Thermodynamic Turbofan Performance of Rolls Royce′s Pearl 15 Engine(Dassault Falcon 10X, Bombardier Global 5500/6500) vs. Pearl 700(Gulfstream G700)

Both engines are built to generate 15,250 lbs f (67.8 kN) rated thrust (ISA, + 15), both fly at 0.925 M (in fact, 1,174 km/hr @ 51,000 ft, faster than the speed of sound at sea level), both have similar size and weight, power-to-weight ratios in the 5.4 - 6.0 range, both take-in an approximate 34-36 kg/s air-mass flow, have a fuel consumption of 223-233 kg/hr (cruise conditions), use approx. 167.3 - 174.9 kg/s air-mass flow and gargle up between 1,084.11 - 1,133.06 kg/hr (that′s 356.65 - 372.75 gph) at take-off conditions per engine. So what is it that makes these two engines so similar, yet so differently well suited for the unfathomable in quality, clockwork-like-precision aircraft they power ?

In order to maximize thrust over the whole sfc vs. Specific Thrust spectrum over which they operate, taking the speed of flight as a constant, all the range of efficiencies, OPR as a constant for their particular engines, BPR constant (1 : 4.8), mass-flow rates (both at take-off and cruise performance conditions constant(s)), fuel-air ratio varying between 0.0135 - 0.0270 (essentially constant), and h04/ha = 5.5, assuming adiabatic, isentropic flow conditions, and not taking the effect of moisture (kg. water / kg. air) into account, considering the psychrometry of the air negligible (for the purposes of this comparison) and assuming MTOWs of 76,304 kg (168,219.10 lbs) for the Dassault Falcon 10X and 50,870 kg (112,147.54 lbs) for the G700, we are left with two very important variables to be solved:

a. Firing Temperature at the entrance to the hp stage of the turbine, T03, (using reheat or liquid injection as possible thrust (N) augmentation techniques) and;

b. Finding the Optimum Fan Pressure Ratios (FPR) for the engine(s) being compared.

1. Effect of Temperature (s) at the Inlet to the HP Stage Turbine

Firing Temperature

(K) (F)

Dassault Falcon 10X 1,056 1,441

Gulfstream G700 1,256 1,800

Temperature at the inlet to the HP Stage Turbine, calculated with a fully choked nozzle, reheat being applied to the burning gas mixture as it passes through the engine core, and mixes-in with the back-stream of both a lean-rich mixture of spent fuel and unused excess air.

The Overall Cycle Efficiency for the Pearl 700 at the above temperature, is below 24 % for a compressor pressure ratio of 25:1, whereas for the Pearl 15 is around 50 % at a temperature of 783 C (1,441 F), for a 43:1 compression ratio. This has good and bad consequences for both engines. For the lower temperature of the Dassault Falcon 10X, this means materials of construction do not have to be so expensive, as lower-alloyed blades can cost less to manufacture and will in general last longer than any other materials used, no matter how good they are. The penalties for increasing life come with a heavy loss of cycle efficiency, though there is a caviate: a lower temperature means a lower environmental impact (SFC = 7%) because of reduced NOx emissions - Good news for the jet-setters that have to face-up to sharp-compliance regulations and ever-more stringent local/international environmental standards, and may be charged a penalty (in the form of exceeding a certain pollution-bubble) on the premises of how high their carbon footprint is on a yearly basis. So, the Pearl 15 (Dassault Falcon 10X′s powerplant) is very efficient at low compression ratios compared to the G700, (at those same operating OPRs), complying with both current CAEP/8 and CAEP/10 standards. Not so-distant-future Chinese, Russian, and Eastern Asian owners of these turbofan power plants, very probably won′t have to worry about these too much, specially if they fly within their own borders. But hopefully most West- European, Canadian and North American buyers with a mind set on the environment, with some conscience and common sense for the tiny-bit of green planet we still do have left, will give some serious thought to this matter before making their final decision to buy either plane.

