CN103016380B - Method for determining performance of blade tip clearance region of cooling fan of automobile engine - Google Patents

Method for determining performance of blade tip clearance region of cooling fan of automobile engine Download PDF

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CN103016380B
CN103016380B CN201210520663.7A CN201210520663A CN103016380B CN 103016380 B CN103016380 B CN 103016380B CN 201210520663 A CN201210520663 A CN 201210520663A CN 103016380 B CN103016380 B CN 103016380B
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blade tip
tip clearance
air
clearance region
guide ring
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CN103016380A (en
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芮宏斌
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Xian University of Technology
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Xian University of Technology
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Abstract

The invention discloses a device for testing performance of a blade tip clearance region of a cooling fan of an automobile engine with a flow guide ring. The device is characterized in that an outlet of an auxiliary fan is communicated with the inlet end of an air chamber test bed; the outlet end of the air chamber test bed is provided with a tested device; an inner cavity of the air chamber test bed is sequentially provided with a front air deflector, a spray nozzle and a rear air deflector along the direction from the inlet end to the outlet end; the auxiliary fan is sequentially connected with a frequency converter and a calculating system by signals; the calculating system is respectively connected with a static pressure difference measurement device and a motor speed regulation device by signals; the motor speed regulation device is connected with a motor by a signal; the tested device comprises the flow guide ring and a seal disc which are fixedly connected together; the periphery of the flow guide ring is provided with an air guide sleeve; and the seal disc is in transmission connection with a motor rotating shaft of the motor. The invention also discloses a method for testing performance of the blade tip clearance region of the cooling fan of the automobile engine with the flow guide ring. Due to utilization of the device, the experimental period is short and detection accuracy is high.

Description

The performance defining method in automobile engine cooling fan blade tip clearance region
Technical field
The invention belongs to automobile technical field, relate to a kind of performance defining method of the automobile engine cooling fan blade tip clearance region with guide ring.
Background technique
The leakage flow that blade tip clearance causes is one of flow phenomenon important in axial turbomachine, and tip leakage flowing can cause occurring adverse current near radial clearance, leakage flow, generation noise, flow losses increase, degradation under mechanical efficiency.Further investigation is in this respect to the Complex Flows significant [1] [2] [3] [4] [5] [6] [7] [8] [9] of overall understanding turbomachine inside.General in the devices such as aerostatic press, turbine, axial-flow pump, maximum functional static pressure is about 1.0 × 10 2~ 3.0 × 10 4kPa, clearance height is in the scope of 0.1 ~ 0.6mm.Early stage research is mainly carried out in this scope.But the work static pressure of automobile engine cooling fan is very little, and blade tip clearance region is also comparatively large, and this has significantly different from the research field in other turbomachine blade tip clearance regions.Automobile engine cooling fan blade tip clearance region is 50 ~ 250kPa in static pressure, and clearance height is in the scope of 3 ~ 20mm.Therefore, may not be suitable in automobile engine cooling fan the achievement in research obtained in early days.
For automobile engine cooling fan, between the guide ring of fan and fan dome, there is certain radial clearance, blade-tip leakage flow easily occurs and moves phenomenon.In order to the flow mechanism in clear and definite automobile engine cooling fan blade tip clearance area leakage whirlpool, reduce the leakage flow occurred between air guide sleeve and guide ring, reduce aerodynamic noise, significantly improve the problems such as automobile engine cooling fan aeroperformance.In addition, in the design of existing automobile engine cooling fan, the means mostly relying on air compartment (air channel) to test are verified and are solved fan aeroperformance, and it is longer which implements testing expenses costliness, cycle, and design cost is high.
On the other hand, in test fan performance affected in the tip clearance for automobile engine cooling fan at present, do not mention a set of full and accurate effective performance defining method and device thereof, determine size [10] [11] [12] [13] of the fluidal texture in automobile engine cooling fan blade tip clearance region to performance impact specially.
Summary of the invention
The object of the invention is, a kind of performance defining method of the automobile engine cooling fan blade tip clearance region with guide ring is proposed, solve in prior art, the means that most dependence air compartment (air channel) is tested are to verify the aeroperformance of cooling fan, can only be represented by fan performance curve (only comprising flow rate pressure, flow-power and flow-relationship between efficiency), accurately can not express the problem of the performance in blade tip clearance region.
