An LES Turbulent Inflow Generator using A Recycling and Rescaling Method
 1.9k Downloads
 4 Citations
Abstract
The present paper describes a recycling and rescaling method for generating turbulent inflow conditions for Large Eddy Simulation. The method is first validated by simulating a turbulent boundary layer and a turbulent mixing layer. It is demonstrated that, with input specification of mean velocities and turbulence rms levels (normal stresses) only, it can produce realistic and selfconsistent turbulence structures. Comparison of shear stress and integral length scale indicates the success of the method in generating turbulent 1point and 2point correlations not specified in the input data. With the turbulent inlet conditions generated by this method, the growth rate of the turbulent boundary/mixing layer is properly predicted. Furthermore, the method can be used for the more complex inlet boundary flow types commonly found in industrial applications, which is demonstrated by generating nonequilibrium turbulent inflow and spanwise inhomogeneous inflow. As a final illustration of the benefits brought by this approach, a dropletladen mixing layer is simulated. The dispersion of droplets in the nearfield immediately downstream of the splitter plate trailing edge where the turbulent mixing layer begins is accurately reproduced due to the realistic turbulent structures captured by the recycling/rescaling method.
Keywords
Turbulent inflow generator Recycling Rescaling Turbulent mixing layer Droplet dispersion1 Introduction
Many engineering applications require accurate prediction of turbulent mixing rates. One important example is the mixing and combustion of fuel and air in gasturbine or IC engines. Fuel and air are often introduced separately and rapidly mixed and burnt in combustion zones. Whether the fuel is in gaseous or liquid (droplet) form it is important to capture the rate of turbulent mixing right from the point where fuel and air first come into contact, particularly when ignition and flame stabilisation performance are of interest. Whilst Large Eddy Simulation (LES) is now widely regarded as a better approach for prediction of turbulent mixing in complex flows than conventional RANS turbulence modelling, this requirement for high accuracy right from the origin of the mixing region simulation is a particularly challenging task for LES, where the optimum approach to inlet boundary condition treatment is still under development.
It has been realised for some time that the quality of specification of LES inlet conditions can exert a significant influence on the simulation accuracy, especially in the region close to the inlet boundary, although this influence can also persist over large downstream distances. Tyacke and Tucker [33], for example, have emphasised the importance of a generally applicable inflow generation method for the complex flows found in turbomachines. Many other authors have observed how inlet conditions affect the predicted flow development, for example Lund et al. [19] for boundary layers, Xiao et al. [38, 39, 40] for liquid jet primary breakup, and McMullan et al. [22] for free shear layers. Reviews of the various approaches suggested for specification/generation of LES inlet conditions can be found in BabaAhmadi and Tabor [4], Tabor and BabaAhmadi [30] and most recently by Wu [37]; in all of these studies great emphasis has been placed on the ability of the proposed method to shorten the adjustment length i.e. the distance downstream of the inlet boundary where the specified inlet unsteady fluctuations adjust to become completely consistently correlated.
In general, two approaches have been followed: (i) synthetic methods, where spatially and temporally correlated unsteady fluctuations, generated in a variety of ways, are superimposed on an inlet mean velocity field, and (ii) recycling/rescaling methods, where a separate (auxiliary) LES simulation is performed, the unsteady velocity field extracted at some selected plane in the auxiliary domain, rescaled, and then imposed at the inlet boundary of the auxiliary domain; the inlet boundary condition for the actual (main) simulation domain is transferred from a selected location within the auxiliary domain to the main simulation inlet boundary. For correct reproduction of the flow development in the immediate nearfield of the main simulation inlet boundary, it is necessary to specify realistic timeseries at the LES inlet boundary (i.e. correctly correlated and an accurate representation of the local flow conditions for both timemean velocity and turbulent fluctuations).
