Streamwise-body-force-model for rapid simulation combining internal and external flow fields

Cui Rong,Li Qiushi,*,Pan Tianyu,Zhang Jian

aNational Key Laboratory on Aero-Engines,Beihang University,Beijing 100083,China

bCollaborative Innovation Center of Advanced Aero-Engine,Beihang University,Beijing 100083,China

cDepartment of Engine Project,Aviation Industry Corporation of China,Beijing 100022,China

Streamwise-body-force-model for rapid simulation combining internal and external flow fields

Cui Ronga,b,Li Qiushia,b,*,Pan Tianyua,b,Zhang Jianc

aNational Key Laboratory on Aero-Engines,Beihang University,Beijing 100083,China

bCollaborative Innovation Center of Advanced Aero-Engine,Beihang University,Beijing 100083,China

cDepartment of Engine Project,Aviation Industry Corporation of China,Beijing 100022,China

A streamwise-body-force-model (SBFM) is developed and applied in the overall flow simulation for the distributed propulsion system,combining internal and external flow fields.In view of axial stage effects,fan or compressor effects could be simplified as body forces along the streamline.These body forces which are functions of local parameters could be added as source terms in Navier-Stokes equations to replace solid boundary conditions of blades and hubs.The validation of SBFM with uniform inlet and distortion inlet of compressors shows that pressure performance characteristics agree well with experimental data.A three-dimensional simulation of the integration configuration,via a blended wing body aircraft with a distributed propulsion system using the SBFM,has been completed.Lift coefficient and drag coefficient agree well with wind tunnel test results.Results show that to reach the goal of rapid integrated simulation combining internal and external flow fields,the computational fluid dynamics method based on SBFM is reasonable.

1.Introduction

Topical research projects dealing with airframe and engines are usually treated as separate,independent endeavors.However,aerodynamic interactions of airframe and engines have increasingly attracted more attention over recent years.On one hand,aerodynamic performance analyses of aircraft are generally based on a clean airframe without a propulsion system.In fact,engines operating under various conditions would affect the aerodynamic performance of the aircraft.On the other hand,the inlet flow of the engines would be affected by the airframe surface,which brings a greater work demand to the engines.As such,the engines would no longer work at the design point,so the effects on aircraft aerodynamic performance should thus be estimated again.Under these aerodynamic interactions of the airframe and engines,it is difficult to estimate aircraft performance by conventional separated research.Therefore,many integrated numerical simulations have attempted to analyze the effect of aerodynamic performance under special flight conditions.Focusing on the influence on the external flow field caused by the inlet with high angles of attack,Murmann1simulated the full aircraft geometry of F/A-18,while the internal structures of the engine were ignored.Bissinger et al.2has shown the detailed analysis of flow in the inlet duct by simulation of the fore body and inlet.To study the inlet/fan interaction,Webster et al.3simulated a single inlet and turbofan stage without the airframe.However,integrated simulations of airframe and engines combining external and internal flow fields are infrequent.

With further study of aerodynamic interactions between airframe and engines,integrated aircraft/engine design will be the future trend,4,5especially for the new blended wing body(BWB)aircraft which is integrated with a distributed propulsion system on the top of the aircraft.6,7In this integrated configuration,the embedded engines are used to ingest the boundary layer that develops on the airframe boundary layer ingestion(BLI),which reduce wetted areas,ram drag and noise and ultimately reach the green goal for the next generation of civil aircraft design.8–11The subject interactions of the airframe and engines are more intimate,so integrated aircraft/engine design is essential.However,to achieve integrated design,the issue of integrated simulations must be solved,which are limited by their appreciable computing needs and convergence difficulties.It is well known that the internal structures of propulsion systems are extremely complex,and therefore,the core parts of the engines are independent in most aero-thermodynamic studies.The simulation of every core part requires considerable computing resources,especially those involving rotating machinery.Complex structures of blades and periodic rotations make the unsteady 3D numerical simulations for a whole compressor a difficult task.The clean airframe simulation also necessitates considerable computing resources,and therefore,the calculating quantities required for simulations which combine airframe with engines would be enormous.Furthermore,the convergence of this simulation combining external and internal flow would likewise be a challenge.Thus,to avoid extremely large calculation efforts,some simplified simulation methods have been put forward to help aircraft aerodynamic performance analysis.Manticˇ-Lugo et al.12analyzed the effects of the BLI propulsion system in transonic flow by using a uniform back-pressure boundary condition to replace fan faces in a 2D simulation.However,the real static pressure at fan faces is difficult to estimate,and the actual performance of the engines may deviate from the real working conditions given the highly distortions.