The technical solution adopted in the present invention is, a kind of performance defining method of the automobile engine cooling fan blade tip clearance region with guide ring, utilizes a kind of performance testing device,
This performance testing device structure comprises air compartment test stand and accessory fan, and air is led in the import of accessory fan, the outlet of accessory fan and the entrance point UNICOM of air compartment test stand; Air compartment test stand outlet end is provided with tested device, and air is led in the air outlet of tested device; The inner chamber of air compartment test stand is disposed with front current plate, nozzle and rear current plate along entrance point to outlet end direction;
Described accessory fan is connected with frequency variator, computing system successively signal, and computing system is connected with differential static pressure measuring device and motor speed control device signal in addition respectively, and motor speed control device is connected with motor signal;
Described tested device comprises the guide ring and seal disc that are fixed together, and the periphery of guide ring is provided with air guide sleeve, and seal disc returns shaft drive with the motor of motor and is connected,
Depend on above-mentioned performance testing device, specifically comprise the following steps:
Under standard operating conditions, namely external pressure is a standard atmospheric pressure, ambient temperature is 20 DEG C, relative moisture is 50%, air density is 1.2kg/m 3tested device is controlled under a constant rotating speed, the rotating speed of regulating and controlling accessory fan is carried out by frequency variator, regulate the tested device import under different flow and exit static pressure, when air flows through nozzle, before and after nozzle, create static pressure difference, obtain static pressure difference value by differential static pressure measuring device;
The work static pressure of tested device is regulated within the scope of 50Pa ~ 250Pa, carries out applied voltage test, simultaneously, the largest circumference speed of the guide ring in tested device blade tip clearance region is set to U=47.4m/s, one group of dimensionless number certificate of flow leakage rate in prediction on such basis, thus obtain the aeroperformance curve in tested device blade tip clearance region.
The invention has the beneficial effects as follows: the impact of leakage flow on aeroperformance that main flow region can be avoided, the important function that more accurate calculating clearance leakage of blade tip amount plays; By apparatus of the present invention, the performance curve in automobile engine cooling fan blade tip clearance region completely can be provided.
Accompanying drawing explanation
Fig. 1 is the car engine cooling system schematic diagram of prior art;
Fig. 2 is the relation schematic diagram of automobile engine cooling fan structure and flow characteristic;
Fig. 3 is the structural model figure that fin embodiment is separated in two, blade tip clearance region;
Fig. 4 is the structural model figure that fin embodiment is separated in three, blade tip clearance region;
Fig. 5 is the structural model figure that fin embodiment is separated in five, blade tip clearance region;
Fig. 6 is the structural representation of the performance testing device in the automobile engine cooling fan blade tip clearance region of band guide ring of the present invention;
Fig. 7 is the schematic cross-section of the performance test test zone in the inventive method;
Fig. 8 is the flowing state model sketch in the blade tip clearance region that the inventive method adopts;
Fig. 9 is the experimental performance curve of the guide ring state of rest inferior lobe top gap area that the inventive method obtains;
Figure 10 is the experimental performance curve of the guide ring rotation motion state inferior lobe top gap area that the inventive method obtains.
In figure, 1. motor support base, 2. motor, 3. fan blade, 4. air guide sleeve, 5. radiator, 6. guide ring, 7. wheel hub, 8. separates fin, 9. expansion chamber, 10. seal disc, 11. motor speed control devices, 12. computing systems, 13. frequency variators, 14. accessory fans, current plate before 15., current plate after 16., 17. nozzles, 18. differential static pressure measuring devices.
Embodiment
The automobile engine cooling fan with guide ring of prior art, is installed with a guide ring jointly in all cooling fan blade outer ends.
With reference to Fig. 1, it is the car engine cooling system schematic diagram of prior art, comprise the motor 2 be arranged on motor support base 1, motor 2 is coaxially connected with cooling fan 3, cooling fan 3 cylindrical is provided with air guide sleeve 4 (defining blade tip clearance region between air guide sleeve and the guide ring of blade tip consolidation), and the direction windward of cooling fan 3 is provided with radiator 5.