Among the synthetic methods, the most straightforward is to superimpose white noise on an assumed or known mean velocity field (e.g. from experimental measurements or a RANS simulation). However, the uncorrelated nature of white noise means the generated turbulence lacks largescale energy containing structures. Such pseudo turbulence is dissipated rapidly downstream of the inflow plane, and a adjustment region of considerable length is then needed to recover realistic and selfconsistent turbulence structures. Several authors have suggested methods whereby some turbulence information is provided at the inlet plane and used to generate a more detailed and physically realistic data set of unsteady inlet velocity conditions. Lee et al. [17] used an inverse Fourier transform of an assumed energy spectrum to reconstruct turbulent fluctuations, but the lack of phase information of real eddies proved problematic. Batten [5] suggested generating turbulent fluctuations from a summation of sine and cosine functions with random phases and amplitudes. Keating et al. [13] applied this method in a turbulent planechannel flow, but still observed very slow development of turbulence structures until they also adopted the controlled forcing method of SpilleKohoff [29]. Jarrin et al. [10] generated synthetic turbulence by directly prescribing coherent modes; this produced the correct friction factor in a channel flow, but still required a length of 6 channel heights to achieve this. Kempf et al. [14] proposed a method that converts white noise into a signal featuring the required lengthscale through a diffusion process. Finally, what has developed into perhaps the most popular approach of this type is the technique based on generation of a digital filter whose coefficients are adjusted to fit specified 1st and 2nd moment onepoint statistics, together with an assumed length scale and a Gaussian 2point correlation function  Klein et al. [15], di Mare et al. [20], Veloudis et al. [35].
All of the above synthetic turbulence generation approaches have two drawbacks. Firstly, the adjustment region problem mentioned above is always present to some extent. Lund et al. [19] found that a development region of some 50 boundary layer thicknesses was required for a wall boundary layer; Le et al. [16] observed that their method required about 10 step heights for attainment of physically consistent turbulence characteristics in a backwardfacing step flow. Secondly, most of the more advanced methods demand an input of turbulence information that is only rarely available, for example turbulence length scales or correlation shapes.
These problems are avoided by methods based on the recycling technique. This approach was first adopted for fullydeveloped duct flows, where periodic boundary conditions (a form of spatial recycling) between inlet and outlet may be used. By applying a carefully designed coordinate transform, Spalart [27] was able to use the recycling approach for DNS of a spatially developing boundary layer. In the transformed frame the velocity field is approximately homogeneous in the main flow direction so periodic conditions can be applied. However, during the coordinate transformation, some extra complex terms are added to the NavierStokes equations to account for the inhomogeneity in the streamwise direction. Furthermore, the streamwise gradients of the mean velocity included in these terms need to be specified explicitly. Therefore, Spalart’s method is complex to program.
Lund et al. [19] produced a simplified version of Spalart’s method requiring no coordinate frame transformation. During the LES solution, an instantaneous velocity field was extracted from a plane near the solution domain exit, rescaled according to selfsimilarity laws for boundary layers (e.g. mean flow scaled following the law of the wall/defect law in the inner/outer regions respectively, fluctuations rescaled using local friction velocities) and then recycled upstream to form the inflow conditions at solution domain inlet. This method is substantially simpler, but is, however, still only applicable to boundary layertype flows because of the particular rescaling concepts adopted. Lund et al. [19] implemented their method in a separate (precursor) LES calculation and imported the eventual inlet conditions for a main calculation from this. Mayor et al. [21] applied the same method, but realised it could be implemented by merging the inflow generation procedure with the main simulation. However, some aspects of Lund et al.’s method can make it difficult to implement [11]. Improved variants of Lund et al.’s approach have continued to be developed, modifying problems identified in both the rescaling and recycling elements, although to date still constructed primarily with spatially developing boundary layers in mind. For example, Liu and Pletcher [18] addressed the problem that the rescaling operation is based on the similarity laws of the boundary layer and, if the downstream data at the recycling plane have not yet reached their equilibrium state, the similarity laws do not strictly apply and incorrect data are recycled, leading to a longer adjustment length and startup transient. A dynamic procedure was proposed where the recycling plane was initially placed close to the inlet plane, and only moved downstream gradually. An alternative dynamic approach has been suggested by Araya et al. [2] using 3 planes (inlet, test and recycling) rather than two and adopting modified scaling laws. Both of these ideas shorten the adjustment length. A second problem with the recycling/rescaling procedure is that a recycling process between two spatially separate planes will inevitably introduce a nonphysical spatial/temporal correlation into the data generated, as demonstrated by Nikitin [24]. Spalart et al. [28], Jewkes et al. [11], and Morgan et al. [23] have investigated methods to remove (or at least reduce) this, which involve introduction of techniques for spanwise scrambling of the data before recycling. This approach has also been successfully implemented in an unstructured CFD code by Arolla [3] and applied to turbomachinery flows. These methods are successful but unfortunately currently limited to flows with spanwise homogeneity. This numerical artefact of recycling/rescaling techniques will not be too problematic if the unphysical frequency introduced has only small energy relative to the true turbulent frequencies of the larger eddies most responsible for mixing, however this is an unwanted feature of recycling/rescaling algorithms and needs to be carefully examined when these are applied until a general method to eliminate this problem is identified.
