Improved jet noise predictions in subsonic flows using an approximate composite asymptotic expansion of the adjoint Green's function in Goldstein's analogy

Our recent work on jet noise modeling (Afsar et al. 2019, PhilTrans. A., vol. 377) has confirmed that non-parallel flow effects are needed to determine the wave propagation aspect of the jet noise problem. The acoustic spectrum calculated using an asymptotic representation of non-parallel flow effects produces the correct spectral shape of the small angle radiation beyond that which can be predicted using a parallel (i.e. non-spreading) mean flow approximation to determine the wave propagation tensor in Goldstein’s generalized acoustic analogy formulation. While the peak noise predicted using this approach works remarkably well at low frequencies (up to and slightly beyond the peak Strouhal number), the high frequency prediction in Afsar et al. (2019) relied upon an ad-hoc composite asymptotic formula for the propagator that was also restricted to the small angle spectra. In this paper we therefore attempt to remedy this defect by using the O(1) frequency locally parallel flow Green’s function as a kind-of outer solution to the propagator tensor in which the non-parallel flow theory used in the latter reference acts as the ’inner’ solution that is valid at low frequencies and is transcendentally small beyond the peak frequency. The hope is that this approach will allow more robust high frequency predictions with a single set of turbulence parameters for the acoustic spectrum at any given acoustic Mach number. In other words, both non-parallel and locally parallel regions of the propagator tensor solution are multiplied by the same turbulence source structure in the acoustic spectrum integral. The paper highlights the basic formalism of the low frequency jet noise theory and sum- marises the technical problems and strategy we use to extend this approach to higher frequen- cies

Towards the prediction of supersonic jet noise predictions using a unified asymptotic approximation for the adjoint vector Green's function

In this paper we continue efforts aimed at modeling jet noise using self-consistent analytical approaches within the generalized acoustic analogy (GAA) formulation. The GAA equations show that the far-field pressure fluctuation is given by a convolution product between a propagator tensor that depends on the (true) non-parallel jet mean flow and a generalized fluctuating stress tensor that is a stationary random function of time and includes the usual fluctuating Reynolds’ stress tensor as well as enthalpy fluctuation components. Here, we focus on approximating the propagator tensor by determining an appropriate asymptotic solution to the adjoint vector Green’s function that it depends on by using an asymptotic approach at all frequencies of interest for jet noise prediction. The Green’s function is then rationally approximated by a composite formula in which the GSA (Goldstein-Sescu-Afsar, J. Fluid Mech., vol. 695, pp. 199-234, 2012) non-parallel flow Green’s function asymptotic solution is used at low frequencies and the O(1) frequency parallel flow Green’s function is used for all frequencies thereafter. The former solution uses the fact that non-parallelism will have a leading order effect on the Green’s function everywhere in the jet under a distinguished scaling in which the jet spread rate is of the same order as the Strouhal number for a slowly-diverging mean flow expansion. Since this solution, however, is expected to apply up to the peak frequency, the latter O(1) frequency Green’s function in a parallel flow must be used at frequencies thereafter. We investigate the predictive capability of the composite Green’s function for the prediction of supersonic axi-symmetric round jets at fixed jet Mach number of 1.5 and two different temperature ratios (isothermal & heated) using Large-eddy simulation data. Our results show that, in the first instance, excellent jet noise predictions are obtained using the non-parallel flow asymptotic approach, remarkably, up to a Strouhal number of 0.5. This is true for both heated and un-heated jets. Furthermore, we develop the analytical approach required to extend this solution by appropriate asymptotic approximation to O(1) frequencies

Analysis of the non-parallel flow-based Green's function in the acoustic analogy for complex axisymmetric jets

This paper considers how a complex axisymmetric jet modifies the structure of the propa- gator tensor in Goldstein’s generalized acoustic analogy. The jet flow we consider is in general a dual stream flow that operates either as a single jet or a complex co-axial jet flow. The latter of which is of interest to turbofan engine manufacturers. The form of the acoustic analogy that we use here is based on our recent work on jet noise modeling (Afsar et al. 2019, PhilTrans. A., vol. 377) that highlighted the importance of non-parallel flow effects in the correct calcu- lation of the propagator. The propagator calculation takes advantage of the fact that mean flow non-parallelism enters the lowest order asymptotic expansion of the former at sufficiently low frequencies of the same order as the jet spread rate. Whilst this might seem restrictive, our previously reported calculations at high subsonic and mildly supersonic jets indicate that the subsequent jet noise predictions remain accurate up to the peak frequency (typically at a Strouhal number based on jet velocity and diameter of ≈ 0.5 − 0.6) for the small angle acoustic radiation. One of critical assumptions of this approach is that the mean flow speed of sound squared is given by either the Crocco relation (in unheated jets) or the Crocco-Busemann relation for heated flows. Our analysis for the dual stream complex axisymmetric jet however shows that the latter assumption (in the form of Crocco-Busemann formula) is no longer an accurate representation of the speed of sound variation. We therefore present a more general form of the asymptotic analysis than that used in Afsar et al. (2019a & b). For the complex jet mean flow field, the mean flow speed of sound is otherwise arbitrary but must remain a single-valued function of the streamwise mean flow. The predictions based on this approach are shown to remain accurate up to the peak frequency. We discuss how to extend the range of validity by utilizing a suitable composite asymptotic solution for the Green’s function problem