With reference to Fig. 2, be the relation schematic diagram of automobile engine cooling fan structure and flow characteristic, be blade tip clearance region between the guide ring 6 and air guide sleeve 4 of cooling fan 3 blade outer end consolidation, produces blade-tip leakage flow and move.
With reference to Fig. 3, Fig. 4, Fig. 5, the performance testing device in the automobile engine cooling fan blade tip clearance region of band guide ring of the present invention, has carried out the structured testing of three kinds of embodiments respectively.In three groups of example structure, the arc section of the gate area of guide ring is same radius and radian is equidistant value, in three groups of structures, the arc section of the gate area of guide ring is same radius and radian, section length L is 49.7mm, and span l and S separating fin is equidistant value.
As Fig. 3 embodiment, the structure in blade tip clearance region is straight-through U-groove bevel (namely separate fin 8 and comprise each one of front and back), and structure is simple, installs easily, is widely used in current automobile engine cooling fan.
As Fig. 4 embodiment, the similar in blade tip clearance region is in labyrinth sealing groove, the interval of U-groove bevel can be regarded as and form two expansion chambers by three separation fins 8, it is 3mm that ε is got in the gap of air guide sleeve cylindrical inner and separation fin top, section length L=49.7mm, the diameter D=362mm of guide ring; Separate the span S=21.6mm of fin, the fin thickness δ 1=2.5mm at entrance and exit place, middle fin thickness δ 2=1.5mm.
As Fig. 5 embodiment, the labyrinth sealing groove that the structure in blade tip clearance region is separated fins 8 formed by five, five radial heights separating fins are consistent, and guide ring end height is consistent, and it is 3mm that ε is got in air guide sleeve cylindrical inner and the gap of separating fin top.
As Fig. 6, the performance testing device in the automobile engine cooling fan blade tip clearance region of band guide ring of the present invention, design [14] [15] [16] [17] according to the air compartment air inlet test requirements document in CNS (GB/T1236-2000), for carrying out the performance test in motor car engine blade tip clearance region
This performance testing device comprises air compartment test stand and accessory fan 14, and air is led in the import of accessory fan 14, the outlet of accessory fan 14 and the entrance point UNICOM of air compartment test stand; Air compartment test stand outlet end is provided with tested device, and air is led in the air outlet of tested device; The inner chamber of air compartment test stand is disposed with front constant-current stabilizer 15, multiinjector flowmeter 17 and rear constant-current stabilizer 16 along entrance point to outlet end direction;
Accessory fan 14 is connected with frequency variator 13, computing system 12 successively signal, and computing system 12 is connected with differential static pressure measuring device 18 and motor speed control device 11 signal in addition respectively.Computing system 12 adopts various sensor to realize the conversion of physical signalling to electrical signal, computer is sent into by Interface Terminal, analog amount variable signal is converted to digital quantity by data collecting card and sends into computer by the parameters such as pressure, temperature, humidity, and rotating speed, power use communication converter to send into computer [18] [19].
(tested device of originally installing is changed to seal disc 10), tested device comprises guide ring 6 and is fixedly connected with seal disc 10, be fixedly connected with and fit together, the impact of leakage flow on performance in main flow region can be avoided like this, calculate clearance leakage of blade tip stream comparatively accurately.The periphery of guide ring 6 is provided with air guide sleeve 4, and the internal-and external diameter location tolerance of air guide sleeve 4 and guide ring 6 controls at ± 0.1mm, and as shown in Figure 7, seal disc 10 returns shaft drive with the motor of motor 2 and is connected, and motor 2 is connected with motor speed control device 11 signal.
