Experimental and Numerical Results on Cavity Effects
in Juncture Flow
B.J.C. Horsten
∗and L.L.M. Veldhuis
†Delft University of Technology, Delft, 2629 HS, The Netherlands
Juncture flow and cavity flow are complex types of flow that are studied frequently because of their practical implementations in aerodynamics. Both flow types have their own characteristics. In some cases, both flows interact. An example of this is the flow near a windtunnel support entry in a model where the support is inserted into a windtunnel
model cavity that houses an internal balance. To get further insight in these support
interference effects, various experimental techniques such as balance measurements, oil flow visualization, pressure measurements and boundary layer measurements are performed,
complemented by RaNS calculations. This survey shows that the flow behavior at the
entrance of the model support in the windtunnel model is complex due to cavity-juncture flow interference effects. An interesting phenomenon is the relieving effect of the cavity on the adverse pressure gradient in front of the support on the model, preventing separation. Furthermore, there is a contamination of the juncture flowfield due to the presence of the cavity leading to vortex formation near the model. This Slit Vortex is seen to affect the windtunnel model pressure distribution. These phenomena create a complex model support interference field. The overall agreement between experiments and calculations is satisfying except for the agreement with the balance measurements. The calculations do not accurately reproduce the balance measurements and are therefore not suitable to calculate the model support interference quantitatively.
I.
Introduction
For many years juncture flow has been a topic of interest for aerodynamicists all over the world. This is not only due to the complex flow pattern (Khan and Ahmed1
) that is still not fully understood but also because of the wide range of applications where this type of flow dominates the flowfield. Examples of this are aircraft wing-fuselage or tail-fuselage junctures, the attachment of sailing boat keels onto the hull (Dickinson2
), the scouring flow around bridge pillars causing erosion of the ground material (Simpson3
) and the attachment of a windtunnel model support to the model. Most of the experimental and numerical studies that focus on juncture flow include a certain appendage such as a wing (Devenport and Simpson4
and Jones and Clarke5
), a cylinder (Pattenden et al.6
and Constantinescu and Koken7
) or any other blunt object attached to a flat plate. The present study focuses on the turbulent flow topology that is encountered when the appendage is not attached to the base body directly but inserted in a body that contains an internal cavity. Both appendage and body are separated by a slit at the appendage entry location. An example of a practical application is the flow near a windtunnel support entry in a windtunnel model where the model houses an internal balance. This is a common case that is often encountered in windtunnel experiments. Because of the complex nature of the flow involved, the problem of model support disturbance is often solved in a practical way by performing dummy measurements (Eckert8
). In the present work, an investigation is setup to study the flow in the direct vicinity of the model support. The goal is to provide knowledge to enable the correction of model support interference in a more theoretical way. Results of numerical simulations are presented and compared to experimental results obtained by performing balance measurements, oil flow visualization, pressure measurements and boundary layer measurements. This study reveals the complexity of the flowfield and shows the need to perform both experimental and numerical work in order to understand the disturbance effects of the appendage (a model support) on the base body (a windtunnel model resembling
∗PhD. student, Department of Aerospace Engineering, Kluyverweg 1 2629 HS Delft, The Netherlands, Member AIAA. †Associate Professor, Department of Aerospace Engineering, Kluyverweg 1 2629 HS Delft, The Netherlands, Member AIAA.
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American Institute of Aeronautics and Astronautics
38th Fluid Dynamics Conference and Exhibit<BR>
an axisymmetrical aircraft fuselage). This paper is organized as follows: First, model support interference will be briefly explained. Some preliminary measurements and calculations on model support interference will be presented. Next, the interference is subdivided into separate contributions. It will be shown that the study of these contributions can be facilitated when numerical viscous flow simulations (Navier-Stokes) are carried out. The setup of such calculations will then be discussed. Several experimental techniques that are applied in order to study the interference are presented and their agreement with the Navier-Stokes calculations are discussed. These techniques will provide with a clearer image of the interference field of the model support and show the ability of a Navier-Stokes calculation to qualitatively resolve the interference flowfield. The numerical results are used in order to comment on the proposed separate contributions that define model support interference. Last, the results of the Navier-Stokes calculations are compared to the balance measurements and statements are made regarding the ability of these calculations to quantitatively determine the model support interference.
II.
General: Model Support Interference
Model support interference can be defined as the interference effect of a model support on the windtunnel model. This interference is usually corrected for during or after the measurements and is one of the corrections necessary to relate windtunnel tests to free-flight conditions. Common ways of determining model support interference are by performing dummy measurements or by numerical flow simulations. In this paper, the model support is said to generate two main disturbance effects: field effects and far-field effects. Near-field effects are seen as disturbance effects in the direct vicinity of the model support. These effects consist of viscous and inviscid disturbances that manifest on the windtunnel model. In case of a typical windtunnel experiment involving an aircraft configuration, these effects are measurable on the fuselage of an aircraft when the model support is inserted in the fuselage (as is common practice when internal balances are used). The far-field effects are the disturbances of the model support in the far-field and consist predominantly of inviscid disturbances on mainly the lifting surfaces of the configuration such as the wing and tail sections. This paper focuses on the model support near-field effects where the support is inserted into an axisymmetrical fuselage, as if the fuselage would accommodate an internal balance. To generate a base for the research on near-field effects, balance measurements and exploratory calculations are performed. The results of these will be discussed in the following section.