Kim and Liou13,14used a body force model developed from Gong's model15,16to simulate the N3-X hybrid wing-body configuration.With the infinite number of blades assumption of compressors,the bladeforces could be modeled as normal and tangential forces to the local flow.15Adding the body force terms as source terms in aerodynamic equations,the turning and loss effects of the fan blades could be simulated,which achieved the integrated simulations.This approach was more accurate than the boundary condition method,while the procedure for generating the body force and the geometry generation of the mail-slot nacelle were comparatively complicated.For the integrated aircraft/engine design,optimization processes need iterative computations,which would likely induce a protracted design period as a result.Therefore,this subject approach was useful for prediction of aircraft performance but could not be widely used for the purpose of integrated aircraft/engine design.

To complete the rapid simulation combining internal and external flow fields,a further simplified yet reasonable body force model is presented via this research endeavor:streamwise-body-force-model (SBFM).The body forces are simplified to 1D terms paralleling of the streamline,and can be extracted more conveniently from the experimental data or CFD results.This new method(i.e.,using the SBFM to simplify the simulation of compressors)could achieve the desired rapid integrated simulation,which combines the external and internal flow fields of the aircraft.Therefore,the aircraft aerodynamic performance could be estimated,and the aerodynamic interactions of airframe and engines could be assessed with this method.Moreover,this method could conserve appreciable computing resources;consequently it would be a fundamental research tool for integrated aircraft/engine designs.As such,the required elapsed period for optimal design could be greatly reduced.

Per the notions and assertions expressed above,the remaining balance of this research endeavor is hence organized as follows:Section 2 explains the derivation process of SBFM;Section 3 presents validation of this model in a low speed compressor and a transonic compressor;Section 4 provides simulation results for a BWB configuration by using the SBFM and the n comparing these results with data obtained from wind tunnel experiments;Section 5 presents a summary and overall conclusion drawn from the acquired data.

2.Streamwise-body-force-model

2.1.Physical basis

Work done by the fans/compressors on flow increases the total pressure and total temperature.A simple axial stage is shown in Fig.1,where c is the absolute velocity of flow,w is the relative velocity to rotor of flow and u is the tangential velocity of rotor.It is assumed that fluid flows into a fan or compressor along an axial direction,x-axis,and the employed physical basis is that rotors change flow direction while stators revert it back to axial,which ultimately means that the circumferential component of velocity is offset.In view of comprehensive effects,the fan or compressor stage could be simplified as a body force along the streamline.Thus,the compressor is simplified as a flow pipe,and the following assumptions are presented:

Fig.1 Schematic of an axial stage.

(1)The flow pipe could be divided into infinite flow pipes in parallel,as shown in Fig.2.Each pipe would match different mass flow rates when the inlet flow is not uniform.

(2)For every pipe,a division into several microcompressors can be instituted.The total pressure and total temperature of the flow would be changed through these micro-compressors.

Fig.2 depicts such a simplified subject case.The divided compressor could be modeled in terms of body force,and the n could likewise be added as source terms in Navier-Stokes equations and modified with local variables.

2.2.Performance of micro-compressor

Each micro-compressor could exhibit a different performance,which affects the pressure distribution along the axial direction.The simplest situation,assumed for this research effort,is that the micro-compressors are uniform.Since the microcompressors in series should match the original compressor characteristics,the total pressure ratioand adiabatic efficiencyof each compressor could be expressed as

Fig.2 Process of simplification of fan/compressor.

where π*and η*are the total pressure ratio and adiabatic efficiency of the original compressor,respectively,k is the specific heat ratio and N the number of micro-compressors in a pipe.

2.3.Aerodynamic equations

The infinite uniform compressors can be symbolically compared to infinite element control volumes.Fluid flows through control volumes and changes the aerodynamic parameters.The forces of a control volume could be assumed as two separate constituents:one F increases the pressure of fluid along the flow direction,while the other f brings friction losses in the direction opposite to flow.The direction of resultant force Φ is still along the streamline.

Assuming the momentum equation on x-axis,17

where Φxis the x-axis component of body force,p is the pressure,ρ is the density,τ is the shear stress,Vxand Vyare the xaxis and y-axis velocity components.

