Broadband shock noise reduction in turbulent jets by water injection
1. Introduction
Three distinct components of noise are present in supersonic jets: turbulent mixing noise, Mach wave radiation, and broadband shock associated noise. Generally the shock-associated noise includes both broadband shock noise and discrete screech tones. Both the broadband shock noise and screech tones are associated with imperfectly expanded jets. The high noise levels radiated by launch vehicles at lift-off induce severe vibration on the launch vehicle structure and payload, and ground support equipment. Consequently the need to reduce acoustic levels from jet exhausts is paramount.
Water injection has been traditionally considered for the suppression of high noise levels from rocket exhausts in launch vehicle environments. For example, large amounts of water are used for the suppression of ignition overpressure (IOP) and lift-off noise during Space Shuttle launches. The water mass flow rate to the SRB exhaust mass flow rate ratio is maintained around one to two in order to meet payload design requirements of 145 dB. Water injection could reduce noise by as much as 8-12 dB. Such a high level of reduction includes reductions in the turbulent mixing noise and shock-associated noise, the latter constituting the predominant component of noise reduction.
Water injection mitigates all the three components of jet noise: the turbulent mixing noise, Mach wave radiation, and shock noise. Two principal mechanisms leading to the diminution of jet noise by water injection are the reduction of jet velocity and jet temperature. The decrease of jet velocity is occasioned through momentum transfer between the liquid and the gaseous phases, and the reduction of the jet temperature is achieved due to partial vaporization of the injected water. The effect of water may also be regarded as effectively increasing the jet density. Important velocity reductions are achieved within a few diameters of the nozzle exit. Noise reductions of the order of 10 dB are realized for both cold and hot jets.
Several design parameters influence the effectiveness of noise reduction by water injection. These include water to jet mass flow rate ratio, axial injection location, water injection angle, number of injectors, method of injection (jet type or spray type), droplet size, water pressure, and water temperature. Optimal injection parameters need to be determined for the design of efficient water injection system. Data of Zoppellari & Juve and of Norum suggest that best noise reductions of the order of 10-12 dB are obtained at injection angles of 45-60&deg;, injection near the nozzle exit (especially for shock-containing jets), and high mass flow rates. Also the optimum number of injectors appears to be around eight. Experiments by Krothappalli et al. and Greska & Krothapalli and Arakeri et al. at reduced water mass flow rate ratios through the use of microjets show sizable noise reduction for application to aircraft jet engines.
Experiments with water injection suggest that the mass flow rate ratio appears to be an important parameter. Tests conducted with water to jet mass flow rate ratios up to four reveal that significant noise reductions can be achieved at high water flow rate ratio. In the case of cold jets, beyond a critical mass flow rate ratio, the velocity reduction and thus the noise reduction is small. For hot jets, only a fraction of the liquid is effective in reducing the air jet velocity due to drop evaporation. At low water flow rates, it is possible to reduce the shock associated noise significantly. At higher mass flow rates, momentum transfer principally affects the mixing noise over a broad range of frequency.
At considerably high mass flow rates, the benefit of velocity reduction of the air jet by momentum transfer between the two phases is partly opposed by the emergence of new parasitic sources linked to water injection, which include the impact noise of air on the water jets, fragmentation of these water jets, and unsteady movement of the droplets. A compromise can be found between significant penetration of water jet into the air jet and low impact noise. A significant parameter is the velocity component of water jets that is perpendicular to the air jet. If this component is high, water penetrates deeply into the air jet and mixing takes place rapidly. If this component is small, water does not produce significant drag and impact noise.
In view of the importance of water injection in jet noise suppression, a theoretical understanding of the mechanism of noise reduction is useful in the design and optimization of water injection systems for launch acoustics application. Based on control volume formulation a simple one-dimensional analytical model has been recently reported by the author for estimating jet mixing noise suppression due to water injection. The method is based on the conception of effective jet properties in conjunction with the scaling laws developed by Kandula for shock-free jet noise. The predictions are found to yield satisfactory agreement with the test data for hot perfectly expanded supersonic jets with regard to turbulent mixing noise reduction with water injection over a wide range of water to jet mass flow rate ratios.
In the presence of water injection, broadband shock noise reductions are considerably higher than those due to turbulent mixing noise. Thus an accurate estimation of the broadband shock noise reduction is important in the design of the water injection systems for jet noise mitigation at launch sites. In this paper derived primarily from, the method of effective jet properties will be applied (extended) to the prediction of broadband shock noise reduction with water injection in imperfectly expanded supersonic jets.
2. Analysis
2.1. Broadband shock noise reduction
The intensity of broadband shock noise is primarily a function of the nozzle pressure ratio and largely independent of the temperature ratio. Harper-Bourne and Fisher found that for a given radiation direction the measured mean square sound pressure due to broadband shock-associated noise scales with the parameter &beta; as: and Mj is the fully expanded jet Mach number. The parameter &beta; characterizes the pressure jump across a normal shock with an upstream Mach number Mj.
