously promoted and applied in residential buildings. However, at present, the level of building energy efficiency in China is far lower than that in developed countries, and the energy consumption per unit area of buildings in China is still three to five times that in developed countries with similar climate. The energy consumption of building heating in northern cold areas has accounted for more than 20% of the local social energy consumption, and most of them use thermal power generation and coal-fired boilers, which also bring serious pollution to the environment. Therefore, building energy conservation is still an important issue for China's construction industry in this century. At the same time, the wall and roof are important enclosure objects of buildings, and the thickness of insulation layer is an important parameter to determine the insulation level of buildings. Therefore, it is of great significance to design the best insulation layer thickness for improving insulation performance and saving heat energy loss and energy waste. Suppose the research object is an air-conditioned building, and the indoor air is kept at a set appropriate value.
B the heating heat load of building in winter includes the heat consumption of building envelope and the heat consumption of cold air infiltration, in which it is considered that the heat consumption of cold air infiltration does not directly affect the thermal resistance of building envelope, and only the influence of roof heat consumption is considered when calculating the optimal thickness of insulation layer.
C. It is assumed that the roof structure and insulation materials are uniform and the thermal conductivity is constant.
D indoor temperature and outdoor temperature remain unchanged, and the heat conduction process is in a stable state.
E. The allowable temperature difference between the indoor air and the inner surface of the envelope is 4 degrees Celsius, that is, the indoor air of a flat-topped house is 4 degrees Celsius higher than the inner wall in winter.
F the roof surface temperature in the northern region is as high as 75 degrees Celsius in summer and minus 40 degrees Celsius in winter. Description of main parameters used in the model
Q Heat loss per unit area through the roof, W/ m2
K heat transfer coefficient of envelope, w/(m2℃)
δ t indoor and outdoor temperature difference,℃.
Qn annual heat consumption, J/m2
Hard disk heating days,℃
Heat transfer resistance of Ri roofing materials from inside to outside, m2 k/w
R thermal resistance of insulation layer, m2 k/w
Di thickness of roof structure material from inside to outside, m
Thickness of insulating layer
I thermal conductivity of each layer of material, w m/k
Thermal conductivity of λ insulation layer, w m/k
W Total annual heating cost per unit area, RMB/m2;
Investment cost of thermal insulation layer per unit area WT, ￥/m2;
WN annual heating cost per unit area
Annual operating cost of heating per unit area, yuan/m2 a.
PWF discount coefficient
I. Bank profits
I current paste rate
Inflation rate
life
P unit volume insulation material cost
C. Electricity price per unit time, RMB/hour
H calorific value of air conditioner per unit area per unit time, J/h
Total efficiency of η heating system
Vi heating or cooling days, d (1) uniform medium thickness is d, and the temperature difference between the two sides is Δ t, then the heat q transferred from the high temperature side to the low temperature side per unit area is proportional to Δ t, that is, q = k Δ t, where k= and r is the heat transfer resistance of the medium.
(2) PWF present value coefficient is the process of converting the currency received or paid on a certain date in the future into present value. The present value of one yuan of funds in different periods is called discount coefficient, which converts the future value of funds into present value.
(3) The so-called HDD (Heating Days) refers to the cumulative degree that the daily average temperature is lower than 65 F (18.3 C) in a period of time (month, season or year). If the average daily temperature is higher than 65 degrees Fahrenheit, there will be no heating day on this day.
problem analysis
Roof is an important enclosure structure of buildings. In order to ensure the function of keeping room temperature and reducing heat loss, especially in cold areas, the heating cost should be taken as an important consideration when the indoor temperature in cold areas reaches the due standard in winter. The thickness of insulation layer is an important parameter to determine the level of building insulation. Generally, with the increase of insulation layer thickness, the insulation performance of the envelope structure is improved, thus reducing the building load, the cost of heating equipment and the operating cost of heating system are also reduced accordingly; However, at the same time, the construction cost of the envelope structure also increases accordingly. Therefore, there must be a certain insulation layer thickness, that is, the economic thickness D, in order to minimize the total construction cost (the sum of construction cost and operation cost). Therefore, it is considered to establish an objective function about the total cost w, including the investment cost of insulation layer and the heating heat consumption cost. Considering the economy and energy saving, the mathematical model of energy-saving building design is established by using the life cycle method. The relationship of insulation layer thickness d is established, and the relationship of calculating economic thickness is obtained, which minimizes the objective function w and obtains the corresponding optimal thickness d. Therefore, the optimal insulation thickness can be obtained. When replacing thermal insulation materials, only the thermal conductivity is changed, and the best thermal insulation materials can be obtained by combining the data. In our model, the total cost of the objective function is divided into two parts, namely, the investment cost of insulation layer per unit area WT and the heating cost per unit area WN.