II.A. Balance Measurements and Exploratory Calculations on Model Support Near-Field Effects
Balance measurements on support near-field effects are performed in the Low Turbulence Tunnel (LTT) of Delft University of Technology, a closed circuit tunnel with a test section with cross sectional dimensions of 1.80 by 1.25 m and a length of 2.60 m. In this test section an axisymmetrical fuselage is mounted to the external balance system of the windtunnel positioned above the test section. An impression of the setup is given in figure 1. An opening is machined into the hollow fuselage at the bottom side, into which a dummy model support is inserted that is attached to the test section floor. Note that the support and fuselage remain separated by a slit as if the forces and moments would be measured by an internal balance. This slit has a width of 2 mm. The model support is inserted into the fuselage at 54 % of the body length measured from the nose of the model into the cylindrical part of the fuselage. The angle of the support trailing edge with the fuselage longitudinal axis is 65◦
. Angle of attack changes of the fuselage are facilitated by the external balance system. The angle of attack changes of the support are performed by a hinge at the support mount to the test section floor. The model under consideration is an axisymmetrical fuselage of length 1.35 m and maximum diameter of 0.16 m. It consists of a nose cone (of length 0.40 m), a cylindrical section (of length 0.47 m) and an ogive shaped tail (of length 0.48 m). Transition strips are applied at 20 % of the body length. The model support has an airfoil shaped cross section with a chord of 91 mm, a maximum thickness of 36 mm and a base width of 17 mm. The trailing edges of the support are not sharp but rounded off with a radius of 3 mm. Transition strips are applied at the quarter chord line of the model support. The accuracy of the balance system in measuring the values of the lift coefficient CL and
the drag coefficient CD is 4 and 3 counts respectively (these numbers are based on a reference wing area
of 0.15 m2
of attack (no angles of sideslip are considered) the forces on the fuselage are measured in both the presence and absence of the model dummy support. When this model support is removed from the setup, the gap in the fuselage is closed by a filling cap. Subtracting the results of these measurements (after minor solid-and wake blockage corrections of the support) provides with the model support near-field effects (expressed in disturbances of the lift- and drag coefficients) on the fuselage. These measurements are performed for an angle of attack range varying from -4 to 15◦
and at several Reynolds numbers (freestream velocities of 40, 50, 60 and 80 m/s).
(a) (b)
Figure 1. Fuselage and support measurement setup used for the balance measurements with (a) The complete setup in the windtunnel (b) A close-up of the support entry in the fuselage.
In addition to the dummy measurements, various numerical techniques are applied in order to calculate the model support near-field effects. These calculations are regarded as exploratory calculations. They are setup with the following philosophy: ”It is recognized that the near-field of the model support is at least qualitatively governed by viscous and vorticity related phenomena. It is however not clear to what extend such phenomena quantitatively determine the value of the near-field model support interference”. In the light of this philosophy, the near-field model support interference is calculated by different numerical models that exclude such physics thereby providing with more information on the quantitative importance of these phenomena. The exploratory calculations are performed using: A 3D panel code with a first order approximation of the disturbance potential on the panels and 3D Euler calculations with second order central and upwind schemes in the discretization of the governing equations. Like for the balance measurements, two calculations are necessary for each angle of attack in order to calculate the interference: One calculation including the model support and one calculation excluding the model support. In the calculations, steady flow is assumed. In all the cases, a 3D representation of the fuselage, model support and windtunnel test section is implemented. The results of these calculations are given together with the results of the balance measurements in figure 2. The interference values in the plots are given in counts and are calculated by using the reference quantities mentioned for the balance measurements. The results for the lift- and drag coefficient are given for a Mach number of 0.176 (corresponding to a velocity of 60 m/s). The results display no Reynolds dependency for the aforementioned range of freestream velocities.
−2 0 2 4 6 8 10 12 14 16 −6 −4 −2 0 2 4 6
Angle of attack, deg
Disturbance in lift coefficient, counts
(a) −2 0 2 4 6 8 10 12 14 16 −15 −10 −5 0 5 10 15 20
Angle of attack, deg
Disturbance in drag coefficient, counts
(b)
Figure 2. Experimental and numerical results on model support near-field interference on the (a) Lift coefficient and (b) Drag coefficient of a generic axisymmetrical fuselage where: Blue solid line = Balance measurements, Blue dashed line = Accuracy bandwidth of the balance measurements, Red solid line = Panel calculations and Black solid line = Euler calculations.
