Category AIRCRAF DESIGN

An aircraft body is not smooth; located all over the body are probes, blisters, bumps, protrusions, surface-protection mats for steps, small ducts (e. g., for cooling), and exhausts (e. g., environmental control and cooling air) – these are unavoidable fea­tures. In addition, there are mismatches at subassembly joints – for example, steps, gaps, and waviness originating during manufacture and treated as discreet rough­ness. Pressurization also causes the fuselage-skin waviness (i. e., areas ballooning up).

In this book, excrescence drag is addressed separately as two types: [16] 2

Excrescence drag due to surface-roughness drag is accounted for by using 2 to 3% of component parasite drag as roughness drag ([1] and [7]). As indicated in dis­cussion after Equation 9.13, it is factored using 3% after computing all component parasite drag, as follows:

fcomp total — E°3( ff + + fn + fp + /othercomp}

The difficulty in understanding the physics of excrescence drag was summarized by Haines ([10]) in his review by stating “… one realises that the analysis of some of these early data seems somewhat confused, because three major factors controlling the level of drag were not immediately recognised as being separate effects.” These factors are as follows:

• how skin friction is affected by the position of the boundary-layer transition

• how surface roughness affects skin friction in a fully turbulent flow

• how geometric shape (nonplanar) affects skin friction

Haines’s study showed that a small but significant amount of excrescence drag results from manufacturing origin and was difficult to understand.

The design criteria for the nozzle-exit area sizing is such that at LRC, the exit-plane static pressure Pe equals the ambient pressure PTO (a perfectly expanded nozzle, Pe, = PTO) to eliminate any base drag. At higher throttle settings, when Pe > PTO, there still is no base drag. At lower settings – for example, idle rating – there is some base drag as a result of the nozzle-exit area being larger than required.

Boat-Tail Drag

The long-duct contour for closure (i. e., “boat-tail” shape) at the aft end is shallow enough to avoid separation, especially with the assistance of entrainment effects of

Spillage drag =

scale)

the exhaust plume. Hence, the boat-tail drag is kept low. At the idle throttle setting, considerable flow separation can occur and the magnitude of boat-tail drag would be higher, but it is still small compared to the nacelle drag.

For bookkeeping purposes and to avoid conflict with aircraft manufactur­ers, engine manufacturers generally include internal drag (e. g., ram, diffuser, and exhaust-pipe drag) in computing the net thrust of an engine. Therefore, this book only needs to estimate the parasite drag (i. e., external drag) of the nacelle. Intake – duct loss is considered engine-installation losses expressed as intake-recovery loss. Intake – and exhaust-duct losses are approximately 1 to 3% in engine thrust at LRC (throttle – and altitude-dependent). The net thrust of the turbofan, incorporating installation losses, is computed using the engine-manufacturer-supplied program and data. These manufacturers work in close liaison to develop the internal contour of the nacelle and intake. External nacelle-contour design and airframe integration remain the responsibility of the aircraft manufacturer.

The long-duct nacelle characteristic length, Lnac, is the length measured from the intake-highlight plane to the exit-area plane. The wetted area AWn, Ren, and basic CFn are estimated as for other components. The incremental parasite drag formulae for the nacelle are provided herein. The supervelocity effect around the nacelle-lip section is included in the intake-drag estimation; hence, it is not com­puted separately. Similarly, the pressure effect is included in the base/boat-tail drag estimation. These two items are addressed this way because of the special consideration of throttle dependency. Following are the relationships used to com­pute the nacelle drag coefficient ACon-

1. ACDn effects (same as the fuselage being axi-symmetric).

Wrapping:

2. Other incremental effects. Drag contributions made by the following effects are given in percentage of CFn. These are typical of the generic nacelle design:

(a) Intake drag at LRC – includes supervelocity effects « 40 to 60%

(higher BPR with higher percentage)

(b) Boat-tail/base drag (throttle-dependent) – includes pressure effects « 10 to 12% (higher value for smaller aircraft)

(c) Excrescence (nonmanufacturing type such as cooling-air intakes) « 20 to 25% (higher value for smaller aircraft)

3. Interference drag. A podded nacelle near the wing or body would have interfer­ence drag as follows (per nacelle). For a wing-mounted nacelle, the higher the overhang forward of the wing, the less would be the interference drag. Typical values of the interference drag by each pylon interacting with the wing or the body) are listed in Table 9.3.