The performance defining method in the automobile engine cooling fan blade tip clearance region of band guide ring of the present invention, utilizes above-mentioned performance testing device, with reference to Fig. 6, Fig. 7, specifically comprises the following steps:
Under standard operating conditions, namely external pressure is a standard atmospheric pressure (101325Pa or 760mmHg), ambient temperature is 20 DEG C, relative moisture is 50%, air density is 1.2kg/m 3tested device is controlled under a constant rotating speed, carried out the rotating speed of regulating and controlling accessory fan 14 by frequency variator 13, regulate the tested device import under different flow and exit static pressure, when air flows through nozzle 17, air-flow forms local contraction at nozzle 17 place, flow velocity increases, and static pressure reduces, so create static pressure difference (or claiming pressure reduction) before and after nozzle 17, air velocity is larger, and the pressure reduction produced before and after nozzle 17 is also larger.By measuring pressure reduction, just can weigh the size of fluid flowing through spray nozzles 17 flow, obtaining static pressure difference value by differential static pressure measuring device 18, this method of measurement is based on law of conservation of energy and flowing equation of continuity [20].The work static pressure of automobile engine cooling fan is 250Pa to the maximum usually, therefore, pressure regulates and carry out applied voltage test within the scope of 50Pa ~ 250Pa, simultaneously, the winding number of automobile engine cooling fan is 2500rpm to the maximum usually, like this, and the largest circumference speed U=47.4m/s of the guide ring 6 in tested device blade tip clearance region, calculate one group of dimensionless number certificate of flow leakage rate, thus obtain the aeroperformance curve in tested device (device) blade tip clearance region.
In addition, air-flow constant-current stabilizer can also be provided with in apparatus of the present invention, be provided with upper and lower sides two cover altogether, upstream side constant-current stabilizer is used for absorbing the kinetic energy of upstream side air-flow, the purposes of downstream side constant-current stabilizer is substantially uniform in order to ensure air-flow before entering measuring plane, for meeting these requirements, need the combination unit (in figure not display) adding some filter screens or perforated plate in air compartment test stand runner.
Theoretical calculation method of the present invention is the sealing principle according to Steam Turbine in Fire Power Plant packing, a series of throttle clearance and expansion cavity is formed between the guide ring and air guide sleeve of automobile engine cooling fan, air-flow is forced to pass through tortuous approach, produce throttling and thermomechanical effect, increase flow resistance by the method expanded step by step and suppress to leak the aeroperformance improving fan.Fig. 8 is blade tip clearance region labyrinth gland internal flow model schematic diagram, in figure, packing is made up of the separation fin be arranged in order and expansion chamber, the hard-wired guide ring of fan leaf tip portion processes some separation fins, separate between fin and air guide sleeve and keep less radial clearance, separate a formation expansion chamber between fin for every two.Air-flow flows to low voltage side from high pressure side, and during gap by annular and separation fin end portion and air guide sleeve, aisle spare diminishes, and speed increases, and pressure reduces, and simultaneous temperature reduces (enthalpy minimizing).Air-flow flows into the expansion chamber separating sudden enlargement after fin end portion subsequently, flow area becomes suddenly large, air-flow forms eddy current in expansion chamber, flow velocity is approximate drops to zero, but pressure is constant, and its kinetic energy is all converted into heat energy, because the heat dissipating capacity of expansion indoor air flow is very little compared with the total amount of heat of air-flow, can ignore, therefore air-flow enthalpy returns to again original numerical value, this process is called throttling process.When it is by next gap, said process repeats.Before and after packing, the overall presure drop of air-flow reduces gradually successively in all separation fin clearances and expansion chamber, repeats throttling process, until pressure reduction is zero, air-flow in the end in an expansion chamber pressure reach consistent with low voltage terminal pressure, no longer leakage current.But this is that blade tip clearance region is in a kind of leakage flow ideally.
The leakage rate in blade tip clearance region ideally can calculate with formula (1) or (2).Subscripting i=1 can be used in the blade tip clearance region having multiple expansion cavity to form, many groups formula simultaneous solution of 2,3....Or, by using the clearance leakage of blade tip mobile performance coefficient φ of ideal flow state awith entrance, discharge state, formula (3) can also be used to calculate the leakage rate G in the blade tip clearance region of perfect condition i.
