Surface pressure fluctuations induced by turbulent boundary-layer flow at ${\mathit{Re}}_{\theta } = 4755$ over small backward- and forward-facing steps are studied with large-eddy simulation. Four step heights that are 53, 13, 3.3 and 0.83 % of the boundary-layer thickness are considered to investigate the effects of step height on surface pressure characteristics and pressure-source mechanisms. The extent to which turbulent velocity fluctuations in the boundary layer and the separated shear layer contribute to the surface pressure fluctuations is examined with scaling of various pressure statistics and two-point correlations. For larger steps, vortical structures develop in the shear layer and the associated intense velocity fluctuations are the dominant source. Downstream of slightly less than one reattachment length from the step, the root-mean-square pressure is found to scale with the local maximum cross-stream Reynolds normal stress ${ \overline{{v}^{\ensuremath{\prime} \hspace{0.167em} 2} } }_{\mathit{max}} $. The pressure frequency spectrum at the maximum ${p}_{\mathit{rms}} $ location consists of an energy-containing range that scales with the mean reattachment length ${x}_{r} $ and a higher frequency range that rolls off with a slope close to $\ensuremath{-} 7/ 3$. As the step height decreases, the boundary-layer turbulent fluctuations become the dominant source, the ${ \overline{{v}^{\ensuremath{\prime} \hspace{0.167em} 2} } }_{\mathit{max}} $ scaling of ${p}_{\mathit{rms}} $ is no longer valid and the roll-off slope of the frequency spectrum becomes steeper. The downstream recovery of a step-perturbed boundary layer towards an equilibrium boundary layer is investigated from the point of view of surface pressure fluctuations. For steps with a strong separated shear layer, pressure fluctuations are found to decay rapidly for up to three reattachment lengths downstream of the step, within which approximately 60 % of the peak ${p}_{\mathit{rms}} $ is dissipated. Farther downstream, recovery is much slower. The pressure-recovery distances estimated for the largest backward and forward steps are 175 and 295 step heights, respectively.

The aeroacoustics of low-Mach-number boundary-layer flow over backward and forward facing steps is studied using large-eddy simulation and Lighthill's theory. The Reynolds number based on the step height and free-stream velocity ranges from 21000 to 328 as the step height is varied from 53% to 0.83% of the unperturbed boundary layer thickness at the step. For the largest step size, statistics of wall pressure fluctuations such as the root mean square values and frequency spectral density yield favourable comparisons with available experimental measurements. A low-frequency Green's function for the step geometry, valid for an acoustically compact step height, is employed to evaluate the volume integral in the solution to Lighthill's equation. Consistent with the result of previous theoretical studies, the steps act primarily as a dipole source aligned in the streamwise direction. The sound from the forward step is shown to be significantly louder than that from the backward step and the underlying reason is analysed in terms of source strength and distribution relative to the Green's function. The forward step generates stronger sources in regions closer to the step corner, which is heavily weighted by the Green's function. A detailed analysis of flow field and Green's function weighted sources reveals that the backward step generates sound mainly through a diffraction mechanism, while the forward step generates sound through a combination of diffraction and turbulence modification by the step. As the step height decreases, the difference in noise level between forward and backward steps is much reduced as turbulence modification becomes less significant.

The structural equilibrium behavior of the general linear second-moment closure model in a stably stratified, spanwise rotating homogeneous shear flow is considered with the aid of bifurcation analysis. A closed form equilibrium solution for the anisotropy tensor a ij , dispersion tensor K ij , dimensionless scalar variance 2 / k͑S / S ͒ 2 , and the ratio of mean to turbulent time scale / Sk is found. The variable of particular interest to bifurcation analysis, / Sk is shown as a function of the parameters characterizing the body forces: ⍀ / S (the ratio of the rotation rate to the mean shear rate) for rotation and Ri g (the gradient Richardson number) for buoyancy; it determines the bifurcation surface in the / Sk − ⍀ / S − Ri g space. It is shown, with the use of the closed form solution, that the Isotropization of Production model does not have a real and stable equilibrium solution when rotational and buoyant forces of certain magnitudes are simultaneously imposed on the flow. When this occurs, time integration of the turbulence model results in a diverging solution. A new set of scalar model coefficients that is consistent with experimental data, predicts turbulence decay past the critical gradient Richardson number Ri g cr = 0.25, and ensures the existence of stable, real solutions for all combinations of rotation and buoyancy is proposed.

The flow-noise induced by small gaps underneath low-Mach-number turbulent boundary layers at Reθ = 4755 is studied using large-eddy simulation and Lighthill's theory. The gap leading-edge height is 13% of the boundary-layer thickness, and the gap width and trailing-edge height are varied to investigate their effects on surface-pressure fluctuations and sound generation. The maximum surface pressure fluctuations, which increase with gap width and trailing-edge height, occur at the trailing edge or near the reattachment point if there is separation from the trailing edge. The downstream recovery towards an equilibrium boundary layer is significantly faster for gap flows compared to step flows, and the recovery distance scales with the reattachment length for gaps with trailing-edge separation. The acoustic field is dominated by the forward-facing step in the gap and resembles forward-step sound for wide gaps and/or asymmetric gaps with trailing edge higher than leading edge. In these cases, the dominant acoustic source mechanisms are the impingement of the separated shear layer from the leading edge onto the trailing edge and the unsteady separation from the trailing edge, coupled with edge diffraction. For narrow and symmetric gaps, the destructive interference of sound from the leading and trailing edges causes a significant decline in low-frequency sound and thereby creates a broad spectral peak in the mid-frequency range. The effects of gap acoustic non-compactness and free-stream convection are investigated by comparing solutions based on a compact gap Green's function with those from a boundary-element calculation. They are found to be negligible at the typical hydroacoustc Mach number of 0.01, but become significant at Mach numbers as low as 0.1 and moderately high frequencies.

Perforation operations are an important part of the well completion process in many field developments today. However, there are two considerations paramount to such a design. First, the post-job well production rate depends critically on a complex system in which the formation, perforations, and wellbore are dynamically and nonlinearly coupled together. Second, perforating operations can place a large dynamic load on downhole equipment. Predicting the spatial loading and its transient behavior is an important step in a completion design that implements risk mitigation to avoid damaging downhole equipment. In this study, we use a numerical modeling tool that has been used to simulate the dynamic behavior of the wellbore-reservoir system during perforating pre-job design. A typical case for this modeling software generates a quantitative prediction for the transient distribution of pressure, mass, velocity, and energy from the perforating event. These transients are commonly analyzed and incorporated into completion designs. In this paper, two critical components of modeling relative to perforating job design will be evaluated and characterized. First, the wellbore-perforation-formation coupling will be evaluated and characterized using a modified version of the code designed to model API RP-19B Section IV flow testing. Section IV experimental data will be compared to numerical predictions. We present successful predictions of pressure transients that match experimental data. The second component of the software evaluated and characterized in this paper is the pressure, volume, temperature (PVT) accuracy and its implementation. NIST thermodynamic data, together with shock tube examples with pressure and temperature ranges relevant for deep-water completions will be used. We demonstrate that, although the current PVT implementation is accurate on typical downhole jobs, it could have limitations at higher pressures and temperatures. Finally, we present an improved numerical implementation for the modeling software.