4. Surface roughness (add later, « 3%.) A long overhang in front of the wing keeps the nacelle free from any interference effects. A short overhang has the highest interference. However, there is little variation of interference drag of a nacelle mounted on a different position at the aft fuselage. Much depends on the proximity of other bodies, such as the wing and empennage. If the nacelle is within one diameter, then interference drag may be increased by another

0. 5%. The center engine is close to the fuselage and with the V-tail, they have increased interference.

By totaling all the components, the flat-plate equivalent of the nacelle drag contribution is given by the following equation (omit the term ACF„_rough in Equa­tion 9.25 if it is accounted for at the end, as shown in Equation 9.27):

fn = (CFn + ACFn_wmp + ACFnJntake + ACfn_boattail

+ A-CFn – excres + ACFn-rough) X Awn (9.25)

Converting the nacelle contribution to CDpmin in terms of the aircraft wing area, it becomes:

[CDpmin]n = fn/SW (9.26)

In the last three decades, the nacelle drag has been reduced by approximately twice as much as what has been achieved in other aircraft components. This demon­strates the complexity of and unknowns associated with the flow field around nacelles. CFD is important in nacelle design and its integration with aircraft.

Center S – duct Center strai ght duct

nacelle of tri-jet nacelle of tri-jet

In this book, nacelle geometry is simplified to the axi-symmetric shape without loss of methodology.

The intake stream tube at cruise operates in a subcritical condition (see Section 10.8), which is complex and makes the intake-drag estimation difficult. There is spillage during the subcritical operation due to the stream tube being smaller than the cross-sectional area at the nacelle highlight diameter, where external flow turns around the lip creating suction (i. e., thrust). This can be considered precompression, ahead of the intake, when the intake velocity is slower compared to the free-stream velocity expressed in the fraction (Vintake/VTO). At (Vintake/VXJ) < 0.8, the excess air flow spills over the nacelle lip. The intake lip acts as the LE of a circular aerofoil. The subcritical air-flow diffusion ahead of the inlet results in preentry drag called addi­tive drag. The net effect results in spillage drag, as described herein. The spillage drag added to the friction drag at the lip results in the intake drag, which is a form of parasite drag. (For the military aircraft intake, see Section 9.17 and Chapter 10.)

• spillage drag = additive drag + lip suction (thrust sign changes to -ve)

• intake drag = spillage drag + friction drag at the lip (supervelocity effect)

Figure 9.6 shows intake-drag variations with the mass flow rate for both sub­sonic and supersonic (i. e., sharp LE) intake.

The nacelle requires different treatment, with the special consideration of throttle – dependent air flowing through as well as over it, like the fuselage. This section pro­vides the definitions and other considerations needed to estimate nacelle parasite drag (see [2], [9], and [21]). The nacelle is described in Section 10.8.

The throttle-dependent variable of the internal flow passing through the tur­bofan engine affects the external flow over the nacelle. The dominant changes in the flow field due to throttle dependency are around the nacelle at the lip and aft end. When the flow field around the nacelle is known, the parasite drag estimation method for the nacelle is the same as for the other components but must also con­sider the throttle-dependent effects.