II.B. A Subdivision of Model Support Near-Field Effects in Separate Contributions
A method that allows a more systematic quantitative and qualitative assessment of the contributions of vorticity and viscosity to support interference proposes a new subdivision of the near-field model support effects in effects that can be studied separately. According to the proposed subdivision, the model support near-field effect can be divided into:
• A pressure disturbance of the support on the fuselage caused by the proximity of the support. The fuselage pressure distribution is contaminated by the presence of the support. Examples of this are the pressure peak upstream the nose of the support on the fuselage and the projection of the low pressure area of the support (due to the acceleration of the flow at the support) on the fuselage. This effect is from now on called the P-effect. This effect is mainly to be found in two regions designated from now on as region A and region B. Their definitions are (figure 3):
– From the model nose to the support gap leading edge (region A)
– From the support gap leading edge to the trailing edge of the support gap (region B)
• The disturbances due to the presence of the model cavity (normally accommodating an internal balance) and the slit separating the model support and fuselage at the support entry location:
– A momentum exchange between the freestream and the fluid inside the cavity leading to distur-bances in the values of the longitudinal and lateral coefficients of the fuselage: The C1-effect. This effect is studied in the slit and internal cavity
– The effects of a complex flow pattern at the slit leading to the contamination of the region around the support: C2-effect. This effect consists of a pressure disturbance and a shear stress distribution disturbance that mainly play a role in region B
• Disturbances in front of, around and aft of the model support on the fuselage due to viscous phenomena, or the V-effect:
– Fuselage boundary layer skewing in front of the support (from a 2D to a 3D boundary layer) and shear effects besides the support on the fuselage. These are the effects on the shear stresses in regions A and B
– The influence of the model support wake on the fuselage. This is also a viscous phenomenon that has an effect on the pressure distribution and the shear stress distribution in a region called region D. The definition of region D: From just aft of the recirculation area to the trailing edge of the fuselage (another effect is the recovery effect of the fuselage boundary layer downstream of the recirculation area. This effect is dependent on the wake influence of the support and therefore not treated separately but included in the wake effect)
Figure 3. A graphical representation of the division of the model fuselage in regions A, B, C and D. Viewpoint is from the bottom of the fuselage looking directly onto the support entry in the fuselage. The flow comes in from the right.
For a study on the separate contributions to the near-field model support disturbance, the following information should be extracted: The magnitude of the effects, the interference and coherence of the effects and the sensitivity of the effects to certain input parameters as for instance angle of attack and sideslip. A method needs to be adopted that is capable of analyzing the near-field flow of the model support such that the aforementioned P-, C1-, C2-, and V-effect can be studied. It will be clear that this needs to be a calculation method taking vorticity, viscosity and turbulent flow features into account. Therefore, Navier-Stokes calculations are set up. It is believed that resolving the smallest scales of the flow is infeasible from the viewpoint of time and computational expenses. It is also thought that most of the disturbance effects (and the interference/coherence between these) are caused by the larger scales. Therefore a RaNS modeling of the flow is chosen (similar calculations on juncture flow are reported by Apsley and Leschziner9
and Pacciori et al.10
).
III.
RaNS Calculations on Model Support Near-Field Interference
The RaNS calculations discussed in this section give a qualitative and quantitative understanding of the disturbance contributions P, C1, C2 and V to the near-field model support disturbances. To insure the integrity of the boundary conditions of the numerical domain, the test section of the windtunnel is modeled. Inside this domain, the complete fuselage and model support are modeled, together with the balance cavity and the slit. Calculations are performed with ”full domains” and with ”half domains” in order to study the importance of unsteady vortex shedding from the model support on the fuselage. The boundary conditions are set such that a windtunnel experiment can be simulated: Mass-flow inlet and pressure outlet boundary conditions are used. In order to reduce the number of cells, the tunnel walls are not discretized by viscous layers. To maintain simulation stability the tunnels are modeled as symmetry planes. Detailed pictures showing the support entrance in the fuselage, the slit and the cavity are given in figure 4.
The unstructured mesh consisting of hexahedral cells is refined in the boundary layers, wakes, regions of elevated vorticity, regions of high geometrical curvature and regions where flow separation is expected. Vis-cous layers covering the boundary layer are generated with the first few cells in the visVis-cous sublayer (no wall functions are used in the calculations). For the calculations as presented herein, several turbulence models are tested and the results of the simulations are compared to experimental data (pressure measurements, flow visualization). The turbulence models that are tested are: Spalart-Allmaras, Standard k − ǫ, Realizable k − ǫ, Standard k − ω and the SST k − ω models. The model that performed the best (for the studied configuration) is the realizable k − ǫ model. This model is likely to provide superior performance for flows involving rotation, boundary layers under strong adverse pressure gradients, separation, and recirculation (Fluent Inc.11
(a) (b)
Figure 4. A close-up of the support entrance in the fuselage showing the slit and cavity where the viewpoint is (a)
From the bottom side looking onto the fuselage from the front and (b) From the front looking at a cross section of the fuselage.