All the above implementations of the recycling/rescaling technique have inherently been restricted to boundary layers. Pierce [25] proposed a quite different rescaling approach which generalised the recycling technique for any inflow profile. Rather than rescale the velocity field of one specified plane to act as the inflow velocities at the inlet plane as in Lund et al. [19], Pierce [25] rescaled the velocity of the whole inflow generation region to constrain the velocity so that the generated velocity field within the inflow simulation domain has userdefined velocity statistics profiles (in particular 1s t moment (mean) velocity and 2n d moment normal stress). With this recycling/rescaling technique, all spatial and temporal correlations characterising the turbulence structures are selfgenerated and selfconsistent with the prespecified 1st and 2nd moment statistics. Due to the advantages of this technique, a recycling and rescaling method (hereafter referred to as R^{2}M) based on the work of Pierce [25], Lund [19] and Spalart [27] is further studied and tested in the current work. The following section describes the LES methodology and code adopted and the algorithm of the R^{2}M approach proposed in the current work in detail. Since mixing regions in practical applications are often associated with a mixing layer formed from the merger of upstream boundary layers, the method is first validated by simulating a spanwise homogeneous turbulent boundary layer and then a mixing layer growing from two merging boundary layers. It is then shown how the method can be used for inlet profiles which depend on both spanwise and transverse coordinates. Finally, as an illustration of the benefits that can be achieved using the present method, it is applied to the problem of dispersion of liquid droplets across a turbulent mixing layer. The measurements of Tageldin and Cetegen [31] are used to illustrate the improvements using the present R^{2}M approach in the nearfield of the splitter plate from which the mixing layer grows. This problem has previously been studied using LES by Jones et al. [12] and the present methodology is therefore contrasted with this prior work to assess its performance.
2 Methodology
2.1 LES algorithm
The LES code used in the present work is an incompressible, pressurebased method. The code (LULES) is based on solving a transformed version of the Cartesian transport equations using a curvilinear orthogonal coordinate system and contravariant velocity decomposition. The spatially filtered transport equations are discretised using the finite volume method. For the momentum equations, spatial derivatives for both convective and diffusive terms are calculated using a second order central differencing scheme; the AdamsBashforth secondorder explicit scheme is used for temporal discretisation. The LES code uses a structured, multiblock, staggered mesh and a multigrid method to speed up solution of the Poisson equation solved to satisfy continuity. A standard Smagorinsky SGS model is incorporated, using Smagorinsky coefficient C _{ S }=0.1, a length scale based on the cube root of the cell volume, and a Van Driest near wall damping function. Details of the transformed equations, discretisation practices, and basic testing/validation of the code have been described fully in Tang et al. [32] and Dianat et al. [7]. The inlet condition methodology is here described as implemented in such a multiblock, structured mesh code, but extension to other mesh types is clearly possible.
2.2 Droplet Lagrangian tracking method
2.3 Recycling and rescaling method (R ^{2}M)
 1.
Create an extra IC domain (1 or more blocks) upstream of the MS inletplane where turbulent inflow needs to be specified. The size of the IC domain in the spanwise (z) and transverse (y) directions is usually fixed by the MS inletplane size for convenience. (When the IC domain has a different size in the z and y directions from the MS inletplane, a mapping procedure is needed as demonstrated in [40].) The size in the streamwise (x) direction is chosen so that the two point spatial correlations fall to zero well within the IC block, as required by the recycling technique.
