IROS2019国际学术会议论文集 1709

Abstract The enrichment of the application scenarios of rotorcrafts presents new challenges for the study of their aerodynamic characteristics such as operating above a building surface of finite size In this paper the ground effect is divided into infinite ground effect and finite ground effect and three types of finite ground effects with different blocked area are studied Through numerical simulations the rotor thrust data and flow field figures in ground effect are obtained Based on the rotor thrust data mathematical models are established to describe the rotor thrust alteration caused by infinite and finite ground effect The analysis of the flow field reveals the mechanism of the finite ground effect I INTRODUCTION With the development of the small sized rotorcraft their application scenarios are greatly enriched For example when flying inside a building the rotorcraft may approach terrains such as stairs walls and eaves These planes that have aerodynamic interference with the rotors are often of finite size the planes are not infinitely extended which will affect the aerodynamic characteristics and control stability of the aircraft In this paper the ground effect is divided into infinite ground effect and finite ground effect in which the finite ground effect is the focus of our research The finite ground effect has an asymmetrical interference effect on the rotor flow field and there is a significant difference from the ground effect under the action of the infinite ground plane At present the research on the finite ground effect of rotors is relatively rare and mainly focuses on the experimental field For example Iboshi s team has experimentally measured the ground effect of rotors hovering over finite ground plane 1 2 but the finite ground effect of a moving rotor has not been reported in relevant experimental research There are also a small number of theoretical modeling studies on finite ground effects In the earlier time there were dynamic inflow models for landing rotorcraft conditions such as the work carried out by Prasad s team in the 1990s 3 6 Besides Itoga 7 Keller 8 and Wachspress 9 have used the panel method combined with the rotor free wake model to analyze the influence of the slope or finite plane on the rotor flow field However the calculation results of these documents are lack of experimental verification and there is no further study into the mechanism of the finite ground effect problem As can be seen a finite ground effect analysis model with wide application and good calculation accuracy has not appeared so far Therefore it is necessary to further study the This Research was supported in part by National Natural Science Fund of China Grant No 61473155 Assembly Pre research Sharing Technology Project Grant No 41412040102 Six talent peaks project in Jiangsu Province Grant No GDZB 039 Primary Research the bottom boundary is set as pressure outlet with 0 Pa gauge pressure the round boundary is set as symmetry and the proximal plane is set as no slip wall An unstructured tetrahedral mesh with prism layer and refinement around the rotor is applied The ANSYS FLUENT double precision solver is applied to perform the CFD simulations As is mentioned before the SRF model is chosen as the rotating flow domain model Incompressible Reynolds averaged Navier Stokes equations with RNG k epsilon turbulence model are solved The near wall treatment term is set as Standard Wall Functions Second order numerical scheme is used for both the convection and diffusion terms The pressure based steady solver is used for pressure velocity coupling Convergence was considered achieved when the value of rotor thrust changed within 0 01 over 1000 iterations III ROTOR THRUST MODELS Through numerical simulations rotor thrust data are obtained Based on the results the influence of the ground effect on the rotor thrust is modeled A Infinite Ground Effect We measure the influence of the ground effect on the rotor thrust by the thrust ratio T k which is defined as T T k T 1 where T denotes the rotor thrust in ground effect and T represents the baseline rotor thrust in free space The thrust ratio changed with non dimensionalized rotor ground distance in infinite ground effect is shown in Fig 3 It can be seen that the rotor will gain extra thrust at the same rotor speed in ground effect compared to the case in free space and as the rotor ground distance increases the thrust enhancement Figure 3 Rotor thrust ratio changed with rotor ground distance in infinite ground effect Figure 4 Model fitting of the infinite ground effect decreases rapidly and the ground effects decays When g h is greater than 1 5R the rotor thrusts are very close to that in free space and the influence of the ground effect on the rotor thrust is almost negligible 6936 It can be seen from Fig 3 that T k is always greater than 1 the smaller the rotor ground distance the greater the rotor thrust enhancement as the rotor ground distance increases the rotor thrust enhancement decreases rapidly Therefore we assume that the ground effect rotor thrust model contains an exponential term as follows ed 11exp T h kE R 2 where E represents the rotor thrust enhancement in ground effect Here e and d are coefficients greater than 0 e is the thrust enhancement coefficient representing the extent of the rotor thrust enhancement in ground effect d is the enhancement decay coefficient which denotes the decay rate of the enhancement of the rotor thrust with increasing rotor ground distance The rotor thrust data are fitted using MATLAB with the above model as shown in Fig 4 It can be seen that the curve fits well and the coefficients in the rotor thrust model are determined as e 0 685 and d 2 933 B Finite Ground Effect with Different Blocked Area Percentages The rotor thrust ratio T k varying with the blocked area percentage p is shown in Fig 5 It can be seen that the rotor still gains extra thrust in finite ground effect with a finite