Civil aircraft nacelles are typically pod-mounted. In this book, only the long duct is considered. Military aircraft engines are generally buried in the aircraft shell (i. e., fuselage). A podded nacelle may be thought of as a wrapped-around wing in an axi-symmetric shape like that of a fuselage. The nacelle section shows aerofoil­like sections in Figure 9.5; the important sources of nacelle drag are listed here (a short duct nacelle [see Figure 10.16] is similar except for the fan exhaust coming out at high speed over the exposed outer surface of the core nozzle, for which its skin friction must be considered):

Throttle-independent drag (external surface)

• skin friction

• wrapping effects of axi-symmetric body

• excrescence effects (includes nonmanufacturing types such as cooling ducts)

Throttle-dependent drag

• inlet drag (front end of the diffuser)

• nacelle base drag (zero for an engine operating at cruise settings and higher)

• boat-tail drag (curvature of the nozzle at the aft end of the nacelle)

Definitions and typical considerations for drag estimation associated with the flow field around an isolated long-duct podded nacelle (approximated to circular

cross-section) are shown in Figure 9.5. Although there is internal flow through the nacelle, the external geometry of the nacelle may be treated as a fuselage, except that there is a lip section similar to the LE of an aerofoil. The prevailing engine – throttle setting is maintained at a rating for LRC or HSC for the mission profile. The intake drag and the base drag/boat-tail drag are explained next.

The wing, empennage, pylon, and winglets are treated as lifting surfaces and use identical methodology to estimate their minimum parasite drag. It is similar to the fuselage methodology except that it does not have the wrapping effect. Here, the

Table 9.2. Typical CDn associated with sharp windshield type canopies

2-abreast-seating aircraft 0.1 sq. ft.

4-abreast-seating aircraft 0.2 sq. ft.

6-abreast-seating aircraft 0.3 sq. ft.

Adjust the values for the following variations: Kinked windshield (less sharp)

Smoothed (single-curvature) windshield Smoothed (double-curvature) windshield
interference drag with the joining body (e. g., for the wing, it is the fuselage) is taken into account bacause it is not included in the fuselage ff.

The methodology for the wing (denoted by the subscript w) is discussed in this section. The Re Rew is calculated first using the wing MAC as the characteristic length. Next, the exposed wing area is computed by subtracting the portion buried in the fuselage and then the wetted area, AWw, using the к factors for the t/c as in Section 9.7.2. Using the Rew, the basic CFwBASIC is obtained from the graph in Figure 9.19b for the flight Mach number. The incremental parasite drag formulae are as follows:

1. 3D effects [1].

(a) Supervelocity:

ACFw = CFw x K1 x (aerofoil t/c ratio)ave (9.15)

where K1 = 1.2 to 1.5 for the supercritical aerofoil and K1 = 1.6 to 2 for the conventional aerofoil

(b) Pressure:

/ 6 0.125

ACFw = CFw x 60 x (aerofoil t/c ratio)4ve x (9.16)

where the aspect ratio, AR > 2 (modified from [1]). The last term of this expression includes the effect of nonelliptical lift distribution.

2. Interference.

where K2 = 0.6 for high – and low-wing designs and CB is the root chord at the fuselage intersection. For the midwing, K2 = 1.2. This is valid for a t/c ratio up to 0.07. For a t/c ratio below 0.07, use the interference drag:

ACFw = 3to5% of CFw

The same relationships apply for the V-tail and H-tail. For pylon interference, use 10 to 12%. Interference drag is not included in the fuselage drag; rather, it is accounted for in the wing drag. (Pylon interference is both at aircraft side and with the nacelle.)

3. Other effects. (9.19)

Excrescence (i. e., nonmanufacturing such as control-surface gaps): Flap gaps: 4 to 5%

Slat gaps: 4 to 5%

Others: 4 to 5%

4. Surface roughness (to be added later).

The flat-plate equivalent of the wing-drag contribution is as follows (the subscripts are self-explanatory):

fw = (Cf w + ACFfwsupervel + ACFw_press + ACf w -inter + ACFw_other + ACFw-rough) x Awwi

which can be converted to CDpmin in terms of the aircraft wing area; that is:

[‘Cnpmin]w — fw/Sw (9.21)

(Note: Omit the term ACFwrough in Equation 9.20 if it is accounted for after comput­ing fs for all components, as shown in Equation 9.27).