 2.
Use the recycling method to provide inflow conditions for the IC block. The velocity field at a plane a short distance upstream of the real MS domain inletplane is recycled. This is to avoid any upstream influence of the flow development in the MS domain. In addition, it is important that the mesh in the IC domain should be uniform in the x and z directions (homogeneous directions) to avoid any spatiallyvarying scaling effects.
 3.
Initialise the velocity field in the IC domain as well as in the MS domain. When initialising in the IC domain, the instantaneous velocity field is generated by superimposing white noise with an intensity of \( u_{target}^{\prime }(y)\), \(v_{target}^{\prime }(y)\), \( w_{target}^{\prime }(y) \) on the mean velocity \(\bar {U}_{target}(y),\, \bar {V}_{target}(y),\, \bar {W}_{target}(y)\).
 4.Run the simulation in both IC and MS domains simultaneously. Rescale the flow field everywhere within the IC domain every k LES time steps as shown below. blackNote: it has been mentioned in the Introduction that the frequency of the recycling/rescaling operation can introduce spurious frequencies into the simulation. The amplitude of these is of concern and will be investigated below, but to demonstrate that this choice has no effect on statistical quantities, two simulations with k=5 and k=10 have been carried out. Figure 2 shows that these produce the same mean velocity and turbulence level, following this test k =10 was used in all other simulations presented.
 Calculate the mean velocity by spatial averaging in the x and z directions and temporal averaging with a weight that decreases exponentially backward in time (see [19] for more about temporal averaging):$$\begin{array}{@{}rcl@{}} \bar{U}^{(n+1)}(y)&=&\frac{k\triangle t}{T}\langle U(x,y,z,t)\rangle_{xz}+\left( 1\frac{k\triangle t}{T}\right)\bar{U}^{n}(y) \end{array} $$(5)Where △t is the computational time step, T is a characteristic time scale for the temporal averaging which will be examined below, 〈 〉_{ x−z } represents spatial averaging in the x−z plane, and U(x,y,z,t) is the current instantaneous solution.$$\begin{array}{@{}rcl@{}} &=&\frac{k\triangle t}{T}\frac{1}{PQ}{\sum}_{i=1}^{P}{\sum}_{j=1}^{Q}U(x_{i},y,z_{j},t)+\left( 1\frac{k\triangle t}{T}\right)\bar{U}^{n}(y) \end{array} $$(6)
 Calculate the rms of the velocity field in a similar way$$ u^{{\prime}(n+1)}(y)=\sqrt{\frac{k\triangle t}{T}\left\langle \left[U(x,y,z,t)\bar{U}^{(n+1)}(y)\right]^{2}\right\rangle_{xz}+\left( 1\frac{k\triangle t}{T}\right) \left[u^{{\prime}n}(y)\right]^{2}} $$(7)
 Rescale the instantaneous velocity to create a new instantaneous velocity field:$$\begin{array}{@{}rcl@{}} U^{new}(x_{i},y,z_{j},t)&=&\frac{u^{\prime}_{target}(y)}{u^{{\prime}(n+1)}(y)}[U(x_{i},y,z_{j},t)\bar{U}^{(n+1)}(y)]+\bar{U}_{target}(y)\\ i&=&1,P;\quad j=1,Q \end{array} $$(8)

Rescale the other two velocity components V and W following the same procedure.

 1.
Create an extra IC domain and use the recycling method in the same way as above.
 2.
Initialise the velocity field in IC and MS domains. When initialising in the IC domain, the instantaneous velocity field is again generated by superimposing white noise with an intensity of \(u_{target}^{\prime }(y,z)\), \(v_{target}^{\prime }(y,z)\), \(w_{target}^{\prime }(y,z) \) on the userspecified mean velocity \(\bar {U}_{target}(y,z),\, \bar {V}_{target}(y,z),\, \bar {W}_{target}(y,z) \).