Effect of non-parallel mean flow on the acoustic spectrum of heated supersonic jets : explanation of 'jet quietening'

Noise measurements of heated axisymmetric jets at fixed supersonic acoustic Mach number indicate that the acoustic spectrum reduces when the temperature ratio increases. The 'spectral quietening' effect has been observed both experimentally and computationally using Large Eddy Simulations (LES). It was explained by Afsar et al. (M. Z. Afsar and M. E. Goldstein & A. M. Fagan AIAAJ., Vol. 49, p. 2522, 2011) through the cancellation introduced by enthalpy flux/momentum flux coupling term using the generalized acoustic analogy formulation. But the parallel flow assumption is known to give inaccurate predictions at high jet speeds. In this paper we therefore extend the non-parallel flow asymptotic theory of Goldstein et al. (M. E. Goldstein, A. Sescu & M. Z. Afsar, J. Fluid Mech., Vol. 695, p. 199, 2012) for the vector Green’s function of the adjoint linearized Euler equations (ALEE) in the analogy. Using a steady Reynolds Averaged Navier Stokes (RANS) calculation for the jet mean flow, we find that the coupling term propagator is positive-definite and asymptotically sub-dominant at low frequencies corresponding to the peak jet noise when non-parallel flow effects are taken into account and self-consistent approximations for the turbulence structure are made. The validity of the non-parallel flow-based acoustic analogy model is assessed at various observation angles by computing the overall sound pressure level (OASPL) and use this to suggest a more rational explanation of the quietening effect. In general, our noise predictions are in very good agreement with acoustic data beyond the peak frequency

Effect of localized wall cooling or heating on streaks in high-speed boundary layers

High-amplitude upstream disturbances and wall surface roughness elements trigger streamwise/Görtler vortices and the associated streaks in boundary layers over flat or concave surfaces. Following the transient growth phase, the fully-developed vortices become sensitive to inviscid secondary instabilities, which ultimately result in a premature transition to turbulence. Our work aims at investigating the effect of cooling/heating on the initiation and development of such streaks in an attempt to gain a better understanding of the conditions and governing mechanisms leading to secondary instabilities in high-speed compressible boundary layers. We conduct a parametric study via a robust and efficient numerical solution to the non-linear compressible boundary region equations (NCBRE) to identify the impact of varying the wall temperature on the development of streaks in supersonic and hypersonic boundary layer flows

Growth and wall-transpiration control of nonlinear unsteady Gortler vortices forced by free-stream vortical disturbances

The generation, nonlinear evolution, and wall-transpiration control of unsteady Gortler vortices in ¨ an incompressible boundary layer over a concave plate is studied theoretically and numerically. Gortler rolls are initiated and driven by free-stream vortical perturbations of which only the low- ¨ frequency components are considered because they penetrate the most into the boundary layer. The formation and development of the disturbances are governed by the nonlinear unsteady boundaryregion equations with the centrifugal force included. These equations are subject to appropriate initial and outer boundary conditions, which account for the influence of the upstream and free-stream forcing in a rigorous and mutually consistent manner. Numerical solutions show that the stabilizing effect on nonlinearity, which also occurs in flat-plate boundary layers, is significantly enhanced in the presence of centrifugal forces. Sufficiently downstream, the nonlinear vortices excited at different free-stream turbulence intensities Tu saturate at the same level, proving that the initial amplitude of the forcing becomes unimportant. At low Tu, the disturbance exhibits a quasi-exponential growth with the growth rate being intensified for more curved plates and for lower frequencies. At higher Tu, in the typical range of turbomachinery applications, the Gortler vortices do not undergo a modal stage ¨ as nonlinearity saturates rapidly, and the wall curvature does not affect the boundary-layer response. Good quantitative agreement with data from direct numerical simulations and experiments is obtained. Steady spanwise-uniform and spanwise-modulated zero-mass-flow-rate wall transpiration is shown to attenuate the growth of the Gortler vortices significantly. A novel modified version of the Fukagata- ¨ Iwamoto-Kasagi identity, used for the first time to study a transitional flow, reveals which terms in the streamwise momentum balance are mostly affected by the wall transpiration, thus offering insight into the increased nonlinear growth of the wall-shear stress

Dietary fibre supplementation enhances radiotherapy tumour control and alleviates intestinal radiation toxicity.