The same procedure is used to compute the parasite drag of the empennage, pylons, and so forth, which are considered to be wing-like lifting surfaces.

fliftingsurface — [(CF + ^CFsupervel + ACF_press + ACf – inter + A-CF^other + ACF-rough), X Awlift^sur

CDpminliftingsurface — fliftingsurface/ Sw

Isolated aircraft components are worked on to estimate component parasite drag. The semi-empirical relations given here embed the necessary corrections required for 3D effects. Associated coefficients and indices are derived from actual flight – test data. (Wind-tunnel tests are conducted at a lower Re and therefore require correction to represent flight-tested results.) The influence of the related drivers is shown as drag increasing byt and drag decreasing by^. For example, an increase of the Re reduces the skin-friction coefficient and is shown as Re (ф).

9.8.1 Fuselage

The fuselage characteristic length, Lfus, is the length from the tip of the nose cone to the end of the tail cone. The wetted area, Awf (t), and fineness ratio (length/ diameter) (ф) of the fuselage are computed. Ensure that cutouts at the wing and

Ml і гагу Aircraft

area shaded

Bubble canopy – long length _|

Civil Aircraft

Figure 9.4. Canopy types for drag estimation empennage junctions are subtracted. Obtain the Ref (^). The corresponding basic CFf for the fuselage using Figures 9.19 and 9.20 is intended for the flat plate at the flight Mach number. Figure 9.19 is accurate and validated over time.

The semi-empirical formulation is required to correct the 2D skin friction drag for the 3D effects and other influencing parameters, as listed herein. These are incre­mental values shown by the symbol A. There are many incremental effects and it is easy to miss some of them.

coefficient CDn is based on the frontal cross-sectional area shown in the military type aircraft in Figure 9.4 (the front view of the raised canopy is shaded). The extent of the raised frontal area contributes to the extent of drag increment and the CDn accounts for the effects of canopy rise. CDn is then converted to ACFfcanopy = (A„ xCDn)/Awf, where Awf is the fuselage wetted area. The dominant types of a raised or bubble-type canopy and their associated CDn are summarized in Table 9.1.

(ii) Windshield-type canopy for larger aircraft. These canopies are typi­cally associated with payload-carrying commercial aircraft from a small Bizjet and larger. Flat panes lower the manufacturing cost but result in a kink at the double-curvature nose cone of the fuselage. A curved and smooth transparent windshield avoids the kink that would reduce drag at an additional cost. Smoother types have curved panes with a single or double curvature. Single-curvature panes come in smaller pieces, with a straight side and a curved side. Double-curvature panes are the most expensive and considerable attention is required during manufacturing to avoid distortion of vision. The values in square feet in Table 9.2 are used to obtain a sharp-edged windshield-type canopy drag.

(b) Body pressurization-fuselage surface waviness (use 5.5%), 5 to 6%

(c) Nonoptimum fuselage shape (interpolate the in-between values)

(i) Nose fineness ratio, Fcf (see Figure 4.17 and Table 4.5)

For Fcf < 1.5: 8%

For 1.5 < Fcf < 1.75: 6%

For Fcf > 1.75: 4%

For military aircraft type with high nose fineness: 3%

(ii) Fuselage closure – above Mach 0.6 (see Table 4.5)

Less than 10 deg: 0 11 to 12 deg closure: 1%

13 to 14 deg: 4%

(iii) Upsweep closure (see Section 3.21) use in conjunction with (iv)

No upsweep: 0 4 deg of upsweep: 2%

10 deg of upsweep: 8%

15 deg of upsweep: 15%

(interpolate in-between values)

(iv) Aft-end cross-sectional shape

Circular: 0 Shallow keel: 0 to 1%

Deep keel: 1 to 2%

(v) Rear-mounted door (with fuselage upsweep): 5 to 10%

(d) Cabin-pressurization leakage (if unknown, use higher value): 3 to 5%

(e) Excrescence (nonmanufacturing types such as windows)

(i) Windows and doors (use higher values for larger aircraft): 2 to 4%

(ii) Miscellaneous: 1%

(f) Wing fuselage belly fairing, if any: 1 to 5%

(use higher value if houses undercarriage)

(g) Undercarriage fairing – typically for high-wing aircraft (if any fairing): 2 to 6%

(based on fairing protrusion height from fuselage)

3. The interference drag increment with the wing and empennage is included in the calculation of lifting-surface drag and therefore is not duplicated when comput­ing the fuselage parasite drag. Totaling the CFf and ACFf from the wetted area AwF of the isolated fuselage, the flat-plate equivalent drag, ff (see Step 6 in Section 9.7.3), is estimated in square feet.