 3.Run the simulation in both IC and MS domains simultaneously. Rescale the flow field in the IC domain every k time steps in the following way:
 Calculate the mean velocity by spatial averaging but now in the streamwise (x) direction only and temporal averaging:Where 〈 〉_{ x } represents spatial averaging in the streamwise direction.$$\begin{array}{@{}rcl@{}} \bar{U}^{(n+1)}(y,z)&=\frac{k\triangle t}{T}\langle U(x,y,z,t)\rangle_{x}+\left( 1\frac{k\triangle t}{T}\right)\bar{U}^{n}(y,z) \end{array} $$(9)
 Calculate the rms of the velocity field in a similar way:$$ \begin{array}{ll} &u^{{\prime}(n+1)}(y,z)=\\ &\sqrt{\frac{k\triangle t}{T}\left\langle \left[U(x,y,z,t)\bar{U}^{(n+1)}(y,z)\right]^{2}\right\rangle_{x}+ \left( 1\frac{k\triangle t}{T}\right) \left[u^{{\prime}n}(y,z)\right]^{2}} \end{array} $$(10)
 Rescale the instantaneous velocity to create a new instantaneous velocity field:$$ U^{new}(x_{i},y,z,t)=\frac{u^{\prime}_{target}(y,z)}{u^{{\prime}(n+1)}(y,z)}[U(x_{i},y,z,t)\bar{U}^{(n+1)}(y,z)]+\bar{U}_{target}(y,z) $$(11)

Rescale the other velocity components V and W following the same procedure.

3 Results
3.1 LES of a turbulent boundary layer
3.2 LES of a nonequilibrium turbulent boundary layer
3.3 LES of a turbulent mixing layer
The turbulent mixing layer studied experimentally by Tageldin and Cetegen [31] is chosen as the next test case. A splitter plate is inserted in the middle of a wide rectangular channel. On the lower side is a high speed flow with a mean velocity of 7.1m/s whilst on the upper side is a low speed flow with a mean velocity of 2m/s. After the trailing edge of the splitter a mixing layer develops and is investigated within the test section 0m m≤x≤200m m. Since the turbulent boundary layers on either side of the splitter significantly affect the initial development of the mixing layer, proper inflow conditions must be prescribed at the inletplane x=0 to obtain a correct prediction of the early shape of the mixing layer,
It is reported in [31] that the boundary layer of the fast stream has a momentum Reynolds number (R e _{ 𝜃 }) of 244.5 at the end of the splitter, but there are no experimental data for mean velocity or rms profiles for the wall boundary layers reported for this test case in the paper. Since the mean velocity and rms normalised by free stream velocity should have similar profiles at similar R e _{ 𝜃 }, the nondimensional profiles corresponding to R e _{ 𝜃 }=300 from DNS of Spalart [27] are used to create the target data.
To investigate the effects of inflow conditions on the development of the mixing layer, an extra simulation with inflows generated by a simple white noise method has been performed. In this simulation, the inflows are specified directly at the inlet of the IC domains, and the IC domains are retained in an attempt to recover some turbulent boundary layer growth on the splitter plane.
Assuming that the free stream velocities of the high speed and low speed flows are U _{ m a x } and U _{ m i n } respectively, the velocity difference is △U = U _{ m a x }−U _{ m i n }. y _{0.5} is the locus of the mixing layer centreline where U = U _{ m i n }+△U/2. The velocity thickness δ of the mixing layer is defined as the distance between the locus where U = U _{ m i n }+10 %△U and U = U _{ m i n }+90 %△U.
Comparing the two simulations with inflow generated either by R^{2}M or the white noise method, the additional cost per time step with R^{2}M is less than 0.5 %, since the time required by the recycling and rescaling algorithm is negligible in comparison with that spent on solving the pressure Poisson equation. Realistic turbulent inflow can be reproduced in two IC domain flowthrough times by R^{2}M. This is also significantly shorter than the tens of MS domain flowthrough times required to obtain the statistics of the turbulent mixing layer. Therefore, the total additional cost arising from R^{2}M is no more than 10 %.