Determination of weight
The cost p per unit volume of insulation layer (including insulation material cost, transportation cost, construction cost and construction management cost, etc.). ) is known and readily available.
Where d is the thickness of the insulating layer (1)
Annual heating heat consumption cost
Heat transfer coefficient k of envelope structure
According to the formula, the concept is: (2) where Ri is the heat transfer resistance of building materials of envelope structure and R is the heat transfer resistance of insulation layer.
Moreover, it is easy to know that r and Ri can be calculated by formulas, where d is the thickness of the material and the thermal conductivity of the material.
Heating degree-days HDD
According to the concept, in order to optimize the calculation, the number of heating days in winter is taken as HDD20, that is, the cumulative number of days in which the average temperature is lower than 20℃ in a heating day. The number of cooling days in summer is HDD25, that is, there is no cooling day when the cumulative temperature is higher than 25℃ or the daily average temperature is lower than 25℃ in a period of time. In fact, it is also considered that 20℃ and 25℃ are suitable indoor temperatures in winter and summer respectively.
The calculation method of heating (cooling) days is as follows:
HDD = Δ t/2 * V is adopted, that is, half of the highest temperature difference when the indoor temperature reaches the appropriate temperature is taken as the average temperature difference during the heating (cooling) time, where Δ t is the difference between the lowest (highest) temperature on the outer surface of the roof in winter (summer) and the appropriate indoor temperature. V is the total number of days of heating (cooling).
So we assume that the lowest temperature on the outer surface of the roof in winter is T 1℃, the highest temperature in summer is T2℃, the number of heating days is V 1, and the number of cooling days is V2, and there are:
HDD 20 =(20-t 1)/2 * v 1(3)
HDD25=(T2-25)/2*V2 (4)
Determination of adhesion coefficient
If g=i, PWF = (1+i)-1;
If g < I, then I = (I-g)/(1+g);
If g>I, then I = (G-I)/(1+I);
Then pwf = [1-(1+I)-n]/I (5)
Annual heat loss per unit area
The annual heat loss per unit area is calculated according to the number of heating days, and a year in Xia Dong is divided into two seasons.
(6)
=
3.4.6 Annual operating cost of heating per unit area WY
WY=
(7)
3.4.7 Annual heating cost per unit area
(8)
Comprehensive (1) to (8) are:
(9)
And as mentioned above, the total cost of building heating has a minimum value d, and its corresponding thickness value is the optimal thickness D.
Derive from w to d, have, get.
Calculation of optimum thickness of (10) perlite insulation layer
Take flat-roofed houses in northern cities as an example. The surface temperature of the roof is as high as 75 degrees Celsius in summer and MINUS 40 degrees Celsius in winter. Gree KFR-26GW/K(2658)D-N5 air conditioner is selected in the calculation, and its parameters are: power: 1P/ refrigeration capacity: 2600W W. After conversion, the calorific value per unit area per unit time of Gree air conditioner is H = 0.72 J/h. The electricity price comes from Changchun Power Supply Bureau: C=0. 47 yuan/kWh. According to the loan interest rate i=7.83%, inflation rate g=4.8% and service life N= 10 in 2007, the discount coefficient PWF=8.58 can be calculated. It is considered that the heating days are four months and the cooling days are two months, that is, V 1= 120, V2=60, (unit: days).
With perlite insulation layer, its thermal conductivity is between 0.047 and 0.054 (unit: w/m.k), and its cost is 186 yuan /m3. Assuming the total efficiency of heating system.
Table 1:
Thermal conductivity of roof envelope, w m/k thickness
Heat transfer resistance
Square meter K/W
theheat transfer coefficient of building envelope
Coating 0.04 1. 1.024
Cement mortar 0.930 15 0.0 16
Floor 0.174 2001.15
Three-felt and four-oil waterproof material 0.668 10 0.05438+04
Perlite insulation layer 0.054—
Figure 1: Relationship between perlite insulation layer D and total heating cost W.
In the process of building heating, in fact, the investment cost of insulation layer WT increases linearly with the increase of insulation layer thickness D, while the relationship between annual heating (cooling) cost WN and insulation layer thickness D is nonlinear, and it starts to decrease rapidly with the increase of D, and when D reaches a certain value, WN becomes flat, which leads to the total annual heating cost W per unit area first decreases and then increases with the increase of D, and reaches the minimum when D = 28.15 mm.