In the presence of water injection, the effective jet properties (jet velocity, temperature, Mach number, etc.) near the exit are obtained from the theory proposed in. In the present context, the effective jet Mach number is obtained as a function of the water to jet mass flow rate ratio. Thus the reduction in the overall sound pressure level (OASPL) can be estimated as where the subscripts1 and 2 respectively refer to the original and effective jet exit conditions. Eq. yields the noise reduction due to water injection as applied to a single isolated shock in the jet. The consideration of noise reduction in the multiple shock system is very complex. Thus it is assumed in the present analysis that the overall noise reduction is proportional to the number of shock cells downstream of the water injection station, nsd. That is, where the quantity &Delta;OASPL is provided by Eq.
2.2. Effective jet exit conditions
2.2.1. Effective jet Mach number
In the following, we briefly review the results for the effective jet properties derived in on the basis of a control volume formulation. An expression for the effective jet Mach number is given by where the effective jet velocity and jet density are obtained as follows.
3. Results and discussion
3.1. Comparisons with experimental data for cold over-expanded jet
For comparison purposes, we consider here the test data of Norum for cold over-expanded jet broadband shock noise reduction with water injection (case D). The jet issues from a convergent-divergent (CD) nozzle. For the cold operation of the Mach 1.5 (design Mach number) CD nozzle, the highest nozzle pressure ratio (NPR) that can be achieved prior to the onset of dominant screech is about 2.27, corresponding to at which broadband shock noise is measured. Data for only one Mach number is available for the cold case. Acoustic data are obtained with injection angles of 45&deg; and 60&deg;, with the injection at 60&deg; yielding a somewhat higher noise reduction. The axial injection location is adjusted by varying the injector ring corresponding to known positions of the shocks in the over-expanded jet plume. Maximum noise reduction is achieved in a direction at 135&deg; to the downstream jet axis.
Fig. 5a shows the dependence of maximum SPL reduction with the water mass flow rate with the injection station upstream of shock cell-1. A total of five shock cells are considered here. The theory shows a nearly linear dependence of SPL reduction with the mass flow rate, while the data suggests a saturation trend after an initially linear increase. In the linear range of the data, the theory suffers a maximum error of about 2.5 dB.
From the preceding comparisons, it is evident that the agreement between the experimental data and the predictions of the proposed model is good at least in the linear phase, when the mass flow rate of the injected water is relatively limited. For higher values of water injection rates, there is a definite trend toward saturation in the experimental results. It is believed that the trend towards saturation in noise reduction at higher mass injection rates is connected with the phenomenon of parasitic noise (referred to in the introduction). A detailed theoretical modeling of this parasitic noise is beyond the scope of the present investigation. An estimate of the parasitic noise, as deduced from the experimental data, is discussed in the following section.
3.2. Deduction of parasitic noise
Fig. 6 shows a composite plot for the case of water injection upstream of shock cell-1. In this plot, the original data are resolved (extrapolated) into two linear segments -- curve-1 and curve-2. Curve-1 extrapolates the second linear segment of the data, and curve-2 extrapolates the third linear segment of the data. It is interesting to note that the slope of curve-2 is very close to that predicted by the theory for the broadband shock noise. We are inclined to believe that the difference between curve-1 and curve-2 represents the parasitic noise, whose magnitude is reflected by a separate curve. With this conjecture, the parasitic noise seems to commence (manifest itself) at a mass flow rate ratio beyond 0.22, and increases linearly with the mass flow rate thereafter. The parasitic noise increases to as high as 7 dB for a mass flow rate ratio of 0.5.
3.3. Comparisons with experimental data for hot over-expanded jet
The only hot jet data for broadband shock noise reduction available for comparison is that of a hot over-expanded supersonic jet at, obtained by Norum. Unfortunately the data are reported only for the highest water mass flow rate ratio of 0.46. As in the cold jet case, largest noise reduction was obtained at 135&deg; to the downstream jet axis. A maximum noise reduction of 6.6 dB was realized in the hot jet case.
According to the proposed theory, we have at a mass flow rate ratio of 0.46, so that for a five-shock system. From Fig. 6, the parasitic noise at this water flow rate ratio is 6 dB. Thus the predicted broadband shock noise reduction is 7.5 dB. This result satisfactorily compares with the measured noise reduction of 6.6 dB.
The reduction in noise due to water injection is generally much larger for broad band shock noise than for jet mixing noise. When the jet temperature is increased at a given NPR, the ratio of shock noise to mixing noise decreases in the forward direction, and the OASPL shifts more to the Mach wave radiation dominated downstream direction. The combination of these two factors is responsible for smaller reduction in broadband shock noise due to water injection for the hot jet relative to the cold jet.
4. Conclusion
An approximate formulation has been developed for the prediction of broadband shock noise reduction by water injection. The proposed formulation agrees satisfactorily with the test data for water injection into over-expanded cold and hot supersonic jets. The results suggest that beyond certain mass flow rate, parasitic noise due to water impact becomes manifest. This result points to the possibility of the existence of an optimum injection water mass flow rate for shock noise reduction purposes.