Fluid could be steady and inviscid,which flows into the compressor along the axial direction and would likewise not be deflected obviously in the body force zone.Thus,the momentum equation on x direction could be simplified as

The dissipative term fis defined as

where h*is the stagnation enthalpy per unit mass.

The energy equation17is expressed as follows:

Simplify the energy equation according to the assumptions of the momentum equation,and the work of the resultant force could be represented as

where

density flow and defined as

q(Ma2)could be expressed as

where

where cpis the specific heat at constant pressure.

At this point,the SBFM is expressed as the functions of local parameters.

3.Model validation

In general,compressors are designed with uniform inlet boundary conditions.However,the engines installed on aircraft would not exhibit uniform inlet flow in real flight conditions,so compressors would not be operating in their design states during such periods.The model validation for this research endeavor thus has two steps:(A)validating the SBFM in the compressor with uniform inlet flow under normal conditions and(B)applying the model in the compressor with a distorted inlet condition to verify applicability.

3.1.Uniform inlet flow

A low speed axial compressor18,19and a transonic axial compressor20,21were studied.According to the casing diameter,the 3D pipeline model is built with an independently verified grid.Extracted from the experimental compressor performance maps,SBFM is expressed as functions of local parameters and added into the partial region to replace the blades and hub for the CFD.Reynolds-averaged Navier-Stokes equations are solved with a one equation Spalart-Allmaras (S-A) turbulence model.Here,the finite-volume implicit method with the second-order Roe flux-difference splitting upwindbiased formulation is used to compute the cell-face flux.The uniform pressure inlet boundary condition is set,with specified total pressure,total temperature and velocity direction.The outlet boundary condition is set as a pressure outlet and the casing is a no Navier-Stokes slip wall.

Compressor performance maps could be drawn by reading inlet and outlet data of CFD results.Fig.3 shows the dimensionless total pressure rise for different flow coefficients of the low speed compressor with the comparison between simulation using SBFM and experimental data.19

Fig.4 shows the total pressure ratio of the transonic compressor.For the low speed compressor,CFD results agree with the experimental data very well.For the transonic compressor,the overall curve of SBFM shifts to the left,compared with experimental curve.21The reason for this deviation may be that SBFM is based on the inviscid assumption,with the real viscous effect being contained in the dissipative term f.However,SBFM is added into the viscous RANS equations,which ultimately means that the viscous effect is double counted.The transonic compressor with high Mach number is influenced more strongly by viscidity,which could reduce the mass flow rate slightly,thus resulting in the performance map shifting to the left.Although error is inevitable in this highly simplified model,the performance maps can describe the performance of the compressor via trend.Thus,SBFM can be used in a proper accuracy range.

3.2.Distortion inlet flow

The disturbances from the external flow field will form a distortion inlet for the compressors,especially for embedded engines with BLI effect on BWB configuration.The turboelectric distributed propulsion of N3-X,proposed as a candidate to meet the N+3 goals,22is on the top of the airframe.The airframe boundary layer could form a fixed total pressure distortion in front of the fans.Fig.5 shows the aerodynamic interactions of the airframe and engines of these integrated configurations.To be used in the fluid field combining internal and external flow,the SBFM should be verified under a distortion inlet condition.

A low speed axial compressor19is studied to validate the SBFM with the aforementioned inlet distortion case.This compressor is composed of 4 IGV,19 rotor blades,and 13 stator vanes.The casing diameter is 450 mm,with a hub/casing ratio of 0.75.The schematic layout of the test rig is illustrated in Fig.6.

Fig.3 Flow coefficient vs total pressure rise coefficient of low speed compressor.19

Fig.4 Total pressure ratio of transonic compressor.

Fig.5 Section view of integrated configuration.

The inlet and outlet total pressure is measured by the total pressure comb at section II-II and section III-III.With a flat baffle of 30%area blockage,a pipeline model(Fig.7)is built with an independently verified grid.The blades and hub are replaced by the body force zone.The numerical model and boundary conditions,however,refer to the above case.The details of the test rig are provided in Ref.19.