G I = α i F i P i - 1 2 κ i - 1 κ i - 1 - 1 1 RT i - 1 { ( P i P i - 1 ) 2 κ i - 1 ( P i P i - 1 ) κ i - 1 + 1 κ i - 1 } , - - - ( 1 )
Will substitute in above formula and obtain:
G I = α i F i 2 κ i - 1 κ i - 1 - 1 { ( P i P i - 1 ) 2 κ i - 1 ( P i P i - 1 ) κ i - 1 + 1 κ i - 1 } P i - 1 v i - 1 , - - - ( 2 )
G I = αF φ α P in v in , - - - ( 3 )
φ α = 1 - λ 2 n 2 / 5 , - - - ( 4 )
In Practical Project, when air-flow is by blade tip clearance region, air-flow does not slow down completely and fully expands in the expansion chamber separating fin formation, but some air-flow is from the inlet to the outlet shown in straight line shape flow at high speed (as Fig. 8).Under the impact that this phenomenon exists, the actual leakage rate G by blade tip clearance region of air-flow eideally by the leakage rate G in blade tip clearance region iinevitable different, then by kinetic energy carry more effect coefficient υ represent the actual leakage rate by blade tip clearance region with ideally by the ratio of the leakage rate in blade tip clearance region, υ=G e/ G i, the large I simultaneous formula (5) of υ value and (6) are tried to achieve, and in formula, the size and Orientation of θ is with reference to shown in Fig. 8,
υ = n 1 + ( n - 1 ) ( 1 - A ) 2 , - - - ( 5 )
A = ϵα / l ( ϵα / l ) + tan θ , - - - ( 6 )
Therefore, expressing from testing the leakage rate formula (7) that obtains, namely carrying more effect coefficient υ with kinetic energy and being multiplied by formula (3) and obtaining; In like manner, carry out the size of theoretical calculation leakage rate with clearance leakage of blade tip mobile performance coefficient Φ, formula (8) is set up; If with the leakage rate G obtained from experiment eexpress clearance leakage of blade tip mobile performance coefficient Φ, then formula (9) is set up; Namely formula (8) is the theoretical value that can characterize clearance leakage of blade tip amount size, and formula (9) is the experimental value that can characterize clearance leakage of blade tip amount size,
G E = Fυα P in v in , - - - ( 7 )
Φ=υαφ a, (8)
Φ = G E ( F P in v in ) - 1 , - - - ( 9 )
λ is pressure ratio, λ=P out/ P in, P inthe entrance absolute pressure in blade tip clearance region, P outit is the outlet absolute pressure in blade tip clearance region;
N is the total number separating fin;
θ separates the angle that the top of fin is basic point Diffusion of gas stream;
α is flow coefficient, α=0.7;
F is air guide sleeve and the cross-sectional flow area separating gap, fin place;
F ithat air guide sleeve internal face separates the cross-sectional flow area in gap, fin place with corresponding i-th;
R is ideal gas constant, R=8.314J/molK;
ν infor the gas specific volume of blade tip clearance area entry, the i.e. inverse of gas density, unit is m 3/ kg, subscript in represents air flow inlet;
ν i-1it is the gas specific volume in corresponding the i-th-1 segmentation fin;
Φ is clearance leakage of blade tip mobile performance coefficient;
P representative pressure, P ifor correspondence separates the absolute pressure of fin inside; The sequence number of subscript i representative segmentation fin, i.e. i-th segmentation fin; The sequence number of subscript i-1 representative segmentation fin, i.e. the i-th-1 segmentation fin;
к is adiabatic index, к i-1correspond to P i-1adiabatic index during state;
T representation temperature, T i-1represent gas total temperature before and after each segmentation fin;
α iit is the flow coefficient in each segmentation fin;
ε is fan leaf top clearance height; L is the span separating fin;
A carries more effect correction factor υ to calculate kinetic energy, the throttle clearance of expression, throttling pitch and throttling width and cavity is long, deeply than an intermediate function.
Regulating static power is respectively 50Pa, 100Pa, 150Pa, 200Pa, 250Pa, under guide ring state of rest, carries out calculating the performance curve obtaining different blade tip clearance regions fluidal texture, as shown in Figure 9.Result of calculation shows: zero dimension performance parameter Φ in blade tip clearance region changes with the number difference of the separation fin in the structure in blade tip clearance region in the drawings, and separate the situation of fin number n=2, zero dimension performance parameter Φ is minimum, and namely leakage rate is minimum.The situation of n=5, zero dimension performance parameter Φ is maximum, and namely leakage rate is maximum.Meanwhile, along with pressure reduces, blade tip clearance region performance is improved, and this has nothing to do with separation fin number.