4. Surface roughness is 2 to 3%. These effects are from the manufacturing origin, discussed in Section 9.8.4. Because surface-roughness drag is the same percent­age for all components, it is convenient to total them after evaluating all com­ponents. In that case, the term ACFfrough is dropped from Equation 9.13 and it is accounted for as shown in Equation 9.27.

Total all the components of parasite drag to obtain CDpmin, as follows. It should include the excrescence-drag increment. Converted into the fuselage contribution to [CDpmin]f in terms of aircraft wing area, it becomes:

CFf = 1.03 x (basic CFf + J2ACFf)

ff = (CFf + ACFfwrap + ACFfsupervel + ACFfpress + ACFfother + ACFfrough) x Awf

[Copmin] f = ff / Sw (9.14)

See the worked-out examples.

In this book, the following seven steps are carried out to estimate the minimum parasite drag, CDpmn

Step 1: Dissect and isolate aircraft components such as the wing, empennage, fuselage, and nacelle. Determine the geometric parameters of the air­craft components such as the characteristic length and wetted areas.

Step 2: Compute the Re per foot at the LRC condition. Then, obtain the com­ponent Re by multiplying its characteristic length.

Step 3: Determine the basic 2D average skin-friction coefficient CFbasic, cor­responding to the Re for each component (see Figure 9.19b).

Step 4: Estimate the ACf as the increment due to 3D effects on each compo­nent.

Step 5: Estimate the interference drag of two adjacent components; avoid duplication of this effect.

Step 6: Add the results obtained in Steps 3, 4, and 5 to obtain the mini­mum parasite drag of a component in terms of flat-plate equivalent area (ft2 or m2); that is, CF = CF_2D + J2ACF for the component:

Cf)comp = (Aw’)comp CF, where (CDpmin)comp = (f)comp! Sw.

Step 7: Total all the component minimum parasite drags. Then, add other drags such as the trim and excrescence drags. Finally, add 3% drag due to surface-roughness effects. The aircraft minimum parasite drag is expressed in the coefficient form, CDpmin.

The semi-empirical formulation for each component is provided in the following subsections.

Computation of the wetted area, Aw, of the aircraft component is shown herein. Skin friction is generated on that part of the surface over which air flows, the so – called wetted area.

Lifting Surfaces

These are approximate to the flat surfaces, with the wetted area slightly more than twice the reference area due to some thickness. Care is needed in removing the areas at intersections, such as the wing area buried in the fuselage. A factor к is used to obtain the wetted area of lifting surfaces, as follows:

Aw = к x (reference area, S – the area buried in the body),

where к = 2.02 for t/c = 0.08%

= 2.04 for t/c = 0.12%

= 2.06 for t/c = 0.16%

The factor к may be interpolated linearly for other t/c ratios.

Fuselage

The fuselage is divided conveniently into sections – typically, for civil transport air­craft, into a constant cross-section mid-fuselage with varying cross-section front – and aft-fuselage closures. The constant cross-section mid-fuselage barrel has a wetted area of Awfmid = perimeter x length.

The forward- and aft-closure cones could be sectioned more finely, treating each thin section as a constant section “slice.” A military aircraft is unlikely to have a constant cross-section barrel, and its wetted area must be computed in this way. The wetted areas must be excluded where the wing and empennage join the fuselage or for any other considerations.

Nacelle

Only the external surface of the nacelle is considered the wetted area and it is com­puted in the same way as the fuselage, taking note of the pylon cutout area. (Internal drag within the intake duct is accounted for as installation effects in engine perfor­mance as a loss of thrust.)