2. Effect of Fan Pressure Ratio (FPR)

Fan Pressure Ratio (FPR)

(min) (max)

Dassault Falcon 10X 1.5667 1.6899

Gulfstream G700 1.5667 1.6899

All OEM′s are extremely sensitive about disclosing this pàrticular aspect of their creation in their design of a turbofan. Truth be told, IT IS a big issue, as it dictates the amount of total mass-flow rate of air going through the engine, which has a direct impact ultimately not only on the momentum thrust at take-off, but also on the limits of speed the aircraft can attain at fully steady-state flight performance conditions - based on the design of the engine′s nacelles, how streamlined they are and their ability to let air pass through - a function of the aspect ratio of the throat of the engine′s rim-diameter to the area occupied by the engine′s core, or by-pass ratio (BPR), where the ratios for both engines here are identical: 1: 4.8 - 6.5 (variable). This means that for every kg. of air passing through them, a maximum of 6.5 kg. go ¨around it¨, and mix at the exit cowl with the hot-thrust combustor gases and un-burnt excess air, augmenting the thrust. The fan of the engine is essentially another ¨low pressure compressor stage¨ (theoretically handling a much lower enthalpy change adiabatically (no-heat added)), or it can also be thought of as a propeller, within the entire engine casing itself.

The rule of gold here, is that it matters not so much how steep your total pressure changes are as a given volume of air compresses more and more through the compressor stages as a ¨block¨ mass-flow of air that enters the engine; what really matters is that the energy changes (of said ¨block¨mass-flow) are incremented in equal amounts through each of the stages, in other words, a steady pressure-rise, and an even velocity drop through the engine-core to the combustor.

In the case of the Pearl 15 and Pearl 700 this rise in pressure (due to the fan alone) is equivalent to 13.27 bars(g), or 451 ft H20, which has a counter-pressure produced by the engine nacelle (and bulk front area of) of 8.47 bars (g), or 283.65 ft H20, to give a final FPR of 13.27 /8.47 = 1.5668.

It is interesting to note that even though both engines look the same, and produce the same thrust, they are inequivocably different from each other.

For starters, the G700, having a slightly higher inlet turbine temperature, is compelled to use materials of better quality, higher alloyed steel, that can endure prolonged periods of afterburn, or high, long, continuous firing temperatures, that merit the fabrication of the three - spooled - geared compressor - combustor - turbine, as a whole monolithic block, so to speak, making the 3LP 10 STG HP compressor, 4LP 2 HP turbine, a highly robust engine - core, with all the difficulties of manufacturing a highly precise, zero tolerance for gaps unit, letting no air leak from stage-to-stage, and a very special Talon nozzle to accelerate the total air-flow as it exits through the back of the engine. In contrast, the Pearl 15 has less stages than the Pearl 700. The Dassault Falcon 10X′s engine architecture is as follows: it has a 1LP 6HP STG compressor, and 1HP 2LP turbine stages, making it a lighter engine, both guaranteeing a ¨smooth¨ enthalpy energy increase throughout the compression process, taking the Overall Performance Efficiency (OPE) higher for the whole engine, once the flow reaches the combustor region, where velocities have to be at a minimum, to ensure good laminar-flow mixing with the fuel, and subsequent stoichiometric mixing of the fuel -rich mixture with air.

Combustion inlet temperature depends on engine pressure ratio, speed and engine altitude, thus the Pearl 700 catches up in efficiency at this point, lowering sfc at a higher turbine inlet temperature (To3) than the Pearl 15, while operating at the same value (or higher) pressure ratios. It will also increase its propulsive thrust more than the Pearl 15 (during this initial climb phase) per smaller losses in the combustor, resulting from difussion, friction and momentum changes in the air-fuel moisture laden flow. The total pressure loss is expected in the range 2-8% of the static pressure.

3. Effects on the Efficiencies

The efficiencies of these engines will be reduced by an equal percentage, regarding the combustor losses. The result is an increased fuel consumption, and a lower power output, which affects the size and weight of the engine: (higher) specific thrust (lbs./(lbsf.hr)) or (kg./(N.hr)). Still, the Pearl 15 at performance conditions has an sfc of 0.02420 kg./(N.hr) as compared to the Pearl 700, with an sfc 0.02499 kg./(N.hr), (these values are estimated at 0.2376 lbs./(lbsf. hr) cruise conditions and 0.2453 lbs./(lbsf. hr) at take-off), giving approximate specific thrusts of 1,436.92 N.s./kg. and 898.95 N.s./kg. for these aircraft, respectively, both pairs of engines mounted on each plane. As a matter of fact, tests are still being carried out on the combustor of the Pearl 15, to see how its efficiency is affected by the massive pressure-gradient loss, since the peak gas temperature is limited by the average gas temperature. The profile factor, which is the ratio between the maximum exit temperature and the average exit temperature, pans-out for both engines at an efficiency of 23.96% (which for short - flights is acceptable enough, sfc not being the critical issue). For long-range flights, however, the OPR has to be augmented in order to increase this efficiency to almost 50 %, which lowers sfc correspondingly, but increases firing temperature at the HP inlet to the turbine, resulting in lower sfcs and correspondingly increased NOx emissions (due to the higher temperature).