Consider the impact of cooling fan rotation motion on leakage rate, control guide ring rotating speed, the maximum rotating speed of cooling fan is about 2500rpm, i.e. the linear velocity U=47.4m/s of guide ring end.Same method regulating static power, respectively at 50Pa, 100Pa, 150Pa, 200Pa, 250Pa, under guide ring rotating speed 2500rpm state, carries out calculating the performance curve obtaining different blade tip clearance regions fluidal texture, as shown in Figure 10.Result of calculation shows: in figure under guide ring rotating speed n=2500rpm state, and the situation of n=3 and n=2 situation are in whole static pressure regulation range, and blade tip clearance region zero dimension performance parameter Φ is very close, and namely leakage rate is more or less the same.But under the low voltage situations of below 100Pa, the zero dimension performance parameter Φ of n=2 increases, namely leakage rate increases.The situation of n=5, zero dimension performance parameter Φ is maximum, and namely leakage rate is maximum.But when 50Pa, and the zero dimension performance parameter Φ of n=2 overlaps.As can be seen from Figure 10, and separate fin n=2, under guide ring state of rest, zero dimension performance parameter Φ compares, and within the scope of total head under turn state, blade tip clearance region performance is largely increased, and namely zero dimension performance parameter Φ significantly reduces.
Reference
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Claims (5)

1. the performance defining method in the automobile engine cooling fan blade tip clearance region with guide ring, is characterized in that, utilize a kind of performance testing device,
The structure of described performance testing device is, comprise air compartment test stand and accessory fan (14), air is led in the import of accessory fan (14), the outlet of accessory fan (14) and the entrance point UNICOM of air compartment test stand, air compartment test stand outlet end is provided with tested device, and air is led in the air outlet of tested device;
The inner chamber of described air compartment test stand is disposed with front current plate (15), nozzle (17) and rear current plate (16) along entrance point to outlet end direction;
Described accessory fan (14) is connected with frequency variator (13), computing system (12) successively signal, computing system (12) is connected with differential static pressure measuring device (18) and motor speed control device (11) signal in addition respectively, and motor speed control device (11) is connected with motor (2) signal;
Described tested device comprises the guide ring (6) and seal disc (10) that are fixed together, the periphery of guide ring (6) is provided with air guide sleeve (4), seal disc (10) returns shaft drive with the motor of motor (2) and is connected
Depend on above-mentioned performance testing device, specifically comprise the following steps:
Under standard operating conditions, namely external pressure is a standard atmospheric pressure, ambient temperature is 20 DEG C, relative moisture is 50%, air density is 1.2kg/m 3tested device is controlled under a constant rotating speed, the rotating speed of regulating and controlling accessory fan (14) is carried out by frequency variator (13), regulate the tested device import under different flow and exit static pressure power, when air flows through nozzle (17), before and after nozzle (17), create static pressure difference, obtain static pressure difference value by differential static pressure measuring device (18);
The work static pressure of tested device is regulated within the scope of 50Pa ~ 250Pa, carries out applied voltage test, simultaneously, the largest circumference speed of the guide ring (6) in tested device blade tip clearance region is set to U=47.4m/s, one group of dimensionless number certificate of flow leakage rate in prediction on such basis, thus obtain the aeroperformance curve in tested device blade tip clearance region.
2. the performance defining method in the automobile engine cooling fan blade tip clearance region of band guide ring according to claim 1, is characterized in that: described air guide sleeve (4) and the internal-and external diameter allowance control of guide ring (6) are at ± 0.1mm.
3. the performance defining method in the automobile engine cooling fan blade tip clearance region of band guide ring according to claim 1, is characterized in that, the structure in described blade tip clearance region is straight-through U-groove bevel, comprises
The structure of two separation fins,
Or the structure of three separation fins,
Or the structure of five separation fins.
4. the performance defining method in the automobile engine cooling fan blade tip clearance region of band guide ring according to claim 1, it is characterized in that, described work static pressure is set to 50Pa, 100Pa, 150Pa, 200Pa, 250Pa respectively, under guide ring state of rest, obtain the performance curve of different blade tip clearance regions fluidal texture;
In addition, work static pressure is set to 50Pa, 100Pa, 150Pa, 200Pa, 250Pa respectively, and guide ring rotating speed is under 2500rpm state, obtains the performance curve of different blade tip clearance regions fluidal texture.
