CN110704946B - Aircraft cabin temperature calculation method - Google Patents

Aircraft cabin temperature calculation method Download PDF

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CN110704946B
CN110704946B CN201910896043.5A CN201910896043A CN110704946B CN 110704946 B CN110704946 B CN 110704946B CN 201910896043 A CN201910896043 A CN 201910896043A CN 110704946 B CN110704946 B CN 110704946B
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temperature
aircraft cabin
cabin
airplane
aircraft
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CN110704946A (en
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陈子行
孙茜
李尧
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Shenyang Aircraft Design and Research Institute Aviation Industry of China AVIC
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Shenyang Aircraft Design and Research Institute Aviation Industry of China AVIC
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Abstract

The application belongs to the technical field of aircraft design, and particularly relates to an aircraft cabin temperature calculation method, which comprises the following steps: step one, establishing a theoretical mathematical model for calculating the temperature of an airplane cabin; step two, simplifying the theoretical mathematical model to obtain an engineering model for calculating the cabin temperature of the airplane; and step three, obtaining an aircraft cabin temperature calculation formula according to the engineering model, and calculating to obtain the aircraft cabin temperature based on the aircraft cabin temperature calculation formula.

Description

Aircraft cabin temperature calculation method
Technical Field
The application belongs to the technical field of airplane design, and particularly relates to an airplane cabin temperature calculation method.
Background
At the preliminary design stage of the airplane, preliminary evaluation needs to be carried out on the temperature of the airplane cabin so as to be used as the reference of the preliminary design of the airplane, the temperature of the airplane cabin is mostly estimated based on experience in the preliminary design process of the airplane at present, great arbitrariness exists, the efficiency is low, and the accuracy of the result is difficult to guarantee due to the lack of theoretical support.
The present application is made in view of the above-mentioned drawbacks of the prior art.
Disclosure of Invention
It is an object of the present application to provide a method of aircraft cabin temperature calculation that overcomes or mitigates at least one of the disadvantages of the prior art.
The technical scheme of the application is as follows:
an aircraft cabin temperature calculation method comprises the following steps:
step one, establishing a theoretical mathematical model for calculating the temperature of an airplane cabin;
step two, simplifying the theoretical mathematical model to obtain an engineering model for calculating the cabin temperature of the airplane;
and thirdly, obtaining an aircraft cabin temperature calculation formula according to the engineering model, and calculating to obtain the aircraft cabin temperature based on the aircraft cabin temperature calculation formula.
According to at least one embodiment of the present application, in the first step, a theoretical mathematical model for calculating the aircraft cabin temperature is established, and the consideration of factors influencing the aircraft cabin temperature includes:
the heat of equipment in the airplane cabin is generated;
the flow and temperature of the cooling air flow of the cooling system in the aircraft cabin;
aircraft cabin exposure area;
aircraft cabin thermal inertia.
According to at least one embodiment of the present application, in step two, the theoretical mathematical model is simplified, including:
assuming the aircraft cabin is thermally insulated;
the temperature in the airplane cabin is assumed to be uniform;
the heat source of the aircraft cabin is assumed to be pneumatic heating and equipment heating in the aircraft cabin, and heat radiation and solar radiation are ignored.
According to at least one embodiment of the present application, in the step two, the engineering model for obtaining the aircraft cabin temperature calculation is:
Q=Q pneumatic power +Q Electric power +Q Cooling
Q = m × Ts' (t); wherein the content of the first and second substances,
q is the aircraft cabin heat absorption rate;
Q pneumatic power The aircraft cabin pneumatic heating rate;
Q electrical power The heating rate of the equipment in the airplane cabin;
Q cooling The heat dissipation rate of cooling airflow of the cooling system in the aircraft cabin is determined;
m is thermal inertia, and the heat absorption capacity of the airplane cabin at the temperature of 1 ℃;
ts' (t) aircraft cabin temperature rate of change.
According to at least one embodiment of the present application, Q Pneumatic drive =CH(t)×[Tr(t)-Ts(t)]X S; wherein the content of the first and second substances,
CH (t) is the convective heat transfer coefficient of air and an airplane cabin;
tr (t) is the recovery temperature of the airplane cabin;
ts (t) is the temperature of the airplane cabin;
and S is the exposed area of the airplane cabin.