pressure-based solver. The pressure-based solver uses a solution algorithm where the governing equations are solved sequentially (i.e., segregated from one another). The first calculations that were set up for the current case include the full domain and were of unsteady kind. It is well known that the flow in the wake of the support is dominated by vortex shedding. Because the flow in the direct near-field of the support-fuselage entry was not understood in advance of the calculations it was therefore chosen to start with unsteady calculations. The timestep adopted in the unsteady calculations is based on hot wire measurements in the support wake. The fluctuations appearing in the lift-, drag- and moment coefficient of the fuselage show no periodic tendency. This is an indication of the fact that the fuselage is not quantitatively affected by unsteady phenomena in the flow. When the results of the balance measurements are reviewed, it is seen that the time-dependent drag signal does not show any unsteady behavior. It is known that due to the inertia of the balance, the periodic behavior of the drag due to vortex shedding can not be fully resolved. It is thought however that because no peak values have been registered in the drag signal, no significant periodic behavior affects the fuselage. The results that are presented in this paper are therefore based on the results of steady calculations. In these calculations half-domains are used (by introducing a symmetry plane) thereby reducing the number of cells and computational time and stabilizing the convergence of the calculations.
IV.
Comparison of RaNS Calculations to Experimental Results
In the following sections, the results of the RaNS calculation where the fuselage is set at an angle of attack and sideslip of 0◦
in a flow with a Mach number of 0.176 are compared to experimental results on oil flow visualizations, pressure measurements and boundary layer measurements. This information will be used in order to study the near-field of the support-fuselage juncture. Finally the calculation will be used in order to acquire information on the separate contributions that determine model support near-field interference. The next section will start with a synthesis of the near-field flow using RaNS results and compare these results to experimental oil flow visualization results. When the topology of the near-field flow is clarified, the results of the subsequent sections will be used in order to strengthen the confidence in the synthesized flowfield and the use of RaNS results in order to perform such a synthesization.
IV.A. Comparison to Oil Flow Visualization Results
When the flow approaches the support on the fuselage, it is affected by an adverse pressure gradient thereby causing the 2D boundary layer to become a skewed 3D boundary layer. This is caused by the presence of the support causing an increase in the pressure in the flowfield in front of it. In the case of a generic juncture flow, the flow would finally separate in front of the support thereby leading to the well known horseshoe vortex wrapped around the support. In this case, the separation in front of the support does not set in. This is due to the pressure difference between the flow just outside the cavity and inside the cavity. The flow is sucked into the cavity and this effect that can be seen as a relieving effect prevents flow separation. A picture showing a cross section of the fuselage and support at the slit leading edge is given in figure 5(a). It is clearly seen in the figure that the flow enters the cavity and hence is prevented to separate in front of the support.
(a) (b)
Figure 5. (a) Streamlines in front of the support (on the model heartline) showing the relieving effect of the cavity on the adverse pressure gradient. In the figure the fuselage, internal cavity, support and the slit separating the support and fuselage at the support entry are clearly discernible. Viewpoint is at the side looking at a longitudinal cut of the model near the support leading edge. The flow comes in from the left. Pressures are relative to a reference pressure (b) A 2D picture of the streamlines around the gap on the fuselage. Viewpoint is from the bottom looking on the fuselage near the entry gap of the support. The flow comes in from the left. Pressures are relative to a reference pressure.
In the unsteady calculations, separation is triggered in front of the support by manipulating the local pressure. This is done as experiment to study the relieving effect. It could be seen that these separation points vanished by the relieving effect of the cavity. Figure 5(b) gives the local streamlines on the fuselage surface around the support entry gap. Again, no signs of separation are visible. The relieving effect can be seen in the pressure distribution as well.
Alongside the support (when traveling in downstream direction) the flow is accelerated due to the support shape. This creates a low pressure area on the support. This low pressure is responsible for a re-entry of flow in the freestream from the cavity. The flow leaving the cavity is the cause of the originating of a vortex which from now on shall be called the ”Slit Vortex”. This Slit Vortex (visualized in figure 6(a)) is convected downstream and influences the flow in the interaction area of support, slit and fuselage. The vortex creates a low pressure area on the fuselage and support, downstream of the maximum thickness of the support (as is seen in figure 6(b)). On the fuselage, the flow is sheared towards the gap leading to a very thin stagnation region (and even local backflow areas) very close to the gap. This is also visualized in figure 6(b).
On the support, the local pressure drop will lead to additional fluid leaving the cavity and joining the Slit Vortex. It is believed that the Slit Vortex keeps growing in strength and magnitude thereby increasing the turbulent kinetic energy in the interaction area. This can be seen in figures 7(a), 7(b), 7(c) and 7(d). In these figures, cross sections of the fuselage are shown that reveal the originating of the Slit Vortex. The influence of the Slit Vortex is also clearly seen as the ”downward bend” of streamlines on the support causing a local stagnation line as seen in figure 8.