Non-toxic approaches to enhance radiotherapy outcomes are beneficial, particularly in ageing populations. Based on preclinical findings showing that high-fibre diets sensitised bladder tumours to irradiation by modifying the gut microbiota, along with clinical evidence of prebiotics enhancing anti-cancer immunity, we hypothesised that dietary fibre and its gut microbiota modification can radiosensitise tumours via secretion of metabolites and/or immunomodulation. We investigated the efficacy of high-fibre diets combined with irradiation in immunoproficient C57BL/6 mice bearing bladder cancer flank allografts. Psyllium plus inulin significantly decreased tumour size and delayed tumour growth following irradiation compared to 0.2% cellulose and raised intratumoural CD8+ cells. Post-irradiation, tumour control positively correlated with Lachnospiraceae family abundance. Psyllium plus resistant starch radiosensitised the tumours, positively correlating with Bacteroides genus abundance and increased caecal isoferulic acid levels, associated with a favourable response in terms of tumour control. Psyllium plus inulin mitigated the acute radiation injury caused by 14 Gy. Psyllium plus inulin increased caecal acetate, butyrate and propionate levels, and psyllium alone and psyllium plus resistant starch increased acetate levels. Human gut microbiota profiles at the phylum level were generally more like mouse 0.2% cellulose profiles than high fibre profiles. These supplements may be useful in combination with radiotherapy in patients with pelvic malignancy

Dietary fibre supplementation enhances radiotherapy tumour control and alleviates intestinal radiation toxicity

Acknowledgements We thank Professor William Kim (University of North Carolina, Chapel Hill) for his generous gift of the UPPL1591 cell line. We thank Dr. Mark Hill (Department of Oncology, University of Oxford) for assistance with irradiation procedures, and Dr. Jia-Yu Ke and Dr. Vijay Indukuri (Research Diets, Inc.) for formulation of the mouse diets. We thank Dr. Graham Horgan (James Hutton Research Institute, Aberdeen) for statistical advice. We thank Grampian Biorepository at Aberdeen Royal Infirmary for providing the faecal samples from cancer patients.Peer reviewe

LEARN: A multi-centre, cross-sectional evaluation of Urology teaching in UK medical schools

OBJECTIVE: To evaluate the status of UK undergraduate urology teaching against the British Association of Urological Surgeons (BAUS) Undergraduate Syllabus for Urology. Secondary objectives included evaluating the type and quantity of teaching provided, the reported performance rate of General Medical Council (GMC)-mandated urological procedures, and the proportion of undergraduates considering urology as a career. MATERIALS AND METHODS: LEARN was a national multicentre cross-sectional study. Year 2 to Year 5 medical students and FY1 doctors were invited to complete a survey between 3rd October and 20th December 2020, retrospectively assessing the urology teaching received to date. Results are reported according to the Checklist for Reporting Results of Internet E-Surveys (CHERRIES). RESULTS: 7,063/8,346 (84.6%) responses from all 39 UK medical schools were included; 1,127/7,063 (16.0%) were from Foundation Year (FY) 1 doctors, who reported that the most frequently taught topics in undergraduate training were on urinary tract infection (96.5%), acute kidney injury (95.9%) and haematuria (94.4%). The most infrequently taught topics were male urinary incontinence (59.4%), male infertility (52.4%) and erectile dysfunction (43.8%). Male and female catheterisation on patients as undergraduates was performed by 92.1% and 73.0% of FY1 doctors respectively, and 16.9% had considered a career in urology. Theory based teaching was mainly prevalent in the early years of medical school, with clinical skills teaching, and clinical placements in the later years of medical school. 20.1% of FY1 doctors reported no undergraduate clinical attachment in urology. CONCLUSION: LEARN is the largest ever evaluation of undergraduate urology teaching. In the UK, teaching seemed satisfactory as evaluated by the BAUS undergraduate syllabus. However, many students report having no clinical attachments in Urology and some newly qualified doctors report never having inserted a catheter, which is a GMC mandated requirement. We recommend a greater emphasis on undergraduate clinical exposure to urology and stricter adherence to GMC mandated procedures