In accordance with at least one embodiment of the present application,
Figure GDA0004083717690000021
wherein, the first and the second end of the pipe are connected with each other,
pr is the Plantt number;
c p is the specific heat at constant pressure;
ρ is the incoming air flow density;
v is the air inflow velocity;
Figure GDA0004083717690000031
is a coefficient of friction, wherein,
Figure GDA0004083717690000032
is Reynolds number, l is aircraft cabin characteristic dimension, μ The viscosity coefficient of the air flowing in;
T is the temperature of the incoming air stream;
Figure GDA0004083717690000033
wherein the content of the first and second substances,
M the incoming air mach number.
According to at least one embodiment of the present application, Q Electric power = K × W; wherein, the first and the second end of the pipe are connected with each other,
k is the heating coefficient of equipment in the airplane cabin;
w is the total electrical power of the equipment in the aircraft cabin.
According to at least one embodiment of the present application, Q Cooling =G(t)×[T λ (t)-TS(t)]X is C; wherein, the first and the second end of the pipe are connected with each other,
g (t) is the flow of cooling airflow of the cooling system in the aircraft cabin;
T λ (t) is the cooling airflow temperature of the cooling system in the aircraft cabin;
c is the specific heat of air in the airplane cabin.
According to at least one embodiment of the present application, in step three, the calculation formula of the aircraft cabin temperature obtained according to the engineering model is:
ts' (t) = aTr (t) + bTs (t) + c; wherein the content of the first and second substances,
Figure GDA0004083717690000034
Figure GDA0004083717690000041
Figure GDA0004083717690000042
in the third step, the specific step of calculating the temperature of the airplane cabin based on the airplane cabin temperature calculation formula is as follows:
Figure GDA0004083717690000043
according to at least one embodiment of the application, in the third step, the parameters a, b and c in the calculation formula of the aircraft cabin temperature are obtained based on the measured data of the aircraft cabin temperature through fitting, and the process specifically comprises the following steps:
measuring the temperature Ts (t) of the airplane cabin and the recovery temperature Tr (t) of the airplane cabin at different moments t;
fitting Ts (t) into a function of time t, and deriving the function to obtain the temperature change rate Ts' (t) of the aircraft cabin at different moments t;
based on the principle of a least square method, a multivariate linear regression function built in Matlab software is adopted to perform parameter fitting on the temperature Ts (t) of the airplane cabin, the recovery temperature Tr (t) of the airplane cabin and the temperature change rate Ts' (t) of the airplane cabin, so as to obtain the numerical values of a, b and c.
Drawings
Fig. 1 is a flowchart of an aircraft cabin temperature calculation method provided in an embodiment of the present application.
Detailed Description
The present application will be described in further detail with reference to the drawings and examples. It is to be understood that the specific embodiments described herein are merely illustrative of the relevant application and are not limiting of the application. It should be noted that, for convenience of description, only the portions related to the present application are shown in the drawings.
It should be noted that, in the present application, the embodiments and features of the embodiments may be combined with each other without conflict. The present application will be described in detail below with reference to the accompanying drawings in conjunction with embodiments.
It should be noted that in the description of the present application, the terms of direction or positional relationship indicated by the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer", etc. are based on the directions or positional relationships shown in the drawings, which are merely for convenience of description, and do not indicate or imply that the device or element must have a specific orientation, be constructed and operated in a specific orientation, and thus, should not be construed as limiting the present application. Furthermore, the terms "first," "second," and "third" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance.
Furthermore, it should be noted that, in the description of the present application, unless otherwise explicitly specified or limited, the terms "mounted," "connected," and "connected" are to be construed broadly, e.g., as being fixedly connected, detachably connected, or integrally connected; can be mechanically or electrically connected; they may be connected directly or indirectly through intervening media, or they may be interconnected between two elements. The specific meaning of the above terms in the present application can be understood by those skilled in the art according to specific situations.
The present application is described in further detail below with reference to fig. 1.
An aircraft cabin temperature calculation method comprises the following steps:
step one, establishing a theoretical mathematical model for calculating the temperature of an airplane cabin;
step two, simplifying the theoretical mathematical model to obtain an engineering model for calculating the cabin temperature of the airplane;
and step three, obtaining an aircraft cabin temperature calculation formula according to the engineering model, and calculating to obtain the aircraft cabin temperature based on the aircraft cabin temperature calculation formula.