3.4 Generation of spanwise inhomogeneous inflow
3.5 LES of dropletladen turbulent mixing layer
Four segments for droplet inlet condition
Segment number  Region (mm)  Liquid volume flux (c c/(c m ^{2}⋅s)×10^{−3})  SMD 

1  −40≤y≤−4.5  2.35  31.66 
2  −4.5≤y≤−2.3  1.92  26.76 
3  −2.3≤y≤−0.8  1.4  21.87 
4  −0.8≤y≤0  0.6  18.80 
4 Conclusion
The work presented here has demonstrated a modified R^{2}M approach for LES inflow condition generation. With only mean and rms values over the inlet plane supplied as input, this method enables realistic and consistent turbulent structures to be generated. It has been validated by applying it to a spanwise homogeneous turbulent boundary layer and a turbulent mixing layer. Furthermore, it was shown how the method can be applied to more complex inflow profiles as shown by successful generation of spanwise inhomogeneous inflow. blackWith the realistic turbulent inflow produced by the R^{2}M approach it was also applied to a twophase flow, namely droplet dispersion across a turbulent mixing layer; the results showed how the nearfield dispersion was significantly better predicted using LES driven by the current inflow generation method. The primary disadvantage of the approach is the cost involved in carrying out a separate LES in the inlet condition domain. However, it is argued that the benefits of the method are sufficient to make this increased cost worthwhile. These benefits are: (i) it is not restricted to naturally developing turbulent boundary layer flow where similarity laws are available as in Lund et al.’s method [19], and it can produce nonequilibrium turbulent inflow; (ii) the method can cope with complex inflow conditions involving spatial variations in both directions across the inlet plane, (iii) only mean velocity and turbulence normal stress variations in the inlet plane are needed, (iv) the method can generate the unspecified 1point and 2point statistical quantities that are consistent with the input data (e.g. Reynolds shear stresses, 2point spatial and temporal correlations, integral length scales), (v) only a short startup transient and very short adjustment length were observed in the test case flows considered, with no evidence of contamination by the numerical aspects of the procedure, e.g. errors associated with the recycling frequency.
Since the recycling/rescaling procedure and the choice of the SGS model used in the LES solution procedure are independent choices, there is no obvious reason why the approach should not work with dynamic SGS models. Hopefully, better results can be expected with the more advanced dynamic SGS models, but this remains to be tested.
Notes
Acknowledgments
The work was supported by RollsRoyceEPSRC Dorothy Hodgkin Postgraduate Award and National Natural Science Foundation of China (Grant Nos. 11402298, 11472303, and 51406233). The simulations were run on Tianhe1A of National Supercomputing Center in Changsha in China.
References
 1.Antonia, R.A., Luxton, R.E.: The response of a turbulent boundary layer to a step change in surface roughness. J. Fluid Mech. 48, 721–761 (1971)CrossRefGoogle Scholar
 2.Araya, G., Castillo, L., Meneveau, C., Jansen, K.: A dynamic multiscale approach for turbulent inflow boundary conditions in spatially developing flows. J. Fluid Mech. 670, 581–605 (2011)CrossRefzbMATHGoogle Scholar
 3.Arolla, S.K.: Inflow turbulence generation for eddyresolving simulations of turbomachinery flows. ASME. J. Fluids Eng. 138(3), 031,201 (2016)CrossRefGoogle Scholar