Fig.8 shows the comparison between CFD results and experimental data with the distortion baffle,as well as the comparison with uniform inlet flow.As shown,under the distortion inlet condition,the simulation using SBFM generally agrees well with the experimental results.In some conditions,however,total pressure rise is slightly lower than the experimental value.Due to the relatively strong effect of disturbance via the baffle for the numerical simulation,fluid in the distortion field cannot flow into the compressor along the axial direction,even with slight separation near the wall.The SBFM is smaller than the real force at hand,which results in an overall lower total pressure than that of experimental value.The maximum error is 3.4%near the stall point,which is still within the acceptable error range.The SBFM can be successfully implemented within a proper accuracy range via the use of distortion inlet.

Fig.7 Mesh of SBFM applied in a low speed compressor with distortion inlet.

Fig.8 Flow coefficient vs total pressure rise coefficient of low speed compressor under uniform and distortion inlet conditions.

4.Numerical simulation combining internal and external flow

4.1.Study object

Fig.6 Schematic layout of test rig.

Fig.9 Scaled model in wind tunnel test.

The SBFM,which has been verified in the internal flow field,could be added into aircraft flow fields to reach the goal of integrated simulation.The experimental data of the integrated configurations are,however,not currently available in open literature.Thus,in order to verify this method,a scaled BWB aircraft model was chosen by the research team.Fig.9 shows the wind tunnel test facility for this scaled model made of alloy.A suction rake is set on the upper surface of the aircraft to replace the real engines and likewise simulate the effect of BLI,which is connected to an ejector device by a pipeline to adjust the suction mass flow rate.The airframe is relatively thin because of the layout of the BWB,and the propulsion system is arranged at the rear airframe.An abdominal support was,therefore,adopted in lieu of a conventional tail support to minimize disturbance effects on the back airframe flow field.This simulation thus depicted an integrated configuration based on the SBFM and associated results were compared with wind tunnel test results.

4.2.CFD model

According to the scaled model in the wind tunnel test,a 3D CFD model is built(Fig.10).The box-shaped zone corresponds to the suction rake to simulate the propulsion system,wherein the SBFM will befilled between the two faces.Focusing on the no Navier-Stokes sideslip flight of this configuration,which means that the flow field issymmetrical,numerical simulations are completed on the half model to save computational resources.

Fig.10 3D CFD model.

Reynolds average Navier-Stokes (RANS) with a one equation S-A turbulence model is solved with a finite-volume implicitly coupled solver with double precision.Because of this complex structure,the computational mesh combing the unstructured tetrahedral grids and structured hexahedral grids are generated with extensive consideration of accuracy and computational resources.Propulsion internal fields are simplified,so hexahedral grids are resultantly generated.The structure of the airframe afterbody containing tails and external fields of the propulsion system is complex,so tetrahedral grids are generated in this field with mesh refinements near the wall.C-H topology is applied to the grid of the entire external flow field.The far-field boundary is defined as 40 times the mean aerodynamic chord away from the aircraft surface.A local mesh refinement approach is used near the wall to improve accuracy.A pressurefar-field boundary condition is used,and the aircraft and propulsion surfaces are no Navier-Stokes slip adiabatic smooth walls.The lift coefficient CLand drag coefficient CDare defined asandwhere L is the lift,D is the drag,ρ0and V0are the density and velocity of the free-stream,respectively,and Srefis the reference area of the integrated configuration.

4.3.Results and discussions

Table 1 provides the wind tunnel test and far-field simulation conditions of the integrated configuration.Minis the suction mass flow rate in wind tunnel test,which could be adjusted by ejector device.Minis also the propulsion inlet mass flow rate in simulation affected by the SBFM.With an Min=0.223 kg/s,the wind tunnel test and flow simulation are completed via angles of attack.

Fig.11 provides lift coefficients CLas the y vary with angle of attack α.The results of CFD based on the SBFM agree well with the wind tunnel test results.When α ≤ 6°,CLlinearly increases with the increase of α.Beyond 6°,the slope of CLis reduced,which is more obvious in the numerical simulation.At αgt;10°,CLlinearly increases with α again,but with the similarly smaller slope.Analysis of numerical simulation results at α =10°indicates that the flow separation has occurred on the airplane surface,and furthermore,the numerical results are less than the test results.The possible rationale for this is that when α gt;10°,the flow separates from the surface of the blended segment,which would in turn flutter the model slightly.Therefore,the test results deviate from the real results due to the increased flexible error of the scaled model and the increased measuring error of balance.

Fig.12 gives the drag coefficients CDas the y vary with angle of attack α.The simulation results agree with the wind tunnel test results in trend.When α ≤ 4°,CDpresents no obvious significant change.When α gt;4°,however,CDrapidly increases with the increase of α.The simulation results being slightly higher than the experimental data are likely due to support interference factors.