(a) (b)
Figure 6. (a) A 3D image of the fuselage and support showing the existence of the Slit Vortex. Viewpoint is from the rear of the support looking upstream. The flow comes in from the left (b) The streamlines on the fuselage besides the gap showing the influence of the Slit Vortex. The effect of the vortex on the pressure is also discernible. Local backflow areas near the cavity can be recognized. Viewpoint is from the bottom looking on the fuselage near the entry gap of the support. The flow comes in from the left. Pressures are relative to a reference pressure.
wake structure even more. Another effect of this outflow is seen in the streamline pattern on the support side. At the trailing edge of the support close to the fuselage, local backflow is identified. On the fuselage, the flow separates leading to a recirculation area as shown in figure 9. This recirculation area closes fast, possibly because the cavity outflow aft of the support will energize the flow but also because the Slit Vortex will transport high momentum fluid into the recirculation area before merging with the base vortex. The closure of the recirculation area leads to a stagnation point. Aft of this stagnation point, a boundary layer will build up again. The fact that in the direct near-field of the support (close to the fuselage) the support wake is governed by a combination of base vortex shedding (not resolved in the steady calculations), the influence of the Slit Vortex and the outflow of the cavity gives the wake a unique structure. The exact spatial and temporal structure of the wake is unclear at the moment. It is however found by measurements that the fuselage is affected by the wake (in the steady calculations this has become an ”averaged wake”) in a steady way. This effect is seen in figure 9 by a divergence of the streamlines.
The flow behavior as extracted from these numerical results can be compared to the results of the experimental oil flow visualizations. A typical result from experiments is given in figure 10(a).
(a) (b)
(c) (d)
Figure 7. (a) The originating of the Slit Vortex: Stagnation in the slit at 40 % of the support chord (b) Exiting of
fluid from the cavity at 50 % of the support chord (c) The origin of the Slit Vortex at 60 % of the support chord (d) Development (growth) of the Slit Vortex at 90 % of the support chord. Pictures are cross sections of the fuselage and support. Viewing direction is upstream.
IV.B. Comparison to Pressure Measurements
During the windtunnel experiments, pressure measurements on the fuselage are carried out at multiple angles of attack and freestream velocities. The pressure orifices are positioned on the cylindrical part and the afterbody of the fuselage. On the cylindrical part of the fuselage, the orifices are placed in front of the support (1 line of orifices on the symmetry line of the model) and besides and aft of the support (3 lines of orifices at increasing distance from the slit). On the ogive shaped afterbody, 3 lines of orifices are machined at 0, 30 and 60◦
from the symmetry line of the model. Figure 11 gives an overview of the pressure orifices as placed on the model.
The pressure orifices with a diameter of 0.4 mm are connected to electronic pressure scanners with a range of 1, 5 and 10 P si. This implies a varying accuracy for the pressure orifices on the model. The comparison between the calculated (RaNS) and measured values of the pressure coefficients are given in figure 12. In the figure, the accuracy bandwidth of the measurements is also plotted.
Figure 8. Streamline curvature at the support due to the influence of the Slit Vortex. The viewpoint is from the side of the model. The flow comes in from the right.
Figure 9. The recirculation area on the fuselage and the influence of the support wake on the fuselage. The viewpoint is from the bottom of the model looking onto the fuselage. The flow comes in from the left. Pressures are relative to a reference pressure.
(a) (b)
(c) (d)
Figure 10. Results of experimental oil flow visualizations showing (a) The streamline pattern near the support leading edge on the fuselage (b) The streamline pattern at the fuselage and support side (c) The streamline pattern at the fuselage afterbody and support side/back (d) The streamline pattern at the fuselage afterbody.
0 5 10 15 20 25 30 35 40 −0.5 −0.4 −0.3 −0.2 −0.1 0 0.1 0.2 0.3 0.4
Pressure hole numbers
Pressure coefficient, − (a) 0 10 20 30 40 50 60 70 80 90 100 −0.15 −0.1 −0.05 0 0.05 0.1 0.15 0.2 0.25
Position of orifices at afterbody in % of afterbody length
Pressure coefficient, − (b) 0 10 20 30 40 50 60 70 80 90 100 −0.15 −0.1 −0.05 0 0.05 0.1 0.15 0.2 0.25
Position of orifices at afterbody in % of afterbody length
Pressure coefficient, − (c) 0 10 20 30 40 50 60 70 80 90 100 −0.15 −0.1 −0.05 0 0.05 0.1 0.15 0.2
Position of orifices at afterbody in % of afterbody length
Pressure coefficient, −
(d)
Figure 12. Comparison of measured (blue line. The dashed blue lines give the accuracy bandwidth of the measurements) and calculated (RaNS, red line) pressure distributions on the fuselage (a) A sequence of pressure points on the cylindrical section of the fuselage. The order of points plotted is in streamwise direction starting closest to the support and ending farthest from the support, (b), (c) and (d) A sequence of pressure points on the tail section of the fuselage. The order
of points plotted is in streamwise direction starting at 0, 30 and at last 60◦ from the symmetry line of the model
respectively.
