1 mathematical model
The fully enclosed scroll compressor, which is the overall simulation of the refrigeration system, is not an isolated system itself. During the operation process, there are complex mass energy migrations inside and outside, which restrict and influence each other in each process, and the state parameters such as temperature and pressure are distributed in three dimensions, forming a complex thermal system with a distributed parameter. Considering the real-time nature of the model simulation, the model is as simple as possible under the premise of conforming to the physical process, and the following assumptions are made: 1) no leakage during the compression process; 2) no static deformation of the moving scroll; 3) no lubrication in the gaseous refrigerant Oil; 4) The spindle speed of the compressor is constant; 5) The process through the suction valve is adiabatic.
The scroll compressor for a common air conditioner cabinet is a structure in which an intake air, a side wall exhaust, and a refrigerant gas and a motor coolant are used. As shown, the direction of the arrow is the direction of flow of the refrigerant. It is the overall energy relationship diagram of the fully enclosed scroll compressor, which can be used to determine the total input and output energy of the compressor. In the system simulation, the input of the compressor module is the suction pressure, the suction ratio ç„“ and the exhaust pressure, and finally the exhaust ratio ç„“ and mass flow are output. According to the above, the heat transfer after the refrigerant flows out of the drain tray is divided into two upper and lower blocks. The entire compressor module is divided into four sections: suction section, intermediate compression section, intermediate exhaust section, and housing heat capacity (including exhaust), as shown.
The structure of the closed scroll compressor is shown in the overall energy relationship of the scroll compressor. The energy relationship of the refrigerant heat transfer relationship and its control body 1. 1 suction link
It can be seen from the energy balance that when the pressure in the inhalation link is p < pi, there are hi'dm d - 2p dV d + dQ 1 d + dQ ic d = h dm d + m dh d - V dp d(1)1. 2 intermediate compression link
Similarly, for the intermediate compression, when pi < p < po, there are 2p dV d + dQ 2 d + dQ co - dQ ic d = m dh d - V dp d ( 2) 1. 3 intermediate exhaust
For the pressure in the intermediate exhaust section p < po, there are 2p dV d + dQ 3 - dQ co d - 2h dm d = m dh d - mv dp d( 3)
1. 4 heat capacity
The gaseous refrigerant flowing out of the static disk discharge port is divided into two parts in the heat capacity part of the casing, as shown, one part is the space surrounded by the upper head and the static disk; one part is the bottom of the frame and the motor and the casing The space enclosed. The gaseous refrigerant exchanges heat with the upper head, the stationary plate, the frame, the motor, and the casing, and the heat transfer amounts are Q tp, Q ob, Q sp, Q mo, Q sh , respectively. The gaseous refrigerant trapped between the motor and the cooling lubricant is ignored here. Thus, the heat capacity of the refrigerant in the casing can be expressed as: hd'dm d - dQ d - ho dm d = h dm d + m dh d - V dp d (4) where dQ = dQ tp + dQ Ob + dQ sp + dQ mo + dQ sh
dQ ob = dQ 1 + dQ 2 + dQ 3.
1. 5 actual gas equation of state
The actual use proves that the M-H equation has a higher precision for R22, that is, the determination of the mass flow rate of f ( p , v, T ) = 0( 5)1.6.
For the inlet, there is a mass flow dm d = 1 A 2 i( pi - pi') (6) where 1 is the inlet flow coefficient obtained by the experiment, A is the effective flow area (m 2), i is The refrigerant density (kg/m 3 ) before entering the suction chamber, and pi - pi' is the pressure drop (Pa) after passing through the inlet.
1. 7 Determination of volume change rate
From the geometric theory of the scroll compressor, the following formula can be obtained:
dV d = P( P - 2t) H - p < pd'( 7)< 2 ( + ) - 4 2 > 2 H + 4 2 3 2 - p > pd' and <
( 8a)< 8 2 - 2 ( + ) > 2 H + 4 2 7 2 - p > pd' and >
(8b) where P is the vortex pitch (m), t is the tooth thickness (m), H is the tooth height (m), and is the motor angular velocity (rad/s), which is the base circle radius (m). Crank angle (rad),
For the exhaust angle (rad).
Equation (7) is suitable for chambers other than the vortex center exhaust chamber of the scroll compressor, and equation (8) is suitable for the central exhaust chamber.
1. 8 Determination of the heat flow rate
1. 8. 1 Heat transfer between the refrigerant gas and the scroll wall
The heat transfer between the gaseous refrigerant and the vortex wall in the compression chamber occurs on the thin-walled boundary layer, where the tangential velocity distribution can be considered to be a logarithmic distribution <5>, using the classical wall function through k- Calculated by the turbulence model, the local heat flow is q = C p TP ry + < 11. 6 q = C p 1/ 2 C 1/ 4 T tk ln( Ey +) + t P(t)y + > 11. 6 P(t) = / 4 sin( / 4)A k 1/ 2 P t - 1 P t - 1/ 4 where y + is the dimensionless distance reflecting turbulence, y + = y( C 1/ 4 K 1 / 2) / r, is the dynamic viscosity coefficient, T is the temperature difference between the vortex and the airflow close to it, t is the turbulent Prandtl number, where 0. 6, P t is the laminar Prandtl number . Other constants C = 0. 09, k = 0. 42, E = 9. 2, t = 0. 9, A = 26.