This calculation is also suitable for determining the optimum insulation thickness of other insulation materials, which will be explained in detail later.
Comparative analysis of optimum thickness of insulation layer made of different materials
The thermal conductivity and unit cost of common thermal insulation materials, as well as the calculated optimal thickness and annual heating cost are shown in Table 2 below:
Thermal conductivity of insulating material, w m/k
Unit cost,
Yuan /m3 optimal thickness,
millimetre
Total annual heating (cooling) cost per unit area, RMB.
urethane foam
0.020 580 9.70 1 1266.00
Perlite insulation layer 0.054186 28.1510484.438+05
Benzene board 0.047 300 20.68
124 19.24
Extruded board 0.025 430 12.59
8934.74
Polyurethane insulation board 0.02832015.468158.05
Polyethylene PEF 0.038 320 18.00
950 1.77
Fig. 2: Optimum thickness of insulating layers made of different materials.
In fact, the insulation effect: polyurethane foam is the best, followed by extruded board, and benzene board is the worst;
Cold and heat resistance: polyurethane foam is the best, followed by extruded board, and benzene board is the worst;
Water absorption rate: extruded board is the lowest, followed by polyurethane, and benzene board is the easiest to absorb water;
Service life: polyurethane foam is the longest, followed by extruded board and benzene board is the worst;
Price: polyurethane foam is the highest, followed by extruded board and benzene board is the lowest;
In-situ foaming (spraying) of polyurethane can be directly sprayed for in-situ molding (liquid expansion), which is convenient for molding and transportation; The other two kinds of plates need to be transported and pasted, which is troublesome and will be damaged to a certain extent, and there are seams. For the calculation of indoor and outdoor temperature difference, this paper adopts half of the highest indoor and outdoor temperature difference as the average temperature difference for a period of time, but in fact, the temperature difference varies with external climate, environment, time and other factors. Therefore, the calculation of outdoor temperature difference should consider the relationship between dynamic load and insulation layer thickness.
This paper focuses on determining the optimal thickness of insulation layer from the perspective of economics. But in fact, the choice of insulation layer thickness is not only related to energy saving, but also related to environmental protection. Energy shortage and the increasingly serious domestic and even the world have become more important and necessary in recent days. If the material selection of the insulation layer of the envelope structure considers its impact on the environment and the amount of pollutants generated by the heat source fuel to be consumed, then the selected thickness will have the best economic and environmental benefits.
In buildings with central heating, the heat transfer resistance of envelope structure should not only be determined according to technical and economic comparison, but also meet the requirements of relevant national energy-saving standards. The minimum thermal resistance of the envelope structure of residential flat-roofed houses and other buildings should be added up according to the following calculation formula, and the minimum heat transfer thermal resistance should be determined according to the following calculation:
Where Rmin—— is the minimum heat transfer resistance of the envelope (m2 k/w)
Ti-indoor calculated temperature in winter, generally 20℃
Te—— outdoor calculated temperature of enclosure structure in winter, in degrees Celsius.
N—— temperature difference correction coefficient, taken as 1.00 for exterior walls and flat roofs.
Δ t —— allowable temperature difference (℃) between indoor air and the inner surface of the envelope.
Rk-heat transfer resistance of the inner surface of the envelope (m2 k/w)
Therefore, the evaluation conditions are added to the model: the minimum insulation layer thickness d should be met, which is also of great significance to the determination of insulation layer thickness in practical projects. Because the actual situation is ever-changing, there will always be small errors between the data we get and the assumptions in actual operation, so a good model can never lead to big changes in the results because of these small changes. In order to comprehensively test our model and consider the actual situation, we set some reasonable initial conditions under the condition of selecting appropriate parameters, and checked the model by computer, and obtained the optimal insulation thickness of a series of insulation materials including pearl insulation layer. The calculated results are close to those used in actual engineering design.
The selection of insulation layer thickness is related to the cost and operation cost of energy-saving buildings. The mathematical model for calculating the economic thickness of insulation layer by life cycle cost analysis method takes into account the heating energy consumption of buildings in their life cycle, which is scientific and simple. In the absence of heating system data, the design code has good pertinence and adaptability, which has certain reference and application value for engineering design and can be used for the design and calculation of new or old buildings and new insulation materials. However, in today's call for people-oriented, comprehensive, coordinated and sustainable development, it should be more reasonable and meaningful to comprehensively consider the thickness of insulation layer from both economic and environmental aspects.