with a range of 1 P si leading to an accuracy of 0.7 %. The probe is positioned close to the fuselage using a Taylor-Hobson scope with an accuracy of 0.02 mm. The boundary layer probe is positioned 53 mm in front of the support on the fuselage (closer to the support was not possible due to the probe geometry and the supposed interference between probe and support in that case). Boundary layer traverses are performed using the probe. Results are compared to the results of the calculations and shown in figure 13 (in the graph the boundary layer velocity V is non-dimensionalized with the freestream velocity outside the boundary layer V∞. The traversing distance from the wall, h, is non-dimensionalized by the 99 % height of the velocity
boundary layer δ99). Some experimental results seem a little wiggly. This might have to do with the angle
of incidence of the boundary layer probe and/or the imperfection in the geometry of the probe. Just in front of the support, the experimental boundary layer seems more susceptible to the adverse pressure gradient (the experimental result shows a less full velocity profile leading to a lower skin friction) than the numerical boundary layer is. Generally this might lead to flow separation in front of the support. This is however not recognized in the measurements and not predicted by the calculations.
pressure coefficient is somewhat larger than the measured one. This means that the base vortices at the back of the support are stronger than the calculations reveal. The first traverse ends with pressure orifice number 18. The traverses following hereafter are also at the front, side and back of the support but further removed from the support. This is clearly seen as the pressure peaks decline in magnitude and the effect of the recirculation area becomes less pronounced. Figures 12(b), (c) and (d) show the pressure distribution on the afterbody of the fuselage. Figure 12(b) shows that the pressure coefficient close to the support is relatively moderate. This is because the boundary layer is recovering from separation. Downstream the boundary layer recovery is noticeable in a decrease in pressure and more downstream the pressure will start to rise again due to the shape of the afterbody. Figures 12(c) and (d) show a similar behavior, although their values close to the support are affected by the recirculation area as shown by the negative values of the pressure coefficients. When numerical and experimental values are compared it can be seen that close to the support the calculated pressure coefficient is considerably lower than the measured one. This has to do with the fact that the calculated recirculation area is larger than is seen in the experimental results. At the afterbody (between 5 and 65 % of the afterbody length) the numerical results yield a higher value of the pressure coefficients than the experimental results. Apparently the numerical model fails to predict the support wake influence on the fuselage. As expected the error decreases when the distance to the support is increased. 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
Non−dimensional boundary layer velocity V/V∞, −
Non−dimensional boundary layer height h/
δ99
, −
Figure 13. Comparison of measured (blue *) and calculated (RaNS, red line) velocity boundary layers on the fuselage for a boundary layer traverse 53 mm in front of the support on the fuselage.
V.
Separate Contributions of Model Support Interference According to RaNS
In section II.B it is mentioned that a subdivision of the near-field model support interference into separate contributions seems unavoidable in order to systematically study the interference both quantitatively and qualitatively. In this section, these separate contributions will be studied and statements will be made regarding their qualitative and quantitative importance to the near-field model support interference. In order to do so, these effects are studied locally in the regions as given in section II.B. This is possible by comparing the results from the presently studied calculation to the results of a calculation where the model support, internal cavity and slit have not been discretized. The results will be discussed in the following sections.
V.A. The P-Effect
As stated in section II.B, the P-effect can be described as a pressure disturbance of the model support on the fuselage due to the proximity of the model support. The fuselage pressure distribution is contaminated by the presence of the support, mainly in regions A and B. An indication of this effect can be obtained by integration of the static pressure over the fuselage parts A and B for the case including the discretization of the internal cavity, slit and model support and the case excluding these. The integration then delivers the pressure effects in lift- and drag direction (dCL, dCD). Results of this exercise are given in table 1.
Table 1. The P-effect in regions A and B for an angle of attack and sideslip of 0◦ and a Mach number of 0.176
Region dCL % dCD %
A 54 99
B 46 1
Total 100 100
the support. In region B, the lift decreases. This is because of the projected underpressure of the support (due to the support shape) on the fuselage causing the local pressure on the fuselage to drop. For the drag coefficient, the P-effect is mainly determined by the contribution in region A because in region B, the fuselage normals have no component in streamwise direction (the angle of attack is 0◦
). In region A, the aforementioned pressure increase (caused by the presence of the support) will create an increase in drag (which is quite logical considering the orientation of the normals on the forebody). When these numbers are translated to a discrete magnitude in counts it will be seen that the P-effect in regions A and B has a moderate impact on the lift coefficient (order of magnitude = 10 counts). This effect is moderate because of the relieving effect of the slit reducing the pressure peaks on the fuselage. The disturbance of the drag coefficient in region A is in the order of 5 counts.