Table 1 Wind tunnel test and far-field simulation conditions.

Fig.11 Variation of CLof scaled BWB aircraft model with different α.

Fig.12 Variation of CDof scaled BWB aircraft model with different α.

Despite these deviations,the numerical simulation results agree with the wind tunnel test results for the entire trend.Therefore,the CFD method based on SBFM for reaching the goal of integrated simulation is reasonable.

This research endeavor has also attempted to use uniformback-pressure boundary conditions to replace the propulsion system inlet faces,as well as mass-flow-inlet boundary conditions to replace outlet faces.The CFD model is the same as the method using SBFM except that there is no additional fluid in the propulsion internal field.The quantity of removed grids in the propulsion internal field is so small that these two methods virtually have almost the same quantity of grids.However,the boundary condition method seems to be more challenging for attainment of stable results.The possible reason for this is that the source terms are more stable than the boundary conditions themselves within the computations.Moreover,the boundary conditions could not exclusively be set to correct values rapidly enough,and thus several iterations are needed to match the real mass flow rates at the inlet and outlet faces of the propulsion system.For a normal PC,with a CPU clock speed of 3.4 GHz and a RAM of 8.00 GB,the method using SBFM can attain the convergence solution in 5 h,which could save more than 5 times the number of hours in comparison to utilizing the boundary conditions method.

For an integrated simulation of the airframe and engines,the static pressure of the inlet face of the propulsion system is not uniform in the real flow.The boundary condition method should estimate the average pressure at the inlet face;however,the pressure is affected both by the engines inside and the airframe outside.The distortion from the airframe boundary layer will change the performance of the engines,while such changes to the mass flow rate will affect the external flow field.The boundary condition method was not able to solve this problem,while the method based on the SBFM is indeed able to consider the aerodynamic interactions of airframe and engines.

5.Conclusions

In this study,a model for simplifying numerical simulation called SBFM has been developed for rapid simulation combining internal and external flow.From basic conservation equations and assumptions,the body force produced by a fan/compressor could be a function of local parameters,such as Ma and p*.From comparisons with experimental results,the following conclusions can be drawn:

(1)SBFM would simplify fan or compressor effects as body forces along the streamline.This model reflects the essence of the work done by the fan or compressor,which increases the total pressure and total temperature of the passed flow.

(2)SBFM could be used in the simulation of a transonic compressor with partial supersonic flow.For the inlet distortion formed by the airframe boundary layer,SBFM could still simulate the performance of compressors by ingesting part of the low energy fluid.The method using SBFM could simulate the aerodynamic interactions of airframe and engines in the integrated simulation.

(3)The method using SBFM for integrated simulation is efficient and high-fidelity,which would contribute to revolutionary advances in future integrated aircraft/engine designs,as well as inverse problem solutions.

Acknowledgements

This work was supported by the National Natural Science Foundation of China(No.51176005).We are very grateful to Gong Yifang for valuable suggestions.We also thank Zhang Shuguang and Wu Jianghao in Beihang University for the wind tunnel test,as well as AVIC Aerodynamics Research Institute.The authors are also thankful to Yang Dong,Lyu Yongzhao and Lu Hanan for valuable discussions.

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Cui Rongis a Ph.D.student at School of Energy and Power Engineering,Beihang University.She received her B.S.degreefrom the same university in 2006.Her main research interest is integrated simulations of airframe and engine.

Li Qiushiis a professor and Ph.D.supervisor at School of Energy and Power Engineering,Beihang University.He received the Ph.D.degree from the same university in 2000.His current research interests are flow instability and compressor aerodynamics.

7 September 2015;revised 22 March 2016;accepted 8 April 2016

Available online 27 August 2016

Aircraft;

Blended wing body;

Boundary layer ingestion;

Distributed propulsion system;

Integrated simulations;

Streamwise-body-forcemodel

©2016 Chinese Society of Aeronautics and Astronautics.Production and hosting by Elsevier Ltd.This is an open access article under the CC BY-NC-ND license(http://creativecommons.org/licenses/by-nc-nd/4.0/).

*Corresponding author at:National Key Laboratory on Aero-Engines,Beihang University,Beijing 100083,China.

E-mail address:liqs@buaa.edu.cn(Q.Li).

Peer review under responsibility of Editorial Committee of CJA.