 4.BabaAhmadi, M.H., Tabor, G.: Inlet conditions for les using mapping and feedback control. Comput. Fluids 38(6), 1299–1311 (2009)CrossRefzbMATHGoogle Scholar
 5.Batten, P.: Interfacing statistical turbulence closures with largeeddy simulation. AIAA J. 42(3), 485–492 (2004)CrossRefGoogle Scholar
 6.Crowe, C.T., Sommerfeld, M., Tsuji, Y.: Multiphase flows with droplets and particles CRC press (1998)Google Scholar
 7.Dianat, M., Yang, Z., Jiang, D., McGuirk, J.J.: Large eddy simulation of scalar mixing in a coaxial confined jet. Flow Turbul. Combust. 77(1), 205–227 (2006)CrossRefzbMATHGoogle Scholar
 8.Edwards, J.R., Choi, J.I., Boles, J.A.: Large eddy/reynoldsaveraged navierstokes simulation of a mach 5 compressioncorner interaction. AIAA J. 46(4), 977–991 (2008)CrossRefGoogle Scholar
 9.Germano, M., Piomelli, U., Moin, P., Cabot, W.H.: A dynamic subgridscale eddy viscosity model. Phys. Fluids 3, 1760–1765 (1991)CrossRefzbMATHGoogle Scholar
 10.Jarrin, N., Benhamadouche, S., Laurence, D., Prosser, R.: A syntheticeddymethod for generating inflow conditions for largeeddy simulations. Int. J. Heat Fluid Flow 27(4), 585–593 (2006)CrossRefzbMATHGoogle Scholar
 11.Jewkes, J.W., Chung, Y.M., Carpenter, P.W.: Modifications to a turbulent inflow generation method for boundarylayer flows. AIAA J. 49(1), 247–250 (2011)CrossRefGoogle Scholar
 12.Jones, W.P., Lyra, S., Marquis, A.J.: Large eddy simulation of a droplet laden turbulent mixing layer. Int. J. Heat Fluid Flow 31(1), 93–100 (2010)CrossRefGoogle Scholar
 13.Keating, A., Piomelli, U., Balaras, E., Kaltenbach, H.J.: A priori and a posteriori tests of inflow conditions for largeeddy simulation. Phys. Fluids 16(12), 4696–4712 (2004)CrossRefzbMATHGoogle Scholar
 14.Kempf, A., Klein, M., Janicka, J.: Efficient generation of initial and inflowconditions for transient turbulent flows in arbitrary geometries. Flow Turbul. Combust. 74(1), 67–84 (2005)CrossRefzbMATHGoogle Scholar
 15.Klein, M., Sadiki, A., Janicka, J.: A digital filter based generation of inflow data for spatially developing direct numerical or large eddy simulations. J. Comp. Phys. 186(2), 652–665 (2003)CrossRefzbMATHGoogle Scholar
 16.Le, H., Moin, P., Kim, J.: Direct numerical simulation of turbulent flow over a backwardfacing step. J. Fluid Mech. 330, 349–374 (1997)CrossRefzbMATHGoogle Scholar
 17.Lee, S., Lele, S. K., Moin, P.: Simulation of spatially evolving turbulence and the applicability of Taylor’s hypothesis in compressible flow. Physics of Fluids A: Fluid Dynamics 4(7), 1521–1530 (1992)CrossRefzbMATHGoogle Scholar
 18.Liu, K., Pletcher, R.H.: Inflow conditions for the large eddy simulation of turbulent boundary layers: a dynamic recycling procedure. J. Comp. Phys. 219(1), 1–6 (2006)CrossRefzbMATHGoogle Scholar
 19.Lund, T.S., Wu, X.H., Squires, K.D.: Generation of turbulent inflow data for spatiallydeveloping boundary layer simulations. J. Comp. Phys. 140(2), 233–258 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
 20.di Mare, L., Klein, M., Jones, W.P., Janicka, J.: Synthetic turbulence inflow conditions for largeeddy simulation. Phys. Fluids 18(2), 025,107 (2006)CrossRefGoogle Scholar
 21.Mayor, S.D., Spalart, P.R., Tripoli, G.J.: Application of a perturbation recycling method in the largeeddy simulation of a mesoscale convective internal boundary layer. J. Atmos. Sci. 59, 2385–2394 (2002)CrossRefGoogle Scholar
 22.McMullan, W.A., Gao, S., Coats, C.M.: The effect of inflow conditions on the transition to turbulence in LES of spatially developing mixing layers. Int. J. Heat Fluid Flow 30, 1054–1066 (2009)CrossRefGoogle Scholar