As for the aircraft cabin temperature calculation method disclosed in the above embodiment, it can be understood by those skilled in the art that the theoretical mathematical model of the aircraft cabin temperature calculation is first established, and then the theoretical mathematical model is simplified to obtain the engineering model of the aircraft cabin temperature calculation, and it can be understood that the simplification of the theoretical mathematical model is performed based on the platform characteristics of the aircraft cabin, so as to obtain a reasonable engineering model of the aircraft cabin temperature calculation, and an aircraft cabin temperature calculation formula is obtained according to the engineering model, so that the aircraft cabin temperature can be calculated, and the efficiency and accuracy of the aircraft cabin temperature calculation can be effectively improved by the method.
In some optional embodiments, in the step one, a theoretical mathematical model of the calculation of the aircraft cabin temperature is established, and the consideration of the factors influencing the aircraft cabin temperature includes:
the heat of equipment in the airplane cabin is generated;
the flow and temperature of the cooling air flow of the cooling system in the aircraft cabin;
aircraft cabin exposure area;
thermal inertia of the aircraft cabin and heat absorption capacity of the aircraft cabin at 1 ℃ of temperature change.
With respect to the aircraft cabin temperature calculation method disclosed in the above embodiments, it can be understood by those skilled in the art that the main factors affecting the aircraft cabin temperature can be divided into external factors and internal factors, wherein,
the external factors comprise the initial temperature of the aircraft cabin, the flight state, the atmospheric environment temperature and the like;
the internal factors comprise the aboard position of the aircraft cabin, the thickness of a skin, the temperature of the surrounding aircraft cabin, the heat productivity of equipment in the aircraft cabin, the temperature and the flow of cooling airflow in the aircraft cabin, the density of the equipment in the aircraft cabin, thermal inertia, the exposed area of the aircraft cabin, heat exchange among the aircraft cabins and the like;
influence the external factor of aircraft cabin temperature and be changed, internal factor is relatively stable, and aircraft cabin temperature changes along with external factor's change, and its change rule is decided by internal factor, can understand, in the internal factor that influences aircraft cabin temperature, some factors are big to aircraft cabin temperature change influence, and some factors influence the aircraft cabin temperature less, through a large amount of measured data calculation and regression analysis, and the factor of influence aircraft cabin temperature is considered in the embodiment of this application includes: the heat productivity of equipment in the aircraft cabin, the flow and temperature of cooling air flow of a cooling system in the aircraft cabin, the exposed area of the aircraft cabin and the thermal inertia of the aircraft cabin.
In some optional embodiments, in step two, the theoretical mathematical model is simplified based on platform characteristics of the aircraft cabin, including:
assuming the aircraft cabin is thermally insulated;
the temperature in the airplane cabin is assumed to be uniform;
the heat source of the aircraft cabin is assumed to be pneumatic heating and equipment heating in the aircraft cabin, and the heat radiation and solar irradiation are ignored.
In some optional embodiments, in the second step, the engineering model for obtaining the aircraft cabin temperature calculation is:
Q=Q pneumatic power +Q Electric power +Q Cooling down
Q = m × Ts' (t); wherein, the first and the second end of the pipe are connected with each other,
q is the aircraft cabin heat absorption rate;
Q pneumatic power The aircraft cabin pneumatic heating rate;
Q electric power The heating rate of the equipment in the airplane cabin;
Q cooling down The heat dissipation rate of cooling airflow of the cooling system in the aircraft cabin is determined;
m is thermal inertia, and the heat absorption capacity of the airplane cabin at the temperature of 1 ℃;
ts' (t) aircraft cabin temperature rate of change.
In some alternative embodiments, Q Pneumatic power =CH(t)×[Tr(t)-Ts(t)]X S; wherein, the first and the second end of the pipe are connected with each other,
CH (t) is the convective heat transfer coefficient of air and an airplane cabin;
tr (t) is the recovery temperature of the airplane cabin;
ts (t) is the temperature of the airplane cabin;
and S is the exposed area of the airplane cabin.
In some of the alternative embodiments, the first and second,
Figure GDA0004083717690000071
wherein it is present>
Pr is the prandtl number;
c p is constant pressure specific heat;
ρ is the air inflow density;
v is the air inflow velocity;
Figure GDA0004083717690000072
is a coefficient of friction, wherein,
Figure GDA0004083717690000081
is Reynolds number, l is aircraft cabin characteristic dimension, μ The viscosity coefficient of the air flowing in;
T is the temperature of the incoming air stream;
Figure GDA0004083717690000082
wherein the content of the first and second substances,
M the incoming air mach number.