5. the performance defining method in the automobile engine cooling fan blade tip clearance region of band guide ring according to claim 1, it is characterized in that, the concrete computational process of the method is: the leakage rate formula (1) in blade tip clearance region ideally or (2) calculate, there is the blade tip clearance region subscripting i=1 that multiple expansion cavity is formed, 2,3... many groups formula simultaneous solution
Or, by using the expansion coefficient φ of ideal flow state awith entrance, discharge state, formula (3) is adopted to calculate the leakage rate G in the blade tip clearance region of perfect condition i,
G I = α i F i P i - 1 2 κ i - 1 κ i - 1 - 1 1 RT i - 1 { ( P i P i - 1 ) 2 κ i - 1 - ( P i P i - 1 ) κ i - 1 + 1 κ i - 1 } , - - - ( 1 )
Will substitute in above formula and obtain:
G I = α i F i 2 κ i - 1 κ i - 1 - 1 { ( P i P i - 1 ) 2 κ i - 1 - ( P i P i - 1 ) κ i - 1 + 1 κ i - 1 } P i - 1 v i - 1 , - - - ( 2 )
G I = αF φ a P in v in , - - - ( 3 )
φ a = 1 - λ 2 n 2 / 5 , - - - ( 4 )
The actual leakage rate G by blade tip clearance region of air-flow eideally by the leakage rate G in blade tip clearance region iinevitable different, then by kinetic energy carry more effect coefficient υ represent the actual leakage rate by blade tip clearance region with ideally by the ratio of the leakage rate in blade tip clearance region, υ=G e/ G i, the size of υ value is tried to achieve by simultaneous formula (5) and (6),
υ = n 1 + ( n - 1 ) ( n - A ) 2 , - - - ( 5 )
A = ϵα / l ( ϵα / l ) + tan θ , - - - ( 6 )
Therefore, expressing from testing the leakage rate formula (7) that obtains, namely carrying more effect coefficient υ with kinetic energy and being multiplied by formula (3) and obtaining; In like manner, carry out the size of theoretical calculation leakage rate with clearance leakage of blade tip mobile performance coefficient Φ, formula (8) is set up; If with the leakage rate G obtained from experiment eexpress clearance leakage of blade tip mobile performance coefficient Φ, then formula (9) is set up; Namely formula (8) is the theoretical value that can characterize clearance leakage of blade tip amount size, and formula (9) is the experimental value that can characterize clearance leakage of blade tip amount size,
G E = Fυα P in v in , - - - ( 7 )
Φ=υαφ a, (8)
Φ = G E ( F P in v in ) - 1 , - - - ( 9 )
λ is pressure ratio, λ=P out/ P in, P inthe entrance absolute pressure in blade tip clearance region, P outit is the outlet absolute pressure in blade tip clearance region;
N is the total number separating fin;
θ separates the angle that the top of fin is basic point Diffusion of gas stream;
α is flow coefficient, α=0.7;
F is air guide sleeve and the cross-sectional flow area separating gap, fin place;
F ithat air guide sleeve internal face separates the cross-sectional flow area in gap, fin place with corresponding i-th;
R is ideal gas constant, R=8.314J/molK;
ν infor the gas specific volume of blade tip clearance area entry, the i.e. inverse of gas density, unit is m 3/ kg, subscript in represents air flow inlet;
ν i-1it is the gas specific volume in corresponding the i-th-1 segmentation fin;
Φ is clearance leakage of blade tip mobile performance coefficient;
P representative pressure, P ifor correspondence separates the absolute pressure of fin inside; The sequence number of subscript i representative segmentation fin, i.e. i-th segmentation fin; The sequence number of subscript i-1 representative segmentation fin, i.e. the i-th-1 segmentation fin;
к is adiabatic index, к i-1correspond to P i-1adiabatic index during state;
T representation temperature, T i-1represent gas total temperature before and after each segmentation fin;
α iit is the flow coefficient in each segmentation fin;
ε is fan leaf top clearance height; L is the span separating fin;
A carries more effect correction factor υ to calculate kinetic energy, the throttle clearance of expression, throttling pitch and throttling width and cavity is long, deeply than an intermediate function.
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