Figure 5 Rotor thrust ratio changed with p in finite ground effect Figure 6 Rotor thrust ratio changed with p k in finite ground effect blocked area percentage compared to in free space But as p decreases the rotor thrust enhancement decreases which means the finite ground effect decreases So we introduce the term containing p into the rotor thrust model and the rotor thrust enhancement in finite ground effect is equal to the rotor thrust enhancement in infinite ground effect multiplied by the blocked area percentage coefficient p fp as follows 11 Tp kEf p E 3 Because the rotor thrust in finite ground effect is between the rotor thrust in free space and the rotor thrust in infinite ground effect the range of p should be 0 to 1 It can be observed from Fig 5 that when p is less than 0 5 the slope of the rotor thrust curve is small which means the rotor thrust enhancement increases slowly as p increases and when p exceeds 0 5 the slope of the rotor thrust curve increases which means the rotor thrust enhancement accelerates Therefore it is supposed that the ratio of the blocked area and the unblocked area has a more direct relation with the rotor thrust enhancement Hence the ratio of the blocked area and the unblocked area p k is introduced into the model which is defined as 1 p p k p 4 Then T k varying with p k is shown in Fig 6 Note that the point at 1p p k is not shown where the rotor thrust is the same as that in infinite ground effect According to the shape of the rotor thrust curve in Fig 6 we assume that p contains an exponential term 1 exp ppp k 5 Then the model of the rotor thrust in finite ground effect with a finite blocked area percentage is ed 11 expexp 1 Tp ph k pR 6 The rotor thrust data obtained through the simulations are fitted with the above model as shown in Fig 7 The coefficient in the model is determined p 0 3566 Figure 7 Model fitting of the finite ground effect with varying p k C Finite Ground Effect with Different Blocked Area Radii The rotor thrust ratio T k varying with the radius of the blocked area r R is shown in Fig 8 It can be seen that the rotor still gains extra thrust in finite ground effect with a finite radius of blocked area compared to in free space But as r decreases the rotor thrust enhancement decreases which means the finite ground effect decreases Based on the ground effect model we introduce the term related to r The rotor thrust enhancement in finite ground effect is equal to the rotor thrust enhancement in infinite ground effect multiplied by the blocked area radius coefficient r f r as follows 11 Tr kEf r E 7 The range of r should be 0 to 1 When 0r 0 r indicating that the rotor thrust in this condition is equal to the rotor thrust in free space when r 1 r indicating that the rotor thrust is equal to the rotor thrust of infinite ground effect at the same rotor ground distance r increases monotonously with the increase of r the closer r is to 0 the 6937 greater the change in r Based on the above analysis it is assumed that the blocked area radius coefficient r is a sigmoid function 2 1 1exp r r r R 8 Then the rotor thrust model in finite ground effect with a finite blocked area radius becomes Figure 8 Rotor thrust ratio changed with r in finite ground effect Figure 9 Model fitting of the finite ground effect with varying r ed 2 11exp 1 exp T r h k rR R 9 The rotor thrust data obtained by simulations are simulated by the above model as shown in Fig 9 The coefficient in the model is determined r 2 171 D Finite Ground Effect with Different Blocked Area Positions The rotor thrust ratio T k varying with the position of the blocked area l R is shown in Fig 10 It can be seen that the rotor thrust enhancement decreases as l R increases which means the finite ground effect decreases The largest slope of the rotor thrust curve appears in the range 0 50 5l R where the rotor thrust variation is the most obvious When 0 5l R the rotor thrust has almost no enhancement compared to in the free space When 0 5l R the rotor thrust is close to that in infinite ground effect Based on the infinite ground effect model we introduce the term related to the blocked area position l The rotor thrust enhancement in finite ground effect is equal to the rotor thrust enhancement in infinite ground effect multiplied by the blocked area position coefficient l f l as follows 11 Tl kEf l E 10 The range of l should be 0 to 1 When l R 0 l indicating that the rotor thrust in this condition is equal to the rotor thrust in free space when l R 1 l indicating that the rotor thrust is equal to the rotor thrust of infinite ground effect at the same rotor ground distance l decreases monotonously with the increase of l R Through the above analysis and the trend of the rotor thrust curve in Fig 10 we assume that the blocked area position coefficient l is a sigmoid function 12 1 1 exp l ll l R 11 Figure 10 Rotor thrust ratio changed with l in finite ground effect Figure 11 Model fitting of the finite ground effect with varying l Then the rotor thrust model in finite ground effect with a finite blocked area position becomes ed 12 1 1exp 1 exp T ll h k Rl R 12 The rotor thrust data obtained by simulations are fitted by the above model as shown in Fig 11 The coefficients in the model are determined as 1 l 4 926 2l 0 150 IV ANALYSIS OF FLOW FIELD Based on the flow field figures obtained from the numerical simulations the distribution of the flow field around the rotor in finite ground effect is analyzed and some conclusions about the mechanism of the ground effect are obtained A Influence of Infinite Ground Effect on Flow Field Fig 12 shows the velocity fields of a rotor with different rotor ground distances in infinite ground effect The white blocks in the figures represent the proximal ground planes Note that in order to clearly show the distribution of the flow field variables the range of the variables is reasonably scaled and therefore the actual value at maximum or minimum value of the legend may