For the method for calculating the cabin temperature of an aircraft disclosed in the above embodiments, it can be understood by those skilled in the art that the recovery temperature refers to the temperature of the airflow when the airflow is stopped at zero speed on the adiabatic solid surface, and is an important parameter in convective heat transfer and aerodynamics of the high-speed airflow, and the sum of the original temperature (static temperature) of the airflow and the temperature rise (dynamic temperature) converted from kinetic energy is called as the total temperature
Figure GDA0004083717690000083
Wherein, V 、Ma 、/>
Figure GDA0004083717690000084
The incoming flow speed, mach number and specific heat ratio of the air flow are respectively.
At the forward stagnation point of the body of the ambient flow, the steady-motion air flow is compressed isentropically to stagnate, raising the temperature to the level of the total temperature, which is called stagnation temperature. When the airflow is stopped due to viscous friction in the boundary layer of the surface of the object to be flowed, on one hand, the temperature of the local gas is increased by the friction heat; at the same time, the temperature gradient caused by this temperature rise leads to heat dissipation. Therefore, after the gas has stagnated, the original kinetic energy is usually not completely converted into an increase in the local temperature, i.e. the local temperature can only actually reach the recovery temperature
Figure GDA0004083717690000085
It is slightly lower than the total temperature T 0 Where r is the temperature recovery coefficient which marks the fraction of kinetic energy that is actually converted into the temperature rise of the gas. For air, prandtl number Pr =0.72, temperature recovery coefficient r = Pr 1/3 . At low flow rates, the total and recovery temperatures are close to the incoming flow temperature. The kinetic energy in the high-speed airflow is very high, namely the temperature of the airflow and the actual wall temperature T w Same or even greater than T w Also low, the wall surface is not only not cooled but also heated as long as the recovery temperature is greater than the wall temperature. At this time, the temperature of the air flow around the wall surface is T r Instead of T w So that high velocity flow determines the direction of heat flow will be the temperature difference T w -T r Rather than T at low flow w -T . The recovery temperature is characterized by the pneumatic heating effect, and the calculation expression of the recovery temperature is based on the fact that the recovery temperature is greater than or equal to->
Figure GDA0004083717690000091
In some alternative embodiments, Q Electrical power = K × W; wherein, the first and the second end of the pipe are connected with each other,
k is the heating coefficient of equipment in the airplane cabin;
w is the total electrical power of the equipment in the aircraft cabin.
In some alternative embodiments, Q Cooling down =G(t)×[T λ (t)-TS(t)]X is C; wherein, the first and the second end of the pipe are connected with each other,
g (t) is the flow of cooling airflow of an aircraft cabin internal cooling system;
T λ (t) is the cooling airflow temperature of the cooling system in the aircraft cabin;
and C is the specific heat of air in the aircraft cabin.
In some optional embodiments, in step three, the calculation formula of the aircraft cabin temperature obtained according to the engineering model is as follows:
ts' (t) = aTr (t) + bTs (t) + c; wherein, the first and the second end of the pipe are connected with each other,
Figure GDA0004083717690000092
Figure GDA0004083717690000093
Figure GDA0004083717690000094
in the third step, the calculation of the aircraft cabin temperature based on the aircraft cabin temperature calculation formula specifically comprises the following steps:
Figure GDA0004083717690000095
in some optional embodiments, in step three, the parameters a, b, and c in the calculation formula of the aircraft cabin temperature are obtained by fitting based on measured data of the aircraft cabin temperature, and the process specifically includes:
measuring the temperature Ts (t) of the airplane cabin and the recovery temperature Tr (t) of the airplane cabin at different moments t;
fitting Ts (t) into a function of time t, and deriving the function to obtain the aircraft cabin temperature change rate Ts' (t) at different moments t;
based on the principle of least square method, parameter fitting is carried out on the temperature Ts (t), the recovery temperature Tr (t) and the temperature change rate Ts' (t) of the aircraft cabin by adopting a multiple linear regression function built in Matlab software, so as to obtain the numerical values of a, b and c.
For the aircraft cabin temperature calculation method disclosed in the above embodiment, it can be understood by those skilled in the art that although the parameters a, b, and c in the aircraft cabin temperature calculation formula have definite expressions, the parameters such as the aircraft cabin thermal inertia m, the aircraft cabin exposed area S, and the aircraft cabin internal cooling airflow flow rate G (t) are difficult to determine and inconvenient to solve, and the parameters a, b, and c in the aircraft cabin temperature calculation formula can be obtained quickly and efficiently by performing recursive analysis according to the similar limited measured aircraft cabin temperature test data, and further the aircraft cabin temperature can be calculated quickly and efficiently.