Conclusions

Therefore, thrust at take-off is 75.32 kN for the Pearl 700, as compared to 76.73 kN, for the Pearl 15 (each engine, 14% greater than its rated power), providing a climb-velocity-to-cruise-height of 56.21 m/s for the heavier Dassault Falcon 10X vs. 58.74 m/s for the Gulfstream 700. Incidentally, the jet-exhaust velocity for the Pearl 700 is 430.46 m/s as opposed to the Pearl 15 at 402.77 m/s, giving a hot-thrust during cruise 6.87 % higher for the former (due to the upgrades in the state-of-the-art materials′ technology).

Unless the uniformity of the combustor′s outlet profile is ensured, to guarantee adequate nozzle life, a higher operating temperature will not do wonders. Therefore, the G700 has yet a clear advantage here over the Pearl 15 (due to the inconclusive experimental data on the combustor in this engine gathered at this early-stage of its mass development).

The average inlet temperature to the turbine affects fuel consumption (expected due to modeling to be 2.55 % lower for the G700 than for the DS Falcon 10X for the same range), at the expense of a reduced take-off propulsive thrust (N), as seen above, but because of the large combustor pressure-gradient and lower OPR, the Pearl 700 is expected to rapidly lose its gas-temperature and power advantage edge over the Pearl 15 as crusing altitude is reached.

Summary and Closing Remarks

The overall efficiency of the engines, both the Pearl 700 and Pearl 15, converge at an average value of 23.96 % for short-range flights, and 50% for long-haul flights.

However, for the Dassault Falcon 10X, the maximizing effects of a higher (more efficient, compression ratio) are mitigated by the expected steep outlet-gradient of combustor temperature increasing the losses during take-off, in the same measure as the sfc is decreased at performance conditions, which consequently gives it a higher Specific Thrust (lower propulsive thrust (N)) at cruise operating conditions compared to that of a Gulfstream 700. This loss in thrust is more due to changes in ambient temperature rather than pressure, as sfc has been shown to be dependent more on the former, and hence its change with altitude is not so marked as that of net thrust loss as the aircraft climbs.

For short legs of flight, the G700 maintains its fuel-consumption level, at 32.2 gph less than the Pearl 15, saving over US $ 161/hr of fuel-costs during operation. Direct Operating Costs (DOCs) for these aircraft are calculated at US $ 7,316 / hr for the G700 vs. US $ 9,512 / hr for the DS Falcon 10X (not including (or limited to) annual depreciation costs, insurance, un-scheduled overhauls and/or other unforseen costs on a 400 hr/yr basis).

Based on these preliminary numbers, sure in the knowledge that both of these splendid aircraft are well below the 2,200 F (1,204 C) threshold for generating serious NOx emissions, both being environmentally-friendly, it would be in the best interest of the owner, the users and ultimately the environment, the continued purchase of the G700, or in the near future, the DS Falcon 10X (available commercially in 2025).

However, it is unclear exactly how this new DS Falcon 10X will perform on short legs of flight, or if its promising uses for the military have yet been explored, having the advantage over the G700 of shorter TOFL @ MTOW and also a shorter LFL (Landing Field Length), similar to the Bombardier 5500 and Bombardier 6500 series long-range aircraft.

So, the final decision of which aircraft outperforms the other, is dependent on the buyer himself/herself, and what he/she will be using the power plant for, with what frequency they will be traveling and the level of satisfaction (productivity: ( range, cabin space and speed )) they expect the plane to fulfill for them.

written by Pedro Baldó

April 2021

ref: https://www.rolls-royce.com/products-and-services/civil-aerospace/business-aviation/pearl-15.aspx#section-overview

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