 23.Morgan, B., Larsson, J., Kawai, S., Lele, S.K.: Improving lowfrequency characteristics of recycling/rescaling inflow turbulence generation. AIAA J. 49(3), 582–597 (2011)CrossRefGoogle Scholar
 24.Nikitin, N.: Spatial periodicity of spatially evolving turbulent flow caused by inflow boundary condition. Phys. Fluids 19(9), 091,703 (2007)CrossRefzbMATHGoogle Scholar
 25.Pierce, C.D.: Progressvariable approach for largeeddy simulation of turbulent combustion. Dissertation for PhD Stanford University (2001)Google Scholar
 26.Schiller, L., Naumann, A.: Über die grundlegenden berechnungen bei der schwerkraftaufbereitung. Z. Ver. Dtsch. Ing. 77, 318–320 (1933)Google Scholar
 27.Spalart, P.R.: Direct simulation of a turbulent boundary layer up to Re = 1410. J. Fluid Mech. 187, 61–98 (1988)CrossRefzbMATHGoogle Scholar
 28.Spalart, P.R., Strelets, M., Travin, A.: Direct numerical simulation of largeeddybreakup devices in a boundary layer. Int. J. Heat Fluid Flow 27(5), 902–910 (2006)CrossRefGoogle Scholar
 29.SpilleKohoff, A.: Generation of turbulent inflow data with a prescribed shearstress profile. In: Third AFOSR International Conference on DNS/LES , in DNS/LES Progress and Challenges, pp. 319–326. C. Liu, L. Sakell, and T. Beutner (Greyden, Columbus, OH, 2001) (2001)Google Scholar
 30.Tabor, G.R., BabaAhmadi, M.H.: Inlet conditions for large eddy simulation: a review. Comput. Fluids 39(4), 553–567 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
 31.Tageldin, M.S., Cetegen, B.M.: Development of mixing and dispersion in an isothermal, dropletladen, confined turbulent mixing layer. Combust. Sci. Technol. 130, 131–169 (1997)CrossRefGoogle Scholar
 32.Tang, G., Yang, Z., McGuirk, J.J.: Numerical methods for largeeddy simulation in general coordinates. Int. J. Numer. Fluids 46, 1–18 (2004)CrossRefzbMATHGoogle Scholar
 33.Tyacke, J.C., Tucker, P.G.: Future use of large eddy simulation in aeroengines. J. Turbomach. 137(8), 081,005 (2015)CrossRefGoogle Scholar
 34.Urbin, G., Knight, D.: Largeeddy simulation of a supersonic boundary layer using an unstructured grid. AIAA J. 39(7), 1288–1295 (2001)CrossRefzbMATHGoogle Scholar
 35.Veloudis, I., Yang, Z., McGuirk, J.J., Page, G.J., Spencer, A.: Novel implementation /assessment of a digital filter approach for generation of LES inlet conditions. Flow Turbul. Combust. 79, 1–24 (2007)CrossRefzbMATHGoogle Scholar
 36.Wang, H., Wang, Z., Sun, M., Qin, N.: Large eddy simulation based studies of jet–cavity interactions in a supersonic flow. Acta Astronaut. 93, 182–192 (2014)CrossRefGoogle Scholar
 37.Wu, X.: Inflow turbulence generation methods. Ann. Rev. Fluid Mech. 49, 23–49 (2017)CrossRefGoogle Scholar
 38.Xiao, F., Dianat, M., McGuirk, J.J.: Large eddy simulation of liquidjet primary breakup in air crossflow. AIAA J. 51, 2878–2893 (2013)CrossRefGoogle Scholar
 39.Xiao, F., Dianat, M., McGuirk, J.J.: Large eddy simulation of single droplet and liquid jet primary breakup using a coupled level set/volume of fluid method. Atomization Sprays 24, 281–302 (2014)CrossRefGoogle Scholar
 40.Xiao, F., Dianat, M., McGuirk, J.J.: LES of turbulent liquid jet primary breakup in turbulent coaxial air flow. Int. J. Multiphase Flow 60, 103–118 (2014)MathSciNetCrossRefGoogle Scholar
 41.Xiao, X., Edwards, J.R., Hassan, H., Baurle, R.: Inflow boundary conditions for hybrid large eddy/reynolds averaged navierstokes simulations. AIAA J. 41(8), 1481–1489 (2003)CrossRefGoogle Scholar
Copyright information
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.