exceed the range of legend By analyzing the velocity field distribution it can be seen that the ground effect has a significant effect on the shape of the rotor wake when the rotor is in proximity to the ground the rotor wake is compressed by the ground in the vertical direction which will induce a radially outward extension of the wake The ground blocks the vertical component of the downwash and to keep the conservation of momentum the horizontal component of the airflow velocity is forced to increase and the airflow radially flowing outward along the ground increases B Influence of Blocked Area Percentage on Flow Field It is noticed from the results that the rotor thrusts in finite ground effects are always greater than that in free space This can be naturally inferred from the mechanism of ground effect the finite ground plane still blocks part of the downwash which reduces the vertical component of the 6938 airflow and the horizontal component is forced to increase resulting in an additional differential pressure on the two sides of the rotor and the extra rotor thrust From the analysis of the simulation results in Section III B it can be seen that the rotor thrust increases with the increase of the blocked area percentage and the trend of increase has a sudden increase when the blocked area percentage exceeds 0 5 Fig 13 shows the horizontal sectional velocity field at the height of the ground the vertical distance from the rotor is 0 5R with different blocked area percentages Similar to the ground effect the plane blocks part of the downwash and the blocked airflow is forced to flow along the ground plane The airflow is compressed causing the pressure difference between the upper and lower surfaces of the rotor to increase resulting in the rotor thrust enhancement The unblocked part of the airflow can freely flow downward When the blocked area is relatively small the blocked downwash can escape to the large space of the unblocked area and as the blocked area increases the escapable space becomes smaller When the blocked area exceeds the half the blocked airflow becomes the majority and the escapable space is less than half of the free space The compression effect of the plane on the airflow becomes stronger and the effect of the increase in the blocked area becomes obvious In fact the investigation of the influence of p k in Section III B is inspired by this flow field analysis The smaller the blocked area the faster the rotor thrust changes As the blocked area increases the rotor thrust gradually approaches that in infinite ground effect C Influence of Blocked Area Radius on Flow Field From the analysis of the influence of the blocked area radius on the rotor thrust in Section III C it can be seen that when the blocked area radius is in range of 0 1R the change in the radius will have a significant effect on the rotor thrust and when the radius is larger than 2R as the radius increases the rotor thrust only slightly changes This is because that after passing through the rotor plane the airflow will form a blade tip vortex with a radius smaller than the rotor radius and the downwash will mainly concentrate in the range of the blade tip vortex Fig 14 shows the vertical sectional velocity field with Figure 12 Influence of infinite ground effect on the flow field Figure 13 Influence of the finite ground effect with different blocked area percentages on the flow field Figure 14 Influence of the finite ground effect with different blocked area radii on the flow field Figure 15 Influence of the finite ground effect with different blocked area positions on the flow field 6939 different radii of the blocked area the vertical distance between the rotor and the ground plane is 0 5R It can be seen that when the radius of the circular blocked area is less than 1R although part of the airflow is blocked by the ground plane it can still bypass the ground plane to flow downward along the edge of the finite circular ground plane In this condition the change of the radius of the circular ground plane has a great influence on the volume of blocked airflow and the rotor thrust when the radius of the circular ground plane is larger than 2R the most of the airflow within the blade tip vortex begin to flow horizontally along the ground plane the blocking effect of the ground plane will be close to a saturation and the enhancement of the rotor thrust will decrease and tend to that in infinite ground effect at the same rotor ground distance D Influence of Blocked Area Position on Flow Field From the analysis of the influence of the blocked area position on the rotor thrust from Section III D the rotor thrust is greatly changed when the range of l is 1R to 1R especially in the range of 0 5R to 0 5R Fig 15 shows the vertical sectional velocity field with different positions of the blocked area the vertical distance between the rotor and the ground plane is 0 5R The results show that the plane blocks part of the downwash while the unblocked part of the airflow flows into the free space When the edge of the ground plane is within the range of the blade tip vortex the plane edge has a significant effect on the shape of the downwash so the rotor thrust significantly changes when the plane edge is on the right outer side pR of the blade tip vortex less airflow is blocked when the plane edge is on the left outer side of the blade tip vortex pR the plane has blocked the main component of the downwash and the change of the blocked area position has less influence on the flow field and rotor thrust V CONCLUSIONS AND FUTURE WORK Based on the infinite ground effect this paper investigates the finite ground effect and studies the effects of three types of finite planes with different blocked area percentages different blocked area radii and different blocked area positions Through numerical simulations the rotor thrust data and flow field figures in finite ground effect are obtained The rotor thrust data show that in these three