The Re has the deciding role in determining the skin-friction coefficient, CF, of a component. First, the Re-per-unit-length speed and altitude is computed. Then, the characteristic lengths of each component [i. e., Re — (pTOLcompV(XJ)/дто] are deter­mined. The characteristic length L of each component is as follows:

axial length from the tip of the nose cone to the end of the tail cone (Lfus) the wing MAC

the MACs of the V-tail and the H-tail

axial length from the nacelle-highlight plane to the nozzle-exit plane (Lnac)

Figure 9.19 shows the basic 2D flat-plate skin-friction coefficient, CFbasic, of a fully turbulent flow for local and average values. For a partial laminar flow, the CFbasic correction is made using factor f1, given in Figure 9.20. It has been shown that the compressibility effect increases the boundary layer, thus reducing the local CF. However, in LRC until the Mcrit is reached, there is little sensitivity of the CF change with Mach number variations; therefore, the incompressible CF line (i. e., the Mach 0 line in Figure 9.19b) is used. At HSC at the Mcrit and above, the appropriate Mach line is used to account for the compressibility effect.

The methodology presented herein considers fully turbulent flow from the LE of all components. Here, no credit is taken for drag reduction due to possible lam­inar flow over a portion of the body and lifting surface. This is because it may not always be possible to keep the aircraft surfaces clear of contamination that would trigger turbulent flow. The certifying agencies recommend this conservative approach.

The basic CF changes with changes in the Re, which depends on speed and altitude of the aircraft. The chapter introduction in Section 9.2 explains that a sub­sonic aircraft CDpmin computed at LRC would cater to the full flight envelope during Phase 1 of a project.

The practiced method to compute CDpmin is first to dissect (i. e., isolate) the air­craft into discrete identifiable components, such as the fuselage, wing, V-tail, H-tail, nacelle, and other smaller geometries (e. g., winglets and ventral fins). The wetted
area and the Re of each component establishes skin friction associated with each component. The 2D flat-plate basic mean skin-friction coefficient, CFbasic, corre­sponding to the Re of the component, is determined from Figure 9.19b for the flight Mach number. Sections 3.5.1 and 9.7.1 explain the worked-out examples carried out in this book for fully turbulent flow, as shown in Figure 9.19.

The various ACf arising from the 3D effects (e. g., supervelocity) and wrapping effects of the components are added to the basic flat-plate CFbasic. Supervelocity effects result from the 3D nature (i. e., curvature) of aircraft-body geometry where, in the critical areas, the local velocity exceeds the free-stream velocity (hence, the term supervelocity). The axi-symmetric curvature of a body (e. g., fuselage) is per­ceived as a wrapping effect when the increased adverse pressure gradient increases the drag. The interference in the flow field is caused by the presence of two bod­ies in proximity (e. g., the fuselage and wing). The flow field of one body interferes with the flow field of the other body, causing more drag. Interference drag must be accounted for when considering the drag of adjacent bodies or components – it must not be duplicated while estimating the drag of the other body.

The design of an aircraft should be streamlined so that there is little separation over the entire body, thereby minimizing parasite drag obtained by taking the total CF (by adding various ACF, to CFbasic). Hereafter, the total CF will be known as the CF. Parasite drag is converted to its flat-plate equivalent expressed in f square feet. Although it can be easily converted into the SI system, in this book, the FPS system is used for comparision with the significant existing data that uses the FPS system. The flat-plate equivalent f is defined as:

fcomponent — (Aw X CF)component

where Aw is the wetted area (unit in ft2).

The minimum parasite drag CDpmin of an aircraft is obtained by totaling the con­tributing fs of all aircraft components with other sundries. Therefore, the minimum parasite drag of the aircraft is obtained by:

(CDpmin ) — (E fcomponent + sundries^ / SW — (Aw X CF)component/S^j (9.8)

The stepwise approach to compute CDpmin is described in the following three sub­sections.