So far, the technical solutions of the present application have been described in connection with the preferred embodiments shown in the drawings, but it is easily understood by those skilled in the art that the scope of the present application is obviously not limited to these specific embodiments. Equivalent changes or substitutions of related technical features can be made by those skilled in the art without departing from the principle of the present application, and the technical scheme after the changes or substitutions will fall into the protection scope of the present application.

Claims (1)

1. An aircraft cabin temperature calculation method is characterized by comprising the following steps:
step one, establishing a theoretical mathematical model for calculating the temperature of an airplane cabin;
step two, simplifying the theoretical mathematical model to obtain an engineering model for calculating the cabin temperature of the airplane;
thirdly, obtaining an aircraft cabin temperature calculation formula according to the engineering model, and calculating to obtain the aircraft cabin temperature based on the aircraft cabin temperature calculation formula;
in the first step, a theoretical mathematical model for calculating the temperature of the airplane cabin is established, and factors influencing the temperature of the airplane cabin are considered to comprise:
the heat of equipment in the airplane cabin is generated;
the flow and temperature of the cooling air flow of the cooling system in the aircraft cabin;
aircraft cabin exposure area;
aircraft cabin thermal inertia;
in the second step, the theoretical mathematical model is simplified, and the method comprises the following steps:
assuming aircraft cabin insulation;
the temperature in the airplane cabin is assumed to be uniform;
the heat source of the aircraft cabin is assumed to be pneumatic heating and equipment heating in the aircraft cabin;
in the second step, the engineering model for calculating the aircraft cabin temperature is obtained as follows:
Q=Q pneumatic drive +Q Electric power +Q Cooling
Q = m × Ts' (t); wherein, the first and the second end of the pipe are connected with each other,
q is the aircraft cabin heat absorption rate;
Q pneumatic drive The aircraft cabin pneumatic heating rate;
Q electric power The heating rate of the equipment in the airplane cabin;
Q cooling down The heat dissipation rate of cooling airflow of the cooling system in the aircraft cabin is determined;
m is thermal inertia, and the heat absorption capacity of the airplane cabin at the temperature of 1 ℃;
ts' (t) aircraft cabin temperature rate of change;
Q pneumatic power =CH(t)×[Tr(t)-Ts(t)]X S; wherein, the first and the second end of the pipe are connected with each other,
CH (t) is the convective heat transfer coefficient of air and an airplane cabin;
tr (t) is the recovery temperature of the airplane cabin;
ts (t) is the temperature of the airplane cabin;
s is the exposed area of the airplane cabin;
Figure FDA0004083717670000021
wherein, the first and the second end of the pipe are connected with each other,
pr is the Plantt number;
c p is the specific heat at constant pressure;
ρ is the incoming air flow density;
v is the air inflow velocity;
Figure FDA0004083717670000022
is a coefficient of friction, wherein,
Figure FDA0004083717670000023
is Reynolds number, l is aircraft cabin characteristic dimension, μ The viscosity coefficient of the air flowing in; />
T Is the temperature of the incoming air stream;
Figure FDA0004083717670000024
wherein the content of the first and second substances,
M the Mach number of the incoming air flow;
Q electric power = K × W; wherein the content of the first and second substances,
k is the heating coefficient of equipment in the airplane cabin;
w is the total electric power of the equipment in the airplane cabin;
Q cooling down =G(t)×[T λ (t)-TS(t)]X is C; wherein the content of the first and second substances,
g (t) is the flow of cooling airflow of the cooling system in the aircraft cabin;
T λ (t) is the cooling airflow temperature of the cooling system in the aircraft cabin;
c is the specific heat of air in the aircraft cabin;
in the third step, the calculation formula of the temperature of the airplane cabin obtained according to the engineering model is as follows:
ts' (t) = aTr (t) + bTs (t) + c; wherein the content of the first and second substances,
Figure FDA0004083717670000031
Figure FDA0004083717670000032
Figure FDA0004083717670000033
in the third step, the step of calculating the aircraft cabin temperature based on the aircraft cabin temperature calculation formula specifically comprises the following steps:
Figure FDA0004083717670000034
parameters a, b and c in the calculation formula of the temperature of the aircraft cabin are obtained by fitting based on actually measured data of the temperature of the aircraft cabin.
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