Это то, что сработало для меня:
public void downloadFile(String filename) throws IOException {
final FacesContext fc = FacesContext.getCurrentInstance();
final ExternalContext externalContext = fc.getExternalContext();
final File file = new File(filename);
externalContext.responseReset();
externalContext.setResponseContentType(ContentType.APPLICATION_OCTET_STREAM.getMimeType());
externalContext.setResponseContentLength(Long.valueOf(file.lastModified()).intValue());
externalContext.setResponseHeader("Content-Disposition", "attachment;filename=" + file.getName());
final HttpServletResponse response = (HttpServletResponse) externalContext.getResponse();
FileInputStream input = new FileInputStream(file);
byte[] buffer = new byte[1024];
final ServletOutputStream out = response.getOutputStream();
while ((input.read(buffer)) != -1) {
out.write(buffer);
}
out.flush();
fc.responseComplete();
}