V.B. The C1-Effect
The C1-effect is described as a momentum exchange between the freestream and the fluid inside the cavity leading to disturbances in the values of the longitudinal and lateral coefficients of the fuselage. For this angle of attack, these values are evaluated with the following result: dCL= -0.1 count and dCD = 4.6 counts (0.2
of which are viscous). From these numbers it can be concluded that for this angle of attack, only the drag of the model is affected. As is to be expected, the flow in the cavity can hardly be called viscous. The intake of high momentum fluid is not governed by viscous processes (because the flow does not separate in front of the support where the momentum exchange is initiated). This would also mean that for a broad range of angles of attack and sideslip, much simpler and faster methods become available for calculating this effect. In addition, multiple Euler calculations on the same geometry are carried out in order to state something on the magnitude of this cavity effect. The results are given in figure 14.
−5 0 5 10 15 20 0 5 10 15 201 2 3 4 5
Angle of attack, deg Angle of sideslip, deg
Drag interference, counts
(a) −5 0 5 10 15 20 0 5 10 15 20 −1 −0.5 0 0.5
Angle of attack, deg Angle of sideslip, deg
Lift interference, counts
(b)
Figure 14. The C1-effect as calculated by an Euler code showing the disturbances in (a) Drag- and (b) Lift-direction.
V.C. The C2-Effect
The C2-effect is described as the effect of a very complicating flow pattern at the slit leading to the contam-ination of the region around the support. In order to study this effect, the viscous and inviscid (pressure) disturbances in region B where the Slit Vortex influences the flow are taken into consideration. In region B, the contribution of viscosity and pressure disturbances to the values of the lift- and drag coefficient are evaluated. The integrated values of the shear stresses and static pressure in this area are compared between the case where the fuselage, internal cavity, slit and model support are modeled and the case where only the fuselage is modeled (table 2).
Table 2. The C2-effect for region B for an angle of attack and sideslip of 0◦ and a Mach number of 0.176
Type of Disturbance dCL % dCD %
Inviscid 100 6
Viscous 0 94
Total 100 100
From table 2 it is seen that the lift interference in region B is determined by pressure disturbances (of magnitude O(10) counts). The viscous disturbance is found to be negligible. This has the important implication that the effect of the Slit Vortex is limited to a change in pressure distribution on the fuselage surface. For the drag of region B, the interference is governed by viscous disturbances. When the magnitude of this contribution is considered (O(1) count) is can be concluded that the C2-effect has no influence on the drag coefficient at this angle of attack and support placement.
V.D. The V-Effect
The V-effect was described as disturbances in front of, around and aft of the model support on the fuselage due to viscous phenomena. Disturbances like these are found by integration of the shear stresses in regions A, B, C and D and by integration of the pressure disturbances in regions C and D, and comparing these between the case where the fuselage, internal cavity, slit and model support are modeled and the case where only the fuselage is modeled. Table 3 gives the values of these disturbances.
Table 3. The V-effect for regions A, B, C and D for an angle of attack and sideslip of 0◦ and a Mach number of 0.176
Region and type of disturbance dCL % dCD %
A: ∆(shear stress) 71 42 B: ∆(shear stress) 0 45 C: ∆(shear stress) 14 5 C: ∆(pressure) 34 0 D: ∆(shear stress) 15 8 D: ∆(pressure) 66 100
Total ∆(shear stress) 100 100
Total ∆(pressure) 100 100
measurements have indicated (up to approximately 30 % of the afterbody length invariant of the angle of attack). In region C, the pressure contribution to the drag coefficient is negligible. This is logical considering the fact that this region has a normal perpendicular to the drag direction. In region D, the pressure increase (believed to be caused by the support wake) causes the local drag to decrease (understandable considering the afterbody normal orientation).
When the results of the Navier-Stokes calculation as presented in the last sections are summarized, some conclusions can be drawn for this configuration:
• The overall qualitative agreement between the calculation and experimental results is satisfying hence creating confidence in the quality of the calculations
• The value of the near-field support interference is mainly determined by a couple of contributions: – The P-effect
– The pressure disturbance of the C2-effect due to the presence of the Slit Vortex
– The pressure disturbance of the V-effect in the recirculation area and at the afterbody of the fuselage
VI.
RaNS vs Balance Measurements
What remains an important topic is how to calculate the total net value of the disturbance of the model support on the fuselage quantitatively. The calculation as described in this paper has provided with a qualitative description of the flowfield in the vicinity of the model support that complies with experimental data. Data regarding the separate contributions to the total near-field disturbance of the model support provide insight into the importance of certain disturbances (mainly quantitatively). But how well does a Navier-Stokes solver perform when it comes down to quantitatively calculating the support interference on for instance the lift- and drag coefficients? In order to answer this question, the values of the disturbances resulting from RaNS simulations are calculated and are shown in figure 15. In this figure, results of two Navier-Stokes calculations are seen, at 0 and 8◦
angle of attack (0◦
sideslip) at a Mach number of 0.176. The values are compared to the measured values of the external balance.