Heat transfer relationship between refrigerant and scroll teeth During the operation of the scroll compressor, the geometry of each chamber is constantly changing, and the local heat flow is a function of the distance from the calculation to the vortex wall. Therefore, the vortex is formed from the calculation. The center line of the two involutes of the cavity is approximated. As shown in the figure, a pair of 3 crankshafts with zero crank angles are engaged. Due to the symmetry of the meshing, the heat flux in the two 1/4 spaces of the diagonal pair in the same chamber are equal and opposite. The heat transfer of the remaining shadows. The arrows in the figure point to the direction of heat transfer.
Where Q 2, 3 = Q 2, 2, Q 3, 3 = Q 3, 2.
Therefore, the heat transfer amount between the two adjacent chambers is Q = QN , 1 - QN , 4 ( 9 ). The heat transfer between the refrigerant and the vortex wall in the inner and outer 1 / 4 space of the Nth compression chamber is QN. , 1 =∫2N + 1 2 + - 2N - 1 2 + - q H 2 1 + 2 + 1 + ( + - 2 )2 d QN , 4 =∫2N + 3 2 + - 2N + 1 2 + - q H 2 1 + 2 + 1 + ( + - 2 ) 2 d is calculated for QN, 1 and QN. When 4 is used, the tw in q is substituted by the temperature of the inner ring wrap and the outer ring wrap.
1. 8. 2 Heat exchange between the refrigerant gas under the upper head and the back of the fixed scroll
Let the temperature of the refrigerant gas here be T f, 1, and the temperature distribution on the back of the fixed scroll. By fitting the experimental data in the literature < 6>, the following polynomial for easy integration is obtained: T - = - 0. 212 7r - 3 + 0. 589 4r - 2 - 0. 387 3r - + 1. 191 6 where T - = T / T i, r - = r / r , T i is the compressor inlet absolute temperature (K), r is Radius of the static disk (m).
Thus, the total heat transfer is Q = ∫r 0 2 r ( T - T f, 1) dr = 2 r 2 a ( 1. 635 35T i - T f, 1) (10) Calculating the geometry of the upper head 1. 8. 3 Heat exchange between the refrigerant gas and the outside atmosphere under the upper head
The upper head is generally a semi-ellipsoid as shown. Since the airflow disturbance around the scroll compressor is extremely small in actual use, and the temperature fluctuation of the casing is also small, the free convection heat transfer formula using the ellipsoidal surface has Q = AN u T air / B(11) , air is the thermal conductivity of air (W / ( m K) ), A is the heat exchange area ( m 2), T is the temperature difference between the average temperature of the upper head and the outside atmosphere, N u = < ( N ul) m + (N ut)m > 1/ m. For other uninjected constants, see the Nusselt number when the fluid is stationary and the heat exchange is only heat conduction: N u, cond = 4 1 - ( C / B) 2 f 1 / 2 - tan - 1 sin(t)N u , t = C - t R 1/ 3 t = 1 2 ln 1 + C/ B 1 - C/ BN u, l = N u, cond + C 1 C - l R 1/ 4 1. 8. 4 Rack Heat exchange between body and refrigerant gas and heat exchange between motor and refrigerant gas
Due to the complexity of the flow structure here, taking into account the real-time nature of the simulation, it is experimentally converted into two parts: forced convection and radiation heat transfer. Forced convection acts on both the frame and the motor surface (including the rotor and stator). Radiant heat transfer is mainly between the stator surface of the motor and the refrigerant gas flowing therethrough. Therefore, Q = m A m( T m - T f) + s A s( T s - T f) + 5. 67< g( T f / 100)4 - g( T m / 100)4 >( 12 Where m, s is the integrated heat transfer coefficient between the motor and the frame and the refrigerant gas determined by the experiment, g is the blackness of the refrigerant, and g is the absorption coefficient of the refrigerant gas to the motor radiation, A m , A s is the conversion area of ​​the motor and the frame respectively.
So far, the mathematical model of the dynamic simulation of the fully enclosed scroll compressor has been established. In the simulation calculation, the initial value is preset, and the fourth-order Runge-Kutta method is used to iteratively iterate, and finally the dynamic change of the required parameters is obtained, and the next step, that is, the specific enthalpy and the exhaust volume required for the simulation of the condenser module are output. parameter.
2 conclusion
1) A mathematical model for dynamic simulation of a fully enclosed scroll compressor was established using the first law of thermodynamics.
2) The heat transfer of each part of the fully enclosed scroll compressor is analyzed in detail. The heat transfer law between the chambers through the vortex wall is analyzed in detail, and the theoretical and experimental formulas required for the simulation are obtained.
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