−2 0 2 4 6 8 10 12 14 16 −6 −4 −2 0 2 4 6 8
Angle of attack, deg
Disturbance in lift coefficient, counts
(a) −2 0 2 4 6 8 10 12 14 16 −15 −10 −5 0 5 10 15 20
Angle of attack, deg
Disturbance in drag coefficient, counts
(b)
Figure 15. Comparison of near-field support interference as measured by an external balance (blue line. The accuracy bandwidth is given by a dashed blue line) and calculated by a Navier-Stokes solver (red line) showing (a) Agreement between disturbances on the lift coefficient (b) Agreement between disturbances on the drag coefficient.
attack is increased this will certainly deliver an increase in lift and drag. For regions B and C, the opposite is true. The support disturbance will provide with net underpressures in these regions. When increasing the angle of attack, these underpressures will generate forces in the negative drag- and lift directions. On the afterbody (region D), overpressures will be generated. These overpressures manifest in regions with a very small curvature of the fuselage. This means that when the angle of attack is increased, positive contributions are generated for the increase in lift and drag. When the total picture of the measured drag interference (figure 15(b)) is inspected, it is seen that the trends are of declining type: The drag interference decreases with angle of attack. Considering the contributions as just mentioned, a couple of conclusions can be drawn from this:
• Pressure mismatches occur: The Navier-Stokes solver underestimates the net (negative) values of pressure disturbance ∆p in regions B and C and overestimates the net (positive) values of ∆p in region D (the delta values are gained by subtracting the pressure distribution of the configuration excluding the support from the configuration including the support)
• Viscous mismatches occur: Viscous stresses are underestimated by the Navier-Stokes solver
0 5 10 15 20 25 30 35 40 −0.5 −0.4 −0.3 −0.2 −0.1 0 0.1 0.2 0.3 0.4
Pressure hole numbers
∆ Pressure coefficient, − (a) 0 10 20 30 40 50 60 70 80 90 100 −0.04 −0.02 0 0.02 0.04 0.06 0.08 0.1 0.12
Position of orifices at afterbody in % of afterbody length
∆
Pressure coefficient, −
(b)
Figure 16. Comparison of pressure disturbances on the fuselage as measured by an external balance (blue line. The dashed blue line gives the measurement accuracy bandwidth) and calculated by a Navier-Stokes solver (red line) for (a) A sequence of pressure points on the cylindrical section of the fuselage. The order of points plotted is as in figure 12(a) (b) A sequence of pressure points on the tail section of the fuselage. The order of points plotted is in streamwise direction at 0◦ from the symmetry line of the model as in figure 12(b).
It is believed that the main reason for the mismatch is given by the first point. This believe is strengthened when inspecting figure 16. In figures 16(a) and 16(b) some aspects become clear:
• From figure 16(a) it is seen that indeed in region B the calculated pressure disturbances are generally underestimated (this is true except for pressure hole 14). This is also true for region C (pressure holes 16 and 17)
• On the afterbody of the fuselage (figure 16(b)) the calculated pressure disturbances are indeed generally too high
• When figure 16(a) is studied, it will be clear that the pressure peak in region A is underestimated by the Navier-Stokes solver. This means that the positive contributions to the lift and drag in this region are underestimated. Therefore (considering the trend of the drag coefficient as measured by the balance) underestimation of underpressures in regions B and C and overestimation in region D become even more likely
amplification factors are introduced that are applied on the disturbance effects resulting from the RaNS calculation, the recalculated net effect of the disturbances can be evaluated. The amplification factors can be estimated by comparing the numerical and experimental pressure distributions. This is merely an exercise in order to verify the statements that have just been made on the inability of the Navier-Stokes solver. By tuning the separate contributions using the knowledge on the calculation deficiencies, the result becomes as given in figure 17. In this figure it is clearly seen that when the inabilities of the Navier-Stokes solver have become clear and the separate disturbance contributions are tuned using this knowledge, the right trends and orders of magnitude of the near-field model support disturbances on the fuselage are calculated. In the figure it is assumed that the values of the disturbance effects in the regions A to D do not change with angle of attack and that thus the trends in the graph are mainly caused by the rotation of the fuselage tangential and normal with angle of attack. This seems a valid assumption for this range of angles of attack as the trends match closely. When the angle of attack would be further increased this assumption will finally become invalid. This is because the increased support bluntness will lead to increased values of the interference.
−5 0 5 10 15 −10 −8 −6 −4 −2 0 2 4 6 8 10
Angle of attack, deg
Disturbance in lift coefficient, counts
(a) −5 0 5 10 15 −15 −10 −5 0 5 10 15 20
Angle of attack, deg
Disturbance in drag coefficient, counts
(b)
Figure 17. Recalculated (red line) near-field interference of the support as compared to balance measurements (blue line. The dashed blue line gives the measurement accuracy bandwidth) for (a) The lift coefficient (b) The drag coefficient.
VII.
Conclusion
recirculation and the support wake influence. This is attributed to the complex physics determining the disturbance flowfield.
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